Properties

Label 547.4.a.b.1.14
Level $547$
Weight $4$
Character 547.1
Self dual yes
Analytic conductor $32.274$
Analytic rank $0$
Dimension $71$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [547,4,Mod(1,547)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(547, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("547.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 547 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 547.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: \(32.2740447731\)
Analytic rank: \(0\)
Dimension: \(71\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Character \(\chi\) \(=\) 547.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.61662 q^{2} +5.98739 q^{3} +5.07997 q^{4} +14.5299 q^{5} -21.6541 q^{6} +21.3024 q^{7} +10.5606 q^{8} +8.84881 q^{9} +O(q^{10})\) \(q-3.61662 q^{2} +5.98739 q^{3} +5.07997 q^{4} +14.5299 q^{5} -21.6541 q^{6} +21.3024 q^{7} +10.5606 q^{8} +8.84881 q^{9} -52.5491 q^{10} -54.2135 q^{11} +30.4158 q^{12} +40.7748 q^{13} -77.0429 q^{14} +86.9961 q^{15} -78.8337 q^{16} +102.739 q^{17} -32.0028 q^{18} +41.9049 q^{19} +73.8114 q^{20} +127.546 q^{21} +196.070 q^{22} +52.3053 q^{23} +63.2307 q^{24} +86.1176 q^{25} -147.467 q^{26} -108.678 q^{27} +108.216 q^{28} +196.430 q^{29} -314.632 q^{30} +107.249 q^{31} +200.627 q^{32} -324.597 q^{33} -371.569 q^{34} +309.522 q^{35} +44.9517 q^{36} -409.454 q^{37} -151.554 q^{38} +244.134 q^{39} +153.445 q^{40} -282.185 q^{41} -461.286 q^{42} +489.222 q^{43} -275.403 q^{44} +128.572 q^{45} -189.169 q^{46} +107.610 q^{47} -472.008 q^{48} +110.794 q^{49} -311.455 q^{50} +615.139 q^{51} +207.135 q^{52} +490.814 q^{53} +393.048 q^{54} -787.716 q^{55} +224.967 q^{56} +250.901 q^{57} -710.414 q^{58} -715.166 q^{59} +441.938 q^{60} +37.2896 q^{61} -387.880 q^{62} +188.501 q^{63} -94.9216 q^{64} +592.453 q^{65} +1173.95 q^{66} -1004.20 q^{67} +521.911 q^{68} +313.172 q^{69} -1119.42 q^{70} -612.234 q^{71} +93.4492 q^{72} +488.999 q^{73} +1480.84 q^{74} +515.620 q^{75} +212.876 q^{76} -1154.88 q^{77} -882.942 q^{78} +389.173 q^{79} -1145.44 q^{80} -889.616 q^{81} +1020.56 q^{82} -605.759 q^{83} +647.930 q^{84} +1492.79 q^{85} -1769.33 q^{86} +1176.10 q^{87} -572.530 q^{88} +1598.67 q^{89} -464.998 q^{90} +868.601 q^{91} +265.710 q^{92} +642.142 q^{93} -389.186 q^{94} +608.874 q^{95} +1201.23 q^{96} +372.859 q^{97} -400.698 q^{98} -479.725 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 71 q + 14 q^{2} + 31 q^{3} + 294 q^{4} + 159 q^{5} + 60 q^{6} + 66 q^{7} + 168 q^{8} + 738 q^{9} + 120 q^{10} + 139 q^{11} + 309 q^{12} + 343 q^{13} + 239 q^{14} + 194 q^{15} + 1346 q^{16} + 842 q^{17} + 423 q^{18} + 157 q^{19} + 1292 q^{20} + 434 q^{21} + 436 q^{22} + 1004 q^{23} + 935 q^{24} + 2206 q^{25} + 812 q^{26} + 1282 q^{27} + 584 q^{28} + 1459 q^{29} + 146 q^{30} + 582 q^{31} + 1428 q^{32} + 1080 q^{33} + 393 q^{34} + 1006 q^{35} + 2996 q^{36} + 1477 q^{37} + 1873 q^{38} + 626 q^{39} + 1272 q^{40} + 1112 q^{41} + 1812 q^{42} + 833 q^{43} + 1392 q^{44} + 3841 q^{45} + 782 q^{46} + 2484 q^{47} + 2034 q^{48} + 4727 q^{49} + 1248 q^{50} + 932 q^{51} + 2118 q^{52} + 5077 q^{53} + 1537 q^{54} + 1736 q^{55} + 2281 q^{56} + 1426 q^{57} + 992 q^{58} + 2977 q^{59} + 1418 q^{60} + 3363 q^{61} + 3438 q^{62} + 3194 q^{63} + 6138 q^{64} + 4640 q^{65} + 288 q^{66} + 955 q^{67} + 8553 q^{68} + 4440 q^{69} + 2203 q^{70} + 2458 q^{71} + 4495 q^{72} + 3724 q^{73} + 2099 q^{74} + 4491 q^{75} + 2260 q^{76} + 9774 q^{77} + 1057 q^{78} + 1638 q^{79} + 8221 q^{80} + 10151 q^{81} + 1018 q^{82} + 6121 q^{83} + 4847 q^{84} + 3836 q^{85} + 2305 q^{86} + 3894 q^{87} + 5815 q^{88} + 8110 q^{89} + 4951 q^{90} + 2312 q^{91} + 13138 q^{92} + 9250 q^{93} - 813 q^{94} + 4858 q^{95} + 6882 q^{96} + 4486 q^{97} + 4216 q^{98} + 4969 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.61662 −1.27867 −0.639335 0.768928i \(-0.720790\pi\)
−0.639335 + 0.768928i \(0.720790\pi\)
\(3\) 5.98739 1.15227 0.576137 0.817353i \(-0.304560\pi\)
0.576137 + 0.817353i \(0.304560\pi\)
\(4\) 5.07997 0.634996
\(5\) 14.5299 1.29959 0.649796 0.760108i \(-0.274854\pi\)
0.649796 + 0.760108i \(0.274854\pi\)
\(6\) −21.6541 −1.47338
\(7\) 21.3024 1.15022 0.575112 0.818075i \(-0.304959\pi\)
0.575112 + 0.818075i \(0.304959\pi\)
\(8\) 10.5606 0.466719
\(9\) 8.84881 0.327734
\(10\) −52.5491 −1.66175
\(11\) −54.2135 −1.48600 −0.743000 0.669292i \(-0.766598\pi\)
−0.743000 + 0.669292i \(0.766598\pi\)
\(12\) 30.4158 0.731689
\(13\) 40.7748 0.869914 0.434957 0.900451i \(-0.356764\pi\)
0.434957 + 0.900451i \(0.356764\pi\)
\(14\) −77.0429 −1.47076
\(15\) 86.9961 1.49749
\(16\) −78.8337 −1.23178
\(17\) 102.739 1.46576 0.732879 0.680359i \(-0.238176\pi\)
0.732879 + 0.680359i \(0.238176\pi\)
\(18\) −32.0028 −0.419063
\(19\) 41.9049 0.505982 0.252991 0.967469i \(-0.418586\pi\)
0.252991 + 0.967469i \(0.418586\pi\)
\(20\) 73.8114 0.825237
\(21\) 127.546 1.32537
\(22\) 196.070 1.90010
\(23\) 52.3053 0.474192 0.237096 0.971486i \(-0.423804\pi\)
0.237096 + 0.971486i \(0.423804\pi\)
\(24\) 63.2307 0.537788
\(25\) 86.1176 0.688941
\(26\) −147.467 −1.11233
\(27\) −108.678 −0.774634
\(28\) 108.216 0.730388
\(29\) 196.430 1.25780 0.628899 0.777487i \(-0.283506\pi\)
0.628899 + 0.777487i \(0.283506\pi\)
