Properties

Label 297.2.a.h.1.2
Level $297$
Weight $2$
Character 297.1
Self dual yes
Analytic conductor $2.372$
Analytic rank $0$
Dimension $3$
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] = [297,2,Mod(1,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 297 = 3^{3} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 297.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: \(2.37155694003\)
Analytic rank: \(0\)
Dimension: \(3\)
Coefficient field: 3.3.564.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - x^{2} - 5x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(0.571993\) of defining polynomial
Character \(\chi\) \(=\) 297.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.571993 q^{2} -1.67282 q^{4} +2.67282 q^{5} +2.57199 q^{7} -2.10083 q^{8} +O(q^{10})\) \(q+0.571993 q^{2} -1.67282 q^{4} +2.67282 q^{5} +2.57199 q^{7} -2.10083 q^{8} +1.52884 q^{10} -1.00000 q^{11} +4.67282 q^{13} +1.47116 q^{14} +2.14399 q^{16} -3.24482 q^{17} +3.52884 q^{19} -4.47116 q^{20} -0.571993 q^{22} +4.52884 q^{23} +2.14399 q^{25} +2.67282 q^{26} -4.30249 q^{28} -5.91764 q^{29} +4.67282 q^{31} +5.42801 q^{32} -1.85601 q^{34} +6.87448 q^{35} -11.3064 q^{37} +2.01847 q^{38} -5.61515 q^{40} -7.06163 q^{41} -2.38880 q^{43} +1.67282 q^{44} +2.59046 q^{46} -9.48963 q^{47} -0.384851 q^{49} +1.22635 q^{50} -7.81681 q^{52} -10.2017 q^{53} -2.67282 q^{55} -5.40332 q^{56} -3.38485 q^{58} +7.96080 q^{59} +5.16246 q^{61} +2.67282 q^{62} -1.18319 q^{64} +12.4896 q^{65} +1.61515 q^{67} +5.42801 q^{68} +3.93216 q^{70} -10.2017 q^{71} +8.48963 q^{73} -6.46721 q^{74} -5.90312 q^{76} -2.57199 q^{77} -11.9361 q^{79} +5.73050 q^{80} -4.03920 q^{82} +14.0185 q^{83} -8.67282 q^{85} -1.36638 q^{86} +2.10083 q^{88} +13.6336 q^{89} +12.0185 q^{91} -7.57595 q^{92} -5.42801 q^{94} +9.43196 q^{95} -12.4504 q^{97} -0.220132 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 3 q + q^{2} + 5 q^{4} - 2 q^{5} + 7 q^{7} + 3 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 3 q + q^{2} + 5 q^{4} - 2 q^{5} + 7 q^{7} + 3 q^{8} - 4 q^{10} - 3 q^{11} + 4 q^{13} + 13 q^{14} + 5 q^{16} + q^{17} + 2 q^{19} - 22 q^{20} - q^{22} + 5 q^{23} + 5 q^{25} - 2 q^{26} + 15 q^{28} + 3 q^{29} + 4 q^{31} + 17 q^{32} - 7 q^{34} - 8 q^{35} - q^{37} - 24 q^{38} - 24 q^{40} + q^{41} + 5 q^{43} - 5 q^{44} - 23 q^{46} - 7 q^{47} + 6 q^{49} + 23 q^{50} - 12 q^{52} - 12 q^{53} + 2 q^{55} + 21 q^{56} - 3 q^{58} + 11 q^{59} - 16 q^{61} - 2 q^{62} - 15 q^{64} + 16 q^{65} + 12 q^{67} + 17 q^{68} - 34 q^{70} - 12 q^{71} + 4 q^{73} - 33 q^{74} - 22 q^{76} - 7 q^{77} + 15 q^{79} - 10 q^{80} - 25 q^{82} + 12 q^{83} - 16 q^{85} - 27 q^{86} - 3 q^{88} + 18 q^{89} + 6 q^{91} - 17 q^{92} - 17 q^{94} + 24 q^{95} - 3 q^{97} + 48 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.571993 0.404460 0.202230 0.979338i \(-0.435181\pi\)
0.202230 + 0.979338i \(0.435181\pi\)
\(3\) 0 0
\(4\) −1.67282 −0.836412
\(5\) 2.67282 1.19532 0.597662 0.801749i \(-0.296097\pi\)
0.597662 + 0.801749i \(0.296097\pi\)
\(6\) 0 0
\(7\) 2.57199 0.972122 0.486061 0.873925i \(-0.338433\pi\)
0.486061 + 0.873925i \(0.338433\pi\)
\(8\) −2.10083 −0.742756
\(9\) 0 0
\(10\) 1.52884 0.483461
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) 4.67282 1.29601 0.648004 0.761637i \(-0.275604\pi\)
0.648004 + 0.761637i \(0.275604\pi\)
\(14\) 1.47116 0.393185
\(15\) 0 0
\(16\) 2.14399 0.535997
\(17\) −3.24482 −0.786984 −0.393492 0.919328i \(-0.628733\pi\)
−0.393492 + 0.919328i \(0.628733\pi\)
\(18\) 0 0
\(19\) 3.52884 0.809571 0.404785 0.914412i \(-0.367346\pi\)
0.404785 + 0.914412i \(0.367346\pi\)
\(20\) −4.47116 −0.999782
\(21\) 0 0
\(22\) −0.571993 −0.121949
\(23\) 4.52884 0.944328 0.472164 0.881511i \(-0.343473\pi\)
0.472164 + 0.881511i \(0.343473\pi\)
\(24\) 0 0
\(25\) 2.14399 0.428797
\(26\) 2.67282 0.524184
\(27\) 0 0
\(28\) −4.30249 −0.813094
\(29\) −5.91764 −1.09888 −0.549439 0.835534i \(-0.685159\pi\)
−0.549439 + 0.835534i \(0.685159\pi\)
\(30\) 0 0
\(31\) 4.67282 0.839264 0.419632 0.907694i \(-0.362159\pi\)
0.419632 + 0.907694i \(0.362159\pi\)
\(32\) 5.42801 0.959545
\(33\) 0 0
\(34\) −1.85601 −0.318304
\(35\) 6.87448 1.16200
\(36\) 0 0
\(37\) −11.3064 −1.85877 −0.929384 0.369114i \(-0.879661\pi\)
−0.929384 + 0.369114i \(0.879661\pi\)
\(38\) 2.01847 0.327439
\(39\) 0 0
\(40\) −5.61515 −0.887833
\(41\) −7.06163 −1.10284 −0.551420 0.834227i \(-0.685914\pi\)
−0.551420 + 0.834227i \(0.685914\pi\)
\(42\) 0 0
\(43\) −2.38880 −0.364289 −0.182145 0.983272i \(-0.558304\pi\)
−0.182145 + 0.983272i \(0.558304\pi\)
\(44\) 1.67282 0.252188
\(45\) 0 0
\(46\) 2.59046 0.381943
\(47\) −9.48963 −1.38421 −0.692103 0.721799i \(-0.743315\pi\)
