Properties

Label 735.4.a.m.1.1
Level $735$
Weight $4$
Character 735.1
Self dual yes
Analytic conductor $43.366$
Analytic rank $0$
Dimension $2$
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] = [735,4,Mod(1,735)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(735, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("735.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 735.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: \(43.3664038542\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 2 \)
Twist minimal: no (minimal twist has level 105)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\) of defining polynomial
Character \(\chi\) \(=\) 735.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-4.23607 q^{2} -3.00000 q^{3} +9.94427 q^{4} +5.00000 q^{5} +12.7082 q^{6} -8.23607 q^{8} +9.00000 q^{9} +O(q^{10})\) \(q-4.23607 q^{2} -3.00000 q^{3} +9.94427 q^{4} +5.00000 q^{5} +12.7082 q^{6} -8.23607 q^{8} +9.00000 q^{9} -21.1803 q^{10} -41.5279 q^{11} -29.8328 q^{12} -88.9706 q^{13} -15.0000 q^{15} -44.6656 q^{16} +120.387 q^{17} -38.1246 q^{18} +112.138 q^{19} +49.7214 q^{20} +175.915 q^{22} -115.279 q^{23} +24.7082 q^{24} +25.0000 q^{25} +376.885 q^{26} -27.0000 q^{27} -144.833 q^{29} +63.5410 q^{30} +258.079 q^{31} +255.095 q^{32} +124.584 q^{33} -509.967 q^{34} +89.4984 q^{36} +48.3344 q^{37} -475.023 q^{38} +266.912 q^{39} -41.1803 q^{40} -200.885 q^{41} -218.217 q^{43} -412.964 q^{44} +45.0000 q^{45} +488.328 q^{46} -575.659 q^{47} +133.997 q^{48} -105.902 q^{50} -361.161 q^{51} -884.748 q^{52} -184.302 q^{53} +114.374 q^{54} -207.639 q^{55} -336.413 q^{57} +613.522 q^{58} +151.502 q^{59} -149.164 q^{60} +529.830 q^{61} -1093.24 q^{62} -723.276 q^{64} -444.853 q^{65} -527.745 q^{66} +1.28485 q^{67} +1197.16 q^{68} +345.836 q^{69} -61.4226 q^{71} -74.1246 q^{72} -484.800 q^{73} -204.748 q^{74} -75.0000 q^{75} +1115.13 q^{76} -1130.66 q^{78} +878.257 q^{79} -223.328 q^{80} +81.0000 q^{81} +850.964 q^{82} -491.830 q^{83} +601.935 q^{85} +924.381 q^{86} +434.498 q^{87} +342.026 q^{88} +415.560 q^{89} -190.623 q^{90} -1146.36 q^{92} -774.237 q^{93} +2438.53 q^{94} +560.689 q^{95} -765.286 q^{96} +1031.70 q^{97} -373.751 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{2} - 6 q^{3} + 2 q^{4} + 10 q^{5} + 12 q^{6} - 12 q^{8} + 18 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{2} - 6 q^{3} + 2 q^{4} + 10 q^{5} + 12 q^{6} - 12 q^{8} + 18 q^{9} - 20 q^{10} - 92 q^{11} - 6 q^{12} - 8 q^{13} - 30 q^{15} + 18 q^{16} + 44 q^{17} - 36 q^{18} + 108 q^{19} + 10 q^{20} + 164 q^{22} - 320 q^{23} + 36 q^{24} + 50 q^{25} + 396 q^{26} - 54 q^{27} - 236 q^{29} + 60 q^{30} + 60 q^{31} + 300 q^{32} + 276 q^{33} - 528 q^{34} + 18 q^{36} + 204 q^{37} - 476 q^{38} + 24 q^{39} - 60 q^{40} - 44 q^{41} + 136 q^{43} - 12 q^{44} + 90 q^{45} + 440 q^{46} - 400 q^{47} - 54 q^{48} - 100 q^{50} - 132 q^{51} - 1528 q^{52} + 16 q^{53} + 108 q^{54} - 460 q^{55} - 324 q^{57} + 592 q^{58} + 464 q^{59} - 30 q^{60} + 684 q^{61} - 1140 q^{62} - 1214 q^{64} - 40 q^{65} - 492 q^{66} + 736 q^{67} + 1804 q^{68} + 960 q^{69} - 740 q^{71} - 108 q^{72} - 424 q^{73} - 168 q^{74} - 150 q^{75} + 1148 q^{76} - 1188 q^{78} - 408 q^{79} + 90 q^{80} + 162 q^{81} + 888 q^{82} - 608 q^{83} + 220 q^{85} + 1008 q^{86} + 708 q^{87} + 532 q^{88} + 1332 q^{89} - 180 q^{90} + 480 q^{92} - 180 q^{93} + 2480 q^{94} + 540 q^{95} - 900 q^{96} + 2448 q^{97} - 828 q^{99}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.23607 −1.49768 −0.748838 0.662753i \(-0.769388\pi\)
−0.748838 + 0.662753i \(0.769388\pi\)
\(3\) −3.00000 −0.577350
\(4\) 9.94427 1.24303
\(5\) 5.00000 0.447214
\(6\) 12.7082 0.864684
\(7\) 0 0
\(8\) −8.23607 −0.363986
\(9\) 9.00000 0.333333
\(10\) −21.1803 −0.669781
\(11\) −41.5279 −1.13828 −0.569142 0.822239i \(-0.692725\pi\)
−0.569142 + 0.822239i \(0.692725\pi\)
\(12\) −29.8328 −0.717666
\(13\) −88.9706 −1.89815 −0.949077 0.315044i \(-0.897981\pi\)
−0.949077 + 0.315044i \(0.897981\pi\)
\(14\) 0 0
\(15\) −15.0000 −0.258199
\(16\) −44.6656 −0.697900
\(17\) 120.387 1.71754 0.858769 0.512364i \(-0.171230\pi\)
0.858769 + 0.512364i \(0.171230\pi\)
\(18\) −38.1246 −0.499225
\(19\) 112.138 1.35401 0.677004 0.735979i \(-0.263278\pi\)
0.677004 + 0.735979i \(0.263278\pi\)
\(20\) 49.7214 0.555902
\(21\) 0 0
\(22\) 175.915 1.70478
\(23\) −115.279 −1.04510 −0.522549 0.852609i \(-0.675019\pi\)
−0.522549 + 0.852609i \(0.675019\pi\)
\(24\) 24.7082 0.210148
\(25\) 25.0000 0.200000
\(26\) 376.885 2.84282
\(27\) −27.0000 −0.192450
\(28\) 0 0
\(29\) −144.833 −0.927406 −0.463703 0.885991i \(-0.653480\pi\)
−0.463703 + 0.885991i \(0.653480\pi\)
\(30\) 63.5410 0.386698
\(31\) 258.079 1.49524 0.747618 0.664128i \(-0.231197\pi\)
0.747618 + 0.664128i \(0.231197\pi\)
\(32\) 255.095 1.40922
\(33\) 124.584 0.657188
\(34\) −509.967 −2.57231
\(35\) 0 0
\(36\) 89.4984 0.414345
\(37\) 48.3344 0.214760 0.107380 0.994218i \(-0.465754\pi\)
0.107380 + 0.994218i \(0.465754\pi\)
\(38\) −475.023 −2.02787
\(39\) 266.912 1.09590
\(40\) −41.1803 −0.162780
