Properties

Label 1849.4.a.h.1.2
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $0$
Dimension $30$
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] = [1849,4,Mod(1,1849)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1849, 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("1849.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1849 = 43^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1849.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: \(109.094531601\)
Analytic rank: \(0\)
Dimension: \(30\)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Character \(\chi\) \(=\) 1849.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.95333 q^{2} -0.318435 q^{3} +16.5355 q^{4} +12.4187 q^{5} +1.57731 q^{6} +3.53619 q^{7} -42.2793 q^{8} -26.8986 q^{9} +O(q^{10})\) \(q-4.95333 q^{2} -0.318435 q^{3} +16.5355 q^{4} +12.4187 q^{5} +1.57731 q^{6} +3.53619 q^{7} -42.2793 q^{8} -26.8986 q^{9} -61.5142 q^{10} +9.73366 q^{11} -5.26549 q^{12} +58.2480 q^{13} -17.5159 q^{14} -3.95456 q^{15} +77.1391 q^{16} +96.5329 q^{17} +133.238 q^{18} +130.512 q^{19} +205.350 q^{20} -1.12605 q^{21} -48.2140 q^{22} +86.1983 q^{23} +13.4632 q^{24} +29.2253 q^{25} -288.522 q^{26} +17.1632 q^{27} +58.4727 q^{28} +78.0061 q^{29} +19.5883 q^{30} -103.809 q^{31} -43.8618 q^{32} -3.09954 q^{33} -478.160 q^{34} +43.9150 q^{35} -444.782 q^{36} +433.942 q^{37} -646.468 q^{38} -18.5482 q^{39} -525.055 q^{40} -265.176 q^{41} +5.57768 q^{42} +160.951 q^{44} -334.047 q^{45} -426.969 q^{46} +515.826 q^{47} -24.5638 q^{48} -330.495 q^{49} -144.763 q^{50} -30.7395 q^{51} +963.161 q^{52} -142.256 q^{53} -85.0151 q^{54} +120.880 q^{55} -149.507 q^{56} -41.5595 q^{57} -386.390 q^{58} -441.215 q^{59} -65.3908 q^{60} +465.998 q^{61} +514.199 q^{62} -95.1185 q^{63} -399.851 q^{64} +723.367 q^{65} +15.3530 q^{66} +445.362 q^{67} +1596.22 q^{68} -27.4486 q^{69} -217.526 q^{70} +978.896 q^{71} +1137.25 q^{72} -28.4218 q^{73} -2149.46 q^{74} -9.30635 q^{75} +2158.08 q^{76} +34.4200 q^{77} +91.8755 q^{78} +6.16526 q^{79} +957.971 q^{80} +720.797 q^{81} +1313.51 q^{82} -773.485 q^{83} -18.6197 q^{84} +1198.82 q^{85} -24.8399 q^{87} -411.532 q^{88} -18.0364 q^{89} +1654.65 q^{90} +205.976 q^{91} +1425.33 q^{92} +33.0563 q^{93} -2555.06 q^{94} +1620.79 q^{95} +13.9671 q^{96} +1468.04 q^{97} +1637.05 q^{98} -261.822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 30 q + 6 q^{2} + 2 q^{3} + 114 q^{4} + 27 q^{5} + 8 q^{6} + 48 q^{7} + 90 q^{8} + 216 q^{9} - 27 q^{10} + 80 q^{11} - 36 q^{12} - 13 q^{13} + 36 q^{14} + 16 q^{15} + 318 q^{16} + 66 q^{17} + 80 q^{18} + 254 q^{19} + 312 q^{20} - 548 q^{21} + 305 q^{22} - 105 q^{23} + 123 q^{24} + 523 q^{25} + 549 q^{26} - 10 q^{27} + 578 q^{28} + 793 q^{29} + 1560 q^{30} - 359 q^{31} + 676 q^{32} + 208 q^{33} + 1007 q^{34} - 514 q^{35} + 776 q^{36} + 510 q^{37} - 2066 q^{38} + 898 q^{39} - 1248 q^{40} - 270 q^{41} - 915 q^{42} + 3256 q^{44} + 807 q^{45} + 1960 q^{46} + 1421 q^{47} - 632 q^{48} + 386 q^{49} - 141 q^{50} + 209 q^{51} + 2825 q^{52} - 21 q^{53} + 2368 q^{54} + 2258 q^{55} + 2521 q^{56} - 1723 q^{57} - 347 q^{58} + 1752 q^{59} + 2711 q^{60} + 1759 q^{61} + 395 q^{62} + 2204 q^{63} + 222 q^{64} + 1151 q^{65} + 160 q^{66} - 3001 q^{67} + 1921 q^{68} + 1660 q^{69} + 1597 q^{70} + 727 q^{71} + 9100 q^{72} + 4623 q^{73} - 2649 q^{74} + 1027 q^{75} + 874 q^{76} + 3556 q^{77} - 4979 q^{78} + 546 q^{79} + 5809 q^{80} - 410 q^{81} - 4397 q^{82} - 492 q^{83} - 10611 q^{84} - 1723 q^{85} + 5937 q^{87} + 3974 q^{88} + 5218 q^{89} + 10492 q^{90} + 1104 q^{91} + 1060 q^{92} + 1997 q^{93} - 2134 q^{94} + 6346 q^{95} - 11984 q^{96} + 2590 q^{97} + 6270 q^{98} - 2693 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.95333 −1.75127 −0.875634 0.482975i \(-0.839556\pi\)
−0.875634 + 0.482975i \(0.839556\pi\)
\(3\) −0.318435 −0.0612828 −0.0306414 0.999530i \(-0.509755\pi\)
−0.0306414 + 0.999530i \(0.509755\pi\)
\(4\) 16.5355 2.06694
\(5\) 12.4187 1.11077 0.555383 0.831595i \(-0.312572\pi\)
0.555383 + 0.831595i \(0.312572\pi\)
\(6\) 1.57731 0.107323
\(7\) 3.53619 0.190936 0.0954681 0.995432i \(-0.469565\pi\)
0.0954681 + 0.995432i \(0.469565\pi\)
\(8\) −42.2793 −1.86850
\(9\) −26.8986 −0.996244
\(10\) −61.5142 −1.94525
\(11\) 9.73366 0.266801 0.133400 0.991062i \(-0.457410\pi\)
0.133400 + 0.991062i \(0.457410\pi\)
\(12\) −5.26549 −0.126668
\(13\) 58.2480 1.24270 0.621350 0.783533i \(-0.286585\pi\)
0.621350 + 0.783533i \(0.286585\pi\)
\(14\) −17.5159 −0.334380
\(15\) −3.95456 −0.0680709
\(16\) 77.1391 1.20530
\(17\) 96.5329 1.37722 0.688608 0.725134i \(-0.258222\pi\)
0.688608 + 0.725134i \(0.258222\pi\)
\(18\) 133.238 1.74469
\(19\) 130.512 1.57587 0.787933 0.615761i \(-0.211151\pi\)
0.787933 + 0.615761i \(0.211151\pi\)
\(20\) 205.350 2.29589
\(21\) −1.12605 −0.0117011
\(22\) −48.2140 −0.467239
\(23\) 86.1983 0.781460 0.390730 0.920505i \(-0.372223\pi\)
0.390730 + 0.920505i \(0.372223\pi\)
\(24\) 13.4632 0.114507
\(25\) 29.2253 0.233802
\(26\) −288.522 −2.17630
\(27\) 17.1632 0.122336
\(28\) 58.4727 0.394653
\(29\) 78.0061 0.499495 0.249748 0.968311i \(-0.419652\pi\)
0.249748 + 0.968311i \(0.419652\pi\)
\(30\) 19.5883 0.119210
\(31\) −103.809 −0.601439 −0.300719 0.953713i \(-0.597227\pi\)
−0.300719 + 0.953713i \(0.597227\pi\)