\(30\) −314.632 −1.91479
\(31\) 107.249 0.621371 0.310685 0.950513i \(-0.399441\pi\)
0.310685 + 0.950513i \(0.399441\pi\)
\(32\) 200.627 1.10832
\(33\) −324.597 −1.71228
\(34\) −371.569 −1.87422
\(35\) 309.522 1.49482
\(36\) 44.9517 0.208110
\(37\) −409.454 −1.81929 −0.909645 0.415386i \(-0.863647\pi\)
−0.909645 + 0.415386i \(0.863647\pi\)
\(38\) −151.554 −0.646984
\(39\) 244.134 1.00238
\(40\) 153.445 0.606545
\(41\) −282.185 −1.07487 −0.537437 0.843304i \(-0.680607\pi\)
−0.537437 + 0.843304i \(0.680607\pi\)
\(42\) −461.286 −1.69471
\(43\) 489.222 1.73501 0.867507 0.497425i \(-0.165721\pi\)
0.867507 + 0.497425i \(0.165721\pi\)
\(44\) −275.403 −0.943604
\(45\) 128.572 0.425921
\(46\) −189.169 −0.606335
\(47\) 107.610 0.333970 0.166985 0.985959i \(-0.446597\pi\)
0.166985 + 0.985959i \(0.446597\pi\)
\(48\) −472.008 −1.41934
\(49\) 110.794 0.323013
\(50\) −311.455 −0.880928
\(51\) 615.139 1.68895
\(52\) 207.135 0.552392
\(53\) 490.814 1.27205 0.636023 0.771670i \(-0.280578\pi\)
0.636023 + 0.771670i \(0.280578\pi\)
\(54\) 393.048 0.990502
\(55\) −787.716 −1.93119
\(56\) 224.967 0.536831
\(57\) 250.901 0.583029
\(58\) −710.414 −1.60831
\(59\) −715.166 −1.57808 −0.789040 0.614342i \(-0.789421\pi\)
−0.789040 + 0.614342i \(0.789421\pi\)
\(60\) 441.938 0.950898
\(61\) 37.2896 0.0782696 0.0391348 0.999234i \(-0.487540\pi\)
0.0391348 + 0.999234i \(0.487540\pi\)
\(62\) −387.880 −0.794528
\(63\) 188.501 0.376967
\(64\) −94.9216 −0.185394
\(65\) 592.453 1.13053
\(66\) 1173.95 2.18944
\(67\) −1004.20 −1.83109 −0.915545 0.402214i \(-0.868241\pi\)
−0.915545 + 0.402214i \(0.868241\pi\)
\(68\) 521.911 0.930751
\(69\) 313.172 0.546399
\(70\) −1119.42 −1.91138
\(71\) −612.234 −1.02336 −0.511682 0.859175i \(-0.670977\pi\)
−0.511682 + 0.859175i \(0.670977\pi\)
\(72\) 93.4492 0.152960
\(73\) 488.999 0.784014 0.392007 0.919962i \(-0.371781\pi\)
0.392007 + 0.919962i \(0.371781\pi\)
\(74\) 1480.84 2.32627
\(75\) 515.620 0.793848
\(76\) 212.876 0.321297
\(77\) −1154.88 −1.70923
\(78\) −882.942 −1.28171
\(79\) 389.173 0.554245 0.277123 0.960835i \(-0.410619\pi\)
0.277123 + 0.960835i \(0.410619\pi\)
\(80\) −1145.44 −1.60081
\(81\) −889.616 −1.22032
\(82\) 1020.56 1.37441
\(83\) −605.759 −0.801092 −0.400546 0.916277i \(-0.631180\pi\)
−0.400546 + 0.916277i \(0.631180\pi\)
\(84\) 647.930 0.841606
\(85\) 1492.79 1.90489
\(86\) −1769.33 −2.21851
\(87\) 1176.10 1.44933
\(88\) −572.530 −0.693544
\(89\) 1598.67 1.90403 0.952015 0.306050i \(-0.0990075\pi\)
0.952015 + 0.306050i \(0.0990075\pi\)
\(90\) −464.998 −0.544612
\(91\) 868.601 1.00060
\(92\) 265.710 0.301110
\(93\) 642.142 0.715989
\(94\) −389.186 −0.427037
\(95\) 608.874 0.657570
\(96\) 1201.23 1.27708
\(97\) 372.859 0.390289 0.195145 0.980774i \(-0.437482\pi\)
0.195145 + 0.980774i \(0.437482\pi\)
\(98\) −400.698 −0.413027
\(99\) −479.725 −0.487012
\(100\) 437.475 0.437475
\(101\) 1418.88 1.39786 0.698931 0.715189i \(-0.253660\pi\)
0.698931 + 0.715189i \(0.253660\pi\)
\(102\) −2224.73 −2.15961
\(103\) 736.959 0.704997 0.352499 0.935812i \(-0.385332\pi\)
0.352499 + 0.935812i \(0.385332\pi\)
\(104\) 430.608 0.406006
\(105\) 1853.23 1.72244
\(106\) −1775.09 −1.62653
\(107\) −359.834 −0.325107 −0.162553 0.986700i \(-0.551973\pi\)
−0.162553 + 0.986700i \(0.551973\pi\)
\(108\) −552.082 −0.491890
\(109\) −638.777 −0.561319 −0.280659 0.959807i \(-0.590553\pi\)
−0.280659 + 0.959807i \(0.590553\pi\)
\(110\) 2848.87 2.46936
\(111\) −2451.56 −2.09632
\(112\) −1679.35 −1.41682
\(113\) −221.620 −0.184498 −0.0922491 0.995736i \(-0.529406\pi\)
−0.0922491 + 0.995736i \(0.529406\pi\)
\(114\) −907.415 −0.745502
\(115\) 759.991 0.616257
\(116\) 997.859 0.798697
\(117\) 360.808 0.285100
\(118\) 2586.49 2.01784
\(119\) 2188.59 1.68595
\(120\) 918.735 0.698905
\(121\) 1608.10 1.20819
\(122\) −134.863 −0.100081
\(123\) −1689.55 −1.23855
\(124\) 544.822 0.394568
\(125\) −564.957 −0.404250
\(126\) −681.738 −0.482016
\(127\) −2071.95 −1.44768 −0.723842 0.689966i \(-0.757626\pi\)
−0.723842 + 0.689966i \(0.757626\pi\)
\(128\) −1261.72 −0.871258
\(129\) 2929.16 1.99921
\(130\) −2142.68 −1.44558
\(131\) 1843.90 1.22979 0.614894 0.788610i \(-0.289199\pi\)
0.614894 + 0.788610i \(0.289199\pi\)
\(132\) −1648.95 −1.08729
\(133\) 892.677 0.581992
\(134\) 3631.83 2.34136
\(135\) −1579.08 −1.00671
\(136\) 1084.99 0.684097
\(137\) 997.082 0.621799 0.310900 0.950443i \(-0.399370\pi\)
0.310900 + 0.950443i \(0.399370\pi\)
\(138\) −1132.63 −0.698664
\(139\) 2960.35 1.80643 0.903213 0.429192i \(-0.141202\pi\)
0.903213 + 0.429192i \(0.141202\pi\)
\(140\) 1572.36 0.949206
\(141\) 644.305 0.384824
\(142\) 2214.22 1.30854
\(143\) −2210.54 −1.29269
\(144\) −697.584 −0.403695
\(145\) 2854.11 1.63463
\(146\) −1768.53 −1.00249
\(147\) 663.364 0.372199
\(148\) −2080.01 −1.15524
\(149\) 1822.08 1.00181 0.500907 0.865501i \(-0.333000\pi\)
0.500907 + 0.865501i \(0.333000\pi\)
\(150\) −1864.80 −1.01507
\(151\) −1262.32 −0.680305 −0.340152 0.940370i \(-0.610479\pi\)
−0.340152 + 0.940370i \(0.610479\pi\)
\(152\) 442.543 0.236151
\(153\) 909.119 0.480378
\(154\) 4176.77 2.18554
\(155\) 1558.32 0.807529
\(156\) 1240.20 0.636507
\(157\) −1307.15 −0.664470 −0.332235 0.943197i \(-0.607803\pi\)
−0.332235 + 0.943197i \(0.607803\pi\)
\(158\) −1407.49 −0.708697
\(159\) 2938.69 1.46574
