Properties

Label 1849.4.a.g.1.9
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $1$
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: \(1\)
Dimension: \(30\)
Twist minimal: no (minimal twist has level 43)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
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)
 
\(f(q)\) \(=\) \(q-2.89826 q^{2} +6.20542 q^{3} +0.399940 q^{4} -21.5042 q^{5} -17.9850 q^{6} -25.5918 q^{7} +22.0270 q^{8} +11.5073 q^{9} +O(q^{10})\) \(q-2.89826 q^{2} +6.20542 q^{3} +0.399940 q^{4} -21.5042 q^{5} -17.9850 q^{6} -25.5918 q^{7} +22.0270 q^{8} +11.5073 q^{9} +62.3249 q^{10} -44.3020 q^{11} +2.48179 q^{12} +22.5787 q^{13} +74.1718 q^{14} -133.443 q^{15} -67.0396 q^{16} -32.0183 q^{17} -33.3511 q^{18} +76.6633 q^{19} -8.60039 q^{20} -158.808 q^{21} +128.399 q^{22} +50.4034 q^{23} +136.687 q^{24} +337.431 q^{25} -65.4390 q^{26} -96.1390 q^{27} -10.2352 q^{28} +52.0400 q^{29} +386.752 q^{30} +267.978 q^{31} +18.0825 q^{32} -274.912 q^{33} +92.7976 q^{34} +550.331 q^{35} +4.60221 q^{36} -73.1460 q^{37} -222.191 q^{38} +140.110 q^{39} -473.673 q^{40} +128.420 q^{41} +460.267 q^{42} -17.7181 q^{44} -247.454 q^{45} -146.082 q^{46} +158.149 q^{47} -416.009 q^{48} +311.939 q^{49} -977.964 q^{50} -198.687 q^{51} +9.03011 q^{52} -419.186 q^{53} +278.636 q^{54} +952.679 q^{55} -563.710 q^{56} +475.728 q^{57} -150.826 q^{58} +208.681 q^{59} -53.3690 q^{60} -307.109 q^{61} -776.672 q^{62} -294.491 q^{63} +483.909 q^{64} -485.537 q^{65} +796.769 q^{66} +345.123 q^{67} -12.8054 q^{68} +312.774 q^{69} -1595.00 q^{70} +399.163 q^{71} +253.470 q^{72} +87.7114 q^{73} +211.997 q^{74} +2093.90 q^{75} +30.6607 q^{76} +1133.77 q^{77} -406.077 q^{78} +221.031 q^{79} +1441.63 q^{80} -907.279 q^{81} -372.196 q^{82} +433.834 q^{83} -63.5135 q^{84} +688.529 q^{85} +322.930 q^{87} -975.839 q^{88} +18.7214 q^{89} +717.188 q^{90} -577.829 q^{91} +20.1583 q^{92} +1662.92 q^{93} -458.357 q^{94} -1648.58 q^{95} +112.210 q^{96} +334.287 q^{97} -904.082 q^{98} -509.794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 30 q - 6 q^{2} - 2 q^{3} + 114 q^{4} - 27 q^{5} + 8 q^{6} - 48 q^{7} - 90 q^{8} + 216 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.89826 −1.02469 −0.512346 0.858779i \(-0.671223\pi\)
−0.512346 + 0.858779i \(0.671223\pi\)
\(3\) 6.20542 1.19423 0.597117 0.802154i \(-0.296313\pi\)
0.597117 + 0.802154i \(0.296313\pi\)
\(4\) 0.399940 0.0499925
\(5\) −21.5042 −1.92339 −0.961697 0.274113i \(-0.911616\pi\)
−0.961697 + 0.274113i \(0.911616\pi\)
\(6\) −17.9850 −1.22372
\(7\) −25.5918 −1.38183 −0.690913 0.722938i \(-0.742791\pi\)
−0.690913 + 0.722938i \(0.742791\pi\)
\(8\) 22.0270 0.973465
\(9\) 11.5073 0.426195
\(10\) 62.3249 1.97089
\(11\) −44.3020 −1.21432 −0.607161 0.794579i \(-0.707692\pi\)
−0.607161 + 0.794579i \(0.707692\pi\)
\(12\) 2.48179 0.0597027
\(13\) 22.5787 0.481708 0.240854 0.970561i \(-0.422573\pi\)
0.240854 + 0.970561i \(0.422573\pi\)
\(14\) 74.1718 1.41595
\(15\) −133.443 −2.29698
\(16\) −67.0396 −1.04749
\(17\) −32.0183 −0.456799 −0.228400 0.973567i \(-0.573349\pi\)
−0.228400 + 0.973567i \(0.573349\pi\)
\(18\) −33.3511 −0.436718
\(19\) 76.6633 0.925673 0.462836 0.886444i \(-0.346832\pi\)
0.462836 + 0.886444i \(0.346832\pi\)
\(20\) −8.60039 −0.0961552
\(21\) −158.808 −1.65022
\(22\) 128.399 1.24431
\(23\) 50.4034 0.456949 0.228475 0.973550i \(-0.426626\pi\)
0.228475 + 0.973550i \(0.426626\pi\)
\(24\) 136.687 1.16254
\(25\) 337.431 2.69945
\(26\) −65.4390 −0.493602
\(27\) −96.1390 −0.685258
\(28\) −10.2352 −0.0690809
\(29\) 52.0400 0.333227 0.166614 0.986022i \(-0.446717\pi\)
0.166614 + 0.986022i \(0.446717\pi\)
\(30\) 386.752 2.35370
\(31\) 267.978 1.55259 0.776296 0.630369i \(-0.217096\pi\)
0.776296 + 0.630369i \(0.217096\pi\)
\(32\) 18.0825 0.0998927
\(33\) −274.912 −1.45019
\(34\) 92.7976 0.468078
\(35\) 550.331 2.65780
\(36\) 4.60221 0.0213065
\(37\) −73.1460 −0.325004 −0.162502 0.986708i \(-0.551956\pi\)
−0.162502 + 0.986708i \(0.551956\pi\)
\(38\) −222.191 −0.948529
\(39\) 140.110 0.575272
\(40\) −473.673 −1.87236
\(41\) 128.420 0.489167 0.244584 0.969628i \(-0.421349\pi\)
0.244584 + 0.969628i \(0.421349\pi\)
\(42\) 460.267 1.69097
\(43\) 0 0
\(44\) −17.7181 −0.0607070
\(45\) −247.454 −0.819740
\(46\) −146.082 −0.468232
\(47\) 158.149 0.490816 0.245408 0.969420i \(-0.421078\pi\)
0.245408 + 0.969420i \(0.421078\pi\)
\(48\) −416.009 −1.25095
\(49\) 311.939 0.909443
\(50\) −977.964 −2.76610
\(51\) −198.687 −0.545525
\(52\) 9.03011 0.0240818
\(53\) −419.186 −1.08641 −0.543204 0.839601i \(-0.682789\pi\)
−0.543204 + 0.839601i \(0.682789\pi\)
\(54\) 278.636 0.702178
\(55\) 952.679 2.33562
\(56\) −563.710 −1.34516
\(57\) 475.728 1.10547
\(58\) −150.826 −0.341455
\(59\) 208.681 0.460474 0.230237 0.973135i \(-0.426050\pi\)
0.230237 + 0.973135i \(0.426050\pi\)
\(60\) −53.3690 −0.114832
\(61\) −307.109 −0.644610 −0.322305 0.946636i \(-0.604458\pi\)
−0.322305 + 0.946636i \(0.604458\pi\)
\(62\) −776.672 −1.59093
\(63\) −294.491 −0.588927
\(64\) 483.909 0.945134
\(65\) −485.537 −0.926514
\(66\) 796.769 1.48599
