Properties

Label 1859.4.a.p.1.5
Level $1859$
Weight $4$
Character 1859.1
Self dual yes
Analytic conductor $109.685$
Analytic rank $0$
Dimension $51$
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] = [1859,4,Mod(1,1859)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1859, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1859.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1859 = 11 \cdot 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1859.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: \(109.684550701\)
Analytic rank: \(0\)
Dimension: \(51\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) \(=\) 1859.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.99679 q^{2} +8.59946 q^{3} +16.9679 q^{4} -10.1780 q^{5} -42.9697 q^{6} -9.94954 q^{7} -44.8107 q^{8} +46.9506 q^{9} +O(q^{10})\) \(q-4.99679 q^{2} +8.59946 q^{3} +16.9679 q^{4} -10.1780 q^{5} -42.9697 q^{6} -9.94954 q^{7} -44.8107 q^{8} +46.9506 q^{9} +50.8572 q^{10} -11.0000 q^{11} +145.915 q^{12} +49.7157 q^{14} -87.5251 q^{15} +88.1662 q^{16} -85.1519 q^{17} -234.602 q^{18} +118.078 q^{19} -172.699 q^{20} -85.5606 q^{21} +54.9647 q^{22} -61.9873 q^{23} -385.347 q^{24} -21.4086 q^{25} +171.565 q^{27} -168.823 q^{28} +202.832 q^{29} +437.345 q^{30} -290.047 q^{31} -82.0626 q^{32} -94.5940 q^{33} +425.486 q^{34} +101.266 q^{35} +796.653 q^{36} +390.052 q^{37} -590.013 q^{38} +456.082 q^{40} -148.007 q^{41} +427.528 q^{42} +326.948 q^{43} -186.647 q^{44} -477.863 q^{45} +309.737 q^{46} +96.8534 q^{47} +758.181 q^{48} -244.007 q^{49} +106.974 q^{50} -732.260 q^{51} -26.3159 q^{53} -857.272 q^{54} +111.958 q^{55} +445.845 q^{56} +1015.41 q^{57} -1013.51 q^{58} -798.970 q^{59} -1485.12 q^{60} +259.628 q^{61} +1449.30 q^{62} -467.137 q^{63} -295.280 q^{64} +472.666 q^{66} -560.359 q^{67} -1444.85 q^{68} -533.057 q^{69} -506.006 q^{70} -343.779 q^{71} -2103.89 q^{72} +898.545 q^{73} -1949.01 q^{74} -184.102 q^{75} +2003.54 q^{76} +109.445 q^{77} -618.949 q^{79} -897.354 q^{80} +207.695 q^{81} +739.558 q^{82} +312.605 q^{83} -1451.78 q^{84} +866.675 q^{85} -1633.69 q^{86} +1744.25 q^{87} +492.917 q^{88} +1484.66 q^{89} +2387.78 q^{90} -1051.79 q^{92} -2494.24 q^{93} -483.956 q^{94} -1201.80 q^{95} -705.694 q^{96} +1163.87 q^{97} +1219.25 q^{98} -516.457 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9} + 212 q^{10} - 561 q^{11} + 209 q^{12} + 280 q^{14} - 284 q^{15} + 1246 q^{16} + 164 q^{17} + 189 q^{18} - 26 q^{19} - 438 q^{20} - 134 q^{21} + 373 q^{23} + 354 q^{24} + 2048 q^{25} + 1470 q^{27} + 1245 q^{28} + 898 q^{29} + 427 q^{30} - 767 q^{31} - 1127 q^{32} - 231 q^{33} - 206 q^{34} + 54 q^{35} + 3415 q^{36} - 395 q^{37} + 1577 q^{38} + 3253 q^{40} + 354 q^{41} + 942 q^{42} + 484 q^{43} - 2574 q^{44} - 1452 q^{45} + 2117 q^{46} - 1925 q^{47} + 1780 q^{48} + 4535 q^{49} + 1093 q^{50} + 230 q^{51} + 1387 q^{53} + 5271 q^{54} + 451 q^{55} + 2568 q^{56} + 5738 q^{57} - 3695 q^{58} - 1145 q^{59} + 1590 q^{60} + 5382 q^{61} - 395 q^{62} - 710 q^{63} + 9839 q^{64} - 803 q^{66} + 210 q^{67} + 1742 q^{68} + 7028 q^{69} + 6747 q^{70} - 3693 q^{71} + 12481 q^{72} - 968 q^{73} + 1735 q^{74} - 727 q^{75} + 2801 q^{76} + 44 q^{77} + 4234 q^{79} - 2390 q^{80} + 7743 q^{81} + 4770 q^{82} + 2798 q^{83} - 14821 q^{84} + 1802 q^{85} - 6558 q^{86} + 1896 q^{87} - 231 q^{88} - 3927 q^{89} + 1927 q^{90} + 1984 q^{92} + 1332 q^{93} + 7590 q^{94} + 4944 q^{95} + 7280 q^{96} - 3913 q^{97} + 15201 q^{98} - 6534 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.99679 −1.76663 −0.883316 0.468779i \(-0.844694\pi\)
−0.883316 + 0.468779i \(0.844694\pi\)
\(3\) 8.59946 1.65497 0.827483 0.561491i \(-0.189772\pi\)
0.827483 + 0.561491i \(0.189772\pi\)
\(4\) 16.9679 2.12099
\(5\) −10.1780 −0.910347 −0.455173 0.890403i \(-0.650423\pi\)
−0.455173 + 0.890403i \(0.650423\pi\)
\(6\) −42.9697 −2.92371
\(7\) −9.94954 −0.537225 −0.268612 0.963248i \(-0.586565\pi\)
−0.268612 + 0.963248i \(0.586565\pi\)
\(8\) −44.8107 −1.98037
\(9\) 46.9506 1.73891
\(10\) 50.8572 1.60825
\(11\) −11.0000 −0.301511
\(12\) 145.915 3.51016
\(13\) 0 0
\(14\) 49.7157 0.949078
\(15\) −87.5251 −1.50659
\(16\) 88.1662 1.37760
\(17\) −85.1519 −1.21485 −0.607423 0.794379i \(-0.707797\pi\)
−0.607423 + 0.794379i \(0.707797\pi\)
\(18\) −234.602 −3.07202
\(19\) 118.078 1.42574 0.712870 0.701296i \(-0.247395\pi\)
0.712870 + 0.701296i \(0.247395\pi\)
\(20\) −172.699 −1.93083
\(21\) −85.5606 −0.889088
\(22\) 54.9647 0.532659
\(23\) −61.9873 −0.561967 −0.280983 0.959713i \(-0.590661\pi\)
−0.280983 + 0.959713i \(0.590661\pi\)
\(24\) −385.347 −3.27744
\(25\) −21.4086 −0.171269
\(26\) 0 0
\(27\) 171.565 1.22287
\(28\) −168.823 −1.13945
\(29\) 202.832 1.29879 0.649396 0.760450i \(-0.275022\pi\)
0.649396 + 0.760450i \(0.275022\pi\)
\(30\) 437.345 2.66159
\(31\) −290.047 −1.68045 −0.840224 0.542239i \(-0.817577\pi\)
−0.840224 + 0.542239i \(0.817577\pi\)
\(32\) −82.0626 −0.453336
\(33\) −94.5940 −0.498991
\(34\) 425.486 2.14618
\(35\) 101.266 0.489061
\(36\) 796.653 3.68821
\(37\) 390.052 1.73308 0.866542 0.499104i \(-0.166337\pi\)
