Properties

Label 547.4.a.a.1.13
Level $547$
Weight $4$
Character 547.1
Self dual yes
Analytic conductor $32.274$
Analytic rank $1$
Dimension $65$
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] = [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: \(1\)
Dimension: \(65\)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
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)
 
\(f(q)\) \(=\) \(q-3.89720 q^{2} +3.45547 q^{3} +7.18817 q^{4} -9.93922 q^{5} -13.4667 q^{6} +29.7950 q^{7} +3.16387 q^{8} -15.0597 q^{9} +O(q^{10})\) \(q-3.89720 q^{2} +3.45547 q^{3} +7.18817 q^{4} -9.93922 q^{5} -13.4667 q^{6} +29.7950 q^{7} +3.16387 q^{8} -15.0597 q^{9} +38.7351 q^{10} +35.6383 q^{11} +24.8385 q^{12} -67.6663 q^{13} -116.117 q^{14} -34.3447 q^{15} -69.8356 q^{16} -113.010 q^{17} +58.6908 q^{18} +71.6030 q^{19} -71.4448 q^{20} +102.956 q^{21} -138.890 q^{22} +178.047 q^{23} +10.9326 q^{24} -26.2119 q^{25} +263.709 q^{26} -145.336 q^{27} +214.171 q^{28} -193.459 q^{29} +133.848 q^{30} +226.450 q^{31} +246.852 q^{32} +123.147 q^{33} +440.424 q^{34} -296.139 q^{35} -108.252 q^{36} -253.122 q^{37} -279.051 q^{38} -233.819 q^{39} -31.4464 q^{40} +235.725 q^{41} -401.239 q^{42} +269.313 q^{43} +256.174 q^{44} +149.682 q^{45} -693.886 q^{46} -570.540 q^{47} -241.315 q^{48} +544.741 q^{49} +102.153 q^{50} -390.504 q^{51} -486.397 q^{52} +168.825 q^{53} +566.404 q^{54} -354.217 q^{55} +94.2673 q^{56} +247.422 q^{57} +753.950 q^{58} -636.666 q^{59} -246.875 q^{60} +95.0644 q^{61} -882.522 q^{62} -448.704 q^{63} -403.348 q^{64} +672.550 q^{65} -479.930 q^{66} +259.671 q^{67} -812.337 q^{68} +615.238 q^{69} +1154.11 q^{70} -542.632 q^{71} -47.6470 q^{72} +56.5424 q^{73} +986.466 q^{74} -90.5746 q^{75} +514.694 q^{76} +1061.84 q^{77} +911.240 q^{78} +602.510 q^{79} +694.111 q^{80} -95.5922 q^{81} -918.668 q^{82} -1241.39 q^{83} +740.063 q^{84} +1123.23 q^{85} -1049.57 q^{86} -668.493 q^{87} +112.755 q^{88} -404.559 q^{89} -583.340 q^{90} -2016.12 q^{91} +1279.83 q^{92} +782.492 q^{93} +2223.51 q^{94} -711.678 q^{95} +852.991 q^{96} -624.109 q^{97} -2122.96 q^{98} -536.704 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9} - 60 q^{10} - 191 q^{11} - 483 q^{12} - 333 q^{13} - 377 q^{14} - 166 q^{15} + 818 q^{16} - 858 q^{17} - 279 q^{18} - 185 q^{19} - 1188 q^{20} - 406 q^{21} - 356 q^{22} - 836 q^{23} - 505 q^{24} + 1156 q^{25} - 696 q^{26} - 1094 q^{27} - 1096 q^{28} - 1209 q^{29} - 1054 q^{30} - 286 q^{31} - 1484 q^{32} - 1296 q^{33} - 763 q^{34} - 1374 q^{35} + 296 q^{36} - 1705 q^{37} - 2535 q^{38} - 622 q^{39} - 888 q^{40} - 1348 q^{41} - 1716 q^{42} - 973 q^{43} - 2568 q^{44} - 4529 q^{45} - 322 q^{46} - 2498 q^{47} - 5358 q^{48} + 2081 q^{49} - 2002 q^{50} - 1108 q^{51} - 3290 q^{52} - 5947 q^{53} - 2783 q^{54} - 1344 q^{55} - 5111 q^{56} - 3134 q^{57} - 1676 q^{58} - 1625 q^{59} - 2902 q^{60} - 3103 q^{61} - 5242 q^{62} - 3106 q^{63} + 1722 q^{64} - 3160 q^{65} - 3672 q^{66} - 2395 q^{67} - 8447 q^{68} - 4944 q^{69} - 597 q^{70} - 2654 q^{71} - 3929 q^{72} - 2116 q^{73} - 3969 q^{74} - 3759 q^{75} - 1844 q^{76} - 9938 q^{77} - 3935 q^{78} - 1206 q^{79} - 11619 q^{80} + 1889 q^{81} - 7674 q^{82} - 4337 q^{83} - 1873 q^{84} - 2624 q^{85} - 3543 q^{86} - 3066 q^{87} - 3689 q^{88} - 5774 q^{89} - 3149 q^{90} - 3148 q^{91} - 8942 q^{92} - 7118 q^{93} - 5137 q^{94} - 2742 q^{95} - 6558 q^{96} - 6378 q^{97} - 7250 q^{98} - 3941 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.89720 −1.37787 −0.688934 0.724824i \(-0.741921\pi\)
−0.688934 + 0.724824i \(0.741921\pi\)
\(3\) 3.45547 0.665006 0.332503 0.943102i \(-0.392107\pi\)
0.332503 + 0.943102i \(0.392107\pi\)
\(4\) 7.18817 0.898521
\(5\) −9.93922 −0.888991 −0.444495 0.895781i \(-0.646617\pi\)
−0.444495 + 0.895781i \(0.646617\pi\)
\(6\) −13.4667 −0.916290
\(7\) 29.7950 1.60878 0.804389 0.594103i \(-0.202493\pi\)
0.804389 + 0.594103i \(0.202493\pi\)
\(8\) 3.16387 0.139824
\(9\) −15.0597 −0.557768
\(10\) 38.7351 1.22491
\(11\) 35.6383 0.976852 0.488426 0.872605i \(-0.337571\pi\)
0.488426 + 0.872605i \(0.337571\pi\)
\(12\) 24.8385 0.597522
\(13\) −67.6663 −1.44364 −0.721818 0.692083i \(-0.756693\pi\)
−0.721818 + 0.692083i \(0.756693\pi\)
\(14\) −116.117 −2.21668
\(15\) −34.3447 −0.591184
\(16\) −69.8356 −1.09118
\(17\) −113.010 −1.61230 −0.806148 0.591714i \(-0.798452\pi\)
−0.806148 + 0.591714i \(0.798452\pi\)
\(18\) 58.6908 0.768530
\(19\) 71.6030 0.864571 0.432286 0.901737i \(-0.357707\pi\)
0.432286 + 0.901737i \(0.357707\pi\)
\(20\) −71.4448 −0.798777
\(21\) 102.956 1.06985
\(22\) −138.890 −1.34597
\(23\) 178.047 1.61415 0.807075 0.590449i \(-0.201049\pi\)
0.807075 + 0.590449i \(0.201049\pi\)
\(24\) 10.9326 0.0929841
\(25\) −26.2119 −0.209696
\(26\) 263.709 1.98914
\(27\) −145.336 −1.03592
\(28\) 214.171 1.44552
\(29\) −193.459 −1.23878 −0.619388 0.785085i \(-0.712619\pi\)
−0.619388 + 0.785085i \(0.712619\pi\)
\(30\) 133.848 0.814573
\(31\) 226.450 1.31199 0.655995 0.754765i \(-0.272249\pi\)
0.655995 + 0.754765i \(0.272249\pi\)
\(32\) 246.852 1.36368
\(33\) 123.147 0.649612
\(34\) 440.424 2.22153
\(35\) −296.139 −1.43019
\(36\) −108.252 −0.501166
\(37\) −253.122 −1.12467 −0.562337 0.826908i \(-0.690098\pi\)
−0.562337 + 0.826908i \(0.690098\pi\)