\(67\) 345.123 0.629305 0.314653 0.949207i \(-0.398112\pi\)
0.314653 + 0.949207i \(0.398112\pi\)
\(68\) −12.8054 −0.0228365
\(69\) 312.774 0.545704
\(70\) −1595.00 −2.72342
\(71\) 399.163 0.667210 0.333605 0.942713i \(-0.391735\pi\)
0.333605 + 0.942713i \(0.391735\pi\)
\(72\) 253.470 0.414885
\(73\) 87.7114 0.140628 0.0703140 0.997525i \(-0.477600\pi\)
0.0703140 + 0.997525i \(0.477600\pi\)
\(74\) 211.997 0.333028
\(75\) 2093.90 3.22377
\(76\) 30.6607 0.0462766
\(77\) 1133.77 1.67798
\(78\) −406.077 −0.589476
\(79\) 221.031 0.314783 0.157392 0.987536i \(-0.449692\pi\)
0.157392 + 0.987536i \(0.449692\pi\)
\(80\) 1441.63 2.01474
\(81\) −907.279 −1.24455
\(82\) −372.196 −0.501246
\(83\) 433.834 0.573729 0.286864 0.957971i \(-0.407387\pi\)
0.286864 + 0.957971i \(0.407387\pi\)
\(84\) −63.5135 −0.0824987
\(85\) 688.529 0.878605
\(86\) 0 0
\(87\) 322.930 0.397951
\(88\) −975.839 −1.18210
\(89\) 18.7214 0.0222973 0.0111487 0.999938i \(-0.496451\pi\)
0.0111487 + 0.999938i \(0.496451\pi\)
\(90\) 717.188 0.839981
\(91\) −577.829 −0.665636
\(92\) 20.1583 0.0228440
\(93\) 1662.92 1.85416
\(94\) −458.357 −0.502935
\(95\) −1648.58 −1.78043
\(96\) 112.210 0.119295
\(97\) 334.287 0.349914 0.174957 0.984576i \(-0.444021\pi\)
0.174957 + 0.984576i \(0.444021\pi\)
\(98\) −904.082 −0.931899
\(99\) −509.794 −0.517538
\(100\) 134.952 0.134952
\(101\) −1303.49 −1.28418 −0.642091 0.766629i \(-0.721933\pi\)
−0.642091 + 0.766629i \(0.721933\pi\)
\(102\) 575.848 0.558995
\(103\) 2084.38 1.99398 0.996992 0.0775103i \(-0.0246971\pi\)
0.996992 + 0.0775103i \(0.0246971\pi\)
\(104\) 497.340 0.468925
\(105\) 3415.04 3.17403
\(106\) 1214.91 1.11323
\(107\) 824.744 0.745150 0.372575 0.928002i \(-0.378475\pi\)
0.372575 + 0.928002i \(0.378475\pi\)
\(108\) −38.4498 −0.0342577
\(109\) −1574.34 −1.38344 −0.691719 0.722166i \(-0.743146\pi\)
−0.691719 + 0.722166i \(0.743146\pi\)
\(110\) −2761.12 −2.39329
\(111\) −453.902 −0.388130
\(112\) 1715.66 1.44745
\(113\) −1504.81 −1.25275 −0.626374 0.779523i \(-0.715462\pi\)
−0.626374 + 0.779523i \(0.715462\pi\)
\(114\) −1378.79 −1.13277
\(115\) −1083.89 −0.878894
\(116\) 20.8129 0.0166588
\(117\) 259.819 0.205301
\(118\) −604.813 −0.471844
\(119\) 819.406 0.631217
\(120\) −2939.34 −2.23603
\(121\) 631.665 0.474579
\(122\) 890.082 0.660527
\(123\) 796.901 0.584180
\(124\) 107.175 0.0776179
\(125\) −4568.16 −3.26871
\(126\) 853.513 0.603468
\(127\) 228.899 0.159933 0.0799667 0.996798i \(-0.474519\pi\)
0.0799667 + 0.996798i \(0.474519\pi\)
\(128\) −1547.16 −1.06836
\(129\) 0 0
\(130\) 1407.21 0.949391
\(131\) −398.299 −0.265646 −0.132823 0.991140i \(-0.542404\pi\)
−0.132823 + 0.991140i \(0.542404\pi\)
\(132\) −109.948 −0.0724983
\(133\) −1961.95 −1.27912
\(134\) −1000.26 −0.644844
\(135\) 2067.39 1.31802
\(136\) −705.268 −0.444678
\(137\) −1309.27 −0.816488 −0.408244 0.912873i \(-0.633859\pi\)
−0.408244 + 0.912873i \(0.633859\pi\)
\(138\) −906.503 −0.559179
\(139\) 1333.29 0.813583 0.406791 0.913521i \(-0.366648\pi\)
0.406791 + 0.913521i \(0.366648\pi\)
\(140\) 220.099 0.132870
\(141\) 981.379 0.586149
\(142\) −1156.88 −0.683684
\(143\) −1000.28 −0.584949
\(144\) −771.441 −0.446436
\(145\) −1119.08 −0.640927
\(146\) −254.211 −0.144100
\(147\) 1935.71 1.08609
\(148\) −29.2540 −0.0162477
\(149\) −1890.48 −1.03943 −0.519713 0.854341i \(-0.673961\pi\)
−0.519713 + 0.854341i \(0.673961\pi\)
\(150\) −6068.68 −3.30337
\(151\) −2113.98 −1.13929 −0.569647 0.821889i \(-0.692920\pi\)
−0.569647 + 0.821889i \(0.692920\pi\)
\(152\) 1688.66 0.901109
\(153\) −368.443 −0.194685
\(154\) −3285.96 −1.71941
\(155\) −5762.66 −2.98625
\(156\) 56.0356 0.0287592
\(157\) 1264.21 0.642643 0.321322 0.946970i \(-0.395873\pi\)
0.321322 + 0.946970i \(0.395873\pi\)
\(158\) −640.605 −0.322556
\(159\) −2601.22 −1.29742
\(160\) −388.850 −0.192133
\(161\) −1289.91 −0.631425
\(162\) 2629.53 1.27528
\(163\) 42.9125 0.0206206 0.0103103 0.999947i \(-0.496718\pi\)
0.0103103 + 0.999947i \(0.496718\pi\)
\(164\) 51.3603 0.0244547
\(165\) 5911.77 2.78928
\(166\) −1257.37 −0.587895
\(167\) 2337.25 1.08301 0.541503 0.840699i \(-0.317855\pi\)
0.541503 + 0.840699i \(0.317855\pi\)
\(168\) −3498.06 −1.60643
\(169\) −1687.20 −0.767958
\(170\) −1995.54 −0.900299
\(171\) 882.185 0.394517
\(172\) 0 0
\(173\) 3506.24 1.54089 0.770446 0.637506i \(-0.220034\pi\)
0.770446 + 0.637506i \(0.220034\pi\)
\(174\) −935.937 −0.407777
\(175\) −8635.46 −3.73017
\(176\) 2969.99 1.27199
\(177\) 1294.95 0.549913
\(178\) −54.2595 −0.0228479
\(179\) 210.751 0.0880017 0.0440009 0.999031i \(-0.485990\pi\)
0.0440009 + 0.999031i \(0.485990\pi\)
\(180\) −98.9668 −0.0409808
\(181\) −1984.99 −0.815155 −0.407577 0.913171i \(-0.633626\pi\)
−0.407577 + 0.913171i \(0.633626\pi\)
\(182\) 1674.70 0.682072
\(183\) −1905.74 −0.769815
\(184\) 1110.24 0.444824
\(185\) 1572.95 0.625110
\(186\) −4819.58 −1.89994
\(187\) 1418.48 0.554702
\(188\) 63.2499 0.0245371
\(189\) 2460.37 0.946907
\(190\) 4778.03 1.82440
\(191\) −3624.62 −1.37313 −0.686566 0.727068i \(-0.740883\pi\)
−0.686566 + 0.727068i \(0.740883\pi\)
\(192\) 3002.86 1.12871