\(32\) −43.8618 −0.242305
\(33\) −3.09954 −0.0163503
\(34\) −478.160 −2.41187
\(35\) 43.9150 0.212085
\(36\) −444.782 −2.05918
\(37\) 433.942 1.92810 0.964050 0.265721i \(-0.0856100\pi\)
0.964050 + 0.265721i \(0.0856100\pi\)
\(38\) −646.468 −2.75976
\(39\) −18.5482 −0.0761562
\(40\) −525.055 −2.07546
\(41\) −265.176 −1.01009 −0.505043 0.863094i \(-0.668523\pi\)
−0.505043 + 0.863094i \(0.668523\pi\)
\(42\) 5.57768 0.0204918
\(43\) 0 0
\(44\) 160.951 0.551461
\(45\) −334.047 −1.10659
\(46\) −426.969 −1.36855
\(47\) 515.826 1.60087 0.800435 0.599419i \(-0.204602\pi\)
0.800435 + 0.599419i \(0.204602\pi\)
\(48\) −24.5638 −0.0738641
\(49\) −330.495 −0.963543
\(50\) −144.763 −0.409450
\(51\) −30.7395 −0.0843997
\(52\) 963.161 2.56858
\(53\) −142.256 −0.368687 −0.184343 0.982862i \(-0.559016\pi\)
−0.184343 + 0.982862i \(0.559016\pi\)
\(54\) −85.0151 −0.214242
\(55\) 120.880 0.296353
\(56\) −149.507 −0.356764
\(57\) −41.5595 −0.0965735
\(58\) −386.390 −0.874750
\(59\) −441.215 −0.973582 −0.486791 0.873518i \(-0.661833\pi\)
−0.486791 + 0.873518i \(0.661833\pi\)
\(60\) −65.3908 −0.140698
\(61\) 465.998 0.978115 0.489057 0.872252i \(-0.337341\pi\)
0.489057 + 0.872252i \(0.337341\pi\)
\(62\) 514.199 1.05328
\(63\) −95.1185 −0.190219
\(64\) −399.851 −0.780959
\(65\) 723.367 1.38035
\(66\) 15.3530 0.0286338
\(67\) 445.362 0.812084 0.406042 0.913854i \(-0.366909\pi\)
0.406042 + 0.913854i \(0.366909\pi\)
\(68\) 1596.22 2.84662
\(69\) −27.4486 −0.0478901
\(70\) −217.526 −0.371418
\(71\) 978.896 1.63625 0.818124 0.575042i \(-0.195014\pi\)
0.818124 + 0.575042i \(0.195014\pi\)
\(72\) 1137.25 1.86148
\(73\) −28.4218 −0.0455688 −0.0227844 0.999740i \(-0.507253\pi\)
−0.0227844 + 0.999740i \(0.507253\pi\)
\(74\) −2149.46 −3.37662
\(75\) −9.30635 −0.0143281
\(76\) 2158.08 3.25722
\(77\) 34.4200 0.0509419
\(78\) 91.8755 0.133370
\(79\) 6.16526 0.00878033 0.00439017 0.999990i \(-0.498603\pi\)
0.00439017 + 0.999990i \(0.498603\pi\)
\(80\) 957.971 1.33881
\(81\) 720.797 0.988747
\(82\) 1313.51 1.76893
\(83\) −773.485 −1.02290 −0.511452 0.859312i \(-0.670892\pi\)
−0.511452 + 0.859312i \(0.670892\pi\)
\(84\) −18.6197 −0.0241855
\(85\) 1198.82 1.52977
\(86\) 0 0
\(87\) −24.8399 −0.0306105
\(88\) −411.532 −0.498516
\(89\) −18.0364 −0.0214815 −0.0107408 0.999942i \(-0.503419\pi\)
−0.0107408 + 0.999942i \(0.503419\pi\)
\(90\) 1654.65 1.93794
\(91\) 205.976 0.237276
\(92\) 1425.33 1.61523
\(93\) 33.0563 0.0368579
\(94\) −2555.06 −2.80355
\(95\) 1620.79 1.75042
\(96\) 13.9671 0.0148491
\(97\) 1468.04 1.53667 0.768336 0.640047i \(-0.221085\pi\)
0.768336 + 0.640047i \(0.221085\pi\)
\(98\) 1637.05 1.68742
\(99\) −261.822 −0.265799
\(100\) 483.255 0.483255
\(101\) 457.985 0.451200 0.225600 0.974220i \(-0.427566\pi\)
0.225600 + 0.974220i \(0.427566\pi\)
\(102\) 152.263 0.147807
\(103\) −1738.76 −1.66335 −0.831674 0.555265i \(-0.812617\pi\)
−0.831674 + 0.555265i \(0.812617\pi\)
\(104\) −2462.68 −2.32198
\(105\) −13.9841 −0.0129972
\(106\) 704.643 0.645669
\(107\) −13.2007 −0.0119267 −0.00596337 0.999982i \(-0.501898\pi\)
−0.00596337 + 0.999982i \(0.501898\pi\)
\(108\) 283.802 0.252860
\(109\) −1087.36 −0.955504 −0.477752 0.878495i \(-0.658548\pi\)
−0.477752 + 0.878495i \(0.658548\pi\)
\(110\) −598.758 −0.518994
\(111\) −138.182 −0.118159
\(112\) 272.778 0.230135
\(113\) 399.977 0.332979 0.166490 0.986043i \(-0.446757\pi\)
0.166490 + 0.986043i \(0.446757\pi\)
\(114\) 205.858 0.169126
\(115\) 1070.47 0.868020
\(116\) 1289.87 1.03243
\(117\) −1566.79 −1.23803
\(118\) 2185.49 1.70500
\(119\) 341.358 0.262960
\(120\) 167.196 0.127190
\(121\) −1236.26 −0.928817
\(122\) −2308.25 −1.71294
\(123\) 84.4413 0.0619010
\(124\) −1716.53 −1.24314
\(125\) −1189.40 −0.851067
\(126\) 471.154 0.333125
\(127\) −935.559 −0.653680 −0.326840 0.945080i \(-0.605984\pi\)
−0.326840 + 0.945080i \(0.605984\pi\)
\(128\) 2331.49 1.60997
\(129\) 0 0
\(130\) −3583.08 −2.41736
\(131\) 133.188 0.0888297 0.0444149 0.999013i \(-0.485858\pi\)
0.0444149 + 0.999013i \(0.485858\pi\)
\(132\) −51.2524 −0.0337951
\(133\) 461.514 0.300890
\(134\) −2206.03 −1.42218
\(135\) 213.145 0.135886
\(136\) −4081.34 −2.57332
\(137\) 520.757 0.324754 0.162377 0.986729i \(-0.448084\pi\)
0.162377 + 0.986729i \(0.448084\pi\)
\(138\) 135.962 0.0838684
\(139\) 1806.24 1.10218 0.551090 0.834446i \(-0.314212\pi\)
0.551090 + 0.834446i \(0.314212\pi\)
\(140\) 726.157 0.438368
\(141\) −164.257 −0.0981059
\(142\) −4848.80 −2.86551
\(143\) 566.966 0.331553
\(144\) −2074.93 −1.20077
\(145\) 968.738 0.554823
\(146\) 140.783 0.0798032
\(147\) 105.241 0.0590487
\(148\) 7175.46 3.98527
\(149\) −1327.42 −0.729841 −0.364920 0.931039i \(-0.618904\pi\)
−0.364920 + 0.931039i \(0.618904\pi\)
\(150\) 46.0975 0.0250923
\(151\) −1591.44 −0.857681 −0.428841 0.903380i \(-0.641078\pi\)
−0.428841 + 0.903380i \(0.641078\pi\)
\(152\) −5517.94 −2.94450
\(153\) −2596.60 −1.37204
\(154\) −170.494 −0.0892129
\(155\) −1289.17 −0.668058
\(156\) −306.704 −0.157410
\(157\) 694.025 0.352798 0.176399 0.984319i \(-0.443555\pi\)
0.176399 + 0.984319i \(0.443555\pi\)
\(158\) −30.5386 −0.0153767
\(159\) 45.2994 0.0225942
\(160\) −544.709 −0.269144
\(161\) 304.813 0.149209
\(162\) −3570.35 −1.73156
\(163\) −2263.22 −1.08754 −0.543769 0.839235i \(-0.683003\pi\)
−0.543769 + 0.839235i \(0.683003\pi\)
