Properties

Label 1849.4.a.m.1.19
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 1.19
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)
 
\(f(q)\) \(=\) \(q-4.20768 q^{2} -0.654616 q^{3} +9.70454 q^{4} +13.9092 q^{5} +2.75441 q^{6} +32.2423 q^{7} -7.17215 q^{8} -26.5715 q^{9} +O(q^{10})\) \(q-4.20768 q^{2} -0.654616 q^{3} +9.70454 q^{4} +13.9092 q^{5} +2.75441 q^{6} +32.2423 q^{7} -7.17215 q^{8} -26.5715 q^{9} -58.5253 q^{10} +62.9144 q^{11} -6.35275 q^{12} +53.0213 q^{13} -135.665 q^{14} -9.10518 q^{15} -47.4582 q^{16} -40.5919 q^{17} +111.804 q^{18} +76.2601 q^{19} +134.982 q^{20} -21.1063 q^{21} -264.724 q^{22} -103.602 q^{23} +4.69501 q^{24} +68.4653 q^{25} -223.096 q^{26} +35.0688 q^{27} +312.896 q^{28} +10.3011 q^{29} +38.3116 q^{30} +13.7002 q^{31} +257.066 q^{32} -41.1848 q^{33} +170.798 q^{34} +448.464 q^{35} -257.864 q^{36} -355.179 q^{37} -320.878 q^{38} -34.7086 q^{39} -99.7587 q^{40} +379.187 q^{41} +88.8086 q^{42} +610.555 q^{44} -369.587 q^{45} +435.924 q^{46} +241.252 q^{47} +31.0669 q^{48} +696.564 q^{49} -288.080 q^{50} +26.5722 q^{51} +514.547 q^{52} -94.7008 q^{53} -147.558 q^{54} +875.088 q^{55} -231.246 q^{56} -49.9211 q^{57} -43.3438 q^{58} -247.647 q^{59} -88.3616 q^{60} +62.6153 q^{61} -57.6460 q^{62} -856.725 q^{63} -701.985 q^{64} +737.482 q^{65} +173.292 q^{66} +256.508 q^{67} -393.926 q^{68} +67.8196 q^{69} -1886.99 q^{70} -345.573 q^{71} +190.575 q^{72} +270.766 q^{73} +1494.48 q^{74} -44.8185 q^{75} +740.069 q^{76} +2028.50 q^{77} +146.042 q^{78} +1026.68 q^{79} -660.105 q^{80} +694.473 q^{81} -1595.50 q^{82} +860.983 q^{83} -204.827 q^{84} -564.601 q^{85} -6.74329 q^{87} -451.232 q^{88} +511.713 q^{89} +1555.10 q^{90} +1709.53 q^{91} -1005.41 q^{92} -8.96838 q^{93} -1015.11 q^{94} +1060.72 q^{95} -168.280 q^{96} +306.610 q^{97} -2930.92 q^{98} -1671.73 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 110 q + 492 q^{4} + 102 q^{6} + 1234 q^{9}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.20768 −1.48764 −0.743819 0.668381i \(-0.766988\pi\)
−0.743819 + 0.668381i \(0.766988\pi\)
\(3\) −0.654616 −0.125981 −0.0629905 0.998014i \(-0.520064\pi\)
−0.0629905 + 0.998014i \(0.520064\pi\)
\(4\) 9.70454 1.21307
\(5\) 13.9092 1.24407 0.622037 0.782987i \(-0.286305\pi\)
0.622037 + 0.782987i \(0.286305\pi\)
\(6\) 2.75441 0.187414
\(7\) 32.2423 1.74092 0.870460 0.492240i \(-0.163822\pi\)
0.870460 + 0.492240i \(0.163822\pi\)
\(8\) −7.17215 −0.316967
\(9\) −26.5715 −0.984129
\(10\) −58.5253 −1.85073
\(11\) 62.9144 1.72449 0.862246 0.506490i \(-0.169057\pi\)
0.862246 + 0.506490i \(0.169057\pi\)
\(12\) −6.35275 −0.152823
\(13\) 53.0213 1.13119 0.565594 0.824684i \(-0.308647\pi\)
0.565594 + 0.824684i \(0.308647\pi\)
\(14\) −135.665 −2.58986
\(15\) −9.10518 −0.156730
\(16\) −47.4582 −0.741535
\(17\) −40.5919 −0.579117 −0.289559 0.957160i \(-0.593509\pi\)
−0.289559 + 0.957160i \(0.593509\pi\)
\(18\) 111.804 1.46403
\(19\) 76.2601 0.920804 0.460402 0.887711i \(-0.347705\pi\)
0.460402 + 0.887711i \(0.347705\pi\)
\(20\) 134.982 1.50915
\(21\) −21.1063 −0.219323
\(22\) −264.724 −2.56542
\(23\) −103.602 −0.939241 −0.469620 0.882868i \(-0.655609\pi\)
−0.469620 + 0.882868i \(0.655609\pi\)
\(24\) 4.69501 0.0399318
\(25\) 68.4653 0.547722
\(26\) −223.096 −1.68280
\(27\) 35.0688 0.249963
\(28\) 312.896 2.11185
\(29\) 10.3011 0.0659611 0.0329805 0.999456i \(-0.489500\pi\)
0.0329805 + 0.999456i \(0.489500\pi\)
\(30\) 38.3116 0.233157
\(31\) 13.7002 0.0793752 0.0396876 0.999212i \(-0.487364\pi\)
0.0396876 + 0.999212i \(0.487364\pi\)
\(32\) 257.066 1.42010
\(33\) −41.1848 −0.217253
\(34\) 170.798 0.861517
\(35\) 448.464 2.16583
\(36\) −257.864 −1.19381
\(37\) −355.179 −1.57814 −0.789068 0.614305i \(-0.789436\pi\)
−0.789068 + 0.614305i \(0.789436\pi\)
\(38\) −320.878 −1.36982
\(39\) −34.7086 −0.142508
\(40\) −99.7587 −0.394331
\(41\) 379.187 1.44437 0.722184 0.691701i \(-0.243138\pi\)
0.722184 + 0.691701i \(0.243138\pi\)
\(42\) 88.8086 0.326273
\(43\) 0 0
\(44\) 610.555 2.09193
\(45\) −369.587 −1.22433
\(46\) 435.924 1.39725
\(47\) 241.252 0.748728 0.374364 0.927282i \(-0.377861\pi\)
0.374364 + 0.927282i \(0.377861\pi\)
\(48\) 31.0669 0.0934193
\(49\) 696.564 2.03080
\(50\) −288.080 −0.814813
\(51\) 26.5722 0.0729578
\(52\) 514.547 1.37221
\(53\) −94.7008 −0.245437 −0.122718 0.992442i \(-0.539161\pi\)
−0.122718 + 0.992442i \(0.539161\pi\)
\(54\) −147.558 −0.371854
\(55\) 875.088 2.14540
\(56\) −231.246 −0.551814
\(57\) −49.9211 −0.116004
\(58\) −43.3438 −0.0981262
\(59\) −247.647 −0.546457 −0.273228 0.961949i \(-0.588091\pi\)
−0.273228 + 0.961949i \(0.588091\pi\)
\(60\) −88.3616 −0.190124
\(61\) 62.6153 0.131427 0.0657137 0.997839i \(-0.479068\pi\)
0.0657137 + 0.997839i \(0.479068\pi\)
\(62\) −57.6460 −0.118082
\(63\) −856.725 −1.71329
\(64\) −701.985 −1.37106
\(65\) 737.482 1.40728
\(66\) 173.292 0.323194
\(67\) 256.508 0.467723 0.233861 0.972270i \(-0.424864\pi\)
0.233861 + 0.972270i \(0.424864\pi\)
\(68\) −393.926 −0.702508
\(69\) 67.8196 0.118326
\(70\) −1886.99 −3.22198