\(160\) 2915.08 1.44036
\(161\) 1114.23 0.545427
\(162\) 3217.41 1.56039
\(163\) 1061.31 0.509989 0.254995 0.966942i \(-0.417926\pi\)
0.254995 + 0.966942i \(0.417926\pi\)
\(164\) −1433.49 −0.682541
\(165\) −4716.36 −2.22526
\(166\) 2190.80 1.02433
\(167\) 1098.53 0.509023 0.254511 0.967070i \(-0.418085\pi\)
0.254511 + 0.967070i \(0.418085\pi\)
\(168\) 1346.97 0.618576
\(169\) −534.419 −0.243249
\(170\) −5398.85 −2.43572
\(171\) 370.809 0.165827
\(172\) 2485.23 1.10173
\(173\) 2018.58 0.887110 0.443555 0.896247i \(-0.353717\pi\)
0.443555 + 0.896247i \(0.353717\pi\)
\(174\) −4253.52 −1.85321
\(175\) 1834.51 0.792436
\(176\) 4273.85 1.83042
\(177\) −4281.98 −1.81838
\(178\) −5781.79 −2.43463
\(179\) 359.017 0.149912 0.0749559 0.997187i \(-0.476118\pi\)
0.0749559 + 0.997187i \(0.476118\pi\)
\(180\) 653.143 0.270458
\(181\) −1169.86 −0.480414 −0.240207 0.970722i \(-0.577215\pi\)
−0.240207 + 0.970722i \(0.577215\pi\)
\(182\) −3141.41 −1.27943
\(183\) 223.267 0.0901880
\(184\) 552.378 0.221314
\(185\) −5949.31 −2.36434
\(186\) −2322.39 −0.915514
\(187\) −5569.84 −2.17811
\(188\) 546.657 0.212070
\(189\) −2315.11 −0.891002
\(190\) −2202.07 −0.840815
\(191\) 1398.55 0.529818 0.264909 0.964273i \(-0.414658\pi\)
0.264909 + 0.964273i \(0.414658\pi\)
\(192\) −568.332 −0.213624
\(193\) 508.410 0.189617 0.0948086 0.995496i \(-0.469776\pi\)
0.0948086 + 0.995496i \(0.469776\pi\)
\(194\) −1348.49 −0.499051
\(195\) 3547.24 1.30268
\(196\) 562.828 0.205112
\(197\) −2535.12 −0.916852 −0.458426 0.888733i \(-0.651587\pi\)
−0.458426 + 0.888733i \(0.651587\pi\)
\(198\) 1734.99 0.622728
\(199\) 201.425 0.0717520 0.0358760 0.999356i \(-0.488578\pi\)
0.0358760 + 0.999356i \(0.488578\pi\)
\(200\) 909.458 0.321542
\(201\) −6012.56 −2.10992
\(202\) −5131.56 −1.78740
\(203\) 4184.44 1.44675
\(204\) 3124.89 1.07248
\(205\) −4100.11 −1.39690
\(206\) −2665.30 −0.901459
\(207\) 462.840 0.155409
\(208\) −3214.42 −1.07154
\(209\) −2271.81 −0.751888
\(210\) −6702.43 −2.20244
\(211\) −5431.97 −1.77229 −0.886143 0.463413i \(-0.846625\pi\)
−0.886143 + 0.463413i \(0.846625\pi\)
\(212\) 2493.32 0.807744
\(213\) −3665.68 −1.17919
\(214\) 1301.38 0.415704
\(215\) 7108.33 2.25481
\(216\) −1147.71 −0.361537
\(217\) 2284.67 0.714715
\(218\) 2310.22 0.717741
\(219\) 2927.83 0.903398
\(220\) −4001.58 −1.22630
\(221\) 4189.16 1.27508
\(222\) 8866.36 2.68050
\(223\) −4297.52 −1.29051 −0.645253 0.763969i \(-0.723248\pi\)
−0.645253 + 0.763969i \(0.723248\pi\)
\(224\) 4273.83 1.27481
\(225\) 762.039 0.225789
\(226\) 801.518 0.235912
\(227\) −4846.60 −1.41709 −0.708547 0.705664i \(-0.750649\pi\)
−0.708547 + 0.705664i \(0.750649\pi\)
\(228\) 1274.57 0.370222
\(229\) −6080.26 −1.75456 −0.877282 0.479976i \(-0.840645\pi\)
−0.877282 + 0.479976i \(0.840645\pi\)
\(230\) −2748.60 −0.787989
\(231\) −6914.71 −1.96950
\(232\) 2074.43 0.587038
\(233\) −3629.10 −1.02039 −0.510193 0.860060i \(-0.670426\pi\)
−0.510193 + 0.860060i \(0.670426\pi\)
\(234\) −1304.91 −0.364549
\(235\) 1563.57 0.434025
\(236\) −3633.02 −1.00207
\(237\) 2330.13 0.638642
\(238\) −7915.31 −2.15577
\(239\) 1384.17 0.374622 0.187311 0.982301i \(-0.440023\pi\)
0.187311 + 0.982301i \(0.440023\pi\)
\(240\) −6858.22 −1.84457
\(241\) 2091.61 0.559055 0.279528 0.960138i \(-0.409822\pi\)
0.279528 + 0.960138i \(0.409822\pi\)
\(242\) −5815.91 −1.54488
\(243\) −2392.17 −0.631513
\(244\) 189.430 0.0497009
\(245\) 1609.82 0.419785
\(246\) 6110.46 1.58370
\(247\) 1708.66 0.440161
\(248\) 1132.62 0.290006
\(249\) −3626.91 −0.923077
\(250\) 2043.24 0.516902
\(251\) 7043.45 1.77123 0.885614 0.464422i \(-0.153738\pi\)
0.885614 + 0.464422i \(0.153738\pi\)
\(252\) 957.581 0.239373
\(253\) −2835.66 −0.704649
\(254\) 7493.47 1.85111
\(255\) 8937.89 2.19495
\(256\) 5322.53 1.29945
\(257\) 3219.14 0.781339 0.390670 0.920531i \(-0.372244\pi\)
0.390670 + 0.920531i \(0.372244\pi\)
\(258\) −10593.7 −2.55633
\(259\) −8722.36 −2.09259
\(260\) 3009.64 0.717885
\(261\) 1738.17 0.412223
\(262\) −6668.69 −1.57249
\(263\) −2563.95 −0.601141 −0.300571 0.953760i \(-0.597177\pi\)
−0.300571 + 0.953760i \(0.597177\pi\)
\(264\) −3427.96 −0.799152
\(265\) 7131.47 1.65314
\(266\) −3228.48 −0.744176
\(267\) 9571.86 2.19396
\(268\) −5101.33 −1.16274
\(269\) 5355.59 1.21389 0.606945 0.794744i \(-0.292395\pi\)
0.606945 + 0.794744i \(0.292395\pi\)
\(270\) 5710.95 1.28725
\(271\) −1304.50 −0.292408 −0.146204 0.989254i \(-0.546706\pi\)
−0.146204 + 0.989254i \(0.546706\pi\)
\(272\) −8099.30 −1.80549
\(273\) 5200.65 1.15296
\(274\) −3606.07 −0.795076
\(275\) −4668.74 −1.02377
\(276\) 1590.91 0.346961
\(277\) −5109.26 −1.10825 −0.554126 0.832433i \(-0.686947\pi\)
−0.554126 + 0.832433i \(0.686947\pi\)
\(278\) −10706.5 −2.30982
\(279\) 949.027 0.203644
\(280\) 3268.75 0.697662
\(281\) −3250.12 −0.689986 −0.344993 0.938605i \(-0.612119\pi\)
−0.344993 + 0.938605i \(0.612119\pi\)
\(282\) −2330.21 −0.492063
\(283\) 8799.91 1.84841 0.924205 0.381896i \(-0.124729\pi\)
0.924205 + 0.381896i \(0.124729\pi\)
\(284\) −3110.13 −0.649832
\(285\) 3645.57 0.757701
\(286\) 7994.70 1.65293
\(287\) −6011.22 −1.23635
\(288\) 1775.31 0.363233
\(289\) 5642.31 1.14845
\(290\) −10322.2 −2.09015
\(291\) 2232.45 0.449720
\(292\) 2484.10 0.497846
\(293\) 3169.56 0.631972 0.315986 0.948764i \(-0.397665\pi\)