\(164\) −4384.82 −2.08779
\(165\) −38.4924 −0.0181614
\(166\) 3831.33 1.79138
\(167\) 866.676 0.401589 0.200795 0.979633i \(-0.435648\pi\)
0.200795 + 0.979633i \(0.435648\pi\)
\(168\) 47.6084 0.0218635
\(169\) 1195.83 0.544301
\(170\) −5938.15 −2.67903
\(171\) −3510.58 −1.56995
\(172\) 0 0
\(173\) −2626.97 −1.15448 −0.577240 0.816575i \(-0.695870\pi\)
−0.577240 + 0.816575i \(0.695870\pi\)
\(174\) 123.040 0.0536072
\(175\) 103.346 0.0446413
\(176\) 750.846 0.321575
\(177\) 140.498 0.0596639
\(178\) 89.3403 0.0376199
\(179\) 609.964 0.254698 0.127349 0.991858i \(-0.459353\pi\)
0.127349 + 0.991858i \(0.459353\pi\)
\(180\) −5523.64 −2.28726
\(181\) −1467.02 −0.602446 −0.301223 0.953554i \(-0.597395\pi\)
−0.301223 + 0.953554i \(0.597395\pi\)
\(182\) −1020.27 −0.415534
\(183\) −148.390 −0.0599416
\(184\) −3644.40 −1.46016
\(185\) 5389.02 2.14167
\(186\) −163.739 −0.0645480
\(187\) 939.618 0.367442
\(188\) 8529.45 3.30890
\(189\) 60.6923 0.0233583
\(190\) −8028.33 −3.06545
\(191\) 640.656 0.242703 0.121351 0.992610i \(-0.461277\pi\)
0.121351 + 0.992610i \(0.461277\pi\)
\(192\) 127.327 0.0478594
\(193\) 205.292 0.0765660 0.0382830 0.999267i \(-0.487811\pi\)
0.0382830 + 0.999267i \(0.487811\pi\)
\(194\) −7271.70 −2.69112
\(195\) −230.345 −0.0845917
\(196\) −5464.91 −1.99159
\(197\) 3746.36 1.35491 0.677454 0.735565i \(-0.263083\pi\)
0.677454 + 0.735565i \(0.263083\pi\)
\(198\) 1296.89 0.465485
\(199\) 166.688 0.0593779 0.0296890 0.999559i \(-0.490548\pi\)
0.0296890 + 0.999559i \(0.490548\pi\)
\(200\) −1235.62 −0.436859
\(201\) −141.819 −0.0497668
\(202\) −2268.55 −0.790173
\(203\) 275.844 0.0953717
\(204\) −508.293 −0.174449
\(205\) −3293.15 −1.12197
\(206\) 8612.64 2.91297
\(207\) −2318.61 −0.778525
\(208\) 4493.20 1.49782
\(209\) 1270.36 0.420442
\(210\) 69.2678 0.0227616
\(211\) −4969.17 −1.62129 −0.810644 0.585539i \(-0.800883\pi\)
−0.810644 + 0.585539i \(0.800883\pi\)
\(212\) −2352.28 −0.762053
\(213\) −311.715 −0.100274
\(214\) 65.3875 0.0208869
\(215\) 0 0
\(216\) −725.647 −0.228584
\(217\) −367.087 −0.114836
\(218\) 5386.04 1.67334
\(219\) 9.05050 0.00279259
\(220\) 1998.81 0.612544
\(221\) 5622.85 1.71147
\(222\) 684.464 0.206929
\(223\) 4304.44 1.29259 0.646293 0.763090i \(-0.276319\pi\)
0.646293 + 0.763090i \(0.276319\pi\)
\(224\) −155.104 −0.0462647
\(225\) −786.119 −0.232924
\(226\) −1981.22 −0.583136
\(227\) 1141.43 0.333742 0.166871 0.985979i \(-0.446634\pi\)
0.166871 + 0.985979i \(0.446634\pi\)
\(228\) −687.208 −0.199612
\(229\) 2198.56 0.634433 0.317216 0.948353i \(-0.397252\pi\)
0.317216 + 0.948353i \(0.397252\pi\)
\(230\) −5302.42 −1.52014
\(231\) −10.9605 −0.00312186
\(232\) −3298.04 −0.933305
\(233\) −2798.50 −0.786849 −0.393424 0.919357i \(-0.628710\pi\)
−0.393424 + 0.919357i \(0.628710\pi\)
\(234\) 7760.83 2.16813
\(235\) 6405.91 1.77819
\(236\) −7295.72 −2.01234
\(237\) −1.96324 −0.000538084 0
\(238\) −1690.86 −0.460514
\(239\) 1924.99 0.520992 0.260496 0.965475i \(-0.416114\pi\)
0.260496 + 0.965475i \(0.416114\pi\)
\(240\) −305.052 −0.0820458
\(241\) 299.388 0.0800218 0.0400109 0.999199i \(-0.487261\pi\)
0.0400109 + 0.999199i \(0.487261\pi\)
\(242\) 6123.59 1.62661
\(243\) −692.933 −0.182929
\(244\) 7705.52 2.02170
\(245\) −4104.34 −1.07027
\(246\) −418.266 −0.108405
\(247\) 7602.05 1.95833
\(248\) 4388.95 1.12379
\(249\) 246.305 0.0626864
\(250\) 5891.51 1.49045
\(251\) 4016.43 1.01002 0.505010 0.863114i \(-0.331489\pi\)
0.505010 + 0.863114i \(0.331489\pi\)
\(252\) −1572.83 −0.393171
\(253\) 839.024 0.208494
\(254\) 4634.13 1.14477
\(255\) −381.746 −0.0937484
\(256\) −8349.84 −2.03853
\(257\) −3740.00 −0.907762 −0.453881 0.891062i \(-0.649961\pi\)
−0.453881 + 0.891062i \(0.649961\pi\)
\(258\) 0 0
\(259\) 1534.50 0.368144
\(260\) 11961.3 2.85310
\(261\) −2098.25 −0.497619
\(262\) −659.725 −0.155565
\(263\) −5952.87 −1.39570 −0.697851 0.716243i \(-0.745860\pi\)
−0.697851 + 0.716243i \(0.745860\pi\)
\(264\) 131.046 0.0305505
\(265\) −1766.64 −0.409525
\(266\) −2286.03 −0.526939
\(267\) 5.74342 0.00131645
\(268\) 7364.29 1.67853
\(269\) 887.028 0.201052 0.100526 0.994934i \(-0.467947\pi\)
0.100526 + 0.994934i \(0.467947\pi\)
\(270\) −1055.78 −0.237973
\(271\) −8634.54 −1.93546 −0.967732 0.251981i \(-0.918918\pi\)
−0.967732 + 0.251981i \(0.918918\pi\)
\(272\) 7446.47 1.65996
\(273\) −65.5899 −0.0145410
\(274\) −2579.48 −0.568731
\(275\) 284.469 0.0623786
\(276\) −453.876 −0.0989860
\(277\) −7032.45 −1.52541 −0.762705 0.646746i \(-0.776129\pi\)
−0.762705 + 0.646746i \(0.776129\pi\)
\(278\) −8946.89 −1.93021
\(279\) 2792.31 0.599180
\(280\) −1856.69 −0.396281
\(281\) −6538.48 −1.38809 −0.694045 0.719932i \(-0.744173\pi\)
−0.694045 + 0.719932i \(0.744173\pi\)
\(282\) 813.620 0.171810
\(283\) −5321.63 −1.11780 −0.558901 0.829235i \(-0.688777\pi\)
−0.558901 + 0.829235i \(0.688777\pi\)
\(284\) 16186.5 3.38202
\(285\) −516.117 −0.107271
\(286\) −2808.37 −0.580638
\(287\) −937.712 −0.192862
\(288\) 1179.82 0.241395
\(289\) 4405.61 0.896725
\(290\) −4798.48 −0.971643
\(291\) −467.476 −0.0941716
\(292\) −469.969 −0.0941879
\(293\) 9700.76 1.93421 0.967106 0.254373i \(-0.0818689\pi\)
0.967106 + 0.254373i \(0.0818689\pi\)
\(294\) −521.295 −0.103410
\(295\) −5479.34 −1.08142
\(296\) −18346.8 −3.60265
\(297\) 167.061 0.0326392
\(298\) 6575.14 1.27815