−0.692103 + 0.721799i \(0.743315\pi\)
\(48\) 0 0
\(49\) −0.384851 −0.0549787
\(50\) 1.22635 0.173431
\(51\) 0 0
\(52\) −7.81681 −1.08400
\(53\) −10.2017 −1.40131 −0.700653 0.713502i \(-0.747108\pi\)
−0.700653 + 0.713502i \(0.747108\pi\)
\(54\) 0 0
\(55\) −2.67282 −0.360403
\(56\) −5.40332 −0.722049
\(57\) 0 0
\(58\) −3.38485 −0.444453
\(59\) 7.96080 1.03641 0.518204 0.855257i \(-0.326601\pi\)
0.518204 + 0.855257i \(0.326601\pi\)
\(60\) 0 0
\(61\) 5.16246 0.660985 0.330492 0.943809i \(-0.392785\pi\)
0.330492 + 0.943809i \(0.392785\pi\)
\(62\) 2.67282 0.339449
\(63\) 0 0
\(64\) −1.18319 −0.147899
\(65\) 12.4896 1.54915
\(66\) 0 0
\(67\) 1.61515 0.197322 0.0986610 0.995121i \(-0.468544\pi\)
0.0986610 + 0.995121i \(0.468544\pi\)
\(68\) 5.42801 0.658243
\(69\) 0 0
\(70\) 3.93216 0.469983
\(71\) −10.2017 −1.21071 −0.605357 0.795954i \(-0.706970\pi\)
−0.605357 + 0.795954i \(0.706970\pi\)
\(72\) 0 0
\(73\) 8.48963 0.993636 0.496818 0.867855i \(-0.334502\pi\)
0.496818 + 0.867855i \(0.334502\pi\)
\(74\) −6.46721 −0.751798
\(75\) 0 0
\(76\) −5.90312 −0.677135
\(77\) −2.57199 −0.293106
\(78\) 0 0
\(79\) −11.9361 −1.34292 −0.671459 0.741042i \(-0.734332\pi\)
−0.671459 + 0.741042i \(0.734332\pi\)
\(80\) 5.73050 0.640689
\(81\) 0 0
\(82\) −4.03920 −0.446055
\(83\) 14.0185 1.53873 0.769364 0.638811i \(-0.220573\pi\)
0.769364 + 0.638811i \(0.220573\pi\)
\(84\) 0 0
\(85\) −8.67282 −0.940700
\(86\) −1.36638 −0.147340
\(87\) 0 0
\(88\) 2.10083 0.223949
\(89\) 13.6336 1.44516 0.722580 0.691287i \(-0.242956\pi\)
0.722580 + 0.691287i \(0.242956\pi\)
\(90\) 0 0
\(91\) 12.0185 1.25988
\(92\) −7.57595 −0.789847
\(93\) 0 0
\(94\) −5.42801 −0.559856
\(95\) 9.43196 0.967699
\(96\) 0 0
\(97\) −12.4504 −1.26415 −0.632075 0.774907i \(-0.717796\pi\)
−0.632075 + 0.774907i \(0.717796\pi\)
\(98\) −0.220132 −0.0222367
\(99\) 0 0
\(100\) −3.58651 −0.358651
\(101\) 9.24482 0.919894 0.459947 0.887946i \(-0.347868\pi\)
0.459947 + 0.887946i \(0.347868\pi\)
\(102\) 0 0
\(103\) 8.38485 0.826184 0.413092 0.910689i \(-0.364449\pi\)
0.413092 + 0.910689i \(0.364449\pi\)
\(104\) −9.81681 −0.962617
\(105\) 0 0
\(106\) −5.83528 −0.566773
\(107\) −15.8168 −1.52907 −0.764534 0.644583i \(-0.777031\pi\)
−0.764534 + 0.644583i \(0.777031\pi\)
\(108\) 0 0
\(109\) −5.14399 −0.492705 −0.246352 0.969180i \(-0.579232\pi\)
−0.246352 + 0.969180i \(0.579232\pi\)
\(110\) −1.52884 −0.145769
\(111\) 0 0
\(112\) 5.51432 0.521054
\(113\) −8.18319 −0.769810 −0.384905 0.922956i \(-0.625766\pi\)
−0.384905 + 0.922956i \(0.625766\pi\)
\(114\) 0 0
\(115\) 12.1048 1.12878
\(116\) 9.89917 0.919115
\(117\) 0 0
\(118\) 4.55352 0.419186
\(119\) −8.34565 −0.765044
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 2.95289 0.267342
\(123\) 0 0
\(124\) −7.81681 −0.701970
\(125\) −7.63362 −0.682772
\(126\) 0 0
\(127\) 17.8168 1.58099 0.790493 0.612471i \(-0.209824\pi\)
0.790493 + 0.612471i \(0.209824\pi\)
\(128\) −11.5328 −1.01936
\(129\) 0 0
\(130\) 7.14399 0.626569
\(131\) 4.20166 0.367101 0.183550 0.983010i \(-0.441241\pi\)
0.183550 + 0.983010i \(0.441241\pi\)
\(132\) 0 0
\(133\) 9.07615 0.787002
\(134\) 0.923855 0.0798089
\(135\) 0 0
\(136\) 6.81681 0.584537
\(137\) −0.489634 −0.0418323 −0.0209161 0.999781i \(-0.506658\pi\)
−0.0209161 + 0.999781i \(0.506658\pi\)
\(138\) 0 0
\(139\) −3.81286 −0.323402 −0.161701 0.986840i \(-0.551698\pi\)
−0.161701 + 0.986840i \(0.551698\pi\)
\(140\) −11.4998 −0.971911
\(141\) 0 0
\(142\) −5.83528 −0.489686
\(143\) −4.67282 −0.390761
\(144\) 0 0
\(145\) −15.8168 −1.31351
\(146\) 4.85601 0.401887
\(147\) 0 0
\(148\) 18.9137 1.55470
\(149\) 9.16246 0.750618 0.375309 0.926900i \(-0.377537\pi\)
0.375309 + 0.926900i \(0.377537\pi\)
\(150\) 0 0
\(151\) 16.0185 1.30356 0.651782 0.758406i \(-0.274022\pi\)
0.651782 + 0.758406i \(0.274022\pi\)
\(152\) −7.41349 −0.601313
\(153\) 0 0
\(154\) −1.47116 −0.118550
\(155\) 12.4896 1.00319
\(156\) 0 0
\(157\) −2.79834 −0.223332 −0.111666 0.993746i \(-0.535619\pi\)
−0.111666 + 0.993746i \(0.535619\pi\)
\(158\) −6.82738 −0.543157
\(159\) 0 0
\(160\) 14.5081 1.14697
\(161\) 11.6481 0.918002
\(162\) 0 0
\(163\) 5.05767 0.396148 0.198074 0.980187i \(-0.436531\pi\)
0.198074 + 0.980187i \(0.436531\pi\)
\(164\) 11.8129 0.922429
\(165\) 0 0
\(166\) 8.01847 0.622354
\(167\) −9.65209 −0.746901 −0.373451 0.927650i \(-0.621825\pi\)
−0.373451 + 0.927650i \(0.621825\pi\)
\(168\) 0 0
\(169\) 8.83528 0.679637
\(170\) −4.96080 −0.380476
\(171\) 0 0
\(172\) 3.99605 0.304696
\(173\) 20.8824 1.58766 0.793829 0.608141i \(-0.208084\pi\)
0.793829 + 0.608141i \(0.208084\pi\)
\(174\) 0 0
\(175\) 5.51432 0.416843
\(176\) −2.14399 −0.161609
\(177\) 0 0
\(178\) 7.79834 0.584510