\(38\) −279.051 −1.19127
\(39\) −233.819 −0.960026
\(40\) −31.4464 −0.124303
\(41\) 235.725 0.897905 0.448952 0.893556i \(-0.351797\pi\)
0.448952 + 0.893556i \(0.351797\pi\)
\(42\) −401.239 −1.47411
\(43\) 269.313 0.955113 0.477557 0.878601i \(-0.341523\pi\)
0.477557 + 0.878601i \(0.341523\pi\)
\(44\) 256.174 0.877722
\(45\) 149.682 0.495850
\(46\) −693.886 −2.22409
\(47\) −570.540 −1.77068 −0.885339 0.464946i \(-0.846074\pi\)
−0.885339 + 0.464946i \(0.846074\pi\)
\(48\) −241.315 −0.725641
\(49\) 544.741 1.58817
\(50\) 102.153 0.288933
\(51\) −390.504 −1.07219
\(52\) −486.397 −1.29714
\(53\) 168.825 0.437546 0.218773 0.975776i \(-0.429795\pi\)
0.218773 + 0.975776i \(0.429795\pi\)
\(54\) 566.404 1.42737
\(55\) −354.217 −0.868412
\(56\) 94.2673 0.224946
\(57\) 247.422 0.574945
\(58\) 753.950 1.70687
\(59\) −636.666 −1.40486 −0.702431 0.711752i \(-0.747902\pi\)
−0.702431 + 0.711752i \(0.747902\pi\)
\(60\) −246.875 −0.531191
\(61\) 95.0644 0.199537 0.0997685 0.995011i \(-0.468190\pi\)
0.0997685 + 0.995011i \(0.468190\pi\)
\(62\) −882.522 −1.80775
\(63\) −448.704 −0.897324
\(64\) −403.348 −0.787789
\(65\) 672.550 1.28338
\(66\) −479.930 −0.895079
\(67\) 259.671 0.473490 0.236745 0.971572i \(-0.423919\pi\)
0.236745 + 0.971572i \(0.423919\pi\)
\(68\) −812.337 −1.44868
\(69\) 615.238 1.07342
\(70\) 1154.11 1.97061
\(71\) −542.632 −0.907022 −0.453511 0.891251i \(-0.649829\pi\)
−0.453511 + 0.891251i \(0.649829\pi\)
\(72\) −47.6470 −0.0779896
\(73\) 56.5424 0.0906547 0.0453273 0.998972i \(-0.485567\pi\)
0.0453273 + 0.998972i \(0.485567\pi\)
\(74\) 986.466 1.54965
\(75\) −90.5746 −0.139449
\(76\) 514.694 0.776836
\(77\) 1061.84 1.57154
\(78\) 911.240 1.32279
\(79\) 602.510 0.858071 0.429036 0.903288i \(-0.358853\pi\)
0.429036 + 0.903288i \(0.358853\pi\)
\(80\) 694.111 0.970050
\(81\) −95.5922 −0.131128
\(82\) −918.668 −1.23719
\(83\) −1241.39 −1.64169 −0.820846 0.571150i \(-0.806498\pi\)
−0.820846 + 0.571150i \(0.806498\pi\)
\(84\) 740.063 0.961279
\(85\) 1123.23 1.43332
\(86\) −1049.57 −1.31602
\(87\) −668.493 −0.823793
\(88\) 112.755 0.136588
\(89\) −404.559 −0.481834 −0.240917 0.970546i \(-0.577448\pi\)
−0.240917 + 0.970546i \(0.577448\pi\)
\(90\) −583.340 −0.683216
\(91\) −2016.12 −2.32249
\(92\) 1279.83 1.45035
\(93\) 782.492 0.872480
\(94\) 2223.51 2.43976
\(95\) −711.678 −0.768596
\(96\) 852.991 0.906854
\(97\) −624.109 −0.653285 −0.326643 0.945148i \(-0.605917\pi\)
−0.326643 + 0.945148i \(0.605917\pi\)
\(98\) −2122.96 −2.18828
\(99\) −536.704 −0.544856
\(100\) −188.416 −0.188416
\(101\) −1966.30 −1.93717 −0.968585 0.248682i \(-0.920002\pi\)
−0.968585 + 0.248682i \(0.920002\pi\)
\(102\) 1521.87 1.47733
\(103\) 934.025 0.893517 0.446759 0.894655i \(-0.352578\pi\)
0.446759 + 0.894655i \(0.352578\pi\)
\(104\) −214.087 −0.201856
\(105\) −1023.30 −0.951083
\(106\) −657.946 −0.602881
\(107\) −151.988 −0.137320 −0.0686601 0.997640i \(-0.521872\pi\)
−0.0686601 + 0.997640i \(0.521872\pi\)
\(108\) −1044.70 −0.930800
\(109\) −2196.56 −1.93021 −0.965104 0.261867i \(-0.915662\pi\)
−0.965104 + 0.261867i \(0.915662\pi\)
\(110\) 1380.46 1.19656
\(111\) −874.655 −0.747915
\(112\) −2080.75 −1.75547
\(113\) −1606.36 −1.33729 −0.668643 0.743583i \(-0.733125\pi\)
−0.668643 + 0.743583i \(0.733125\pi\)
\(114\) −964.253 −0.792198
\(115\) −1769.65 −1.43496
\(116\) −1390.62 −1.11307
\(117\) 1019.04 0.805213
\(118\) 2481.21 1.93571
\(119\) −3367.14 −2.59383
\(120\) −108.662 −0.0826620
\(121\) −60.9081 −0.0457611
\(122\) −370.485 −0.274936
\(123\) 814.541 0.597112
\(124\) 1627.76 1.17885
\(125\) 1502.93 1.07541
\(126\) 1748.69 1.23639
\(127\) 130.605 0.0912546 0.0456273 0.998959i \(-0.485471\pi\)
0.0456273 + 0.998959i \(0.485471\pi\)
\(128\) −402.890 −0.278209
\(129\) 930.604 0.635156
\(130\) −2621.06 −1.76833
\(131\) −1228.07 −0.819059 −0.409529 0.912297i \(-0.634307\pi\)
−0.409529 + 0.912297i \(0.634307\pi\)
\(132\) 885.203 0.583690
\(133\) 2133.41 1.39090
\(134\) −1011.99 −0.652407
\(135\) 1444.53 0.920927
\(136\) −357.550 −0.225438
\(137\) −201.322 −0.125548 −0.0627739 0.998028i \(-0.519995\pi\)
−0.0627739 + 0.998028i \(0.519995\pi\)
\(138\) −2397.70 −1.47903
\(139\) 2040.03 1.24484 0.622422 0.782682i \(-0.286149\pi\)
0.622422 + 0.782682i \(0.286149\pi\)
\(140\) −2128.70 −1.28505
\(141\) −1971.49 −1.17751
\(142\) 2114.74 1.24976
\(143\) −2411.52 −1.41022
\(144\) 1051.70 0.608625
\(145\) 1922.83 1.10126
\(146\) −220.357 −0.124910
\(147\) 1882.34 1.05614
\(148\) −1819.48 −1.01054
\(149\) −3280.48 −1.80368 −0.901838 0.432074i \(-0.857782\pi\)
−0.901838 + 0.432074i \(0.857782\pi\)
\(150\) 352.987 0.192142
\(151\) 1152.01 0.620858 0.310429 0.950597i \(-0.399527\pi\)
0.310429 + 0.950597i \(0.399527\pi\)
\(152\) 226.542 0.120888
\(153\) 1701.90 0.899286
\(154\) −4138.22 −2.16537
\(155\) −2250.74 −1.16635
\(156\) −1680.73 −0.862604
\(157\) −3328.26 −1.69187 −0.845936 0.533284i \(-0.820958\pi\)
−0.845936 + 0.533284i \(0.820958\pi\)
\(158\) −2348.10 −1.18231
\(159\) 583.371 0.290970
\(160\) −2453.52 −1.21230
\(161\) 5304.92 2.59681
\(162\) 372.542 0.180677
\(163\) 280.168 0.134628 0.0673142 0.997732i \(-0.478557\pi\)
0.0673142 + 0.997732i \(0.478557\pi\)
\(164\) 1694.43 0.806786
\(165\) −1223.99 −0.577499
\(166\) 4837.95 2.26204
