Properties

Label 1849.4.a.m.1.14
Level $1849$
Weight $4$
Character 1849.1
Self dual yes
Analytic conductor $109.095$
Analytic rank $0$
Dimension $110$
CM no
Inner twists $2$

Related objects

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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: \(110\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
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)
 
\(f(q)\) \(=\) \(q-4.62802 q^{2} -8.10864 q^{3} +13.4186 q^{4} -17.9110 q^{5} +37.5270 q^{6} -27.1680 q^{7} -25.0774 q^{8} +38.7501 q^{9} +O(q^{10})\) \(q-4.62802 q^{2} -8.10864 q^{3} +13.4186 q^{4} -17.9110 q^{5} +37.5270 q^{6} -27.1680 q^{7} -25.0774 q^{8} +38.7501 q^{9} +82.8927 q^{10} -26.9318 q^{11} -108.807 q^{12} -21.2445 q^{13} +125.734 q^{14} +145.234 q^{15} +8.71017 q^{16} -8.28413 q^{17} -179.336 q^{18} +131.030 q^{19} -240.341 q^{20} +220.296 q^{21} +124.641 q^{22} -42.4012 q^{23} +203.344 q^{24} +195.805 q^{25} +98.3199 q^{26} -95.2771 q^{27} -364.557 q^{28} +103.779 q^{29} -672.147 q^{30} -145.326 q^{31} +160.309 q^{32} +218.380 q^{33} +38.3391 q^{34} +486.608 q^{35} +519.972 q^{36} -370.571 q^{37} -606.409 q^{38} +172.264 q^{39} +449.163 q^{40} +275.150 q^{41} -1019.53 q^{42} -361.387 q^{44} -694.054 q^{45} +196.234 q^{46} +331.305 q^{47} -70.6277 q^{48} +395.103 q^{49} -906.192 q^{50} +67.1730 q^{51} -285.071 q^{52} +223.453 q^{53} +440.944 q^{54} +482.376 q^{55} +681.305 q^{56} -1062.47 q^{57} -480.293 q^{58} -364.823 q^{59} +1948.84 q^{60} +381.036 q^{61} +672.570 q^{62} -1052.76 q^{63} -811.594 q^{64} +380.510 q^{65} -1010.67 q^{66} -348.629 q^{67} -111.161 q^{68} +343.816 q^{69} -2252.03 q^{70} +262.187 q^{71} -971.753 q^{72} -223.890 q^{73} +1715.01 q^{74} -1587.71 q^{75} +1758.24 q^{76} +731.683 q^{77} -797.241 q^{78} +1165.37 q^{79} -156.008 q^{80} -273.684 q^{81} -1273.40 q^{82} -819.505 q^{83} +2956.06 q^{84} +148.377 q^{85} -841.508 q^{87} +675.380 q^{88} -886.496 q^{89} +3212.10 q^{90} +577.170 q^{91} -568.966 q^{92} +1178.39 q^{93} -1533.29 q^{94} -2346.88 q^{95} -1299.89 q^{96} -1463.59 q^{97} -1828.54 q^{98} -1043.61 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9} + 102 q^{10} + 360 q^{11} + 166 q^{13} + 496 q^{14} + 540 q^{15} + 2204 q^{16} + 610 q^{17} + 896 q^{21} + 1508 q^{23} + 1086 q^{24} + 3168 q^{25} + 2312 q^{31} + 2760 q^{35} + 8334 q^{36} + 3626 q^{38} + 1462 q^{40} + 3598 q^{41} + 1596 q^{44} + 4448 q^{47} + 7194 q^{49} + 3620 q^{52} + 3818 q^{53} - 2570 q^{54} - 714 q^{56} + 3236 q^{57} + 3242 q^{58} + 8556 q^{59} + 178 q^{60} + 7308 q^{64} + 4202 q^{66} + 1992 q^{67} + 8994 q^{68} + 8256 q^{74} + 4784 q^{78} + 13752 q^{79} + 19678 q^{81} + 7620 q^{83} + 11390 q^{84} + 6012 q^{87} - 476 q^{90} + 8022 q^{92} + 7392 q^{95} + 16760 q^{96} - 1186 q^{97} + 11068 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.62802 −1.63625 −0.818127 0.575038i \(-0.804987\pi\)
−0.818127 + 0.575038i \(0.804987\pi\)
\(3\) −8.10864 −1.56051 −0.780254 0.625462i \(-0.784910\pi\)
−0.780254 + 0.625462i \(0.784910\pi\)
\(4\) 13.4186 1.67733
\(5\) −17.9110 −1.60201 −0.801006 0.598656i \(-0.795702\pi\)
−0.801006 + 0.598656i \(0.795702\pi\)
\(6\) 37.5270 2.55339
\(7\) −27.1680 −1.46694 −0.733468 0.679724i \(-0.762100\pi\)
−0.733468 + 0.679724i \(0.762100\pi\)
\(8\) −25.0774 −1.10828
\(9\) 38.7501 1.43519
\(10\) 82.8927 2.62130
\(11\) −26.9318 −0.738203 −0.369101 0.929389i \(-0.620334\pi\)
−0.369101 + 0.929389i \(0.620334\pi\)
\(12\) −108.807 −2.61748
\(13\) −21.2445 −0.453243 −0.226621 0.973983i \(-0.572768\pi\)
−0.226621 + 0.973983i \(0.572768\pi\)
\(14\) 125.734 2.40028
\(15\) 145.234 2.49995
\(16\) 8.71017 0.136096
\(17\) −8.28413 −0.118188 −0.0590940 0.998252i \(-0.518821\pi\)
−0.0590940 + 0.998252i \(0.518821\pi\)
\(18\) −179.336 −2.34833
\(19\) 131.030 1.58212 0.791061 0.611738i \(-0.209529\pi\)
0.791061 + 0.611738i \(0.209529\pi\)
\(20\) −240.341 −2.68710
\(21\) 220.296 2.28917
\(22\) 124.641 1.20789
\(23\) −42.4012 −0.384403 −0.192201 0.981355i \(-0.561563\pi\)
−0.192201 + 0.981355i \(0.561563\pi\)
\(24\) 203.344 1.72948
\(25\) 195.805 1.56644
\(26\) 98.3199 0.741620
\(27\) −95.2771 −0.679114
\(28\) −364.557 −2.46053
\(29\) 103.779 0.664528 0.332264 0.943186i \(-0.392188\pi\)
0.332264 + 0.943186i \(0.392188\pi\)
\(30\) −672.147 −4.09056
\(31\) −145.326 −0.841976 −0.420988 0.907066i \(-0.638316\pi\)
−0.420988 + 0.907066i \(0.638316\pi\)
\(32\) 160.309 0.885589
\(33\) 218.380 1.15197
\(34\) 38.3391 0.193386
\(35\) 486.608 2.35005
\(36\) 519.972 2.40728
\(37\) −370.571 −1.64653 −0.823263 0.567660i \(-0.807849\pi\)
−0.823263 + 0.567660i \(0.807849\pi\)
\(38\) −606.409 −2.58875
\(39\) 172.264 0.707289
\(40\) 449.163 1.77547
\(41\) 275.150 1.04808 0.524038 0.851695i \(-0.324425\pi\)
0.524038 + 0.851695i \(0.324425\pi\)
\(42\) −1019.53 −3.74566
\(43\) 0 0
\(44\) −361.387 −1.23821
\(45\) −694.054 −2.29919
\(46\) 196.234 0.628981
\(47\) 331.305 1.02821 0.514105 0.857727i \(-0.328124\pi\)
0.514105 + 0.857727i \(0.328124\pi\)
\(48\) −70.6277 −0.212380
\(49\) 395.103 1.15190
\(50\) −906.192 −2.56310
\(51\) 67.1730 0.184433
\(52\) −285.071 −0.760235