0.866542 + 0.499104i \(0.166337\pi\)
\(38\) −590.013 −2.51876
\(39\) 0 0
\(40\) 456.082 1.80282
\(41\) −148.007 −0.563775 −0.281887 0.959448i \(-0.590960\pi\)
−0.281887 + 0.959448i \(0.590960\pi\)
\(42\) 427.528 1.57069
\(43\) 326.948 1.15951 0.579757 0.814789i \(-0.303147\pi\)
0.579757 + 0.814789i \(0.303147\pi\)
\(44\) −186.647 −0.639501
\(45\) −477.863 −1.58301
\(46\) 309.737 0.992788
\(47\) 96.8534 0.300586 0.150293 0.988642i \(-0.451978\pi\)
0.150293 + 0.988642i \(0.451978\pi\)
\(48\) 758.181 2.27988
\(49\) −244.007 −0.711390
\(50\) 106.974 0.302569
\(51\) −732.260 −2.01053
\(52\) 0 0
\(53\) −26.3159 −0.0682031 −0.0341015 0.999418i \(-0.510857\pi\)
−0.0341015 + 0.999418i \(0.510857\pi\)
\(54\) −857.272 −2.16037
\(55\) 111.958 0.274480
\(56\) 445.845 1.06390
\(57\) 1015.41 2.35955
\(58\) −1013.51 −2.29449
\(59\) −798.970 −1.76300 −0.881501 0.472183i \(-0.843466\pi\)
−0.881501 + 0.472183i \(0.843466\pi\)
\(60\) −1485.12 −3.19546
\(61\) 259.628 0.544949 0.272475 0.962163i \(-0.412158\pi\)
0.272475 + 0.962163i \(0.412158\pi\)
\(62\) 1449.30 2.96873
\(63\) −467.137 −0.934187
\(64\) −295.280 −0.576719
\(65\) 0 0
\(66\) 472.666 0.881533
\(67\) −560.359 −1.02177 −0.510887 0.859648i \(-0.670683\pi\)
−0.510887 + 0.859648i \(0.670683\pi\)
\(68\) −1444.85 −2.57667
\(69\) −533.057 −0.930036
\(70\) −506.006 −0.863990
\(71\) −343.779 −0.574635 −0.287317 0.957835i \(-0.592763\pi\)
−0.287317 + 0.957835i \(0.592763\pi\)
\(72\) −2103.89 −3.44369
\(73\) 898.545 1.44064 0.720320 0.693642i \(-0.243995\pi\)
0.720320 + 0.693642i \(0.243995\pi\)
\(74\) −1949.01 −3.06172
\(75\) −184.102 −0.283444
\(76\) 2003.54 3.02398
\(77\) 109.445 0.161979
\(78\) 0 0
\(79\) −618.949 −0.881483 −0.440742 0.897634i \(-0.645284\pi\)
−0.440742 + 0.897634i \(0.645284\pi\)
\(80\) −897.354 −1.25409
\(81\) 207.695 0.284904
\(82\) 739.558 0.995982
\(83\) 312.605 0.413408 0.206704 0.978404i \(-0.433726\pi\)
0.206704 + 0.978404i \(0.433726\pi\)
\(84\) −1451.78 −1.88574
\(85\) 866.675 1.10593
\(86\) −1633.69 −2.04843
\(87\) 1744.25 2.14946
\(88\) 492.917 0.597104
\(89\) 1484.66 1.76824 0.884121 0.467258i \(-0.154758\pi\)
0.884121 + 0.467258i \(0.154758\pi\)
\(90\) 2387.78 2.79660
\(91\) 0 0
\(92\) −1051.79 −1.19192
\(93\) −2494.24 −2.78109
\(94\) −483.956 −0.531024
\(95\) −1201.80 −1.29792
\(96\) −705.694 −0.750256
\(97\) 1163.87 1.21828 0.609140 0.793063i \(-0.291515\pi\)
0.609140 + 0.793063i \(0.291515\pi\)
\(98\) 1219.25 1.25676
\(99\) −516.457 −0.524302
\(100\) −363.259 −0.363259
\(101\) −1208.60 −1.19069 −0.595347 0.803468i \(-0.702986\pi\)
−0.595347 + 0.803468i \(0.702986\pi\)
\(102\) 3658.95 3.55186
\(103\) −307.769 −0.294421 −0.147211 0.989105i \(-0.547029\pi\)
−0.147211 + 0.989105i \(0.547029\pi\)
\(104\) 0 0
\(105\) 870.835 0.809379
\(106\) 131.495 0.120490
\(107\) −34.9235 −0.0315531 −0.0157765 0.999876i \(-0.505022\pi\)
−0.0157765 + 0.999876i \(0.505022\pi\)
\(108\) 2911.09 2.59370
\(109\) 1831.40 1.60932 0.804662 0.593734i \(-0.202347\pi\)
0.804662 + 0.593734i \(0.202347\pi\)
\(110\) −559.430 −0.484905
\(111\) 3354.23 2.86820
\(112\) −877.213 −0.740079
\(113\) 625.296 0.520557 0.260278 0.965534i \(-0.416186\pi\)
0.260278 + 0.965534i \(0.416186\pi\)
\(114\) −5073.79 −4.16846
\(115\) 630.905 0.511585
\(116\) 3441.63 2.75472
\(117\) 0 0
\(118\) 3992.29 3.11457
\(119\) 847.222 0.652645
\(120\) 3922.06 2.98361
\(121\) 121.000 0.0909091
\(122\) −1297.30 −0.962724
\(123\) −1272.78 −0.933028
\(124\) −4921.48 −3.56421
\(125\) 1490.14 1.06626
\(126\) 2334.19 1.65036
\(127\) 1447.57 1.01143 0.505714 0.862701i \(-0.331229\pi\)
0.505714 + 0.862701i \(0.331229\pi\)
\(128\) 2131.95 1.47219
\(129\) 2811.57 1.91896
\(130\) 0 0
\(131\) 1971.98 1.31521 0.657604 0.753364i \(-0.271570\pi\)
0.657604 + 0.753364i \(0.271570\pi\)
\(132\) −1605.06 −1.05835
\(133\) −1174.83 −0.765943
\(134\) 2800.00 1.80510
\(135\) −1746.18 −1.11324
\(136\) 3815.71 2.40584
\(137\) −2007.87 −1.25215 −0.626073 0.779765i \(-0.715339\pi\)
−0.626073 + 0.779765i \(0.715339\pi\)
\(138\) 2663.57 1.64303
\(139\) −271.756 −0.165828 −0.0829138 0.996557i \(-0.526423\pi\)
−0.0829138 + 0.996557i \(0.526423\pi\)
\(140\) 1718.27 1.03729
\(141\) 832.886 0.497459
\(142\) 1717.79 1.01517
\(143\) 0 0
\(144\) 4139.46 2.39552
\(145\) −2064.42 −1.18235
\(146\) −4489.84 −2.54508
\(147\) −2098.32 −1.17733
\(148\) 6618.36 3.67585
\(149\) −335.937 −0.184705 −0.0923524 0.995726i \(-0.529439\pi\)
−0.0923524 + 0.995726i \(0.529439\pi\)
\(150\) 919.921 0.500741
\(151\) 2819.45 1.51950 0.759748 0.650217i \(-0.225322\pi\)
0.759748 + 0.650217i \(0.225322\pi\)
\(152\) −5291.17 −2.82349
\(153\) −3997.94 −2.11251
\(154\) −546.873 −0.286158
\(155\) 2952.09 1.52979
\(156\) 0 0
\(157\) 2087.34 1.06107 0.530534 0.847664i \(-0.321992\pi\)
0.530534 + 0.847664i \(0.321992\pi\)
\(158\) 3092.75 1.55726
\(159\) −226.302 −0.112874
\(160\) 835.232 0.412693
\(161\) 616.745 0.301902
\(162\) −1037.81 −0.503320
\(163\) −1070.88 −0.514588 −0.257294 0.966333i \(-0.582831\pi\)
−0.257294 + 0.966333i \(0.582831\pi\)
\(164\) −2511.36 −1.19576
\(165\) 962.776 0.454255
\(166\) −1562.02 −0.730340