\(71\) −345.573 −0.577633 −0.288816 0.957384i \(-0.593262\pi\)
−0.288816 + 0.957384i \(0.593262\pi\)
\(72\) 190.575 0.311937
\(73\) 270.766 0.434121 0.217060 0.976158i \(-0.430353\pi\)
0.217060 + 0.976158i \(0.430353\pi\)
\(74\) 1494.48 2.34770
\(75\) −44.8185 −0.0690026
\(76\) 740.069 1.11700
\(77\) 2028.50 3.00220
\(78\) 146.042 0.212001
\(79\) 1026.68 1.46215 0.731077 0.682295i \(-0.239018\pi\)
0.731077 + 0.682295i \(0.239018\pi\)
\(80\) −660.105 −0.922525
\(81\) 694.473 0.952638
\(82\) −1595.50 −2.14870
\(83\) 860.983 1.13862 0.569308 0.822124i \(-0.307211\pi\)
0.569308 + 0.822124i \(0.307211\pi\)
\(84\) −204.827 −0.266053
\(85\) −564.601 −0.720465
\(86\) 0 0
\(87\) −6.74329 −0.00830984
\(88\) −451.232 −0.546608
\(89\) 511.713 0.609455 0.304727 0.952440i \(-0.401435\pi\)
0.304727 + 0.952440i \(0.401435\pi\)
\(90\) 1555.10 1.82136
\(91\) 1709.53 1.96931
\(92\) −1005.41 −1.13936
\(93\) −8.96838 −0.00999976
\(94\) −1015.11 −1.11384
\(95\) 1060.72 1.14555
\(96\) −168.280 −0.178906
\(97\) 306.610 0.320943 0.160472 0.987040i \(-0.448698\pi\)
0.160472 + 0.987040i \(0.448698\pi\)
\(98\) −2930.92 −3.02109
\(99\) −1671.73 −1.69712
\(100\) 664.424 0.664424
\(101\) 104.607 0.103057 0.0515286 0.998672i \(-0.483591\pi\)
0.0515286 + 0.998672i \(0.483591\pi\)
\(102\) −111.807 −0.108535
\(103\) −110.014 −0.105243 −0.0526215 0.998615i \(-0.516758\pi\)
−0.0526215 + 0.998615i \(0.516758\pi\)
\(104\) −380.276 −0.358550
\(105\) −293.572 −0.272854
\(106\) 398.470 0.365121
\(107\) 750.436 0.678013 0.339007 0.940784i \(-0.389909\pi\)
0.339007 + 0.940784i \(0.389909\pi\)
\(108\) 340.326 0.303221
\(109\) −716.691 −0.629785 −0.314893 0.949127i \(-0.601968\pi\)
−0.314893 + 0.949127i \(0.601968\pi\)
\(110\) −3682.09 −3.19157
\(111\) 232.506 0.198815
\(112\) −1530.16 −1.29095
\(113\) 791.259 0.658720 0.329360 0.944204i \(-0.393167\pi\)
0.329360 + 0.944204i \(0.393167\pi\)
\(114\) 210.052 0.172572
\(115\) −1441.02 −1.16849
\(116\) 99.9677 0.0800153
\(117\) −1408.85 −1.11324
\(118\) 1042.02 0.812930
\(119\) −1308.78 −1.00820
\(120\) 65.3037 0.0496782
\(121\) 2627.22 1.97387
\(122\) −263.465 −0.195516
\(123\) −248.222 −0.181963
\(124\) 132.954 0.0962874
\(125\) −786.351 −0.562667
\(126\) 3604.82 2.54875
\(127\) −2092.69 −1.46217 −0.731086 0.682285i \(-0.760986\pi\)
−0.731086 + 0.682285i \(0.760986\pi\)
\(128\) 897.197 0.619545
\(129\) 0 0
\(130\) −3103.09 −2.09353
\(131\) −2426.04 −1.61804 −0.809022 0.587779i \(-0.800003\pi\)
−0.809022 + 0.587779i \(0.800003\pi\)
\(132\) −399.680 −0.263543
\(133\) 2458.80 1.60304
\(134\) −1079.30 −0.695803
\(135\) 487.778 0.310972
\(136\) 291.132 0.183561
\(137\) −36.6355 −0.0228466 −0.0114233 0.999935i \(-0.503636\pi\)
−0.0114233 + 0.999935i \(0.503636\pi\)
\(138\) −285.363 −0.176027
\(139\) −697.573 −0.425665 −0.212832 0.977089i \(-0.568269\pi\)
−0.212832 + 0.977089i \(0.568269\pi\)
\(140\) 4352.13 2.62730
\(141\) −157.928 −0.0943255
\(142\) 1454.06 0.859309
\(143\) 3335.80 1.95073
\(144\) 1261.04 0.729766
\(145\) 143.280 0.0820605
\(146\) −1139.30 −0.645814
\(147\) −455.982 −0.255842
\(148\) −3446.85 −1.91439
\(149\) 1444.54 0.794238 0.397119 0.917767i \(-0.370010\pi\)
0.397119 + 0.917767i \(0.370010\pi\)
\(150\) 188.582 0.102651
\(151\) −3298.40 −1.77761 −0.888807 0.458282i \(-0.848465\pi\)
−0.888807 + 0.458282i \(0.848465\pi\)
\(152\) −546.949 −0.291865
\(153\) 1078.59 0.569926
\(154\) −8535.29 −4.46619
\(155\) 190.559 0.0987487
\(156\) −336.831 −0.172872
\(157\) 1357.08 0.689853 0.344926 0.938630i \(-0.387904\pi\)
0.344926 + 0.938630i \(0.387904\pi\)
\(158\) −4319.93 −2.17516
\(159\) 61.9927 0.0309204
\(160\) 3575.58 1.76671
\(161\) −3340.37 −1.63514
\(162\) −2922.12 −1.41718
\(163\) −762.254 −0.366284 −0.183142 0.983086i \(-0.558627\pi\)
−0.183142 + 0.983086i \(0.558627\pi\)
\(164\) 3679.84 1.75212
\(165\) −572.847 −0.270279
\(166\) −3622.74 −1.69385
\(167\) 865.240 0.400924 0.200462 0.979701i \(-0.435756\pi\)
0.200462 + 0.979701i \(0.435756\pi\)
\(168\) 151.378 0.0695181
\(169\) 614.254 0.279588
\(170\) 2375.66 1.07179
\(171\) −2026.34 −0.906189
\(172\) 0 0
\(173\) 2433.22 1.06933 0.534666 0.845063i \(-0.320437\pi\)
0.534666 + 0.845063i \(0.320437\pi\)
\(174\) 28.3736 0.0123620
\(175\) 2207.48 0.953540
\(176\) −2985.81 −1.27877
\(177\) 162.114 0.0688431
\(178\) −2153.12 −0.906648
\(179\) 175.349 0.0732192 0.0366096 0.999330i \(-0.488344\pi\)
0.0366096 + 0.999330i \(0.488344\pi\)
\(180\) −3586.68 −1.48519
\(181\) −133.089 −0.0546542 −0.0273271 0.999627i \(-0.508700\pi\)
−0.0273271 + 0.999627i \(0.508700\pi\)
\(182\) −7193.13 −2.92962
\(183\) −40.9890 −0.0165574
\(184\) 743.050 0.297709
\(185\) −4940.25 −1.96332
\(186\) 37.7360 0.0148760
\(187\) −2553.82 −0.998683
\(188\) 2341.24 0.908258
\(189\) 1130.70 0.435164
\(190\) −4463.15 −1.70416
\(191\) −2348.28 −0.889612 −0.444806 0.895627i \(-0.646727\pi\)
−0.444806 + 0.895627i \(0.646727\pi\)
\(192\) 459.531 0.172728
\(193\) −4157.01 −1.55040 −0.775202 0.631714i \(-0.782352\pi\)
−0.775202 + 0.631714i \(0.782352\pi\)
\(194\) −1290.11 −0.477448
\(195\) −482.768 −0.177291
