Properties

Label 547.4.a.a.1.5
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 1.5
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)
 
\(f(q)\) \(=\) \(q-4.96544 q^{2} +7.58541 q^{3} +16.6556 q^{4} +8.10387 q^{5} -37.6649 q^{6} -24.7619 q^{7} -42.9790 q^{8} +30.5385 q^{9} +O(q^{10})\) \(q-4.96544 q^{2} +7.58541 q^{3} +16.6556 q^{4} +8.10387 q^{5} -37.6649 q^{6} -24.7619 q^{7} -42.9790 q^{8} +30.5385 q^{9} -40.2393 q^{10} -48.7621 q^{11} +126.340 q^{12} +36.0175 q^{13} +122.954 q^{14} +61.4712 q^{15} +80.1649 q^{16} -14.2566 q^{17} -151.637 q^{18} +113.687 q^{19} +134.975 q^{20} -187.829 q^{21} +242.125 q^{22} -84.8338 q^{23} -326.014 q^{24} -59.3272 q^{25} -178.843 q^{26} +26.8409 q^{27} -412.425 q^{28} +1.19799 q^{29} -305.232 q^{30} -111.912 q^{31} -54.2220 q^{32} -369.880 q^{33} +70.7904 q^{34} -200.667 q^{35} +508.638 q^{36} -194.631 q^{37} -564.504 q^{38} +273.207 q^{39} -348.297 q^{40} +187.980 q^{41} +932.655 q^{42} -255.816 q^{43} -812.163 q^{44} +247.480 q^{45} +421.238 q^{46} -238.064 q^{47} +608.084 q^{48} +270.151 q^{49} +294.586 q^{50} -108.142 q^{51} +599.894 q^{52} -408.484 q^{53} -133.277 q^{54} -395.162 q^{55} +1064.24 q^{56} +862.359 q^{57} -5.94856 q^{58} +69.9138 q^{59} +1023.84 q^{60} -367.303 q^{61} +555.694 q^{62} -756.190 q^{63} -372.083 q^{64} +291.881 q^{65} +1836.62 q^{66} +670.008 q^{67} -237.453 q^{68} -643.500 q^{69} +996.401 q^{70} -101.170 q^{71} -1312.51 q^{72} +177.461 q^{73} +966.429 q^{74} -450.021 q^{75} +1893.52 q^{76} +1207.44 q^{77} -1356.60 q^{78} +48.9511 q^{79} +649.646 q^{80} -620.940 q^{81} -933.403 q^{82} -159.520 q^{83} -3128.41 q^{84} -115.534 q^{85} +1270.24 q^{86} +9.08725 q^{87} +2095.75 q^{88} -1162.41 q^{89} -1228.85 q^{90} -891.860 q^{91} -1412.96 q^{92} -848.901 q^{93} +1182.09 q^{94} +921.301 q^{95} -411.296 q^{96} -874.733 q^{97} -1341.42 q^{98} -1489.12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 65 q - 12 q^{2} - 35 q^{3} + 234 q^{4} - 151 q^{5} - 60 q^{6} - 74 q^{7} - 144 q^{8} + 468 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.96544 −1.75555 −0.877775 0.479074i \(-0.840973\pi\)
−0.877775 + 0.479074i \(0.840973\pi\)
\(3\) 7.58541 1.45981 0.729907 0.683547i \(-0.239563\pi\)
0.729907 + 0.683547i \(0.239563\pi\)
\(4\) 16.6556 2.08195
\(5\) 8.10387 0.724833 0.362416 0.932016i \(-0.381952\pi\)
0.362416 + 0.932016i \(0.381952\pi\)
\(6\) −37.6649 −2.56277
\(7\) −24.7619 −1.33702 −0.668508 0.743705i \(-0.733067\pi\)
−0.668508 + 0.743705i \(0.733067\pi\)
\(8\) −42.9790 −1.89942
\(9\) 30.5385 1.13106
\(10\) −40.2393 −1.27248
\(11\) −48.7621 −1.33657 −0.668287 0.743904i \(-0.732972\pi\)
−0.668287 + 0.743904i \(0.732972\pi\)
\(12\) 126.340 3.03926
\(13\) 36.0175 0.768419 0.384210 0.923246i \(-0.374474\pi\)
0.384210 + 0.923246i \(0.374474\pi\)
\(14\) 122.954 2.34720
\(15\) 61.4712 1.05812
\(16\) 80.1649 1.25258
\(17\) −14.2566 −0.203396 −0.101698 0.994815i \(-0.532428\pi\)
−0.101698 + 0.994815i \(0.532428\pi\)
\(18\) −151.637 −1.98562
\(19\) 113.687 1.37271 0.686355 0.727267i \(-0.259210\pi\)
0.686355 + 0.727267i \(0.259210\pi\)
\(20\) 134.975 1.50907
\(21\) −187.829 −1.95179
\(22\) 242.125 2.34642
\(23\) −84.8338 −0.769090 −0.384545 0.923106i \(-0.625642\pi\)
−0.384545 + 0.923106i \(0.625642\pi\)
\(24\) −326.014 −2.77280
\(25\) −59.3272 −0.474618
\(26\) −178.843 −1.34900
\(27\) 26.8409 0.191316
\(28\) −412.425 −2.78360
\(29\) 1.19799 0.00767108 0.00383554 0.999993i \(-0.498779\pi\)
0.00383554 + 0.999993i \(0.498779\pi\)
\(30\) −305.232 −1.85758
\(31\) −111.912 −0.648388 −0.324194 0.945991i \(-0.605093\pi\)
−0.324194 + 0.945991i \(0.605093\pi\)
\(32\) −54.2220 −0.299537
\(33\) −369.880 −1.95115
\(34\) 70.7904 0.357072
\(35\) −200.667 −0.969113
\(36\) 508.638 2.35480
\(37\) −194.631 −0.864788 −0.432394 0.901685i \(-0.642331\pi\)
−0.432394 + 0.901685i \(0.642331\pi\)
\(38\) −564.504 −2.40986
\(39\) 273.207 1.12175
\(40\) −348.297 −1.37676
\(41\) 187.980 0.716037 0.358018 0.933715i \(-0.383453\pi\)
0.358018 + 0.933715i \(0.383453\pi\)
\(42\) 932.655 3.42647
\(43\) −255.816 −0.907246 −0.453623 0.891194i \(-0.649869\pi\)
−0.453623 + 0.891194i \(0.649869\pi\)
\(44\) −812.163 −2.78268
\(45\) 247.480 0.819826
\(46\) 421.238 1.35018
\(47\) −238.064 −0.738833 −0.369416 0.929264i \(-0.620442\pi\)
−0.369416 + 0.929264i \(0.620442\pi\)
\(48\) 608.084 1.82853
\(49\) 270.151 0.787611
\(50\) 294.586 0.833215
\(51\) −108.142 −0.296920
\(52\) 599.894 1.59981
\(53\) −408.484 −1.05867 −0.529336 0.848412i \(-0.677559\pi\)
−0.529336 + 0.848412i \(0.677559\pi\)
\(54\) −133.277 −0.335865
\(55\) −395.162 −0.968792
\(56\) 1064.24 2.53956
\(57\) 862.359 2.00390
\(58\) −5.94856 −0.0134670
\(59\) 69.9138 0.154271 0.0771356 0.997021i \(-0.475423\pi\)
0.0771356 + 0.997021i \(0.475423\pi\)
\(60\) 1023.84 2.20296
\(61\) −367.303 −0.770956 −0.385478 0.922717i \(-0.625963\pi\)
−0.385478 + 0.922717i \(0.625963\pi\)
\(62\) 555.694 1.13828
\(63\) −756.190 −1.51224
\(64\) −372.083 −0.726724
\(65\) 291.881 0.556975
\(66\) 1836.62 3.42534
\(67\) 670.008 1.22171 0.610854 0.791743i \(-0.290826\pi\)