\(41\) −200.885 −0.765196 −0.382598 0.923915i \(-0.624971\pi\)
−0.382598 + 0.923915i \(0.624971\pi\)
\(42\) 0 0
\(43\) −218.217 −0.773901 −0.386950 0.922101i \(-0.626472\pi\)
−0.386950 + 0.922101i \(0.626472\pi\)
\(44\) −412.964 −1.41493
\(45\) 45.0000 0.149071
\(46\) 488.328 1.56522
\(47\) −575.659 −1.78657 −0.893283 0.449496i \(-0.851604\pi\)
−0.893283 + 0.449496i \(0.851604\pi\)
\(48\) 133.997 0.402933
\(49\) 0 0
\(50\) −105.902 −0.299535
\(51\) −361.161 −0.991621
\(52\) −884.748 −2.35947
\(53\) −184.302 −0.477657 −0.238828 0.971062i \(-0.576763\pi\)
−0.238828 + 0.971062i \(0.576763\pi\)
\(54\) 114.374 0.288228
\(55\) −207.639 −0.509056
\(56\) 0 0
\(57\) −336.413 −0.781737
\(58\) 613.522 1.38895
\(59\) 151.502 0.334302 0.167151 0.985931i \(-0.446543\pi\)
0.167151 + 0.985931i \(0.446543\pi\)
\(60\) −149.164 −0.320950
\(61\) 529.830 1.11209 0.556047 0.831151i \(-0.312317\pi\)
0.556047 + 0.831151i \(0.312317\pi\)
\(62\) −1093.24 −2.23938
\(63\) 0 0
\(64\) −723.276 −1.41265
\(65\) −444.853 −0.848880
\(66\) −527.745 −0.984256
\(67\) 1.28485 0.00234283 0.00117142 0.999999i \(-0.499627\pi\)
0.00117142 + 0.999999i \(0.499627\pi\)
\(68\) 1197.16 2.13496
\(69\) 345.836 0.603388
\(70\) 0 0
\(71\) −61.4226 −0.102669 −0.0513347 0.998682i \(-0.516348\pi\)
−0.0513347 + 0.998682i \(0.516348\pi\)
\(72\) −74.1246 −0.121329
\(73\) −484.800 −0.777282 −0.388641 0.921389i \(-0.627055\pi\)
−0.388641 + 0.921389i \(0.627055\pi\)
\(74\) −204.748 −0.321641
\(75\) −75.0000 −0.115470
\(76\) 1115.13 1.68308
\(77\) 0 0
\(78\) −1130.66 −1.64130
\(79\) 878.257 1.25078 0.625390 0.780312i \(-0.284940\pi\)
0.625390 + 0.780312i \(0.284940\pi\)
\(80\) −223.328 −0.312111
\(81\) 81.0000 0.111111
\(82\) 850.964 1.14602
\(83\) −491.830 −0.650426 −0.325213 0.945641i \(-0.605436\pi\)
−0.325213 + 0.945641i \(0.605436\pi\)
\(84\) 0 0
\(85\) 601.935 0.768106
\(86\) 924.381 1.15905
\(87\) 434.498 0.535438
\(88\) 342.026 0.414320
\(89\) 415.560 0.494936 0.247468 0.968896i \(-0.420401\pi\)
0.247468 + 0.968896i \(0.420401\pi\)
\(90\) −190.623 −0.223260
\(91\) 0 0
\(92\) −1146.36 −1.29909
\(93\) −774.237 −0.863275
\(94\) 2438.53 2.67570
\(95\) 560.689 0.605531
\(96\) −765.286 −0.813611
\(97\) 1031.70 1.07993 0.539964 0.841688i \(-0.318438\pi\)
0.539964 + 0.841688i \(0.318438\pi\)
\(98\) 0 0
\(99\) −373.751 −0.379428
\(100\) 248.607 0.248607
\(101\) −1447.19 −1.42576 −0.712878 0.701288i \(-0.752609\pi\)
−0.712878 + 0.701288i \(0.752609\pi\)
\(102\) 1529.90 1.48513
\(103\) 163.567 0.156473 0.0782364 0.996935i \(-0.475071\pi\)
0.0782364 + 0.996935i \(0.475071\pi\)
\(104\) 732.768 0.690902
\(105\) 0 0
\(106\) 780.715 0.715375
\(107\) −129.653 −0.117141 −0.0585703 0.998283i \(-0.518654\pi\)
−0.0585703 + 0.998283i \(0.518654\pi\)
\(108\) −268.495 −0.239222
\(109\) 566.681 0.497965 0.248983 0.968508i \(-0.419904\pi\)
0.248983 + 0.968508i \(0.419904\pi\)
\(110\) 879.574 0.762401
\(111\) −145.003 −0.123992
\(112\) 0 0
\(113\) 809.890 0.674230 0.337115 0.941463i \(-0.390549\pi\)
0.337115 + 0.941463i \(0.390549\pi\)
\(114\) 1425.07 1.17079
\(115\) −576.393 −0.467382
\(116\) −1440.26 −1.15280
\(117\) −800.735 −0.632718
\(118\) −641.771 −0.500676
\(119\) 0 0
\(120\) 123.541 0.0939808
\(121\) 393.563 0.295690
\(122\) −2244.39 −1.66556
\(123\) 602.656 0.441786
\(124\) 2566.41 1.85863
\(125\) 125.000 0.0894427
\(126\) 0 0
\(127\) −2584.25 −1.80563 −0.902816 0.430028i \(-0.858504\pi\)
−0.902816 + 0.430028i \(0.858504\pi\)
\(128\) 1023.08 0.706473
\(129\) 654.650 0.446812
\(130\) 1884.43 1.27135
\(131\) 1421.10 0.947804 0.473902 0.880578i \(-0.342845\pi\)
0.473902 + 0.880578i \(0.342845\pi\)
\(132\) 1238.89 0.816908
\(133\) 0 0
\(134\) −5.44272 −0.00350880
\(135\) −135.000 −0.0860663
\(136\) −991.515 −0.625160
\(137\) 104.878 0.0654037 0.0327019 0.999465i \(-0.489589\pi\)
0.0327019 + 0.999465i \(0.489589\pi\)
\(138\) −1464.98 −0.903679
\(139\) 913.160 0.557217 0.278609 0.960405i \(-0.410127\pi\)
0.278609 + 0.960405i \(0.410127\pi\)
\(140\) 0 0
\(141\) 1726.98 1.03147
\(142\) 260.190 0.153765
\(143\) 3694.76 2.16064
\(144\) −401.991 −0.232633
\(145\) −724.164 −0.414749
\(146\) 2053.65 1.16412
\(147\) 0 0
\(148\) 480.650 0.266954
\(149\) 1781.45 0.979476 0.489738 0.871870i \(-0.337092\pi\)
0.489738 + 0.871870i \(0.337092\pi\)
\(150\) 317.705 0.172937
\(151\) 1407.53 0.758564 0.379282 0.925281i \(-0.376171\pi\)
0.379282 + 0.925281i \(0.376171\pi\)
\(152\) −923.574 −0.492841
\(153\) 1083.48 0.572512
\(154\) 0 0
\(155\) 1290.39 0.668690
\(156\) 2654.24 1.36224
\(157\) 1598.94 0.812798 0.406399 0.913696i \(-0.366784\pi\)
0.406399 + 0.913696i \(0.366784\pi\)
\(158\) −3720.36 −1.87326
\(159\) 552.906 0.275775
\(160\) 1275.48 0.630220
\(161\) 0 0
\(162\) −343.122 −0.166408
\(163\) −204.892 −0.0984562 −0.0492281 0.998788i \(-0.515676\pi\)
−0.0492281 + 0.998788i \(0.515676\pi\)
\(164\) −1997.66 −0.951165
\(165\) 622.918 0.293904
\(166\) 2083.42 0.974127
\(167\) 1165.94 0.540259 0.270129 0.962824i \(-0.412933\pi\)
0.270129 + 0.962824i \(0.412933\pi\)
\(168\) 0 0
\(169\) 5718.76 2.60299