\(167\) 665.104 0.308188 0.154094 0.988056i \(-0.450754\pi\)
0.154094 + 0.988056i \(0.450754\pi\)
\(168\) 325.738 0.149591
\(169\) 2381.73 1.08408
\(170\) −4377.47 −1.97492
\(171\) −1078.32 −0.482230
\(172\) 1935.87 0.858189
\(173\) 1250.56 0.549587 0.274794 0.961503i \(-0.411390\pi\)
0.274794 + 0.961503i \(0.411390\pi\)
\(174\) 2605.25 1.13508
\(175\) −780.984 −0.337353
\(176\) −2488.82 −1.06592
\(177\) −2199.98 −0.934241
\(178\) 1576.65 0.663903
\(179\) −2223.89 −0.928609 −0.464305 0.885676i \(-0.653696\pi\)
−0.464305 + 0.885676i \(0.653696\pi\)
\(180\) 1075.94 0.445532
\(181\) −1493.99 −0.613520 −0.306760 0.951787i \(-0.599245\pi\)
−0.306760 + 0.951787i \(0.599245\pi\)
\(182\) 7857.21 3.20008
\(183\) 328.492 0.132693
\(184\) 563.318 0.225698
\(185\) 2515.83 0.999826
\(186\) −3049.53 −1.20216
\(187\) −4027.50 −1.57497
\(188\) −4101.14 −1.59099
\(189\) −4330.29 −1.66657
\(190\) 2773.55 1.05902
\(191\) 2211.47 0.837780 0.418890 0.908037i \(-0.362419\pi\)
0.418890 + 0.908037i \(0.362419\pi\)
\(192\) −1393.76 −0.523884
\(193\) −3108.68 −1.15942 −0.579710 0.814823i \(-0.696834\pi\)
−0.579710 + 0.814823i \(0.696834\pi\)
\(194\) 2432.28 0.900141
\(195\) 2323.98 0.853454
\(196\) 3915.69 1.42700
\(197\) 588.092 0.212689 0.106345 0.994329i \(-0.466085\pi\)
0.106345 + 0.994329i \(0.466085\pi\)
\(198\) 2091.64 0.750740
\(199\) −2863.82 −1.02015 −0.510077 0.860129i \(-0.670383\pi\)
−0.510077 + 0.860129i \(0.670383\pi\)
\(200\) −82.9311 −0.0293206
\(201\) 897.285 0.314874
\(202\) 7663.07 2.66917
\(203\) −5764.12 −1.99292
\(204\) −2807.01 −0.963382
\(205\) −2342.92 −0.798229
\(206\) −3640.08 −1.23115
\(207\) −2681.34 −0.900321
\(208\) 4725.52 1.57527
\(209\) 2551.81 0.844558
\(210\) 3988.00 1.31047
\(211\) −579.519 −0.189079 −0.0945396 0.995521i \(-0.530138\pi\)
−0.0945396 + 0.995521i \(0.530138\pi\)
\(212\) 1213.54 0.393144
\(213\) −1875.05 −0.603174
\(214\) 592.329 0.189209
\(215\) −2676.76 −0.849087
\(216\) −459.824 −0.144848
\(217\) 6747.08 2.11070
\(218\) 8560.45 2.65957
\(219\) 195.381 0.0602859
\(220\) −2546.17 −0.780286
\(221\) 7647.00 2.32757
\(222\) 3408.71 1.03053
\(223\) 1754.27 0.526793 0.263396 0.964688i \(-0.415157\pi\)
0.263396 + 0.964688i \(0.415157\pi\)
\(224\) 7354.96 2.19386
\(225\) 394.745 0.116961
\(226\) 6260.30 1.84261
\(227\) 906.638 0.265091 0.132546 0.991177i \(-0.457685\pi\)
0.132546 + 0.991177i \(0.457685\pi\)
\(228\) 1778.51 0.516600
\(229\) 3291.34 0.949773 0.474886 0.880047i \(-0.342489\pi\)
0.474886 + 0.880047i \(0.342489\pi\)
\(230\) 6896.69 1.97719
\(231\) 3669.17 1.04508
\(232\) −612.080 −0.173211
\(233\) 710.066 0.199648 0.0998240 0.995005i \(-0.468172\pi\)
0.0998240 + 0.995005i \(0.468172\pi\)
\(234\) −3971.39 −1.10948
\(235\) 5670.72 1.57412
\(236\) −4576.46 −1.26230
\(237\) 2081.95 0.570622
\(238\) 13122.4 3.57395
\(239\) 1172.59 0.317359 0.158679 0.987330i \(-0.449276\pi\)
0.158679 + 0.987330i \(0.449276\pi\)
\(240\) 2398.48 0.645088
\(241\) −4164.61 −1.11314 −0.556568 0.830802i \(-0.687882\pi\)
−0.556568 + 0.830802i \(0.687882\pi\)
\(242\) 237.371 0.0630528
\(243\) 3593.76 0.948723
\(244\) 683.339 0.179288
\(245\) −5414.30 −1.41186
\(246\) −3174.43 −0.822741
\(247\) −4845.11 −1.24813
\(248\) 716.459 0.183448
\(249\) −4289.59 −1.09173
\(250\) −5857.21 −1.48177
\(251\) 5355.66 1.34680 0.673399 0.739279i \(-0.264834\pi\)
0.673399 + 0.739279i \(0.264834\pi\)
\(252\) −3225.36 −0.806265
\(253\) 6345.32 1.57678
\(254\) −508.994 −0.125737
\(255\) 3881.30 0.953163
\(256\) 4796.93 1.17112
\(257\) −899.111 −0.218230 −0.109115 0.994029i \(-0.534802\pi\)
−0.109115 + 0.994029i \(0.534802\pi\)
\(258\) −3626.75 −0.875161
\(259\) −7541.76 −1.80935
\(260\) 4834.41 1.15314
\(261\) 2913.44 0.690949
\(262\) 4786.02 1.12855
\(263\) −1950.08 −0.457212 −0.228606 0.973519i \(-0.573417\pi\)
−0.228606 + 0.973519i \(0.573417\pi\)
\(264\) 389.622 0.0908316
\(265\) −1677.99 −0.388974
\(266\) −8314.32 −1.91648
\(267\) −1397.94 −0.320422
\(268\) 1866.56 0.425441
\(269\) 2126.86 0.482071 0.241035 0.970516i \(-0.422513\pi\)
0.241035 + 0.970516i \(0.422513\pi\)
\(270\) −5629.61 −1.26892
\(271\) 1834.40 0.411188 0.205594 0.978637i \(-0.434087\pi\)
0.205594 + 0.978637i \(0.434087\pi\)
\(272\) 7892.14 1.75931
\(273\) −6966.63 −1.54447
\(274\) 784.590 0.172988
\(275\) −934.150 −0.204841
\(276\) 4422.43 0.964490
\(277\) 1157.49 0.251073 0.125536 0.992089i \(-0.459935\pi\)
0.125536 + 0.992089i \(0.459935\pi\)
\(278\) −7950.42 −1.71523
\(279\) −3410.28 −0.731785
\(280\) −936.944 −0.199975
\(281\) −1540.07 −0.326949 −0.163475 0.986548i \(-0.552270\pi\)
−0.163475 + 0.986548i \(0.552270\pi\)
\(282\) 7683.27 1.62245
\(283\) −7277.32 −1.52859 −0.764296 0.644865i \(-0.776914\pi\)
−0.764296 + 0.644865i \(0.776914\pi\)
\(284\) −3900.53 −0.814978
\(285\) −2459.18 −0.511120
\(286\) 9398.16 1.94309
\(287\) 7023.43 1.44453
\(288\) −3717.53 −0.760616
\(289\) 7858.34 1.59950
\(290\) −7493.67 −1.51739
\(291\) −2156.59 −0.434438
\(292\) 406.437 0.0814551
\(293\) −3281.32 −0.654256 −0.327128 0.944980i \(-0.606081\pi\)
−0.327128 + 0.944980i \(0.606081\pi\)
\(294\) −7335.84 −1.45522
\(295\) 6327.96 1.24891
\(296\) −800.844 −0.157257
\(297\) −5179.54 −1.01194
\(298\) 12784.7 2.48523
\(299\) −12047.8 −2.33024