\(196\) 6759.83 2.46350
\(197\) −2234.19 −0.808017 −0.404009 0.914755i \(-0.632383\pi\)
−0.404009 + 0.914755i \(0.632383\pi\)
\(198\) 7034.09 2.52470
\(199\) 2743.66 0.977352 0.488676 0.872465i \(-0.337480\pi\)
0.488676 + 0.872465i \(0.337480\pi\)
\(200\) −491.043 −0.173610
\(201\) −167.914 −0.0589242
\(202\) −440.152 −0.153312
\(203\) 332.132 0.114833
\(204\) 257.871 0.0885027
\(205\) 5274.19 1.79690
\(206\) 462.905 0.156564
\(207\) 2752.86 0.924334
\(208\) −2516.30 −0.838816
\(209\) 4797.86 1.58792
\(210\) 1235.25 0.405908
\(211\) 2833.03 0.924332 0.462166 0.886793i \(-0.347072\pi\)
0.462166 + 0.886793i \(0.347072\pi\)
\(212\) −919.028 −0.297731
\(213\) 226.218 0.0727708
\(214\) −3157.59 −1.00864
\(215\) 0 0
\(216\) −251.518 −0.0792299
\(217\) 441.726 0.138186
\(218\) 3015.61 0.936892
\(219\) −177.248 −0.0546909
\(220\) 8492.33 2.60251
\(221\) −2152.24 −0.655091
\(222\) −978.310 −0.295765
\(223\) 1008.77 0.302924 0.151462 0.988463i \(-0.451602\pi\)
0.151462 + 0.988463i \(0.451602\pi\)
\(224\) 8288.39 2.47228
\(225\) −1819.22 −0.539029
\(226\) −3329.36 −0.979937
\(227\) −1858.00 −0.543259 −0.271630 0.962402i \(-0.587563\pi\)
−0.271630 + 0.962402i \(0.587563\pi\)
\(228\) −484.461 −0.140720
\(229\) 6638.58 1.91568 0.957838 0.287308i \(-0.0927604\pi\)
0.957838 + 0.287308i \(0.0927604\pi\)
\(230\) 6063.35 1.73828
\(231\) −1327.89 −0.378220
\(232\) −73.8813 −0.0209075
\(233\) −1258.53 −0.353860 −0.176930 0.984223i \(-0.556617\pi\)
−0.176930 + 0.984223i \(0.556617\pi\)
\(234\) 5928.00 1.65609
\(235\) 3355.62 0.931474
\(236\) −2403.30 −0.662889
\(237\) −672.080 −0.184204
\(238\) 5506.91 1.49983
\(239\) −4792.66 −1.29712 −0.648559 0.761164i \(-0.724628\pi\)
−0.648559 + 0.761164i \(0.724628\pi\)
\(240\) 432.116 0.116221
\(241\) −3314.50 −0.885915 −0.442957 0.896543i \(-0.646071\pi\)
−0.442957 + 0.896543i \(0.646071\pi\)
\(242\) −11054.5 −2.93641
\(243\) −1401.47 −0.369977
\(244\) 607.653 0.159430
\(245\) 9688.64 2.52647
\(246\) 1044.44 0.270695
\(247\) 4043.41 1.04160
\(248\) −98.2600 −0.0251593
\(249\) −563.614 −0.143444
\(250\) 3308.71 0.837045
\(251\) −7328.40 −1.84289 −0.921443 0.388513i \(-0.872989\pi\)
−0.921443 + 0.388513i \(0.872989\pi\)
\(252\) −8314.12 −2.07833
\(253\) −6518.07 −1.61971
\(254\) 8805.35 2.17518
\(255\) 369.597 0.0907649
\(256\) 1840.77 0.449406
\(257\) 7534.47 1.82874 0.914372 0.404874i \(-0.132685\pi\)
0.914372 + 0.404874i \(0.132685\pi\)
\(258\) 0 0
\(259\) −11451.8 −2.74741
\(260\) 7156.93 1.70713
\(261\) −273.716 −0.0649142
\(262\) 10208.0 2.40706
\(263\) 3168.33 0.742843 0.371422 0.928464i \(-0.378870\pi\)
0.371422 + 0.928464i \(0.378870\pi\)
\(264\) 295.384 0.0688622
\(265\) −1317.21 −0.305342
\(266\) −10345.8 −2.38475
\(267\) −334.976 −0.0767797
\(268\) 2489.29 0.567379
\(269\) 3734.70 0.846501 0.423251 0.906013i \(-0.360889\pi\)
0.423251 + 0.906013i \(0.360889\pi\)
\(270\) −2052.41 −0.462614
\(271\) 2562.20 0.574326 0.287163 0.957882i \(-0.407288\pi\)
0.287163 + 0.957882i \(0.407288\pi\)
\(272\) 1926.42 0.429436
\(273\) −1119.08 −0.248095
\(274\) 154.151 0.0339875
\(275\) 4307.45 0.944543
\(276\) 658.158 0.143538
\(277\) −586.811 −0.127285 −0.0636427 0.997973i \(-0.520272\pi\)
−0.0636427 + 0.997973i \(0.520272\pi\)
\(278\) 2935.16 0.633235
\(279\) −364.035 −0.0781154
\(280\) −3216.45 −0.686498
\(281\) 2001.37 0.424881 0.212441 0.977174i \(-0.431859\pi\)
0.212441 + 0.977174i \(0.431859\pi\)
\(282\) 664.508 0.140322
\(283\) 2224.86 0.467330 0.233665 0.972317i \(-0.424928\pi\)
0.233665 + 0.972317i \(0.424928\pi\)
\(284\) −3353.62 −0.700708
\(285\) −694.362 −0.144317
\(286\) −14036.0 −2.90197
\(287\) 12225.9 2.51453
\(288\) −6830.63 −1.39756
\(289\) −3265.29 −0.664623
\(290\) −602.877 −0.122076
\(291\) −200.712 −0.0404328
\(292\) 2627.66 0.526618
\(293\) −5130.85 −1.02303 −0.511514 0.859275i \(-0.670915\pi\)
−0.511514 + 0.859275i \(0.670915\pi\)
\(294\) 1918.63 0.380600
\(295\) −3444.57 −0.679833
\(296\) 2547.40 0.500218
\(297\) 2206.33 0.431058
\(298\) −6078.16 −1.18154
\(299\) −5493.11 −1.06246
\(300\) −434.943 −0.0837048
\(301\) 0 0
\(302\) 13878.6 2.64445
\(303\) −68.4773 −0.0129832
\(304\) −3619.17 −0.682808
\(305\) 870.928 0.163506
\(306\) −4538.35 −0.847844
\(307\) −1662.64 −0.309094 −0.154547 0.987985i \(-0.549392\pi\)
−0.154547 + 0.987985i \(0.549392\pi\)
\(308\) 19685.7 3.64187
\(309\) 72.0172 0.0132586
\(310\) −801.809 −0.146902
\(311\) 7499.02 1.36730 0.683650 0.729810i \(-0.260391\pi\)
0.683650 + 0.729810i \(0.260391\pi\)
\(312\) 248.935 0.0451705
\(313\) −4871.56 −0.879734 −0.439867 0.898063i \(-0.644974\pi\)
−0.439867 + 0.898063i \(0.644974\pi\)
\(314\) −5710.16 −1.02625
\(315\) −11916.3 −2.13146
\(316\) 9963.43 1.77369
\(317\) 6985.74 1.23772 0.618862 0.785500i \(-0.287594\pi\)
0.618862 + 0.785500i \(0.287594\pi\)
\(318\) −260.845 −0.0459983
\(319\) 648.090 0.113749
\(320\) −9764.04 −1.70571
\(321\) −491.248 −0.0854168
\(322\) 14055.2 2.43250
\(323\) −3095.55 −0.533253
\(324\) 6739.54 1.15561
\(325\) 3630.12 0.619577
\(326\) 3207.32 0.544899
\(327\) 469.158 0.0793410