0.610854 + 0.791743i \(0.290826\pi\)
\(68\) −237.453 −0.423461
\(69\) −643.500 −1.12273
\(70\) 996.401 1.70132
\(71\) −101.170 −0.169108 −0.0845540 0.996419i \(-0.526947\pi\)
−0.0845540 + 0.996419i \(0.526947\pi\)
\(72\) −1312.51 −2.14835
\(73\) 177.461 0.284524 0.142262 0.989829i \(-0.454562\pi\)
0.142262 + 0.989829i \(0.454562\pi\)
\(74\) 966.429 1.51818
\(75\) −450.021 −0.692853
\(76\) 1893.52 2.85792
\(77\) 1207.44 1.78702
\(78\) −1356.60 −1.96928
\(79\) 48.9511 0.0697143 0.0348572 0.999392i \(-0.488902\pi\)
0.0348572 + 0.999392i \(0.488902\pi\)
\(80\) 649.646 0.907908
\(81\) −620.940 −0.851769
\(82\) −933.403 −1.25704
\(83\) −159.520 −0.210959 −0.105480 0.994421i \(-0.533638\pi\)
−0.105480 + 0.994421i \(0.533638\pi\)
\(84\) −3128.41 −4.06354
\(85\) −115.534 −0.147428
\(86\) 1270.24 1.59271
\(87\) 9.08725 0.0111983
\(88\) 2095.75 2.53872
\(89\) −1162.41 −1.38444 −0.692220 0.721687i \(-0.743367\pi\)
−0.692220 + 0.721687i \(0.743367\pi\)
\(90\) −1228.85 −1.43924
\(91\) −891.860 −1.02739
\(92\) −1412.96 −1.60121
\(93\) −848.901 −0.946526
\(94\) 1182.09 1.29706
\(95\) 921.301 0.994985
\(96\) −411.296 −0.437268
\(97\) −874.733 −0.915625 −0.457813 0.889049i \(-0.651367\pi\)
−0.457813 + 0.889049i \(0.651367\pi\)
\(98\) −1341.42 −1.38269
\(99\) −1489.12 −1.51174
\(100\) −988.132 −0.988132
\(101\) −1697.11 −1.67197 −0.835983 0.548755i \(-0.815102\pi\)
−0.835983 + 0.548755i \(0.815102\pi\)
\(102\) 536.974 0.521259
\(103\) 939.716 0.898960 0.449480 0.893290i \(-0.351609\pi\)
0.449480 + 0.893290i \(0.351609\pi\)
\(104\) −1548.00 −1.45955
\(105\) −1522.14 −1.41472
\(106\) 2028.30 1.85855
\(107\) −318.861 −0.288088 −0.144044 0.989571i \(-0.546011\pi\)
−0.144044 + 0.989571i \(0.546011\pi\)
\(108\) 447.052 0.398311
\(109\) 1489.05 1.30849 0.654245 0.756282i \(-0.272986\pi\)
0.654245 + 0.756282i \(0.272986\pi\)
\(110\) 1962.15 1.70076
\(111\) −1476.36 −1.26243
\(112\) −1985.03 −1.67471
\(113\) −1338.16 −1.11402 −0.557009 0.830507i \(-0.688051\pi\)
−0.557009 + 0.830507i \(0.688051\pi\)
\(114\) −4282.00 −3.51794
\(115\) −687.483 −0.557462
\(116\) 19.9533 0.0159708
\(117\) 1099.92 0.869124
\(118\) −347.153 −0.270831
\(119\) 353.020 0.271944
\(120\) −2641.97 −2.00982
\(121\) 1046.74 0.786430
\(122\) 1823.82 1.35345
\(123\) 1425.90 1.04528
\(124\) −1863.97 −1.34991
\(125\) −1493.76 −1.06885
\(126\) 3754.82 2.65481
\(127\) 1175.44 0.821290 0.410645 0.911795i \(-0.365304\pi\)
0.410645 + 0.911795i \(0.365304\pi\)
\(128\) 2281.33 1.57534
\(129\) −1940.47 −1.32441
\(130\) −1449.32 −0.977797
\(131\) −35.1901 −0.0234700 −0.0117350 0.999931i \(-0.503735\pi\)
−0.0117350 + 0.999931i \(0.503735\pi\)
\(132\) −6160.59 −4.06220
\(133\) −2815.09 −1.83533
\(134\) −3326.89 −2.14477
\(135\) 217.515 0.138672
\(136\) 612.735 0.386335
\(137\) −442.539 −0.275976 −0.137988 0.990434i \(-0.544063\pi\)
−0.137988 + 0.990434i \(0.544063\pi\)
\(138\) 3195.26 1.97100
\(139\) 2147.66 1.31052 0.655259 0.755404i \(-0.272559\pi\)
0.655259 + 0.755404i \(0.272559\pi\)
\(140\) −3342.24 −2.01765
\(141\) −1805.81 −1.07856
\(142\) 502.354 0.296878
\(143\) −1756.29 −1.02705
\(144\) 2448.11 1.41673
\(145\) 9.70837 0.00556025
\(146\) −881.174 −0.499496
\(147\) 2049.20 1.14976
\(148\) −3241.70 −1.80045
\(149\) −1403.54 −0.771693 −0.385847 0.922563i \(-0.626091\pi\)
−0.385847 + 0.922563i \(0.626091\pi\)
\(150\) 2234.56 1.21634
\(151\) 376.317 0.202809 0.101405 0.994845i \(-0.467666\pi\)
0.101405 + 0.994845i \(0.467666\pi\)
\(152\) −4886.14 −2.60735
\(153\) −435.375 −0.230052
\(154\) −5995.48 −3.13720
\(155\) −906.923 −0.469973
\(156\) 4550.44 2.33543
\(157\) −2982.66 −1.51619 −0.758095 0.652144i \(-0.773870\pi\)
−0.758095 + 0.652144i \(0.773870\pi\)
\(158\) −243.064 −0.122387
\(159\) −3098.52 −1.54546
\(160\) −439.408 −0.217114
\(161\) 2100.64 1.02829
\(162\) 3083.24 1.49532
\(163\) 1919.41 0.922330 0.461165 0.887314i \(-0.347432\pi\)
0.461165 + 0.887314i \(0.347432\pi\)
\(164\) 3130.92 1.49076
\(165\) −2997.46 −1.41426
\(166\) 792.089 0.370349
\(167\) 1247.74 0.578160 0.289080 0.957305i \(-0.406651\pi\)
0.289080 + 0.957305i \(0.406651\pi\)
\(168\) 8072.71 3.70728
\(169\) −899.742 −0.409532
\(170\) 573.676 0.258817
\(171\) 3471.81 1.55261
\(172\) −4260.78 −1.88884
\(173\) −3436.13 −1.51008 −0.755040 0.655678i \(-0.772383\pi\)
−0.755040 + 0.655678i \(0.772383\pi\)
\(174\) −45.1222 −0.0196592
\(175\) 1469.05 0.634571
\(176\) −3909.01 −1.67416
\(177\) 530.325 0.225207
\(178\) 5771.88 2.43045
\(179\) 825.434 0.344669 0.172335 0.985038i \(-0.444869\pi\)
0.172335 + 0.985038i \(0.444869\pi\)
\(180\) 4121.94 1.70684
\(181\) −1184.11 −0.486266 −0.243133 0.969993i \(-0.578175\pi\)
−0.243133 + 0.969993i \(0.578175\pi\)
\(182\) 4428.48 1.80363
\(183\) −2786.14 −1.12545
\(184\) 3646.07 1.46083
\(185\) −1577.27 −0.626826
\(186\) 4215.17 1.66167
\(187\) 695.182 0.271854
\(188\) −3965.10 −1.53822
\(189\) −664.631 −0.255793
\(190\) −4574.67 −1.74674
\(191\) 3726.42 1.41170 0.705848 0.708363i \(-0.250566\pi\)
0.705848 + 0.708363i \(0.250566\pi\)
\(192\) −2822.40 −1.06088