\(170\) −2549.84 −1.15037
\(171\) 1009.24 0.451336
\(172\) −2170.01 −0.961985
\(173\) 2538.00 1.11538 0.557690 0.830049i \(-0.311688\pi\)
0.557690 + 0.830049i \(0.311688\pi\)
\(174\) −1840.56 −0.801913
\(175\) 0 0
\(176\) 1854.87 0.794409
\(177\) −454.505 −0.193009
\(178\) −1760.34 −0.741254
\(179\) 392.255 0.163791 0.0818954 0.996641i \(-0.473903\pi\)
0.0818954 + 0.996641i \(0.473903\pi\)
\(180\) 447.492 0.185301
\(181\) 2978.08 1.22298 0.611489 0.791253i \(-0.290571\pi\)
0.611489 + 0.791253i \(0.290571\pi\)
\(182\) 0 0
\(183\) −1589.49 −0.642068
\(184\) 949.443 0.380401
\(185\) 241.672 0.0960436
\(186\) 3279.72 1.29291
\(187\) −4999.41 −1.95504
\(188\) −5724.51 −2.22076
\(189\) 0 0
\(190\) −2375.12 −0.906890
\(191\) −1097.37 −0.415722 −0.207861 0.978158i \(-0.566650\pi\)
−0.207861 + 0.978158i \(0.566650\pi\)
\(192\) 2169.83 0.815592
\(193\) 3500.31 1.30548 0.652740 0.757582i \(-0.273619\pi\)
0.652740 + 0.757582i \(0.273619\pi\)
\(194\) −4370.34 −1.61738
\(195\) 1334.56 0.490101
\(196\) 0 0
\(197\) 1573.96 0.569237 0.284618 0.958641i \(-0.408133\pi\)
0.284618 + 0.958641i \(0.408133\pi\)
\(198\) 1583.23 0.568260
\(199\) 3396.62 1.20995 0.604976 0.796244i \(-0.293183\pi\)
0.604976 + 0.796244i \(0.293183\pi\)
\(200\) −205.902 −0.0727972
\(201\) −3.85456 −0.00135263
\(202\) 6130.42 2.13532
\(203\) 0 0
\(204\) −3591.48 −1.23262
\(205\) −1004.43 −0.342206
\(206\) −692.879 −0.234346
\(207\) −1037.51 −0.348366
\(208\) 3973.93 1.32472
\(209\) −4656.84 −1.54125
\(210\) 0 0
\(211\) 3337.81 1.08903 0.544513 0.838753i \(-0.316715\pi\)
0.544513 + 0.838753i \(0.316715\pi\)
\(212\) −1832.75 −0.593744
\(213\) 184.268 0.0592762
\(214\) 549.220 0.175439
\(215\) −1091.08 −0.346099
\(216\) 222.374 0.0700492
\(217\) 0 0
\(218\) −2400.50 −0.745791
\(219\) 1454.40 0.448764
\(220\) −2064.82 −0.632774
\(221\) −10710.9 −3.26015
\(222\) 614.243 0.185700
\(223\) −127.328 −0.0382356 −0.0191178 0.999817i \(-0.506086\pi\)
−0.0191178 + 0.999817i \(0.506086\pi\)
\(224\) 0 0
\(225\) 225.000 0.0666667
\(226\) −3430.75 −1.00978
\(227\) −3844.12 −1.12398 −0.561990 0.827144i \(-0.689964\pi\)
−0.561990 + 0.827144i \(0.689964\pi\)
\(228\) −3345.39 −0.971726
\(229\) −2536.95 −0.732080 −0.366040 0.930599i \(-0.619287\pi\)
−0.366040 + 0.930599i \(0.619287\pi\)
\(230\) 2441.64 0.699987
\(231\) 0 0
\(232\) 1192.85 0.337563
\(233\) 3987.44 1.12114 0.560570 0.828107i \(-0.310582\pi\)
0.560570 + 0.828107i \(0.310582\pi\)
\(234\) 3391.97 0.947607
\(235\) −2878.30 −0.798976
\(236\) 1506.57 0.415549
\(237\) −2634.77 −0.722138
\(238\) 0 0
\(239\) −3367.18 −0.911317 −0.455659 0.890155i \(-0.650596\pi\)
−0.455659 + 0.890155i \(0.650596\pi\)
\(240\) 669.984 0.180197
\(241\) 939.551 0.251128 0.125564 0.992086i \(-0.459926\pi\)
0.125564 + 0.992086i \(0.459926\pi\)
\(242\) −1667.16 −0.442848
\(243\) −243.000 −0.0641500
\(244\) 5268.77 1.38237
\(245\) 0 0
\(246\) −2552.89 −0.661653
\(247\) −9976.96 −2.57012
\(248\) −2125.56 −0.544246
\(249\) 1475.49 0.375523
\(250\) −529.508 −0.133956
\(251\) 1403.96 0.353056 0.176528 0.984296i \(-0.443513\pi\)
0.176528 + 0.984296i \(0.443513\pi\)
\(252\) 0 0
\(253\) 4787.28 1.18962
\(254\) 10947.1 2.70425
\(255\) −1805.80 −0.443466
\(256\) 1452.36 0.354579
\(257\) 1964.86 0.476905 0.238453 0.971154i \(-0.423360\pi\)
0.238453 + 0.971154i \(0.423360\pi\)
\(258\) −2773.14 −0.669179
\(259\) 0 0
\(260\) −4423.74 −1.05519
\(261\) −1303.50 −0.309135
\(262\) −6019.89 −1.41950
\(263\) −393.821 −0.0923347 −0.0461673 0.998934i \(-0.514701\pi\)
−0.0461673 + 0.998934i \(0.514701\pi\)
\(264\) −1026.08 −0.239208
\(265\) −921.509 −0.213615
\(266\) 0 0
\(267\) −1246.68 −0.285751
\(268\) 12.7769 0.00291222
\(269\) 1877.03 0.425444 0.212722 0.977113i \(-0.431767\pi\)
0.212722 + 0.977113i \(0.431767\pi\)
\(270\) 571.869 0.128899
\(271\) 689.909 0.154646 0.0773228 0.997006i \(-0.475363\pi\)
0.0773228 + 0.997006i \(0.475363\pi\)
\(272\) −5377.16 −1.19867
\(273\) 0 0
\(274\) −444.269 −0.0979536
\(275\) −1038.20 −0.227657
\(276\) 3439.09 0.750031
\(277\) 6289.13 1.36418 0.682088 0.731270i \(-0.261072\pi\)
0.682088 + 0.731270i \(0.261072\pi\)
\(278\) −3868.21 −0.834531
\(279\) 2322.71 0.498412
\(280\) 0 0
\(281\) −1954.87 −0.415010 −0.207505 0.978234i \(-0.566534\pi\)
−0.207505 + 0.978234i \(0.566534\pi\)
\(282\) −7315.60 −1.54481
\(283\) −5033.96 −1.05738 −0.528688 0.848816i \(-0.677316\pi\)
−0.528688 + 0.848816i \(0.677316\pi\)
\(284\) −610.803 −0.127621
\(285\) −1682.07 −0.349604
\(286\) −15651.2 −3.23594
\(287\) 0 0
\(288\) 2295.86 0.469738
\(289\) 9580.03 1.94993
\(290\) 3067.61 0.621159
\(291\) −3095.09 −0.623497
\(292\) −4820.99 −0.966188
\(293\) −6369.12 −1.26993 −0.634963 0.772543i \(-0.718985\pi\)
−0.634963 + 0.772543i \(0.718985\pi\)
\(294\) 0 0
\(295\) 757.508 0.149504
\(296\) −398.085 −0.0781697
\(297\) 1121.25 0.219063
\(298\) −7546.34 −1.46694
\(299\) 10256.4 1.98376
\(300\) −745.820 −0.143533
\(301\) 0 0
\(302\) −5962.39 −1.13608
\(303\) 4341.58 0.823160
\(304\) −5008.70 −0.944963
\(305\) 2649.15 0.497344
\(306\) −4589.71 −0.857438