\(328\) −2719.59 −0.457818
\(329\) 7778.51 1.30348
\(330\) 2410.35 0.402078
\(331\) 370.542 0.0615313 0.0307656 0.999527i \(-0.490205\pi\)
0.0307656 + 0.999527i \(0.490205\pi\)
\(332\) 8355.45 1.38122
\(333\) 9437.63 1.55309
\(334\) −3640.65 −0.596430
\(335\) 3567.82 0.581882
\(336\) 1001.67 0.162635
\(337\) 11879.9 1.92029 0.960147 0.279496i \(-0.0901674\pi\)
0.960147 + 0.279496i \(0.0901674\pi\)
\(338\) −2584.58 −0.415925
\(339\) −517.971 −0.0829862
\(340\) −5479.19 −0.873973
\(341\) 861.941 0.136882
\(342\) 8526.20 1.34808
\(343\) 11399.7 1.79454
\(344\) 0 0
\(345\) 943.316 0.147207
\(346\) −10238.2 −1.59078
\(347\) −303.121 −0.0468944 −0.0234472 0.999725i \(-0.507464\pi\)
−0.0234472 + 0.999725i \(0.507464\pi\)
\(348\) −65.4405 −0.0100804
\(349\) −10202.5 −1.56484 −0.782420 0.622752i \(-0.786015\pi\)
−0.782420 + 0.622752i \(0.786015\pi\)
\(350\) −9288.35 −1.41852
\(351\) 1859.39 0.282755
\(352\) 16173.2 2.44896
\(353\) −3136.89 −0.472973 −0.236487 0.971635i \(-0.575996\pi\)
−0.236487 + 0.971635i \(0.575996\pi\)
\(354\) −682.123 −0.102414
\(355\) −4806.63 −0.718619
\(356\) 4965.94 0.739310
\(357\) 856.747 0.127014
\(358\) −737.813 −0.108924
\(359\) 10568.7 1.55375 0.776873 0.629658i \(-0.216805\pi\)
0.776873 + 0.629658i \(0.216805\pi\)
\(360\) 2650.74 0.388073
\(361\) −1043.40 −0.152121
\(362\) 559.995 0.0813057
\(363\) −1719.82 −0.248670
\(364\) 16590.2 2.38890
\(365\) 3766.14 0.540079
\(366\) 172.469 0.0246314
\(367\) −9473.38 −1.34743 −0.673715 0.738992i \(-0.735302\pi\)
−0.673715 + 0.738992i \(0.735302\pi\)
\(368\) 4916.77 0.696480
\(369\) −10075.6 −1.42144
\(370\) 20787.0 2.92071
\(371\) −3053.37 −0.427286
\(372\) −87.0340 −0.0121304
\(373\) −5578.79 −0.774421 −0.387210 0.921991i \(-0.626561\pi\)
−0.387210 + 0.921991i \(0.626561\pi\)
\(374\) 10745.6 1.48568
\(375\) 514.758 0.0708854
\(376\) −1730.30 −0.237322
\(377\) 546.179 0.0746144
\(378\) −4757.61 −0.647367
\(379\) 8371.04 1.13454 0.567271 0.823531i \(-0.307999\pi\)
0.567271 + 0.823531i \(0.307999\pi\)
\(380\) 10293.8 1.38963
\(381\) 1369.91 0.184206
\(382\) 9880.82 1.32342
\(383\) 12121.8 1.61721 0.808607 0.588349i \(-0.200222\pi\)
0.808607 + 0.588349i \(0.200222\pi\)
\(384\) −587.320 −0.0780509
\(385\) 28214.8 3.73496
\(386\) 17491.3 2.30644
\(387\) 0 0
\(388\) 2975.51 0.389326
\(389\) 5594.57 0.729192 0.364596 0.931166i \(-0.381207\pi\)
0.364596 + 0.931166i \(0.381207\pi\)
\(390\) 2031.33 0.263745
\(391\) 4205.41 0.543930
\(392\) −4995.86 −0.643697
\(393\) 1588.12 0.203843
\(394\) 9400.74 1.20204
\(395\) 14280.2 1.81903
\(396\) −16223.4 −2.05872
\(397\) 12141.0 1.53486 0.767428 0.641135i \(-0.221536\pi\)
0.767428 + 0.641135i \(0.221536\pi\)
\(398\) −11544.4 −1.45395
\(399\) −1609.57 −0.201953
\(400\) −3249.24 −0.406155
\(401\) −2199.51 −0.273910 −0.136955 0.990577i \(-0.543732\pi\)
−0.136955 + 0.990577i \(0.543732\pi\)
\(402\) 706.529 0.0876579
\(403\) 726.402 0.0897883
\(404\) 1015.16 0.125015
\(405\) 9659.55 1.18515
\(406\) −1397.50 −0.170830
\(407\) −22345.9 −2.72148
\(408\) −190.579 −0.0231252
\(409\) 3786.14 0.457732 0.228866 0.973458i \(-0.426498\pi\)
0.228866 + 0.973458i \(0.426498\pi\)
\(410\) −22192.1 −2.67314
\(411\) 23.9822 0.00287824
\(412\) −1067.64 −0.127667
\(413\) −7984.71 −0.951337
\(414\) −11583.1 −1.37507
\(415\) 11975.6 1.41652
\(416\) 13630.0 1.60640
\(417\) 456.643 0.0536257
\(418\) −20187.8 −2.36225
\(419\) 1056.05 0.123130 0.0615651 0.998103i \(-0.480391\pi\)
0.0615651 + 0.998103i \(0.480391\pi\)
\(420\) −2848.98 −0.330990
\(421\) −15903.1 −1.84103 −0.920513 0.390712i \(-0.872229\pi\)
−0.920513 + 0.390712i \(0.872229\pi\)
\(422\) −11920.5 −1.37507
\(423\) −6410.42 −0.736845
\(424\) 679.208 0.0777955
\(425\) −2779.14 −0.317195
\(426\) −951.850 −0.108257
\(427\) 2018.86 0.228804
\(428\) 7282.64 0.822476
\(429\) −2183.67 −0.245754
\(430\) 0 0
\(431\) −8420.44 −0.941064 −0.470532 0.882383i \(-0.655938\pi\)
−0.470532 + 0.882383i \(0.655938\pi\)
\(432\) −1664.30 −0.185356
\(433\) −14918.0 −1.65569 −0.827844 0.560959i \(-0.810433\pi\)
−0.827844 + 0.560959i \(0.810433\pi\)
\(434\) −1858.64 −0.205570
\(435\) −93.7936 −0.0103381
\(436\) −6955.16 −0.763972
\(437\) −7900.71 −0.864856
\(438\) 745.803 0.0813603
\(439\) −759.012 −0.0825186 −0.0412593 0.999148i \(-0.513137\pi\)
−0.0412593 + 0.999148i \(0.513137\pi\)
\(440\) −6276.26 −0.680021
\(441\) −18508.7 −1.99857
\(442\) 9055.91 0.974538
\(443\) 6067.89 0.650777 0.325388 0.945580i \(-0.394505\pi\)
0.325388 + 0.945580i \(0.394505\pi\)
\(444\) 2256.36 0.241176
\(445\) 7117.51 0.758208
\(446\) −4244.56 −0.450641
\(447\) −945.621 −0.100059
\(448\) −22633.6 −2.38691
\(449\) −1182.72 −0.124311 −0.0621557 0.998066i \(-0.519798\pi\)
−0.0621557 + 0.998066i \(0.519798\pi\)
\(450\) 7654.71 0.801881
\(451\) 23856.4 2.49080
\(452\) 7678.80 0.799072
\(453\) 2159.18 0.223945
\(454\) 7817.86 0.808173
\(455\) 23778.1 2.44997
\(456\) 358.042 0.0367694
\(457\) 14176.7 1.45112 0.725558 0.688161i \(-0.241582\pi\)
0.725558 + 0.688161i \(0.241582\pi\)
\(458\) −27933.0 −2.84983