\(53\) 223.453 0.579126 0.289563 0.957159i \(-0.406490\pi\)
0.289563 + 0.957159i \(0.406490\pi\)
\(54\) 440.944 1.11120
\(55\) 482.376 1.18261
\(56\) 681.305 1.62577
\(57\) −1062.47 −2.46891
\(58\) −480.293 −1.08734
\(59\) −364.823 −0.805016 −0.402508 0.915417i \(-0.631861\pi\)
−0.402508 + 0.915417i \(0.631861\pi\)
\(60\) 1948.84 4.19324
\(61\) 381.036 0.799781 0.399891 0.916563i \(-0.369048\pi\)
0.399891 + 0.916563i \(0.369048\pi\)
\(62\) 672.570 1.37769
\(63\) −1052.76 −2.10533
\(64\) −811.594 −1.58514
\(65\) 380.510 0.726100
\(66\) −1010.67 −1.88492
\(67\) −348.629 −0.635699 −0.317849 0.948141i \(-0.602961\pi\)
−0.317849 + 0.948141i \(0.602961\pi\)
\(68\) −111.161 −0.198240
\(69\) 343.816 0.599864
\(70\) −2252.03 −3.84528
\(71\) 262.187 0.438251 0.219126 0.975697i \(-0.429680\pi\)
0.219126 + 0.975697i \(0.429680\pi\)
\(72\) −971.753 −1.59059
\(73\) −223.890 −0.358964 −0.179482 0.983761i \(-0.557442\pi\)
−0.179482 + 0.983761i \(0.557442\pi\)
\(74\) 1715.01 2.69413
\(75\) −1587.71 −2.44445
\(76\) 1758.24 2.65373
\(77\) 731.683 1.08290
\(78\) −797.241 −1.15730
\(79\) 1165.37 1.65967 0.829835 0.558009i \(-0.188434\pi\)
0.829835 + 0.558009i \(0.188434\pi\)
\(80\) −156.008 −0.218028
\(81\) −273.684 −0.375424
\(82\) −1273.40 −1.71492
\(83\) −819.505 −1.08376 −0.541882 0.840455i \(-0.682288\pi\)
−0.541882 + 0.840455i \(0.682288\pi\)
\(84\) 2956.06 3.83968
\(85\) 148.377 0.189339
\(86\) 0 0
\(87\) −841.508 −1.03700
\(88\) 675.380 0.818133
\(89\) −886.496 −1.05582 −0.527912 0.849299i \(-0.677025\pi\)
−0.527912 + 0.849299i \(0.677025\pi\)
\(90\) 3212.10 3.76205
\(91\) 577.170 0.664878
\(92\) −568.966 −0.644769
\(93\) 1178.39 1.31391
\(94\) −1533.29 −1.68241
\(95\) −2346.88 −2.53458
\(96\) −1299.89 −1.38197
\(97\) −1463.59 −1.53201 −0.766007 0.642832i \(-0.777759\pi\)
−0.766007 + 0.642832i \(0.777759\pi\)
\(98\) −1828.54 −1.88480
\(99\) −1043.61 −1.05946
\(100\) 2627.43 2.62743
\(101\) 98.8379 0.0973736 0.0486868 0.998814i \(-0.484496\pi\)
0.0486868 + 0.998814i \(0.484496\pi\)
\(102\) −310.878 −0.301780
\(103\) 102.876 0.0984141 0.0492071 0.998789i \(-0.484331\pi\)
0.0492071 + 0.998789i \(0.484331\pi\)
\(104\) 532.757 0.502318
\(105\) −3945.73 −3.66727
\(106\) −1034.15 −0.947597
\(107\) 963.342 0.870371 0.435186 0.900341i \(-0.356683\pi\)
0.435186 + 0.900341i \(0.356683\pi\)
\(108\) −1278.49 −1.13910
\(109\) −935.346 −0.821926 −0.410963 0.911652i \(-0.634807\pi\)
−0.410963 + 0.911652i \(0.634807\pi\)
\(110\) −2232.45 −1.93505
\(111\) 3004.83 2.56942
\(112\) −236.638 −0.199645
\(113\) 317.314 0.264163 0.132082 0.991239i \(-0.457834\pi\)
0.132082 + 0.991239i \(0.457834\pi\)
\(114\) 4917.15 4.03977
\(115\) 759.450 0.615818
\(116\) 1392.57 1.11463
\(117\) −823.224 −0.650488
\(118\) 1688.41 1.31721
\(119\) 225.064 0.173374
\(120\) −3642.10 −2.77064
\(121\) −605.680 −0.455057
\(122\) −1763.44 −1.30864
\(123\) −2231.09 −1.63553
\(124\) −1950.07 −1.41227
\(125\) −1268.20 −0.907448
\(126\) 4872.21 3.44485
\(127\) 291.872 0.203933 0.101966 0.994788i \(-0.467487\pi\)
0.101966 + 0.994788i \(0.467487\pi\)
\(128\) 2473.61 1.70811
\(129\) 0 0
\(130\) −1761.01 −1.18808
\(131\) −1658.08 −1.10585 −0.552927 0.833230i \(-0.686489\pi\)
−0.552927 + 0.833230i \(0.686489\pi\)
\(132\) 2930.36 1.93223
\(133\) −3559.82 −2.32087
\(134\) 1613.46 1.04016
\(135\) 1706.51 1.08795
\(136\) 207.745 0.130985
\(137\) −524.125 −0.326854 −0.163427 0.986555i \(-0.552255\pi\)
−0.163427 + 0.986555i \(0.552255\pi\)
\(138\) −1591.19 −0.981530
\(139\) −251.305 −0.153348 −0.0766741 0.997056i \(-0.524430\pi\)
−0.0766741 + 0.997056i \(0.524430\pi\)
\(140\) 6529.60 3.94180
\(141\) −2686.44 −1.60453
\(142\) −1213.41 −0.717090
\(143\) 572.151 0.334585
\(144\) 337.520 0.195324
\(145\) −1858.79 −1.06458
\(146\) 1036.17 0.587356
\(147\) −3203.75 −1.79755
\(148\) −4972.54 −2.76176
\(149\) 2652.79 1.45856 0.729279 0.684217i \(-0.239856\pi\)
0.729279 + 0.684217i \(0.239856\pi\)
\(150\) 7347.98 3.99974
\(151\) −2927.52 −1.57774 −0.788868 0.614562i \(-0.789333\pi\)
−0.788868 + 0.614562i \(0.789333\pi\)
\(152\) −3285.89 −1.75343
\(153\) −321.010 −0.169622
\(154\) −3386.25 −1.77189
\(155\) 2602.93 1.34885
\(156\) 2311.54 1.18635
\(157\) −1869.65 −0.950412 −0.475206 0.879875i \(-0.657626\pi\)
−0.475206 + 0.879875i \(0.657626\pi\)
\(158\) −5393.34 −2.71564
\(159\) −1811.90 −0.903731
\(160\) −2871.30 −1.41872
\(161\) 1151.96 0.563895
\(162\) 1266.62 0.614289
\(163\) −2200.87 −1.05758 −0.528789 0.848753i \(-0.677354\pi\)
−0.528789 + 0.848753i \(0.677354\pi\)
\(164\) 3692.12 1.75797
\(165\) −3911.41 −1.84547
\(166\) 3792.69 1.77331
\(167\) −2704.67 −1.25326 −0.626628 0.779319i \(-0.715565\pi\)
−0.626628 + 0.779319i \(0.715565\pi\)
\(168\) −5524.46 −2.53703
\(169\) −1745.67 −0.794571
\(170\) −686.694 −0.309806
\(171\) 5077.41 2.27064
\(172\) 0 0
\(173\) 1112.09 0.488733 0.244367 0.969683i \(-0.421420\pi\)
0.244367 + 0.969683i \(0.421420\pi\)
\(174\) 3894.52 1.69680
\(175\) −5319.65 −2.29787
\(176\) −234.580 −0.100467
\(177\) 2958.22 1.25623
\(178\) 4102.72 1.72760
\(179\) 3332.30 1.39144 0.695719 0.718314i \(-0.255086\pi\)