\(299\) 5020.88 0.971120
\(300\) −153.885 −0.0296152
\(301\) 0 0
\(302\) 7882.95 1.50203
\(303\) −145.839 −0.0276508
\(304\) 10067.6 1.89939
\(305\) 5787.12 1.08646
\(306\) 12861.8 2.40282
\(307\) 917.394 0.170549 0.0852743 0.996358i \(-0.472823\pi\)
0.0852743 + 0.996358i \(0.472823\pi\)
\(308\) 569.153 0.105294
\(309\) 553.681 0.101935
\(310\) 6385.71 1.16995
\(311\) 2039.76 0.371911 0.185956 0.982558i \(-0.440462\pi\)
0.185956 + 0.982558i \(0.440462\pi\)
\(312\) 784.204 0.142298
\(313\) 1019.23 0.184058 0.0920290 0.995756i \(-0.470665\pi\)
0.0920290 + 0.995756i \(0.470665\pi\)
\(314\) −3437.74 −0.617844
\(315\) −1181.25 −0.211289
\(316\) 101.946 0.0181484
\(317\) −200.716 −0.0355626 −0.0177813 0.999842i \(-0.505660\pi\)
−0.0177813 + 0.999842i \(0.505660\pi\)
\(318\) −224.383 −0.0395685
\(319\) 759.284 0.133266
\(320\) −4965.65 −0.867463
\(321\) 4.20357 0.000730904 0
\(322\) −1509.84 −0.261305
\(323\) 12598.7 2.17031
\(324\) 11918.7 2.04368
\(325\) 1702.31 0.290546
\(326\) 11210.5 1.90457
\(327\) 346.253 0.0585560
\(328\) 11211.4 1.88734
\(329\) 1824.06 0.305664
\(330\) 190.666 0.0318054
\(331\) 11939.2 1.98259 0.991297 0.131641i \(-0.0420247\pi\)
0.991297 + 0.131641i \(0.0420247\pi\)
\(332\) −12790.0 −2.11428
\(333\) −11672.4 −1.92086
\(334\) −4292.93 −0.703290
\(335\) 5530.84 0.902036
\(336\) −86.8622 −0.0141033
\(337\) −9933.49 −1.60567 −0.802837 0.596199i \(-0.796677\pi\)
−0.802837 + 0.596199i \(0.796677\pi\)
\(338\) −5923.35 −0.953218
\(339\) −127.367 −0.0204059
\(340\) 19823.1 3.16193
\(341\) −1010.44 −0.160464
\(342\) 17389.1 2.74940
\(343\) −2381.61 −0.374911
\(344\) 0 0
\(345\) −340.877 −0.0531947
\(346\) 13012.3 2.02180
\(347\) −3888.13 −0.601515 −0.300757 0.953701i \(-0.597239\pi\)
−0.300757 + 0.953701i \(0.597239\pi\)
\(348\) −410.740 −0.0632700
\(349\) −1958.57 −0.300401 −0.150201 0.988656i \(-0.547992\pi\)
−0.150201 + 0.988656i \(0.547992\pi\)
\(350\) −511.908 −0.0781789
\(351\) 999.722 0.152026
\(352\) −426.936 −0.0646470
\(353\) −2805.65 −0.423030 −0.211515 0.977375i \(-0.567840\pi\)
−0.211515 + 0.977375i \(0.567840\pi\)
\(354\) −695.936 −0.104487
\(355\) 12156.7 1.81749
\(356\) −298.241 −0.0444010
\(357\) −108.701 −0.0161150
\(358\) −3021.36 −0.446044
\(359\) 5817.68 0.855279 0.427639 0.903949i \(-0.359345\pi\)
0.427639 + 0.903949i \(0.359345\pi\)
\(360\) 14123.3 2.06767
\(361\) 10174.3 1.48335
\(362\) 7266.64 1.05504
\(363\) 393.667 0.0569206
\(364\) 3405.92 0.490436
\(365\) −352.963 −0.0506163
\(366\) 735.026 0.104974
\(367\) 1916.69 0.272617 0.136308 0.990666i \(-0.456476\pi\)
0.136308 + 0.990666i \(0.456476\pi\)
\(368\) 6649.26 0.941893
\(369\) 7132.86 1.00629
\(370\) −26693.6 −3.75064
\(371\) −503.045 −0.0703956
\(372\) 546.603 0.0761830
\(373\) 6773.49 0.940263 0.470132 0.882596i \(-0.344206\pi\)
0.470132 + 0.882596i \(0.344206\pi\)
\(374\) −4654.24 −0.643490
\(375\) 378.747 0.0521558
\(376\) −21808.7 −2.99122
\(377\) 4543.70 0.620722
\(378\) −300.629 −0.0409066
\(379\) 7501.32 1.01667 0.508333 0.861160i \(-0.330262\pi\)
0.508333 + 0.861160i \(0.330262\pi\)
\(380\) 26800.6 3.61801
\(381\) 297.915 0.0400594
\(382\) −3173.38 −0.425037
\(383\) 3690.85 0.492411 0.246206 0.969218i \(-0.420816\pi\)
0.246206 + 0.969218i \(0.420816\pi\)
\(384\) −742.428 −0.0986637
\(385\) 427.454 0.0565845
\(386\) −1016.88 −0.134088
\(387\) 0 0
\(388\) 24274.8 3.17621
\(389\) 3452.25 0.449964 0.224982 0.974363i \(-0.427768\pi\)
0.224982 + 0.974363i \(0.427768\pi\)
\(390\) 1140.98 0.148143
\(391\) 8320.97 1.07624
\(392\) 13973.1 1.80038
\(393\) −42.4117 −0.00544374
\(394\) −18557.0 −2.37281
\(395\) 76.5648 0.00975290
\(396\) −4329.36 −0.549390
\(397\) −5704.24 −0.721128 −0.360564 0.932734i \(-0.617416\pi\)
−0.360564 + 0.932734i \(0.617416\pi\)
\(398\) −825.662 −0.103987
\(399\) −146.962 −0.0184394
\(400\) 2254.41 0.281802
\(401\) −10612.3 −1.32158 −0.660788 0.750573i \(-0.729778\pi\)
−0.660788 + 0.750573i \(0.729778\pi\)
\(402\) 702.476 0.0871551
\(403\) −6046.65 −0.747407
\(404\) 7573.02 0.932604
\(405\) 8951.39 1.09827
\(406\) −1366.35 −0.167021
\(407\) 4223.85 0.514418
\(408\) 1299.64 0.157701
\(409\) 9169.13 1.10852 0.554260 0.832344i \(-0.313001\pi\)
0.554260 + 0.832344i \(0.313001\pi\)
\(410\) 16312.1 1.96487
\(411\) −165.827 −0.0199018
\(412\) −28751.2 −3.43804
\(413\) −1560.22 −0.185892
\(414\) 11484.9 1.36341
\(415\) −9605.71 −1.13621
\(416\) −2554.86 −0.301112
\(417\) −575.169 −0.0675447
\(418\) −6292.50 −0.736307
\(419\) 9637.63 1.12370 0.561849 0.827240i \(-0.310090\pi\)
0.561849 + 0.827240i \(0.310090\pi\)
\(420\) −231.234 −0.0268644
\(421\) −7920.50 −0.916916 −0.458458 0.888716i \(-0.651598\pi\)
−0.458458 + 0.888716i \(0.651598\pi\)
\(422\) 24614.0 2.83931
\(423\) −13875.0 −1.59486
\(424\) 6014.49 0.688890
\(425\) 2821.20 0.321996
\(426\) 1544.03 0.175606
\(427\) 1647.86 0.186757
\(428\) −218.280 −0.0246518
\(429\) −180.542 −0.0203185
\(430\) 0 0
\(431\) 11681.4 1.30550 0.652751 0.757572i \(-0.273615\pi\)
0.652751 + 0.757572i \(0.273615\pi\)
\(432\) 1323.95 0.147451
\(433\) 1330.29 0.147644 0.0738219 0.997271i \(-0.476480\pi\)
0.0738219 + 0.997271i \(0.476480\pi\)
\(434\) 1818.30 0.201109
\(435\) −308.480 −0.0340011
\(436\) −17980.0 −1.97497
\(437\) 11249.9 1.23148
\(438\) −44.8302 −0.00489057