0.315986 + 0.948764i \(0.397665\pi\)
\(294\) −2399.14 −0.475920
\(295\) −10391.3 −2.05086
\(296\) −4324.09 −0.849098
\(297\) 5891.83 1.15111
\(298\) −6589.76 −1.28099
\(299\) 2132.74 0.412506
\(300\) 2619.33 0.504091
\(301\) 10421.6 1.99565
\(302\) 4565.33 0.869885
\(303\) 8495.40 1.61072
\(304\) −3303.52 −0.623256
\(305\) 541.814 0.101719
\(306\) −3287.94 −0.614245
\(307\) 7647.86 1.42178 0.710890 0.703303i \(-0.248292\pi\)
0.710890 + 0.703303i \(0.248292\pi\)
\(308\) −5866.75 −1.08536
\(309\) 4412.46 0.812349
\(310\) −5635.85 −1.03256
\(311\) −8400.00 −1.53158 −0.765788 0.643093i \(-0.777651\pi\)
−0.765788 + 0.643093i \(0.777651\pi\)
\(312\) 2578.22 0.467829
\(313\) −5970.25 −1.07814 −0.539071 0.842260i \(-0.681225\pi\)
−0.539071 + 0.842260i \(0.681225\pi\)
\(314\) 4727.47 0.849638
\(315\) 2738.90 0.489904
\(316\) 1976.99 0.351944
\(317\) 2352.99 0.416899 0.208449 0.978033i \(-0.433158\pi\)
0.208449 + 0.978033i \(0.433158\pi\)
\(318\) −10628.1 −1.87420
\(319\) −10649.2 −1.86909
\(320\) −1379.20 −0.240936
\(321\) −2154.46 −0.374612
\(322\) −4029.75 −0.697421
\(323\) 4305.27 0.741647
\(324\) −4519.23 −0.774902
\(325\) 3511.43 0.599319
\(326\) −3838.36 −0.652108
\(327\) −3824.61 −0.646793
\(328\) −2980.05 −0.501664
\(329\) 2292.36 0.384140
\(330\) 17057.3 2.84538
\(331\) −8514.82 −1.41395 −0.706974 0.707240i \(-0.749940\pi\)
−0.706974 + 0.707240i \(0.749940\pi\)
\(332\) −3077.24 −0.508691
\(333\) −3623.18 −0.596243
\(334\) −3972.97 −0.650872
\(335\) −14591.0 −2.37967
\(336\) −10054.9 −1.63256
\(337\) −3182.38 −0.514407 −0.257204 0.966357i \(-0.582801\pi\)
−0.257204 + 0.966357i \(0.582801\pi\)
\(338\) 1932.79 0.311036
\(339\) −1326.93 −0.212592
\(340\) 7583.31 1.20960
\(341\) −5814.35 −0.923357
\(342\) −1341.08 −0.212038
\(343\) −4946.56 −0.778686
\(344\) 5166.50 0.809764
\(345\) 4550.36 0.710096
\(346\) −7300.46 −1.13432
\(347\) 7946.55 1.22938 0.614688 0.788771i \(-0.289282\pi\)
0.614688 + 0.788771i \(0.289282\pi\)
\(348\) 5974.57 0.920318
\(349\) −7110.75 −1.09063 −0.545314 0.838232i \(-0.683590\pi\)
−0.545314 + 0.838232i \(0.683590\pi\)
\(350\) −6634.75 −1.01326
\(351\) −4431.33 −0.673865
\(352\) −10876.7 −1.64696
\(353\) 9352.21 1.41011 0.705054 0.709154i \(-0.250923\pi\)
0.705054 + 0.709154i \(0.250923\pi\)
\(354\) 15486.3 2.32511
\(355\) −8895.69 −1.32996
\(356\) 8121.20 1.20905
\(357\) 13103.9 1.94267
\(358\) −1298.43 −0.191688
\(359\) 14.1011 0.00207306 0.00103653 0.999999i \(-0.499670\pi\)
0.00103653 + 0.999999i \(0.499670\pi\)
\(360\) 1357.81 0.198785
\(361\) −5102.98 −0.743982
\(362\) 4230.94 0.614290
\(363\) 9628.35 1.39217
\(364\) 4412.47 0.635374
\(365\) 7105.10 1.01890
\(366\) −807.474 −0.115321
\(367\) −7009.17 −0.996937 −0.498468 0.866908i \(-0.666104\pi\)
−0.498468 + 0.866908i \(0.666104\pi\)
\(368\) −4123.42 −0.584098
\(369\) −2497.00 −0.352273
\(370\) 21516.4 3.02321
\(371\) 10455.5 1.46314
\(372\) 3262.06 0.454651
\(373\) −3331.77 −0.462499 −0.231250 0.972894i \(-0.574281\pi\)
−0.231250 + 0.972894i \(0.574281\pi\)
\(374\) 20144.0 2.78509
\(375\) −3382.61 −0.465807
\(376\) 1136.43 0.155870
\(377\) 8009.39 1.09418
\(378\) 8372.88 1.13930
\(379\) 8291.57 1.12377 0.561886 0.827215i \(-0.310076\pi\)
0.561886 + 0.827215i \(0.310076\pi\)
\(380\) 3093.06 0.417555
\(381\) −12405.6 −1.66813
\(382\) −5058.02 −0.677463
\(383\) −6622.40 −0.883521 −0.441761 0.897133i \(-0.645646\pi\)
−0.441761 + 0.897133i \(0.645646\pi\)
\(384\) −7554.39 −1.00393
\(385\) −16780.3 −2.22130
\(386\) −1838.73 −0.242458
\(387\) 4329.03 0.568623
\(388\) 1894.11 0.247832
\(389\) 12619.6 1.64484 0.822418 0.568883i \(-0.192624\pi\)
0.822418 + 0.568883i \(0.192624\pi\)
\(390\) −12829.0 −1.66570
\(391\) 5373.80 0.695051
\(392\) 1170.05 0.150756
\(393\) 11040.1 1.41705
\(394\) 9168.58 1.17235
\(395\) 5654.64 0.720293
\(396\) −2436.99 −0.309251
\(397\) 1074.44 0.135831 0.0679153 0.997691i \(-0.478365\pi\)
0.0679153 + 0.997691i \(0.478365\pi\)
\(398\) −728.479 −0.0917471
\(399\) 5344.80 0.670614
\(400\) −6788.97 −0.848621
\(401\) −3731.07 −0.464640 −0.232320 0.972639i \(-0.574632\pi\)
−0.232320 + 0.972639i \(0.574632\pi\)
\(402\) 21745.2 2.69789
\(403\) 4373.05 0.540539
\(404\) 7207.88 0.887637
\(405\) −12926.0 −1.58592
\(406\) −15133.5 −1.84991
\(407\) 22197.9 2.70346
\(408\) 6496.26 0.788267
\(409\) 4666.38 0.564150 0.282075 0.959392i \(-0.408977\pi\)
0.282075 + 0.959392i \(0.408977\pi\)
\(410\) 14828.6 1.78617
\(411\) 5969.92 0.716483
\(412\) 3743.73 0.447671
\(413\) −15234.8 −1.81514
\(414\) −1673.92 −0.198717
\(415\) −8801.61 −1.04109
\(416\) 8180.50 0.964139
\(417\) 17724.7 2.08150
\(418\) 8216.30 0.961417
\(419\) −8102.57 −0.944717 −0.472359 0.881406i \(-0.656597\pi\)
−0.472359 + 0.881406i \(0.656597\pi\)
\(420\) 9414.34 1.09375
\(421\) −4283.67 −0.495898 −0.247949 0.968773i \(-0.579757\pi\)
−0.247949 + 0.968773i \(0.579757\pi\)
\(422\) 19645.4 2.26617
\(423\) 952.224 0.109453
\(424\) 5183.31 0.593688
\(425\) 8847.64 1.00982
\(426\) 13257.4 1.50780
\(427\) 794.359 0.0900275
\(428\) −1827.95 −0.206442
\(429\) −13235.4 −1.48953
\(430\) −25708.2 −2.88316
\(431\) 8589.77 0.959987 0.479994 0.877272i \(-0.340639\pi\)
0.479994 + 0.877272i \(0.340639\pi\)
\(432\) 8567.50 0.954176
\(433\) −8146.55 −0.904153 −0.452077 0.891979i \(-0.649317\pi\)