0.695719 + 0.718314i \(0.255086\pi\)
\(180\) −9313.24 −3.85649
\(181\) 1439.34 0.591079 0.295539 0.955331i \(-0.404501\pi\)
0.295539 + 0.955331i \(0.404501\pi\)
\(182\) −2671.16 −1.08791
\(183\) −3089.68 −1.24807
\(184\) 1063.31 0.426025
\(185\) 6637.31 2.63775
\(186\) −5453.63 −2.14989
\(187\) 223.106 0.0872467
\(188\) 4445.66 1.72464
\(189\) 2588.49 0.996217
\(190\) 10861.4 4.14721
\(191\) 1385.59 0.524908 0.262454 0.964944i \(-0.415468\pi\)
0.262454 + 0.964944i \(0.415468\pi\)
\(192\) 6580.92 2.47363
\(193\) 1882.56 0.702123 0.351061 0.936352i \(-0.385821\pi\)
0.351061 + 0.936352i \(0.385821\pi\)
\(194\) 6773.55 2.50676
\(195\) −3085.42 −1.13309
\(196\) 5301.73 1.93212
\(197\) −5286.88 −1.91205 −0.956026 0.293281i \(-0.905253\pi\)
−0.956026 + 0.293281i \(0.905253\pi\)
\(198\) 4829.84 1.73354
\(199\) −4740.76 −1.68876 −0.844381 0.535743i \(-0.820032\pi\)
−0.844381 + 0.535743i \(0.820032\pi\)
\(200\) −4910.30 −1.73605
\(201\) 2826.91 0.992013
\(202\) −457.424 −0.159328
\(203\) −2819.48 −0.974820
\(204\) 901.368 0.309355
\(205\) −4928.21 −1.67903
\(206\) −476.112 −0.161030
\(207\) −1643.05 −0.551690
\(208\) −185.043 −0.0616847
\(209\) −3528.86 −1.16793
\(210\) 18260.9 6.00059
\(211\) −4360.95 −1.42285 −0.711423 0.702764i \(-0.751949\pi\)
−0.711423 + 0.702764i \(0.751949\pi\)
\(212\) 2998.43 0.971383
\(213\) −2125.98 −0.683895
\(214\) −4458.37 −1.42415
\(215\) 0 0
\(216\) 2389.31 0.752646
\(217\) 3948.21 1.23512
\(218\) 4328.80 1.34488
\(219\) 1815.45 0.560167
\(220\) 6472.81 1.98362
\(221\) 175.992 0.0535678
\(222\) −13906.4 −4.20422
\(223\) 3349.18 1.00573 0.502864 0.864365i \(-0.332280\pi\)
0.502864 + 0.864365i \(0.332280\pi\)
\(224\) −4355.27 −1.29910
\(225\) 7587.47 2.24814
\(226\) −1468.54 −0.432238
\(227\) −3572.45 −1.04455 −0.522273 0.852778i \(-0.674916\pi\)
−0.522273 + 0.852778i \(0.674916\pi\)
\(228\) −14256.9 −4.14117
\(229\) −5180.16 −1.49482 −0.747412 0.664361i \(-0.768704\pi\)
−0.747412 + 0.664361i \(0.768704\pi\)
\(230\) −3514.75 −1.00763
\(231\) −5932.96 −1.68987
\(232\) −2602.52 −0.736481
\(233\) −2409.88 −0.677582 −0.338791 0.940862i \(-0.610018\pi\)
−0.338791 + 0.940862i \(0.610018\pi\)
\(234\) 3809.90 1.06436
\(235\) −5934.03 −1.64720
\(236\) −4895.42 −1.35027
\(237\) −9449.54 −2.58993
\(238\) −1041.60 −0.283684
\(239\) 1035.13 0.280154 0.140077 0.990141i \(-0.455265\pi\)
0.140077 + 0.990141i \(0.455265\pi\)
\(240\) 1265.01 0.340235
\(241\) 335.817 0.0897589 0.0448795 0.998992i \(-0.485710\pi\)
0.0448795 + 0.998992i \(0.485710\pi\)
\(242\) 2803.10 0.744588
\(243\) 4791.69 1.26497
\(244\) 5112.97 1.34149
\(245\) −7076.70 −1.84536
\(246\) 10325.5 2.67615
\(247\) −2783.66 −0.717085
\(248\) 3644.39 0.933142
\(249\) 6645.07 1.69122
\(250\) 5869.24 1.48481
\(251\) 1094.80 0.275312 0.137656 0.990480i \(-0.456043\pi\)
0.137656 + 0.990480i \(0.456043\pi\)
\(252\) −14126.6 −3.53132
\(253\) 1141.94 0.283767
\(254\) −1350.79 −0.333685
\(255\) −1203.14 −0.295465
\(256\) −4955.16 −1.20976
\(257\) −1121.45 −0.272196 −0.136098 0.990695i \(-0.543456\pi\)
−0.136098 + 0.990695i \(0.543456\pi\)
\(258\) 0 0
\(259\) 10067.7 2.41535
\(260\) 5105.92 1.21791
\(261\) 4021.45 0.953722
\(262\) 7673.62 1.80946
\(263\) −2318.07 −0.543492 −0.271746 0.962369i \(-0.587601\pi\)
−0.271746 + 0.962369i \(0.587601\pi\)
\(264\) −5476.41 −1.27670
\(265\) −4002.28 −0.927767
\(266\) 16475.0 3.79753
\(267\) 7188.28 1.64762
\(268\) −4678.12 −1.06627
\(269\) 4467.82 1.01267 0.506334 0.862337i \(-0.331000\pi\)
0.506334 + 0.862337i \(0.331000\pi\)
\(270\) −7897.77 −1.78016
\(271\) 7459.35 1.67204 0.836020 0.548699i \(-0.184877\pi\)
0.836020 + 0.548699i \(0.184877\pi\)
\(272\) −72.1562 −0.0160850
\(273\) −4680.07 −1.03755
\(274\) 2425.66 0.534817
\(275\) −5273.38 −1.15635
\(276\) 4613.54 1.00617
\(277\) −534.456 −0.115929 −0.0579645 0.998319i \(-0.518461\pi\)
−0.0579645 + 0.998319i \(0.518461\pi\)
\(278\) 1163.04 0.250916
\(279\) −5631.38 −1.20839
\(280\) −12202.9 −2.60451
\(281\) −3148.15 −0.668338 −0.334169 0.942513i \(-0.608456\pi\)
−0.334169 + 0.942513i \(0.608456\pi\)
\(282\) 12432.9 2.62542
\(283\) 7594.95 1.59531 0.797656 0.603113i \(-0.206073\pi\)
0.797656 + 0.603113i \(0.206073\pi\)
\(284\) 3518.18 0.735090
\(285\) 19030.0 3.95523
\(286\) −2647.93 −0.547466
\(287\) −7475.28 −1.53746
\(288\) 6211.97 1.27099
\(289\) −4844.37 −0.986032
\(290\) 8602.54 1.74193
\(291\) 11867.8 2.39072
\(292\) −3004.30 −0.602100
\(293\) −187.454 −0.0373761 −0.0186881 0.999825i \(-0.505949\pi\)
−0.0186881 + 0.999825i \(0.505949\pi\)
\(294\) 14827.0 2.94125
\(295\) 6534.36 1.28964
\(296\) 9292.97 1.82481
\(297\) 2565.98 0.501324
\(298\) −12277.2 −2.38657
\(299\) 900.791 0.174228
\(300\) −21304.9 −4.10013
\(301\) 0 0
\(302\) 13548.6 2.58158
\(303\) −801.441 −0.151952
\(304\) 1141.29 0.215321
\(305\) −6824.75 −1.28126
\(306\) 1485.64 0.277545
\(307\) −4496.18 −0.835865 −0.417933 0.908478i \(-0.637245\pi\)
−0.417933 + 0.908478i \(0.637245\pi\)
\(308\) 9818.17 1.81637
\(309\) −834.183 −0.153576
\(310\) −12046.4 −2.20707
\(311\) 4628.31 0.843883 0.421942 0.906623i \(-0.361349\pi\)
0.421942 + 0.906623i \(0.361349\pi\)