\(193\) −2385.96 −0.889872 −0.444936 0.895562i \(-0.646774\pi\)
−0.444936 + 0.895562i \(0.646774\pi\)
\(194\) −968.852 −0.358554
\(195\) −3012.96 −1.10647
\(196\) 124.757 0.0454653
\(197\) −879.761 −0.318175 −0.159087 0.987265i \(-0.550855\pi\)
−0.159087 + 0.987265i \(0.550855\pi\)
\(198\) 1477.52 0.530316
\(199\) 409.595 0.145907 0.0729533 0.997335i \(-0.476758\pi\)
0.0729533 + 0.997335i \(0.476758\pi\)
\(200\) 7432.59 2.62782
\(201\) 2141.63 0.751538
\(202\) 3777.87 1.31589
\(203\) −1331.80 −0.460462
\(204\) −79.4629 −0.0272721
\(205\) −2761.57 −0.940862
\(206\) −6041.09 −2.04322
\(207\) 580.005 0.194749
\(208\) −1513.67 −0.504586
\(209\) −3396.34 −1.12407
\(210\) −9897.68 −3.25240
\(211\) 4857.26 1.58477 0.792387 0.610018i \(-0.208838\pi\)
0.792387 + 0.610018i \(0.208838\pi\)
\(212\) −167.649 −0.0543122
\(213\) 2476.97 0.796805
\(214\) −2390.33 −0.763549
\(215\) 0 0
\(216\) −2117.65 −0.667074
\(217\) −6858.04 −2.14541
\(218\) 4562.87 1.41760
\(219\) 544.286 0.167943
\(220\) 381.014 0.116763
\(221\) −722.932 −0.220044
\(222\) 1315.53 0.397714
\(223\) −117.917 −0.0354095 −0.0177048 0.999843i \(-0.505636\pi\)
−0.0177048 + 0.999843i \(0.505636\pi\)
\(224\) −462.764 −0.138034
\(225\) 3882.90 1.15049
\(226\) 4361.34 1.28368
\(227\) 4470.82 1.30722 0.653610 0.756832i \(-0.273254\pi\)
0.653610 + 0.756832i \(0.273254\pi\)
\(228\) 190.263 0.0552651
\(229\) 5589.76 1.61302 0.806510 0.591220i \(-0.201354\pi\)
0.806510 + 0.591220i \(0.201354\pi\)
\(230\) 3141.39 0.900595
\(231\) 7035.50 2.00390
\(232\) 1146.28 0.324385
\(233\) −4104.15 −1.15396 −0.576978 0.816759i \(-0.695768\pi\)
−0.576978 + 0.816759i \(0.695768\pi\)
\(234\) −753.023 −0.210370
\(235\) −3400.86 −0.944033
\(236\) 83.4598 0.0230202
\(237\) 1371.59 0.375925
\(238\) −2374.86 −0.646803
\(239\) 3722.43 1.00746 0.503732 0.863860i \(-0.331960\pi\)
0.503732 + 0.863860i \(0.331960\pi\)
\(240\) 8945.94 2.40607
\(241\) 4626.46 1.23658 0.618291 0.785949i \(-0.287825\pi\)
0.618291 + 0.785949i \(0.287825\pi\)
\(242\) −1830.73 −0.486297
\(243\) −3034.29 −0.801029
\(244\) −122.825 −0.0322256
\(245\) −6708.00 −1.74922
\(246\) −2309.63 −0.598604
\(247\) 1730.96 0.445904
\(248\) 5902.76 1.51139
\(249\) 2692.12 0.685166
\(250\) 13239.7 3.34942
\(251\) 1136.12 0.285702 0.142851 0.989744i \(-0.454373\pi\)
0.142851 + 0.989744i \(0.454373\pi\)
\(252\) −117.779 −0.0294419
\(253\) −2232.97 −0.554884
\(254\) −663.411 −0.163882
\(255\) 4272.61 1.04926
\(256\) 612.798 0.149609
\(257\) 6235.33 1.51342 0.756710 0.653750i \(-0.226805\pi\)
0.756710 + 0.653750i \(0.226805\pi\)
\(258\) 0 0
\(259\) 1871.94 0.449099
\(260\) −194.185 −0.0463187
\(261\) 598.838 0.142020
\(262\) 1154.38 0.272205
\(263\) −7120.70 −1.66951 −0.834755 0.550622i \(-0.814391\pi\)
−0.834755 + 0.550622i \(0.814391\pi\)
\(264\) −6055.49 −1.41170
\(265\) 9014.26 2.08959
\(266\) 5686.25 1.31070
\(267\) 116.174 0.0266282
\(268\) 138.028 0.0314605
\(269\) 4139.98 0.938360 0.469180 0.883102i \(-0.344550\pi\)
0.469180 + 0.883102i \(0.344550\pi\)
\(270\) −5991.85 −1.35057
\(271\) −2761.65 −0.619033 −0.309517 0.950894i \(-0.600167\pi\)
−0.309517 + 0.950894i \(0.600167\pi\)
\(272\) 2146.50 0.478494
\(273\) −3585.67 −0.794925
\(274\) 3794.62 0.836648
\(275\) −14948.9 −3.27800
\(276\) 125.091 0.0272811
\(277\) −6788.15 −1.47242 −0.736211 0.676753i \(-0.763387\pi\)
−0.736211 + 0.676753i \(0.763387\pi\)
\(278\) −3864.22 −0.833671
\(279\) 3083.70 0.661706
\(280\) 12122.1 2.58727
\(281\) 2258.93 0.479560 0.239780 0.970827i \(-0.422925\pi\)
0.239780 + 0.970827i \(0.422925\pi\)
\(282\) −2844.30 −0.600622
\(283\) 2447.93 0.514185 0.257093 0.966387i \(-0.417235\pi\)
0.257093 + 0.966387i \(0.417235\pi\)
\(284\) 159.641 0.0333555
\(285\) −10230.2 −2.12625
\(286\) 2899.08 0.599392
\(287\) −3286.50 −0.675944
\(288\) 208.080 0.0425737
\(289\) −3887.83 −0.791334
\(290\) 3243.39 0.656753
\(291\) 2074.39 0.417880
\(292\) 35.0793 0.00703034
\(293\) −7628.90 −1.52111 −0.760555 0.649274i \(-0.775073\pi\)
−0.760555 + 0.649274i \(0.775073\pi\)
\(294\) −5610.21 −1.11291
\(295\) −4487.52 −0.885673
\(296\) −1611.19 −0.316380
\(297\) 4259.15 0.832124
\(298\) 5479.12 1.06509
\(299\) 1138.04 0.220116
\(300\) 837.434 0.161164
\(301\) 0 0
\(302\) 6126.88 1.16742
\(303\) −8088.72 −1.53361
\(304\) −5139.48 −0.969636
\(305\) 6604.13 1.23984
\(306\) 1067.85 0.199492
\(307\) −4363.26 −0.811154 −0.405577 0.914061i \(-0.632929\pi\)
−0.405577 + 0.914061i \(0.632929\pi\)
\(308\) 453.438 0.0838865
\(309\) 12934.5 2.38128
\(310\) 16701.7 3.05998
\(311\) −1370.87 −0.249951 −0.124975 0.992160i \(-0.539885\pi\)
−0.124975 + 0.992160i \(0.539885\pi\)
\(312\) 3086.21 0.560007
\(313\) 3305.03 0.596841 0.298421 0.954434i \(-0.403540\pi\)
0.298421 + 0.954434i \(0.403540\pi\)
\(314\) −3664.02 −0.658511
\(315\) 6332.80 1.13274
\(316\) 88.3989 0.0157368
\(317\) 4457.62 0.789794 0.394897 0.918725i \(-0.370780\pi\)
0.394897 + 0.918725i \(0.370780\pi\)
\(318\) 7539.04 1.32946
\(319\) −2305.48 −0.404645
\(320\) −10406.1 −1.81787
\(321\) 5117.89 0.889883
\(322\) 3738.51 0.647015
\(323\) −2454.63 −0.422847