\(193\) 5013.91 1.87000 0.934998 0.354653i \(-0.115401\pi\)
0.934998 + 0.354653i \(0.115401\pi\)
\(194\) 4343.43 1.60742
\(195\) 2214.04 0.813080
\(196\) 4499.53 1.63977
\(197\) 2191.77 0.792677 0.396339 0.918104i \(-0.370281\pi\)
0.396339 + 0.918104i \(0.370281\pi\)
\(198\) 7394.14 2.65393
\(199\) 4879.38 1.73814 0.869071 0.494687i \(-0.164717\pi\)
0.869071 + 0.494687i \(0.164717\pi\)
\(200\) 2549.83 0.901499
\(201\) 5082.29 1.78347
\(202\) 8426.89 2.93522
\(203\) −29.6645 −0.0102564
\(204\) −1801.18 −0.618175
\(205\) 1523.36 0.519007
\(206\) −4666.10 −1.57817
\(207\) −2590.70 −0.869883
\(208\) 2887.34 0.962504
\(209\) −5543.59 −1.83473
\(210\) 7558.12 2.48362
\(211\) −444.708 −0.145095 −0.0725474 0.997365i \(-0.523113\pi\)
−0.0725474 + 0.997365i \(0.523113\pi\)
\(212\) −6803.56 −2.20410
\(213\) −767.417 −0.246866
\(214\) 1583.29 0.505753
\(215\) −2073.10 −0.657601
\(216\) −1153.60 −0.363390
\(217\) 2771.16 0.866905
\(218\) −7393.81 −2.29712
\(219\) 1346.12 0.415352
\(220\) −6581.66 −2.01698
\(221\) −513.487 −0.156294
\(222\) 7330.77 2.21626
\(223\) −4404.74 −1.32271 −0.661353 0.750075i \(-0.730017\pi\)
−0.661353 + 0.750075i \(0.730017\pi\)
\(224\) 1342.64 0.400486
\(225\) −1811.76 −0.536819
\(226\) 6644.58 1.95571
\(227\) −5707.87 −1.66892 −0.834460 0.551068i \(-0.814220\pi\)
−0.834460 + 0.551068i \(0.814220\pi\)
\(228\) 14363.1 4.17203
\(229\) 1699.96 0.490553 0.245277 0.969453i \(-0.421121\pi\)
0.245277 + 0.969453i \(0.421121\pi\)
\(230\) 3413.66 0.978651
\(231\) 9158.93 2.60872
\(232\) −51.4885 −0.0145706
\(233\) −4306.59 −1.21087 −0.605437 0.795893i \(-0.707002\pi\)
−0.605437 + 0.795893i \(0.707002\pi\)
\(234\) −5461.59 −1.52579
\(235\) −1929.24 −0.535530
\(236\) 1164.46 0.321185
\(237\) 371.314 0.101770
\(238\) −1752.90 −0.477411
\(239\) −4789.38 −1.29623 −0.648116 0.761542i \(-0.724443\pi\)
−0.648116 + 0.761542i \(0.724443\pi\)
\(240\) 4927.83 1.32538
\(241\) −6583.12 −1.75957 −0.879784 0.475374i \(-0.842313\pi\)
−0.879784 + 0.475374i \(0.842313\pi\)
\(242\) −5197.52 −1.38062
\(243\) −5434.79 −1.43474
\(244\) −6117.66 −1.60509
\(245\) 2189.27 0.570886
\(246\) −7080.25 −1.83504
\(247\) 4094.70 1.05482
\(248\) 4809.88 1.23156
\(249\) −1210.03 −0.307961
\(250\) 7417.20 1.87642
\(251\) 3819.34 0.960455 0.480228 0.877144i \(-0.340554\pi\)
0.480228 + 0.877144i \(0.340554\pi\)
\(252\) −12594.8 −3.14841
\(253\) 4136.67 1.02795
\(254\) −5836.60 −1.44181
\(255\) −876.371 −0.215218
\(256\) −8351.16 −2.03886
\(257\) 3484.27 0.845692 0.422846 0.906202i \(-0.361031\pi\)
0.422846 + 0.906202i \(0.361031\pi\)
\(258\) 9635.29 2.32507
\(259\) 4819.43 1.15623
\(260\) 4861.46 1.15960
\(261\) 36.5848 0.00867641
\(262\) 174.734 0.0412028
\(263\) −4054.76 −0.950675 −0.475337 0.879804i \(-0.657674\pi\)
−0.475337 + 0.879804i \(0.657674\pi\)
\(264\) 15897.1 3.70606
\(265\) −3310.30 −0.767360
\(266\) 13978.2 3.22202
\(267\) −8817.35 −2.02102
\(268\) 11159.4 2.54354
\(269\) −7449.35 −1.68846 −0.844228 0.535983i \(-0.819941\pi\)
−0.844228 + 0.535983i \(0.819941\pi\)
\(270\) −1080.06 −0.243446
\(271\) 5040.21 1.12978 0.564891 0.825166i \(-0.308918\pi\)
0.564891 + 0.825166i \(0.308918\pi\)
\(272\) −1142.88 −0.254769
\(273\) −6765.13 −1.49980
\(274\) 2197.40 0.484489
\(275\) 2892.92 0.634362
\(276\) −10717.9 −2.33747
\(277\) −1081.07 −0.234495 −0.117248 0.993103i \(-0.537407\pi\)
−0.117248 + 0.993103i \(0.537407\pi\)
\(278\) −10664.1 −2.30068
\(279\) −3417.63 −0.733363
\(280\) 8624.48 1.84075
\(281\) 4002.13 0.849633 0.424817 0.905279i \(-0.360339\pi\)
0.424817 + 0.905279i \(0.360339\pi\)
\(282\) 8966.65 1.89346
\(283\) 9166.84 1.92548 0.962742 0.270422i \(-0.0871632\pi\)
0.962742 + 0.270422i \(0.0871632\pi\)
\(284\) −1685.05 −0.352075
\(285\) 6988.45 1.45249
\(286\) 8720.74 1.80304
\(287\) −4654.73 −0.957352
\(288\) −1655.86 −0.338793
\(289\) −4709.75 −0.958630
\(290\) −48.2063 −0.00976129
\(291\) −6635.21 −1.33664
\(292\) 2955.73 0.592366
\(293\) 4939.97 0.984969 0.492485 0.870321i \(-0.336089\pi\)
0.492485 + 0.870321i \(0.336089\pi\)
\(294\) −10175.2 −2.01847
\(295\) 566.573 0.111821
\(296\) 8365.05 1.64260
\(297\) −1308.82 −0.255708
\(298\) 6969.19 1.35475
\(299\) −3055.50 −0.590984
\(300\) −7495.39 −1.44249
\(301\) 6334.48 1.21300
\(302\) −1868.58 −0.356042
\(303\) −12873.3 −2.44076
\(304\) 9113.67 1.71942
\(305\) −2976.58 −0.558814
\(306\) 2161.83 0.403868
\(307\) −4270.20 −0.793853 −0.396927 0.917850i \(-0.629923\pi\)
−0.396927 + 0.917850i \(0.629923\pi\)
\(308\) 20110.7 3.72049
\(309\) 7128.13 1.31231
\(310\) 4503.27 0.825060
\(311\) −684.110 −0.124734 −0.0623670 0.998053i \(-0.519865\pi\)
−0.0623670 + 0.998053i \(0.519865\pi\)
\(312\) −11742.2 −2.13067
\(313\) −7603.60 −1.37310 −0.686551 0.727082i \(-0.740876\pi\)
−0.686551 + 0.727082i \(0.740876\pi\)
\(314\) 14810.2 2.66175
\(315\) −6128.07 −1.09612
\(316\) 815.311 0.145142
\(317\) −3810.42 −0.675125 −0.337562 0.941303i \(-0.609602\pi\)
−0.337562 + 0.941303i \(0.609602\pi\)
\(318\) 15385.5 2.71314
\(319\) −58.4165 −0.0102530
\(320\) −3015.31 −0.526753