\(179\) −5.56804 −0.416175 −0.208087 0.978110i \(-0.566724\pi\)
−0.208087 + 0.978110i \(0.566724\pi\)
\(180\) 0 0
\(181\) −26.7490 −1.98824 −0.994118 0.108306i \(-0.965457\pi\)
−0.994118 + 0.108306i \(0.965457\pi\)
\(182\) 6.87448 0.509571
\(183\) 0 0
\(184\) −9.51432 −0.701405
\(185\) −30.2201 −2.22183
\(186\) 0 0
\(187\) 3.24482 0.237285
\(188\) 15.8745 1.15777
\(189\) 0 0
\(190\) 5.39502 0.391396
\(191\) 8.51037 0.615788 0.307894 0.951421i \(-0.400376\pi\)
0.307894 + 0.951421i \(0.400376\pi\)
\(192\) 0 0
\(193\) −5.52884 −0.397974 −0.198987 0.980002i \(-0.563765\pi\)
−0.198987 + 0.980002i \(0.563765\pi\)
\(194\) −7.12156 −0.511298
\(195\) 0 0
\(196\) 0.643787 0.0459848
\(197\) 14.9753 1.06695 0.533474 0.845817i \(-0.320886\pi\)
0.533474 + 0.845817i \(0.320886\pi\)
\(198\) 0 0
\(199\) 0.0968776 0.00686747 0.00343373 0.999994i \(-0.498907\pi\)
0.00343373 + 0.999994i \(0.498907\pi\)
\(200\) −4.50415 −0.318492
\(201\) 0 0
\(202\) 5.28797 0.372060
\(203\) −15.2201 −1.06824
\(204\) 0 0
\(205\) −18.8745 −1.31825
\(206\) 4.79608 0.334159
\(207\) 0 0
\(208\) 10.0185 0.694656
\(209\) −3.52884 −0.244095
\(210\) 0 0
\(211\) 8.19771 0.564353 0.282177 0.959362i \(-0.408944\pi\)
0.282177 + 0.959362i \(0.408944\pi\)
\(212\) 17.0656 1.17207
\(213\) 0 0
\(214\) −9.04711 −0.618448
\(215\) −6.38485 −0.435443
\(216\) 0 0
\(217\) 12.0185 0.815867
\(218\) −2.94233 −0.199279
\(219\) 0 0
\(220\) 4.47116 0.301446
\(221\) −15.1625 −1.01994
\(222\) 0 0
\(223\) −3.73050 −0.249813 −0.124906 0.992169i \(-0.539863\pi\)
−0.124906 + 0.992169i \(0.539863\pi\)
\(224\) 13.9608 0.932795
\(225\) 0 0
\(226\) −4.68073 −0.311357
\(227\) 18.3849 1.22025 0.610123 0.792307i \(-0.291120\pi\)
0.610123 + 0.792307i \(0.291120\pi\)
\(228\) 0 0
\(229\) −27.5081 −1.81779 −0.908893 0.417029i \(-0.863071\pi\)
−0.908893 + 0.417029i \(0.863071\pi\)
\(230\) 6.92385 0.456545
\(231\) 0 0
\(232\) 12.4320 0.816198
\(233\) 5.61515 0.367861 0.183930 0.982939i \(-0.441118\pi\)
0.183930 + 0.982939i \(0.441118\pi\)
\(234\) 0 0
\(235\) −25.3641 −1.65457
\(236\) −13.3170 −0.866863
\(237\) 0 0
\(238\) −4.77365 −0.309430
\(239\) −17.4504 −1.12877 −0.564387 0.825510i \(-0.690888\pi\)
−0.564387 + 0.825510i \(0.690888\pi\)
\(240\) 0 0
\(241\) −0.0784065 −0.00505060 −0.00252530 0.999997i \(-0.500804\pi\)
−0.00252530 + 0.999997i \(0.500804\pi\)
\(242\) 0.571993 0.0367691
\(243\) 0 0
\(244\) −8.63588 −0.552856
\(245\) −1.02864 −0.0657173
\(246\) 0 0
\(247\) 16.4896 1.04921
\(248\) −9.81681 −0.623368
\(249\) 0 0
\(250\) −4.36638 −0.276154
\(251\) −5.94233 −0.375076 −0.187538 0.982257i \(-0.560051\pi\)
−0.187538 + 0.982257i \(0.560051\pi\)
\(252\) 0 0
\(253\) −4.52884 −0.284726
\(254\) 10.1911 0.639446
\(255\) 0 0
\(256\) −4.23030 −0.264394
\(257\) 18.7098 1.16708 0.583542 0.812083i \(-0.301667\pi\)
0.583542 + 0.812083i \(0.301667\pi\)
\(258\) 0 0
\(259\) −29.0801 −1.80695
\(260\) −20.8930 −1.29573
\(261\) 0 0
\(262\) 2.40332 0.148478
\(263\) −1.42405 −0.0878109 −0.0439055 0.999036i \(-0.513980\pi\)
−0.0439055 + 0.999036i \(0.513980\pi\)
\(264\) 0 0
\(265\) −27.2672 −1.67501
\(266\) 5.19149 0.318311
\(267\) 0 0
\(268\) −2.70186 −0.165042
\(269\) 8.67282 0.528791 0.264396 0.964414i \(-0.414828\pi\)
0.264396 + 0.964414i \(0.414828\pi\)
\(270\) 0 0
\(271\) 25.3681 1.54100 0.770500 0.637440i \(-0.220006\pi\)
0.770500 + 0.637440i \(0.220006\pi\)
\(272\) −6.95684 −0.421821
\(273\) 0 0
\(274\) −0.280067 −0.0169195
\(275\) −2.14399 −0.129287
\(276\) 0 0
\(277\) 6.69129 0.402041 0.201020 0.979587i \(-0.435574\pi\)
0.201020 + 0.979587i \(0.435574\pi\)
\(278\) −2.18093 −0.130803
\(279\) 0 0
\(280\) −14.4421 −0.863082
\(281\) −7.16641 −0.427512 −0.213756 0.976887i \(-0.568570\pi\)
−0.213756 + 0.976887i \(0.568570\pi\)
\(282\) 0 0
\(283\) −13.3272 −0.792218 −0.396109 0.918203i \(-0.629640\pi\)
−0.396109 + 0.918203i \(0.629640\pi\)
\(284\) 17.0656 1.01266
\(285\) 0 0
\(286\) −2.67282 −0.158047
\(287\) −18.1625 −1.07210
\(288\) 0 0
\(289\) −6.47116 −0.380657
\(290\) −9.04711 −0.531265
\(291\) 0 0
\(292\) −14.2017 −0.831089
\(293\) −3.81681 −0.222980 −0.111490 0.993766i \(-0.535562\pi\)
−0.111490 + 0.993766i \(0.535562\pi\)
\(294\) 0 0
\(295\) 21.2778 1.23884
\(296\) 23.7529 1.38061
\(297\) 0 0
\(298\) 5.24086 0.303595
\(299\) 21.1625 1.22386
\(300\) 0 0
\(301\) −6.14399 −0.354133
\(302\) 9.16246 0.527240
\(303\) 0 0
\(304\) 7.56578 0.433927
\(305\) 13.7983 0.790091
\(306\) 0 0
\(307\) −3.05372 −0.174285 −0.0871425 0.996196i \(-0.527774\pi\)
−0.0871425 + 0.996196i \(0.527774\pi\)
\(308\) 4.30249 0.245157
\(309\) 0 0
\(310\) 7.14399 0.405751
\(311\) 11.0185 0.624800 0.312400 0.949951i \(-0.398867\pi\)
0.312400 + 0.949951i \(0.398867\pi\)