\(307\) 6619.83 1.23066 0.615332 0.788268i \(-0.289022\pi\)
0.615332 + 0.788268i \(0.289022\pi\)
\(308\) 0 0
\(309\) −490.700 −0.0903396
\(310\) −5466.20 −1.00148
\(311\) 9909.22 1.80675 0.903377 0.428848i \(-0.141080\pi\)
0.903377 + 0.428848i \(0.141080\pi\)
\(312\) −2198.30 −0.398892
\(313\) 422.336 0.0762678 0.0381339 0.999273i \(-0.487859\pi\)
0.0381339 + 0.999273i \(0.487859\pi\)
\(314\) −6773.22 −1.21731
\(315\) 0 0
\(316\) 8733.63 1.55476
\(317\) −4902.78 −0.868668 −0.434334 0.900752i \(-0.643016\pi\)
−0.434334 + 0.900752i \(0.643016\pi\)
\(318\) −2342.15 −0.413022
\(319\) 6014.60 1.05565
\(320\) −3616.38 −0.631755
\(321\) 388.960 0.0676312
\(322\) 0 0
\(323\) 13499.9 2.32556
\(324\) 805.486 0.138115
\(325\) −2224.26 −0.379631
\(326\) 867.935 0.147455
\(327\) −1700.04 −0.287500
\(328\) 1654.51 0.278521
\(329\) 0 0
\(330\) −2638.72 −0.440172
\(331\) −5281.74 −0.877071 −0.438535 0.898714i \(-0.644503\pi\)
−0.438535 + 0.898714i \(0.644503\pi\)
\(332\) −4890.89 −0.808501
\(333\) 435.009 0.0715867
\(334\) −4939.01 −0.809133
\(335\) 6.42426 0.00104775
\(336\) 0 0
\(337\) 4459.60 0.720860 0.360430 0.932786i \(-0.382630\pi\)
0.360430 + 0.932786i \(0.382630\pi\)
\(338\) −24225.1 −3.89843
\(339\) −2429.67 −0.389267
\(340\) 5985.80 0.954782
\(341\) −10717.5 −1.70200
\(342\) −4275.21 −0.675956
\(343\) 0 0
\(344\) 1797.25 0.281689
\(345\) 1729.18 0.269843
\(346\) −10751.2 −1.67048
\(347\) 5261.97 0.814056 0.407028 0.913416i \(-0.366565\pi\)
0.407028 + 0.913416i \(0.366565\pi\)
\(348\) 4320.77 0.665568
\(349\) −960.325 −0.147292 −0.0736461 0.997284i \(-0.523464\pi\)
−0.0736461 + 0.997284i \(0.523464\pi\)
\(350\) 0 0
\(351\) 2402.21 0.365300
\(352\) −10593.6 −1.60409
\(353\) 8925.80 1.34581 0.672907 0.739727i \(-0.265045\pi\)
0.672907 + 0.739727i \(0.265045\pi\)
\(354\) 1925.31 0.289066
\(355\) −307.113 −0.0459151
\(356\) 4132.45 0.615222
\(357\) 0 0
\(358\) −1661.62 −0.245306
\(359\) −3056.27 −0.449314 −0.224657 0.974438i \(-0.572126\pi\)
−0.224657 + 0.974438i \(0.572126\pi\)
\(360\) −370.623 −0.0542599
\(361\) 5715.88 0.833340
\(362\) −12615.4 −1.83162
\(363\) −1180.69 −0.170717
\(364\) 0 0
\(365\) −2424.00 −0.347611
\(366\) 6733.18 0.961610
\(367\) 1813.52 0.257943 0.128971 0.991648i \(-0.458832\pi\)
0.128971 + 0.991648i \(0.458832\pi\)
\(368\) 5148.99 0.729375
\(369\) −1807.97 −0.255065
\(370\) −1023.74 −0.143842
\(371\) 0 0
\(372\) −7699.22 −1.07308
\(373\) −4517.48 −0.627094 −0.313547 0.949573i \(-0.601517\pi\)
−0.313547 + 0.949573i \(0.601517\pi\)
\(374\) 21177.9 2.92802
\(375\) −375.000 −0.0516398
\(376\) 4741.17 0.650285
\(377\) 12885.9 1.76036
\(378\) 0 0
\(379\) −4931.24 −0.668340 −0.334170 0.942513i \(-0.608456\pi\)
−0.334170 + 0.942513i \(0.608456\pi\)
\(380\) 5575.64 0.752696
\(381\) 7752.75 1.04248
\(382\) 4648.53 0.622617
\(383\) 1482.37 0.197770 0.0988849 0.995099i \(-0.468472\pi\)
0.0988849 + 0.995099i \(0.468472\pi\)
\(384\) −3069.25 −0.407883
\(385\) 0 0
\(386\) −14827.5 −1.95519
\(387\) −1963.95 −0.257967
\(388\) 10259.5 1.34239
\(389\) −5448.98 −0.710217 −0.355109 0.934825i \(-0.615556\pi\)
−0.355109 + 0.934825i \(0.615556\pi\)
\(390\) −5653.28 −0.734013
\(391\) −13878.0 −1.79500
\(392\) 0 0
\(393\) −4263.31 −0.547215
\(394\) −6667.38 −0.852532
\(395\) 4391.28 0.559366
\(396\) −3716.68 −0.471642
\(397\) 13675.9 1.72891 0.864453 0.502713i \(-0.167665\pi\)
0.864453 + 0.502713i \(0.167665\pi\)
\(398\) −14388.3 −1.81212
\(399\) 0 0
\(400\) −1116.64 −0.139580
\(401\) 14109.9 1.75714 0.878570 0.477613i \(-0.158498\pi\)
0.878570 + 0.477613i \(0.158498\pi\)
\(402\) 16.3282 0.00202581
\(403\) −22961.4 −2.83819
\(404\) −14391.3 −1.77226
\(405\) 405.000 0.0496904
\(406\) 0 0
\(407\) −2007.22 −0.244458
\(408\) 2974.55 0.360936
\(409\) 13995.6 1.69203 0.846015 0.533159i \(-0.178995\pi\)
0.846015 + 0.533159i \(0.178995\pi\)
\(410\) 4254.82 0.512514
\(411\) −314.633 −0.0377609
\(412\) 1626.55 0.194501
\(413\) 0 0
\(414\) 4394.95 0.521740
\(415\) −2459.15 −0.290879
\(416\) −22696.0 −2.67491
\(417\) −2739.48 −0.321709
\(418\) 19726.7 2.30829
\(419\) 9840.61 1.14736 0.573682 0.819078i \(-0.305515\pi\)
0.573682 + 0.819078i \(0.305515\pi\)
\(420\) 0 0
\(421\) −12660.5 −1.46564 −0.732822 0.680420i \(-0.761797\pi\)
−0.732822 + 0.680420i \(0.761797\pi\)
\(422\) −14139.2 −1.63101
\(423\) −5180.93 −0.595522
\(424\) 1517.92 0.173860
\(425\) 3009.67 0.343507
\(426\) −780.571 −0.0887765
\(427\) 0 0
\(428\) −1289.31 −0.145610
\(429\) −11084.3 −1.24744
\(430\) 4621.90 0.518344
\(431\) −4578.91 −0.511736 −0.255868 0.966712i \(-0.582361\pi\)
−0.255868 + 0.966712i \(0.582361\pi\)
\(432\) 1205.97 0.134311
\(433\) 3279.88 0.364020 0.182010 0.983297i \(-0.441740\pi\)
0.182010 + 0.983297i \(0.441740\pi\)
\(434\) 0 0
\(435\) 2172.49 0.239455
\(436\) 5635.23 0.618988
\(437\) −12927.1 −1.41507
\(438\) −6160.94 −0.672103
\(439\) 427.807 0.0465105 0.0232552 0.999730i \(-0.492597\pi\)
0.0232552 + 0.999730i \(0.492597\pi\)
\(440\) 1710.13 0.185289
\(441\) 0 0
\(442\) 45372.1 4.88265
\(443\) 15441.2 1.65605 0.828027 0.560688i \(-0.189463\pi\)