\(459\) −1423.51 −0.144758
\(460\) −13984.4 −1.41745
\(461\) −4125.95 −0.416843 −0.208422 0.978039i \(-0.566833\pi\)
−0.208422 + 0.978039i \(0.566833\pi\)
\(462\) 5587.34 0.562655
\(463\) −10697.8 −1.07380 −0.536899 0.843646i \(-0.680405\pi\)
−0.536899 + 0.843646i \(0.680405\pi\)
\(464\) −488.873 −0.0489124
\(465\) −124.743 −0.0124405
\(466\) 5295.50 0.526415
\(467\) −15719.7 −1.55764 −0.778821 0.627246i \(-0.784182\pi\)
−0.778821 + 0.627246i \(0.784182\pi\)
\(468\) −13672.3 −1.35043
\(469\) 8270.40 0.814268
\(470\) −14119.4 −1.38570
\(471\) −888.368 −0.0869083
\(472\) 1776.16 0.173209
\(473\) 0 0
\(474\) 2827.89 0.274028
\(475\) 5221.17 0.504345
\(476\) −12701.1 −1.22301
\(477\) 2516.34 0.241541
\(478\) 20165.9 1.92964
\(479\) −9517.11 −0.907824 −0.453912 0.891046i \(-0.649972\pi\)
−0.453912 + 0.891046i \(0.649972\pi\)
\(480\) −2340.63 −0.222572
\(481\) −18832.0 −1.78517
\(482\) 13946.3 1.31792
\(483\) 2186.66 0.205997
\(484\) 25496.0 2.39444
\(485\) 4264.69 0.399278
\(486\) 5896.93 0.550392
\(487\) −2176.30 −0.202500 −0.101250 0.994861i \(-0.532284\pi\)
−0.101250 + 0.994861i \(0.532284\pi\)
\(488\) −449.087 −0.0416582
\(489\) 498.984 0.0461449
\(490\) −40766.6 −3.75847
\(491\) 6458.88 0.593656 0.296828 0.954931i \(-0.404071\pi\)
0.296828 + 0.954931i \(0.404071\pi\)
\(492\) −2408.88 −0.220733
\(493\) −418.143 −0.0381992
\(494\) −17013.3 −1.54953
\(495\) −23252.4 −2.11135
\(496\) −650.188 −0.0588594
\(497\) −11142.0 −1.00561
\(498\) 2371.50 0.213393
\(499\) 10223.0 0.917120 0.458560 0.888664i \(-0.348365\pi\)
0.458560 + 0.888664i \(0.348365\pi\)
\(500\) −7631.18 −0.682553
\(501\) −566.400 −0.0505088
\(502\) 30835.5 2.74155
\(503\) 5795.18 0.513707 0.256853 0.966450i \(-0.417314\pi\)
0.256853 + 0.966450i \(0.417314\pi\)
\(504\) 6144.56 0.543056
\(505\) 1455.00 0.128211
\(506\) 27425.9 2.40955
\(507\) −402.101 −0.0352227
\(508\) −20308.6 −1.77371
\(509\) 1571.98 0.136889 0.0684447 0.997655i \(-0.478196\pi\)
0.0684447 + 0.997655i \(0.478196\pi\)
\(510\) −1555.14 −0.135025
\(511\) 8730.12 0.755769
\(512\) −14922.9 −1.28810
\(513\) 2674.35 0.230166
\(514\) −31702.6 −2.72051
\(515\) −1530.21 −0.130930
\(516\) 0 0
\(517\) 15178.2 1.29118
\(518\) 48185.4 4.08715
\(519\) −1592.83 −0.134716
\(520\) −5289.33 −0.446063
\(521\) 9189.64 0.772755 0.386377 0.922341i \(-0.373726\pi\)
0.386377 + 0.922341i \(0.373726\pi\)
\(522\) 1151.71 0.0965689
\(523\) −9173.46 −0.766974 −0.383487 0.923546i \(-0.625277\pi\)
−0.383487 + 0.923546i \(0.625277\pi\)
\(524\) −23543.6 −1.96280
\(525\) −1445.05 −0.120128
\(526\) −13331.3 −1.10508
\(527\) −556.118 −0.0459675
\(528\) 1954.56 0.161101
\(529\) −1433.60 −0.117827
\(530\) 5542.39 0.454238
\(531\) 6580.36 0.537784
\(532\) 23861.5 1.94460
\(533\) 20105.0 1.63385
\(534\) 1409.47 0.114220
\(535\) 10438.0 0.843499
\(536\) −1839.71 −0.148253
\(537\) −114.787 −0.00922422
\(538\) −15714.4 −1.25929
\(539\) 43823.9 3.50210
\(540\) 4733.66 0.377230
\(541\) −5530.27 −0.439492 −0.219746 0.975557i \(-0.570523\pi\)
−0.219746 + 0.975557i \(0.570523\pi\)
\(542\) −10780.9 −0.854389
\(543\) 87.1222 0.00688539
\(544\) −10434.8 −0.822406
\(545\) −9968.59 −0.783500
\(546\) 4708.74 0.369076
\(547\) −14776.3 −1.15501 −0.577504 0.816388i \(-0.695973\pi\)
−0.577504 + 0.816388i \(0.695973\pi\)
\(548\) −355.531 −0.0277145
\(549\) −1663.78 −0.129341
\(550\) −18124.4 −1.40514
\(551\) 785.565 0.0607372
\(552\) −486.413 −0.0375056
\(553\) 33102.4 2.54549
\(554\) 2469.11 0.189355
\(555\) 3233.97 0.247341
\(556\) −6769.63 −0.516360
\(557\) 25533.5 1.94235 0.971176 0.238364i \(-0.0766111\pi\)
0.971176 + 0.238364i \(0.0766111\pi\)
\(558\) 1531.74 0.116207
\(559\) 0 0
\(560\) −21283.3 −1.60604
\(561\) 1671.77 0.125815
\(562\) −8421.11 −0.632070
\(563\) −25508.4 −1.90950 −0.954751 0.297405i \(-0.903879\pi\)
−0.954751 + 0.297405i \(0.903879\pi\)
\(564\) −1532.61 −0.114423
\(565\) 11005.8 0.819497
\(566\) −9361.50 −0.695218
\(567\) 22391.4 1.65847
\(568\) 2478.50 0.183091
\(569\) 1770.95 0.130478 0.0652391 0.997870i \(-0.479219\pi\)
0.0652391 + 0.997870i \(0.479219\pi\)
\(570\) 2921.65 0.214692
\(571\) −13023.1 −0.954468 −0.477234 0.878776i \(-0.658361\pi\)
−0.477234 + 0.878776i \(0.658361\pi\)
\(572\) 32372.4 2.36636
\(573\) 1537.23 0.112074
\(574\) −51442.5 −3.74071
\(575\) −7093.15 −0.514443
\(576\) 18652.8 1.34930
\(577\) −7547.32 −0.544539 −0.272270 0.962221i \(-0.587774\pi\)
−0.272270 + 0.962221i \(0.587774\pi\)
\(578\) 13739.3 0.988719
\(579\) 2721.24 0.195321
\(580\) 1390.47 0.0995450
\(581\) 27760.1 1.98224
\(582\) 844.530 0.0601493
\(583\) −5958.05 −0.423254
\(584\) −1941.98 −0.137602
\(585\) −19596.0 −1.38495
\(586\) 21589.0 1.52190
\(587\) −7727.05 −0.543321 −0.271661 0.962393i \(-0.587573\pi\)
−0.271661 + 0.962393i \(0.587573\pi\)
\(588\) −4425.10 −0.310354
\(589\) 1044.78 0.0730889
\(590\) 14493.6 1.01135
\(591\) 1462.54 0.101795
\(592\) 16856.2 1.17024
\(593\) 12011.5 0.831790 0.415895 0.909413i \(-0.363468\pi\)
0.415895 + 0.909413i \(0.363468\pi\)
\(594\) −9283.53 −0.641259
\(595\) −18204.0 −1.25427
\(596\) 14018.6 0.963464