\(321\) −2418.69 −0.420555
\(322\) −10430.6 −1.80521
\(323\) −1620.78 −0.279204
\(324\) −10342.1 −1.77334
\(325\) −2136.82 −0.364705
\(326\) −9530.73 −1.61920
\(327\) 11295.1 1.91015
\(328\) −8079.19 −1.36006
\(329\) 5894.90 0.987831
\(330\) 14883.7 2.48280
\(331\) 4888.58 0.811784 0.405892 0.913921i \(-0.366961\pi\)
0.405892 + 0.913921i \(0.366961\pi\)
\(332\) −2656.91 −0.439207
\(333\) −5943.74 −0.978123
\(334\) −6195.57 −1.01499
\(335\) 5429.66 0.885534
\(336\) −15057.3 −2.44477
\(337\) 389.321 0.0629307 0.0314654 0.999505i \(-0.489983\pi\)
0.0314654 + 0.999505i \(0.489983\pi\)
\(338\) 4467.62 0.718954
\(339\) −10150.5 −1.62626
\(340\) −1924.29 −0.306939
\(341\) 5457.07 0.866619
\(342\) −17239.1 −2.72568
\(343\) 1803.89 0.283968
\(344\) 10994.7 1.72324
\(345\) −5214.84 −0.813790
\(346\) 17061.9 2.65102
\(347\) −11977.0 −1.85291 −0.926454 0.376407i \(-0.877159\pi\)
−0.926454 + 0.376407i \(0.877159\pi\)
\(348\) 151.354 0.0233144
\(349\) 10612.8 1.62776 0.813880 0.581033i \(-0.197351\pi\)
0.813880 + 0.581033i \(0.197351\pi\)
\(350\) −7294.50 −1.11402
\(351\) 966.742 0.147011
\(352\) 2643.98 0.400354
\(353\) 6749.97 1.01775 0.508873 0.860841i \(-0.330062\pi\)
0.508873 + 0.860841i \(0.330062\pi\)
\(354\) −2633.30 −0.395362
\(355\) −819.869 −0.122575
\(356\) −19360.7 −2.88234
\(357\) 2677.81 0.396987
\(358\) −4098.65 −0.605084
\(359\) 9935.82 1.46070 0.730351 0.683072i \(-0.239356\pi\)
0.730351 + 0.683072i \(0.239356\pi\)
\(360\) −10636.5 −1.55720
\(361\) 6065.63 0.884331
\(362\) 5879.63 0.853664
\(363\) 7939.94 1.14804
\(364\) −14854.5 −2.13897
\(365\) 1438.12 0.206232
\(366\) 13834.4 1.97579
\(367\) 1683.82 0.239495 0.119748 0.992804i \(-0.461791\pi\)
0.119748 + 0.992804i \(0.461791\pi\)
\(368\) −6800.69 −0.963344
\(369\) 5740.62 0.809877
\(370\) 7831.82 1.10042
\(371\) 10114.8 1.41546
\(372\) −14139.0 −1.97062
\(373\) −10055.0 −1.39579 −0.697896 0.716200i \(-0.745880\pi\)
−0.697896 + 0.716200i \(0.745880\pi\)
\(374\) −3451.88 −0.477253
\(375\) −11330.8 −1.56032
\(376\) 10231.7 1.40336
\(377\) 43.1486 0.00589460
\(378\) 3300.19 0.449057
\(379\) −578.881 −0.0784567 −0.0392284 0.999230i \(-0.512490\pi\)
−0.0392284 + 0.999230i \(0.512490\pi\)
\(380\) 15344.9 2.07151
\(381\) 8916.23 1.19893
\(382\) −18503.3 −2.47830
\(383\) 5701.70 0.760687 0.380343 0.924845i \(-0.375806\pi\)
0.380343 + 0.924845i \(0.375806\pi\)
\(384\) 17304.8 2.29970
\(385\) 9784.94 1.29529
\(386\) −24896.3 −3.28287
\(387\) −7812.23 −1.02615
\(388\) −14569.2 −1.90629
\(389\) 11672.4 1.52137 0.760686 0.649120i \(-0.224863\pi\)
0.760686 + 0.649120i \(0.224863\pi\)
\(390\) −10993.7 −1.42740
\(391\) 1209.44 0.156430
\(392\) −11610.8 −1.49601
\(393\) −266.931 −0.0342618
\(394\) −10883.1 −1.39158
\(395\) 396.694 0.0505312
\(396\) −24802.2 −3.14737
\(397\) 3126.95 0.395308 0.197654 0.980272i \(-0.436668\pi\)
0.197654 + 0.980272i \(0.436668\pi\)
\(398\) −24228.3 −3.05139
\(399\) −21353.6 −2.67925
\(400\) −4755.96 −0.594495
\(401\) 78.6521 0.00979476 0.00489738 0.999988i \(-0.498441\pi\)
0.00489738 + 0.999988i \(0.498441\pi\)
\(402\) −25235.8 −3.13096
\(403\) −4030.80 −0.498234
\(404\) −28266.4 −3.48096
\(405\) −5032.02 −0.617390
\(406\) 147.297 0.0180055
\(407\) 9490.61 1.15585
\(408\) 4647.85 0.563977
\(409\) 12122.5 1.46557 0.732786 0.680459i \(-0.238220\pi\)
0.732786 + 0.680459i \(0.238220\pi\)
\(410\) −7564.18 −0.911142
\(411\) −3356.84 −0.402873
\(412\) 15651.6 1.87159
\(413\) −1731.20 −0.206263
\(414\) 12864.0 1.52712
\(415\) −1292.73 −0.152910
\(416\) −1952.94 −0.230170
\(417\) 16290.9 1.91311
\(418\) 27526.4 3.22095
\(419\) 1463.14 0.170595 0.0852974 0.996356i \(-0.472816\pi\)
0.0852974 + 0.996356i \(0.472816\pi\)
\(420\) −25352.2 −2.94539
\(421\) 13782.9 1.59558 0.797791 0.602935i \(-0.206002\pi\)
0.797791 + 0.602935i \(0.206002\pi\)
\(422\) 2208.17 0.254721
\(423\) −7270.10 −0.835661
\(424\) 17556.2 2.01086
\(425\) 845.805 0.0965354
\(426\) 3810.56 0.433386
\(427\) 9095.11 1.03078
\(428\) −5310.83 −0.599786
\(429\) −13322.2 −1.49930
\(430\) 10293.9 1.15445
\(431\) −13402.6 −1.49787 −0.748933 0.662645i \(-0.769434\pi\)
−0.748933 + 0.662645i \(0.769434\pi\)
\(432\) 2151.70 0.239638
\(433\) −13100.9 −1.45402 −0.727009 0.686628i \(-0.759090\pi\)
−0.727009 + 0.686628i \(0.759090\pi\)
\(434\) −13760.0 −1.52189
\(435\) 73.6420 0.00811693
\(436\) 24801.1 2.72422
\(437\) −9644.46 −1.05574
\(438\) −6684.07 −0.729171
\(439\) 5610.14 0.609926 0.304963 0.952364i \(-0.401356\pi\)
0.304963 + 0.952364i \(0.401356\pi\)
\(440\) 16983.7 1.84015
\(441\) 8249.99 0.890831
\(442\) 2549.69 0.274381
\(443\) 11572.3 1.24112 0.620562 0.784157i \(-0.286904\pi\)
0.620562 + 0.784157i \(0.286904\pi\)
\(444\) −24589.6 −2.62832
\(445\) −9420.02 −1.00349
\(446\) 21871.5 2.32207
\(447\) −10646.4 −1.12653
\(448\) 9213.47 0.971642
\(449\) 9808.82 1.03097 0.515486 0.856898i \(-0.327611\pi\)
0.515486 + 0.856898i \(0.327611\pi\)
\(450\) 8996.21 0.942412
\(451\) −9166.28 −0.957036
\(452\) −22288.0 −2.31933
\(453\) 2854.52 0.296064
\(454\) 28342.1 2.92987
\(455\) −7227.52 −0.744685