0.828027 + 0.560688i \(0.189463\pi\)
\(444\) −1441.95 −0.154126
\(445\) 2077.80 0.221342
\(446\) 539.371 0.0572645
\(447\) −5344.35 −0.565501
\(448\) 0 0
\(449\) 9382.02 0.986113 0.493057 0.869997i \(-0.335880\pi\)
0.493057 + 0.869997i \(0.335880\pi\)
\(450\) −953.115 −0.0998451
\(451\) 8342.34 0.871010
\(452\) 8053.77 0.838091
\(453\) −4222.59 −0.437957
\(454\) 16284.0 1.68336
\(455\) 0 0
\(456\) 2770.72 0.284542
\(457\) 13570.4 1.38905 0.694524 0.719469i \(-0.255615\pi\)
0.694524 + 0.719469i \(0.255615\pi\)
\(458\) 10746.7 1.09642
\(459\) −3250.45 −0.330540
\(460\) −5731.81 −0.580972
\(461\) −1251.88 −0.126477 −0.0632386 0.997998i \(-0.520143\pi\)
−0.0632386 + 0.997998i \(0.520143\pi\)
\(462\) 0 0
\(463\) 7934.36 0.796417 0.398209 0.917295i \(-0.369632\pi\)
0.398209 + 0.917295i \(0.369632\pi\)
\(464\) 6469.05 0.647237
\(465\) −3871.18 −0.386069
\(466\) −16891.1 −1.67911
\(467\) −7583.76 −0.751466 −0.375733 0.926728i \(-0.622609\pi\)
−0.375733 + 0.926728i \(0.622609\pi\)
\(468\) −7962.73 −0.786490
\(469\) 0 0
\(470\) 12192.7 1.19661
\(471\) −4796.82 −0.469269
\(472\) −1247.78 −0.121681
\(473\) 9062.07 0.880919
\(474\) 11161.1 1.08153
\(475\) 2803.44 0.270802
\(476\) 0 0
\(477\) −1658.72 −0.159219
\(478\) 14263.6 1.36486
\(479\) 5829.34 0.556053 0.278027 0.960573i \(-0.410320\pi\)
0.278027 + 0.960573i \(0.410320\pi\)
\(480\) −3826.43 −0.363858
\(481\) −4300.34 −0.407648
\(482\) −3980.00 −0.376108
\(483\) 0 0
\(484\) 3913.70 0.367553
\(485\) 5158.49 0.482959
\(486\) 1029.36 0.0960760
\(487\) −19902.1 −1.85185 −0.925925 0.377708i \(-0.876712\pi\)
−0.925925 + 0.377708i \(0.876712\pi\)
\(488\) −4363.71 −0.404787
\(489\) 614.675 0.0568437
\(490\) 0 0
\(491\) −16821.6 −1.54613 −0.773065 0.634327i \(-0.781277\pi\)
−0.773065 + 0.634327i \(0.781277\pi\)
\(492\) 5992.98 0.549155
\(493\) −17436.0 −1.59285
\(494\) 42263.1 3.84920
\(495\) −1868.75 −0.169685
\(496\) −11527.3 −1.04353
\(497\) 0 0
\(498\) −6250.27 −0.562412
\(499\) 6031.83 0.541126 0.270563 0.962702i \(-0.412790\pi\)
0.270563 + 0.962702i \(0.412790\pi\)
\(500\) 1243.03 0.111180
\(501\) −3497.82 −0.311919
\(502\) −5947.27 −0.528764
\(503\) 17176.4 1.52258 0.761290 0.648412i \(-0.224566\pi\)
0.761290 + 0.648412i \(0.224566\pi\)
\(504\) 0 0
\(505\) −7235.97 −0.637617
\(506\) −20279.2 −1.78166
\(507\) −17156.3 −1.50284
\(508\) −25698.5 −2.24446
\(509\) −4706.59 −0.409854 −0.204927 0.978777i \(-0.565696\pi\)
−0.204927 + 0.978777i \(0.565696\pi\)
\(510\) 7649.51 0.664169
\(511\) 0 0
\(512\) −14336.9 −1.23752
\(513\) −3027.72 −0.260579
\(514\) −8323.28 −0.714250
\(515\) 817.833 0.0699768
\(516\) 6510.02 0.555402
\(517\) 23905.9 2.03362
\(518\) 0 0
\(519\) −7614.01 −0.643965
\(520\) 3663.84 0.308981
\(521\) 8557.18 0.719572 0.359786 0.933035i \(-0.382850\pi\)
0.359786 + 0.933035i \(0.382850\pi\)
\(522\) 5521.69 0.462985
\(523\) −18248.5 −1.52572 −0.762858 0.646566i \(-0.776204\pi\)
−0.762858 + 0.646566i \(0.776204\pi\)
\(524\) 14131.8 1.17815
\(525\) 0 0
\(526\) 1668.25 0.138287
\(527\) 31069.3 2.56813
\(528\) −5564.60 −0.458652
\(529\) 1122.16 0.0922302
\(530\) 3903.58 0.319925
\(531\) 1363.51 0.111434
\(532\) 0 0
\(533\) 17872.9 1.45246
\(534\) 5281.03 0.427963
\(535\) −648.266 −0.0523869
\(536\) −10.5821 −0.000852758 0
\(537\) −1176.77 −0.0945646
\(538\) −7951.22 −0.637177
\(539\) 0 0
\(540\) −1342.48 −0.106983
\(541\) −5734.17 −0.455696 −0.227848 0.973697i \(-0.573169\pi\)
−0.227848 + 0.973697i \(0.573169\pi\)
\(542\) −2922.50 −0.231609
\(543\) −8934.24 −0.706087
\(544\) 30710.1 2.42038
\(545\) 2833.41 0.222697
\(546\) 0 0
\(547\) −8002.52 −0.625527 −0.312763 0.949831i \(-0.601255\pi\)
−0.312763 + 0.949831i \(0.601255\pi\)
\(548\) 1042.93 0.0812991
\(549\) 4768.47 0.370698
\(550\) 4397.87 0.340956
\(551\) −16241.2 −1.25572
\(552\) −2848.33 −0.219625
\(553\) 0 0
\(554\) −26641.2 −2.04310
\(555\) −725.016 −0.0554508
\(556\) 9080.71 0.692640
\(557\) 1276.82 0.0971289 0.0485644 0.998820i \(-0.484535\pi\)
0.0485644 + 0.998820i \(0.484535\pi\)
\(558\) −9839.16 −0.746460
\(559\) 19414.9 1.46898
\(560\) 0 0
\(561\) 14998.2 1.12875
\(562\) 8280.96 0.621550
\(563\) −11027.7 −0.825507 −0.412753 0.910843i \(-0.635433\pi\)
−0.412753 + 0.910843i \(0.635433\pi\)
\(564\) 17173.5 1.28216
\(565\) 4049.45 0.301525
\(566\) 21324.2 1.58361
\(567\) 0 0
\(568\) 505.881 0.0373702
\(569\) −4519.03 −0.332948 −0.166474 0.986046i \(-0.553238\pi\)
−0.166474 + 0.986046i \(0.553238\pi\)
\(570\) 7125.35 0.523593
\(571\) 3598.81 0.263758 0.131879 0.991266i \(-0.457899\pi\)
0.131879 + 0.991266i \(0.457899\pi\)
\(572\) 36741.7 2.68575
\(573\) 3292.11 0.240017
\(574\) 0 0
\(575\) −2881.97 −0.209020
\(576\) −6509.48 −0.470883
\(577\) 3439.23 0.248140 0.124070 0.992273i \(-0.460405\pi\)
0.124070 + 0.992273i \(0.460405\pi\)
\(578\) −40581.6 −2.92037
\(579\) −10500.9 −0.753720
\(580\) −7201.28 −0.515547
\(581\) 0 0
\(582\) 13111.0 0.933797
\(583\) 7653.66 0.543709
\(584\) 3992.85 0.282920
\(585\) −4003.68 −0.282960
\(586\) 26980.0 1.90194
\(587\) −21285.2 −1.49665 −0.748327 0.663330i \(-0.769143\pi\)