\(167\) −3711.75 −1.71991 −0.859953 0.510374i \(-0.829507\pi\)
−0.859953 + 0.510374i \(0.829507\pi\)
\(168\) 3834.03 1.76072
\(169\) 0 0
\(170\) −4330.59 −1.95377
\(171\) 5543.86 2.47924
\(172\) 5547.62 2.45931
\(173\) −40.5410 −0.0178166 −0.00890831 0.999960i \(-0.502836\pi\)
−0.00890831 + 0.999960i \(0.502836\pi\)
\(174\) −8715.63 −3.79730
\(175\) 213.006 0.0920099
\(176\) −969.828 −0.415361
\(177\) −6870.71 −2.91771
\(178\) −7418.53 −3.12383
\(179\) 288.006 0.120260 0.0601301 0.998191i \(-0.480848\pi\)
0.0601301 + 0.998191i \(0.480848\pi\)
\(180\) −8108.33 −3.35755
\(181\) 3327.39 1.36643 0.683213 0.730219i \(-0.260582\pi\)
0.683213 + 0.730219i \(0.260582\pi\)
\(182\) 0 0
\(183\) 2232.66 0.901872
\(184\) 2777.69 1.11290
\(185\) −3969.94 −1.57771
\(186\) 12463.2 4.91315
\(187\) 936.671 0.366290
\(188\) 1643.40 0.637538
\(189\) −1706.99 −0.656959
\(190\) 6005.14 2.29294
\(191\) 2851.33 1.08018 0.540091 0.841607i \(-0.318390\pi\)
0.540091 + 0.841607i \(0.318390\pi\)
\(192\) −2539.25 −0.954450
\(193\) −890.551 −0.332141 −0.166071 0.986114i \(-0.553108\pi\)
−0.166071 + 0.986114i \(0.553108\pi\)
\(194\) −5815.61 −2.15225
\(195\) 0 0
\(196\) −4140.28 −1.50885
\(197\) 3291.09 1.19026 0.595129 0.803630i \(-0.297101\pi\)
0.595129 + 0.803630i \(0.297101\pi\)
\(198\) 2580.63 0.926248
\(199\) −1146.44 −0.408387 −0.204193 0.978931i \(-0.565457\pi\)
−0.204193 + 0.978931i \(0.565457\pi\)
\(200\) 959.334 0.339176
\(201\) −4818.79 −1.69100
\(202\) 6039.12 2.10352
\(203\) −2018.09 −0.697743
\(204\) −12424.9 −4.26430
\(205\) 1506.41 0.513230
\(206\) 1537.86 0.520134
\(207\) −2910.34 −0.977211
\(208\) 0 0
\(209\) −1298.86 −0.429877
\(210\) −4351.38 −1.42987
\(211\) 3675.73 1.19928 0.599639 0.800270i \(-0.295311\pi\)
0.599639 + 0.800270i \(0.295311\pi\)
\(212\) −446.525 −0.144658
\(213\) −2956.31 −0.951001
\(214\) 174.505 0.0557427
\(215\) −3327.67 −1.05556
\(216\) −7687.92 −2.42174
\(217\) 2885.83 0.902779
\(218\) −9151.11 −2.84308
\(219\) 7727.00 2.38421
\(220\) 1899.69 0.582168
\(221\) 0 0
\(222\) −16760.4 −5.06704
\(223\) −3171.24 −0.952294 −0.476147 0.879366i \(-0.657967\pi\)
−0.476147 + 0.879366i \(0.657967\pi\)
\(224\) 816.485 0.243543
\(225\) −1005.15 −0.297822
\(226\) −3124.47 −0.919632
\(227\) −3526.96 −1.03125 −0.515623 0.856816i \(-0.672439\pi\)
−0.515623 + 0.856816i \(0.672439\pi\)
\(228\) 17229.4 5.00458
\(229\) 6076.99 1.75362 0.876810 0.480837i \(-0.159667\pi\)
0.876810 + 0.480837i \(0.159667\pi\)
\(230\) −3152.50 −0.903782
\(231\) 941.167 0.268070
\(232\) −9089.04 −2.57209
\(233\) 244.038 0.0686157 0.0343078 0.999411i \(-0.489077\pi\)
0.0343078 + 0.999411i \(0.489077\pi\)
\(234\) 0 0
\(235\) −985.772 −0.273637
\(236\) −13556.8 −3.73930
\(237\) −5322.62 −1.45882
\(238\) −4233.39 −1.15298
\(239\) −2163.92 −0.585657 −0.292829 0.956165i \(-0.594597\pi\)
−0.292829 + 0.956165i \(0.594597\pi\)
\(240\) −7716.76 −2.07548
\(241\) −2150.23 −0.574723 −0.287361 0.957822i \(-0.592778\pi\)
−0.287361 + 0.957822i \(0.592778\pi\)
\(242\) −604.611 −0.160603
\(243\) −2846.18 −0.751369
\(244\) 4405.33 1.15583
\(245\) 2483.50 0.647611
\(246\) 6359.80 1.64832
\(247\) 0 0
\(248\) 12997.2 3.32791
\(249\) 2688.23 0.684177
\(250\) −7445.94 −1.88369
\(251\) 502.969 0.126483 0.0632413 0.997998i \(-0.479856\pi\)
0.0632413 + 0.997998i \(0.479856\pi\)
\(252\) −7926.33 −1.98140
\(253\) 681.860 0.169439
\(254\) −7233.22 −1.78682
\(255\) 7452.93 1.83028
\(256\) −8290.68 −2.02409
\(257\) 5172.87 1.25554 0.627772 0.778398i \(-0.283967\pi\)
0.627772 + 0.778398i \(0.283967\pi\)
\(258\) −14048.8 −3.39009
\(259\) −3880.83 −0.931055
\(260\) 0 0
\(261\) 9523.10 2.25849
\(262\) −9853.54 −2.32349
\(263\) −2695.62 −0.632011 −0.316005 0.948757i \(-0.602342\pi\)
−0.316005 + 0.948757i \(0.602342\pi\)
\(264\) 4238.82 0.988187
\(265\) 267.843 0.0620884
\(266\) 5870.36 1.35314
\(267\) 12767.3 2.92638
\(268\) −9508.12 −2.16717
\(269\) 3727.17 0.844793 0.422397 0.906411i \(-0.361189\pi\)
0.422397 + 0.906411i \(0.361189\pi\)
\(270\) 8725.30 1.96668
\(271\) 3317.84 0.743707 0.371854 0.928291i \(-0.378722\pi\)
0.371854 + 0.928291i \(0.378722\pi\)
\(272\) −7507.52 −1.67357
\(273\) 0 0
\(274\) 10032.9 2.21208
\(275\) 235.495 0.0516395
\(276\) −9044.85 −1.97259
\(277\) 4520.71 0.980589 0.490294 0.871557i \(-0.336889\pi\)
0.490294 + 0.871557i \(0.336889\pi\)
\(278\) 1357.91 0.292956
\(279\) −13617.9 −2.92215
\(280\) −4537.81 −0.968521
\(281\) 3526.53 0.748667 0.374333 0.927294i \(-0.377872\pi\)
0.374333 + 0.927294i \(0.377872\pi\)
\(282\) −4161.76 −0.878826
\(283\) −3367.83 −0.707409 −0.353705 0.935357i \(-0.615078\pi\)
−0.353705 + 0.935357i \(0.615078\pi\)
\(284\) −5833.21 −1.21879
\(285\) −10334.8 −2.14801
\(286\) 0 0
\(287\) 1472.60 0.302874
\(288\) −3852.89 −0.788312
\(289\) 2337.85 0.475849
\(290\) 10315.5 2.08878
\(291\) 10008.6 2.01621
\(292\) 15246.4 3.05558
\(293\) 5144.64 1.02578 0.512889 0.858455i \(-0.328575\pi\)
0.512889 + 0.858455i \(0.328575\pi\)
\(294\) 10484.9 2.07990
\(295\) 8131.91 1.60494
\(296\) −17478.5 −3.43215
\(297\) −1887.21 −0.368711
\(298\) 1678.61 0.326305
\(299\) 0 0
\(300\) −3123.83 −0.601181