\(312\) −4319.93 −0.783872
\(313\) 7309.28 1.31995 0.659976 0.751287i \(-0.270567\pi\)
0.659976 + 0.751287i \(0.270567\pi\)
\(314\) 8652.81 1.55511
\(315\) 18856.1 3.37276
\(316\) 15637.6 2.78381
\(317\) 2626.74 0.465402 0.232701 0.972548i \(-0.425244\pi\)
0.232701 + 0.972548i \(0.425244\pi\)
\(318\) 8385.53 1.47873
\(319\) −2794.96 −0.490556
\(320\) 14536.5 2.53942
\(321\) −7811.39 −1.35822
\(322\) −5331.29 −0.922675
\(323\) −1085.47 −0.186988
\(324\) −3672.46 −0.629709
\(325\) −4159.78 −0.709978
\(326\) 10185.7 1.73047
\(327\) 7584.39 1.28262
\(328\) −6900.05 −1.16156
\(329\) −9000.92 −1.50832
\(330\) 18102.1 3.01966
\(331\) 9551.68 1.58613 0.793063 0.609140i \(-0.208485\pi\)
0.793063 + 0.609140i \(0.208485\pi\)
\(332\) −10996.6 −1.81782
\(333\) −14359.6 −2.36307
\(334\) 12517.3 2.05064
\(335\) 6244.31 1.01840
\(336\) 1918.82 0.311547
\(337\) −6719.78 −1.08620 −0.543101 0.839668i \(-0.682750\pi\)
−0.543101 + 0.839668i \(0.682750\pi\)
\(338\) 8079.02 1.30012
\(339\) −2572.99 −0.412229
\(340\) 1991.02 0.317583
\(341\) 3913.87 0.621549
\(342\) −23498.4 −3.71534
\(343\) −1415.53 −0.222831
\(344\) 0 0
\(345\) −6158.11 −0.960990
\(346\) −5146.79 −0.799691
\(347\) −350.904 −0.0542868 −0.0271434 0.999632i \(-0.508641\pi\)
−0.0271434 + 0.999632i \(0.508641\pi\)
\(348\) −11291.9 −1.73939
\(349\) −1148.96 −0.176225 −0.0881127 0.996111i \(-0.528084\pi\)
−0.0881127 + 0.996111i \(0.528084\pi\)
\(350\) 24619.5 3.75990
\(351\) 2024.11 0.307803
\(352\) −4317.40 −0.653744
\(353\) 9613.89 1.44956 0.724781 0.688979i \(-0.241941\pi\)
0.724781 + 0.688979i \(0.241941\pi\)
\(354\) −13690.7 −2.05552
\(355\) −4696.03 −0.702083
\(356\) −11895.5 −1.77096
\(357\) −1824.96 −0.270552
\(358\) −15421.9 −2.27675
\(359\) 11546.8 1.69755 0.848774 0.528757i \(-0.177342\pi\)
0.848774 + 0.528757i \(0.177342\pi\)
\(360\) 17405.1 2.54814
\(361\) 10309.8 1.50311
\(362\) −6661.30 −0.967155
\(363\) 4911.24 0.710120
\(364\) 7744.82 1.11522
\(365\) 4010.11 0.575065
\(366\) 14299.1 2.04215
\(367\) 2521.04 0.358575 0.179288 0.983797i \(-0.442621\pi\)
0.179288 + 0.983797i \(0.442621\pi\)
\(368\) −369.322 −0.0523159
\(369\) 10662.1 1.50419
\(370\) −30717.6 −4.31604
\(371\) −6070.79 −0.849541
\(372\) 15812.4 2.20386
\(373\) −9791.01 −1.35914 −0.679570 0.733610i \(-0.737834\pi\)
−0.679570 + 0.733610i \(0.737834\pi\)
\(374\) −1032.54 −0.142758
\(375\) 10283.4 1.41608
\(376\) −8308.30 −1.13954
\(377\) −2204.73 −0.301192
\(378\) −11979.6 −1.63006
\(379\) −1072.81 −0.145400 −0.0726999 0.997354i \(-0.523162\pi\)
−0.0726999 + 0.997354i \(0.523162\pi\)
\(380\) −31491.9 −4.25131
\(381\) −2366.68 −0.318239
\(382\) −6412.53 −0.858883
\(383\) 1715.35 0.228852 0.114426 0.993432i \(-0.463497\pi\)
0.114426 + 0.993432i \(0.463497\pi\)
\(384\) −20057.6 −2.66552
\(385\) −13105.2 −1.73481
\(386\) −8712.54 −1.14885
\(387\) 0 0
\(388\) −19639.4 −2.56969
\(389\) 1269.47 0.165463 0.0827313 0.996572i \(-0.473636\pi\)
0.0827313 + 0.996572i \(0.473636\pi\)
\(390\) 14279.4 1.85401
\(391\) 351.257 0.0454318
\(392\) −9908.16 −1.27663
\(393\) 13444.8 1.72569
\(394\) 24467.8 3.12860
\(395\) −20872.9 −2.65881
\(396\) −14003.8 −1.77706
\(397\) 1029.48 0.130147 0.0650733 0.997880i \(-0.479272\pi\)
0.0650733 + 0.997880i \(0.479272\pi\)
\(398\) 21940.4 2.76324
\(399\) 28865.3 3.62174
\(400\) 1705.50 0.213187
\(401\) 7787.03 0.969741 0.484870 0.874586i \(-0.338867\pi\)
0.484870 + 0.874586i \(0.338867\pi\)
\(402\) −13083.0 −1.62319
\(403\) 3087.36 0.381619
\(404\) 1326.27 0.163327
\(405\) 4901.97 0.601434
\(406\) 13048.6 1.59505
\(407\) 9980.12 1.21547
\(408\) −1684.53 −0.204403
\(409\) 6662.70 0.805500 0.402750 0.915310i \(-0.368054\pi\)
0.402750 + 0.915310i \(0.368054\pi\)
\(410\) 22807.9 2.74732
\(411\) 4249.94 0.510059
\(412\) 1380.45 0.165073
\(413\) 9911.53 1.18091
\(414\) 7604.08 0.902705
\(415\) 14678.2 1.73620
\(416\) −3405.67 −0.401386
\(417\) 2037.74 0.239301
\(418\) 16331.7 1.91102
\(419\) −2462.39 −0.287101 −0.143551 0.989643i \(-0.545852\pi\)
−0.143551 + 0.989643i \(0.545852\pi\)
\(420\) −52946.2 −6.15121
\(421\) −3437.41 −0.397931 −0.198966 0.980006i \(-0.563758\pi\)
−0.198966 + 0.980006i \(0.563758\pi\)
\(422\) 20182.6 2.32814
\(423\) 12838.1 1.47567
\(424\) −5603.64 −0.641832
\(425\) −1622.08 −0.185135
\(426\) 9839.07 1.11902
\(427\) −10352.0 −1.17323
\(428\) 12926.7 1.45990
\(429\) −4639.36 −0.522123
\(430\) 0 0
\(431\) −13486.2 −1.50721 −0.753604 0.657328i \(-0.771686\pi\)
−0.753604 + 0.657328i \(0.771686\pi\)
\(432\) −829.879 −0.0924250
\(433\) −3114.54 −0.345670 −0.172835 0.984951i \(-0.555293\pi\)
−0.172835 + 0.984951i \(0.555293\pi\)
\(434\) −18272.4 −2.02098
\(435\) 15072.3 1.66129
\(436\) −12551.0 −1.37864
\(437\) −5555.83 −0.608172
\(438\) −8401.93 −0.916575
\(439\) 695.858 0.0756526 0.0378263 0.999284i \(-0.487957\pi\)
0.0378263 + 0.999284i \(0.487957\pi\)
\(440\) −12096.8 −1.31066
\(441\) 15310.3 1.65320
\(442\) −814.494 −0.0876506
\(443\) 16844.9 1.80660 0.903299 0.429011i \(-0.141138\pi\)
0.903299 + 0.429011i \(0.141138\pi\)
\(444\) 40320.6 4.30975
\(445\) 15878.1 1.69144
\(446\) −15500.1 −1.64563
\(447\) −21510.5 −2.27609