\(597\) −1796.05 −0.123128
\(598\) 23113.2 1.58055
\(599\) 4737.78 0.323172 0.161586 0.986859i \(-0.448339\pi\)
0.161586 + 0.986859i \(0.448339\pi\)
\(600\) 321.445 0.0218716
\(601\) −4096.54 −0.278039 −0.139020 0.990290i \(-0.544395\pi\)
−0.139020 + 0.990290i \(0.544395\pi\)
\(602\) 0 0
\(603\) −6815.80 −0.460300
\(604\) −32009.4 −2.15636
\(605\) 36542.5 2.45565
\(606\) 288.131 0.0193144
\(607\) 7628.52 0.510102 0.255051 0.966928i \(-0.417908\pi\)
0.255051 + 0.966928i \(0.417908\pi\)
\(608\) 19603.9 1.30764
\(609\) −217.419 −0.0144668
\(610\) −3664.58 −0.243237
\(611\) 12791.5 0.846953
\(612\) 10467.2 0.691359
\(613\) 4190.40 0.276099 0.138049 0.990425i \(-0.455917\pi\)
0.138049 + 0.990425i \(0.455917\pi\)
\(614\) 6995.85 0.459820
\(615\) −3452.57 −0.226376
\(616\) −14548.7 −0.951599
\(617\) 16915.3 1.10370 0.551851 0.833943i \(-0.313922\pi\)
0.551851 + 0.833943i \(0.313922\pi\)
\(618\) −303.025 −0.0197240
\(619\) 23926.2 1.55359 0.776797 0.629751i \(-0.216843\pi\)
0.776797 + 0.629751i \(0.216843\pi\)
\(620\) 1849.28 0.119789
\(621\) −3633.20 −0.234775
\(622\) −31553.4 −2.03405
\(623\) 16498.8 1.06101
\(624\) 1647.21 0.105675
\(625\) −19495.7 −1.24772
\(626\) 20497.9 1.30873
\(627\) −3140.76 −0.200048
\(628\) 13169.8 0.836838
\(629\) 14417.4 0.913926
\(630\) 50140.1 3.17084
\(631\) −21858.0 −1.37901 −0.689503 0.724283i \(-0.742171\pi\)
−0.689503 + 0.724283i \(0.742171\pi\)
\(632\) −7363.48 −0.463455
\(633\) −1854.55 −0.116448
\(634\) −29393.7 −1.84128
\(635\) −29107.5 −1.81905
\(636\) 601.611 0.0375085
\(637\) 36932.7 2.29722
\(638\) −2726.95 −0.169218
\(639\) 9182.38 0.568465
\(640\) 12479.3 0.770760
\(641\) 31069.9 1.91449 0.957244 0.289281i \(-0.0934161\pi\)
0.957244 + 0.289281i \(0.0934161\pi\)
\(642\) 2067.01 0.127069
\(643\) −8457.95 −0.518739 −0.259369 0.965778i \(-0.583515\pi\)
−0.259369 + 0.965778i \(0.583515\pi\)
\(644\) −32416.7 −1.98354
\(645\) 0 0
\(646\) 13025.1 0.793288
\(647\) −21034.7 −1.27814 −0.639072 0.769147i \(-0.720682\pi\)
−0.639072 + 0.769147i \(0.720682\pi\)
\(648\) −4980.87 −0.301955
\(649\) −15580.6 −0.942360
\(650\) −15274.4 −0.921707
\(651\) −289.161 −0.0174088
\(652\) −7397.33 −0.444328
\(653\) 16312.9 0.977603 0.488802 0.872395i \(-0.337434\pi\)
0.488802 + 0.872395i \(0.337434\pi\)
\(654\) −1974.06 −0.118031
\(655\) −33744.2 −2.01297
\(656\) −17995.6 −1.07105
\(657\) −7194.66 −0.427231
\(658\) −32729.5 −1.93910
\(659\) 13578.7 0.802655 0.401328 0.915935i \(-0.368549\pi\)
0.401328 + 0.915935i \(0.368549\pi\)
\(660\) −5559.22 −0.327867
\(661\) 20138.0 1.18499 0.592495 0.805574i \(-0.298143\pi\)
0.592495 + 0.805574i \(0.298143\pi\)
\(662\) −1559.12 −0.0915363
\(663\) 1408.89 0.0825290
\(664\) −6175.10 −0.360904
\(665\) 34199.9 1.99431
\(666\) −39710.5 −2.31044
\(667\) −1067.22 −0.0619533
\(668\) 8396.76 0.486348
\(669\) −660.355 −0.0381626
\(670\) −15012.2 −0.865630
\(671\) 3939.41 0.226646
\(672\) −5425.72 −0.311461
\(673\) 1613.56 0.0924195 0.0462098 0.998932i \(-0.485286\pi\)
0.0462098 + 0.998932i \(0.485286\pi\)
\(674\) −49986.7 −2.85670
\(675\) 2400.99 0.136910
\(676\) 5961.05 0.339159
\(677\) −10688.3 −0.606772 −0.303386 0.952868i \(-0.598117\pi\)
−0.303386 + 0.952868i \(0.598117\pi\)
\(678\) 2179.45 0.123453
\(679\) 9885.79 0.558736
\(680\) 4049.40 0.228364
\(681\) 1216.28 0.0684403
\(682\) −3626.77 −0.203631
\(683\) −7229.87 −0.405042 −0.202521 0.979278i \(-0.564913\pi\)
−0.202521 + 0.979278i \(0.564913\pi\)
\(684\) −19664.7 −1.09927
\(685\) −509.570 −0.0284229
\(686\) −47966.3 −2.66962
\(687\) −4345.73 −0.241339
\(688\) 0 0
\(689\) −5021.16 −0.277635
\(690\) −3969.17 −0.218991
\(691\) −25962.1 −1.42930 −0.714649 0.699483i \(-0.753414\pi\)
−0.714649 + 0.699483i \(0.753414\pi\)
\(692\) 23613.3 1.29717
\(693\) −53900.3 −2.95455
\(694\) 1275.43 0.0697620
\(695\) −9702.67 −0.529559
\(696\) 48.3639 0.00263395
\(697\) −15392.0 −0.836459
\(698\) 42928.9 2.32791
\(699\) 823.857 0.0445796
\(700\) 21422.5 1.15671
\(701\) −6626.06 −0.357008 −0.178504 0.983939i \(-0.557126\pi\)
−0.178504 + 0.983939i \(0.557126\pi\)
\(702\) −7823.71 −0.420637
\(703\) −27086.0 −1.45315
\(704\) −44165.0 −2.36439
\(705\) −2196.64 −0.117348
\(706\) 13199.0 0.703613
\(707\) 3372.76 0.179414
\(708\) 1573.24 0.0835114
\(709\) −29713.2 −1.57391 −0.786956 0.617009i \(-0.788344\pi\)
−0.786956 + 0.617009i \(0.788344\pi\)
\(710\) 20224.8 1.06904
\(711\) −27280.3 −1.43895
\(712\) −3670.08 −0.193177
\(713\) −1419.37 −0.0745524
\(714\) −3604.91 −0.188950
\(715\) 46398.3 2.42685
\(716\) 1701.68 0.0888198
\(717\) 3137.35 0.163412
\(718\) −44469.7 −2.31141
\(719\) 24939.1 1.29356 0.646782 0.762675i \(-0.276114\pi\)
0.646782 + 0.762675i \(0.276114\pi\)
\(720\) 17540.0 0.907883
\(721\) −3547.11 −0.183220
\(722\) 4390.27 0.226301
\(723\) 2169.72 0.111608
\(724\) −1291.57 −0.0662993
\(725\) 705.270 0.0361284
\(726\) 7236.46 0.369932
\(727\) −29226.9 −1.49101 −0.745507 0.666498i \(-0.767793\pi\)
−0.745507 + 0.666498i \(0.767793\pi\)
\(728\) −12261.0 −0.624206
\(729\) −17833.4 −0.906028
\(730\) −15846.7 −0.803441