\(312\) 0 0
\(313\) −5.63362 −0.318431 −0.159216 0.987244i \(-0.550896\pi\)
−0.159216 + 0.987244i \(0.550896\pi\)
\(314\) −1.60063 −0.0903288
\(315\) 0 0
\(316\) 19.9670 1.12323
\(317\) −28.4112 −1.59573 −0.797867 0.602834i \(-0.794038\pi\)
−0.797867 + 0.602834i \(0.794038\pi\)
\(318\) 0 0
\(319\) 5.91764 0.331324
\(320\) −3.16246 −0.176787
\(321\) 0 0
\(322\) 6.66266 0.371295
\(323\) −11.4504 −0.637119
\(324\) 0 0
\(325\) 10.0185 0.555725
\(326\) 2.89296 0.160226
\(327\) 0 0
\(328\) 14.8353 0.819141
\(329\) −24.4073 −1.34562
\(330\) 0 0
\(331\) −30.9977 −1.70379 −0.851895 0.523713i \(-0.824547\pi\)
−0.851895 + 0.523713i \(0.824547\pi\)
\(332\) −23.4504 −1.28701
\(333\) 0 0
\(334\) −5.52093 −0.302092
\(335\) 4.31701 0.235863
\(336\) 0 0
\(337\) 7.45043 0.405851 0.202925 0.979194i \(-0.434955\pi\)
0.202925 + 0.979194i \(0.434955\pi\)
\(338\) 5.05372 0.274886
\(339\) 0 0
\(340\) 14.5081 0.786812
\(341\) −4.67282 −0.253048
\(342\) 0 0
\(343\) −18.9938 −1.02557
\(344\) 5.01847 0.270578
\(345\) 0 0
\(346\) 11.9446 0.642145
\(347\) 20.8930 1.12159 0.560796 0.827954i \(-0.310495\pi\)
0.560796 + 0.827954i \(0.310495\pi\)
\(348\) 0 0
\(349\) −26.9114 −1.44054 −0.720268 0.693696i \(-0.755981\pi\)
−0.720268 + 0.693696i \(0.755981\pi\)
\(350\) 3.15415 0.168597
\(351\) 0 0
\(352\) −5.42801 −0.289314
\(353\) 11.8353 0.629928 0.314964 0.949104i \(-0.398007\pi\)
0.314964 + 0.949104i \(0.398007\pi\)
\(354\) 0 0
\(355\) −27.2672 −1.44719
\(356\) −22.8066 −1.20875
\(357\) 0 0
\(358\) −3.18488 −0.168326
\(359\) 2.83754 0.149760 0.0748799 0.997193i \(-0.476143\pi\)
0.0748799 + 0.997193i \(0.476143\pi\)
\(360\) 0 0
\(361\) −6.54731 −0.344595
\(362\) −15.3002 −0.804162
\(363\) 0 0
\(364\) −20.1048 −1.05378
\(365\) 22.6913 1.18772
\(366\) 0 0
\(367\) 5.22239 0.272607 0.136303 0.990667i \(-0.456478\pi\)
0.136303 + 0.990667i \(0.456478\pi\)
\(368\) 9.70977 0.506157
\(369\) 0 0
\(370\) −17.2857 −0.898641
\(371\) −26.2386 −1.36224
\(372\) 0 0
\(373\) 34.3434 1.77823 0.889117 0.457681i \(-0.151320\pi\)
0.889117 + 0.457681i \(0.151320\pi\)
\(374\) 1.85601 0.0959722
\(375\) 0 0
\(376\) 19.9361 1.02813
\(377\) −27.6521 −1.42416
\(378\) 0 0
\(379\) −31.1625 −1.60071 −0.800354 0.599528i \(-0.795355\pi\)
−0.800354 + 0.599528i \(0.795355\pi\)
\(380\) −15.7780 −0.809395
\(381\) 0 0
\(382\) 4.86787 0.249062
\(383\) 14.7776 0.755100 0.377550 0.925989i \(-0.376767\pi\)
0.377550 + 0.925989i \(0.376767\pi\)
\(384\) 0 0
\(385\) −6.87448 −0.350356
\(386\) −3.16246 −0.160965
\(387\) 0 0
\(388\) 20.8274 1.05735
\(389\) 1.63362 0.0828278 0.0414139 0.999142i \(-0.486814\pi\)
0.0414139 + 0.999142i \(0.486814\pi\)
\(390\) 0 0
\(391\) −14.6952 −0.743171
\(392\) 0.808506 0.0408357
\(393\) 0 0
\(394\) 8.56578 0.431538
\(395\) −31.9031 −1.60522
\(396\) 0 0
\(397\) 11.9216 0.598328 0.299164 0.954202i \(-0.403292\pi\)
0.299164 + 0.954202i \(0.403292\pi\)
\(398\) 0.0554133 0.00277762
\(399\) 0 0
\(400\) 4.59668 0.229834
\(401\) 17.1809 0.857975 0.428987 0.903311i \(-0.358870\pi\)
0.428987 + 0.903311i \(0.358870\pi\)
\(402\) 0 0
\(403\) 21.8353 1.08769
\(404\) −15.4649 −0.769410
\(405\) 0 0
\(406\) −8.70581 −0.432062
\(407\) 11.3064 0.560440
\(408\) 0 0
\(409\) 33.7490 1.66878 0.834390 0.551175i \(-0.185820\pi\)
0.834390 + 0.551175i \(0.185820\pi\)
\(410\) −10.7961 −0.533180
\(411\) 0 0
\(412\) −14.0264 −0.691030
\(413\) 20.4751 1.00751
\(414\) 0 0
\(415\) 37.4689 1.83928
\(416\) 25.3641 1.24358
\(417\) 0 0
\(418\) −2.01847 −0.0987266
\(419\) 7.91369 0.386609 0.193304 0.981139i \(-0.438079\pi\)
0.193304 + 0.981139i \(0.438079\pi\)
\(420\) 0 0
\(421\) 9.85601 0.480353 0.240176 0.970729i \(-0.422795\pi\)
0.240176 + 0.970729i \(0.422795\pi\)
\(422\) 4.68903 0.228259
\(423\) 0 0
\(424\) 21.4320 1.04083
\(425\) −6.95684 −0.337456
\(426\) 0 0
\(427\) 13.2778 0.642558
\(428\) 26.4587 1.27893
\(429\) 0 0
\(430\) −3.65209 −0.176119
\(431\) 17.2857 0.832623 0.416312 0.909222i \(-0.363323\pi\)
0.416312 + 0.909222i \(0.363323\pi\)
\(432\) 0 0
\(433\) 23.5450 1.13150 0.565751 0.824576i \(-0.308586\pi\)
0.565751 + 0.824576i \(0.308586\pi\)
\(434\) 6.87448 0.329986
\(435\) 0 0
\(436\) 8.60498 0.412104
\(437\) 15.9815 0.764500
\(438\) 0 0
\(439\) 0.388804 0.0185566 0.00927829 0.999957i \(-0.497047\pi\)
0.00927829 + 0.999957i \(0.497047\pi\)
\(440\) 5.61515 0.267692
\(441\) 0 0
\(442\) −8.67282 −0.412524
\(443\) −13.7490 −0.653233 −0.326617 0.945157i \(-0.605909\pi\)
−0.326617 + 0.945157i \(0.605909\pi\)
\(444\) 0 0
\(445\) 36.4403 1.72743
\(446\) −2.13382 −0.101039
\(447\) 0 0
\(448\) −3.04316 −0.143776
\(449\) 37.9691 1.79187 0.895936 0.444182i \(-0.146506\pi\)
0.895936 + 0.444182i \(0.146506\pi\)