\(456\) −37063.4 −3.80625
\(457\) 900.338 0.0921576 0.0460788 0.998938i \(-0.485327\pi\)
0.0460788 + 0.998938i \(0.485327\pi\)
\(458\) −8441.06 −0.861190
\(459\) −382.660 −0.0389130
\(460\) −11450.5 −1.16061
\(461\) 3486.89 0.352279 0.176140 0.984365i \(-0.443639\pi\)
0.176140 + 0.984365i \(0.443639\pi\)
\(462\) −45478.2 −4.57973
\(463\) −15319.6 −1.53771 −0.768857 0.639421i \(-0.779174\pi\)
−0.768857 + 0.639421i \(0.779174\pi\)
\(464\) 96.0368 0.00960861
\(465\) −6879.38 −0.686073
\(466\) 21384.1 2.12575
\(467\) 9616.18 0.952856 0.476428 0.879214i \(-0.341931\pi\)
0.476428 + 0.879214i \(0.341931\pi\)
\(468\) 18319.8 1.80948
\(469\) −16590.7 −1.63344
\(470\) 9579.52 0.940149
\(471\) −22624.7 −2.21335
\(472\) −3004.83 −0.293026
\(473\) 12474.1 1.21260
\(474\) −1843.74 −0.178662
\(475\) −6744.70 −0.651512
\(476\) 5879.77 0.566174
\(477\) −12474.5 −1.19742
\(478\) 23781.4 2.27560
\(479\) −15661.1 −1.49389 −0.746944 0.664887i \(-0.768480\pi\)
−0.746944 + 0.664887i \(0.768480\pi\)
\(480\) −3333.09 −0.316946
\(481\) −7010.12 −0.664519
\(482\) 32688.1 3.08901
\(483\) 15934.3 1.50111
\(484\) 17434.1 1.63731
\(485\) −7088.72 −0.663675
\(486\) 26986.1 2.51876
\(487\) 14574.2 1.35610 0.678048 0.735018i \(-0.262826\pi\)
0.678048 + 0.735018i \(0.262826\pi\)
\(488\) 15786.3 1.46437
\(489\) 14559.5 1.34643
\(490\) −10870.7 −1.00222
\(491\) 2813.82 0.258627 0.129314 0.991604i \(-0.458723\pi\)
0.129314 + 0.991604i \(0.458723\pi\)
\(492\) 23749.3 2.17622
\(493\) −17.0793 −0.00156027
\(494\) −20332.0 −1.85178
\(495\) −12067.6 −1.09576
\(496\) −8971.43 −0.812156
\(497\) 2505.16 0.226100
\(498\) 6008.32 0.540641
\(499\) −4377.59 −0.392721 −0.196361 0.980532i \(-0.562912\pi\)
−0.196361 + 0.980532i \(0.562912\pi\)
\(500\) −24879.6 −2.22530
\(501\) 9464.60 0.844006
\(502\) −18964.7 −1.68613
\(503\) 7305.30 0.647569 0.323784 0.946131i \(-0.395045\pi\)
0.323784 + 0.946131i \(0.395045\pi\)
\(504\) 32500.3 2.87238
\(505\) −13753.2 −1.21190
\(506\) −20540.4 −1.80461
\(507\) −6824.91 −0.597840
\(508\) 19577.8 1.70989
\(509\) −9795.72 −0.853021 −0.426511 0.904483i \(-0.640257\pi\)
−0.426511 + 0.904483i \(0.640257\pi\)
\(510\) 4351.57 0.377825
\(511\) −4394.27 −0.380413
\(512\) 23216.6 2.00398
\(513\) 3051.45 0.262622
\(514\) −17300.9 −1.48465
\(515\) 7615.34 0.651596
\(516\) −32319.7 −2.75736
\(517\) 11608.5 0.987505
\(518\) −23930.6 −2.02983
\(519\) −26064.4 −2.20444
\(520\) −12544.8 −1.05793
\(521\) 21063.8 1.77125 0.885624 0.464403i \(-0.153731\pi\)
0.885624 + 0.464403i \(0.153731\pi\)
\(522\) −181.660 −0.0152319
\(523\) 7842.74 0.655715 0.327858 0.944727i \(-0.393673\pi\)
0.327858 + 0.944727i \(0.393673\pi\)
\(524\) −586.113 −0.0488635
\(525\) 11143.4 0.926356
\(526\) 20133.7 1.66896
\(527\) 1595.49 0.131880
\(528\) −29651.4 −2.44396
\(529\) −4970.22 −0.408500
\(530\) 16437.1 1.34714
\(531\) 2135.06 0.174489
\(532\) −46887.1 −3.82108
\(533\) 6770.56 0.550216
\(534\) 43782.1 3.54801
\(535\) −2584.01 −0.208816
\(536\) −28796.3 −2.32054
\(537\) 6261.26 0.503153
\(538\) 36989.3 2.96417
\(539\) −13173.1 −1.05270
\(540\) 3622.86 0.288709
\(541\) −16264.3 −1.29253 −0.646264 0.763114i \(-0.723670\pi\)
−0.646264 + 0.763114i \(0.723670\pi\)
\(542\) −25026.9 −1.98339
\(543\) −8981.96 −0.709858
\(544\) 773.022 0.0609247
\(545\) 12067.1 0.948437
\(546\) 33591.9 2.63296
\(547\) 547.000 0.0427569
\(548\) −7370.77 −0.574568
\(549\) −11216.9 −0.871994
\(550\) −14364.6 −1.11365
\(551\) 136.195 0.0105302
\(552\) 27657.0 2.13254
\(553\) −1212.12 −0.0932091
\(554\) 5368.00 0.411668
\(555\) −11964.2 −0.915049
\(556\) 35770.6 2.72844
\(557\) 5243.78 0.398898 0.199449 0.979908i \(-0.436085\pi\)
0.199449 + 0.979908i \(0.436085\pi\)
\(558\) 16970.1 1.28745
\(559\) −9213.84 −0.697145
\(560\) −16086.5 −1.21389
\(561\) 5273.24 0.396856
\(562\) −19872.3 −1.49157
\(563\) −9019.83 −0.675205 −0.337602 0.941289i \(-0.609616\pi\)
−0.337602 + 0.941289i \(0.609616\pi\)
\(564\) −30076.9 −2.24551
\(565\) −10844.3 −0.807476
\(566\) −45517.4 −3.38028
\(567\) 15375.6 1.13883
\(568\) 4348.19 0.321208
\(569\) 19137.7 1.41000 0.705002 0.709205i \(-0.250946\pi\)
0.705002 + 0.709205i \(0.250946\pi\)
\(570\) −34700.8 −2.54992
\(571\) 7331.59 0.537333 0.268667 0.963233i \(-0.413417\pi\)
0.268667 + 0.963233i \(0.413417\pi\)
\(572\) −29252.0 −2.13827
\(573\) 28266.4 2.06081
\(574\) 23112.8 1.68068
\(575\) 5032.95 0.365024
\(576\) −11362.8 −0.821965
\(577\) 14847.9 1.07128 0.535639 0.844447i \(-0.320071\pi\)
0.535639 + 0.844447i \(0.320071\pi\)
\(578\) 23386.0 1.68292
\(579\) 38032.6 2.72985
\(580\) 161.699 0.0115762
\(581\) 3950.02 0.282056
\(582\) 32946.7 2.34654
\(583\) 19918.5 1.41499
\(584\) −7627.11 −0.540432
\(585\) 8913.61 0.629970
\(586\) −24529.1 −1.72916
\(587\) −5219.58 −0.367010 −0.183505 0.983019i \(-0.558744\pi\)
−0.183505 + 0.983019i \(0.558744\pi\)
\(588\) 34130.8 2.39376
\(589\) −12722.9 −0.890048
\(590\) −2813.28 −0.196307
\(591\) 16625.5 1.15716
\(592\) −15602.6 −1.08321
\(593\) 3989.63 0.276280 0.138140 0.990413i \(-0.455888\pi\)
0.138140 + 0.990413i \(0.455888\pi\)