\(324\) −362.857 −0.0622183
\(325\) 7618.75 1.30034
\(326\) −124.372 −0.0211298
\(327\) −9769.47 −1.65215
\(328\) 2828.71 0.476187
\(329\) −4047.30 −0.678222
\(330\) −17133.9 −2.85815
\(331\) 1446.18 0.240149 0.120074 0.992765i \(-0.461687\pi\)
0.120074 + 0.992765i \(0.461687\pi\)
\(332\) 173.508 0.0286821
\(333\) −841.710 −0.138515
\(334\) −6773.98 −1.10975
\(335\) −7421.59 −1.21040
\(336\) 10646.4 1.72860
\(337\) −957.005 −0.154692 −0.0773462 0.997004i \(-0.524645\pi\)
−0.0773462 + 0.997004i \(0.524645\pi\)
\(338\) 4889.96 0.786920
\(339\) −9337.97 −1.49607
\(340\) 275.370 0.0439236
\(341\) −11872.0 −1.88535
\(342\) −2556.80 −0.404258
\(343\) 794.905 0.125134
\(344\) 0 0
\(345\) −6725.96 −1.04961
\(346\) −10162.0 −1.57894
\(347\) −5663.55 −0.876183 −0.438092 0.898930i \(-0.644345\pi\)
−0.438092 + 0.898930i \(0.644345\pi\)
\(348\) 129.153 0.0198946
\(349\) 8397.53 1.28799 0.643996 0.765029i \(-0.277275\pi\)
0.643996 + 0.765029i \(0.277275\pi\)
\(350\) 25027.8 3.82227
\(351\) −2170.69 −0.330094
\(352\) −801.091 −0.121302
\(353\) 11111.3 1.67534 0.837669 0.546178i \(-0.183918\pi\)
0.837669 + 0.546178i \(0.183918\pi\)
\(354\) −3753.12 −0.563492
\(355\) −8583.68 −1.28331
\(356\) 7.48742 0.00111470
\(357\) 5084.76 0.753821
\(358\) −610.814 −0.0901746
\(359\) −1277.78 −0.187851 −0.0939255 0.995579i \(-0.529942\pi\)
−0.0939255 + 0.995579i \(0.529942\pi\)
\(360\) −5450.67 −0.797988
\(361\) −981.731 −0.143130
\(362\) 5753.02 0.835282
\(363\) 3919.75 0.566759
\(364\) −231.097 −0.0332768
\(365\) −1886.16 −0.270483
\(366\) 5523.33 0.788823
\(367\) −4649.71 −0.661343 −0.330671 0.943746i \(-0.607275\pi\)
−0.330671 + 0.943746i \(0.607275\pi\)
\(368\) −3379.02 −0.478651
\(369\) 1477.76 0.208480
\(370\) −4558.82 −0.640545
\(371\) 10727.7 1.50123
\(372\) 665.067 0.0926939
\(373\) −8278.57 −1.14919 −0.574595 0.818438i \(-0.694840\pi\)
−0.574595 + 0.818438i \(0.694840\pi\)
\(374\) −4111.12 −0.568398
\(375\) −28347.4 −3.90360
\(376\) 3483.54 0.477792
\(377\) 1174.99 0.160518
\(378\) −7130.80 −0.970288
\(379\) 6040.29 0.818651 0.409326 0.912388i \(-0.365764\pi\)
0.409326 + 0.912388i \(0.365764\pi\)
\(380\) −659.334 −0.0890083
\(381\) 1420.42 0.190998
\(382\) 10505.1 1.40704
\(383\) −7225.42 −0.963973 −0.481986 0.876179i \(-0.660085\pi\)
−0.481986 + 0.876179i \(0.660085\pi\)
\(384\) −9600.75 −1.27588
\(385\) −24380.7 −3.22742
\(386\) 6915.15 0.911844
\(387\) 0 0
\(388\) 133.695 0.0174931
\(389\) 5861.61 0.763998 0.381999 0.924163i \(-0.375236\pi\)
0.381999 + 0.924163i \(0.375236\pi\)
\(390\) 8732.36 1.13379
\(391\) −1613.83 −0.208734
\(392\) 6871.08 0.885311
\(393\) −2471.62 −0.317243
\(394\) 2549.78 0.326031
\(395\) −4753.09 −0.605452
\(396\) −203.887 −0.0258730
\(397\) −10532.9 −1.33156 −0.665782 0.746146i \(-0.731902\pi\)
−0.665782 + 0.746146i \(0.731902\pi\)
\(398\) −1187.12 −0.149509
\(399\) −12174.7 −1.52757
\(400\) −22621.2 −2.82765
\(401\) 5013.05 0.624289 0.312144 0.950035i \(-0.398953\pi\)
0.312144 + 0.950035i \(0.398953\pi\)
\(402\) −6207.02 −0.770094
\(403\) 6050.60 0.747895
\(404\) −521.318 −0.0641994
\(405\) 19510.3 2.39377
\(406\) 3859.90 0.471831
\(407\) 3240.51 0.394659
\(408\) −4376.48 −0.531049
\(409\) −12564.0 −1.51895 −0.759473 0.650539i \(-0.774543\pi\)
−0.759473 + 0.650539i \(0.774543\pi\)
\(410\) 8003.77 0.964093
\(411\) −8124.59 −0.975077
\(412\) 833.627 0.0996841
\(413\) −5340.52 −0.636295
\(414\) −1681.01 −0.199558
\(415\) −9329.26 −1.10351
\(416\) 408.279 0.0481191
\(417\) 8273.61 0.971608
\(418\) 9843.49 1.15182
\(419\) −13524.0 −1.57683 −0.788413 0.615146i \(-0.789097\pi\)
−0.788413 + 0.615146i \(0.789097\pi\)
\(420\) 1365.81 0.158678
\(421\) 16298.4 1.88678 0.943389 0.331688i \(-0.107618\pi\)
0.943389 + 0.331688i \(0.107618\pi\)
\(422\) −14077.6 −1.62391
\(423\) 1819.86 0.209183
\(424\) −9233.40 −1.05758
\(425\) −10804.0 −1.23311
\(426\) −7178.92 −0.816479
\(427\) 7859.45 0.890739
\(428\) 329.848 0.0372519
\(429\) −6207.16 −0.698565
\(430\) 0 0
\(431\) 1648.67 0.184255 0.0921274 0.995747i \(-0.470633\pi\)
0.0921274 + 0.995747i \(0.470633\pi\)
\(432\) 6445.12 0.717803
\(433\) −4180.27 −0.463952 −0.231976 0.972722i \(-0.574519\pi\)
−0.231976 + 0.972722i \(0.574519\pi\)
\(434\) 19876.4 2.19838
\(435\) −6944.36 −0.765417
\(436\) −629.643 −0.0691615
\(437\) 3864.09 0.422985
\(438\) −1577.49 −0.172089
\(439\) 6108.96 0.664157 0.332078 0.943252i \(-0.392250\pi\)
0.332078 + 0.943252i \(0.392250\pi\)
\(440\) 20984.6 2.27365
\(441\) 3589.56 0.387600
\(442\) 2095.25 0.225477
\(443\) 14676.2 1.57401 0.787004 0.616948i \(-0.211631\pi\)
0.787004 + 0.616948i \(0.211631\pi\)
\(444\) −181.533 −0.0194036
\(445\) −402.588 −0.0428866
\(446\) 341.755 0.0362838
\(447\) −11731.2 −1.24132
\(448\) −12384.1 −1.30601
\(449\) −9548.52 −1.00361 −0.501807 0.864980i \(-0.667331\pi\)
−0.501807 + 0.864980i \(0.667331\pi\)
\(450\) −11253.7 −1.17890
\(451\) −5689.27 −0.594007
\(452\) −601.833 −0.0626280
\(453\) −13118.1 −1.36058
\(454\) −12957.6 −1.33950
\(455\) 12425.7 1.28028
\(456\) 10478.9 1.07614
\(457\) −11740.0 −1.20170 −0.600849 0.799363i \(-0.705171\pi\)