\(448\) 22049.4 2.32531
\(449\) −109.155 −0.0114729 −0.00573646 0.999984i \(-0.501826\pi\)
−0.00573646 + 0.999984i \(0.501826\pi\)
\(450\) −35115.0 −3.67852
\(451\) −7410.26 −0.773693
\(452\) 4257.92 0.443088
\(453\) 23738.2 2.46207
\(454\) 16533.4 1.70914
\(455\) −10337.7 −1.06514
\(456\) 26644.1 2.73624
\(457\) 1458.15 0.149254 0.0746271 0.997212i \(-0.476223\pi\)
0.0746271 + 0.997212i \(0.476223\pi\)
\(458\) 23973.9 2.44591
\(459\) 789.287 0.0802631
\(460\) 10190.8 1.03293
\(461\) −13360.3 −1.34979 −0.674893 0.737916i \(-0.735810\pi\)
−0.674893 + 0.737916i \(0.735810\pi\)
\(462\) 27457.9 2.76506
\(463\) 10181.3 1.02195 0.510976 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(464\) 903.935 0.0904399
\(465\) −21106.2 −2.10490
\(466\) 11153.0 1.10870
\(467\) −6856.74 −0.679426 −0.339713 0.940529i \(-0.610330\pi\)
−0.339713 + 0.940529i \(0.610330\pi\)
\(468\) −11046.5 −1.09108
\(469\) 9471.57 0.932529
\(470\) 27462.8 2.69524
\(471\) 15160.4 1.48313
\(472\) 9148.83 0.892180
\(473\) 0 0
\(474\) 43732.7 4.23778
\(475\) 25656.3 2.47830
\(476\) 3020.04 0.290805
\(477\) 8658.83 0.831154
\(478\) −4790.60 −0.458403
\(479\) −13897.5 −1.32567 −0.662834 0.748767i \(-0.730646\pi\)
−0.662834 + 0.748767i \(0.730646\pi\)
\(480\) 23282.3 2.21393
\(481\) 7872.58 0.746276
\(482\) −1554.17 −0.146868
\(483\) −9340.82 −0.879963
\(484\) −8127.39 −0.763278
\(485\) 26214.5 2.45431
\(486\) −22176.0 −2.06981
\(487\) −6523.20 −0.606970 −0.303485 0.952836i \(-0.598150\pi\)
−0.303485 + 0.952836i \(0.598150\pi\)
\(488\) −9555.41 −0.886379
\(489\) 17846.0 1.65036
\(490\) 32751.1 3.01948
\(491\) −17751.6 −1.63161 −0.815805 0.578327i \(-0.803706\pi\)
−0.815805 + 0.578327i \(0.803706\pi\)
\(492\) −29938.1 −2.74332
\(493\) −859.720 −0.0785392
\(494\) 12882.8 1.17333
\(495\) 18692.1 1.69727
\(496\) −1265.81 −0.114590
\(497\) −7123.10 −0.642886
\(498\) −30753.5 −2.76727
\(499\) −13680.8 −1.22733 −0.613666 0.789566i \(-0.710306\pi\)
−0.613666 + 0.789566i \(0.710306\pi\)
\(500\) −17017.4 −1.52209
\(501\) 21931.2 1.95572
\(502\) −5066.77 −0.450480
\(503\) 12076.8 1.07053 0.535265 0.844684i \(-0.320212\pi\)
0.535265 + 0.844684i \(0.320212\pi\)
\(504\) 26400.6 2.33329
\(505\) −1770.29 −0.155994
\(506\) −5284.93 −0.464315
\(507\) 14155.0 1.23994
\(508\) 3916.51 0.342061
\(509\) −2357.43 −0.205288 −0.102644 0.994718i \(-0.532730\pi\)
−0.102644 + 0.994718i \(0.532730\pi\)
\(510\) 5568.15 0.483455
\(511\) 6082.66 0.526578
\(512\) 3143.75 0.271358
\(513\) −12484.1 −1.07444
\(514\) 5190.12 0.445382
\(515\) −1842.61 −0.157661
\(516\) 0 0
\(517\) −8922.64 −0.759028
\(518\) −46593.5 −3.95212
\(519\) −9017.56 −0.762672
\(520\) −9542.23 −0.804720
\(521\) 7560.92 0.635796 0.317898 0.948125i \(-0.397023\pi\)
0.317898 + 0.948125i \(0.397023\pi\)
\(522\) −18611.4 −1.56053
\(523\) −13283.5 −1.11061 −0.555304 0.831648i \(-0.687398\pi\)
−0.555304 + 0.831648i \(0.687398\pi\)
\(524\) −22249.1 −1.85488
\(525\) 43135.1 3.58585
\(526\) 10728.1 0.889291
\(527\) 1203.90 0.0995114
\(528\) 1902.13 0.156779
\(529\) −10369.1 −0.852234
\(530\) 18522.7 1.51806
\(531\) −14136.9 −1.15535
\(532\) −47767.9 −3.89286
\(533\) −5845.40 −0.475033
\(534\) −33267.5 −2.69593
\(535\) −17254.4 −1.39435
\(536\) 8742.72 0.704530
\(537\) −27020.4 −2.17135
\(538\) −20677.2 −1.65698
\(539\) −10640.8 −0.850338
\(540\) 22899.0 1.82484
\(541\) −10761.0 −0.855176 −0.427588 0.903974i \(-0.640637\pi\)
−0.427588 + 0.903974i \(0.640637\pi\)
\(542\) −34522.0 −2.73588
\(543\) −11671.1 −0.922383
\(544\) −1328.02 −0.104666
\(545\) 16753.0 1.31673
\(546\) 21659.5 1.69769
\(547\) −20661.6 −1.61504 −0.807521 0.589839i \(-0.799191\pi\)
−0.807521 + 0.589839i \(0.799191\pi\)
\(548\) −7033.03 −0.548241
\(549\) 14765.2 1.14784
\(550\) 24405.3 1.89209
\(551\) 13598.2 1.05136
\(552\) −8622.04 −0.664816
\(553\) −31660.7 −2.43463
\(554\) 2473.47 0.189689
\(555\) −53819.6 −4.11624
\(556\) −3372.16 −0.257215
\(557\) −17603.1 −1.33908 −0.669538 0.742777i \(-0.733508\pi\)
−0.669538 + 0.742777i \(0.733508\pi\)
\(558\) 26062.1 1.97724
\(559\) 0 0
\(560\) 4238.44 0.319833
\(561\) −1809.09 −0.136149
\(562\) 14569.7 1.09357
\(563\) 4080.71 0.305473 0.152737 0.988267i \(-0.451191\pi\)
0.152737 + 0.988267i \(0.451191\pi\)
\(564\) −36048.2 −2.69132
\(565\) −5683.43 −0.423192
\(566\) −35149.6 −2.61033
\(567\) 7435.47 0.550724
\(568\) −6574.97 −0.485704
\(569\) 5719.77 0.421415 0.210708 0.977549i \(-0.432423\pi\)
0.210708 + 0.977549i \(0.432423\pi\)
\(570\) −88071.4 −6.47176
\(571\) −6951.99 −0.509512 −0.254756 0.967005i \(-0.581995\pi\)
−0.254756 + 0.967005i \(0.581995\pi\)
\(572\) 7677.47 0.561208
\(573\) −11235.2 −0.819124
\(574\) 34595.8 2.51568
\(575\) −8302.39 −0.602145
\(576\) −31449.3 −2.27498
\(577\) 207.650 0.0149819 0.00749097 0.999972i \(-0.497616\pi\)
0.00749097 + 0.999972i \(0.497616\pi\)
\(578\) 22419.9 1.61340
\(579\) −15265.0 −1.09567
\(580\) −24942.4 −1.78565
\(581\) 22264.3 1.58981
\(582\) −54924.3 −3.91183
\(583\) −6017.99 −0.427512
\(584\) 5614.60 0.397832
\(585\) 14744.8 1.04209
\(586\) 867.543 0.0611568
\(587\) −19920.8 −1.40071 −0.700357 0.713793i \(-0.746976\pi\)