\(439\) −9593.16 −1.04295 −0.521477 0.853266i \(-0.674619\pi\)
−0.521477 + 0.853266i \(0.674619\pi\)
\(440\) −5110.71 −0.553735
\(441\) 8889.86 0.959925
\(442\) −27851.9 −2.99723
\(443\) 8919.62 0.956623 0.478311 0.878190i \(-0.341249\pi\)
0.478311 + 0.878190i \(0.341249\pi\)
\(444\) −2284.92 −0.244228
\(445\) −223.989 −0.0238609
\(446\) −21321.3 −2.26366
\(447\) 422.696 0.0447267
\(448\) −1413.95 −0.149113
\(449\) −14843.4 −1.56014 −0.780068 0.625694i \(-0.784816\pi\)
−0.780068 + 0.625694i \(0.784816\pi\)
\(450\) 3893.91 0.407913
\(451\) −2581.13 −0.269492
\(452\) 6613.82 0.688248
\(453\) 506.772 0.0525612
\(454\) −5653.88 −0.584471
\(455\) 2557.96 0.263558
\(456\) 1757.11 0.180447
\(457\) 13541.6 1.38610 0.693051 0.720889i \(-0.256266\pi\)
0.693051 + 0.720889i \(0.256266\pi\)
\(458\) −10890.2 −1.11106
\(459\) 1656.81 0.168483
\(460\) 17700.9 1.79414
\(461\) 12039.0 1.21629 0.608146 0.793825i \(-0.291914\pi\)
0.608146 + 0.793825i \(0.291914\pi\)
\(462\) 54.2912 0.00546722
\(463\) −13045.9 −1.30949 −0.654745 0.755850i \(-0.727224\pi\)
−0.654745 + 0.755850i \(0.727224\pi\)
\(464\) 6017.32 0.602041
\(465\) 410.518 0.0409405
\(466\) 13861.9 1.37798
\(467\) 8743.50 0.866383 0.433192 0.901302i \(-0.357387\pi\)
0.433192 + 0.901302i \(0.357387\pi\)
\(468\) −25907.7 −2.55894
\(469\) 1574.88 0.155056
\(470\) −31730.6 −3.11409
\(471\) −221.002 −0.0216205
\(472\) 18654.3 1.81913
\(473\) 0 0
\(474\) 9.72456 0.000942329 0
\(475\) 3814.24 0.368441
\(476\) 5644.54 0.543523
\(477\) 3826.49 0.367302
\(478\) −9535.11 −0.912397
\(479\) −1878.47 −0.179185 −0.0895924 0.995979i \(-0.528556\pi\)
−0.0895924 + 0.995979i \(0.528556\pi\)
\(480\) 173.454 0.0164939
\(481\) 25276.3 2.39605
\(482\) −1482.97 −0.140140
\(483\) −97.0632 −0.00914395
\(484\) −20442.1 −1.91981
\(485\) 18231.2 1.70688
\(486\) 3432.33 0.320357
\(487\) −10129.4 −0.942520 −0.471260 0.881994i \(-0.656201\pi\)
−0.471260 + 0.881994i \(0.656201\pi\)
\(488\) −19702.1 −1.82760
\(489\) 720.687 0.0666474
\(490\) 20330.2 1.87433
\(491\) 9039.71 0.830868 0.415434 0.909623i \(-0.363630\pi\)
0.415434 + 0.909623i \(0.363630\pi\)
\(492\) 1396.28 0.127946
\(493\) 7530.16 0.687913
\(494\) −37655.5 −3.42956
\(495\) −3251.50 −0.295240
\(496\) −8007.71 −0.724913
\(497\) 3461.56 0.312419
\(498\) −1220.03 −0.109781
\(499\) −11297.8 −1.01354 −0.506771 0.862081i \(-0.669161\pi\)
−0.506771 + 0.862081i \(0.669161\pi\)
\(500\) −19667.4 −1.75910
\(501\) −275.980 −0.0246105
\(502\) −19894.7 −1.76881
\(503\) −8507.23 −0.754113 −0.377056 0.926190i \(-0.623064\pi\)
−0.377056 + 0.926190i \(0.623064\pi\)
\(504\) 4021.54 0.355424
\(505\) 5687.60 0.501178
\(506\) −4155.97 −0.365129
\(507\) −380.794 −0.0333563
\(508\) −15469.9 −1.35112
\(509\) 963.852 0.0839332 0.0419666 0.999119i \(-0.486638\pi\)
0.0419666 + 0.999119i \(0.486638\pi\)
\(510\) 1890.91 0.164179
\(511\) −100.505 −0.00870073
\(512\) 22707.6 1.96005
\(513\) 2240.00 0.192784
\(514\) 18525.5 1.58973
\(515\) −21593.2 −1.84759
\(516\) 0 0
\(517\) 5020.87 0.427113
\(518\) −7600.90 −0.644719
\(519\) 836.520 0.0707498
\(520\) −30583.4 −2.57918
\(521\) 2246.41 0.188900 0.0944500 0.995530i \(-0.469891\pi\)
0.0944500 + 0.995530i \(0.469891\pi\)
\(522\) 10393.4 0.871465
\(523\) 5441.13 0.454921 0.227461 0.973787i \(-0.426958\pi\)
0.227461 + 0.973787i \(0.426958\pi\)
\(524\) 2202.33 0.183606
\(525\) −32.9090 −0.00273575
\(526\) 29486.5 2.44425
\(527\) −10021.0 −0.828311
\(528\) −239.096 −0.0197070
\(529\) −4736.85 −0.389320
\(530\) 8750.78 0.717188
\(531\) 11868.1 0.969926
\(532\) 7631.37 0.621921
\(533\) −15446.0 −1.25523
\(534\) −28.4491 −0.00230545
\(535\) −163.936 −0.0132478
\(536\) −18829.6 −1.51738
\(537\) −194.234 −0.0156086
\(538\) −4393.74 −0.352096
\(539\) −3216.93 −0.257074
\(540\) 3524.47 0.280869
\(541\) 8047.68 0.639550 0.319775 0.947493i \(-0.396393\pi\)
0.319775 + 0.947493i \(0.396393\pi\)
\(542\) 42769.8 3.38952
\(543\) 467.150 0.0369196
\(544\) −4234.11 −0.333706
\(545\) −13503.6 −1.06134
\(546\) 324.889 0.0254651
\(547\) −5703.27 −0.445803 −0.222902 0.974841i \(-0.571553\pi\)
−0.222902 + 0.974841i \(0.571553\pi\)
\(548\) 8610.99 0.671247
\(549\) −12534.7 −0.974441
\(550\) −1409.07 −0.109242
\(551\) 10180.7 0.787138
\(552\) 1160.50 0.0894825
\(553\) 21.8015 0.00167648
\(554\) 34834.1 2.67140
\(555\) −1716.05 −0.131248
\(556\) 29867.0 2.27814
\(557\) −20648.4 −1.57074 −0.785369 0.619027i \(-0.787527\pi\)
−0.785369 + 0.619027i \(0.787527\pi\)
\(558\) −13831.2 −1.04932
\(559\) 0 0
\(560\) 3387.57 0.255626
\(561\) −299.207 −0.0225179
\(562\) 32387.3 2.43092
\(563\) 12005.8 0.898728 0.449364 0.893349i \(-0.351651\pi\)
0.449364 + 0.893349i \(0.351651\pi\)
\(564\) −2716.07 −0.202779
\(565\) 4967.21 0.369862
\(566\) 26359.8 1.95757
\(567\) 2548.87 0.188788
\(568\) −41387.0 −3.05732
\(569\) 12384.5 0.912450 0.456225 0.889864i \(-0.349201\pi\)
0.456225 + 0.889864i \(0.349201\pi\)
\(570\) 2556.50 0.187860
\(571\) 5347.17 0.391895 0.195948 0.980614i \(-0.437222\pi\)
0.195948 + 0.980614i \(0.437222\pi\)
\(572\) 9375.08 0.685300
\(573\) −204.007 −0.0148735
\(574\) 4644.80 0.337753
\(575\) 2519.17 0.182707
\(576\) 10755.4 0.778026
\(577\) −14667.0 −1.05822 −0.529112 0.848552i \(-0.677475\pi\)
−0.529112 + 0.848552i \(0.677475\pi\)
\(578\) −21822.4 −1.57041
\(579\) −65.3721 −0.00469218
\(580\) 16018.6 1.14678