\(450\) 0 0
\(451\) 7.06163 0.332519
\(452\) 13.6890 0.643878
\(453\) 0 0
\(454\) 10.5160 0.493541
\(455\) 32.1233 1.50596
\(456\) 0 0
\(457\) −17.7384 −0.829768 −0.414884 0.909874i \(-0.636178\pi\)
−0.414884 + 0.909874i \(0.636178\pi\)
\(458\) −15.7345 −0.735223
\(459\) 0 0
\(460\) −20.2492 −0.944122
\(461\) −26.7882 −1.24765 −0.623825 0.781564i \(-0.714422\pi\)
−0.623825 + 0.781564i \(0.714422\pi\)
\(462\) 0 0
\(463\) 35.0577 1.62927 0.814634 0.579975i \(-0.196938\pi\)
0.814634 + 0.579975i \(0.196938\pi\)
\(464\) −12.6873 −0.588995
\(465\) 0 0
\(466\) 3.21183 0.148785
\(467\) 16.0841 0.744281 0.372141 0.928176i \(-0.378624\pi\)
0.372141 + 0.928176i \(0.378624\pi\)
\(468\) 0 0
\(469\) 4.15415 0.191821
\(470\) −14.5081 −0.669209
\(471\) 0 0
\(472\) −16.7243 −0.769798
\(473\) 2.38880 0.109837
\(474\) 0 0
\(475\) 7.56578 0.347142
\(476\) 13.9608 0.639892
\(477\) 0 0
\(478\) −9.98153 −0.456545
\(479\) −42.3249 −1.93387 −0.966937 0.255014i \(-0.917920\pi\)
−0.966937 + 0.255014i \(0.917920\pi\)
\(480\) 0 0
\(481\) −52.8330 −2.40898
\(482\) −0.0448480 −0.00204277
\(483\) 0 0
\(484\) −1.67282 −0.0760374
\(485\) −33.2778 −1.51107
\(486\) 0 0
\(487\) 24.3664 1.10415 0.552073 0.833796i \(-0.313837\pi\)
0.552073 + 0.833796i \(0.313837\pi\)
\(488\) −10.8454 −0.490950
\(489\) 0 0
\(490\) −0.588374 −0.0265800
\(491\) 22.8560 1.03148 0.515739 0.856746i \(-0.327518\pi\)
0.515739 + 0.856746i \(0.327518\pi\)
\(492\) 0 0
\(493\) 19.2017 0.864799
\(494\) 9.43196 0.424364
\(495\) 0 0
\(496\) 10.0185 0.449843
\(497\) −26.2386 −1.17696
\(498\) 0 0
\(499\) 21.0841 0.943852 0.471926 0.881638i \(-0.343559\pi\)
0.471926 + 0.881638i \(0.343559\pi\)
\(500\) 12.7697 0.571078
\(501\) 0 0
\(502\) −3.39897 −0.151703
\(503\) 26.8930 1.19910 0.599549 0.800338i \(-0.295347\pi\)
0.599549 + 0.800338i \(0.295347\pi\)
\(504\) 0 0
\(505\) 24.7098 1.09957
\(506\) −2.59046 −0.115160
\(507\) 0 0
\(508\) −29.8044 −1.32236
\(509\) −30.9898 −1.37360 −0.686800 0.726846i \(-0.740985\pi\)
−0.686800 + 0.726846i \(0.740985\pi\)
\(510\) 0 0
\(511\) 21.8353 0.965936
\(512\) 20.6459 0.912428
\(513\) 0 0
\(514\) 10.7019 0.472039
\(515\) 22.4112 0.987557
\(516\) 0 0
\(517\) 9.48963 0.417354
\(518\) −16.6336 −0.730839
\(519\) 0 0
\(520\) −26.2386 −1.15064
\(521\) −9.48737 −0.415649 −0.207825 0.978166i \(-0.566638\pi\)
−0.207825 + 0.978166i \(0.566638\pi\)
\(522\) 0 0
\(523\) 15.1664 0.663181 0.331590 0.943423i \(-0.392415\pi\)
0.331590 + 0.943423i \(0.392415\pi\)
\(524\) −7.02864 −0.307047
\(525\) 0 0
\(526\) −0.814549 −0.0355160
\(527\) −15.1625 −0.660487
\(528\) 0 0
\(529\) −2.48963 −0.108245
\(530\) −15.5967 −0.677476
\(531\) 0 0
\(532\) −15.1828 −0.658257
\(533\) −32.9977 −1.42929
\(534\) 0 0
\(535\) −42.2755 −1.82773
\(536\) −3.39315 −0.146562
\(537\) 0 0
\(538\) 4.96080 0.213875
\(539\) 0.384851 0.0165767
\(540\) 0 0
\(541\) −32.4112 −1.39347 −0.696734 0.717330i \(-0.745364\pi\)
−0.696734 + 0.717330i \(0.745364\pi\)
\(542\) 14.5104 0.623274
\(543\) 0 0
\(544\) −17.6129 −0.755146
\(545\) −13.7490 −0.588941
\(546\) 0 0
\(547\) 17.7345 0.758270 0.379135 0.925341i \(-0.376222\pi\)
0.379135 + 0.925341i \(0.376222\pi\)
\(548\) 0.819071 0.0349890
\(549\) 0 0
\(550\) −1.22635 −0.0522916
\(551\) −20.8824 −0.889620
\(552\) 0 0
\(553\) −30.6996 −1.30548
\(554\) 3.82738 0.162610
\(555\) 0 0
\(556\) 6.37824 0.270498
\(557\) −5.64814 −0.239319 −0.119660 0.992815i \(-0.538180\pi\)
−0.119660 + 0.992815i \(0.538180\pi\)
\(558\) 0 0
\(559\) −11.1625 −0.472122
\(560\) 14.7388 0.622828
\(561\) 0 0
\(562\) −4.09914 −0.172912
\(563\) −17.9506 −0.756529 −0.378264 0.925698i \(-0.623479\pi\)
−0.378264 + 0.925698i \(0.623479\pi\)
\(564\) 0 0
\(565\) −21.8722 −0.920171
\(566\) −7.62306 −0.320421
\(567\) 0 0
\(568\) 21.4320 0.899265
\(569\) 34.4218 1.44304 0.721518 0.692395i \(-0.243445\pi\)
0.721518 + 0.692395i \(0.243445\pi\)
\(570\) 0 0
\(571\) −27.5882 −1.15453 −0.577265 0.816557i \(-0.695880\pi\)
−0.577265 + 0.816557i \(0.695880\pi\)
\(572\) 7.81681 0.326837
\(573\) 0 0
\(574\) −10.3888 −0.433620
\(575\) 9.70977 0.404925
\(576\) 0 0
\(577\) −10.0577 −0.418706 −0.209353 0.977840i \(-0.567136\pi\)
−0.209353 + 0.977840i \(0.567136\pi\)
\(578\) −3.70146 −0.153961
\(579\) 0 0
\(580\) 26.4587 1.09864
\(581\) 36.0554 1.49583
\(582\) 0 0
\(583\) 10.2017 0.422510
\(584\) −17.8353 −0.738029
\(585\) 0 0
\(586\) −2.18319 −0.0901867
\(587\) 18.3720 0.758295 0.379147 0.925336i \(-0.376217\pi\)
0.379147 + 0.925336i \(0.376217\pi\)
\(588\) 0 0
\(589\) 16.4896 0.679444
\(590\) 12.1708 0.501062
\(591\) 0 0
\(592\) −24.2409 −0.996293
\(593\) −13.8208 −0.567551 −0.283775 0.958891i \(-0.591587\pi\)
−0.283775 + 0.958891i \(0.591587\pi\)