\(594\) 6498.86 0.448908
\(595\) 2860.83 0.197114
\(596\) −23376.8 −1.60663
\(597\) 37012.1 2.53736
\(598\) 15171.9 1.03750
\(599\) 17960.6 1.22513 0.612563 0.790422i \(-0.290139\pi\)
0.612563 + 0.790422i \(0.290139\pi\)
\(600\) 19341.5 1.31602
\(601\) 13827.5 0.938496 0.469248 0.883067i \(-0.344525\pi\)
0.469248 + 0.883067i \(0.344525\pi\)
\(602\) −31453.5 −2.12948
\(603\) 20461.0 1.38182
\(604\) 6267.79 0.422240
\(605\) 8482.64 0.570030
\(606\) 63921.5 4.28487
\(607\) −3326.63 −0.222445 −0.111222 0.993796i \(-0.535477\pi\)
−0.111222 + 0.993796i \(0.535477\pi\)
\(608\) −6164.31 −0.411177
\(609\) −225.017 −0.0149724
\(610\) 14780.0 0.981025
\(611\) −8574.45 −0.567733
\(612\) −7251.45 −0.478958
\(613\) 5455.39 0.359447 0.179724 0.983717i \(-0.442480\pi\)
0.179724 + 0.983717i \(0.442480\pi\)
\(614\) 21203.4 1.39365
\(615\) 11555.4 0.757653
\(616\) −51894.6 −3.39431
\(617\) −6279.23 −0.409712 −0.204856 0.978792i \(-0.565673\pi\)
−0.204856 + 0.978792i \(0.565673\pi\)
\(618\) −35394.3 −2.30383
\(619\) −6058.99 −0.393427 −0.196713 0.980461i \(-0.563027\pi\)
−0.196713 + 0.980461i \(0.563027\pi\)
\(620\) −15105.4 −0.978461
\(621\) −2277.02 −0.147139
\(622\) 3396.91 0.218977
\(623\) 28783.4 1.85102
\(624\) 21901.6 1.40508
\(625\) −4689.38 −0.300120
\(626\) 37755.2 2.41055
\(627\) −42050.4 −2.67836
\(628\) −49678.0 −3.15664
\(629\) 2774.78 0.175895
\(630\) 30428.6 1.92429
\(631\) 17595.0 1.11006 0.555030 0.831830i \(-0.312707\pi\)
0.555030 + 0.831830i \(0.312707\pi\)
\(632\) −2103.87 −0.132417
\(633\) −3373.30 −0.211811
\(634\) 18920.4 1.18521
\(635\) 9525.65 0.595298
\(636\) −51607.8 −3.21758
\(637\) 9730.14 0.605215
\(638\) 290.064 0.0179996
\(639\) −3089.58 −0.191271
\(640\) 18487.6 1.14186
\(641\) −8462.48 −0.521447 −0.260724 0.965413i \(-0.583961\pi\)
−0.260724 + 0.965413i \(0.583961\pi\)
\(642\) 12009.9 0.738305
\(643\) 19888.7 1.21981 0.609903 0.792476i \(-0.291208\pi\)
0.609903 + 0.792476i \(0.291208\pi\)
\(644\) 34987.6 2.14084
\(645\) −15725.3 −0.959975
\(646\) 8047.91 0.490156
\(647\) −23954.5 −1.45556 −0.727781 0.685809i \(-0.759448\pi\)
−0.727781 + 0.685809i \(0.759448\pi\)
\(648\) 26687.4 1.61787
\(649\) −3409.14 −0.206195
\(650\) 10610.2 0.640258
\(651\) 21020.4 1.26552
\(652\) 31969.0 1.92025
\(653\) 20195.9 1.21030 0.605151 0.796111i \(-0.293113\pi\)
0.605151 + 0.796111i \(0.293113\pi\)
\(654\) −56085.1 −3.35337
\(655\) −285.176 −0.0170118
\(656\) 15069.4 0.896891
\(657\) 5419.40 0.321813
\(658\) −29270.8 −1.73419
\(659\) 17827.1 1.05379 0.526894 0.849931i \(-0.323357\pi\)
0.526894 + 0.849931i \(0.323357\pi\)
\(660\) −49924.6 −2.94442
\(661\) −16220.9 −0.954491 −0.477245 0.878770i \(-0.658365\pi\)
−0.477245 + 0.878770i \(0.658365\pi\)
\(662\) −24274.0 −1.42513
\(663\) −3895.01 −0.228159
\(664\) 6856.02 0.400701
\(665\) −22813.2 −1.33031
\(666\) 29513.3 1.71714
\(667\) −101.630 −0.00589975
\(668\) 20781.8 1.20370
\(669\) −33411.8 −1.93090
\(670\) −26960.7 −1.55460
\(671\) 17910.4 1.03044
\(672\) 10184.5 0.584635
\(673\) −11195.9 −0.641261 −0.320630 0.947204i \(-0.603895\pi\)
−0.320630 + 0.947204i \(0.603895\pi\)
\(674\) −1933.15 −0.110478
\(675\) −1592.40 −0.0908020
\(676\) −14985.8 −0.852627
\(677\) −21610.9 −1.22684 −0.613422 0.789755i \(-0.710207\pi\)
−0.613422 + 0.789755i \(0.710207\pi\)
\(678\) 50401.9 2.85497
\(679\) 21660.0 1.22421
\(680\) 4965.53 0.280028
\(681\) −43296.6 −2.43631
\(682\) −27096.8 −1.52139
\(683\) 18699.8 1.04763 0.523814 0.851833i \(-0.324509\pi\)
0.523814 + 0.851833i \(0.324509\pi\)
\(684\) 57825.3 3.23246
\(685\) −3586.28 −0.200036
\(686\) −8957.11 −0.498519
\(687\) 12894.9 0.716116
\(688\) −20507.5 −1.13639
\(689\) −14712.6 −0.813504
\(690\) 25894.0 1.42865
\(691\) −29727.9 −1.63662 −0.818309 0.574778i \(-0.805088\pi\)
−0.818309 + 0.574778i \(0.805088\pi\)
\(692\) −57230.9 −3.14392
\(693\) 36873.4 2.02122
\(694\) 59471.1 3.25287
\(695\) 17404.4 0.949906
\(696\) −390.561 −0.0212704
\(697\) −2679.95 −0.145639
\(698\) −52697.1 −2.85761
\(699\) −32667.2 −1.76765
\(700\) 24468.0 1.32115
\(701\) −19538.7 −1.05274 −0.526368 0.850257i \(-0.676447\pi\)
−0.526368 + 0.850257i \(0.676447\pi\)
\(702\) −4800.30 −0.258085
\(703\) −22126.9 −1.18710
\(704\) 18143.5 0.971321
\(705\) −14634.1 −0.781774
\(706\) −33516.6 −1.78670
\(707\) 42023.6 2.23544
\(708\) 8832.89 0.468871
\(709\) −15264.0 −0.808534 −0.404267 0.914641i \(-0.632473\pi\)
−0.404267 + 0.914641i \(0.632473\pi\)
\(710\) 4071.01 0.215187
\(711\) 1494.89 0.0788507
\(712\) 49959.2 2.62964
\(713\) 9493.94 0.498669
\(714\) −13296.5 −0.696931
\(715\) −14232.7 −0.744439
\(716\) 13748.1 0.717586
\(717\) −36329.4 −1.89226
\(718\) −49335.7 −2.56434
\(719\) 1647.58 0.0854582 0.0427291 0.999087i \(-0.486395\pi\)
0.0427291 + 0.999087i \(0.486395\pi\)
\(720\) 19839.2 1.02689
\(721\) −23269.1 −1.20192
\(722\) −30118.5 −1.55249
\(723\) −49935.7 −2.56864
\(724\) −19722.1 −1.01238
\(725\) −71.0735 −0.00364083
\(726\) −39425.3 −2.01544
\(727\) −1838.94 −0.0938138 −0.0469069 0.998899i \(-0.514936\pi\)
−0.0469069 + 0.998899i \(0.514936\pi\)