−0.452077 + 0.891979i \(0.649317\pi\)
\(434\) −8262.78 −0.913885
\(435\) 17088.6 1.88354
\(436\) −3244.97 −0.356435
\(437\) 2191.85 0.239933
\(438\) −10588.8 −1.15515
\(439\) −16379.0 −1.78070 −0.890351 0.455274i \(-0.849541\pi\)
−0.890351 + 0.455274i \(0.849541\pi\)
\(440\) −8318.79 −0.901325
\(441\) 980.391 0.105862
\(442\) −15150.6 −1.63041
\(443\) −4534.63 −0.486335 −0.243168 0.969984i \(-0.578187\pi\)
−0.243168 + 0.969984i \(0.578187\pi\)
\(444\) −12453.8 −1.33116
\(445\) 23228.5 2.47446
\(446\) 15542.5 1.65013
\(447\) 10909.5 1.15436
\(448\) −2022.06 −0.213244
\(449\) −17706.1 −1.86103 −0.930513 0.366258i \(-0.880639\pi\)
−0.930513 + 0.366258i \(0.880639\pi\)
\(450\) −2756.01 −0.288710
\(451\) 15298.2 1.59726
\(452\) −1125.82 −0.117156
\(453\) −7557.99 −0.783897
\(454\) 17528.3 1.81199
\(455\) 12620.7 1.30037
\(456\) 2649.68 0.272111
\(457\) −7191.90 −0.736156 −0.368078 0.929795i \(-0.619984\pi\)
−0.368078 + 0.929795i \(0.619984\pi\)
\(458\) 21990.0 2.24351
\(459\) −11165.5 −1.13543
\(460\) 3860.73 0.391321
\(461\) −9509.22 −0.960713 −0.480356 0.877073i \(-0.659493\pi\)
−0.480356 + 0.877073i \(0.659493\pi\)
\(462\) 25007.9 2.51834
\(463\) 1945.35 0.195265 0.0976327 0.995223i \(-0.468873\pi\)
0.0976327 + 0.995223i \(0.468873\pi\)
\(464\) −15485.3 −1.54933
\(465\) 9330.25 0.930494
\(466\) 13125.1 1.30474
\(467\) 14631.5 1.44981 0.724907 0.688846i \(-0.241883\pi\)
0.724907 + 0.688846i \(0.241883\pi\)
\(468\) 1832.90 0.181038
\(469\) −21392.0 −2.10616
\(470\) −5654.83 −0.554974
\(471\) −7826.41 −0.765651
\(472\) −7552.62 −0.736520
\(473\) −26522.4 −2.57823
\(474\) −8427.20 −0.816612
\(475\) 3608.75 0.348592
\(476\) 11118.0 1.07057
\(477\) 4343.12 0.416892
\(478\) −5006.03 −0.479018
\(479\) 2595.61 0.247592 0.123796 0.992308i \(-0.460493\pi\)
0.123796 + 0.992308i \(0.460493\pi\)
\(480\) 17453.7 1.65969
\(481\) −16695.4 −1.58263
\(482\) −7564.56 −0.714847
\(483\) 6671.33 0.628481
\(484\) 8169.13 0.767198
\(485\) 5417.59 0.507217
\(486\) 8651.57 0.807497
\(487\) −18820.5 −1.75121 −0.875603 0.483031i \(-0.839536\pi\)
−0.875603 + 0.483031i \(0.839536\pi\)
\(488\) 393.803 0.0365299
\(489\) 6354.48 0.587647
\(490\) −5822.10 −0.536767
\(491\) −10108.6 −0.929109 −0.464555 0.885544i \(-0.653786\pi\)
−0.464555 + 0.885544i \(0.653786\pi\)
\(492\) −8582.86 −0.786474
\(493\) 20181.0 1.84363
\(494\) −6179.60 −0.562820
\(495\) −6970.35 −0.632917
\(496\) −8454.84 −0.765390
\(497\) −13042.1 −1.17710
\(498\) 13117.2 1.18031
\(499\) −4987.03 −0.447395 −0.223698 0.974659i \(-0.571813\pi\)
−0.223698 + 0.974659i \(0.571813\pi\)
\(500\) −2869.96 −0.256697
\(501\) 6577.33 0.586533
\(502\) −25473.5 −2.26482
\(503\) 4958.41 0.439532 0.219766 0.975553i \(-0.429471\pi\)
0.219766 + 0.975553i \(0.429471\pi\)
\(504\) 1990.70 0.175938
\(505\) 20616.2 1.81665
\(506\) 10255.5 0.901013
\(507\) −3199.77 −0.280290
\(508\) −10525.4 −0.919274
\(509\) 13928.5 1.21291 0.606455 0.795118i \(-0.292591\pi\)
0.606455 + 0.795118i \(0.292591\pi\)
\(510\) −32325.0 −2.80662
\(511\) 10416.9 0.901790
\(512\) −9155.85 −0.790303
\(513\) −4554.15 −0.391951
\(514\) −11642.4 −0.999075
\(515\) 10707.9 0.916209
\(516\) 14880.0 1.26949
\(517\) −5833.93 −0.496279
\(518\) 31545.5 2.67573
\(519\) 12086.0 1.02219
\(520\) 6256.68 0.527642
\(521\) −2042.22 −0.171730 −0.0858651 0.996307i \(-0.527365\pi\)
−0.0858651 + 0.996307i \(0.527365\pi\)
\(522\) −6286.32 −0.527097
\(523\) −11834.7 −0.989471 −0.494735 0.869044i \(-0.664735\pi\)
−0.494735 + 0.869044i \(0.664735\pi\)
\(524\) 9366.95 0.780910
\(525\) 10983.9 0.913103
\(526\) 9272.86 0.768661
\(527\) 11018.7 0.910779
\(528\) 25589.2 2.10914
\(529\) −9431.15 −0.775142
\(530\) −25791.8 −2.11382
\(531\) −6328.37 −0.517190
\(532\) 4534.77 0.369563
\(533\) −11506.0 −0.935048
\(534\) −34617.8 −2.80536
\(535\) −5228.34 −0.422507
\(536\) −10605.0 −0.854605
\(537\) 2149.58 0.172739
\(538\) −19369.2 −1.55216
\(539\) −6006.51 −0.479997
\(540\) −8021.69 −0.639257
\(541\) 9265.77 0.736352 0.368176 0.929756i \(-0.379982\pi\)
0.368176 + 0.929756i \(0.379982\pi\)
\(542\) 4717.88 0.373894
\(543\) −7004.39 −0.553568
\(544\) 20612.2 1.62452
\(545\) −9281.36 −0.729486
\(546\) −18808.8 −1.47425
\(547\) −547.000 −0.0427569
\(548\) 5065.15 0.394840
\(549\) 329.969 0.0256516
\(550\) 16885.1 1.30906
\(551\) 8231.39 0.636423
\(552\) 3307.30 0.255015
\(553\) 8290.33 0.637506
\(554\) 18478.3 1.41709
\(555\) −35620.9 −2.72436
\(556\) 15038.5 1.14707
\(557\) −3706.74 −0.281974 −0.140987 0.990011i \(-0.545028\pi\)
−0.140987 + 0.990011i \(0.545028\pi\)
\(558\) −3432.27 −0.260394
\(559\) 19947.9 1.50931
\(560\) −24400.7 −1.84129
\(561\) −33348.8 −2.50978
\(562\) 11754.5 0.882265
\(563\) −9943.90 −0.744379 −0.372189 0.928157i \(-0.621393\pi\)
−0.372189 + 0.928157i \(0.621393\pi\)
\(564\) 3273.05 0.244362
\(565\) −3220.12 −0.239772
\(566\) −31826.0 −2.36351
\(567\) −18951.0 −1.40365
\(568\) −6465.59 −0.477623
\(569\) −6200.20 −0.456812 −0.228406 0.973566i \(-0.573351\pi\)
−0.228406 + 0.973566i \(0.573351\pi\)
\(570\) −13184.6 −0.968849
\(571\) 10773.1 0.789562 0.394781 0.918775i \(-0.370820\pi\)
0.394781 + 0.918775i \(0.370820\pi\)
\(572\) −11229.5 −0.820854
\(573\) 8373.65 0.610496
\(574\) 21740.3 1.58088
\(575\) 4504.41 0.326690
\(576\) −839.943 −0.0607598