−0.600849 + 0.799363i \(0.705171\pi\)
\(458\) −16200.6 −1.65285
\(459\) 3078.21 0.313025
\(460\) −433.489 −0.0439381
\(461\) 8505.48 0.859305 0.429652 0.902994i \(-0.358636\pi\)
0.429652 + 0.902994i \(0.358636\pi\)
\(462\) −20390.7 −2.05338
\(463\) −15636.9 −1.56957 −0.784784 0.619769i \(-0.787226\pi\)
−0.784784 + 0.619769i \(0.787226\pi\)
\(464\) −3488.74 −0.349053
\(465\) −35759.8 −3.56628
\(466\) 11894.9 1.18245
\(467\) 1591.28 0.157678 0.0788392 0.996887i \(-0.474879\pi\)
0.0788392 + 0.996887i \(0.474879\pi\)
\(468\) 103.912 0.0102635
\(469\) −8832.31 −0.869591
\(470\) 9856.59 0.967342
\(471\) 7844.96 0.767467
\(472\) 4596.61 0.448255
\(473\) 0 0
\(474\) −3975.22 −0.385207
\(475\) 25868.6 2.49880
\(476\) 327.713 0.0315561
\(477\) −4823.68 −0.463021
\(478\) −10788.6 −1.03234
\(479\) −9244.11 −0.881783 −0.440891 0.897560i \(-0.645338\pi\)
−0.440891 + 0.897560i \(0.645338\pi\)
\(480\) −2412.98 −0.229452
\(481\) −1651.54 −0.156557
\(482\) −13408.7 −1.26712
\(483\) −8004.45 −0.754069
\(484\) 252.628 0.0237254
\(485\) −7188.58 −0.673024
\(486\) 8794.19 0.820808
\(487\) 2684.94 0.249828 0.124914 0.992168i \(-0.460135\pi\)
0.124914 + 0.992168i \(0.460135\pi\)
\(488\) −6764.68 −0.627505
\(489\) 266.290 0.0246259
\(490\) 19441.6 1.79241
\(491\) 10476.7 0.962947 0.481473 0.876461i \(-0.340102\pi\)
0.481473 + 0.876461i \(0.340102\pi\)
\(492\) 318.712 0.0292046
\(493\) −1666.23 −0.152218
\(494\) −5016.77 −0.456914
\(495\) 10962.7 0.995429
\(496\) −17965.2 −1.62633
\(497\) −10215.3 −0.921968
\(498\) −7802.49 −0.702084
\(499\) 14762.9 1.32440 0.662201 0.749326i \(-0.269623\pi\)
0.662201 + 0.749326i \(0.269623\pi\)
\(500\) −1826.99 −0.163411
\(501\) 14503.6 1.29336
\(502\) −3292.78 −0.292757
\(503\) −11354.1 −1.00647 −0.503237 0.864149i \(-0.667858\pi\)
−0.503237 + 0.864149i \(0.667858\pi\)
\(504\) −6486.75 −0.573299
\(505\) 28030.6 2.46999
\(506\) 6471.74 0.568585
\(507\) −10469.8 −0.917121
\(508\) 91.5459 0.00799546
\(509\) −17946.4 −1.56279 −0.781396 0.624036i \(-0.785492\pi\)
−0.781396 + 0.624036i \(0.785492\pi\)
\(510\) −12383.2 −1.07517
\(511\) −2244.69 −0.194323
\(512\) 10601.2 0.915061
\(513\) −7370.34 −0.634324
\(514\) −18071.6 −1.55079
\(515\) −44823.0 −3.83522
\(516\) 0 0
\(517\) −7006.30 −0.596009
\(518\) −5425.37 −0.460187
\(519\) 21757.7 1.84018
\(520\) −10694.9 −0.901929
\(521\) 3271.82 0.275127 0.137564 0.990493i \(-0.456073\pi\)
0.137564 + 0.990493i \(0.456073\pi\)
\(522\) −1735.59 −0.145526
\(523\) 4629.62 0.387073 0.193536 0.981093i \(-0.438004\pi\)
0.193536 + 0.981093i \(0.438004\pi\)
\(524\) −159.296 −0.0132803
\(525\) −53586.7 −4.45469
\(526\) 20637.7 1.71073
\(527\) −8580.22 −0.709223
\(528\) 18430.0 1.51906
\(529\) −9626.50 −0.791197
\(530\) −26125.7 −2.14119
\(531\) 2401.35 0.196251
\(532\) −784.662 −0.0639463
\(533\) 2899.56 0.235636
\(534\) −336.703 −0.0272857
\(535\) −17735.5 −1.43322
\(536\) 7602.02 0.612607
\(537\) 1307.80 0.105095
\(538\) −11998.8 −0.961530
\(539\) −13819.5 −1.10436
\(540\) 826.833 0.0658911
\(541\) −11418.8 −0.907452 −0.453726 0.891141i \(-0.649906\pi\)
−0.453726 + 0.891141i \(0.649906\pi\)
\(542\) 8003.98 0.634318
\(543\) −12317.7 −0.973485
\(544\) −578.972 −0.0456309
\(545\) 33855.0 2.66090
\(546\) 10392.2 0.814553
\(547\) 6243.35 0.488019 0.244009 0.969773i \(-0.421537\pi\)
0.244009 + 0.969773i \(0.421537\pi\)
\(548\) −523.630 −0.0408182
\(549\) −3533.98 −0.274729
\(550\) 43325.8 3.35894
\(551\) 3989.56 0.308459
\(552\) 6889.48 0.531224
\(553\) −5656.56 −0.434976
\(554\) 19673.9 1.50878
\(555\) 9760.80 0.746528
\(556\) 533.235 0.0406730
\(557\) −1313.79 −0.0999412 −0.0499706 0.998751i \(-0.515913\pi\)
−0.0499706 + 0.998751i \(0.515913\pi\)
\(558\) −8937.37 −0.678045
\(559\) 0 0
\(560\) −36893.9 −2.78402
\(561\) 8802.24 0.662444
\(562\) −6546.98 −0.491401
\(563\) −12978.3 −0.971525 −0.485763 0.874091i \(-0.661458\pi\)
−0.485763 + 0.874091i \(0.661458\pi\)
\(564\) 392.492 0.0293030
\(565\) 32359.7 2.40953
\(566\) −7094.75 −0.526881
\(567\) 23218.9 1.71976
\(568\) 8792.35 0.649505
\(569\) −19149.9 −1.41091 −0.705454 0.708756i \(-0.749257\pi\)
−0.705454 + 0.708756i \(0.749257\pi\)
\(570\) 29649.7 2.17875
\(571\) 3603.81 0.264124 0.132062 0.991241i \(-0.457840\pi\)
0.132062 + 0.991241i \(0.457840\pi\)
\(572\) −400.052 −0.0292430
\(573\) −22492.3 −1.63984
\(574\) 9525.15 0.692634
\(575\) 17007.7 1.23351
\(576\) 5568.46 0.402811
\(577\) 11668.0 0.841843 0.420921 0.907097i \(-0.361707\pi\)
0.420921 + 0.907097i \(0.361707\pi\)
\(578\) 11267.9 0.810874
\(579\) −14805.9 −1.06271
\(580\) −447.564 −0.0320415
\(581\) −11102.6 −0.792793
\(582\) −6012.14 −0.428198
\(583\) 18570.8 1.31925
\(584\) 1932.02 0.136896
\(585\) −5587.19 −0.394875
\(586\) 22110.6 1.55867
\(587\) 21935.6 1.54238 0.771191 0.636603i \(-0.219661\pi\)
0.771191 + 0.636603i \(0.219661\pi\)
\(588\) 774.168 0.0542962
\(589\) 20544.1 1.43719
\(590\) 13006.0 0.907542
\(591\) −5459.29 −0.379975
\(592\) 4903.68 0.340439
\(593\) −10763.9 −0.745396 −0.372698 0.927953i \(-0.621567\pi\)
−0.372698 + 0.927953i \(0.621567\pi\)
\(594\) −12344.1 −0.852670
\(595\) −17620.7 −1.21408