−0.700357 + 0.713793i \(0.746976\pi\)
\(588\) −42989.8 −3.01508
\(589\) −19042.0 −1.33211
\(590\) −30241.2 −2.11019
\(591\) 42869.4 2.98377
\(592\) −3227.74 −0.224086
\(593\) −21162.6 −1.46550 −0.732752 0.680495i \(-0.761765\pi\)
−0.732752 + 0.680495i \(0.761765\pi\)
\(594\) −11875.4 −0.820293
\(595\) −4031.12 −0.277748
\(596\) 35596.7 2.44648
\(597\) 38441.1 2.63533
\(598\) −4168.88 −0.285081
\(599\) 14057.7 0.958901 0.479451 0.877569i \(-0.340836\pi\)
0.479451 + 0.877569i \(0.340836\pi\)
\(600\) 39815.8 2.70912
\(601\) −13682.7 −0.928666 −0.464333 0.885661i \(-0.653706\pi\)
−0.464333 + 0.885661i \(0.653706\pi\)
\(602\) 0 0
\(603\) −13509.4 −0.912347
\(604\) −39283.3 −2.64638
\(605\) 10848.4 0.729006
\(606\) 3709.09 0.248633
\(607\) −21386.3 −1.43005 −0.715027 0.699096i \(-0.753586\pi\)
−0.715027 + 0.699096i \(0.753586\pi\)
\(608\) 21005.2 1.40111
\(609\) 22862.1 1.52122
\(610\) 31585.1 2.09646
\(611\) −7038.41 −0.466028
\(612\) −4307.51 −0.284511
\(613\) 6950.38 0.457950 0.228975 0.973432i \(-0.426463\pi\)
0.228975 + 0.973432i \(0.426463\pi\)
\(614\) 20808.4 1.36769
\(615\) 39961.1 2.62014
\(616\) −18348.7 −1.20015
\(617\) −21710.1 −1.41656 −0.708278 0.705934i \(-0.750528\pi\)
−0.708278 + 0.705934i \(0.750528\pi\)
\(618\) 3860.62 0.251289
\(619\) 11841.9 0.768929 0.384465 0.923140i \(-0.374386\pi\)
0.384465 + 0.923140i \(0.374386\pi\)
\(620\) 34927.7 2.26247
\(621\) 4039.86 0.261053
\(622\) −21420.0 −1.38081
\(623\) 24084.4 1.54883
\(624\) 1500.45 0.0962595
\(625\) −1760.95 −0.112701
\(626\) −33827.5 −2.15977
\(627\) 28614.3 1.82256
\(628\) −25088.2 −1.59415
\(629\) 3069.86 0.194600
\(630\) −87266.4 −5.51869
\(631\) −3519.70 −0.222056 −0.111028 0.993817i \(-0.535414\pi\)
−0.111028 + 0.993817i \(0.535414\pi\)
\(632\) −29224.4 −1.83937
\(633\) 35361.4 2.22036
\(634\) −12156.6 −0.761516
\(635\) −5227.73 −0.326702
\(636\) −24313.2 −1.51585
\(637\) −8393.74 −0.522091
\(638\) 12935.1 0.802675
\(639\) 10159.7 0.628972
\(640\) −44304.9 −2.73641
\(641\) −3923.72 −0.241775 −0.120887 0.992666i \(-0.538574\pi\)
−0.120887 + 0.992666i \(0.538574\pi\)
\(642\) 36151.3 2.22240
\(643\) −12134.0 −0.744198 −0.372099 0.928193i \(-0.621362\pi\)
−0.372099 + 0.928193i \(0.621362\pi\)
\(644\) 15457.7 0.945835
\(645\) 0 0
\(646\) 5023.57 0.305959
\(647\) 28496.2 1.73153 0.865766 0.500449i \(-0.166832\pi\)
0.865766 + 0.500449i \(0.166832\pi\)
\(648\) 6863.30 0.416074
\(649\) 9825.33 0.594265
\(650\) 19251.6 1.16170
\(651\) −32014.6 −1.92742
\(652\) −29532.6 −1.77390
\(653\) −8815.15 −0.528275 −0.264138 0.964485i \(-0.585087\pi\)
−0.264138 + 0.964485i \(0.585087\pi\)
\(654\) −35100.7 −2.09870
\(655\) 29697.9 1.77159
\(656\) 2396.60 0.142640
\(657\) −8675.76 −0.515181
\(658\) 41656.5 2.46799
\(659\) −2797.40 −0.165358 −0.0826791 0.996576i \(-0.526348\pi\)
−0.0826791 + 0.996576i \(0.526348\pi\)
\(660\) −52485.7 −3.09546
\(661\) −21286.4 −1.25257 −0.626283 0.779596i \(-0.715424\pi\)
−0.626283 + 0.779596i \(0.715424\pi\)
\(662\) −44205.4 −2.59530
\(663\) −1427.05 −0.0835931
\(664\) 20551.1 1.20111
\(665\) 63760.1 3.71806
\(666\) 66456.8 3.86659
\(667\) −4400.37 −0.255447
\(668\) −36292.9 −2.10212
\(669\) −27157.3 −1.56945
\(670\) −28898.8 −1.66636
\(671\) −10262.0 −0.590401
\(672\) 35315.4 2.02726
\(673\) −28413.7 −1.62744 −0.813721 0.581256i \(-0.802562\pi\)
−0.813721 + 0.581256i \(0.802562\pi\)
\(674\) 31099.3 1.77730
\(675\) −18655.8 −1.06379
\(676\) −23424.5 −1.33275
\(677\) −29392.6 −1.66861 −0.834305 0.551303i \(-0.814131\pi\)
−0.834305 + 0.551303i \(0.814131\pi\)
\(678\) 11907.9 0.674511
\(679\) 39763.0 2.24737
\(680\) −3720.92 −0.209840
\(681\) 28967.7 1.63002
\(682\) −18113.5 −1.01701
\(683\) −1108.89 −0.0621236 −0.0310618 0.999517i \(-0.509889\pi\)
−0.0310618 + 0.999517i \(0.509889\pi\)
\(684\) 68131.8 3.80860
\(685\) 9387.63 0.523625
\(686\) 6551.09 0.364609
\(687\) 42004.1 2.33269
\(688\) 0 0
\(689\) −4747.14 −0.262484
\(690\) 28499.9 1.57242
\(691\) 16069.1 0.884659 0.442329 0.896853i \(-0.354152\pi\)
0.442329 + 0.896853i \(0.354152\pi\)
\(692\) 14922.7 0.819765
\(693\) 28352.8 1.55416
\(694\) 1623.99 0.0888270
\(695\) 4501.13 0.245666
\(696\) 21102.9 1.14929
\(697\) −2279.37 −0.123870
\(698\) 5317.43 0.288349
\(699\) 19540.9 1.05737
\(700\) −71382.3 −3.85428
\(701\) −20319.8 −1.09482 −0.547408 0.836866i \(-0.684386\pi\)
−0.547408 + 0.836866i \(0.684386\pi\)
\(702\) −9367.63 −0.503644
\(703\) −48555.8 −2.60500
\(704\) 21857.7 1.17016
\(705\) 48116.9 2.57048
\(706\) −44493.3 −2.37185
\(707\) −2685.23 −0.142841
\(708\) 39695.2 2.10711
\(709\) −30651.7 −1.62362 −0.811810 0.583921i \(-0.801518\pi\)
−0.811810 + 0.583921i \(0.801518\pi\)
\(710\) 21733.4 1.14879
\(711\) 45158.0 2.38194
\(712\) 22231.0 1.17015
\(713\) 6161.98 0.323658
\(714\) 8445.96 0.442692
\(715\) −10247.8 −0.536009
\(716\) 44714.8 2.33390
\(717\) −8393.48 −0.437183
\(718\) −53439.1 −2.77762
\(719\) −10638.1 −0.551788 −0.275894 0.961188i \(-0.588974\pi\)
−0.275894 + 0.961188i \(0.588974\pi\)
\(720\) −6045.33 −0.312911
\(721\) −2794.93 −0.144367
\(722\) −47714.1 −2.45947
\(723\) −2723.02 −0.140070
\(724\) 19313.9 0.991432