\(301\) −3252.98 −0.622919
\(302\) −14088.2 −2.68439
\(303\) −10393.3 −1.97056
\(304\) 10410.5 1.96410
\(305\) −2642.49 −0.496093
\(306\) 19976.8 3.73203
\(307\) −8322.60 −1.54722 −0.773609 0.633663i \(-0.781551\pi\)
−0.773609 + 0.633663i \(0.781551\pi\)
\(308\) 1857.05 0.343556
\(309\) −2646.65 −0.487257
\(310\) −14751.0 −2.70258
\(311\) 6866.90 1.25205 0.626023 0.779805i \(-0.284682\pi\)
0.626023 + 0.779805i \(0.284682\pi\)
\(312\) 0 0
\(313\) −1954.64 −0.352979 −0.176490 0.984302i \(-0.556474\pi\)
−0.176490 + 0.984302i \(0.556474\pi\)
\(314\) −10430.0 −1.87452
\(315\) 4754.52 0.850434
\(316\) −10502.3 −1.86961
\(317\) 3097.55 0.548820 0.274410 0.961613i \(-0.411517\pi\)
0.274410 + 0.961613i \(0.411517\pi\)
\(318\) 1130.78 0.199406
\(319\) −2231.15 −0.391601
\(320\) 3005.36 0.525014
\(321\) −300.323 −0.0522193
\(322\) −3081.74 −0.533350
\(323\) −10054.6 −1.73205
\(324\) 3524.15 0.604277
\(325\) 0 0
\(326\) 5350.96 0.909087
\(327\) 15749.0 2.66338
\(328\) 6632.28 1.11648
\(329\) −963.647 −0.161482
\(330\) −4810.79 −0.802501
\(331\) 2904.59 0.482329 0.241164 0.970484i \(-0.422471\pi\)
0.241164 + 0.970484i \(0.422471\pi\)
\(332\) 5304.25 0.876833
\(333\) 18313.2 3.01368
\(334\) 18546.9 3.03844
\(335\) 5703.33 0.930168
\(336\) −7543.56 −1.22481
\(337\) −3911.44 −0.632254 −0.316127 0.948717i \(-0.602383\pi\)
−0.316127 + 0.948717i \(0.602383\pi\)
\(338\) 0 0
\(339\) 5377.21 0.861504
\(340\) 14705.6 2.34566
\(341\) 3190.51 0.506674
\(342\) −27701.5 −4.37990
\(343\) 5840.45 0.919401
\(344\) −14650.8 −2.29627
\(345\) 5425.44 0.846655
\(346\) 202.575 0.0314754
\(347\) −6199.11 −0.959036 −0.479518 0.877532i \(-0.659188\pi\)
−0.479518 + 0.877532i \(0.659188\pi\)
\(348\) 29596.2 4.55897
\(349\) 9339.47 1.43247 0.716233 0.697862i \(-0.245865\pi\)
0.716233 + 0.697862i \(0.245865\pi\)
\(350\) −1064.35 −0.162548
\(351\) 0 0
\(352\) 902.689 0.136686
\(353\) −1538.08 −0.231909 −0.115954 0.993255i \(-0.536993\pi\)
−0.115954 + 0.993255i \(0.536993\pi\)
\(354\) 34331.5 5.15451
\(355\) 3498.98 0.523117
\(356\) 25191.5 3.75042
\(357\) 7285.65 1.08011
\(358\) −1439.11 −0.212456
\(359\) 3856.14 0.566906 0.283453 0.958986i \(-0.408520\pi\)
0.283453 + 0.958986i \(0.408520\pi\)
\(360\) 21413.3 3.13495
\(361\) 7083.53 1.03273
\(362\) −16626.3 −2.41397
\(363\) 1040.53 0.150451
\(364\) 0 0
\(365\) −9145.38 −1.31148
\(366\) −11156.1 −1.59328
\(367\) 7807.63 1.11050 0.555252 0.831682i \(-0.312622\pi\)
0.555252 + 0.831682i \(0.312622\pi\)
\(368\) −5465.18 −0.774164
\(369\) −6949.01 −0.980355
\(370\) 19837.0 2.78723
\(371\) 261.831 0.0366404
\(372\) −42322.0 −5.89865
\(373\) 1707.02 0.236960 0.118480 0.992956i \(-0.462198\pi\)
0.118480 + 0.992956i \(0.462198\pi\)
\(374\) −4680.35 −0.647099
\(375\) 12814.4 1.76463
\(376\) −4340.06 −0.595270
\(377\) 0 0
\(378\) 8529.46 1.16060
\(379\) −7494.31 −1.01572 −0.507858 0.861441i \(-0.669563\pi\)
−0.507858 + 0.861441i \(0.669563\pi\)
\(380\) −20392.0 −2.75287
\(381\) 12448.3 1.67388
\(382\) −14247.5 −1.90828
\(383\) 1912.26 0.255123 0.127562 0.991831i \(-0.459285\pi\)
0.127562 + 0.991831i \(0.459285\pi\)
\(384\) 18333.6 2.43642
\(385\) −1113.93 −0.147457
\(386\) 4449.90 0.586771
\(387\) 15350.4 2.01629
\(388\) 19748.4 2.58395
\(389\) 1802.21 0.234899 0.117449 0.993079i \(-0.462528\pi\)
0.117449 + 0.993079i \(0.462528\pi\)
\(390\) 0 0
\(391\) 5278.33 0.682703
\(392\) 10934.1 1.40881
\(393\) 16957.9 2.17663
\(394\) −16444.9 −2.10275
\(395\) 6299.65 0.802455
\(396\) −8763.19 −1.11204
\(397\) −8612.12 −1.08874 −0.544370 0.838845i \(-0.683231\pi\)
−0.544370 + 0.838845i \(0.683231\pi\)
\(398\) 5728.51 0.721468
\(399\) −10102.9 −1.26761
\(400\) −1887.52 −0.235940
\(401\) 6830.18 0.850581 0.425290 0.905057i \(-0.360172\pi\)
0.425290 + 0.905057i \(0.360172\pi\)
\(402\) 24078.5 2.98737
\(403\) 0 0
\(404\) −20507.4 −2.52545
\(405\) −2113.92 −0.259361
\(406\) 10084.0 1.23266
\(407\) −4290.57 −0.522544
\(408\) 32813.1 3.98159
\(409\) 13767.3 1.66443 0.832213 0.554457i \(-0.187074\pi\)
0.832213 + 0.554457i \(0.187074\pi\)
\(410\) −7527.21 −0.906689
\(411\) −17266.6 −2.07226
\(412\) −5222.19 −0.624463
\(413\) 7949.39 0.947128
\(414\) 14542.4 1.72637
\(415\) −3181.69 −0.376345
\(416\) 0 0
\(417\) −2336.95 −0.274439
\(418\) 6490.14 0.759434
\(419\) −6227.23 −0.726063 −0.363031 0.931777i \(-0.618258\pi\)
−0.363031 + 0.931777i \(0.618258\pi\)
\(420\) 14776.2 1.71668
\(421\) 10023.7 1.16039 0.580194 0.814478i \(-0.302977\pi\)
0.580194 + 0.814478i \(0.302977\pi\)
\(422\) −18366.8 −2.11868
\(423\) 4547.33 0.522692
\(424\) 1179.23 0.135067
\(425\) 1822.98 0.208065
\(426\) 14772.1 1.68007
\(427\) −2583.17 −0.292760
\(428\) −592.578 −0.0669237
\(429\) 0 0
\(430\) 16627.7 1.86478
\(431\) 9244.20 1.03313 0.516563 0.856249i \(-0.327211\pi\)
0.516563 + 0.856249i \(0.327211\pi\)
\(432\) 15126.2 1.68463
\(433\) 15672.7 1.73945 0.869726 0.493535i \(-0.164295\pi\)
0.869726 + 0.493535i \(0.164295\pi\)
\(434\) −14419.9 −1.59488
\(435\) −17752.9 −1.95675
\(436\) 31075.0 3.41335
\(437\) −7319.36 −0.801219
\(438\) −38610.2 −4.21202
\(439\) −10815.1 −1.17580 −0.587902 0.808932i \(-0.700046\pi\)