\(596\) −756.079 −0.0519634
\(597\) 2541.71 0.174247
\(598\) −3298.35 −0.225551
\(599\) −16831.8 −1.14813 −0.574064 0.818810i \(-0.694634\pi\)
−0.574064 + 0.818810i \(0.694634\pi\)
\(600\) 46122.3 3.13823
\(601\) 21858.0 1.48354 0.741770 0.670654i \(-0.233987\pi\)
0.741770 + 0.670654i \(0.233987\pi\)
\(602\) 0 0
\(603\) 3971.42 0.268207
\(604\) −845.465 −0.0569561
\(605\) −13583.5 −0.912804
\(606\) 23443.2 1.57148
\(607\) 16133.2 1.07879 0.539396 0.842052i \(-0.318653\pi\)
0.539396 + 0.842052i \(0.318653\pi\)
\(608\) 1386.27 0.0924680
\(609\) −8264.36 −0.549899
\(610\) −19140.5 −1.27045
\(611\) 3570.79 0.236430
\(612\) −147.355 −0.00973280
\(613\) 14424.6 0.950415 0.475208 0.879874i \(-0.342373\pi\)
0.475208 + 0.879874i \(0.342373\pi\)
\(614\) 12645.9 0.831182
\(615\) −17136.7 −1.12361
\(616\) 24973.5 1.63346
\(617\) −12177.9 −0.794592 −0.397296 0.917691i \(-0.630051\pi\)
−0.397296 + 0.917691i \(0.630051\pi\)
\(618\) −37487.5 −2.44008
\(619\) −9555.90 −0.620491 −0.310246 0.950656i \(-0.600411\pi\)
−0.310246 + 0.950656i \(0.600411\pi\)
\(620\) −2304.72 −0.149290
\(621\) −4845.73 −0.313128
\(622\) 3973.13 0.256122
\(623\) −479.113 −0.0308110
\(624\) −9392.93 −0.602593
\(625\) 56055.8 3.58757
\(626\) −9578.85 −0.611578
\(627\) −21075.7 −1.34240
\(628\) 505.608 0.0321273
\(629\) 2342.01 0.148461
\(630\) −18354.1 −1.16071
\(631\) 14800.3 0.933740 0.466870 0.884326i \(-0.345382\pi\)
0.466870 + 0.884326i \(0.345382\pi\)
\(632\) 4868.64 0.306430
\(633\) 30141.3 1.89259
\(634\) −12919.4 −0.809295
\(635\) −4922.30 −0.307615
\(636\) −1040.33 −0.0648614
\(637\) 7043.17 0.438086
\(638\) 6681.88 0.414637
\(639\) 4593.27 0.284361
\(640\) 33270.4 2.05488
\(641\) −12808.0 −0.789214 −0.394607 0.918850i \(-0.629119\pi\)
−0.394607 + 0.918850i \(0.629119\pi\)
\(642\) −14833.0 −0.911856
\(643\) 3164.25 0.194068 0.0970342 0.995281i \(-0.469064\pi\)
0.0970342 + 0.995281i \(0.469064\pi\)
\(644\) −515.887 −0.0315665
\(645\) 0 0
\(646\) 7114.18 0.433287
\(647\) −18517.4 −1.12519 −0.562593 0.826734i \(-0.690196\pi\)
−0.562593 + 0.826734i \(0.690196\pi\)
\(648\) −19984.6 −1.21153
\(649\) −9244.98 −0.559164
\(650\) −22081.1 −1.33245
\(651\) −42557.0 −2.56212
\(652\) 17.1624 0.00103088
\(653\) −21579.1 −1.29319 −0.646596 0.762833i \(-0.723808\pi\)
−0.646596 + 0.762833i \(0.723808\pi\)
\(654\) 28314.5 1.69294
\(655\) 8565.11 0.510941
\(656\) −8609.23 −0.512399
\(657\) 1009.32 0.0599349
\(658\) 11730.2 0.694968
\(659\) 2264.45 0.133855 0.0669274 0.997758i \(-0.478680\pi\)
0.0669274 + 0.997758i \(0.478680\pi\)
\(660\) 2364.35 0.139443
\(661\) −14720.0 −0.866174 −0.433087 0.901352i \(-0.642576\pi\)
−0.433087 + 0.901352i \(0.642576\pi\)
\(662\) −4191.41 −0.246078
\(663\) −4486.10 −0.262784
\(664\) 9556.06 0.558505
\(665\) 42190.2 2.46025
\(666\) 2439.50 0.141935
\(667\) 2622.99 0.152268
\(668\) 934.760 0.0541422
\(669\) −731.726 −0.0422872
\(670\) 21509.7 1.24029
\(671\) 13605.5 0.782765
\(672\) −2871.64 −0.164845
\(673\) 5130.48 0.293857 0.146928 0.989147i \(-0.453061\pi\)
0.146928 + 0.989147i \(0.453061\pi\)
\(674\) 2773.65 0.158512
\(675\) −32440.3 −1.84982
\(676\) −674.779 −0.0383921
\(677\) −339.763 −0.0192883 −0.00964413 0.999953i \(-0.503070\pi\)
−0.00964413 + 0.999953i \(0.503070\pi\)
\(678\) 27063.9 1.53301
\(679\) −8555.00 −0.483521
\(680\) 15166.2 0.855291
\(681\) 27743.3 1.56113
\(682\) 34408.1 1.93190
\(683\) 10488.8 0.587616 0.293808 0.955864i \(-0.405077\pi\)
0.293808 + 0.955864i \(0.405077\pi\)
\(684\) 352.821 0.0197229
\(685\) 28154.9 1.57043
\(686\) −2303.84 −0.128223
\(687\) 34686.8 1.92632
\(688\) 0 0
\(689\) −9464.66 −0.523331
\(690\) 19493.6 1.07552
\(691\) 30039.5 1.65377 0.826887 0.562368i \(-0.190109\pi\)
0.826887 + 0.562368i \(0.190109\pi\)
\(692\) 1402.28 0.0770329
\(693\) 13046.5 0.715147
\(694\) 16414.5 0.897817
\(695\) −28671.3 −1.56484
\(696\) 7113.18 0.387391
\(697\) −4111.80 −0.223451
\(698\) −24338.3 −1.31980
\(699\) −25468.0 −1.37809
\(700\) −3453.66 −0.186480
\(701\) −21987.7 −1.18468 −0.592342 0.805687i \(-0.701797\pi\)
−0.592342 + 0.805687i \(0.701797\pi\)
\(702\) 6291.24 0.338244
\(703\) −5607.62 −0.300847
\(704\) −21438.1 −1.14770
\(705\) −21103.8 −1.12740
\(706\) −32203.5 −1.71670
\(707\) 33358.7 1.77452
\(708\) 517.903 0.0274915
\(709\) 18478.4 0.978805 0.489402 0.872058i \(-0.337215\pi\)
0.489402 + 0.872058i \(0.337215\pi\)
\(710\) 24877.8 1.31499
\(711\) 2543.45 0.134159
\(712\) 412.375 0.0217057
\(713\) 13507.0 0.709456
\(714\) −14737.0 −0.772434
\(715\) 21510.2 1.12509
\(716\) 84.2879 0.00439942
\(717\) 23099.2 1.20315
\(718\) 3703.34 0.192489
\(719\) −26993.9 −1.40014 −0.700071 0.714073i \(-0.746848\pi\)
−0.700071 + 0.714073i \(0.746848\pi\)
\(720\) 16589.2 0.858673
\(721\) −53343.0 −2.75534
\(722\) 2845.32 0.146664
\(723\) 28709.1 1.47677
\(724\) −793.875 −0.0407516
\(725\) 17559.9 0.899529
\(726\) −11360.5 −0.580753
\(727\) −2671.91 −0.136308 −0.0681539 0.997675i \(-0.521711\pi\)
−0.0681539 + 0.997675i \(0.521711\pi\)
\(728\) −12727.8 −0.647973
\(729\) 5667.46 0.287937
\(730\) 5466.60 0.277162
\(731\) 0 0