\(577\) 22073.6 1.59261 0.796305 0.604896i \(-0.206785\pi\)
0.796305 + 0.604896i \(0.206785\pi\)
\(578\) −20406.1 −1.46848
\(579\) 3044.05 0.218491
\(580\) 14498.8 1.03798
\(581\) −12904.1 −0.921435
\(582\) −8073.93 −0.575043
\(583\) −26608.7 −1.89026
\(584\) 5164.14 0.365914
\(585\) 5242.50 0.370514
\(586\) −11463.1 −0.808083
\(587\) −12786.4 −0.899066 −0.449533 0.893264i \(-0.648410\pi\)
−0.449533 + 0.893264i \(0.648410\pi\)
\(588\) 3369.87 0.236345
\(589\) 4494.27 0.314402
\(590\) 37581.4 2.62237
\(591\) −15178.7 −1.05646
\(592\) 32278.7 2.24096
\(593\) 23546.2 1.63057 0.815285 0.579060i \(-0.196580\pi\)
0.815285 + 0.579060i \(0.196580\pi\)
\(594\) −21308.5 −1.47188
\(595\) 31800.0 2.19105
\(596\) 9256.09 0.636148
\(597\) 1206.01 0.0826779
\(598\) −7713.31 −0.527459
\(599\) −15023.7 −1.02480 −0.512398 0.858748i \(-0.671243\pi\)
−0.512398 + 0.858748i \(0.671243\pi\)
\(600\) 5445.28 0.370504
\(601\) −9311.82 −0.632008 −0.316004 0.948758i \(-0.602341\pi\)
−0.316004 + 0.948758i \(0.602341\pi\)
\(602\) −37691.0 −2.55178
\(603\) −8886.02 −0.600111
\(604\) −6412.54 −0.431991
\(605\) 23365.6 1.57016
\(606\) −30724.7 −2.05958
\(607\) −3513.63 −0.234948 −0.117474 0.993076i \(-0.537480\pi\)
−0.117474 + 0.993076i \(0.537480\pi\)
\(608\) 8407.25 0.560788
\(609\) 25053.9 1.66705
\(610\) −1959.54 −0.130065
\(611\) 4387.78 0.290525
\(612\) 4618.30 0.305039
\(613\) −7779.37 −0.512570 −0.256285 0.966601i \(-0.582499\pi\)
−0.256285 + 0.966601i \(0.582499\pi\)
\(614\) −27659.4 −1.81799
\(615\) −24549.0 −1.60961
\(616\) −12196.3 −0.797730
\(617\) 9268.56 0.604762 0.302381 0.953187i \(-0.402218\pi\)
0.302381 + 0.953187i \(0.402218\pi\)
\(618\) −15958.2 −1.03873
\(619\) −12797.5 −0.830976 −0.415488 0.909599i \(-0.636389\pi\)
−0.415488 + 0.909599i \(0.636389\pi\)
\(620\) 7916.20 0.512778
\(621\) −5684.45 −0.367325
\(622\) 30379.7 1.95838
\(623\) 34055.6 2.19006
\(624\) −19246.0 −1.23471
\(625\) −18973.5 −1.21430
\(626\) 21592.2 1.37859
\(627\) −13602.2 −0.866381
\(628\) −6640.28 −0.421936
\(629\) −42066.9 −2.66664
\(630\) −9905.58 −0.626425
\(631\) 881.562 0.0556171 0.0278086 0.999613i \(-0.491147\pi\)
0.0278086 + 0.999613i \(0.491147\pi\)
\(632\) 4109.92 0.258677
\(633\) −32523.3 −2.04216
\(634\) −8509.87 −0.533076
\(635\) −30105.2 −1.88140
\(636\) 14928.5 0.930742
\(637\) 4517.58 0.280994
\(638\) 38514.0 2.38994
\(639\) −5417.55 −0.335391
\(640\) −18332.6 −1.13228
\(641\) 4417.49 0.272200 0.136100 0.990695i \(-0.456543\pi\)
0.136100 + 0.990695i \(0.456543\pi\)
\(642\) 7791.89 0.479005
\(643\) −15534.9 −0.952776 −0.476388 0.879235i \(-0.658054\pi\)
−0.476388 + 0.879235i \(0.658054\pi\)
\(644\) 5660.26 0.346344
\(645\) 42560.4 2.59816
\(646\) −15570.6 −0.948321
\(647\) −3809.34 −0.231469 −0.115735 0.993280i \(-0.536922\pi\)
−0.115735 + 0.993280i \(0.536922\pi\)
\(648\) −9394.93 −0.569549
\(649\) 38771.7 2.34502
\(650\) −12699.5 −0.766332
\(651\) 13679.2 0.823547
\(652\) 5391.43 0.323841
\(653\) 5394.29 0.323270 0.161635 0.986851i \(-0.448323\pi\)
0.161635 + 0.986851i \(0.448323\pi\)
\(654\) 13832.2 0.827034
\(655\) 26791.6 1.59822
\(656\) 22245.7 1.32400
\(657\) 4327.06 0.256948
\(658\) −8290.61 −0.491188
\(659\) 5590.04 0.330436 0.165218 0.986257i \(-0.447167\pi\)
0.165218 + 0.986257i \(0.447167\pi\)
\(660\) −23959.0 −1.41303
\(661\) −17701.4 −1.04161 −0.520805 0.853676i \(-0.674368\pi\)
−0.520805 + 0.853676i \(0.674368\pi\)
\(662\) 30794.9 1.80797
\(663\) 25082.1 1.46924
\(664\) −6397.20 −0.373885
\(665\) 12970.5 0.756352
\(666\) 13103.7 0.762398
\(667\) 10274.3 0.596438
\(668\) 5580.50 0.323228
\(669\) −25730.9 −1.48702
\(670\) 52770.1 3.04281
\(671\) −2021.60 −0.116309
\(672\) 25589.1 1.46893
\(673\) 15556.0 0.890996 0.445498 0.895283i \(-0.353027\pi\)
0.445498 + 0.895283i \(0.353027\pi\)
\(674\) 11509.5 0.657757
\(675\) −9359.11 −0.533677
\(676\) −2714.83 −0.154462
\(677\) −30896.1 −1.75396 −0.876982 0.480523i \(-0.840447\pi\)
−0.876982 + 0.480523i \(0.840447\pi\)
\(678\) 4799.00 0.271835
\(679\) 7942.79 0.448920
\(680\) 15764.8 0.889047
\(681\) −29018.5 −1.63288
\(682\) 21028.3 1.18067
\(683\) −16765.5 −0.939260 −0.469630 0.882863i \(-0.655613\pi\)
−0.469630 + 0.882863i \(0.655613\pi\)
\(684\) 1883.70 0.105300
\(685\) 14487.5 0.808085
\(686\) 17889.9 0.995682
\(687\) −36404.9 −2.02174
\(688\) −38567.1 −2.13715
\(689\) 20012.8 1.10657
\(690\) −16456.9 −0.907978
\(691\) 24887.6 1.37014 0.685072 0.728475i \(-0.259771\pi\)
0.685072 + 0.728475i \(0.259771\pi\)
\(692\) 10254.3 0.563312
\(693\) −10219.3 −0.560173
\(694\) −28739.7 −1.57197
\(695\) 43013.5 2.34762
\(696\) 12420.4 0.676429
\(697\) −28991.4 −1.57551
\(698\) 25716.9 1.39455
\(699\) −21728.8 −1.17576
\(700\) 9319.28 0.503194
\(701\) −3157.12 −0.170104 −0.0850518 0.996377i \(-0.527106\pi\)
−0.0850518 + 0.996377i \(0.527106\pi\)
\(702\) 16026.4 0.861651
\(703\) −17158.1 −0.920528
\(704\) 5146.03 0.275495
\(705\) 9361.67 0.500115
\(706\) −33823.4 −1.80306
\(707\) 30225.6 1.60785
\(708\) −21752.3 −1.15466
\(709\) 29588.2 1.56729 0.783644 0.621210i \(-0.213359\pi\)
0.783644 + 0.621210i \(0.213359\pi\)
\(710\) 32172.4 1.70057
\(711\) 3443.72 0.181645
\(712\) 16883.0 0.888648
\(713\) 5609.70 0.294649
\(714\) −47392.0 −2.48404
\(715\) −32118.9 −1.67997
\(716\) 1823.80 0.0951935
\(717\) 8287.57 0.431667