\(594\) 0 0
\(595\) −22.3064 −0.914475
\(596\) −15.3272 −0.627826
\(597\) 0 0
\(598\) 12.1048 0.495001
\(599\) 8.24086 0.336713 0.168356 0.985726i \(-0.446154\pi\)
0.168356 + 0.985726i \(0.446154\pi\)
\(600\) 0 0
\(601\) −8.75123 −0.356970 −0.178485 0.983943i \(-0.557120\pi\)
−0.178485 + 0.983943i \(0.557120\pi\)
\(602\) −3.51432 −0.143233
\(603\) 0 0
\(604\) −26.7961 −1.09032
\(605\) 2.67282 0.108666
\(606\) 0 0
\(607\) 25.4504 1.03300 0.516501 0.856287i \(-0.327234\pi\)
0.516501 + 0.856287i \(0.327234\pi\)
\(608\) 19.1546 0.776820
\(609\) 0 0
\(610\) 7.89256 0.319560
\(611\) −44.3434 −1.79394
\(612\) 0 0
\(613\) 18.7512 0.757355 0.378678 0.925529i \(-0.376379\pi\)
0.378678 + 0.925529i \(0.376379\pi\)
\(614\) −1.74671 −0.0704914
\(615\) 0 0
\(616\) 5.40332 0.217706
\(617\) −2.34791 −0.0945232 −0.0472616 0.998883i \(-0.515049\pi\)
−0.0472616 + 0.998883i \(0.515049\pi\)
\(618\) 0 0
\(619\) 3.85375 0.154895 0.0774477 0.996996i \(-0.475323\pi\)
0.0774477 + 0.996996i \(0.475323\pi\)
\(620\) −20.8930 −0.839081
\(621\) 0 0
\(622\) 6.30249 0.252707
\(623\) 35.0656 1.40487
\(624\) 0 0
\(625\) −31.1233 −1.24493
\(626\) −3.22239 −0.128793
\(627\) 0 0
\(628\) 4.68113 0.186797
\(629\) 36.6873 1.46282
\(630\) 0 0
\(631\) 16.5081 0.657177 0.328589 0.944473i \(-0.393427\pi\)
0.328589 + 0.944473i \(0.393427\pi\)
\(632\) 25.0757 0.997460
\(633\) 0 0
\(634\) −16.2510 −0.645411
\(635\) 47.6212 1.88979
\(636\) 0 0
\(637\) −1.79834 −0.0712528
\(638\) 3.38485 0.134008
\(639\) 0 0
\(640\) −30.8251 −1.21847
\(641\) −8.34791 −0.329723 −0.164861 0.986317i \(-0.552718\pi\)
−0.164861 + 0.986317i \(0.552718\pi\)
\(642\) 0 0
\(643\) 15.4689 0.610034 0.305017 0.952347i \(-0.401338\pi\)
0.305017 + 0.952347i \(0.401338\pi\)
\(644\) −19.4853 −0.767828
\(645\) 0 0
\(646\) −6.54957 −0.257689
\(647\) −23.4610 −0.922347 −0.461173 0.887310i \(-0.652571\pi\)
−0.461173 + 0.887310i \(0.652571\pi\)
\(648\) 0 0
\(649\) −7.96080 −0.312489
\(650\) 5.73050 0.224769
\(651\) 0 0
\(652\) −8.46060 −0.331343
\(653\) −16.5759 −0.648667 −0.324333 0.945943i \(-0.605140\pi\)
−0.324333 + 0.945943i \(0.605140\pi\)
\(654\) 0 0
\(655\) 11.2303 0.438804
\(656\) −15.1400 −0.591119
\(657\) 0 0
\(658\) −13.9608 −0.544249
\(659\) −41.7305 −1.62559 −0.812795 0.582550i \(-0.802055\pi\)
−0.812795 + 0.582550i \(0.802055\pi\)
\(660\) 0 0
\(661\) 27.5266 1.07066 0.535330 0.844643i \(-0.320187\pi\)
0.535330 + 0.844643i \(0.320187\pi\)
\(662\) −17.7305 −0.689115
\(663\) 0 0
\(664\) −29.4504 −1.14290
\(665\) 24.2589 0.940721
\(666\) 0 0
\(667\) −26.8000 −1.03770
\(668\) 16.1462 0.624717
\(669\) 0 0
\(670\) 2.46930 0.0953974
\(671\) −5.16246 −0.199294
\(672\) 0 0
\(673\) 8.22013 0.316863 0.158431 0.987370i \(-0.449356\pi\)
0.158431 + 0.987370i \(0.449356\pi\)
\(674\) 4.26160 0.164151
\(675\) 0 0
\(676\) −14.7799 −0.568456
\(677\) 15.9546 0.613184 0.306592 0.951841i \(-0.400811\pi\)
0.306592 + 0.951841i \(0.400811\pi\)
\(678\) 0 0
\(679\) −32.0224 −1.22891
\(680\) 18.2201 0.698710
\(681\) 0 0
\(682\) −2.67282 −0.102348
\(683\) 9.37429 0.358697 0.179349 0.983786i \(-0.442601\pi\)
0.179349 + 0.983786i \(0.442601\pi\)
\(684\) 0 0
\(685\) −1.30871 −0.0500031
\(686\) −10.8643 −0.414802
\(687\) 0 0
\(688\) −5.12156 −0.195258
\(689\) −47.6706 −1.81610
\(690\) 0 0
\(691\) −22.6050 −0.859934 −0.429967 0.902845i \(-0.641475\pi\)
−0.429967 + 0.902845i \(0.641475\pi\)
\(692\) −34.9326 −1.32794
\(693\) 0 0
\(694\) 11.9506 0.453640
\(695\) −10.1911 −0.386570
\(696\) 0 0
\(697\) 22.9137 0.867918
\(698\) −15.3932 −0.582640
\(699\) 0 0
\(700\) −9.22448 −0.348653
\(701\) 38.2162 1.44341 0.721703 0.692203i \(-0.243360\pi\)
0.721703 + 0.692203i \(0.243360\pi\)
\(702\) 0 0
\(703\) −39.8986 −1.50480
\(704\) 1.18319 0.0445931
\(705\) 0 0
\(706\) 6.76970 0.254781
\(707\) 23.7776 0.894249
\(708\) 0 0
\(709\) 31.8824 1.19737 0.598684 0.800985i \(-0.295690\pi\)
0.598684 + 0.800985i \(0.295690\pi\)
\(710\) −15.5967 −0.585333
\(711\) 0 0
\(712\) −28.6419 −1.07340
\(713\) 21.1625 0.792540
\(714\) 0 0
\(715\) −12.4896 −0.467086
\(716\) 9.31435 0.348094
\(717\) 0 0
\(718\) 1.62306 0.0605719
\(719\) 21.4320 0.799277 0.399639 0.916673i \(-0.369136\pi\)
0.399639 + 0.916673i \(0.369136\pi\)
\(720\) 0 0
\(721\) 21.5658 0.803152
\(722\) −3.74502 −0.139375
\(723\) 0 0
\(724\) 44.7463 1.66298
\(725\) −12.6873 −0.471196
\(726\) 0 0
\(727\) 6.19110 0.229615 0.114808 0.993388i \(-0.463375\pi\)
0.114808 + 0.993388i \(0.463375\pi\)
\(728\) −25.2488 −0.935782
\(729\) 0 0
\(730\) 12.9793 0.480384
\(731\) 7.75123 0.286690
\(732\) 0 0
\(733\) −11.7384 −0.433568 −0.216784 0.976220i \(-0.569557\pi\)
−0.216784 + 0.976220i \(0.569557\pi\)
\(734\) 2.98717 0.110259