−0.748327 + 0.663330i \(0.769143\pi\)
\(588\) 0 0
\(589\) 28940.4 2.02456
\(590\) −3208.85 −0.223909
\(591\) −4721.87 −0.328649
\(592\) −2158.89 −0.149881
\(593\) 14200.8 0.983404 0.491702 0.870764i \(-0.336375\pi\)
0.491702 + 0.870764i \(0.336375\pi\)
\(594\) −4749.70 −0.328085
\(595\) 0 0
\(596\) 17715.2 1.21752
\(597\) −10189.9 −0.698566
\(598\) −43446.8 −2.97103
\(599\) −8885.05 −0.606065 −0.303033 0.952980i \(-0.597999\pi\)
−0.303033 + 0.952980i \(0.597999\pi\)
\(600\) 617.705 0.0420295
\(601\) 2052.89 0.139333 0.0696664 0.997570i \(-0.477807\pi\)
0.0696664 + 0.997570i \(0.477807\pi\)
\(602\) 0 0
\(603\) 11.5637 0.000780943 0
\(604\) 13996.9 0.942920
\(605\) 1967.82 0.132237
\(606\) −18391.2 −1.23283
\(607\) −10280.0 −0.687404 −0.343702 0.939079i \(-0.611681\pi\)
−0.343702 + 0.939079i \(0.611681\pi\)
\(608\) 28605.8 1.90809
\(609\) 0 0
\(610\) −11222.0 −0.744860
\(611\) 51216.8 3.39118
\(612\) 10774.4 0.711652
\(613\) 23409.5 1.54242 0.771208 0.636584i \(-0.219653\pi\)
0.771208 + 0.636584i \(0.219653\pi\)
\(614\) −28042.0 −1.84314
\(615\) 3013.28 0.197573
\(616\) 0 0
\(617\) −6632.75 −0.432779 −0.216389 0.976307i \(-0.569428\pi\)
−0.216389 + 0.976307i \(0.569428\pi\)
\(618\) 2078.64 0.135299
\(619\) −10734.0 −0.696990 −0.348495 0.937311i \(-0.613307\pi\)
−0.348495 + 0.937311i \(0.613307\pi\)
\(620\) 12832.0 0.831205
\(621\) 3112.52 0.201129
\(622\) −41976.1 −2.70593
\(623\) 0 0
\(624\) −11921.8 −0.764829
\(625\) 625.000 0.0400000
\(626\) −1789.04 −0.114225
\(627\) 13970.5 0.889839
\(628\) 15900.3 1.01034
\(629\) 5818.83 0.368858
\(630\) 0 0
\(631\) −17071.0 −1.07700 −0.538499 0.842626i \(-0.681008\pi\)
−0.538499 + 0.842626i \(0.681008\pi\)
\(632\) −7233.38 −0.455267
\(633\) −10013.4 −0.628749
\(634\) 20768.5 1.30098
\(635\) −12921.3 −0.807503
\(636\) 5498.24 0.342798
\(637\) 0 0
\(638\) −25478.2 −1.58102
\(639\) −552.804 −0.0342231
\(640\) 5115.41 0.315945
\(641\) −19389.7 −1.19477 −0.597386 0.801954i \(-0.703794\pi\)
−0.597386 + 0.801954i \(0.703794\pi\)
\(642\) −1647.66 −0.101290
\(643\) 25409.3 1.55839 0.779196 0.626780i \(-0.215628\pi\)
0.779196 + 0.626780i \(0.215628\pi\)
\(644\) 0 0
\(645\) 3273.25 0.199820
\(646\) −57186.6 −3.48294
\(647\) 6039.08 0.366956 0.183478 0.983024i \(-0.441264\pi\)
0.183478 + 0.983024i \(0.441264\pi\)
\(648\) −667.122 −0.0404429
\(649\) −6291.54 −0.380531
\(650\) 9422.14 0.568564
\(651\) 0 0
\(652\) −2037.50 −0.122384
\(653\) −30666.2 −1.83776 −0.918882 0.394532i \(-0.870907\pi\)
−0.918882 + 0.394532i \(0.870907\pi\)
\(654\) 7201.50 0.430582
\(655\) 7105.51 0.423871
\(656\) 8972.67 0.534031
\(657\) −4363.20 −0.259094
\(658\) 0 0
\(659\) −2765.96 −0.163500 −0.0817500 0.996653i \(-0.526051\pi\)
−0.0817500 + 0.996653i \(0.526051\pi\)
\(660\) 6194.47 0.365332
\(661\) −27261.8 −1.60418 −0.802089 0.597204i \(-0.796278\pi\)
−0.802089 + 0.597204i \(0.796278\pi\)
\(662\) 22373.8 1.31357
\(663\) 32132.7 1.88225
\(664\) 4050.74 0.236746
\(665\) 0 0
\(666\) −1842.73 −0.107214
\(667\) 16696.1 0.969230
\(668\) 11594.4 0.671560
\(669\) 381.985 0.0220753
\(670\) −27.2136 −0.00156918
\(671\) −22002.7 −1.26588
\(672\) 0 0
\(673\) −1048.17 −0.0600356 −0.0300178 0.999549i \(-0.509556\pi\)
−0.0300178 + 0.999549i \(0.509556\pi\)
\(674\) −18891.2 −1.07961
\(675\) −675.000 −0.0384900
\(676\) 56869.0 3.23560
\(677\) 34554.7 1.96166 0.980831 0.194860i \(-0.0624252\pi\)
0.980831 + 0.194860i \(0.0624252\pi\)
\(678\) 10292.2 0.582996
\(679\) 0 0
\(680\) −4957.58 −0.279580
\(681\) 11532.4 0.648930
\(682\) 45399.9 2.54905
\(683\) 14711.6 0.824192 0.412096 0.911140i \(-0.364797\pi\)
0.412096 + 0.911140i \(0.364797\pi\)
\(684\) 10036.2 0.561026
\(685\) 524.389 0.0292494
\(686\) 0 0
\(687\) 7610.85 0.422667
\(688\) 9746.79 0.540106
\(689\) 16397.4 0.906666
\(690\) −7324.92 −0.404138
\(691\) 24522.6 1.35005 0.675024 0.737796i \(-0.264133\pi\)
0.675024 + 0.737796i \(0.264133\pi\)
\(692\) 25238.6 1.38646
\(693\) 0 0
\(694\) −22290.1 −1.21919
\(695\) 4565.80 0.249195
\(696\) −3578.56 −0.194892
\(697\) −24184.0 −1.31425
\(698\) 4068.00 0.220596
\(699\) −11962.3 −0.647291
\(700\) 0 0
\(701\) 19912.2 1.07286 0.536429 0.843946i \(-0.319773\pi\)
0.536429 + 0.843946i \(0.319773\pi\)
\(702\) −10175.9 −0.547101
\(703\) 5420.11 0.290787
\(704\) 30036.1 1.60799
\(705\) 8634.89 0.461289
\(706\) −37810.3 −2.01559
\(707\) 0 0
\(708\) −4519.72 −0.239917
\(709\) 6208.79 0.328880 0.164440 0.986387i \(-0.447418\pi\)
0.164440 + 0.986387i \(0.447418\pi\)
\(710\) 1300.95 0.0687660
\(711\) 7904.31 0.416927
\(712\) −3422.58 −0.180150
\(713\) −29751.0 −1.56267
\(714\) 0 0
\(715\) 18473.8 0.966267
\(716\) 3900.69 0.203597
\(717\) 10101.5 0.526149
\(718\) 12946.6 0.672927
\(719\) −13063.6 −0.677593 −0.338797 0.940860i \(-0.610020\pi\)
−0.338797 + 0.940860i \(0.610020\pi\)
\(720\) −2009.95 −0.104037
\(721\) 0 0
\(722\) −24212.9 −1.24807
\(723\) −2818.65 −0.144989
\(724\) 29614.8 1.52020
\(725\) −3620.82 −0.185481
\(726\) 5001.49 0.255678
\(727\) 12897.0 0.657940 0.328970 0.944340i \(-0.393298\pi\)
0.328970 + 0.944340i \(0.393298\pi\)
\(728\) 0 0