\(728\) 38331.3 1.95144
\(729\) −24459.8 −1.24268
\(730\) −7140.92 −0.362051
\(731\) 3647.07 0.184530
\(732\) −46405.0 −2.34314
\(733\) −25709.6 −1.29551 −0.647754 0.761850i \(-0.724292\pi\)
−0.647754 + 0.761850i \(0.724292\pi\)
\(734\) −8360.92 −0.420446
\(735\) 16606.5 0.833387
\(736\) 4599.86 0.230371
\(737\) −32671.0 −1.63290
\(738\) −28504.7 −1.42178
\(739\) 31114.5 1.54880 0.774400 0.632696i \(-0.218052\pi\)
0.774400 + 0.632696i \(0.218052\pi\)
\(740\) −26270.3 −1.30502
\(741\) 31060.0 1.53983
\(742\) −50224.6 −2.48491
\(743\) −25606.2 −1.26433 −0.632166 0.774833i \(-0.717834\pi\)
−0.632166 + 0.774833i \(0.717834\pi\)
\(744\) 36484.9 1.79785
\(745\) −11374.1 −0.559349
\(746\) 49927.7 2.45038
\(747\) −4871.51 −0.238607
\(748\) 11578.7 0.565987
\(749\) 7895.59 0.385178
\(750\) 56262.6 2.73922
\(751\) −31811.8 −1.54571 −0.772856 0.634582i \(-0.781172\pi\)
−0.772856 + 0.634582i \(0.781172\pi\)
\(752\) −19084.3 −0.925444
\(753\) 28971.2 1.40209
\(754\) −214.252 −0.0103483
\(755\) 3049.62 0.147003
\(756\) −11069.9 −0.532549
\(757\) −7006.96 −0.336423 −0.168211 0.985751i \(-0.553799\pi\)
−0.168211 + 0.985751i \(0.553799\pi\)
\(758\) 2874.40 0.137735
\(759\) 31378.4 1.50061
\(760\) −39596.6 −1.88990
\(761\) 11883.4 0.566062 0.283031 0.959111i \(-0.408660\pi\)
0.283031 + 0.959111i \(0.408660\pi\)
\(762\) −44273.0 −2.10478
\(763\) −36871.8 −1.74947
\(764\) 62065.8 2.93909
\(765\) −3528.23 −0.166749
\(766\) −28311.4 −1.33542
\(767\) 2518.12 0.118545
\(768\) −63347.0 −2.97635
\(769\) 32666.7 1.53185 0.765925 0.642930i \(-0.222281\pi\)
0.765925 + 0.642930i \(0.222281\pi\)
\(770\) −48586.6 −2.27395
\(771\) 26429.6 1.23455
\(772\) 83509.8 3.89324
\(773\) −23040.7 −1.07208 −0.536039 0.844193i \(-0.680080\pi\)
−0.536039 + 0.844193i \(0.680080\pi\)
\(774\) 38791.2 1.80145
\(775\) 6639.44 0.307736
\(776\) 37595.1 1.73916
\(777\) 36557.4 1.68789
\(778\) −57958.6 −2.67084
\(779\) 21370.8 0.982910
\(780\) 36876.2 1.69279
\(781\) 4933.26 0.226025
\(782\) −6005.42 −0.274621
\(783\) 32.1552 0.00146760
\(784\) 21656.6 0.986543
\(785\) −24171.1 −1.09898
\(786\) 1325.43 0.0601484
\(787\) −37650.0 −1.70531 −0.852654 0.522476i \(-0.825008\pi\)
−0.852654 + 0.522476i \(0.825008\pi\)
\(788\) 36505.4 1.65032
\(789\) −30757.1 −1.38781
\(790\) −1969.76 −0.0887100
\(791\) 33135.5 1.48946
\(792\) 64000.9 2.87143
\(793\) −13229.3 −0.592417
\(794\) −15526.7 −0.693983
\(795\) −25110.0 −1.12020
\(796\) 81269.2 3.61873
\(797\) 41360.9 1.83824 0.919121 0.393976i \(-0.128901\pi\)
0.919121 + 0.393976i \(0.128901\pi\)
\(798\) 106030. 4.70355
\(799\) 3393.98 0.150276
\(800\) 3216.84 0.142166
\(801\) −35498.2 −1.56588
\(802\) −390.543 −0.0171952
\(803\) −8653.37 −0.380288
\(804\) 84648.7 3.71309
\(805\) 17023.4 0.745335
\(806\) 20014.7 0.874674
\(807\) −56506.4 −2.46483
\(808\) 72940.1 3.17577
\(809\) −7123.11 −0.309562 −0.154781 0.987949i \(-0.549467\pi\)
−0.154781 + 0.987949i \(0.549467\pi\)
\(810\) 24986.2 1.08386
\(811\) 26529.7 1.14869 0.574343 0.818615i \(-0.305258\pi\)
0.574343 + 0.818615i \(0.305258\pi\)
\(812\) −494.081 −0.0213532
\(813\) 38232.1 1.64927
\(814\) −47125.1 −2.02916
\(815\) 15554.7 0.668535
\(816\) −8669.21 −0.371916
\(817\) −29082.8 −1.24538
\(818\) −60193.6 −2.57288
\(819\) −27236.1 −1.16203
\(820\) 25372.6 1.08055
\(821\) 38289.6 1.62767 0.813835 0.581096i \(-0.197376\pi\)
0.813835 + 0.581096i \(0.197376\pi\)
\(822\) 16668.2 0.707263
\(823\) −13423.1 −0.568531 −0.284265 0.958746i \(-0.591750\pi\)
−0.284265 + 0.958746i \(0.591750\pi\)
\(824\) −40388.1 −1.70751
\(825\) 21944.0 0.926050
\(826\) 8596.16 0.362105
\(827\) −10248.3 −0.430918 −0.215459 0.976513i \(-0.569125\pi\)
−0.215459 + 0.976513i \(0.569125\pi\)
\(828\) −43149.7 −1.81106
\(829\) 9897.05 0.414643 0.207321 0.978273i \(-0.433525\pi\)
0.207321 + 0.978273i \(0.433525\pi\)
\(830\) 6418.99 0.268441
\(831\) −8200.37 −0.342320
\(832\) −13401.5 −0.558429
\(833\) −3851.43 −0.160197
\(834\) −80891.4 −3.35856
\(835\) 10111.5 0.419069
\(836\) −92332.0 −3.81982
\(837\) −3003.83 −0.124047
\(838\) −7265.15 −0.299488
\(839\) −10366.7 −0.426577 −0.213289 0.976989i \(-0.568417\pi\)
−0.213289 + 0.976989i \(0.568417\pi\)
\(840\) 65420.2 2.68716
\(841\) −24387.6 −0.999941
\(842\) −68438.4 −2.80112
\(843\) 30357.8 1.24031
\(844\) −7406.90 −0.302080
\(845\) −7291.40 −0.296842
\(846\) 36099.3 1.46704
\(847\) −25919.2 −1.05147
\(848\) −32746.1 −1.32607
\(849\) 69534.2 2.81085
\(850\) −4199.80 −0.169473
\(851\) 16511.3 0.665100
\(852\) −12781.8 −0.513964
\(853\) 6459.57 0.259286 0.129643 0.991561i \(-0.458617\pi\)
0.129643 + 0.991561i \(0.458617\pi\)
\(854\) −45161.2 −1.80959
\(855\) 28135.2 1.12538
\(856\) 13704.3 0.547201
\(857\) −18813.2 −0.749880 −0.374940 0.927049i \(-0.622337\pi\)
−0.374940 + 0.927049i \(0.622337\pi\)
\(858\) 66150.4 2.63210
\(859\) 11778.2 0.467830 0.233915 0.972257i \(-0.424846\pi\)
0.233915 + 0.972257i \(0.424846\pi\)
\(860\) −34528.8 −1.36910
\(861\) −35308.1 −1.39756
\(862\) 66549.8 2.62958
\(863\) −7300.66 −0.287969 −0.143985 0.989580i \(-0.545992\pi\)