\(732\) −762.180 −0.0384850
\(733\) −6471.71 −0.326109 −0.163055 0.986617i \(-0.552135\pi\)
−0.163055 + 0.986617i \(0.552135\pi\)
\(734\) 13476.1 0.677672
\(735\) −41626.0 −2.08898
\(736\) 911.420 0.0456459
\(737\) −15289.6 −0.764180
\(738\) −4282.95 −0.213628
\(739\) 7029.25 0.349899 0.174949 0.984577i \(-0.444024\pi\)
0.174949 + 0.984577i \(0.444024\pi\)
\(740\) 629.084 0.0312508
\(741\) 10741.3 0.532513
\(742\) −31091.7 −1.53829
\(743\) −23560.5 −1.16332 −0.581662 0.813431i \(-0.697597\pi\)
−0.581662 + 0.813431i \(0.697597\pi\)
\(744\) 36629.1 1.80496
\(745\) 40653.3 1.99923
\(746\) 23993.5 1.17757
\(747\) 4992.24 0.244520
\(748\) 567.305 0.0277309
\(749\) −21106.7 −1.02967
\(750\) 82158.2 3.99999
\(751\) −20853.5 −1.01326 −0.506629 0.862164i \(-0.669108\pi\)
−0.506629 + 0.862164i \(0.669108\pi\)
\(752\) −10602.2 −0.514126
\(753\) 7050.11 0.341195
\(754\) −3405.45 −0.164481
\(755\) 45459.5 2.19131
\(756\) 983.999 0.0473382
\(757\) −18722.3 −0.898910 −0.449455 0.893303i \(-0.648382\pi\)
−0.449455 + 0.893303i \(0.648382\pi\)
\(758\) −17506.4 −0.838865
\(759\) −13856.5 −0.662661
\(760\) −36313.4 −1.73319
\(761\) 16358.5 0.779233 0.389616 0.920977i \(-0.372608\pi\)
0.389616 + 0.920977i \(0.372608\pi\)
\(762\) −4116.74 −0.195714
\(763\) 40290.3 1.91167
\(764\) −1449.63 −0.0686462
\(765\) 7923.08 0.374457
\(766\) 20941.2 0.987775
\(767\) 4711.74 0.221814
\(768\) 3802.67 0.178668
\(769\) −10838.7 −0.508263 −0.254131 0.967170i \(-0.581790\pi\)
−0.254131 + 0.967170i \(0.581790\pi\)
\(770\) 70661.9 3.30711
\(771\) 38692.8 1.80738
\(772\) −954.240 −0.0444869
\(773\) −7220.23 −0.335955 −0.167978 0.985791i \(-0.553724\pi\)
−0.167978 + 0.985791i \(0.553724\pi\)
\(774\) 0 0
\(775\) 90424.2 4.19114
\(776\) 7363.34 0.340629
\(777\) 11616.2 0.536329
\(778\) −16988.5 −0.782862
\(779\) 9845.12 0.452809
\(780\) −1205.00 −0.0553154
\(781\) −17683.7 −0.810208
\(782\) 4677.32 0.213888
\(783\) −5003.08 −0.228347
\(784\) −20912.3 −0.952636
\(785\) −27185.9 −1.23606
\(786\) 7163.40 0.325076
\(787\) 30348.7 1.37460 0.687302 0.726372i \(-0.258795\pi\)
0.687302 + 0.726372i \(0.258795\pi\)
\(788\) −351.851 −0.0159063
\(789\) −44186.9 −1.99379
\(790\) 13775.7 0.620402
\(791\) 38510.7 1.73108
\(792\) −11229.2 −0.503805
\(793\) −6934.11 −0.310514
\(794\) 30527.1 1.36444
\(795\) 55937.3 2.49546
\(796\) 163.813 0.00729423
\(797\) −1900.17 −0.0844509 −0.0422254 0.999108i \(-0.513445\pi\)
−0.0422254 + 0.999108i \(0.513445\pi\)
\(798\) 35285.6 1.56528
\(799\) −5063.66 −0.224204
\(800\) 6101.60 0.269655
\(801\) 215.432 0.00950300
\(802\) −14529.1 −0.639703
\(803\) −3885.79 −0.170768
\(804\) 856.524 0.0375712
\(805\) 27738.6 1.21448
\(806\) −17536.2 −0.766362
\(807\) 25690.3 1.12062
\(808\) −28712.0 −1.25011
\(809\) −18024.2 −0.783309 −0.391654 0.920112i \(-0.628097\pi\)
−0.391654 + 0.920112i \(0.628097\pi\)
\(810\) −56546.1 −2.45287
\(811\) 28590.6 1.23792 0.618958 0.785424i \(-0.287555\pi\)
0.618958 + 0.785424i \(0.287555\pi\)
\(812\) −532.638 −0.0230196
\(813\) −17137.2 −0.739271
\(814\) −9391.87 −0.404404
\(815\) −922.799 −0.0396616
\(816\) 13319.9 0.571434
\(817\) 0 0
\(818\) 36413.7 1.55645
\(819\) −6649.22 −0.283691
\(820\) −1104.46 −0.0470360
\(821\) 9514.04 0.404436 0.202218 0.979340i \(-0.435185\pi\)
0.202218 + 0.979340i \(0.435185\pi\)
\(822\) 23547.2 0.999153
\(823\) −44795.5 −1.89729 −0.948646 0.316338i \(-0.897546\pi\)
−0.948646 + 0.316338i \(0.897546\pi\)
\(824\) 45912.7 1.94107
\(825\) −92764.0 −3.91470
\(826\) 15478.2 0.652006
\(827\) −36045.1 −1.51561 −0.757806 0.652480i \(-0.773729\pi\)
−0.757806 + 0.652480i \(0.773729\pi\)
\(828\) 231.967 0.00973600
\(829\) −37164.1 −1.55701 −0.778506 0.627637i \(-0.784022\pi\)
−0.778506 + 0.627637i \(0.784022\pi\)
\(830\) 27038.7 1.13075
\(831\) −42123.4 −1.75842
\(832\) 10926.0 0.455278
\(833\) −9987.77 −0.415433
\(834\) −23979.1 −0.995598
\(835\) −50260.8 −2.08305
\(836\) −1358.33 −0.0561948
\(837\) −25763.2 −1.06393
\(838\) 39196.1 1.61576
\(839\) −2120.52 −0.0872567 −0.0436284 0.999048i \(-0.513892\pi\)
−0.0436284 + 0.999048i \(0.513892\pi\)
\(840\) 75222.9 3.08981
\(841\) −21680.8 −0.888960
\(842\) −47237.0 −1.93337
\(843\) 14017.6 0.572707
\(844\) 1942.61 0.0792268
\(845\) 36282.0 1.47709
\(846\) −5274.43 −0.214348
\(847\) −16165.4 −0.655786
\(848\) 28102.0 1.13800
\(849\) 15190.4 0.614057
\(850\) 31312.8 1.26355
\(851\) −3686.81 −0.148510
\(852\) 990.640 0.0398342
\(853\) −30242.2 −1.21392 −0.606960 0.794732i \(-0.707611\pi\)
−0.606960 + 0.794732i \(0.707611\pi\)
\(854\) −22778.8 −0.912733
\(855\) −18970.7 −0.758811
\(856\) 18166.6 0.725377
\(857\) 19083.9 0.760668 0.380334 0.924849i \(-0.375809\pi\)
0.380334 + 0.924849i \(0.375809\pi\)
\(858\) 17990.0 0.715814
\(859\) 25660.8 1.01925 0.509625 0.860397i \(-0.329784\pi\)
0.509625 + 0.860397i \(0.329784\pi\)
\(860\) 0 0
\(861\) −20394.1 −0.807235
\(862\) −4778.29 −0.188804
\(863\) −26806.1 −1.05735 −0.528674 0.848825i \(-0.677310\pi\)
−0.528674 + 0.848825i \(0.677310\pi\)
\(864\) −1738.44 −0.0684523
\(865\) −75398.8 −2.96374
\(866\) 12115.5 0.475407
\(867\) −24125.6 −0.945038