\(735\) 0 0
\(736\) 24.5826 0.906125
\(737\) −1.61515 −0.0594948
\(738\) 0 0
\(739\) −28.1378 −1.03506 −0.517532 0.855664i \(-0.673149\pi\)
−0.517532 + 0.855664i \(0.673149\pi\)
\(740\) 50.5530 1.85836
\(741\) 0 0
\(742\) −15.0083 −0.550972
\(743\) −14.0784 −0.516487 −0.258243 0.966080i \(-0.583144\pi\)
−0.258243 + 0.966080i \(0.583144\pi\)
\(744\) 0 0
\(745\) 24.4896 0.897231
\(746\) 19.6442 0.719225
\(747\) 0 0
\(748\) −5.42801 −0.198468
\(749\) −40.6807 −1.48644
\(750\) 0 0
\(751\) 19.7753 0.721613 0.360806 0.932641i \(-0.382502\pi\)
0.360806 + 0.932641i \(0.382502\pi\)
\(752\) −20.3456 −0.741929
\(753\) 0 0
\(754\) −15.8168 −0.576014
\(755\) 42.8145 1.55818
\(756\) 0 0
\(757\) 1.73276 0.0629782 0.0314891 0.999504i \(-0.489975\pi\)
0.0314891 + 0.999504i \(0.489975\pi\)
\(758\) −17.8247 −0.647423
\(759\) 0 0
\(760\) −19.8149 −0.718764
\(761\) −29.6151 −1.07355 −0.536774 0.843726i \(-0.680357\pi\)
−0.536774 + 0.843726i \(0.680357\pi\)
\(762\) 0 0
\(763\) −13.2303 −0.478969
\(764\) −14.2363 −0.515053
\(765\) 0 0
\(766\) 8.45269 0.305408
\(767\) 37.1994 1.34319
\(768\) 0 0
\(769\) −8.90086 −0.320973 −0.160487 0.987038i \(-0.551306\pi\)
−0.160487 + 0.987038i \(0.551306\pi\)
\(770\) −3.93216 −0.141705
\(771\) 0 0
\(772\) 9.24877 0.332871
\(773\) 33.3227 1.19853 0.599266 0.800550i \(-0.295459\pi\)
0.599266 + 0.800550i \(0.295459\pi\)
\(774\) 0 0
\(775\) 10.0185 0.359874
\(776\) 26.1562 0.938954
\(777\) 0 0
\(778\) 0.934420 0.0335006
\(779\) −24.9193 −0.892828
\(780\) 0 0
\(781\) 10.2017 0.365044
\(782\) −8.40558 −0.300583
\(783\) 0 0
\(784\) −0.825115 −0.0294684
\(785\) −7.47947 −0.266954
\(786\) 0 0
\(787\) −28.3355 −1.01005 −0.505025 0.863104i \(-0.668517\pi\)
−0.505025 + 0.863104i \(0.668517\pi\)
\(788\) −25.0511 −0.892407
\(789\) 0 0
\(790\) −18.2484 −0.649248
\(791\) −21.0471 −0.748349
\(792\) 0 0
\(793\) 24.1233 0.856642
\(794\) 6.81907 0.242000
\(795\) 0 0
\(796\) −0.162059 −0.00574403
\(797\) 13.5288 0.479216 0.239608 0.970870i \(-0.422981\pi\)
0.239608 + 0.970870i \(0.422981\pi\)
\(798\) 0 0
\(799\) 30.7921 1.08935
\(800\) 11.6376 0.411450
\(801\) 0 0
\(802\) 9.82738 0.347017
\(803\) −8.48963 −0.299593
\(804\) 0 0
\(805\) 31.1334 1.09731
\(806\) 12.4896 0.439929
\(807\) 0 0
\(808\) −19.4218 −0.683256
\(809\) 39.1849 1.37767 0.688834 0.724920i \(-0.258123\pi\)
0.688834 + 0.724920i \(0.258123\pi\)
\(810\) 0 0
\(811\) −11.2263 −0.394210 −0.197105 0.980382i \(-0.563154\pi\)
−0.197105 + 0.980382i \(0.563154\pi\)
\(812\) 25.4606 0.893492
\(813\) 0 0
\(814\) 6.46721 0.226676
\(815\) 13.5183 0.473524
\(816\) 0 0
\(817\) −8.42970 −0.294918
\(818\) 19.3042 0.674955
\(819\) 0 0
\(820\) 31.5737 1.10260
\(821\) 16.8291 0.587339 0.293669 0.955907i \(-0.405124\pi\)
0.293669 + 0.955907i \(0.405124\pi\)
\(822\) 0 0
\(823\) 26.0448 0.907866 0.453933 0.891036i \(-0.350020\pi\)
0.453933 + 0.891036i \(0.350020\pi\)
\(824\) −17.6151 −0.613653
\(825\) 0 0
\(826\) 11.7116 0.407500
\(827\) −50.0139 −1.73916 −0.869578 0.493796i \(-0.835609\pi\)
−0.869578 + 0.493796i \(0.835609\pi\)
\(828\) 0 0
\(829\) −9.99774 −0.347236 −0.173618 0.984813i \(-0.555546\pi\)
−0.173618 + 0.984813i \(0.555546\pi\)
\(830\) 21.4320 0.743914
\(831\) 0 0
\(832\) −5.52884 −0.191678
\(833\) 1.24877 0.0432673
\(834\) 0 0
\(835\) −25.7983 −0.892788
\(836\) 5.90312 0.204164
\(837\) 0 0
\(838\) 4.52658 0.156368
\(839\) −28.4583 −0.982491 −0.491245 0.871021i \(-0.663458\pi\)
−0.491245 + 0.871021i \(0.663458\pi\)
\(840\) 0 0
\(841\) 6.01847 0.207533
\(842\) 5.63757 0.194284
\(843\) 0 0
\(844\) −13.7133 −0.472032
\(845\) 23.6151 0.812386
\(846\) 0 0
\(847\) 2.57199 0.0883747
\(848\) −21.8722 −0.751095
\(849\) 0 0
\(850\) −3.97927 −0.136488
\(851\) −51.2050 −1.75529
\(852\) 0 0
\(853\) −2.20166 −0.0753834 −0.0376917 0.999289i \(-0.512000\pi\)
−0.0376917 + 0.999289i \(0.512000\pi\)
\(854\) 7.59482 0.259889
\(855\) 0 0
\(856\) 33.2284 1.13572
\(857\) 24.1272 0.824170 0.412085 0.911145i \(-0.364801\pi\)
0.412085 + 0.911145i \(0.364801\pi\)
\(858\) 0 0
\(859\) −12.6728 −0.432391 −0.216196 0.976350i \(-0.569365\pi\)
−0.216196 + 0.976350i \(0.569365\pi\)
\(860\) 10.6807 0.364210
\(861\) 0 0
\(862\) 9.88731 0.336763
\(863\) −28.2488 −0.961599 −0.480800 0.876830i \(-0.659654\pi\)
−0.480800 + 0.876830i \(0.659654\pi\)
\(864\) 0 0
\(865\) 55.8149 1.89777
\(866\) 13.4676 0.457648
\(867\) 0 0
\(868\) −20.1048 −0.682401
\(869\) 11.9361 0.404905
\(870\) 0 0
\(871\) 7.54731 0.255731
\(872\) 10.8066 0.365959
\(873\) 0 0
\(874\) 9.14133 0.309210
\(875\) −19.6336 −0.663738
\(876\) 0 0
\(877\) 3.23820 0.109346 0.0546732 0.998504i \(-0.482588\pi\)
0.0546732 + 0.998504i \(0.482588\pi\)