\(718\) −50.9983 −0.00265075
\(719\) −9248.18 −0.479693 −0.239846 0.970811i \(-0.577097\pi\)
−0.239846 + 0.970811i \(0.577097\pi\)
\(720\) −10135.8 −0.524639
\(721\) 15699.0 0.810904
\(722\) 18455.5 0.951308
\(723\) 12523.3 0.644185
\(724\) −5942.84 −0.305061
\(725\) 16916.1 0.866549
\(726\) −34822.1 −1.78012
\(727\) 6815.64 0.347700 0.173850 0.984772i \(-0.444379\pi\)
0.173850 + 0.984772i \(0.444379\pi\)
\(728\) 9172.99 0.466997
\(729\) 9696.81 0.492649
\(730\) −25696.5 −1.30283
\(731\) 50262.2 2.54311
\(732\) 1134.19 0.0572690
\(733\) −4348.84 −0.219138 −0.109569 0.993979i \(-0.534947\pi\)
−0.109569 + 0.993979i \(0.534947\pi\)
\(734\) 25349.5 1.27475
\(735\) 9638.60 0.483708
\(736\) 10493.8 0.525555
\(737\) 54441.4 2.72100
\(738\) 9030.71 0.450440
\(739\) −25559.3 −1.27228 −0.636139 0.771574i \(-0.719470\pi\)
−0.636139 + 0.771574i \(0.719470\pi\)
\(740\) −30222.3 −1.50135
\(741\) 10230.4 0.507185
\(742\) −37813.7 −1.87087
\(743\) −36199.4 −1.78738 −0.893691 0.448682i \(-0.851894\pi\)
−0.893691 + 0.448682i \(0.851894\pi\)
\(744\) 6781.43 0.334166
\(745\) 26474.6 1.30195
\(746\) 12049.7 0.591384
\(747\) −5360.25 −0.262545
\(748\) −28294.7 −1.38309
\(749\) −7665.33 −0.373946
\(750\) 12233.6 0.595613
\(751\) −20181.2 −0.980590 −0.490295 0.871556i \(-0.663111\pi\)
−0.490295 + 0.871556i \(0.663111\pi\)
\(752\) −8483.31 −0.411376
\(753\) 42171.8 2.04094
\(754\) −28967.0 −1.39909
\(755\) −18341.3 −0.884119
\(756\) −11760.7 −0.565783
\(757\) −3516.85 −0.168854 −0.0844269 0.996430i \(-0.526906\pi\)
−0.0844269 + 0.996430i \(0.526906\pi\)
\(758\) −29987.5 −1.43693
\(759\) −16978.2 −0.811948
\(760\) 6430.11 0.306901
\(761\) 9277.47 0.441929 0.220965 0.975282i \(-0.429079\pi\)
0.220965 + 0.975282i \(0.429079\pi\)
\(762\) 44866.3 2.13298
\(763\) −13607.5 −0.645642
\(764\) 7104.58 0.336433
\(765\) 13209.4 0.624296
\(766\) 23950.7 1.12973
\(767\) −29160.7 −1.37279
\(768\) 31868.0 1.49732
\(769\) −20386.4 −0.955986 −0.477993 0.878364i \(-0.658636\pi\)
−0.477993 + 0.878364i \(0.658636\pi\)
\(770\) 60687.9 2.84031
\(771\) 19274.2 0.900316
\(772\) 2582.71 0.120406
\(773\) −30068.2 −1.39907 −0.699533 0.714601i \(-0.746608\pi\)
−0.699533 + 0.714601i \(0.746608\pi\)
\(774\) −15656.5 −0.727081
\(775\) 9236.03 0.428088
\(776\) 3937.63 0.182155
\(777\) −52224.1 −2.41124
\(778\) −45640.5 −2.10320
\(779\) −11824.9 −0.543867
\(780\) 18019.9 0.827200
\(781\) 33191.4 1.52072
\(782\) −19435.0 −0.888740
\(783\) −21347.7 −0.974334
\(784\) −8734.26 −0.397880
\(785\) −18992.7 −0.863541
\(786\) −39928.0 −1.81194
\(787\) −12502.9 −0.566305 −0.283152 0.959075i \(-0.591380\pi\)
−0.283152 + 0.959075i \(0.591380\pi\)
\(788\) −12878.3 −0.582198
\(789\) −15351.4 −0.692679
\(790\) −20450.7 −0.921017
\(791\) −4721.05 −0.212214
\(792\) −5066.21 −0.227298
\(793\) 1520.48 0.0680878
\(794\) −3885.85 −0.173682
\(795\) 42698.8 1.90487
\(796\) 1023.23 0.0455622
\(797\) −9870.48 −0.438683 −0.219342 0.975648i \(-0.570391\pi\)
−0.219342 + 0.975648i \(0.570391\pi\)
\(798\) −19330.2 −0.857494
\(799\) 11055.8 0.489519
\(800\) 17277.5 0.763564
\(801\) 14146.3 0.624015
\(802\) 13493.9 0.594121
\(803\) −26510.3 −1.16504
\(804\) −30543.6 −1.33979
\(805\) 16189.6 0.708832
\(806\) −15815.7 −0.691171
\(807\) 32066.0 1.39873
\(808\) 14984.3 0.652409
\(809\) −24562.1 −1.06744 −0.533720 0.845662i \(-0.679206\pi\)
−0.533720 + 0.845662i \(0.679206\pi\)
\(810\) 46748.6 2.02787
\(811\) 22676.5 0.981849 0.490924 0.871202i \(-0.336659\pi\)
0.490924 + 0.871202i \(0.336659\pi\)
\(812\) 21256.8 0.918680
\(813\) −7810.54 −0.336935
\(814\) −80281.5 −3.45684
\(815\) 15420.7 0.662778
\(816\) −48493.6 −2.08041
\(817\) 20500.8 0.877885
\(818\) −16876.5 −0.721362
\(819\) 7686.09 0.327929
\(820\) −20828.4 −0.887026
\(821\) −9836.99 −0.418165 −0.209082 0.977898i \(-0.567048\pi\)
−0.209082 + 0.977898i \(0.567048\pi\)
\(822\) −21590.9 −0.916145
\(823\) −29849.3 −1.26425 −0.632127 0.774865i \(-0.717818\pi\)
−0.632127 + 0.774865i \(0.717818\pi\)
\(824\) 7782.76 0.329036
\(825\) −27953.5 −1.17966
\(826\) 55098.5 2.32097
\(827\) −32963.1 −1.38602 −0.693011 0.720927i \(-0.743716\pi\)
−0.693011 + 0.720927i \(0.743716\pi\)
\(828\) 2351.22 0.0986840
\(829\) 7716.35 0.323281 0.161641 0.986850i \(-0.448321\pi\)
0.161641 + 0.986850i \(0.448321\pi\)
\(830\) 31832.1 1.33121
\(831\) −30591.1 −1.27701
\(832\) −3870.40 −0.161277
\(833\) 11382.8 0.473459
\(834\) −64103.7 −2.66155
\(835\) 15961.5 0.661522
\(836\) −11540.8 −0.477446
\(837\) −11655.6 −0.481335
\(838\) 29304.0 1.20798
\(839\) −29201.2 −1.20159 −0.600797 0.799402i \(-0.705150\pi\)
−0.600797 + 0.799402i \(0.705150\pi\)
\(840\) 19571.3 0.803897
\(841\) 14195.8 0.582056
\(842\) 15492.4 0.634090
\(843\) −19459.8 −0.795053
\(844\) −27594.2 −1.12539
\(845\) −7765.05 −0.316125
\(846\) −3443.84 −0.139954
\(847\) 34256.5 1.38969
\(848\) −38692.6 −1.56688
\(849\) 52688.5 2.12987
\(850\) −31998.6 −1.29123
\(851\) −21416.6 −0.862693
\(852\) −18621.6 −0.748784
\(853\) −20411.2 −0.819303 −0.409652 0.912242i \(-0.634350\pi\)
−0.409652 + 0.912242i \(0.634350\pi\)
\(854\) −2872.90 −0.115115
\(855\) 5387.81 0.215508
\(856\) −3800.08 −0.151734
\(857\) −15868.0 −0.632484 −0.316242 0.948679i \(-0.602421\pi\)
−0.316242 + 0.948679i \(0.602421\pi\)
\(858\) 47867.4 1.90462