\(868\) −2742.80 −0.107254
\(869\) −9792.09 −0.382248
\(870\) 20126.6 0.784316
\(871\) 7792.42 0.303141
\(872\) −34678.1 −1.34673
\(873\) 3846.72 0.149132
\(874\) −11199.2 −0.433430
\(875\) 116907. 4.51679
\(876\) 217.682 0.00839587
\(877\) 37676.2 1.45067 0.725333 0.688398i \(-0.241686\pi\)
0.725333 + 0.688398i \(0.241686\pi\)
\(878\) −17705.4 −0.680556
\(879\) −47340.5 −1.81656
\(880\) −63867.2 −2.44655
\(881\) −10062.6 −0.384810 −0.192405 0.981316i \(-0.561629\pi\)
−0.192405 + 0.981316i \(0.561629\pi\)
\(882\) −10403.5 −0.397170
\(883\) 4862.49 0.185318 0.0926591 0.995698i \(-0.470463\pi\)
0.0926591 + 0.995698i \(0.470463\pi\)
\(884\) −289.129 −0.0110005
\(885\) −27847.0 −1.05770
\(886\) −42535.4 −1.61287
\(887\) 27243.1 1.03127 0.515634 0.856809i \(-0.327557\pi\)
0.515634 + 0.856809i \(0.327557\pi\)
\(888\) −9998.09 −0.377831
\(889\) −5857.94 −0.221000
\(890\) 1166.81 0.0439455
\(891\) 40194.3 1.51129
\(892\) −47.1598 −0.00177021
\(893\) 12124.2 0.454335
\(894\) 34000.3 1.27197
\(895\) −4532.04 −0.169262
\(896\) 39594.5 1.47629
\(897\) 7062.03 0.262870
\(898\) 27674.1 1.02839
\(899\) 13945.6 0.517366
\(900\) 1552.93 0.0575158
\(901\) 13421.6 0.496270
\(902\) 16489.0 0.608674
\(903\) 0 0
\(904\) −33146.4 −1.21951
\(905\) 42685.6 1.56786
\(906\) 38019.9 1.39418
\(907\) −2391.74 −0.0875596 −0.0437798 0.999041i \(-0.513940\pi\)
−0.0437798 + 0.999041i \(0.513940\pi\)
\(908\) 1788.06 0.0653511
\(909\) −14999.6 −0.547311
\(910\) −36013.1 −1.31189
\(911\) 14501.2 0.527385 0.263692 0.964607i \(-0.415060\pi\)
0.263692 + 0.964607i \(0.415060\pi\)
\(912\) −31892.6 −1.15797
\(913\) −19219.7 −0.696692
\(914\) 34025.7 1.23137
\(915\) 40981.4 1.48066
\(916\) 2235.57 0.0806389
\(917\) 10193.2 0.367076
\(918\) −8921.47 −0.320754
\(919\) 26321.1 0.944779 0.472389 0.881390i \(-0.343392\pi\)
0.472389 + 0.881390i \(0.343392\pi\)
\(920\) −23874.7 −0.855572
\(921\) −27075.8 −0.968707
\(922\) −24651.1 −0.880522
\(923\) 9012.57 0.321400
\(924\) 2813.77 0.100180
\(925\) −24681.7 −0.877330
\(926\) 45320.0 1.60832
\(927\) 23985.5 0.849825
\(928\) 941.014 0.0332870
\(929\) 5321.18 0.187925 0.0939625 0.995576i \(-0.470047\pi\)
0.0939625 + 0.995576i \(0.470047\pi\)
\(930\) 103641. 3.65433
\(931\) 23914.3 0.841847
\(932\) −1641.41 −0.0576891
\(933\) −8506.80 −0.298500
\(934\) −4611.96 −0.161572
\(935\) −30503.2 −1.06691
\(936\) 5723.02 0.199853
\(937\) 45519.2 1.58703 0.793515 0.608551i \(-0.208249\pi\)
0.793515 + 0.608551i \(0.208249\pi\)
\(938\) 25598.4 0.891062
\(939\) 20509.1 0.712768
\(940\) −1360.14 −0.0471945
\(941\) −22898.3 −0.793264 −0.396632 0.917978i \(-0.629821\pi\)
−0.396632 + 0.917978i \(0.629821\pi\)
\(942\) −22736.8 −0.786416
\(943\) 6472.81 0.223525
\(944\) −13989.9 −0.482343
\(945\) −52908.3 −1.82128
\(946\) 0 0
\(947\) 7576.46 0.259981 0.129990 0.991515i \(-0.458505\pi\)
0.129990 + 0.991515i \(0.458505\pi\)
\(948\) 548.552 0.0187934
\(949\) 1980.41 0.0677416
\(950\) −74974.0 −2.56050
\(951\) 27661.4 0.943199
\(952\) 18049.1 0.614468
\(953\) 10070.1 0.342289 0.171144 0.985246i \(-0.445254\pi\)
0.171144 + 0.985246i \(0.445254\pi\)
\(954\) 13980.3 0.474454
\(955\) 77944.5 2.64107
\(956\) 1488.75 0.0503656
\(957\) −14306.4 −0.483241
\(958\) 26791.9 0.903555
\(959\) 33506.6 1.12824
\(960\) −64574.1 −2.17096
\(961\) 42021.4 1.41054
\(962\) 4786.60 0.160422
\(963\) 9490.54 0.317579
\(964\) 1850.30 0.0618198
\(965\) 51308.2 1.71157
\(966\) 23199.0 0.772688
\(967\) 12667.8 0.421271 0.210636 0.977565i \(-0.432447\pi\)
0.210636 + 0.977565i \(0.432447\pi\)
\(968\) 13913.7 0.461986
\(969\) −15232.0 −0.504978
\(970\) 20834.4 0.689642
\(971\) −57726.9 −1.90787 −0.953936 0.300011i \(-0.903010\pi\)
−0.953936 + 0.300011i \(0.903010\pi\)
\(972\) −1213.53 −0.0400454
\(973\) −34121.2 −1.12423
\(974\) −7781.66 −0.255996
\(975\) 47277.5 1.55292
\(976\) 20588.4 0.675225
\(977\) −35376.7 −1.15844 −0.579222 0.815170i \(-0.696644\pi\)
−0.579222 + 0.815170i \(0.696644\pi\)
\(978\) −771.779 −0.0252339
\(979\) −829.394 −0.0270761
\(980\) −2682.80 −0.0874477
\(981\) −18116.4 −0.589614
\(982\) −30364.2 −0.986723
\(983\) −9770.00 −0.317004 −0.158502 0.987359i \(-0.550666\pi\)
−0.158502 + 0.987359i \(0.550666\pi\)
\(984\) 17553.3 0.568679
\(985\) 18918.6 0.611975
\(986\) 4829.19 0.155976
\(987\) −25115.2 −0.809956
\(988\) 692.278 0.0222918
\(989\) 0 0
\(990\) −31772.9 −1.02001
\(991\) −16535.4 −0.530036 −0.265018 0.964244i \(-0.585378\pi\)
−0.265018 + 0.964244i \(0.585378\pi\)
\(992\) 4845.72 0.155093
\(993\) 8974.16 0.286794
\(994\) 29606.6 0.944733
\(995\) −8808.02 −0.280636
\(996\) 1076.69 0.0342532
\(997\) 16753.6 0.532187 0.266094 0.963947i \(-0.414267\pi\)
0.266094 + 0.963947i \(0.414267\pi\)
\(998\) −42786.7 −1.35710
\(999\) 7032.19 0.222711
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.g.1.9 30
43.2 odd 14 43.4.e.a.4.8 60
43.22 odd 14 43.4.e.a.11.8 yes 60
43.42 odd 2 1849.4.a.h.1.22 30
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.4.e.a.4.8 60 43.2 odd 14
43.4.e.a.11.8 yes 60 43.22 odd 14
1849.4.a.g.1.9 30 1.1 even 1 trivial
1849.4.a.h.1.22 30 43.42 odd 2