\(731\) 0 0
\(732\) −397.780 −0.0200852
\(733\) −13372.7 −0.673849 −0.336925 0.941532i \(-0.609387\pi\)
−0.336925 + 0.941532i \(0.609387\pi\)
\(734\) 39860.9 2.00449
\(735\) −6342.34 −0.318287
\(736\) −26632.6 −1.33382
\(737\) 16138.1 0.806584
\(738\) 42394.7 2.11460
\(739\) 4818.31 0.239843 0.119922 0.992783i \(-0.461736\pi\)
0.119922 + 0.992783i \(0.461736\pi\)
\(740\) −47942.8 −2.38164
\(741\) −2646.88 −0.131222
\(742\) 12847.6 0.635647
\(743\) −15211.9 −0.751106 −0.375553 0.926801i \(-0.622547\pi\)
−0.375553 + 0.926801i \(0.622547\pi\)
\(744\) 64.3226 0.00316960
\(745\) 20092.4 0.988091
\(746\) 23473.8 1.15206
\(747\) −22877.6 −1.12055
\(748\) −24783.6 −1.21147
\(749\) 24195.8 1.18037
\(750\) −2165.94 −0.105452
\(751\) 27003.6 1.31208 0.656042 0.754724i \(-0.272229\pi\)
0.656042 + 0.754724i \(0.272229\pi\)
\(752\) −11449.4 −0.555208
\(753\) 4797.29 0.232169
\(754\) −2298.14 −0.110999
\(755\) −45878.0 −2.21148
\(756\) 10972.9 0.527884
\(757\) −28606.3 −1.37346 −0.686732 0.726910i \(-0.740956\pi\)
−0.686732 + 0.726910i \(0.740956\pi\)
\(758\) −35222.6 −1.68779
\(759\) 4266.83 0.204053
\(760\) −7607.61 −0.363101
\(761\) −11237.8 −0.535310 −0.267655 0.963515i \(-0.586249\pi\)
−0.267655 + 0.963515i \(0.586249\pi\)
\(762\) −5764.12 −0.274032
\(763\) −23107.8 −1.09640
\(764\) −22789.0 −1.07916
\(765\) 15002.3 0.709031
\(766\) −51004.5 −2.40583
\(767\) −13130.6 −0.618145
\(768\) −1205.00 −0.0566166
\(769\) −29016.9 −1.36070 −0.680348 0.732889i \(-0.738171\pi\)
−0.680348 + 0.732889i \(0.738171\pi\)
\(770\) −118719. −5.55627
\(771\) −4932.19 −0.230387
\(772\) −40341.8 −1.88074
\(773\) −35838.2 −1.66754 −0.833772 0.552109i \(-0.813823\pi\)
−0.833772 + 0.552109i \(0.813823\pi\)
\(774\) 0 0
\(775\) 937.989 0.0434756
\(776\) −2199.05 −0.101729
\(777\) 7496.52 0.346121
\(778\) −23540.1 −1.08477
\(779\) 28916.9 1.32998
\(780\) −4685.04 −0.215066
\(781\) −21741.5 −0.996123
\(782\) −17695.0 −0.809172
\(783\) 361.248 0.0164878
\(784\) −33057.7 −1.50591
\(785\) 18875.9 0.858228
\(786\) −6682.30 −0.303244
\(787\) 19880.4 0.900455 0.450228 0.892914i \(-0.351343\pi\)
0.450228 + 0.892914i \(0.351343\pi\)
\(788\) −21681.8 −0.980179
\(789\) −2074.04 −0.0935841
\(790\) −60086.6 −2.70606
\(791\) 25512.0 1.14678
\(792\) 11989.9 0.537932
\(793\) 3319.94 0.148669
\(794\) −51085.3 −2.28331
\(795\) 862.268 0.0384673
\(796\) 26626.0 1.18559
\(797\) 11240.1 0.499555 0.249778 0.968303i \(-0.419643\pi\)
0.249778 + 0.968303i \(0.419643\pi\)
\(798\) 6772.55 0.300433
\(799\) −9792.89 −0.433601
\(800\) 17600.1 0.777822
\(801\) −13597.0 −0.599782
\(802\) 9254.81 0.407480
\(803\) 17035.1 0.748637
\(804\) −1629.53 −0.0714790
\(805\) −46461.8 −2.03424
\(806\) −3056.47 −0.133572
\(807\) −2444.80 −0.106643
\(808\) −750.256 −0.0326657
\(809\) 7574.05 0.329159 0.164579 0.986364i \(-0.447373\pi\)
0.164579 + 0.986364i \(0.447373\pi\)
\(810\) −40644.3 −1.76308
\(811\) −8976.71 −0.388674 −0.194337 0.980935i \(-0.562256\pi\)
−0.194337 + 0.980935i \(0.562256\pi\)
\(812\) 3223.19 0.139300
\(813\) −1677.26 −0.0723542
\(814\) 94024.2 4.04858
\(815\) −10602.3 −0.455685
\(816\) −1261.07 −0.0541007
\(817\) 0 0
\(818\) −15930.8 −0.680939
\(819\) −45424.6 −1.93805
\(820\) 51183.5 2.17976
\(821\) 38991.5 1.65750 0.828752 0.559616i \(-0.189051\pi\)
0.828752 + 0.559616i \(0.189051\pi\)
\(822\) −100.909 −0.00428178
\(823\) −4200.77 −0.177922 −0.0889610 0.996035i \(-0.528355\pi\)
−0.0889610 + 0.996035i \(0.528355\pi\)
\(824\) 789.039 0.0333586
\(825\) −2819.73 −0.118994
\(826\) 33597.1 1.41524
\(827\) 27413.1 1.15266 0.576329 0.817218i \(-0.304485\pi\)
0.576329 + 0.817218i \(0.304485\pi\)
\(828\) 26715.3 1.12128
\(829\) −28260.3 −1.18398 −0.591992 0.805944i \(-0.701658\pi\)
−0.591992 + 0.805944i \(0.701658\pi\)
\(830\) −50389.3 −2.10728
\(831\) 384.136 0.0160355
\(832\) −37220.1 −1.55093
\(833\) −28274.9 −1.17607
\(834\) −1921.41 −0.0797756
\(835\) 12034.8 0.498779
\(836\) 46561.0 1.92625
\(837\) 480.449 0.0198408
\(838\) −4443.53 −0.183173
\(839\) −12924.7 −0.531837 −0.265919 0.963995i \(-0.585675\pi\)
−0.265919 + 0.963995i \(0.585675\pi\)
\(840\) 2105.54 0.0864857
\(841\) −24282.9 −0.995649
\(842\) 66915.3 2.73878
\(843\) −1310.13 −0.0535270
\(844\) 27493.3 1.12128
\(845\) 8543.77 0.347828
\(846\) 26973.0 1.09616
\(847\) 84707.7 3.43635
\(848\) 4494.33 0.182000
\(849\) −1456.43 −0.0588747
\(850\) 11693.7 0.471872
\(851\) 36797.3 1.48225
\(852\) 2195.34 0.0882758
\(853\) 39780.9 1.59680 0.798401 0.602126i \(-0.205680\pi\)
0.798401 + 0.602126i \(0.205680\pi\)
\(854\) −8494.71 −0.340378
\(855\) −28184.8 −1.12737
\(856\) −5382.24 −0.214908
\(857\) 9841.41 0.392271 0.196135 0.980577i \(-0.437161\pi\)
0.196135 + 0.980577i \(0.437161\pi\)
\(858\) 9188.18 0.365594
\(859\) 25413.1 1.00941 0.504705 0.863292i \(-0.331601\pi\)
0.504705 + 0.863292i \(0.331601\pi\)
\(860\) 0 0
\(861\) −8003.25 −0.316783
\(862\) 35430.5 1.39996
\(863\) −13442.2 −0.530219 −0.265110 0.964218i \(-0.585408\pi\)
−0.265110 + 0.964218i \(0.585408\pi\)
\(864\) 9014.99 0.354972
\(865\) 33844.1 1.33033