\(859\) 10889.4 0.432530 0.216265 0.976335i \(-0.430613\pi\)
0.216265 + 0.976335i \(0.430613\pi\)
\(860\) 36110.1 1.43180
\(861\) −35991.5 −1.42461
\(862\) −31066.0 −1.22751
\(863\) 25076.0 0.989104 0.494552 0.869148i \(-0.335332\pi\)
0.494552 + 0.869148i \(0.335332\pi\)
\(864\) −21803.7 −0.858539
\(865\) 29329.8 1.15288
\(866\) 29463.0 1.15611
\(867\) 33782.7 1.32332
\(868\) 11606.0 0.453842
\(869\) −21098.4 −0.823608
\(870\) −61803.2 −2.40842
\(871\) −40946.2 −1.59289
\(872\) −6745.90 −0.261978
\(873\) 3299.36 0.127911
\(874\) −7927.11 −0.306795
\(875\) −12034.9 −0.464978
\(876\) 14873.3 0.573654
\(877\) 47178.1 1.81652 0.908262 0.418402i \(-0.137410\pi\)
0.908262 + 0.418402i \(0.137410\pi\)
\(878\) 59236.8 2.27693
\(879\) 18977.4 0.728204
\(880\) 62098.6 2.37880
\(881\) 16533.0 0.632248 0.316124 0.948718i \(-0.397618\pi\)
0.316124 + 0.948718i \(0.397618\pi\)
\(882\) −3545.71 −0.135363
\(883\) 6961.19 0.265303 0.132652 0.991163i \(-0.457651\pi\)
0.132652 + 0.991163i \(0.457651\pi\)
\(884\) 21280.8 0.809673
\(885\) −62216.6 −2.36315
\(886\) 16400.0 0.621862
\(887\) 46916.1 1.77597 0.887987 0.459869i \(-0.152104\pi\)
0.887987 + 0.459869i \(0.152104\pi\)
\(888\) −25890.0 −0.978393
\(889\) −44137.6 −1.66516
\(890\) −84008.8 −3.16402
\(891\) 48229.2 1.81340
\(892\) −21831.3 −0.819467
\(893\) 4509.40 0.168983
\(894\) −39455.5 −1.47605
\(895\) 5216.48 0.194824
\(896\) −26877.6 −1.00214
\(897\) 12769.5 0.475320
\(898\) 64036.2 2.37964
\(899\) 21066.9 0.781559
\(900\) 3871.14 0.143375
\(901\) 50425.7 1.86451
\(902\) −55327.9 −2.04237
\(903\) 62398.2 2.29954
\(904\) −2340.45 −0.0861088
\(905\) −16997.9 −0.624342
\(906\) 27334.4 1.00235
\(907\) −16314.1 −0.597245 −0.298623 0.954371i \(-0.596527\pi\)
−0.298623 + 0.954371i \(0.596527\pi\)
\(908\) −24620.6 −0.899849
\(909\) 12555.4 0.458127
\(910\) −45644.3 −1.66274
\(911\) 29827.8 1.08479 0.542393 0.840125i \(-0.317518\pi\)
0.542393 + 0.840125i \(0.317518\pi\)
\(912\) −19779.5 −0.718162
\(913\) 32840.3 1.19042
\(914\) 26010.4 0.941300
\(915\) 3244.05 0.117208
\(916\) −30887.6 −1.11414
\(917\) 39279.5 1.41453
\(918\) 40381.4 1.45184
\(919\) 17571.6 0.630722 0.315361 0.948972i \(-0.397874\pi\)
0.315361 + 0.948972i \(0.397874\pi\)
\(920\) 8025.99 0.287619
\(921\) 45790.7 1.63828
\(922\) 34391.3 1.22843
\(923\) −24963.7 −0.890239
\(924\) −35126.5 −1.25063
\(925\) −35261.2 −1.25338
\(926\) −7035.59 −0.249680
\(927\) 6521.21 0.231051
\(928\) 39409.1 1.39404
\(929\) −45309.8 −1.60018 −0.800089 0.599881i \(-0.795215\pi\)
−0.800089 + 0.599881i \(0.795215\pi\)
\(930\) −33744.0 −1.18979
\(931\) 4642.80 0.163439
\(932\) −18435.7 −0.647941
\(933\) −50294.1 −1.76480
\(934\) −52916.5 −1.85383
\(935\) −80929.2 −2.83066
\(936\) 3810.37 0.133062
\(937\) 8210.91 0.286274 0.143137 0.989703i \(-0.454281\pi\)
0.143137 + 0.989703i \(0.454281\pi\)
\(938\) 77366.8 2.69309
\(939\) −35746.2 −1.24232
\(940\) 7942.87 0.275604
\(941\) 49966.4 1.73099 0.865493 0.500922i \(-0.167006\pi\)
0.865493 + 0.500922i \(0.167006\pi\)
\(942\) 28305.2 0.979015
\(943\) −14759.8 −0.509697
\(944\) 56379.2 1.94384
\(945\) −33638.3 −1.15794
\(946\) 95921.6 3.29670
\(947\) −42167.2 −1.44694 −0.723468 0.690358i \(-0.757453\pi\)
−0.723468 + 0.690358i \(0.757453\pi\)
\(948\) 11837.0 0.405535
\(949\) 19938.8 0.682024
\(950\) −13051.5 −0.445733
\(951\) 14088.3 0.480382
\(952\) 23112.9 0.786864
\(953\) 8537.38 0.290192 0.145096 0.989418i \(-0.453651\pi\)
0.145096 + 0.989418i \(0.453651\pi\)
\(954\) −15707.4 −0.533068
\(955\) 20320.7 0.688548
\(956\) 7031.55 0.237884
\(957\) −63760.7 −2.15370
\(958\) −9387.34 −0.316588
\(959\) 21240.3 0.715208
\(960\) −8257.80 −0.277624
\(961\) −18288.6 −0.613898
\(962\) 60380.9 2.02366
\(963\) −3184.10 −0.106549
\(964\) 10625.3 0.354998
\(965\) 7387.13 0.246425
\(966\) −24127.7 −0.803619
\(967\) 17713.6 0.589069 0.294534 0.955641i \(-0.404835\pi\)
0.294534 + 0.955641i \(0.404835\pi\)
\(968\) 16982.6 0.563887
\(969\) 25777.3 0.854580
\(970\) −19593.4 −0.648563
\(971\) 30230.2 0.999107 0.499554 0.866283i \(-0.333497\pi\)
0.499554 + 0.866283i \(0.333497\pi\)
\(972\) −12152.1 −0.401008
\(973\) 63062.6 2.07779
\(974\) 68066.6 2.23921
\(975\) 21024.3 0.690580
\(976\) −2939.68 −0.0964106
\(977\) 37908.1 1.24134 0.620668 0.784073i \(-0.286861\pi\)
0.620668 + 0.784073i \(0.286861\pi\)
\(978\) −22981.8 −0.751407
\(979\) −86669.5 −2.82939
\(980\) 8177.82 0.266562
\(981\) −5652.42 −0.183963
\(982\) 36558.8 1.18802
\(983\) −36870.4 −1.19632 −0.598160 0.801377i \(-0.704101\pi\)
−0.598160 + 0.801377i \(0.704101\pi\)
\(984\) −17842.7 −0.578054
\(985\) −36835.0 −1.19153
\(986\) −72987.2 −2.35739
\(987\) 13725.3 0.442634
\(988\) 8679.96 0.279500
\(989\) 25588.9 0.822730
\(990\) 25209.2 0.809292
\(991\) −13385.1 −0.429053 −0.214526 0.976718i \(-0.568821\pi\)
−0.214526 + 0.976718i \(0.568821\pi\)
\(992\) 21517.0 0.688675
\(993\) −50981.5 −1.62925
\(994\) 47168.3 1.50512
\(995\) 2926.68 0.0932483
\(996\) −18424.6 −0.586151
\(997\) −25690.0 −0.816058 −0.408029 0.912969i \(-0.633784\pi\)
−0.408029 + 0.912969i \(0.633784\pi\)
\(998\) 18036.2 0.572071
\(999\) 44498.7 1.40929
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 547.4.a.b.1.14 71
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.4.a.b.1.14 71 1.1 even 1 trivial