\(725\) 20320.5 1.04094
\(726\) −22729.4 −1.16194
\(727\) 24420.8 1.24583 0.622913 0.782291i \(-0.285949\pi\)
0.622913 + 0.782291i \(0.285949\pi\)
\(728\) −14474.0 −0.736869
\(729\) −31464.6 −1.59857
\(730\) −18558.9 −0.940952
\(731\) 0 0
\(732\) −41459.3 −2.09341
\(733\) −18873.8 −0.951049 −0.475524 0.879703i \(-0.657742\pi\)
−0.475524 + 0.879703i \(0.657742\pi\)
\(734\) −11667.4 −0.586720
\(735\) 57382.4 2.87970
\(736\) −6797.29 −0.340423
\(737\) 9389.19 0.469275
\(738\) −49344.3 −2.46123
\(739\) −13017.8 −0.647994 −0.323997 0.946058i \(-0.605027\pi\)
−0.323997 + 0.946058i \(0.605027\pi\)
\(740\) 89063.4 4.42437
\(741\) 22571.7 1.11902
\(742\) 28095.8 1.39006
\(743\) −15017.9 −0.741525 −0.370762 0.928728i \(-0.620904\pi\)
−0.370762 + 0.928728i \(0.620904\pi\)
\(744\) −29551.1 −1.45618
\(745\) −47514.2 −2.33663
\(746\) 45313.1 2.22390
\(747\) −31755.9 −1.55540
\(748\) 2993.77 0.146341
\(749\) −26172.1 −1.27678
\(750\) −47591.6 −2.31707
\(751\) −33475.8 −1.62656 −0.813281 0.581871i \(-0.802321\pi\)
−0.813281 + 0.581871i \(0.802321\pi\)
\(752\) 2885.73 0.139936
\(753\) −8877.36 −0.429627
\(754\) 10203.6 0.492827
\(755\) 52434.9 2.52755
\(756\) 34733.9 1.67098
\(757\) 25911.7 1.24409 0.622046 0.782981i \(-0.286302\pi\)
0.622046 + 0.782981i \(0.286302\pi\)
\(758\) 4964.99 0.237911
\(759\) −9259.58 −0.442821
\(760\) 58853.8 2.80901
\(761\) 37213.7 1.77266 0.886331 0.463052i \(-0.153246\pi\)
0.886331 + 0.463052i \(0.153246\pi\)
\(762\) 10953.1 0.520719
\(763\) 25411.5 1.20571
\(764\) 18592.6 0.880442
\(765\) 5749.63 0.271736
\(766\) −7938.70 −0.374461
\(767\) 7750.47 0.364867
\(768\) 40179.6 1.88783
\(769\) 34874.0 1.63536 0.817679 0.575675i \(-0.195261\pi\)
0.817679 + 0.575675i \(0.195261\pi\)
\(770\) 60651.2 2.83859
\(771\) 9093.47 0.424765
\(772\) 25261.3 1.17769
\(773\) 24556.5 1.14261 0.571304 0.820738i \(-0.306438\pi\)
0.571304 + 0.820738i \(0.306438\pi\)
\(774\) 0 0
\(775\) −28455.5 −1.31891
\(776\) 36703.2 1.69790
\(777\) −81635.2 −3.76917
\(778\) −5875.16 −0.270739
\(779\) 36052.8 1.65818
\(780\) −41402.1 −1.90055
\(781\) −7061.15 −0.323518
\(782\) −1625.63 −0.0743380
\(783\) −9887.78 −0.451290
\(784\) 3441.41 0.156770
\(785\) 33487.5 1.52257
\(786\) −62222.6 −2.82367
\(787\) 9587.48 0.434252 0.217126 0.976144i \(-0.430332\pi\)
0.217126 + 0.976144i \(0.430332\pi\)
\(788\) −70942.5 −3.20714
\(789\) 18796.4 0.848124
\(790\) 96600.4 4.35049
\(791\) −8620.81 −0.387511
\(792\) 26171.0 1.17417
\(793\) −8094.90 −0.362495
\(794\) −4764.46 −0.212953
\(795\) 32453.1 1.44779
\(796\) −63614.4 −2.83260
\(797\) 3512.54 0.156111 0.0780556 0.996949i \(-0.475129\pi\)
0.0780556 + 0.996949i \(0.475129\pi\)
\(798\) −133589. −5.92609
\(799\) −2744.58 −0.121522
\(800\) 31389.3 1.38722
\(801\) −34351.8 −1.51531
\(802\) −36038.6 −1.58674
\(803\) 6029.76 0.264988
\(804\) 37933.2 1.66393
\(805\) −20632.8 −0.903366
\(806\) −14288.4 −0.624426
\(807\) −36228.0 −1.58028
\(808\) −2478.60 −0.107917
\(809\) 5036.49 0.218879 0.109440 0.993993i \(-0.465094\pi\)
0.109440 + 0.993993i \(0.465094\pi\)
\(810\) −22686.4 −0.984099
\(811\) −8272.59 −0.358187 −0.179094 0.983832i \(-0.557316\pi\)
−0.179094 + 0.983832i \(0.557316\pi\)
\(812\) −37833.5 −1.63509
\(813\) −60485.2 −2.60923
\(814\) −46188.3 −1.98882
\(815\) 39419.8 1.69425
\(816\) 585.089 0.0251007
\(817\) 0 0
\(818\) −30835.2 −1.31800
\(819\) 22365.4 0.954225
\(820\) −66129.8 −2.81628
\(821\) 35068.1 1.49073 0.745363 0.666659i \(-0.232276\pi\)
0.745363 + 0.666659i \(0.232276\pi\)
\(822\) −19668.8 −0.834586
\(823\) 18610.5 0.788241 0.394121 0.919059i \(-0.371049\pi\)
0.394121 + 0.919059i \(0.371049\pi\)
\(824\) −2579.86 −0.109070
\(825\) 42760.0 1.80450
\(826\) −45870.8 −1.93226
\(827\) 23150.2 0.973412 0.486706 0.873566i \(-0.338198\pi\)
0.486706 + 0.873566i \(0.338198\pi\)
\(828\) −22047.5 −0.925365
\(829\) 1109.11 0.0464668 0.0232334 0.999730i \(-0.492604\pi\)
0.0232334 + 0.999730i \(0.492604\pi\)
\(830\) −67931.0 −2.84087
\(831\) 4333.71 0.180908
\(832\) 17241.9 0.718455
\(833\) −3273.08 −0.136141
\(834\) −9430.71 −0.391557
\(835\) 48443.4 2.00773
\(836\) −47352.4 −1.95899
\(837\) 13846.2 0.571797
\(838\) 11396.0 0.469770
\(839\) 27967.9 1.15085 0.575423 0.817856i \(-0.304838\pi\)
0.575423 + 0.817856i \(0.304838\pi\)
\(840\) 98948.8 4.06435
\(841\) −13618.9 −0.558403
\(842\) 15908.4 0.651117
\(843\) 25527.2 1.04295
\(844\) −58517.9 −2.38658
\(845\) 31266.8 1.27291
\(846\) −59415.1 −2.41458
\(847\) 16455.1 0.667539
\(848\) 1946.32 0.0788170
\(849\) −61584.7 −2.48950
\(850\) 7507.01 0.302927
\(851\) 15712.7 0.632930
\(852\) −28527.7 −1.14711
\(853\) −7589.83 −0.304655 −0.152328 0.988330i \(-0.548677\pi\)
−0.152328 + 0.988330i \(0.548677\pi\)
\(854\) 47909.3 1.91970
\(855\) −90941.8 −3.63759
\(856\) −24158.1 −0.964613
\(857\) −28883.4 −1.15127 −0.575635 0.817707i \(-0.695245\pi\)
−0.575635 + 0.817707i \(0.695245\pi\)
\(858\) 21471.1 0.854325
\(859\) 6651.57 0.264201 0.132101 0.991236i \(-0.457828\pi\)
0.132101 + 0.991236i \(0.457828\pi\)
\(860\) 0 0
\(861\) 60614.3 2.39922
\(862\) 62414.4 2.46618
\(863\) 31395.0 1.23835 0.619175 0.785253i \(-0.287467\pi\)