\(300\) −651.065 −0.125298
\(301\) 8024.18 1.53656
\(302\) −4489.63 −0.855461
\(303\) −6794.49 −1.28823
\(304\) −5000.44 −0.943404
\(305\) −944.866 −0.177386
\(306\) −6632.66 −1.23910
\(307\) 4409.16 0.819688 0.409844 0.912156i \(-0.365583\pi\)
0.409844 + 0.912156i \(0.365583\pi\)
\(308\) 7632.71 1.41206
\(309\) 3227.50 0.594194
\(310\) 8771.58 1.60707
\(311\) −3722.70 −0.678762 −0.339381 0.940649i \(-0.610218\pi\)
−0.339381 + 0.940649i \(0.610218\pi\)
\(312\) −739.772 −0.134235
\(313\) −6210.79 −1.12158 −0.560790 0.827958i \(-0.689502\pi\)
−0.560790 + 0.827958i \(0.689502\pi\)
\(314\) 12970.9 2.33118
\(315\) 4459.77 0.797713
\(316\) 4330.94 0.770995
\(317\) 2533.52 0.448885 0.224442 0.974487i \(-0.427944\pi\)
0.224442 + 0.974487i \(0.427944\pi\)
\(318\) −2273.51 −0.400919
\(319\) −6894.57 −1.21010
\(320\) 4008.97 0.700337
\(321\) −525.191 −0.0913188
\(322\) −20674.3 −3.57806
\(323\) −8091.88 −1.39394
\(324\) −687.133 −0.117821
\(325\) 1773.67 0.302724
\(326\) −1091.87 −0.185500
\(327\) −7590.16 −1.28360
\(328\) 745.803 0.125549
\(329\) −16999.2 −2.84863
\(330\) 4770.12 0.795717
\(331\) 5686.83 0.944339 0.472170 0.881508i \(-0.343471\pi\)
0.472170 + 0.881508i \(0.343471\pi\)
\(332\) −8923.33 −1.47509
\(333\) 3811.94 0.627307
\(334\) −2592.04 −0.424642
\(335\) −2580.93 −0.420928
\(336\) −7189.97 −1.16740
\(337\) 1659.25 0.268205 0.134103 0.990967i \(-0.457185\pi\)
0.134103 + 0.990967i \(0.457185\pi\)
\(338\) −9282.09 −1.49373
\(339\) −5550.72 −0.889303
\(340\) 8074.00 1.28786
\(341\) 8070.32 1.28162
\(342\) 4202.43 0.664449
\(343\) 6010.86 0.946227
\(344\) 852.071 0.133548
\(345\) −6114.98 −0.954259
\(346\) −4873.70 −0.757259
\(347\) 107.939 0.0166988 0.00834939 0.999965i \(-0.497342\pi\)
0.00834939 + 0.999965i \(0.497342\pi\)
\(348\) −4805.24 −0.740195
\(349\) 892.258 0.136852 0.0684262 0.997656i \(-0.478202\pi\)
0.0684262 + 0.997656i \(0.478202\pi\)
\(350\) 3043.65 0.464829
\(351\) 9834.36 1.49550
\(352\) 8797.41 1.33211
\(353\) 8396.01 1.26593 0.632966 0.774179i \(-0.281837\pi\)
0.632966 + 0.774179i \(0.281837\pi\)
\(354\) 8573.76 1.28726
\(355\) 5393.33 0.806334
\(356\) −2908.04 −0.432938
\(357\) −11635.1 −1.72491
\(358\) 8666.93 1.27950
\(359\) 5054.88 0.743138 0.371569 0.928405i \(-0.378820\pi\)
0.371569 + 0.928405i \(0.378820\pi\)
\(360\) 473.574 0.0693320
\(361\) −1732.01 −0.252517
\(362\) 5822.36 0.845349
\(363\) −210.466 −0.0304314
\(364\) −14492.2 −2.08681
\(365\) −561.988 −0.0805912
\(366\) −1280.20 −0.182834
\(367\) 6389.49 0.908798 0.454399 0.890798i \(-0.349854\pi\)
0.454399 + 0.890798i \(0.349854\pi\)
\(368\) −12434.0 −1.76133
\(369\) −3549.96 −0.500822
\(370\) −9804.70 −1.37763
\(371\) 5030.14 0.703914
\(372\) 5624.69 0.783942
\(373\) −4305.83 −0.597714 −0.298857 0.954298i \(-0.596605\pi\)
−0.298857 + 0.954298i \(0.596605\pi\)
\(374\) 15696.0 2.17011
\(375\) 5193.32 0.715152
\(376\) −1805.11 −0.247584
\(377\) 13090.7 1.78834
\(378\) 16876.0 2.29632
\(379\) 10177.6 1.37938 0.689692 0.724103i \(-0.257746\pi\)
0.689692 + 0.724103i \(0.257746\pi\)
\(380\) −5115.66 −0.690600
\(381\) 451.302 0.0606848
\(382\) −8618.52 −1.15435
\(383\) 4254.81 0.567652 0.283826 0.958876i \(-0.408396\pi\)
0.283826 + 0.958876i \(0.408396\pi\)
\(384\) −1392.17 −0.185011
\(385\) −10553.9 −1.39708
\(386\) 12115.2 1.59753
\(387\) −4055.78 −0.532731
\(388\) −4486.20 −0.586990
\(389\) 13055.6 1.70166 0.850832 0.525437i \(-0.176098\pi\)
0.850832 + 0.525437i \(0.176098\pi\)
\(390\) −9057.01 −1.17595
\(391\) −20121.2 −2.60249
\(392\) 1723.49 0.222064
\(393\) −4243.55 −0.544679
\(394\) −2291.91 −0.293058
\(395\) −5988.47 −0.762817
\(396\) −3857.92 −0.489565
\(397\) −5512.97 −0.696947 −0.348473 0.937319i \(-0.613300\pi\)
−0.348473 + 0.937319i \(0.613300\pi\)
\(398\) 11160.9 1.40564
\(399\) 7371.93 0.924958
\(400\) 1830.53 0.228816
\(401\) −2561.08 −0.318938 −0.159469 0.987203i \(-0.550978\pi\)
−0.159469 + 0.987203i \(0.550978\pi\)
\(402\) −3496.90 −0.433854
\(403\) −15323.1 −1.89404
\(404\) −14134.1 −1.74059
\(405\) 950.111 0.116571
\(406\) 22463.9 2.74597
\(407\) −9020.84 −1.09864
\(408\) −1235.50 −0.149918
\(409\) −8140.79 −0.984196 −0.492098 0.870540i \(-0.663770\pi\)
−0.492098 + 0.870540i \(0.663770\pi\)
\(410\) 9130.84 1.09985
\(411\) −695.661 −0.0834900
\(412\) 6713.93 0.802844
\(413\) −18969.4 −2.26011
\(414\) 10449.7 1.24052
\(415\) 12338.5 1.45945
\(416\) −16703.6 −1.96866
\(417\) 7049.28 0.827829
\(418\) −9944.92 −1.16369
\(419\) −6967.71 −0.812398 −0.406199 0.913785i \(-0.633146\pi\)
−0.406199 + 0.913785i \(0.633146\pi\)
\(420\) −7355.65 −0.854568
\(421\) −11309.5 −1.30924 −0.654622 0.755956i \(-0.727172\pi\)
−0.654622 + 0.755956i \(0.727172\pi\)
\(422\) 2258.50 0.260526
\(423\) 8592.18 0.987627
\(424\) 534.141 0.0611796
\(425\) 2962.22 0.338091
\(426\) 7307.44 0.831095
\(427\) 2832.44 0.321011
\(428\) −1092.52 −0.123385
\(429\) −8332.92 −0.937803
\(430\) 10431.9 1.16993
\(431\) −405.096 −0.0452733 −0.0226367 0.999744i \(-0.507206\pi\)
−0.0226367 + 0.999744i \(0.507206\pi\)
\(432\) 10149.6 1.13038
\(433\) −820.746 −0.0910913 −0.0455457 0.998962i \(-0.514503\pi\)
−0.0455457 + 0.998962i \(0.514503\pi\)
\(434\) −26294.7 −2.90827
\(435\) 6644.30 0.732344
\(436\) −15789.3 −1.73433
\(437\) 12748.7 1.39555