\(878\) 0.222393 0.00750540
\(879\) 0 0
\(880\) −5.73050 −0.193175
\(881\) 8.29854 0.279585 0.139792 0.990181i \(-0.455356\pi\)
0.139792 + 0.990181i \(0.455356\pi\)
\(882\) 0 0
\(883\) 28.9872 0.975496 0.487748 0.872984i \(-0.337818\pi\)
0.487748 + 0.872984i \(0.337818\pi\)
\(884\) 25.3641 0.853088
\(885\) 0 0
\(886\) −7.86432 −0.264207
\(887\) 30.5002 1.02410 0.512048 0.858957i \(-0.328887\pi\)
0.512048 + 0.858957i \(0.328887\pi\)
\(888\) 0 0
\(889\) 45.8247 1.53691
\(890\) 20.8436 0.698679
\(891\) 0 0
\(892\) 6.24047 0.208946
\(893\) −33.4874 −1.12061
\(894\) 0 0
\(895\) −14.8824 −0.497463
\(896\) −29.6623 −0.990947
\(897\) 0 0
\(898\) 21.7181 0.724741
\(899\) −27.6521 −0.922249
\(900\) 0 0
\(901\) 33.1025 1.10280
\(902\) 4.03920 0.134491
\(903\) 0 0
\(904\) 17.1915 0.571781
\(905\) −71.4953 −2.37658
\(906\) 0 0
\(907\) 11.9322 0.396201 0.198100 0.980182i \(-0.436523\pi\)
0.198100 + 0.980182i \(0.436523\pi\)
\(908\) −30.7546 −1.02063
\(909\) 0 0
\(910\) 18.3743 0.609102
\(911\) 15.4403 0.511559 0.255779 0.966735i \(-0.417668\pi\)
0.255779 + 0.966735i \(0.417668\pi\)
\(912\) 0 0
\(913\) −14.0185 −0.463944
\(914\) −10.1462 −0.335608
\(915\) 0 0
\(916\) 46.0162 1.52042
\(917\) 10.8066 0.356867
\(918\) 0 0
\(919\) −26.3289 −0.868509 −0.434255 0.900790i \(-0.642988\pi\)
−0.434255 + 0.900790i \(0.642988\pi\)
\(920\) −25.4301 −0.838405
\(921\) 0 0
\(922\) −15.3227 −0.504625
\(923\) −47.6706 −1.56910
\(924\) 0 0
\(925\) −24.2409 −0.797035
\(926\) 20.0528 0.658974
\(927\) 0 0
\(928\) −32.1210 −1.05442
\(929\) 43.3747 1.42308 0.711539 0.702647i \(-0.247999\pi\)
0.711539 + 0.702647i \(0.247999\pi\)
\(930\) 0 0
\(931\) −1.35808 −0.0445091
\(932\) −9.39315 −0.307683
\(933\) 0 0
\(934\) 9.19997 0.301032
\(935\) 8.67282 0.283632
\(936\) 0 0
\(937\) 26.0554 0.851193 0.425597 0.904913i \(-0.360064\pi\)
0.425597 + 0.904913i \(0.360064\pi\)
\(938\) 2.37615 0.0775840
\(939\) 0 0
\(940\) 42.4297 1.38390
\(941\) −26.2505 −0.855741 −0.427870 0.903840i \(-0.640736\pi\)
−0.427870 + 0.903840i \(0.640736\pi\)
\(942\) 0 0
\(943\) −31.9810 −1.04144
\(944\) 17.0678 0.555511
\(945\) 0 0
\(946\) 1.36638 0.0444248
\(947\) −9.10252 −0.295792 −0.147896 0.989003i \(-0.547250\pi\)
−0.147896 + 0.989003i \(0.547250\pi\)
\(948\) 0 0
\(949\) 39.6706 1.28776
\(950\) 4.32757 0.140405
\(951\) 0 0
\(952\) 17.5328 0.568241
\(953\) 28.3888 0.919604 0.459802 0.888022i \(-0.347920\pi\)
0.459802 + 0.888022i \(0.347920\pi\)
\(954\) 0 0
\(955\) 22.7467 0.736066
\(956\) 29.1915 0.944120
\(957\) 0 0
\(958\) −24.2096 −0.782176
\(959\) −1.25934 −0.0406661
\(960\) 0 0
\(961\) −9.16472 −0.295636
\(962\) −30.2201 −0.974336
\(963\) 0 0
\(964\) 0.131160 0.00422438
\(965\) −14.7776 −0.475708
\(966\) 0 0
\(967\) 48.2241 1.55078 0.775391 0.631481i \(-0.217553\pi\)
0.775391 + 0.631481i \(0.217553\pi\)
\(968\) −2.10083 −0.0675232
\(969\) 0 0
\(970\) −19.0347 −0.611167
\(971\) −19.0946 −0.612775 −0.306388 0.951907i \(-0.599120\pi\)
−0.306388 + 0.951907i \(0.599120\pi\)
\(972\) 0 0
\(973\) −9.80664 −0.314387
\(974\) 13.9374 0.446583
\(975\) 0 0
\(976\) 11.0682 0.354286
\(977\) 14.4033 0.460803 0.230402 0.973096i \(-0.425996\pi\)
0.230402 + 0.973096i \(0.425996\pi\)
\(978\) 0 0
\(979\) −13.6336 −0.435732
\(980\) 1.72073 0.0549667
\(981\) 0 0
\(982\) 13.0735 0.417192
\(983\) 22.1312 0.705874 0.352937 0.935647i \(-0.385183\pi\)
0.352937 + 0.935647i \(0.385183\pi\)
\(984\) 0 0
\(985\) 40.0264 1.27535
\(986\) 10.9832 0.349777
\(987\) 0 0
\(988\) −27.5843 −0.877572
\(989\) −10.8185 −0.344008
\(990\) 0 0
\(991\) −49.3826 −1.56869 −0.784345 0.620325i \(-0.787001\pi\)
−0.784345 + 0.620325i \(0.787001\pi\)
\(992\) 25.3641 0.805312
\(993\) 0 0
\(994\) −15.0083 −0.476035
\(995\) 0.258937 0.00820884
\(996\) 0 0
\(997\) −20.7361 −0.656720 −0.328360 0.944553i \(-0.606496\pi\)
−0.328360 + 0.944553i \(0.606496\pi\)
\(998\) 12.0599 0.381751
\(999\) 0 0
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 297.2.a.h.1.2 yes 3
3.2 odd 2 297.2.a.g.1.2 3
4.3 odd 2 4752.2.a.bg.1.3 3
5.4 even 2 7425.2.a.bm.1.2 3
9.2 odd 6 891.2.e.t.595.2 6
9.4 even 3 891.2.e.q.298.2 6
9.5 odd 6 891.2.e.t.298.2 6
9.7 even 3 891.2.e.q.595.2 6
11.10 odd 2 3267.2.a.t.1.2 3
12.11 even 2 4752.2.a.bo.1.1 3
15.14 odd 2 7425.2.a.bn.1.2 3
33.32 even 2 3267.2.a.w.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
297.2.a.g.1.2 3 3.2 odd 2
297.2.a.h.1.2 yes 3 1.1 even 1 trivial
891.2.e.q.298.2 6 9.4 even 3
891.2.e.q.595.2 6 9.7 even 3
891.2.e.t.298.2 6 9.5 odd 6
891.2.e.t.595.2 6 9.2 odd 6
3267.2.a.t.1.2 3 11.10 odd 2
3267.2.a.w.1.2 3 33.32 even 2
4752.2.a.bg.1.3 3 4.3 odd 2
4752.2.a.bo.1.1 3 12.11 even 2
7425.2.a.bm.1.2 3 5.4 even 2
7425.2.a.bn.1.2 3 15.14 odd 2