−0.587902 + 0.808932i \(0.700046\pi\)
\(440\) −5016.90 −0.543572
\(441\) −11456.3 −1.23704
\(442\) 0 0
\(443\) 5596.30 0.600199 0.300100 0.953908i \(-0.402980\pi\)
0.300100 + 0.953908i \(0.402980\pi\)
\(444\) 56914.3 6.08340
\(445\) −15110.8 −1.60971
\(446\) 15846.0 1.68235
\(447\) −2888.87 −0.305680
\(448\) 2937.90 0.309828
\(449\) −16603.1 −1.74510 −0.872549 0.488527i \(-0.837535\pi\)
−0.872549 + 0.488527i \(0.837535\pi\)
\(450\) 5022.51 0.526141
\(451\) 1628.07 0.169984
\(452\) 10610.0 1.10409
\(453\) 24245.8 2.51471
\(454\) 17623.5 1.82183
\(455\) 0 0
\(456\) −45501.2 −4.67278
\(457\) 15233.1 1.55925 0.779624 0.626248i \(-0.215410\pi\)
0.779624 + 0.626248i \(0.215410\pi\)
\(458\) −30365.4 −3.09800
\(459\) −14609.1 −1.48560
\(460\) 10705.1 1.08506
\(461\) −15626.2 −1.57871 −0.789355 0.613937i \(-0.789585\pi\)
−0.789355 + 0.613937i \(0.789585\pi\)
\(462\) −4702.81 −0.473581
\(463\) −4820.16 −0.483827 −0.241914 0.970298i \(-0.577775\pi\)
−0.241914 + 0.970298i \(0.577775\pi\)
\(464\) 17882.9 1.78921
\(465\) 25386.4 2.53175
\(466\) −1219.41 −0.121219
\(467\) −1382.23 −0.136964 −0.0684818 0.997652i \(-0.521815\pi\)
−0.0684818 + 0.997652i \(0.521815\pi\)
\(468\) 0 0
\(469\) 5575.32 0.548922
\(470\) 4925.70 0.483416
\(471\) 17950.0 1.75603
\(472\) 35802.4 3.49139
\(473\) −3596.43 −0.349607
\(474\) 26596.0 2.57720
\(475\) −2527.90 −0.244185
\(476\) 14375.6 1.38425
\(477\) −1235.55 −0.118599
\(478\) 10812.6 1.03464
\(479\) −5537.16 −0.528183 −0.264091 0.964498i \(-0.585072\pi\)
−0.264091 + 0.964498i \(0.585072\pi\)
\(480\) 7182.54 0.682993
\(481\) 0 0
\(482\) 10744.2 1.01532
\(483\) 5303.67 0.499638
\(484\) 2053.11 0.192817
\(485\) −11845.9 −1.10906
\(486\) 14221.8 1.32739
\(487\) 2985.52 0.277796 0.138898 0.990307i \(-0.455644\pi\)
0.138898 + 0.990307i \(0.455644\pi\)
\(488\) −11634.1 −1.07920
\(489\) −9208.98 −0.851625
\(490\) −12409.5 −1.14409
\(491\) −14284.6 −1.31295 −0.656474 0.754349i \(-0.727953\pi\)
−0.656474 + 0.754349i \(0.727953\pi\)
\(492\) −21596.3 −1.97894
\(493\) −17271.5 −1.57783
\(494\) 0 0
\(495\) 5256.49 0.477296
\(496\) −25572.3 −2.31498
\(497\) 3420.44 0.308708
\(498\) −13432.5 −1.20869
\(499\) −6738.75 −0.604545 −0.302272 0.953222i \(-0.597745\pi\)
−0.302272 + 0.953222i \(0.597745\pi\)
\(500\) 25284.6 2.26152
\(501\) −31919.1 −2.84638
\(502\) −2513.23 −0.223448
\(503\) −2629.88 −0.233123 −0.116561 0.993183i \(-0.537187\pi\)
−0.116561 + 0.993183i \(0.537187\pi\)
\(504\) 20932.7 1.85003
\(505\) 12301.1 1.08395
\(506\) −3407.11 −0.299337
\(507\) 0 0
\(508\) 24562.3 2.14523
\(509\) 5693.59 0.495803 0.247902 0.968785i \(-0.420259\pi\)
0.247902 + 0.968785i \(0.420259\pi\)
\(510\) −37240.7 −3.23343
\(511\) −8940.11 −0.773948
\(512\) 24371.1 2.10364
\(513\) 20258.1 1.74350
\(514\) −25847.7 −2.21808
\(515\) 3132.47 0.268025
\(516\) 47706.5 4.07008
\(517\) −1065.39 −0.0906299
\(518\) 19391.7 1.64483
\(519\) −348.631 −0.0294859
\(520\) 0 0
\(521\) 17275.8 1.45272 0.726358 0.687316i \(-0.241211\pi\)
0.726358 + 0.687316i \(0.241211\pi\)
\(522\) −47584.9 −3.98991
\(523\) −2205.46 −0.184394 −0.0921969 0.995741i \(-0.529389\pi\)
−0.0921969 + 0.995741i \(0.529389\pi\)
\(524\) 33460.3 2.78954
\(525\) 1831.73 0.152273
\(526\) 13469.4 1.11653
\(527\) 24698.0 2.04149
\(528\) −8340.00 −0.687409
\(529\) −8324.58 −0.684193
\(530\) −1338.35 −0.109687
\(531\) −37512.2 −3.06571
\(532\) −19934.3 −1.62455
\(533\) 0 0
\(534\) −63795.3 −5.16983
\(535\) 355.451 0.0287242
\(536\) 25110.1 2.02349
\(537\) 2476.70 0.199027
\(538\) −18623.9 −1.49244
\(539\) 2684.07 0.214492
\(540\) −29629.0 −2.36117
\(541\) 16236.4 1.29031 0.645153 0.764054i \(-0.276794\pi\)
0.645153 + 0.764054i \(0.276794\pi\)
\(542\) −16578.6 −1.31386
\(543\) 28613.7 2.26139
\(544\) 6987.79 0.550733
\(545\) −18640.0 −1.46504
\(546\) 0 0
\(547\) 18132.1 1.41732 0.708660 0.705551i \(-0.249300\pi\)
0.708660 + 0.705551i \(0.249300\pi\)
\(548\) −34069.3 −2.65578
\(549\) 12189.7 0.947619
\(550\) −1176.72 −0.0912280
\(551\) 23950.1 1.85174
\(552\) 23886.6 1.84182
\(553\) 6158.25 0.473554
\(554\) −22589.0 −1.73234
\(555\) −34139.3 −2.61105
\(556\) −4611.13 −0.351718
\(557\) −1588.05 −0.120804 −0.0604019 0.998174i \(-0.519238\pi\)
−0.0604019 + 0.998174i \(0.519238\pi\)
\(558\) 68045.6 5.16237
\(559\) 0 0
\(560\) 8928.26 0.673728
\(561\) 8054.86 0.606197
\(562\) −17621.3 −1.32262
\(563\) 7948.65 0.595019 0.297509 0.954719i \(-0.403844\pi\)
0.297509 + 0.954719i \(0.403844\pi\)
\(564\) 14132.3 1.05510
\(565\) −6364.26 −0.473887
\(566\) 16828.3 1.24973
\(567\) −2066.47 −0.153057
\(568\) 15405.0 1.13799
\(569\) 14065.1 1.03627 0.518135 0.855299i \(-0.326626\pi\)
0.518135 + 0.855299i \(0.326626\pi\)
\(570\) 51641.0 3.79474
\(571\) 8812.31 0.645856 0.322928 0.946424i \(-0.395333\pi\)
0.322928 + 0.946424i \(0.395333\pi\)
\(572\) 0 0
\(573\) 24519.8 1.78766
\(574\) −7358.26 −0.535066
\(575\) 1327.06 0.0962475
\(576\) −13863.6 −1.00286
\(577\) −23605.9 −1.70316 −0.851582 0.524222i \(-0.824356\pi\)
−0.851582 + 0.524222i \(0.824356\pi\)
\(578\) −11681.7 −0.840650
\(579\) −7658.26 −0.549683
\(580\) −35028.9 −2.50775