\(438\) −761.438 −0.0830660
\(439\) −1206.67 −0.131188 −0.0655938 0.997846i \(-0.520894\pi\)
−0.0655938 + 0.997846i \(0.520894\pi\)
\(440\) −1120.70 −0.121425
\(441\) −8203.65 −0.885827
\(442\) −29801.9 −3.20708
\(443\) 14106.9 1.51295 0.756476 0.654021i \(-0.226919\pi\)
0.756476 + 0.654021i \(0.226919\pi\)
\(444\) −6287.17 −0.672018
\(445\) 4021.00 0.428346
\(446\) −6836.75 −0.725851
\(447\) −11335.6 −1.19945
\(448\) −12017.8 −1.26738
\(449\) 3882.59 0.408086 0.204043 0.978962i \(-0.434592\pi\)
0.204043 + 0.978962i \(0.434592\pi\)
\(450\) −1538.40 −0.161157
\(451\) 8400.86 0.877119
\(452\) −11546.8 −1.20158
\(453\) 3980.75 0.412874
\(454\) −3533.35 −0.365261
\(455\) 20038.6 2.06467
\(456\) 782.810 0.0803913
\(457\) −2328.16 −0.238308 −0.119154 0.992876i \(-0.538018\pi\)
−0.119154 + 0.992876i \(0.538018\pi\)
\(458\) −12827.0 −1.30866
\(459\) 16424.5 1.67022
\(460\) −12720.6 −1.28935
\(461\) −1481.31 −0.149656 −0.0748281 0.997196i \(-0.523841\pi\)
−0.0748281 + 0.997196i \(0.523841\pi\)
\(462\) −14299.5 −1.43998
\(463\) −6262.08 −0.628561 −0.314280 0.949330i \(-0.601763\pi\)
−0.314280 + 0.949330i \(0.601763\pi\)
\(464\) 13510.3 1.35173
\(465\) −7777.36 −0.775627
\(466\) −2767.27 −0.275089
\(467\) −11953.6 −1.18447 −0.592234 0.805766i \(-0.701754\pi\)
−0.592234 + 0.805766i \(0.701754\pi\)
\(468\) 7325.01 0.723501
\(469\) 7736.89 0.761741
\(470\) −22099.9 −2.16892
\(471\) −11500.7 −1.12510
\(472\) −2014.33 −0.196434
\(473\) 9597.88 0.933004
\(474\) −8113.79 −0.786242
\(475\) −1876.85 −0.181297
\(476\) −24203.6 −2.33061
\(477\) −2542.46 −0.244049
\(478\) −4569.83 −0.437278
\(479\) −7020.73 −0.669698 −0.334849 0.942272i \(-0.608685\pi\)
−0.334849 + 0.942272i \(0.608685\pi\)
\(480\) −8478.06 −0.806185
\(481\) 17127.8 1.62362
\(482\) 16230.3 1.53376
\(483\) 18331.0 1.72689
\(484\) −437.817 −0.0411173
\(485\) 6203.15 0.580764
\(486\) −14005.6 −1.30722
\(487\) 2152.74 0.200308 0.100154 0.994972i \(-0.468066\pi\)
0.100154 + 0.994972i \(0.468066\pi\)
\(488\) 300.771 0.0279001
\(489\) 968.112 0.0895287
\(490\) 21100.6 1.94536
\(491\) −15458.2 −1.42082 −0.710408 0.703790i \(-0.751490\pi\)
−0.710408 + 0.703790i \(0.751490\pi\)
\(492\) 5855.06 0.536517
\(493\) 21862.9 1.99727
\(494\) 18882.4 1.71975
\(495\) 5334.42 0.484372
\(496\) −15814.3 −1.43162
\(497\) −16167.7 −1.45920
\(498\) 16717.4 1.50427
\(499\) 8252.41 0.740338 0.370169 0.928964i \(-0.379300\pi\)
0.370169 + 0.928964i \(0.379300\pi\)
\(500\) 10803.3 0.966277
\(501\) 2298.25 0.204946
\(502\) −20872.1 −1.85571
\(503\) 5936.35 0.526220 0.263110 0.964766i \(-0.415252\pi\)
0.263110 + 0.964766i \(0.415252\pi\)
\(504\) −1419.64 −0.125468
\(505\) 19543.5 1.72213
\(506\) −24729.0 −2.17260
\(507\) 8230.01 0.720922
\(508\) 938.812 0.0819942
\(509\) 6924.41 0.602985 0.301492 0.953469i \(-0.402515\pi\)
0.301492 + 0.953469i \(0.402515\pi\)
\(510\) −15126.2 −1.31333
\(511\) 1684.68 0.145843
\(512\) −15471.5 −1.33545
\(513\) −10406.5 −0.895630
\(514\) 3504.01 0.300692
\(515\) −9283.48 −0.794328
\(516\) 6689.34 0.570701
\(517\) −20333.1 −1.72969
\(518\) 29391.7 2.49305
\(519\) 4321.28 0.365478
\(520\) 2127.86 0.179448
\(521\) 14323.1 1.20443 0.602215 0.798334i \(-0.294285\pi\)
0.602215 + 0.798334i \(0.294285\pi\)
\(522\) −11354.3 −0.952037
\(523\) −3168.12 −0.264880 −0.132440 0.991191i \(-0.542281\pi\)
−0.132440 + 0.991191i \(0.542281\pi\)
\(524\) −8827.55 −0.735941
\(525\) −2698.67 −0.224342
\(526\) 7599.84 0.629979
\(527\) −25591.2 −2.11532
\(528\) −8600.06 −0.708844
\(529\) 19533.9 1.60548
\(530\) 6539.47 0.535955
\(531\) 9588.01 0.783586
\(532\) 15335.3 1.24976
\(533\) −15950.7 −1.29625
\(534\) 5448.06 0.441499
\(535\) 1510.65 0.122076
\(536\) 821.564 0.0662055
\(537\) −7684.57 −0.617530
\(538\) −8288.81 −0.664230
\(539\) 19413.7 1.55140
\(540\) 10383.5 0.827472
\(541\) 8148.79 0.647585 0.323793 0.946128i \(-0.395042\pi\)
0.323793 + 0.946128i \(0.395042\pi\)
\(542\) −7149.03 −0.566563
\(543\) −5162.42 −0.407994
\(544\) −27896.9 −2.19865
\(545\) 21832.1 1.71594
\(546\) 27150.4 2.12807
\(547\) 547.000 0.0427569
\(548\) −1447.13 −0.112807
\(549\) −1431.64 −0.111295
\(550\) 3640.57 0.282244
\(551\) −13852.3 −1.07101
\(552\) 1946.53 0.150090
\(553\) 17951.8 1.38045
\(554\) −4510.99 −0.345945
\(555\) 8693.39 0.664890
\(556\) 14664.1 1.11852
\(557\) −18207.3 −1.38504 −0.692520 0.721399i \(-0.743500\pi\)
−0.692520 + 0.721399i \(0.743500\pi\)
\(558\) 13290.5 1.00830
\(559\) −18223.4 −1.37884
\(560\) 20681.0 1.56059
\(561\) −13916.9 −1.04737
\(562\) 6001.95 0.450493
\(563\) 25323.1 1.89563 0.947816 0.318818i \(-0.103286\pi\)
0.947816 + 0.318818i \(0.103286\pi\)
\(564\) −14171.4 −1.05802
\(565\) 15965.9 1.18884
\(566\) 28361.2 2.10620
\(567\) −2848.17 −0.210955
\(568\) −1716.81 −0.126824
\(569\) 5359.03 0.394837 0.197419 0.980319i \(-0.436744\pi\)
0.197419 + 0.980319i \(0.436744\pi\)
\(570\) 9583.92 0.704257
\(571\) 6668.17 0.488712 0.244356 0.969686i \(-0.421424\pi\)
0.244356 + 0.969686i \(0.421424\pi\)
\(572\) −17334.4 −1.26711
\(573\) 7641.65 0.557129
\(574\) −27371.7 −1.99037
\(575\) −4666.97 −0.338480
\(576\) 6074.31 0.439403
\(577\) −7081.74 −0.510948 −0.255474 0.966816i \(-0.582231\pi\)
−0.255474 + 0.966816i \(0.582231\pi\)
\(578\) −30625.5 −2.20390