\(729\) 729.000 0.0370370
\(730\) 10268.2 0.520609
\(731\) −26270.5 −1.32920
\(732\) −15806.3 −0.798112
\(733\) −11699.6 −0.589540 −0.294770 0.955568i \(-0.595243\pi\)
−0.294770 + 0.955568i \(0.595243\pi\)
\(734\) −7682.19 −0.386315
\(735\) 0 0
\(736\) −29407.0 −1.47277
\(737\) −53.3571 −0.00266681
\(738\) 7658.68 0.382005
\(739\) 14974.0 0.745368 0.372684 0.927958i \(-0.378438\pi\)
0.372684 + 0.927958i \(0.378438\pi\)
\(740\) 2403.25 0.119385
\(741\) 29930.9 1.48386
\(742\) 0 0
\(743\) 18500.7 0.913492 0.456746 0.889597i \(-0.349015\pi\)
0.456746 + 0.889597i \(0.349015\pi\)
\(744\) 6376.67 0.314220
\(745\) 8907.24 0.438035
\(746\) 19136.3 0.939184
\(747\) −4426.47 −0.216809
\(748\) −49715.5 −2.43019
\(749\) 0 0
\(750\) 1588.53 0.0773397
\(751\) −26348.4 −1.28025 −0.640125 0.768271i \(-0.721117\pi\)
−0.640125 + 0.768271i \(0.721117\pi\)
\(752\) 25712.2 1.24684
\(753\) −4211.88 −0.203837
\(754\) −54585.4 −2.63645
\(755\) 7037.65 0.339240
\(756\) 0 0
\(757\) −28061.7 −1.34732 −0.673659 0.739042i \(-0.735278\pi\)
−0.673659 + 0.739042i \(0.735278\pi\)
\(758\) 20889.1 1.00096
\(759\) −14361.8 −0.686826
\(760\) −4617.87 −0.220405
\(761\) 3579.22 0.170495 0.0852476 0.996360i \(-0.472832\pi\)
0.0852476 + 0.996360i \(0.472832\pi\)
\(762\) −32841.2 −1.56130
\(763\) 0 0
\(764\) −10912.5 −0.516757
\(765\) 5417.41 0.256035
\(766\) −6279.44 −0.296195
\(767\) −13479.2 −0.634557
\(768\) −4357.07 −0.204716
\(769\) −4339.61 −0.203499 −0.101749 0.994810i \(-0.532444\pi\)
−0.101749 + 0.994810i \(0.532444\pi\)
\(770\) 0 0
\(771\) −5894.58 −0.275341
\(772\) 34808.0 1.62276
\(773\) −10005.1 −0.465537 −0.232769 0.972532i \(-0.574778\pi\)
−0.232769 + 0.972532i \(0.574778\pi\)
\(774\) 8319.43 0.386351
\(775\) 6451.97 0.299047
\(776\) −8497.14 −0.393079
\(777\) 0 0
\(778\) 23082.3 1.06368
\(779\) −22526.8 −1.03608
\(780\) 13271.2 0.609212
\(781\) 2550.75 0.116867
\(782\) 58788.4 2.68832
\(783\) 3910.49 0.178479
\(784\) 0 0
\(785\) 7994.70 0.363494
\(786\) 18059.7 0.819550
\(787\) −17826.8 −0.807443 −0.403721 0.914882i \(-0.632284\pi\)
−0.403721 + 0.914882i \(0.632284\pi\)
\(788\) 15651.8 0.707581
\(789\) 1181.46 0.0533094
\(790\) −18601.8 −0.837749
\(791\) 0 0
\(792\) 3078.24 0.138107
\(793\) −47139.3 −2.11093
\(794\) −57932.2 −2.58934
\(795\) 2764.53 0.123330
\(796\) 33777.0 1.50401
\(797\) −36723.0 −1.63211 −0.816057 0.577971i \(-0.803845\pi\)
−0.816057 + 0.577971i \(0.803845\pi\)
\(798\) 0 0
\(799\) −69301.9 −3.06849
\(800\) 6377.38 0.281843
\(801\) 3740.04 0.164979
\(802\) −59770.4 −2.63163
\(803\) 20132.7 0.884767
\(804\) −38.3307 −0.00168137
\(805\) 0 0
\(806\) 97266.2 4.25069
\(807\) −5631.08 −0.245630
\(808\) 11919.2 0.518955
\(809\) 5657.55 0.245870 0.122935 0.992415i \(-0.460769\pi\)
0.122935 + 0.992415i \(0.460769\pi\)
\(810\) −1715.61 −0.0744201
\(811\) −7532.41 −0.326139 −0.163070 0.986615i \(-0.552139\pi\)
−0.163070 + 0.986615i \(0.552139\pi\)
\(812\) 0 0
\(813\) −2069.73 −0.0892847
\(814\) 8502.73 0.366119
\(815\) −1024.46 −0.0440309
\(816\) 16131.5 0.692053
\(817\) −24470.3 −1.04787
\(818\) −59286.5 −2.53411
\(819\) 0 0
\(820\) −9988.30 −0.425374
\(821\) −6489.25 −0.275854 −0.137927 0.990442i \(-0.544044\pi\)
−0.137927 + 0.990442i \(0.544044\pi\)
\(822\) 1332.81 0.0565535
\(823\) 7901.57 0.334668 0.167334 0.985900i \(-0.446484\pi\)
0.167334 + 0.985900i \(0.446484\pi\)
\(824\) −1347.15 −0.0569539
\(825\) 3114.59 0.131438
\(826\) 0 0
\(827\) −37815.8 −1.59007 −0.795033 0.606566i \(-0.792547\pi\)
−0.795033 + 0.606566i \(0.792547\pi\)
\(828\) −10317.3 −0.433031
\(829\) −26073.5 −1.09236 −0.546182 0.837667i \(-0.683919\pi\)
−0.546182 + 0.837667i \(0.683919\pi\)
\(830\) 10417.1 0.435643
\(831\) −18867.4 −0.787608
\(832\) 64350.2 2.68142
\(833\) 0 0
\(834\) 11604.6 0.481817
\(835\) 5829.71 0.241611
\(836\) −46308.9 −1.91582
\(837\) −6968.13 −0.287758
\(838\) −41685.5 −1.71838
\(839\) 15590.3 0.641523 0.320762 0.947160i \(-0.396061\pi\)
0.320762 + 0.947160i \(0.396061\pi\)
\(840\) 0 0
\(841\) −3412.46 −0.139918
\(842\) 53630.8 2.19506
\(843\) 5864.61 0.239606
\(844\) 33192.1 1.35370
\(845\) 28593.8 1.16409
\(846\) 21946.8 0.891899
\(847\) 0 0
\(848\) 8231.96 0.333357
\(849\) 15101.9 0.610477
\(850\) −12749.2 −0.514463
\(851\) −5571.92 −0.224445
\(852\) 1832.41 0.0736823
\(853\) 17476.1 0.701488 0.350744 0.936471i \(-0.385929\pi\)
0.350744 + 0.936471i \(0.385929\pi\)
\(854\) 0 0
\(855\) 5046.20 0.201844
\(856\) 1067.83 0.0426376
\(857\) 5694.54 0.226980 0.113490 0.993539i \(-0.463797\pi\)
0.113490 + 0.993539i \(0.463797\pi\)
\(858\) 46953.7 1.86827
\(859\) −27313.6 −1.08490 −0.542448 0.840089i \(-0.682503\pi\)
−0.542448 + 0.840089i \(0.682503\pi\)
\(860\) −10850.0 −0.430213
\(861\) 0 0
\(862\) 19396.6 0.766415
\(863\) −9046.07 −0.356815 −0.178408 0.983957i \(-0.557095\pi\)
−0.178408 + 0.983957i \(0.557095\pi\)
\(864\) −6887.57 −0.271204
\(865\) 12690.0 0.498813
\(866\) −13893.8 −0.545185
\(867\) −28740.1 −1.12580
\(868\) 0 0
\(869\) −36472.1 −1.42374
\(870\) −9202.82 −0.358626
\(871\) −114.314 −0.00444705
\(872\) −4667.22 −0.181252