\(581\) −3110.28 −0.222093
\(582\) −50011.1 −3.56190
\(583\) 289.475 0.0205640
\(584\) −40264.4 −2.85300
\(585\) 0 0
\(586\) −25706.7 −1.81217
\(587\) 17011.1 1.19612 0.598060 0.801451i \(-0.295938\pi\)
0.598060 + 0.801451i \(0.295938\pi\)
\(588\) −35604.1 −2.49709
\(589\) −34248.3 −2.39588
\(590\) −40633.4 −2.83534
\(591\) 28301.6 1.96984
\(592\) 34389.4 2.38749
\(593\) 2224.19 0.154025 0.0770123 0.997030i \(-0.475462\pi\)
0.0770123 + 0.997030i \(0.475462\pi\)
\(594\) 9429.99 0.651376
\(595\) −8623.02 −0.594133
\(596\) −5700.14 −0.391756
\(597\) −9858.75 −0.675866
\(598\) 0 0
\(599\) 19673.7 1.34198 0.670991 0.741465i \(-0.265869\pi\)
0.670991 + 0.741465i \(0.265869\pi\)
\(600\) 8249.75 0.561324
\(601\) 11698.6 0.794004 0.397002 0.917818i \(-0.370051\pi\)
0.397002 + 0.917818i \(0.370051\pi\)
\(602\) 16254.5 1.10047
\(603\) −26309.2 −1.77677
\(604\) 47840.2 3.22283
\(605\) −1231.54 −0.0827588
\(606\) 51933.1 3.48125
\(607\) 6836.66 0.457152 0.228576 0.973526i \(-0.426593\pi\)
0.228576 + 0.973526i \(0.426593\pi\)
\(608\) −9689.83 −0.646340
\(609\) −17354.4 −1.15474
\(610\) 13203.9 0.876413
\(611\) 0 0
\(612\) −67836.5 −4.48060
\(613\) −249.182 −0.0164182 −0.00820910 0.999966i \(-0.502613\pi\)
−0.00820910 + 0.999966i \(0.502613\pi\)
\(614\) 41586.3 2.73336
\(615\) 12954.3 0.849379
\(616\) −4904.30 −0.320779
\(617\) −10289.6 −0.671383 −0.335691 0.941972i \(-0.608970\pi\)
−0.335691 + 0.941972i \(0.608970\pi\)
\(618\) 13224.7 0.860803
\(619\) −1258.08 −0.0816906 −0.0408453 0.999165i \(-0.513005\pi\)
−0.0408453 + 0.999165i \(0.513005\pi\)
\(620\) 50090.8 3.24467
\(621\) −10634.8 −0.687215
\(622\) −34312.4 −2.21190
\(623\) −14771.7 −0.949943
\(624\) 0 0
\(625\) −12490.6 −0.799398
\(626\) 9766.90 0.623585
\(627\) −11169.5 −0.711431
\(628\) 35417.7 2.25051
\(629\) −33213.6 −2.10543
\(630\) −23757.3 −1.50240
\(631\) −5559.42 −0.350740 −0.175370 0.984503i \(-0.556112\pi\)
−0.175370 + 0.984503i \(0.556112\pi\)
\(632\) 27735.5 1.74566
\(633\) 31609.3 1.98477
\(634\) −15477.8 −0.969563
\(635\) −14733.4 −0.920751
\(636\) −3839.87 −0.239404
\(637\) 0 0
\(638\) 11148.6 0.691814
\(639\) −16140.6 −0.999239
\(640\) −21699.0 −1.34020
\(641\) 27189.2 1.67536 0.837681 0.546160i \(-0.183911\pi\)
0.837681 + 0.546160i \(0.183911\pi\)
\(642\) 1500.65 0.0922522
\(643\) 11158.3 0.684357 0.342179 0.939635i \(-0.388835\pi\)
0.342179 + 0.939635i \(0.388835\pi\)
\(644\) 10464.9 0.640331
\(645\) −28616.2 −1.74692
\(646\) 50240.7 3.05990
\(647\) −29322.4 −1.78173 −0.890866 0.454266i \(-0.849902\pi\)
−0.890866 + 0.454266i \(0.849902\pi\)
\(648\) −9306.95 −0.564215
\(649\) 8788.67 0.531565
\(650\) 0 0
\(651\) 24816.6 1.49407
\(652\) −18170.6 −1.09143
\(653\) −25517.5 −1.52922 −0.764608 0.644495i \(-0.777068\pi\)
−0.764608 + 0.644495i \(0.777068\pi\)
\(654\) −78694.6 −4.70520
\(655\) −20070.7 −1.19730
\(656\) −13049.2 −0.776654
\(657\) 42187.3 2.50515
\(658\) 4815.14 0.285279
\(659\) −5612.95 −0.331790 −0.165895 0.986143i \(-0.553051\pi\)
−0.165895 + 0.986143i \(0.553051\pi\)
\(660\) 16336.3 0.963468
\(661\) −27212.7 −1.60129 −0.800643 0.599141i \(-0.795509\pi\)
−0.800643 + 0.599141i \(0.795509\pi\)
\(662\) −14513.6 −0.852097
\(663\) 0 0
\(664\) −14008.0 −0.818701
\(665\) 11957.4 0.697273
\(666\) −91507.1 −5.32406
\(667\) −12573.0 −0.729879
\(668\) −62980.7 −3.64790
\(669\) −27270.9 −1.57601
\(670\) −28498.3 −1.64326
\(671\) −2855.90 −0.164308
\(672\) 7021.33 0.403056
\(673\) 9591.29 0.549357 0.274678 0.961536i \(-0.411429\pi\)
0.274678 + 0.961536i \(0.411429\pi\)
\(674\) 19544.6 1.11696
\(675\) −3672.96 −0.209440
\(676\) 0 0
\(677\) −736.743 −0.0418247 −0.0209124 0.999781i \(-0.506657\pi\)
−0.0209124 + 0.999781i \(0.506657\pi\)
\(678\) −26868.8 −1.52196
\(679\) −11580.0 −0.654490
\(680\) −38836.3 −2.19015
\(681\) −30330.0 −1.70668
\(682\) −15942.3 −0.895107
\(683\) 5276.86 0.295627 0.147814 0.989015i \(-0.452776\pi\)
0.147814 + 0.989015i \(0.452776\pi\)
\(684\) 94067.6 5.25843
\(685\) 20436.1 1.13989
\(686\) −29183.5 −1.62424
\(687\) 52258.8 2.90218
\(688\) 28825.8 1.59734
\(689\) 0 0
\(690\) −27109.8 −1.49573
\(691\) 20497.2 1.12844 0.564219 0.825625i \(-0.309177\pi\)
0.564219 + 0.825625i \(0.309177\pi\)
\(692\) −687.896 −0.0377888
\(693\) 5138.51 0.281668
\(694\) 30975.6 1.69426
\(695\) 2765.93 0.150961
\(696\) −78160.8 −4.25672
\(697\) 12603.1 0.684899
\(698\) −46667.3 −2.53064
\(699\) 2098.59 0.113557
\(700\) 3614.26 0.195152
\(701\) 9115.38 0.491132 0.245566 0.969380i \(-0.421026\pi\)
0.245566 + 0.969380i \(0.421026\pi\)
\(702\) 0 0
\(703\) 46056.7 2.47093
\(704\) 3248.08 0.173887
\(705\) −8477.11 −0.452860
\(706\) 7685.46 0.409697
\(707\) 12025.0 0.639671
\(708\) −116581. −6.18842
\(709\) 16439.1 0.870781 0.435390 0.900242i \(-0.356610\pi\)
0.435390 + 0.900242i \(0.356610\pi\)
\(710\) −17483.7 −0.924155
\(711\) −29060.0 −1.53282
\(712\) −66528.5 −3.50177
\(713\) 17979.2 0.944357
\(714\) −36404.8 −1.90815
\(715\) 0 0
\(716\) 4886.86 0.255070
\(717\) −18608.5 −0.969243
\(718\) −19268.3 −1.00151
\(719\) 27336.5 1.41791 0.708956 0.705253i \(-0.249167\pi\)
0.708956 + 0.705253i \(0.249167\pi\)