0.619175 + 0.785253i \(0.287467\pi\)
\(864\) −15273.7 −0.601416
\(865\) −19918.7 −0.782956
\(866\) 14414.1 0.565604
\(867\) 39281.3 1.53871
\(868\) 52979.5 2.07171
\(869\) −31385.4 −1.22517
\(870\) −69754.9 −2.71829
\(871\) 7406.43 0.288126
\(872\) 23456.1 0.910922
\(873\) −56714.4 −2.19873
\(874\) 25712.5 0.995124
\(875\) 34454.4 1.33117
\(876\) 24360.8 0.939582
\(877\) −16966.2 −0.653259 −0.326630 0.945152i \(-0.605913\pi\)
−0.326630 + 0.945152i \(0.605913\pi\)
\(878\) −3220.45 −0.123787
\(879\) 1520.00 0.0583257
\(880\) 4201.58 0.160949
\(881\) 28409.0 1.08641 0.543204 0.839601i \(-0.317211\pi\)
0.543204 + 0.839601i \(0.317211\pi\)
\(882\) −70856.2 −2.70505
\(883\) −10627.6 −0.405036 −0.202518 0.979278i \(-0.564913\pi\)
−0.202518 + 0.979278i \(0.564913\pi\)
\(884\) 2361.57 0.0898507
\(885\) −52984.8 −2.01250
\(886\) −77958.4 −2.95605
\(887\) −108.704 −0.00411489 −0.00205745 0.999998i \(-0.500655\pi\)
−0.00205745 + 0.999998i \(0.500655\pi\)
\(888\) −75353.4 −2.84763
\(889\) −7929.59 −0.299156
\(890\) −73484.0 −2.76763
\(891\) 7370.80 0.277139
\(892\) 44941.3 1.68694
\(893\) 43410.9 1.62675
\(894\) 99551.2 3.72426
\(895\) −59684.9 −2.22910
\(896\) −67203.1 −2.50569
\(897\) −7304.19 −0.271884
\(898\) 505.171 0.0187726
\(899\) −15081.8 −0.559516
\(900\) 101813. 3.77086
\(901\) −1851.12 −0.0684457
\(902\) 34294.9 1.26596
\(903\) 0 0
\(904\) −7957.44 −0.292766
\(905\) −25780.1 −0.946915
\(906\) −109861. −4.02857
\(907\) −13689.8 −0.501171 −0.250586 0.968094i \(-0.580623\pi\)
−0.250586 + 0.968094i \(0.580623\pi\)
\(908\) −47937.3 −1.75204
\(909\) 3829.97 0.139749
\(910\) 47843.2 1.74284
\(911\) 13891.9 0.505223 0.252612 0.967568i \(-0.418710\pi\)
0.252612 + 0.967568i \(0.418710\pi\)
\(912\) −9254.33 −0.336010
\(913\) 22070.7 0.800037
\(914\) −6748.33 −0.244218
\(915\) 55339.4 1.99942
\(916\) −69510.5 −2.50731
\(917\) 45046.7 1.62222
\(918\) −3652.84 −0.131331
\(919\) 48072.7 1.72554 0.862770 0.505596i \(-0.168727\pi\)
0.862770 + 0.505596i \(0.168727\pi\)
\(920\) −19045.1 −0.682497
\(921\) 36457.9 1.30437
\(922\) 61831.8 2.20859
\(923\) −5570.01 −0.198634
\(924\) −79612.0 −2.83446
\(925\) −72559.7 −2.57919
\(926\) −47119.2 −1.67217
\(927\) 3986.44 0.141243
\(928\) 16636.7 0.588499
\(929\) −27959.3 −0.987423 −0.493712 0.869626i \(-0.664360\pi\)
−0.493712 + 0.869626i \(0.664360\pi\)
\(930\) 97680.2 3.44415
\(931\) 51770.2 1.82245
\(932\) −32337.2 −1.13653
\(933\) −37529.3 −1.31689
\(934\) 31733.2 1.11171
\(935\) −3996.06 −0.139770
\(936\) 20644.4 0.720921
\(937\) −8650.71 −0.301608 −0.150804 0.988564i \(-0.548186\pi\)
−0.150804 + 0.988564i \(0.548186\pi\)
\(938\) −43834.6 −1.52585
\(939\) −59268.3 −2.05980
\(940\) −79626.4 −2.76290
\(941\) −38299.6 −1.32681 −0.663407 0.748258i \(-0.730890\pi\)
−0.663407 + 0.748258i \(0.730890\pi\)
\(942\) −70162.5 −2.42677
\(943\) −11666.7 −0.402884
\(944\) −3177.67 −0.109560
\(945\) −46362.6 −1.59595
\(946\) 0 0
\(947\) 9535.13 0.327191 0.163596 0.986527i \(-0.447691\pi\)
0.163596 + 0.986527i \(0.447691\pi\)
\(948\) −126800. −4.34416
\(949\) 4756.43 0.162698
\(950\) −118738. −4.05513
\(951\) −21299.3 −0.726265
\(952\) −5644.02 −0.192147
\(953\) −18679.6 −0.634932 −0.317466 0.948270i \(-0.602832\pi\)
−0.317466 + 0.948270i \(0.602832\pi\)
\(954\) −40073.3 −1.35998
\(955\) −24817.3 −0.840909
\(956\) 13890.0 0.469910
\(957\) 22663.3 0.765518
\(958\) 64318.1 2.16913
\(959\) 14239.5 0.479475
\(960\) −117871. −3.96279
\(961\) −8671.48 −0.291077
\(962\) −36434.5 −1.22110
\(963\) 37329.5 1.24915
\(964\) 4506.20 0.150555
\(965\) −33718.6 −1.12481
\(966\) 43229.5 1.43984
\(967\) −17137.5 −0.569911 −0.284956 0.958541i \(-0.591979\pi\)
−0.284956 + 0.958541i \(0.591979\pi\)
\(968\) 15188.9 0.504329
\(969\) 8801.67 0.291796
\(970\) −121321. −4.01587
\(971\) −21152.2 −0.699081 −0.349540 0.936921i \(-0.613662\pi\)
−0.349540 + 0.936921i \(0.613662\pi\)
\(972\) 64297.8 2.12176
\(973\) 6827.46 0.224952
\(974\) 30189.5 0.993157
\(975\) 33730.1 1.10793
\(976\) 3318.89 0.108847
\(977\) −36352.9 −1.19041 −0.595205 0.803574i \(-0.702929\pi\)
−0.595205 + 0.803574i \(0.702929\pi\)
\(978\) −82591.9 −2.70041
\(979\) 23874.9 0.779412
\(980\) −94959.4 −3.09527
\(981\) −36244.7 −1.17962
\(982\) 82155.0 2.66973
\(983\) −16139.9 −0.523687 −0.261844 0.965110i \(-0.584330\pi\)
−0.261844 + 0.965110i \(0.584330\pi\)
\(984\) 55950.0 1.81262
\(985\) 94693.4 3.06313
\(986\) 3978.81 0.128510
\(987\) 72985.2 2.35374
\(988\) −37352.8 −1.20278
\(989\) 0 0
\(990\) −86507.5 −2.77716
\(991\) −38726.1 −1.24135 −0.620674 0.784069i \(-0.713141\pi\)
−0.620674 + 0.784069i \(0.713141\pi\)
\(992\) −23297.0 −0.745644
\(993\) −77451.1 −2.47516
\(994\) 32965.9 1.05193
\(995\) 84912.0 2.70542
\(996\) 89167.6 2.83673
\(997\) 44312.0 1.40760 0.703799 0.710399i \(-0.251485\pi\)
0.703799 + 0.710399i \(0.251485\pi\)
\(998\) 63315.3 2.00823
\(999\) 35306.9 1.11818
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.m.1.14 110
43.42 odd 2 inner 1849.4.a.m.1.97 yes 110
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.m.1.14 110 1.1 even 1 trivial
1849.4.a.m.1.97 yes 110 43.42 odd 2 inner