\(579\) −10742.0 −0.771020
\(580\) 13821.7 0.989506
\(581\) −36987.2 −2.64112
\(582\) 8404.66 0.598599
\(583\) 6016.65 0.427417
\(584\) 178.893 0.0126757
\(585\) −10128.4 −0.715827
\(586\) 12788.0 0.901478
\(587\) −21128.1 −1.48561 −0.742803 0.669510i \(-0.766504\pi\)
−0.742803 + 0.669510i \(0.766504\pi\)
\(588\) 13530.5 0.948963
\(589\) 16214.5 1.13431
\(590\) −24661.3 −1.72083
\(591\) 2032.13 0.141440
\(592\) 17676.9 1.22722
\(593\) −27207.3 −1.88410 −0.942050 0.335474i \(-0.891104\pi\)
−0.942050 + 0.335474i \(0.891104\pi\)
\(594\) 20185.7 1.39433
\(595\) 33466.7 2.30589
\(596\) −23580.7 −1.62064
\(597\) −9895.84 −0.678408
\(598\) 46952.8 3.21077
\(599\) 17939.7 1.22370 0.611850 0.790974i \(-0.290426\pi\)
0.611850 + 0.790974i \(0.290426\pi\)
\(600\) −286.566 −0.0194983
\(601\) 25217.0 1.71152 0.855758 0.517375i \(-0.173091\pi\)
0.855758 + 0.517375i \(0.173091\pi\)
\(602\) −31271.8 −2.11718
\(603\) −3910.57 −0.264098
\(604\) 8280.87 0.557854
\(605\) 605.378 0.0406812
\(606\) 26479.5 1.77501
\(607\) −21271.4 −1.42237 −0.711185 0.703004i \(-0.751841\pi\)
−0.711185 + 0.703004i \(0.751841\pi\)
\(608\) 17675.4 1.17900
\(609\) −19917.7 −1.32530
\(610\) 3682.33 0.244415
\(611\) 38606.4 2.55621
\(612\) 12233.6 0.808028
\(613\) −2331.98 −0.153651 −0.0768253 0.997045i \(-0.524478\pi\)
−0.0768253 + 0.997045i \(0.524478\pi\)
\(614\) −17183.4 −1.12942
\(615\) −8095.90 −0.530827
\(616\) 3359.53 0.219739
\(617\) −4293.64 −0.280155 −0.140077 0.990141i \(-0.544735\pi\)
−0.140077 + 0.990141i \(0.544735\pi\)
\(618\) −12578.2 −0.818721
\(619\) −19118.3 −1.24141 −0.620704 0.784045i \(-0.713153\pi\)
−0.620704 + 0.784045i \(0.713153\pi\)
\(620\) −16178.7 −1.04799
\(621\) −25876.7 −1.67214
\(622\) 14508.1 0.935245
\(623\) −12053.8 −0.775163
\(624\) 16328.9 1.04756
\(625\) −11661.4 −0.746332
\(626\) 24204.7 1.54539
\(627\) 8817.71 0.561636
\(628\) −23924.1 −1.52018
\(629\) 28605.4 1.81331
\(630\) −17380.6 −1.09914
\(631\) −5338.95 −0.336831 −0.168415 0.985716i \(-0.553865\pi\)
−0.168415 + 0.985716i \(0.553865\pi\)
\(632\) 1906.26 0.119979
\(633\) −2002.51 −0.125739
\(634\) −9873.62 −0.618504
\(635\) −1298.11 −0.0811245
\(636\) 4193.37 0.261443
\(637\) −36860.6 −2.29273
\(638\) 26869.5 1.66736
\(639\) 8171.88 0.505907
\(640\) 4004.41 0.247325
\(641\) −6625.69 −0.408267 −0.204134 0.978943i \(-0.565438\pi\)
−0.204134 + 0.978943i \(0.565438\pi\)
\(642\) 2046.78 0.125825
\(643\) 24100.7 1.47813 0.739067 0.673632i \(-0.235267\pi\)
0.739067 + 0.673632i \(0.235267\pi\)
\(644\) 38132.7 2.33329
\(645\) −9249.47 −0.564647
\(646\) 31535.7 1.92067
\(647\) −2466.44 −0.149870 −0.0749349 0.997188i \(-0.523875\pi\)
−0.0749349 + 0.997188i \(0.523875\pi\)
\(648\) −302.441 −0.0183349
\(649\) −22689.7 −1.37234
\(650\) −6912.33 −0.417114
\(651\) 23314.3 1.40363
\(652\) 2013.89 0.120967
\(653\) −31485.7 −1.88688 −0.943440 0.331544i \(-0.892431\pi\)
−0.943440 + 0.331544i \(0.892431\pi\)
\(654\) 29580.4 1.76863
\(655\) 12206.0 0.728135
\(656\) −16462.0 −0.979776
\(657\) −851.513 −0.0505642
\(658\) 66249.4 3.92503
\(659\) 14179.6 0.838175 0.419088 0.907946i \(-0.362350\pi\)
0.419088 + 0.907946i \(0.362350\pi\)
\(660\) −8798.23 −0.518895
\(661\) 22865.9 1.34551 0.672754 0.739866i \(-0.265111\pi\)
0.672754 + 0.739866i \(0.265111\pi\)
\(662\) −22162.7 −1.30118
\(663\) 26424.0 1.54785
\(664\) −3927.60 −0.229549
\(665\) −21204.4 −1.23650
\(666\) −14855.9 −0.864347
\(667\) −34444.9 −1.99957
\(668\) 4780.88 0.276913
\(669\) 6061.84 0.350320
\(670\) 10058.4 0.579984
\(671\) 3387.94 0.194918
\(672\) 25414.8 1.45893
\(673\) 31403.4 1.79868 0.899341 0.437248i \(-0.144047\pi\)
0.899341 + 0.437248i \(0.144047\pi\)
\(674\) −6466.44 −0.369552
\(675\) 3809.54 0.217229
\(676\) 17120.3 0.974073
\(677\) −31721.6 −1.80083 −0.900414 0.435033i \(-0.856737\pi\)
−0.900414 + 0.435033i \(0.856737\pi\)
\(678\) 21632.3 1.22534
\(679\) −18595.3 −1.05099
\(680\) 3553.76 0.200413
\(681\) 3132.86 0.176287
\(682\) −31451.6 −1.76590
\(683\) 15444.2 0.865238 0.432619 0.901577i \(-0.357590\pi\)
0.432619 + 0.901577i \(0.357590\pi\)
\(684\) −7751.16 −0.433294
\(685\) 2000.98 0.111611
\(686\) −23425.5 −1.30378
\(687\) 11373.1 0.631604
\(688\) −18807.6 −1.04220
\(689\) −11423.8 −0.631657
\(690\) 23831.3 1.31484
\(691\) −24734.6 −1.36172 −0.680861 0.732413i \(-0.738394\pi\)
−0.680861 + 0.732413i \(0.738394\pi\)
\(692\) 8989.26 0.493816
\(693\) −15991.1 −0.876552
\(694\) −420.661 −0.0230087
\(695\) −20276.3 −1.10666
\(696\) −2115.02 −0.115186
\(697\) −26639.4 −1.44769
\(698\) −3477.31 −0.188564
\(699\) 2453.61 0.132767
\(700\) −5613.85 −0.303119
\(701\) 25510.2 1.37448 0.687238 0.726433i \(-0.258823\pi\)
0.687238 + 0.726433i \(0.258823\pi\)
\(702\) −38326.5 −2.06060
\(703\) −18124.3 −0.972362
\(704\) −14374.7 −0.769553
\(705\) 19595.0 1.04680
\(706\) −32720.9 −1.74429
\(707\) −58585.9 −3.11648
\(708\) −15813.8 −0.839435
\(709\) 3299.69 0.174785 0.0873924 0.996174i \(-0.472147\pi\)
0.0873924 + 0.996174i \(0.472147\pi\)
\(710\) −21018.9 −1.11102
\(711\) −9073.63 −0.478604
\(712\) −1279.97 −0.0673721
\(713\) 40318.9 2.11775
\(714\) 45344.1 2.37670
\(715\) 23968.6 1.25367
\(716\) −15985.7 −0.834375
\(717\) 4051.86 0.211045
\(718\) −19699.9 −1.02395
\(719\) 36828.1 1.91023 0.955117 0.296230i \(-0.0957294\pi\)