\(866\) 62770.1 2.46306
\(867\) 2137.52 0.0837299
\(868\) 4286.75 0.167629
\(869\) 64592.8 2.52147
\(870\) 394.653 0.0153793
\(871\) 13600.4 0.529083
\(872\) 5140.22 0.199621
\(873\) −8147.07 −0.315850
\(874\) 33243.6 1.28659
\(875\) −25353.8 −0.979558
\(876\) −1720.11 −0.0663438
\(877\) −26400.6 −1.01652 −0.508258 0.861205i \(-0.669711\pi\)
−0.508258 + 0.861205i \(0.669711\pi\)
\(878\) 3193.68 0.122758
\(879\) 3358.74 0.128882
\(880\) −41530.1 −1.59089
\(881\) 777.294 0.0297250 0.0148625 0.999890i \(-0.495269\pi\)
0.0148625 + 0.999890i \(0.495269\pi\)
\(882\) 77878.8 2.97315
\(883\) −27263.3 −1.03905 −0.519527 0.854454i \(-0.673892\pi\)
−0.519527 + 0.854454i \(0.673892\pi\)
\(884\) −20886.5 −0.794669
\(885\) 2254.87 0.0856460
\(886\) −25531.7 −0.968120
\(887\) 12790.6 0.484178 0.242089 0.970254i \(-0.422167\pi\)
0.242089 + 0.970254i \(0.422167\pi\)
\(888\) −1667.57 −0.0630179
\(889\) −67473.0 −2.54552
\(890\) −29948.2 −1.12794
\(891\) 43692.4 1.64282
\(892\) 9789.61 0.367467
\(893\) 18397.9 0.689432
\(894\) 3978.87 0.148851
\(895\) 2438.97 0.0910901
\(896\) 28927.7 1.07858
\(897\) 3595.88 0.133850
\(898\) 4976.49 0.184930
\(899\) 141.128 0.00523567
\(900\) −17654.7 −0.653879
\(901\) 3844.09 0.142137
\(902\) −100380. −3.70541
\(903\) 0 0
\(904\) −5675.03 −0.208793
\(905\) −1851.16 −0.0679940
\(906\) −9085.15 −0.333150
\(907\) −3260.09 −0.119349 −0.0596744 0.998218i \(-0.519006\pi\)
−0.0596744 + 0.998218i \(0.519006\pi\)
\(908\) −18031.0 −0.659010
\(909\) −2779.56 −0.101421
\(910\) −100051. −3.64466
\(911\) 19935.7 0.725026 0.362513 0.931979i \(-0.381919\pi\)
0.362513 + 0.931979i \(0.381919\pi\)
\(912\) 2369.17 0.0860208
\(913\) 54168.3 1.96354
\(914\) −59651.1 −2.15874
\(915\) −570.124 −0.0205986
\(916\) 64424.4 2.32384
\(917\) −78220.9 −2.81688
\(918\) 5989.67 0.215347
\(919\) 28506.6 1.02323 0.511614 0.859216i \(-0.329048\pi\)
0.511614 + 0.859216i \(0.329048\pi\)
\(920\) 10335.2 0.370372
\(921\) 1088.39 0.0389400
\(922\) 17360.7 0.620112
\(923\) −18322.7 −0.653412
\(924\) −12886.6 −0.458807
\(925\) −24317.4 −0.864381
\(926\) 45012.9 1.59742
\(927\) 2923.24 0.103573
\(928\) 2648.07 0.0936715
\(929\) −39402.4 −1.39155 −0.695775 0.718260i \(-0.744939\pi\)
−0.695775 + 0.718260i \(0.744939\pi\)
\(930\) 524.877 0.0185069
\(931\) 53120.1 1.86997
\(932\) −12213.5 −0.429256
\(933\) −4908.98 −0.172254
\(934\) 66143.3 2.31721
\(935\) −35521.5 −1.24244
\(936\) 10104.5 0.352859
\(937\) −16653.4 −0.580621 −0.290310 0.956933i \(-0.593759\pi\)
−0.290310 + 0.956933i \(0.593759\pi\)
\(938\) −34799.2 −1.21134
\(939\) 3189.00 0.110830
\(940\) 32564.7 1.12994
\(941\) 37396.5 1.29553 0.647764 0.761841i \(-0.275704\pi\)
0.647764 + 0.761841i \(0.275704\pi\)
\(942\) 3737.96 0.129288
\(943\) −39284.6 −1.35661
\(944\) 11752.9 0.405217
\(945\) 15727.1 0.541377
\(946\) 0 0
\(947\) 30801.6 1.05693 0.528467 0.848954i \(-0.322767\pi\)
0.528467 + 0.848954i \(0.322767\pi\)
\(948\) −6522.23 −0.223452
\(949\) 14356.4 0.491072
\(950\) −21969.0 −0.750283
\(951\) −4572.98 −0.155930
\(952\) 9386.74 0.319565
\(953\) −36744.1 −1.24896 −0.624480 0.781041i \(-0.714689\pi\)
−0.624480 + 0.781041i \(0.714689\pi\)
\(954\) −10587.9 −0.359326
\(955\) −32662.7 −1.10674
\(956\) −46510.5 −1.57349
\(957\) −424.250 −0.0143303
\(958\) 40044.9 1.35051
\(959\) −1181.21 −0.0397741
\(960\) 6391.70 0.214887
\(961\) −29603.3 −0.993700
\(962\) 79239.1 2.65569
\(963\) −19940.2 −0.667252
\(964\) −32165.7 −1.07467
\(965\) −57820.6 −1.92882
\(966\) −9200.76 −0.306449
\(967\) 15876.7 0.527985 0.263992 0.964525i \(-0.414961\pi\)
0.263992 + 0.964525i \(0.414961\pi\)
\(968\) −18842.8 −0.625653
\(969\) 2026.40 0.0671798
\(970\) −17944.4 −0.593980
\(971\) 18855.2 0.623163 0.311582 0.950219i \(-0.399141\pi\)
0.311582 + 0.950219i \(0.399141\pi\)
\(972\) −13600.6 −0.448807
\(973\) −22491.4 −0.741048
\(974\) 9157.17 0.301247
\(975\) −2376.33 −0.0780550
\(976\) −2971.61 −0.0974580
\(977\) −17915.0 −0.586646 −0.293323 0.956013i \(-0.594761\pi\)
−0.293323 + 0.956013i \(0.594761\pi\)
\(978\) −2099.56 −0.0686469
\(979\) 32194.1 1.05100
\(980\) 94023.7 3.06477
\(981\) 19043.5 0.619790
\(982\) −27176.9 −0.883146
\(983\) −5064.00 −0.164310 −0.0821550 0.996620i \(-0.526180\pi\)
−0.0821550 + 0.996620i \(0.526180\pi\)
\(984\) 1780.29 0.0576763
\(985\) −31075.7 −1.00523
\(986\) 1759.41 0.0568266
\(987\) −5091.94 −0.164213
\(988\) 39239.4 1.26353
\(989\) 0 0
\(990\) 97838.5 3.14092
\(991\) −22909.7 −0.734361 −0.367181 0.930150i \(-0.619677\pi\)
−0.367181 + 0.930150i \(0.619677\pi\)
\(992\) 3521.86 0.112721
\(993\) −242.563 −0.00775177
\(994\) 46882.1 1.49599
\(995\) 38162.1 1.21590
\(996\) −5469.61 −0.174007
\(997\) −6909.86 −0.219496 −0.109748 0.993959i \(-0.535004\pi\)
−0.109748 + 0.993959i \(0.535004\pi\)
\(998\) −43014.9 −1.36434
\(999\) −12455.7 −0.394475
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.1.19 110
43.42 odd 2 inner 1849.4.a.m.1.92 yes 110
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1849.4.a.m.1.19 110 1.1 even 1 trivial
1849.4.a.m.1.92 yes 110 43.42 odd 2 inner