\(581\) −2735.19 −0.195309
\(582\) 2315.57 0.164920
\(583\) −1384.67 −0.0983659
\(584\) 1201.65 0.0851451
\(585\) −19457.6 −1.37516
\(586\) −48051.1 −3.38732
\(587\) 10701.6 0.752472 0.376236 0.926524i \(-0.377218\pi\)
0.376236 + 0.926524i \(0.377218\pi\)
\(588\) 1740.22 0.122050
\(589\) −13548.3 −0.947786
\(590\) 27141.0 1.89386
\(591\) −1192.97 −0.0830326
\(592\) 33473.9 2.32394
\(593\) 26097.6 1.80725 0.903627 0.428320i \(-0.140894\pi\)
0.903627 + 0.428320i \(0.140894\pi\)
\(594\) −827.507 −0.0571600
\(595\) 4239.24 0.292088
\(596\) −21949.5 −1.50854
\(597\) −53.0793 −0.00363885
\(598\) −24870.1 −1.70069
\(599\) 21865.5 1.49149 0.745743 0.666234i \(-0.232095\pi\)
0.745743 + 0.666234i \(0.232095\pi\)
\(600\) 393.466 0.0267719
\(601\) 20916.6 1.41965 0.709823 0.704380i \(-0.248775\pi\)
0.709823 + 0.704380i \(0.248775\pi\)
\(602\) 0 0
\(603\) −11979.6 −0.809035
\(604\) −26315.3 −1.77278
\(605\) −15352.8 −1.03170
\(606\) 722.387 0.0484240
\(607\) 5440.14 0.363770 0.181885 0.983320i \(-0.441780\pi\)
0.181885 + 0.983320i \(0.441780\pi\)
\(608\) −5724.48 −0.381839
\(609\) −87.8384 −0.00584465
\(610\) −28665.5 −1.90268
\(611\) 30045.8 1.98940
\(612\) −42936.1 −2.83593
\(613\) 20121.1 1.32575 0.662875 0.748730i \(-0.269336\pi\)
0.662875 + 0.748730i \(0.269336\pi\)
\(614\) −4544.16 −0.298676
\(615\) 1048.66 0.0687575
\(616\) −1455.25 −0.0951848
\(617\) −2560.72 −0.167084 −0.0835419 0.996504i \(-0.526623\pi\)
−0.0835419 + 0.996504i \(0.526623\pi\)
\(618\) −2742.57 −0.178515
\(619\) −5669.37 −0.368128 −0.184064 0.982914i \(-0.558925\pi\)
−0.184064 + 0.982914i \(0.558925\pi\)
\(620\) −21317.2 −1.38083
\(621\) 1479.44 0.0956004
\(622\) −10103.6 −0.651316
\(623\) −63.7801 −0.00410160
\(624\) −1430.79 −0.0917909
\(625\) −18424.0 −1.17914
\(626\) −5048.57 −0.322335
\(627\) −404.526 −0.0257659
\(628\) 11476.1 0.729212
\(629\) 41889.7 2.65541
\(630\) 5851.14 0.370024
\(631\) −7445.04 −0.469703 −0.234851 0.972031i \(-0.575460\pi\)
−0.234851 + 0.972031i \(0.575460\pi\)
\(632\) −260.663 −0.0164060
\(633\) 1582.36 0.0993571
\(634\) 994.213 0.0622796
\(635\) −11618.5 −0.726086
\(636\) 749.048 0.0467008
\(637\) −19250.7 −1.19739
\(638\) −3760.99 −0.233384
\(639\) −26330.9 −1.63010
\(640\) 28954.2 1.78830
\(641\) −10314.8 −0.635585 −0.317792 0.948160i \(-0.602942\pi\)
−0.317792 + 0.948160i \(0.602942\pi\)
\(642\) −20.8217 −0.00128001
\(643\) −1904.97 −0.116835 −0.0584175 0.998292i \(-0.518605\pi\)
−0.0584175 + 0.998292i \(0.518605\pi\)
\(644\) 5040.24 0.308406
\(645\) 0 0
\(646\) −62405.5 −3.80079
\(647\) 21967.1 1.33480 0.667399 0.744700i \(-0.267407\pi\)
0.667399 + 0.744700i \(0.267407\pi\)
\(648\) −30474.7 −1.84747
\(649\) −4294.64 −0.259752
\(650\) −8432.13 −0.508824
\(651\) 116.893 0.00703750
\(652\) −37423.4 −2.24788
\(653\) 19436.1 1.16477 0.582383 0.812914i \(-0.302120\pi\)
0.582383 + 0.812914i \(0.302120\pi\)
\(654\) −1715.11 −0.102547
\(655\) 1654.03 0.0986691
\(656\) −20455.4 −1.21746
\(657\) 764.507 0.0453977
\(658\) −9035.16 −0.535300
\(659\) 22294.7 1.31787 0.658936 0.752199i \(-0.271007\pi\)
0.658936 + 0.752199i \(0.271007\pi\)
\(660\) −636.491 −0.0375385
\(661\) 2771.21 0.163067 0.0815336 0.996671i \(-0.474018\pi\)
0.0815336 + 0.996671i \(0.474018\pi\)
\(662\) −59138.9 −3.47205
\(663\) −1790.51 −0.104883
\(664\) 32702.3 1.91129
\(665\) 5731.43 0.334218
\(666\) 57817.5 3.36394
\(667\) 6723.99 0.390336
\(668\) 14330.9 0.830060
\(669\) −1370.68 −0.0792133
\(670\) −27396.1 −1.57971
\(671\) 4535.87 0.260962
\(672\) 49.3904 0.00283523
\(673\) −2838.17 −0.162561 −0.0812803 0.996691i \(-0.525901\pi\)
−0.0812803 + 0.996691i \(0.525901\pi\)
\(674\) 49203.9 2.81196
\(675\) 501.599 0.0286023
\(676\) 19773.7 1.12504
\(677\) 19477.4 1.10573 0.552863 0.833272i \(-0.313535\pi\)
0.552863 + 0.833272i \(0.313535\pi\)
\(678\) 630.889 0.0357362
\(679\) 5191.27 0.293406
\(680\) −50685.1 −2.85836
\(681\) −363.471 −0.0204526
\(682\) 5005.04 0.281016
\(683\) 10684.6 0.598587 0.299294 0.954161i \(-0.403249\pi\)
0.299294 + 0.954161i \(0.403249\pi\)
\(684\) −58049.3 −3.24499
\(685\) 6467.15 0.360726
\(686\) 11796.9 0.656570
\(687\) −700.099 −0.0388798
\(688\) 0 0
\(689\) −8286.14 −0.458167
\(690\) 1688.48 0.0931582
\(691\) −18492.3 −1.01806 −0.509030 0.860749i \(-0.669996\pi\)
−0.509030 + 0.860749i \(0.669996\pi\)
\(692\) −43438.3 −2.38624
\(693\) −925.850 −0.0507506
\(694\) 19259.2 1.05341
\(695\) 22431.2 1.22426
\(696\) 1050.21 0.0571956
\(697\) −25598.2 −1.39111
\(698\) 9701.47 0.526083
\(699\) 891.140 0.0482203
\(700\) 1708.88 0.0922709
\(701\) −26750.8 −1.44132 −0.720658 0.693291i \(-0.756160\pi\)
−0.720658 + 0.693291i \(0.756160\pi\)
\(702\) −4951.96 −0.266239
\(703\) 56634.6 3.03843
\(704\) −3892.01 −0.208360
\(705\) −2039.87 −0.108973
\(706\) 13897.3 0.740839
\(707\) 1619.52 0.0861504
\(708\) 2323.21 0.123322
\(709\) 19220.7 1.01812 0.509060 0.860731i \(-0.329993\pi\)
0.509060 + 0.860731i \(0.329993\pi\)
\(710\) −60216.0 −3.18291
\(711\) −165.837 −0.00874736
\(712\) 762.565 0.0401381
\(713\) −8948.13 −0.470000
\(714\) 538.430 0.0282216
\(715\) 7041.01 0.368278
\(716\) 10086.1 0.526445
\(717\) −612.983 −0.0319279
\(718\) −28816.9 −1.49782
\(719\) −15744.5 −0.816647 −0.408323 0.912837i \(-0.633886\pi\)
−0.408323 + 0.912837i \(0.633886\pi\)
\(720\) −25768.1 −1.33378