−0.143985 + 0.989580i \(0.545992\pi\)
\(864\) −1455.37 −0.0573063
\(865\) −27845.9 −1.09456
\(866\) 65051.8 2.55260
\(867\) −35725.4 −1.39942
\(868\) 46155.4 1.80486
\(869\) −2386.96 −0.0931783
\(870\) −365.665 −0.0142497
\(871\) 24132.0 0.938784
\(872\) −63998.1 −2.48538
\(873\) −26713.0 −1.03562
\(874\) 47889.0 1.85340
\(875\) 36988.4 1.42907
\(876\) 22420.4 0.864744
\(877\) 3116.91 0.120012 0.0600061 0.998198i \(-0.480888\pi\)
0.0600061 + 0.998198i \(0.480888\pi\)
\(878\) −27856.8 −1.07075
\(879\) 37471.7 1.43787
\(880\) −31678.1 −1.21349
\(881\) −13333.5 −0.509896 −0.254948 0.966955i \(-0.582058\pi\)
−0.254948 + 0.966955i \(0.582058\pi\)
\(882\) −40964.9 −1.56390
\(883\) −24300.6 −0.926138 −0.463069 0.886322i \(-0.653252\pi\)
−0.463069 + 0.886322i \(0.653252\pi\)
\(884\) −8552.45 −0.325396
\(885\) 4297.69 0.163237
\(886\) −57461.7 −2.17885
\(887\) −46623.4 −1.76489 −0.882447 0.470412i \(-0.844105\pi\)
−0.882447 + 0.470412i \(0.844105\pi\)
\(888\) 63452.4 2.39789
\(889\) −29106.2 −1.09808
\(890\) 46774.6 1.76167
\(891\) 30278.3 1.13845
\(892\) −73363.7 −2.75381
\(893\) −27064.6 −1.01420
\(894\) 52864.2 1.97768
\(895\) 6689.21 0.249828
\(896\) −56490.1 −2.10625
\(897\) −23177.2 −0.862726
\(898\) −48705.1 −1.80992
\(899\) −134.070 −0.00497384
\(900\) −30176.1 −1.11763
\(901\) 5823.60 0.215330
\(902\) 45514.7 1.68012
\(903\) 48049.7 1.77076
\(904\) 57513.0 2.11599
\(905\) −9595.88 −0.352462
\(906\) −14173.9 −0.519755
\(907\) −21815.4 −0.798643 −0.399322 0.916811i \(-0.630754\pi\)
−0.399322 + 0.916811i \(0.630754\pi\)
\(908\) −95068.2 −3.47461
\(909\) −51827.1 −1.89109
\(910\) 35887.9 1.30733
\(911\) −7359.25 −0.267643 −0.133822 0.991005i \(-0.542725\pi\)
−0.133822 + 0.991005i \(0.542725\pi\)
\(912\) 69130.9 2.51004
\(913\) 7778.53 0.281963
\(914\) −4470.58 −0.161787
\(915\) −22578.6 −0.815764
\(916\) 28313.9 1.02131
\(917\) 871.373 0.0313798
\(918\) 1900.08 0.0683137
\(919\) −23998.6 −0.861415 −0.430707 0.902492i \(-0.641736\pi\)
−0.430707 + 0.902492i \(0.641736\pi\)
\(920\) 29547.3 1.05886
\(921\) −32391.2 −1.15888
\(922\) −17314.0 −0.618444
\(923\) −3643.89 −0.129946
\(924\) 152548. 5.43123
\(925\) 11546.9 0.410444
\(926\) 76068.5 2.69953
\(927\) 28697.5 1.01677
\(928\) −64.9575 −0.00229777
\(929\) 29123.4 1.02853 0.514267 0.857630i \(-0.328064\pi\)
0.514267 + 0.857630i \(0.328064\pi\)
\(930\) 34159.2 1.20443
\(931\) 30712.5 1.08116
\(932\) −71728.9 −2.52098
\(933\) −5189.25 −0.182088
\(934\) −47748.6 −1.67279
\(935\) 5633.66 0.197049
\(936\) −47273.5 −1.65083
\(937\) −11375.5 −0.396607 −0.198304 0.980141i \(-0.563543\pi\)
−0.198304 + 0.980141i \(0.563543\pi\)
\(938\) 82379.9 2.86759
\(939\) −57676.4 −2.00447
\(940\) −32132.7 −1.11495
\(941\) −1296.11 −0.0449012 −0.0224506 0.999748i \(-0.507147\pi\)
−0.0224506 + 0.999748i \(0.507147\pi\)
\(942\) 112342. 3.88565
\(943\) −15947.0 −0.550697
\(944\) 5604.63 0.193236
\(945\) −5386.09 −0.185407
\(946\) −61939.5 −2.12878
\(947\) 13965.0 0.479200 0.239600 0.970872i \(-0.422984\pi\)
0.239600 + 0.970872i \(0.422984\pi\)
\(948\) 6184.47 0.211880
\(949\) 6391.70 0.218634
\(950\) 33490.4 1.14376
\(951\) −28903.6 −0.985556
\(952\) −15172.5 −0.516536
\(953\) −27964.9 −0.950549 −0.475274 0.879838i \(-0.657651\pi\)
−0.475274 + 0.879838i \(0.657651\pi\)
\(954\) 61941.3 2.10212
\(955\) 30198.4 1.02324
\(956\) −79770.1 −2.69869
\(957\) −443.113 −0.0149674
\(958\) 77764.1 2.62259
\(959\) 10958.1 0.368984
\(960\) −22872.4 −0.768962
\(961\) −17266.7 −0.579593
\(962\) 34808.3 1.16660
\(963\) −9737.53 −0.325844
\(964\) −109646. −3.66334
\(965\) 40632.1 1.35543
\(966\) −79120.6 −2.63526
\(967\) 35904.7 1.19402 0.597010 0.802234i \(-0.296355\pi\)
0.597010 + 0.802234i \(0.296355\pi\)
\(968\) −44987.8 −1.49376
\(969\) −12294.3 −0.407586
\(970\) 35198.7 1.16511
\(971\) −30558.8 −1.00997 −0.504983 0.863129i \(-0.668501\pi\)
−0.504983 + 0.863129i \(0.668501\pi\)
\(972\) −90519.8 −2.98706
\(973\) −53180.1 −1.75218
\(974\) −72367.2 −2.38069
\(975\) −16208.6 −0.532402
\(976\) −29444.8 −0.965681
\(977\) 32885.2 1.07686 0.538430 0.842670i \(-0.319018\pi\)
0.538430 + 0.842670i \(0.319018\pi\)
\(978\) −72294.5 −2.36372
\(979\) 56681.5 1.85041
\(980\) 36463.6 1.18856
\(981\) 45473.5 1.47998
\(982\) −13971.9 −0.454033
\(983\) −39192.1 −1.27165 −0.635825 0.771833i \(-0.719340\pi\)
−0.635825 + 0.771833i \(0.719340\pi\)
\(984\) −61284.0 −1.98543
\(985\) 17761.9 0.574558
\(986\) 84.8062 0.00273913
\(987\) 44715.3 1.44205
\(988\) 68199.8 2.19608
\(989\) 21701.8 0.697754
\(990\) 59921.2 1.92366
\(991\) −33614.0 −1.07748 −0.538741 0.842472i \(-0.681100\pi\)
−0.538741 + 0.842472i \(0.681100\pi\)
\(992\) 6068.11 0.194216
\(993\) 37081.9 1.18505
\(994\) −12439.2 −0.396930
\(995\) 39541.9 1.25986
\(996\) −20153.8 −0.641161
\(997\) 3945.30 0.125325 0.0626624 0.998035i \(-0.480041\pi\)
0.0626624 + 0.998035i \(0.480041\pi\)
\(998\) 21736.7 0.689441
\(999\) −5224.08 −0.165448
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.1.5 65
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
547.4.a.a.1.5 65 1.1 even 1 trivial