\(873\) 9285.28 0.359976
\(874\) 54760.0 2.11932
\(875\) 0 0
\(876\) 14463.0 0.557829
\(877\) −2104.29 −0.0810224 −0.0405112 0.999179i \(-0.512899\pi\)
−0.0405112 + 0.999179i \(0.512899\pi\)
\(878\) −1812.22 −0.0696576
\(879\) 19107.4 0.733192
\(880\) 9274.34 0.355270
\(881\) 22589.6 0.863861 0.431931 0.901907i \(-0.357833\pi\)
0.431931 + 0.901907i \(0.357833\pi\)
\(882\) 0 0
\(883\) −2419.71 −0.0922193 −0.0461096 0.998936i \(-0.514682\pi\)
−0.0461096 + 0.998936i \(0.514682\pi\)
\(884\) −106512. −4.05248
\(885\) −2272.52 −0.0863164
\(886\) −65409.8 −2.48023
\(887\) −13177.0 −0.498806 −0.249403 0.968400i \(-0.580234\pi\)
−0.249403 + 0.968400i \(0.580234\pi\)
\(888\) 1194.26 0.0451313
\(889\) 0 0
\(890\) −8801.71 −0.331499
\(891\) −3363.76 −0.126476
\(892\) −1266.19 −0.0475281
\(893\) −64553.2 −2.41902
\(894\) 22639.0 0.846937
\(895\) 1961.28 0.0732495
\(896\) 0 0
\(897\) −30769.2 −1.14532
\(898\) −39742.9 −1.47688
\(899\) −37378.3 −1.38669
\(900\) 2237.46 0.0828689
\(901\) −22187.5 −0.820393
\(902\) −35338.7 −1.30449
\(903\) 0 0
\(904\) −6670.31 −0.245411
\(905\) 14890.4 0.546932
\(906\) 17887.2 0.655918
\(907\) 9189.14 0.336406 0.168203 0.985752i \(-0.446204\pi\)
0.168203 + 0.985752i \(0.446204\pi\)
\(908\) −38227.0 −1.39714
\(909\) −13024.8 −0.475252
\(910\) 0 0
\(911\) −17045.8 −0.619928 −0.309964 0.950748i \(-0.600317\pi\)
−0.309964 + 0.950748i \(0.600317\pi\)
\(912\) 15026.1 0.545575
\(913\) 20424.6 0.740369
\(914\) −57485.0 −2.08034
\(915\) −7947.45 −0.287141
\(916\) −25228.1 −0.910001
\(917\) 0 0
\(918\) 13769.1 0.495042
\(919\) −30825.0 −1.10645 −0.553223 0.833033i \(-0.686602\pi\)
−0.553223 + 0.833033i \(0.686602\pi\)
\(920\) 4747.21 0.170121
\(921\) −19859.5 −0.710524
\(922\) 5303.06 0.189422
\(923\) 5464.81 0.194882
\(924\) 0 0
\(925\) 1208.36 0.0429520
\(926\) −33610.5 −1.19277
\(927\) 1472.10 0.0521576
\(928\) −36946.2 −1.30691
\(929\) 5785.88 0.204336 0.102168 0.994767i \(-0.467422\pi\)
0.102168 + 0.994767i \(0.467422\pi\)
\(930\) 16398.6 0.578206
\(931\) 0 0
\(932\) 39652.2 1.39362
\(933\) −29727.7 −1.04313
\(934\) 32125.3 1.12545
\(935\) −24997.1 −0.874323
\(936\) 6594.91 0.230301
\(937\) 13680.9 0.476986 0.238493 0.971144i \(-0.423347\pi\)
0.238493 + 0.971144i \(0.423347\pi\)
\(938\) 0 0
\(939\) −1267.01 −0.0440333
\(940\) −28622.6 −0.993155
\(941\) 45448.8 1.57448 0.787242 0.616644i \(-0.211508\pi\)
0.787242 + 0.616644i \(0.211508\pi\)
\(942\) 20319.6 0.702813
\(943\) 23157.8 0.799705
\(944\) −6766.91 −0.233310
\(945\) 0 0
\(946\) −38387.6 −1.31933
\(947\) −7788.45 −0.267255 −0.133628 0.991032i \(-0.542663\pi\)
−0.133628 + 0.991032i \(0.542663\pi\)
\(948\) −26200.9 −0.897642
\(949\) 43133.0 1.47540
\(950\) −11875.6 −0.405573
\(951\) 14708.4 0.501526
\(952\) 0 0
\(953\) 6149.43 0.209024 0.104512 0.994524i \(-0.466672\pi\)
0.104512 + 0.994524i \(0.466672\pi\)
\(954\) 7026.44 0.238458
\(955\) −5486.85 −0.185917
\(956\) −33484.2 −1.13280
\(957\) −18043.8 −0.609481
\(958\) −24693.5 −0.832788
\(959\) 0 0
\(960\) 10849.1 0.364744
\(961\) 36813.7 1.23573
\(962\) 18216.5 0.610524
\(963\) −1166.88 −0.0390469
\(964\) 9343.15 0.312160
\(965\) 17501.5 0.583829
\(966\) 0 0
\(967\) 23902.9 0.794896 0.397448 0.917625i \(-0.369896\pi\)
0.397448 + 0.917625i \(0.369896\pi\)
\(968\) −3241.42 −0.107627
\(969\) −40499.8 −1.34266
\(970\) −21851.7 −0.723316
\(971\) 8015.06 0.264898 0.132449 0.991190i \(-0.457716\pi\)
0.132449 + 0.991190i \(0.457716\pi\)
\(972\) −2416.46 −0.0797407
\(973\) 0 0
\(974\) 84306.7 2.77347
\(975\) 6672.79 0.219180
\(976\) −23665.2 −0.776131
\(977\) −34861.1 −1.14156 −0.570780 0.821103i \(-0.693359\pi\)
−0.570780 + 0.821103i \(0.693359\pi\)
\(978\) −2603.80 −0.0851334
\(979\) −17257.3 −0.563378
\(980\) 0 0
\(981\) 5100.13 0.165988
\(982\) 71257.6 2.31560
\(983\) −6620.83 −0.214824 −0.107412 0.994215i \(-0.534256\pi\)
−0.107412 + 0.994215i \(0.534256\pi\)
\(984\) −4963.52 −0.160804
\(985\) 7869.78 0.254570
\(986\) 73860.0 2.38558
\(987\) 0 0
\(988\) −99213.6 −3.19474
\(989\) 25155.7 0.808802
\(990\) 7916.17 0.254134
\(991\) 10360.1 0.332089 0.166045 0.986118i \(-0.446900\pi\)
0.166045 + 0.986118i \(0.446900\pi\)
\(992\) 65834.7 2.10711
\(993\) 15845.2 0.506377
\(994\) 0 0
\(995\) 16983.1 0.541107
\(996\) 14672.7 0.466788
\(997\) 40309.3 1.28045 0.640225 0.768188i \(-0.278841\pi\)
0.640225 + 0.768188i \(0.278841\pi\)
\(998\) −25551.3 −0.810432
\(999\) −1305.03 −0.0413306
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 735.4.a.m.1.1 2
3.2 odd 2 2205.4.a.be.1.2 2
7.6 odd 2 105.4.a.d.1.1 2
21.20 even 2 315.4.a.l.1.2 2
28.27 even 2 1680.4.a.bd.1.1 2
35.13 even 4 525.4.d.k.274.4 4
35.27 even 4 525.4.d.k.274.1 4
35.34 odd 2 525.4.a.o.1.2 2
105.104 even 2 1575.4.a.n.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
105.4.a.d.1.1 2 7.6 odd 2
315.4.a.l.1.2 2 21.20 even 2
525.4.a.o.1.2 2 35.34 odd 2
525.4.d.k.274.1 4 35.27 even 4
525.4.d.k.274.4 4 35.13 even 4
735.4.a.m.1.1 2 1.1 even 1 trivial
1575.4.a.n.1.1 2 105.104 even 2
1680.4.a.bd.1.1 2 28.27 even 2
2205.4.a.be.1.2 2 3.2 odd 2