\(721\) −6148.57 −0.317593
\(722\) −50396.8 −2.59775
\(723\) −95.3355 −0.00490396
\(724\) −24257.9 −1.24522
\(725\) 2279.75 0.116783
\(726\) −1949.96 −0.0996832
\(727\) −23957.5 −1.22219 −0.611097 0.791556i \(-0.709271\pi\)
−0.611097 + 0.791556i \(0.709271\pi\)
\(728\) −8708.50 −0.443350
\(729\) −19240.9 −0.977537
\(730\) 1748.35 0.0886427
\(731\) 0 0
\(732\) −2453.71 −0.123896
\(733\) −2994.98 −0.150917 −0.0754586 0.997149i \(-0.524042\pi\)
−0.0754586 + 0.997149i \(0.524042\pi\)
\(734\) −9494.00 −0.477425
\(735\) 1306.97 0.0655893
\(736\) −3780.81 −0.189351
\(737\) 4335.00 0.216665
\(738\) −35331.5 −1.76229
\(739\) −6010.04 −0.299165 −0.149582 0.988749i \(-0.547793\pi\)
−0.149582 + 0.988749i \(0.547793\pi\)
\(740\) 89110.2 4.42670
\(741\) −2420.76 −0.120012
\(742\) 2491.75 0.123282
\(743\) 12435.1 0.613995 0.306998 0.951710i \(-0.400676\pi\)
0.306998 + 0.951710i \(0.400676\pi\)
\(744\) −1397.60 −0.0688688
\(745\) −16484.9 −0.810683
\(746\) −33551.4 −1.64665
\(747\) 20805.7 1.01906
\(748\) 15537.1 0.759481
\(749\) −46.6802 −0.00227724
\(750\) −1876.06 −0.0913388
\(751\) −33154.2 −1.61094 −0.805468 0.592640i \(-0.798086\pi\)
−0.805468 + 0.592640i \(0.798086\pi\)
\(752\) 39790.4 1.92953
\(753\) −1278.97 −0.0618969
\(754\) −22506.5 −1.08705
\(755\) −19763.7 −0.952684
\(756\) 1003.58 0.0482801
\(757\) −2104.38 −0.101037 −0.0505185 0.998723i \(-0.516087\pi\)
−0.0505185 + 0.998723i \(0.516087\pi\)
\(758\) −37156.5 −1.78046
\(759\) −267.175 −0.0127771
\(760\) −68525.9 −3.27065
\(761\) 7428.23 0.353841 0.176921 0.984225i \(-0.443386\pi\)
0.176921 + 0.984225i \(0.443386\pi\)
\(762\) −1475.67 −0.0701547
\(763\) −3845.10 −0.182440
\(764\) 10593.6 0.501652
\(765\) −32246.5 −1.52402
\(766\) −18282.0 −0.862344
\(767\) −25699.9 −1.20987
\(768\) 2658.88 0.124927
\(769\) 27269.3 1.27874 0.639372 0.768897i \(-0.279194\pi\)
0.639372 + 0.768897i \(0.279194\pi\)
\(770\) −2117.32 −0.0990947
\(771\) 1190.95 0.0556302
\(772\) 3394.61 0.158257
\(773\) −21246.0 −0.988571 −0.494285 0.869300i \(-0.664570\pi\)
−0.494285 + 0.869300i \(0.664570\pi\)
\(774\) 0 0
\(775\) −3033.84 −0.140618
\(776\) −62067.7 −2.87127
\(777\) −488.639 −0.0225609
\(778\) −17100.2 −0.788008
\(779\) −34608.6 −1.59176
\(780\) −3808.88 −0.174846
\(781\) 9528.23 0.436552
\(782\) −41216.6 −1.88478
\(783\) 1338.83 0.0611060
\(784\) −25494.1 −1.16136
\(785\) 8618.93 0.391876
\(786\) 210.080 0.00953345
\(787\) 36931.1 1.67275 0.836374 0.548159i \(-0.184671\pi\)
0.836374 + 0.548159i \(0.184671\pi\)
\(788\) 61947.9 2.80051
\(789\) 1895.60 0.0855326
\(790\) −379.251 −0.0170799
\(791\) 1414.39 0.0635778
\(792\) 11069.6 0.496644
\(793\) 27143.5 1.21550
\(794\) 28255.0 1.26289
\(795\) 562.561 0.0250969
\(796\) 2756.27 0.122731
\(797\) 8617.90 0.383013 0.191507 0.981491i \(-0.438663\pi\)
0.191507 + 0.981491i \(0.438663\pi\)
\(798\) 727.953 0.0322923
\(799\) 49794.2 2.20475
\(800\) −1281.87 −0.0566514
\(801\) 485.154 0.0214008
\(802\) 52566.2 2.31443
\(803\) −276.648 −0.0121578
\(804\) −2345.05 −0.102865
\(805\) 3785.40 0.165736
\(806\) 29951.1 1.30891
\(807\) −282.461 −0.0123211
\(808\) −19363.3 −0.843066
\(809\) −12821.8 −0.557218 −0.278609 0.960405i \(-0.589873\pi\)
−0.278609 + 0.960405i \(0.589873\pi\)
\(810\) −44339.2 −1.92336
\(811\) 26275.3 1.13767 0.568835 0.822452i \(-0.307394\pi\)
0.568835 + 0.822452i \(0.307394\pi\)
\(812\) 4561.22 0.197128
\(813\) 2749.54 0.118611
\(814\) −20922.1 −0.900884
\(815\) −28106.3 −1.20800
\(816\) −2371.22 −0.101727
\(817\) 0 0
\(818\) −45417.8 −1.94131
\(819\) −5540.46 −0.236385
\(820\) −54454.0 −2.31904
\(821\) 41560.4 1.76671 0.883355 0.468704i \(-0.155279\pi\)
0.883355 + 0.468704i \(0.155279\pi\)
\(822\) 821.398 0.0348535
\(823\) −21443.6 −0.908234 −0.454117 0.890942i \(-0.650045\pi\)
−0.454117 + 0.890942i \(0.650045\pi\)
\(824\) 73513.3 3.10796
\(825\) −90.5848 −0.00382274
\(826\) 7728.29 0.325547
\(827\) −39485.6 −1.66028 −0.830139 0.557557i \(-0.811739\pi\)
−0.830139 + 0.557557i \(0.811739\pi\)
\(828\) −38339.5 −1.60916
\(829\) 9431.88 0.395154 0.197577 0.980287i \(-0.436693\pi\)
0.197577 + 0.980287i \(0.436693\pi\)
\(830\) 47580.3 1.98980
\(831\) 2239.38 0.0934815
\(832\) −23290.5 −0.970497
\(833\) −31903.7 −1.32701
\(834\) 2849.00 0.118289
\(835\) 10763.0 0.446072
\(836\) 21006.0 0.869028
\(837\) −1781.69 −0.0735773
\(838\) −47738.4 −1.96790
\(839\) 33753.5 1.38891 0.694457 0.719534i \(-0.255644\pi\)
0.694457 + 0.719534i \(0.255644\pi\)
\(840\) 591.236 0.0242852
\(841\) −18304.1 −0.750504
\(842\) 39232.9 1.60577
\(843\) 2082.08 0.0850660
\(844\) −82167.8 −3.35110
\(845\) 14850.7 0.604592
\(846\) 68727.5 2.79302
\(847\) −4371.63 −0.177345
\(848\) −10973.5 −0.444378
\(849\) 1694.59 0.0685021
\(850\) −13974.4 −0.563902
\(851\) 37405.1 1.50673
\(852\) −5154.36 −0.207260
\(853\) −4810.50 −0.193093 −0.0965466 0.995328i \(-0.530780\pi\)
−0.0965466 + 0.995328i \(0.530780\pi\)
\(854\) −8162.39 −0.327062
\(855\) −43597.0 −1.74385
\(856\) 558.116 0.0222851
\(857\) −18134.3 −0.722821 −0.361410 0.932407i \(-0.617705\pi\)
−0.361410 + 0.932407i \(0.617705\pi\)
\(858\) 894.284 0.0355832
\(859\) 3895.00 0.154710 0.0773549 0.997004i \(-0.475353\pi\)
0.0773549 + 0.997004i \(0.475353\pi\)
\(860\) 0 0
\(861\) 298.600 0.0118191
\(862\) −57861.7 −2.28628