0.955117 + 0.296230i \(0.0957294\pi\)
\(720\) −10453.1 −0.541062
\(721\) 27829.3 1.43747
\(722\) 6749.99 0.347935
\(723\) −14390.7 −0.740242
\(724\) −10739.0 −0.551260
\(725\) 5070.95 0.259766
\(726\) 820.228 0.0419305
\(727\) −18832.9 −0.960759 −0.480380 0.877061i \(-0.659501\pi\)
−0.480380 + 0.877061i \(0.659501\pi\)
\(728\) −6378.73 −0.324741
\(729\) 14999.1 0.762034
\(730\) 2190.18 0.111044
\(731\) −30435.2 −1.53993
\(732\) 2361.26 0.119228
\(733\) 28389.7 1.43055 0.715277 0.698841i \(-0.246300\pi\)
0.715277 + 0.698841i \(0.246300\pi\)
\(734\) −24901.1 −1.25220
\(735\) −18708.9 −0.938898
\(736\) 43951.4 2.20118
\(737\) 9254.24 0.462530
\(738\) 13834.9 0.690067
\(739\) 20926.6 1.04168 0.520838 0.853655i \(-0.325619\pi\)
0.520838 + 0.853655i \(0.325619\pi\)
\(740\) 18084.2 0.898364
\(741\) −16742.1 −0.830011
\(742\) −19603.5 −0.969901
\(743\) 3593.16 0.177416 0.0887081 0.996058i \(-0.471726\pi\)
0.0887081 + 0.996058i \(0.471726\pi\)
\(744\) 2475.70 0.121994
\(745\) 32605.5 1.60345
\(746\) 16780.7 0.823571
\(747\) 18695.0 0.915682
\(748\) −28950.4 −1.41515
\(749\) −4528.49 −0.220918
\(750\) −20239.4 −0.985386
\(751\) 26375.6 1.28157 0.640786 0.767719i \(-0.278608\pi\)
0.640786 + 0.767719i \(0.278608\pi\)
\(752\) 39844.0 1.93213
\(753\) 18506.3 0.895628
\(754\) −51017.0 −2.46410
\(755\) −11450.1 −0.551937
\(756\) −31126.8 −1.49745
\(757\) 19750.9 0.948294 0.474147 0.880446i \(-0.342757\pi\)
0.474147 + 0.880446i \(0.342757\pi\)
\(758\) −39664.0 −1.90061
\(759\) 21926.1 1.04857
\(760\) −2251.65 −0.107469
\(761\) 7056.82 0.336149 0.168075 0.985774i \(-0.446245\pi\)
0.168075 + 0.985774i \(0.446245\pi\)
\(762\) −1758.82 −0.0836157
\(763\) −65446.6 −3.10528
\(764\) 15896.4 0.752763
\(765\) −16915.6 −0.799457
\(766\) −16581.8 −0.782149
\(767\) 43080.8 2.02811
\(768\) 16575.6 0.778805
\(769\) −5780.19 −0.271052 −0.135526 0.990774i \(-0.543272\pi\)
−0.135526 + 0.990774i \(0.543272\pi\)
\(770\) 41130.7 1.92499
\(771\) −3106.85 −0.145124
\(772\) −22345.7 −1.04176
\(773\) −38813.6 −1.80599 −0.902994 0.429653i \(-0.858636\pi\)
−0.902994 + 0.429653i \(0.858636\pi\)
\(774\) 15806.2 0.734033
\(775\) −5935.70 −0.275118
\(776\) −1974.60 −0.0913452
\(777\) −26060.3 −1.20323
\(778\) −50880.5 −2.34467
\(779\) 16878.6 0.776302
\(780\) 16705.1 0.766847
\(781\) −19338.5 −0.886025
\(782\) 78416.3 3.58589
\(783\) 28116.6 1.28328
\(784\) −38042.3 −1.73298
\(785\) 33080.3 1.50406
\(786\) 16538.0 0.750495
\(787\) 39826.5 1.80389 0.901946 0.431849i \(-0.142139\pi\)
0.901946 + 0.431849i \(0.142139\pi\)
\(788\) 4227.30 0.191106
\(789\) −6738.43 −0.304049
\(790\) 23338.3 1.05106
\(791\) −47861.4 −2.15140
\(792\) −1698.06 −0.0761842
\(793\) −6432.66 −0.288059
\(794\) 21485.1 0.960301
\(795\) −5798.25 −0.258670
\(796\) −20585.6 −0.916630
\(797\) −15985.8 −0.710471 −0.355236 0.934777i \(-0.615599\pi\)
−0.355236 + 0.934777i \(0.615599\pi\)
\(798\) −28729.9 −1.27447
\(799\) 64477.0 2.85486
\(800\) −6470.48 −0.285957
\(801\) 6092.55 0.268751
\(802\) 9981.03 0.439454
\(803\) 2015.08 0.0885562
\(804\) 6449.84 0.282921
\(805\) −52726.7 −2.30854
\(806\) 59717.0 2.60973
\(807\) 7349.31 0.320580
\(808\) −6221.11 −0.270864
\(809\) −3314.23 −0.144032 −0.0720162 0.997403i \(-0.522943\pi\)
−0.0720162 + 0.997403i \(0.522943\pi\)
\(810\) −3702.77 −0.160620
\(811\) −33298.1 −1.44174 −0.720872 0.693068i \(-0.756259\pi\)
−0.720872 + 0.693068i \(0.756259\pi\)
\(812\) −41433.5 −1.79068
\(813\) 6338.72 0.273443
\(814\) 35156.0 1.51378
\(815\) −2784.65 −0.119683
\(816\) 27271.1 1.16995
\(817\) 19283.6 0.825763
\(818\) 31726.3 1.35609
\(819\) 30362.2 1.29541
\(820\) −16841.3 −0.717225
\(821\) −8056.63 −0.342483 −0.171241 0.985229i \(-0.554778\pi\)
−0.171241 + 0.985229i \(0.554778\pi\)
\(822\) 2711.13 0.115038
\(823\) 26454.6 1.12047 0.560237 0.828332i \(-0.310710\pi\)
0.560237 + 0.828332i \(0.310710\pi\)
\(824\) 2955.13 0.124936
\(825\) −3227.93 −0.136221
\(826\) 73927.7 3.11413
\(827\) −10029.0 −0.421695 −0.210848 0.977519i \(-0.567622\pi\)
−0.210848 + 0.977519i \(0.567622\pi\)
\(828\) −19274.0 −0.808957
\(829\) −5565.05 −0.233151 −0.116576 0.993182i \(-0.537192\pi\)
−0.116576 + 0.993182i \(0.537192\pi\)
\(830\) −48085.4 −2.01093
\(831\) 3999.69 0.166965
\(832\) 27293.1 1.13728
\(833\) −61561.3 −2.56059
\(834\) −27472.4 −1.14064
\(835\) −6610.62 −0.273976
\(836\) 18342.9 0.758853
\(837\) −32911.4 −1.35912
\(838\) 27154.6 1.11938
\(839\) 36168.6 1.48830 0.744148 0.668015i \(-0.232856\pi\)
0.744148 + 0.668015i \(0.232856\pi\)
\(840\) −3237.58 −0.132985
\(841\) 13037.5 0.534566
\(842\) 44075.4 1.80397
\(843\) −5321.66 −0.217423
\(844\) −4165.68 −0.169892
\(845\) −23672.6 −0.963741
\(846\) −33485.4 −1.36082
\(847\) −1814.75 −0.0736195
\(848\) −11790.0 −0.477442
\(849\) −25146.6 −1.01652
\(850\) −11544.4 −0.465845
\(851\) −45067.7 −1.81539
\(852\) −13478.2 −0.541965
\(853\) −17788.6 −0.714034 −0.357017 0.934098i \(-0.616206\pi\)
−0.357017 + 0.934098i \(0.616206\pi\)
\(854\) −11038.6 −0.442310
\(855\) 10717.7 0.428698
\(856\) −480.871 −0.0192007
\(857\) 19234.2 0.766661 0.383330 0.923611i \(-0.374777\pi\)
0.383330 + 0.923611i \(0.374777\pi\)
\(858\) 32475.1 1.29217
\(859\) −18203.3 −0.723037 −0.361519 0.932365i \(-0.617742\pi\)