\(720\) −42131.4 −2.18075
\(721\) 3062.16 0.158170
\(722\) −35394.9 −1.82446
\(723\) −18490.8 −0.951147
\(724\) 56458.8 2.89817
\(725\) −4342.36 −0.222443
\(726\) −5199.33 −0.265792
\(727\) 31683.6 1.61634 0.808170 0.588950i \(-0.200458\pi\)
0.808170 + 0.588950i \(0.200458\pi\)
\(728\) 0 0
\(729\) −30083.4 −1.52839
\(730\) 45697.5 2.31691
\(731\) −27840.2 −1.40863
\(732\) 37883.5 1.91286
\(733\) 8125.89 0.409463 0.204732 0.978818i \(-0.434368\pi\)
0.204732 + 0.978818i \(0.434368\pi\)
\(734\) −39013.1 −1.96185
\(735\) 21356.7 1.07177
\(736\) 5086.84 0.254760
\(737\) 6163.95 0.308076
\(738\) 34722.7 1.73193
\(739\) 7426.81 0.369688 0.184844 0.982768i \(-0.440822\pi\)
0.184844 + 0.982768i \(0.440822\pi\)
\(740\) −67361.5 −3.34630
\(741\) 0 0
\(742\) −1308.31 −0.0647300
\(743\) −7474.38 −0.369056 −0.184528 0.982827i \(-0.559076\pi\)
−0.184528 + 0.982827i \(0.559076\pi\)
\(744\) 111769. 5.50758
\(745\) 3419.16 0.168145
\(746\) −8529.61 −0.418621
\(747\) 14677.0 0.718881
\(748\) 15893.3 0.776895
\(749\) 347.472 0.0169511
\(750\) −64031.0 −3.11744
\(751\) −3881.02 −0.188576 −0.0942879 0.995545i \(-0.530057\pi\)
−0.0942879 + 0.995545i \(0.530057\pi\)
\(752\) 8539.20 0.414086
\(753\) 4325.26 0.209324
\(754\) 0 0
\(755\) −28696.4 −1.38327
\(756\) −28964.0 −1.39340
\(757\) 13052.4 0.626682 0.313341 0.949641i \(-0.398552\pi\)
0.313341 + 0.949641i \(0.398552\pi\)
\(758\) 37447.5 1.79440
\(759\) 5863.62 0.280416
\(760\) 53853.5 2.57036
\(761\) 25895.4 1.23352 0.616760 0.787152i \(-0.288445\pi\)
0.616760 + 0.787152i \(0.288445\pi\)
\(762\) −62201.8 −2.95713
\(763\) −18221.6 −0.864568
\(764\) 48381.0 2.29105
\(765\) 40690.9 1.92312
\(766\) −9555.18 −0.450709
\(767\) 0 0
\(768\) −71295.3 −3.34980
\(769\) 23302.8 1.09275 0.546373 0.837542i \(-0.316008\pi\)
0.546373 + 0.837542i \(0.316008\pi\)
\(770\) 5566.07 0.260503
\(771\) 44483.8 2.07788
\(772\) −15110.8 −0.704467
\(773\) 10182.0 0.473768 0.236884 0.971538i \(-0.423874\pi\)
0.236884 + 0.971538i \(0.423874\pi\)
\(774\) −76702.8 −3.56205
\(775\) 6209.50 0.287809
\(776\) −52153.8 −2.41264
\(777\) −33373.1 −1.54087
\(778\) −9005.25 −0.414979
\(779\) −17476.4 −0.803796
\(780\) 0 0
\(781\) 3781.57 0.173259
\(782\) −26374.7 −1.20608
\(783\) 34798.8 1.58826
\(784\) −21513.1 −0.980008
\(785\) −21244.9 −0.965939
\(786\) −84735.1 −3.84529
\(787\) −26826.2 −1.21506 −0.607530 0.794297i \(-0.707840\pi\)
−0.607530 + 0.794297i \(0.707840\pi\)
\(788\) 55842.9 2.52452
\(789\) −23180.8 −1.04596
\(790\) −31478.0 −1.41764
\(791\) −6221.41 −0.279656
\(792\) 23142.8 1.03831
\(793\) 0 0
\(794\) 43033.0 1.92340
\(795\) 2303.30 0.102754
\(796\) −19452.7 −0.866182
\(797\) −502.155 −0.0223177 −0.0111589 0.999938i \(-0.503552\pi\)
−0.0111589 + 0.999938i \(0.503552\pi\)
\(798\) 50481.9 2.23940
\(799\) −8247.25 −0.365165
\(800\) 1756.85 0.0776424
\(801\) 69705.7 3.07482
\(802\) −34129.0 −1.50266
\(803\) −9884.00 −0.434369
\(804\) −81764.6 −3.58659
\(805\) −6277.22 −0.274836
\(806\) 0 0
\(807\) 32051.6 1.39810
\(808\) 54158.2 2.35802
\(809\) 19896.8 0.864691 0.432345 0.901708i \(-0.357686\pi\)
0.432345 + 0.901708i \(0.357686\pi\)
\(810\) 10562.8 0.458196
\(811\) 29534.8 1.27880 0.639401 0.768874i \(-0.279182\pi\)
0.639401 + 0.768874i \(0.279182\pi\)
\(812\) −34242.7 −1.47990
\(813\) 28531.6 1.23081
\(814\) 21439.1 0.923144
\(815\) 10899.4 0.468453
\(816\) −64560.6 −2.76970
\(817\) 38605.5 1.65317
\(818\) −68792.4 −2.94043
\(819\) 0 0
\(820\) 25560.6 1.08855
\(821\) −2221.45 −0.0944327 −0.0472164 0.998885i \(-0.515035\pi\)
−0.0472164 + 0.998885i \(0.515035\pi\)
\(822\) 86277.5 3.66092
\(823\) −17096.9 −0.724131 −0.362066 0.932153i \(-0.617928\pi\)
−0.362066 + 0.932153i \(0.617928\pi\)
\(824\) 13791.3 0.583063
\(825\) 2025.13 0.0854616
\(826\) −39721.4 −1.67323
\(827\) −4093.79 −0.172134 −0.0860672 0.996289i \(-0.527430\pi\)
−0.0860672 + 0.996289i \(0.527430\pi\)
\(828\) −49382.4 −2.07265
\(829\) −15871.1 −0.664927 −0.332464 0.943116i \(-0.607880\pi\)
−0.332464 + 0.943116i \(0.607880\pi\)
\(830\) 15898.2 0.664863
\(831\) 38875.6 1.62284
\(832\) 0 0
\(833\) 20777.6 0.864229
\(834\) 11677.3 0.484833
\(835\) 37778.2 1.56571
\(836\) −22039.0 −0.911763
\(837\) −49761.7 −2.05498
\(838\) 31116.2 1.28269
\(839\) −1830.35 −0.0753167 −0.0376584 0.999291i \(-0.511990\pi\)
−0.0376584 + 0.999291i \(0.511990\pi\)
\(840\) −39022.7 −1.60287
\(841\) 16751.9 0.686863
\(842\) −50086.1 −2.04998
\(843\) 30326.3 1.23902
\(844\) 62369.4 2.54365
\(845\) 0 0
\(846\) −22722.0 −0.923404
\(847\) −1203.89 −0.0488386
\(848\) −2320.17 −0.0939563
\(849\) −28961.5 −1.17074
\(850\) −9109.07 −0.367575
\(851\) −24178.2 −0.973936
\(852\) −50162.4 −2.01706
\(853\) 3596.23 0.144352 0.0721761 0.997392i \(-0.477006\pi\)
0.0721761 + 0.997392i \(0.477006\pi\)
\(854\) 12907.6 0.517199
\(855\) −56425.3 −2.25697
\(856\) 1564.94 0.0624868
\(857\) −14566.2 −0.580595 −0.290298 0.956936i \(-0.593754\pi\)
−0.290298 + 0.956936i \(0.593754\pi\)
\(858\) 0 0
\(859\) −18351.6 −0.728926 −0.364463 0.931218i \(-0.618747\pi\)
−0.364463 + 0.931218i \(0.618747\pi\)
\(860\) −56463.6 −2.23883
\(861\) 12663.5 0.501246