\(863\) 13915.3 0.548878 0.274439 0.961605i \(-0.411508\pi\)
0.274439 + 0.961605i \(0.411508\pi\)
\(864\) −752.809 −0.0296425
\(865\) −32623.7 −1.28236
\(866\) −6589.38 −0.258564
\(867\) −1402.90 −0.0549538
\(868\) −6069.97 −0.237360
\(869\) 60.0105 0.00234260
\(870\) 1528.00 0.0595451
\(871\) 25941.5 1.00918
\(872\) 45972.7 1.78536
\(873\) −39488.3 −1.53090
\(874\) −55724.5 −2.15665
\(875\) −4205.95 −0.162499
\(876\) 149.655 0.00577210
\(877\) 4738.08 0.182433 0.0912164 0.995831i \(-0.470925\pi\)
0.0912164 + 0.995831i \(0.470925\pi\)
\(878\) 47518.1 1.82649
\(879\) −3089.06 −0.118534
\(880\) 9324.56 0.357194
\(881\) −26778.4 −1.02405 −0.512024 0.858971i \(-0.671104\pi\)
−0.512024 + 0.858971i \(0.671104\pi\)
\(882\) −44034.5 −1.68109
\(883\) −24306.7 −0.926372 −0.463186 0.886261i \(-0.653294\pi\)
−0.463186 + 0.886261i \(0.653294\pi\)
\(884\) 92976.7 3.53750
\(885\) 1744.81 0.0662726
\(886\) −44181.9 −1.67530
\(887\) −26914.4 −1.01882 −0.509412 0.860523i \(-0.670137\pi\)
−0.509412 + 0.860523i \(0.670137\pi\)
\(888\) 5842.25 0.220781
\(889\) −3308.31 −0.124811
\(890\) 1109.49 0.0417869
\(891\) 7015.99 0.263798
\(892\) 71176.1 2.67170
\(893\) 67321.3 2.52276
\(894\) −2093.76 −0.0783285
\(895\) 7574.99 0.282910
\(896\) 8244.58 0.307402
\(897\) −1598.82 −0.0595130
\(898\) 73524.1 2.73222
\(899\) −8097.71 −0.300416
\(900\) −12998.9 −0.481440
\(901\) −13732.4 −0.507761
\(902\) 12785.2 0.471952
\(903\) 0 0
\(904\) −16910.7 −0.622171
\(905\) −18218.5 −0.669177
\(906\) −2510.21 −0.0920487
\(907\) 41966.5 1.53636 0.768178 0.640236i \(-0.221163\pi\)
0.768178 + 0.640236i \(0.221163\pi\)
\(908\) 18874.1 0.689824
\(909\) −12319.2 −0.449506
\(910\) −12670.4 −0.461561
\(911\) 26977.3 0.981117 0.490558 0.871408i \(-0.336793\pi\)
0.490558 + 0.871408i \(0.336793\pi\)
\(912\) −3205.86 −0.116400
\(913\) −7528.83 −0.272911
\(914\) −67076.0 −2.42743
\(915\) −1842.82 −0.0665812
\(916\) 36354.3 1.31133
\(917\) 470.978 0.0169608
\(918\) −8206.75 −0.295058
\(919\) 16827.5 0.604014 0.302007 0.953306i \(-0.402343\pi\)
0.302007 + 0.953306i \(0.402343\pi\)
\(920\) −45258.9 −1.62189
\(921\) −292.130 −0.0104517
\(922\) −59633.0 −2.13005
\(923\) 57018.7 2.03336
\(924\) −181.238 −0.00645270
\(925\) 12682.1 0.450794
\(926\) 64620.7 2.29327
\(927\) 46770.1 1.65710
\(928\) −3421.49 −0.121030
\(929\) −22663.1 −0.800379 −0.400190 0.916432i \(-0.631056\pi\)
−0.400190 + 0.916432i \(0.631056\pi\)
\(930\) −2033.43 −0.0716978
\(931\) −43133.5 −1.51842
\(932\) −46274.6 −1.62637
\(933\) −649.532 −0.0227918
\(934\) −43309.5 −1.51727
\(935\) 11668.9 0.408143
\(936\) 66242.7 2.31326
\(937\) −38575.3 −1.34493 −0.672465 0.740129i \(-0.734765\pi\)
−0.672465 + 0.740129i \(0.734765\pi\)
\(938\) −7800.93 −0.271545
\(939\) −324.558 −0.0112796
\(940\) 105925. 3.67542
\(941\) −22927.5 −0.794278 −0.397139 0.917758i \(-0.629997\pi\)
−0.397139 + 0.917758i \(0.629997\pi\)
\(942\) 1094.70 0.0378632
\(943\) −22857.7 −0.789342
\(944\) −34035.0 −1.17346
\(945\) 753.722 0.0259456
\(946\) 0 0
\(947\) 54420.4 1.86740 0.933698 0.358060i \(-0.116562\pi\)
0.933698 + 0.358060i \(0.116562\pi\)
\(948\) −32.4631 −0.00111219
\(949\) −1655.51 −0.0566283
\(950\) −18893.2 −0.645239
\(951\) 63.9150 0.00217937
\(952\) −14432.4 −0.491341
\(953\) 14552.8 0.494661 0.247331 0.968931i \(-0.420447\pi\)
0.247331 + 0.968931i \(0.420447\pi\)
\(954\) −18953.9 −0.643244
\(955\) 7956.14 0.269586
\(956\) 31830.7 1.07686
\(957\) −241.783 −0.00816690
\(958\) 9304.69 0.313800
\(959\) 1841.49 0.0620073
\(960\) 1581.24 0.0531606
\(961\) −19014.8 −0.638272
\(962\) −125202. −4.19612
\(963\) 355.080 0.0118819
\(964\) 4950.53 0.165400
\(965\) 2549.47 0.0850469
\(966\) 480.787 0.0160135
\(967\) 21132.6 0.702771 0.351386 0.936231i \(-0.385711\pi\)
0.351386 + 0.936231i \(0.385711\pi\)
\(968\) 52268.0 1.73549
\(969\) −4011.86 −0.133003
\(970\) −90305.5 −2.98921
\(971\) −43710.7 −1.44464 −0.722319 0.691560i \(-0.756924\pi\)
−0.722319 + 0.691560i \(0.756924\pi\)
\(972\) −11458.0 −0.378103
\(973\) 6387.19 0.210446
\(974\) 50174.4 1.65061
\(975\) −542.077 −0.0178055
\(976\) 35946.7 1.17892
\(977\) 5105.55 0.167186 0.0835932 0.996500i \(-0.473360\pi\)
0.0835932 + 0.996500i \(0.473360\pi\)
\(978\) −3569.80 −0.116717
\(979\) −175.560 −0.00573128
\(980\) −67867.4 −2.21219
\(981\) 29248.4 0.951916
\(982\) −44776.7 −1.45507
\(983\) 31668.3 1.02753 0.513765 0.857931i \(-0.328250\pi\)
0.513765 + 0.857931i \(0.328250\pi\)
\(984\) −3570.12 −0.115662
\(985\) 46525.0 1.50499
\(986\) −37299.4 −1.20472
\(987\) −580.844 −0.0187320
\(988\) 125704. 4.04774
\(989\) 0 0
\(990\) 16105.8 0.517045
\(991\) −33652.0 −1.07870 −0.539350 0.842082i \(-0.681330\pi\)
−0.539350 + 0.842082i \(0.681330\pi\)
\(992\) 4553.24 0.145731
\(993\) −3801.87 −0.121499
\(994\) −17146.3 −0.547129
\(995\) 2070.06 0.0659550
\(996\) 4072.77 0.129569
\(997\) 8769.30 0.278562 0.139281 0.990253i \(-0.455521\pi\)
0.139281 + 0.990253i \(0.455521\pi\)
\(998\) 55961.6 1.77498
\(999\) 7447.84 0.235875
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 1849.4.a.h.1.2 30
43.21 even 7 43.4.e.a.11.1 yes 60
43.41 even 7 43.4.e.a.4.1 60
43.42 odd 2 1849.4.a.g.1.29 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.e.a.4.1 60 43.41 even 7
43.4.e.a.11.1 yes 60 43.21 even 7
1849.4.a.g.1.29 30 43.42 odd 2
1849.4.a.h.1.2 30 1.1 even 1 trivial