−0.361519 + 0.932365i \(0.617742\pi\)
\(860\) −19241.0 −0.762922
\(861\) 24269.2 0.960620
\(862\) 1578.74 0.0623807
\(863\) −1220.53 −0.0481429 −0.0240714 0.999710i \(-0.507663\pi\)
−0.0240714 + 0.999710i \(0.507663\pi\)
\(864\) −35876.6 −1.41267
\(865\) −12429.6 −0.488578
\(866\) 3198.61 0.125512
\(867\) 27154.2 1.06368
\(868\) 48499.2 1.89651
\(869\) 21472.4 0.838208
\(870\) −25894.2 −1.00907
\(871\) −17571.0 −0.683548
\(872\) −6949.64 −0.269890
\(873\) 9398.91 0.364381
\(874\) −49684.3 −1.92288
\(875\) 44779.7 1.73009
\(876\) 1404.43 0.0541681
\(877\) −5026.94 −0.193555 −0.0967774 0.995306i \(-0.530853\pi\)
−0.0967774 + 0.995306i \(0.530853\pi\)
\(878\) 4702.65 0.180759
\(879\) −11338.5 −0.435084
\(880\) 24737.0 0.947594
\(881\) −26103.7 −0.998246 −0.499123 0.866531i \(-0.666344\pi\)
−0.499123 + 0.866531i \(0.666344\pi\)
\(882\) 31971.2 1.22055
\(883\) 34260.1 1.30571 0.652857 0.757481i \(-0.273570\pi\)
0.652857 + 0.757481i \(0.273570\pi\)
\(884\) 54967.9 2.09137
\(885\) 21866.1 0.830531
\(886\) −54977.3 −2.08465
\(887\) −42206.8 −1.59771 −0.798854 0.601525i \(-0.794560\pi\)
−0.798854 + 0.601525i \(0.794560\pi\)
\(888\) −2767.29 −0.104577
\(889\) 3891.38 0.146808
\(890\) −15670.7 −0.590204
\(891\) −3406.75 −0.128092
\(892\) 12610.0 0.473334
\(893\) −40852.4 −1.53088
\(894\) 44177.2 1.65269
\(895\) 22103.7 0.825525
\(896\) −12004.1 −0.447576
\(897\) −41630.9 −1.54963
\(898\) −15131.2 −0.562289
\(899\) −43808.9 −1.62526
\(900\) 2837.49 0.105092
\(901\) −19079.0 −0.705454
\(902\) −32739.8 −1.20856
\(903\) 27727.3 1.02182
\(904\) −5082.30 −0.186985
\(905\) 14849.0 0.545413
\(906\) −15513.8 −0.568886
\(907\) −35714.2 −1.30747 −0.653733 0.756725i \(-0.726798\pi\)
−0.653733 + 0.756725i \(0.726798\pi\)
\(908\) 6517.07 0.238190
\(909\) 29611.9 1.08049
\(910\) −78094.5 −2.84484
\(911\) −18645.2 −0.678092 −0.339046 0.940770i \(-0.610104\pi\)
−0.339046 + 0.940770i \(0.610104\pi\)
\(912\) −17278.9 −0.627369
\(913\) −44241.1 −1.60369
\(914\) 9073.31 0.328357
\(915\) −3264.96 −0.117963
\(916\) 23658.7 0.853391
\(917\) −36590.2 −1.31768
\(918\) −64009.5 −2.30134
\(919\) −7917.55 −0.284196 −0.142098 0.989853i \(-0.545385\pi\)
−0.142098 + 0.989853i \(0.545385\pi\)
\(920\) −5598.94 −0.200643
\(921\) 15235.7 0.545097
\(922\) 5772.97 0.206207
\(923\) 36717.9 1.30941
\(924\) 26374.6 0.939027
\(925\) 6634.81 0.235839
\(926\) 24404.6 0.866074
\(927\) −14066.2 −0.498375
\(928\) −47755.9 −1.68929
\(929\) 32441.3 1.14571 0.572856 0.819656i \(-0.305836\pi\)
0.572856 + 0.819656i \(0.305836\pi\)
\(930\) 30309.9 1.06871
\(931\) 39005.1 1.37308
\(932\) 5104.08 0.179388
\(933\) −12863.7 −0.451381
\(934\) 46585.6 1.63204
\(935\) 40030.2 1.40014
\(936\) 3224.10 0.112589
\(937\) 52043.1 1.81449 0.907244 0.420605i \(-0.138182\pi\)
0.907244 + 0.420605i \(0.138182\pi\)
\(938\) −30152.2 −1.04958
\(939\) −21461.2 −0.745857
\(940\) 40762.1 1.41438
\(941\) 35207.1 1.21968 0.609840 0.792524i \(-0.291234\pi\)
0.609840 + 0.792524i \(0.291234\pi\)
\(942\) 44820.5 1.55025
\(943\) 41970.3 1.44935
\(944\) 44461.9 1.53296
\(945\) 43039.7 1.48157
\(946\) −37404.8 −1.28556
\(947\) 29820.4 1.02327 0.511634 0.859204i \(-0.329040\pi\)
0.511634 + 0.859204i \(0.329040\pi\)
\(948\) 14965.4 0.512716
\(949\) −3826.02 −0.130872
\(950\) 7314.47 0.249803
\(951\) 8754.49 0.298511
\(952\) −10653.2 −0.362680
\(953\) 51897.8 1.76404 0.882022 0.471208i \(-0.156182\pi\)
0.882022 + 0.471208i \(0.156182\pi\)
\(954\) 9908.48 0.336267
\(955\) −21980.2 −0.744779
\(956\) 8428.79 0.285153
\(957\) −23824.0 −0.804723
\(958\) 27361.2 0.922755
\(959\) −5998.37 −0.201979
\(960\) 13852.9 0.465728
\(961\) 21488.7 0.721317
\(962\) −66750.6 −2.23714
\(963\) 2288.90 0.0765928
\(964\) −29935.9 −1.00018
\(965\) 30897.9 1.03071
\(966\) −71439.5 −2.37943
\(967\) 4411.28 0.146698 0.0733491 0.997306i \(-0.476631\pi\)
0.0733491 + 0.997306i \(0.476631\pi\)
\(968\) −192.705 −0.00639852
\(969\) −27961.2 −0.926981
\(970\) −24174.9 −0.800217
\(971\) 37197.8 1.22939 0.614693 0.788766i \(-0.289280\pi\)
0.614693 + 0.788766i \(0.289280\pi\)
\(972\) 25832.6 0.852448
\(973\) 60782.8 2.00268
\(974\) −8389.65 −0.275998
\(975\) 6128.85 0.201313
\(976\) −6638.88 −0.217731
\(977\) −8254.57 −0.270304 −0.135152 0.990825i \(-0.543152\pi\)
−0.135152 + 0.990825i \(0.543152\pi\)
\(978\) −3772.93 −0.123359
\(979\) −14417.8 −0.470680
\(980\) −38918.9 −1.26859
\(981\) 33079.6 1.07661
\(982\) 60243.9 1.95770
\(983\) −40483.9 −1.31357 −0.656783 0.754080i \(-0.728083\pi\)
−0.656783 + 0.754080i \(0.728083\pi\)
\(984\) 2577.10 0.0834908
\(985\) −5845.17 −0.189079
\(986\) −85204.1 −2.75198
\(987\) −58740.4 −1.89435
\(988\) −34827.5 −1.12147
\(989\) 47950.5 1.54170
\(990\) −20789.3 −0.667401
\(991\) 39541.4 1.26748 0.633740 0.773546i \(-0.281519\pi\)
0.633740 + 0.773546i \(0.281519\pi\)
\(992\) 55899.8 1.78913
\(993\) 19650.7 0.627991
\(994\) 63008.8 2.01058
\(995\) 28464.1 0.906908
\(996\) −30834.3 −0.980946
\(997\) 118.681 0.00376998 0.00188499 0.999998i \(-0.499400\pi\)
0.00188499 + 0.999998i \(0.499400\pi\)
\(998\) −32161.3 −1.02009
\(999\) 36787.7 1.16508
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.a.1.13 65
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.4.a.a.1.13 65 1.1 even 1 trivial