\(862\) −46191.3 −1.82515
\(863\) −9255.00 −0.365057 −0.182528 0.983201i \(-0.558428\pi\)
−0.182528 + 0.983201i \(0.558428\pi\)
\(864\) −14079.0 −0.554374
\(865\) 412.626 0.0162193
\(866\) −78313.3 −3.07297
\(867\) 20104.2 0.787514
\(868\) 48966.5 1.91478
\(869\) 6808.43 0.265777
\(870\) 88707.5 3.45686
\(871\) 0 0
\(872\) −82066.2 −3.18706
\(873\) 54644.4 2.11848
\(874\) 36573.3 1.41546
\(875\) −14826.3 −0.572822
\(876\) 131111. 5.05688
\(877\) 17153.7 0.660476 0.330238 0.943898i \(-0.392871\pi\)
0.330238 + 0.943898i \(0.392871\pi\)
\(878\) 54040.9 2.07721
\(879\) 44241.1 1.69763
\(880\) 9870.90 0.378123
\(881\) −19571.0 −0.748428 −0.374214 0.927342i \(-0.622088\pi\)
−0.374214 + 0.927342i \(0.622088\pi\)
\(882\) 57244.5 2.18540
\(883\) 37138.6 1.41542 0.707709 0.706505i \(-0.249729\pi\)
0.707709 + 0.706505i \(0.249729\pi\)
\(884\) 0 0
\(885\) 69930.0 2.65613
\(886\) −27963.5 −1.06033
\(887\) 11738.9 0.444366 0.222183 0.975005i \(-0.428682\pi\)
0.222183 + 0.975005i \(0.428682\pi\)
\(888\) −150305. −5.68009
\(889\) −14402.7 −0.543364
\(890\) 75505.6 2.84377
\(891\) −2284.65 −0.0859018
\(892\) −53809.2 −2.01980
\(893\) 11436.3 0.428557
\(894\) 14435.1 0.540024
\(895\) −2931.32 −0.109479
\(896\) −21211.9 −0.790895
\(897\) 0 0
\(898\) 82962.2 3.08294
\(899\) −58830.8 −2.18255
\(900\) −17055.2 −0.631676
\(901\) 2240.85 0.0828562
\(902\) −8135.14 −0.300300
\(903\) −27973.9 −1.03091
\(904\) −28019.9 −1.03090
\(905\) −33866.1 −1.24392
\(906\) −121151. −4.44257
\(907\) 32379.7 1.18539 0.592696 0.805426i \(-0.298064\pi\)
0.592696 + 0.805426i \(0.298064\pi\)
\(908\) −59845.1 −2.18726
\(909\) −56744.5 −2.07051
\(910\) 0 0
\(911\) −39029.9 −1.41945 −0.709725 0.704479i \(-0.751181\pi\)
−0.709725 + 0.704479i \(0.751181\pi\)
\(912\) 89524.9 3.25051
\(913\) −3438.66 −0.124647
\(914\) −76116.8 −2.75462
\(915\) −22723.9 −0.821017
\(916\) 103114. 3.71940
\(917\) −19620.2 −0.706562
\(918\) 72998.3 2.62451
\(919\) −18246.4 −0.654944 −0.327472 0.944861i \(-0.606197\pi\)
−0.327472 + 0.944861i \(0.606197\pi\)
\(920\) −28271.3 −1.01313
\(921\) −71569.9 −2.56059
\(922\) 78080.9 2.78900
\(923\) 0 0
\(924\) 15969.6 0.568573
\(925\) −8350.47 −0.296823
\(926\) 24085.3 0.854744
\(927\) −14449.9 −0.511973
\(928\) −16644.9 −0.588790
\(929\) −21810.4 −0.770263 −0.385132 0.922862i \(-0.625844\pi\)
−0.385132 + 0.922862i \(0.625844\pi\)
\(930\) −126850. −4.47267
\(931\) −28811.9 −1.01426
\(932\) 4140.81 0.145533
\(933\) 59051.6 2.07209
\(934\) 6906.71 0.241964
\(935\) −9533.42 −0.333451
\(936\) 0 0
\(937\) −42280.6 −1.47412 −0.737058 0.675830i \(-0.763785\pi\)
−0.737058 + 0.675830i \(0.763785\pi\)
\(938\) −27858.7 −0.969742
\(939\) −16808.8 −0.584169
\(940\) −16726.5 −0.580380
\(941\) 29896.5 1.03571 0.517853 0.855470i \(-0.326732\pi\)
0.517853 + 0.855470i \(0.326732\pi\)
\(942\) −89692.1 −3.10226
\(943\) 9174.53 0.316823
\(944\) −70442.2 −2.42871
\(945\) 17373.7 0.598060
\(946\) 17970.6 0.617626
\(947\) −43408.9 −1.48954 −0.744772 0.667318i \(-0.767442\pi\)
−0.744772 + 0.667318i \(0.767442\pi\)
\(948\) −90313.7 −3.09415
\(949\) 0 0
\(950\) 12631.4 0.431385
\(951\) 26637.3 0.908279
\(952\) −37964.6 −1.29248
\(953\) −56267.7 −1.91258 −0.956291 0.292416i \(-0.905541\pi\)
−0.956291 + 0.292416i \(0.905541\pi\)
\(954\) 6173.77 0.209521
\(955\) −29020.7 −0.983340
\(956\) −36717.1 −1.24217
\(957\) −19186.7 −0.648086
\(958\) 27668.0 0.933104
\(959\) 19977.4 0.672683
\(960\) 25844.4 0.868881
\(961\) 54336.1 1.82391
\(962\) 0 0
\(963\) −1639.68 −0.0548680
\(964\) −36484.8 −1.21898
\(965\) 9064.02 0.302364
\(966\) −26501.3 −0.882677
\(967\) −4785.60 −0.159146 −0.0795732 0.996829i \(-0.525356\pi\)
−0.0795732 + 0.996829i \(0.525356\pi\)
\(968\) −5422.09 −0.180034
\(969\) −86464.2 −2.86649
\(970\) 59191.2 1.95929
\(971\) 2162.54 0.0714720 0.0357360 0.999361i \(-0.488622\pi\)
0.0357360 + 0.999361i \(0.488622\pi\)
\(972\) −48293.7 −1.59364
\(973\) 2703.85 0.0890867
\(974\) −14918.0 −0.490763
\(975\) 0 0
\(976\) 22890.4 0.750720
\(977\) −5430.36 −0.177822 −0.0889112 0.996040i \(-0.528339\pi\)
−0.0889112 + 0.996040i \(0.528339\pi\)
\(978\) 46015.3 1.50451
\(979\) −16331.2 −0.533145
\(980\) 42139.7 1.37357
\(981\) 85985.4 2.79847
\(982\) 71377.4 2.31949
\(983\) 18109.5 0.587594 0.293797 0.955868i \(-0.405081\pi\)
0.293797 + 0.955868i \(0.405081\pi\)
\(984\) 57034.0 1.84774
\(985\) −33496.7 −1.08355
\(986\) 86302.3 2.78745
\(987\) −8286.84 −0.267247
\(988\) 0 0
\(989\) −20266.6 −0.651608
\(990\) −26265.6 −0.843207
\(991\) 33767.4 1.08240 0.541200 0.840894i \(-0.317970\pi\)
0.541200 + 0.840894i \(0.317970\pi\)
\(992\) 23802.0 0.761808
\(993\) 24977.9 0.798238
\(994\) −17091.2 −0.545373
\(995\) 11668.4 0.371773
\(996\) 45613.7 1.45113
\(997\) 36561.6 1.16140 0.580701 0.814117i \(-0.302779\pi\)
0.580701 + 0.814117i \(0.302779\pi\)
\(998\) 33672.1 1.06801
\(999\) 66919.1 2.11935
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 1859.4.a.p.1.5 51
13.12 even 2 1859.4.a.q.1.47 yes 51
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1859.4.a.p.1.5 51 1.1 even 1 trivial
1859.4.a.q.1.47 yes 51 13.12 even 2