Properties

Label 9801.2.a.bx.1.6
Level $9801$
Weight $2$
Character 9801.1
Self dual yes
Analytic conductor $78.261$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [9801,2,Mod(1,9801)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(9801, 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("9801.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 9801 = 3^{4} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 9801.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: \(78.2613790211\)
Analytic rank: \(0\)
Dimension: \(8\)
Coefficient field: 8.8.287107358976.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 15x^{6} + 74x^{4} - 147x^{2} + 100 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Root \(1.23950\) of defining polynomial
Character \(\chi\) \(=\) 9801.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.683225 q^{2} -1.53320 q^{4} +2.18081 q^{5} -3.85674 q^{7} -2.41397 q^{8} +O(q^{10})\) \(q+0.683225 q^{2} -1.53320 q^{4} +2.18081 q^{5} -3.85674 q^{7} -2.41397 q^{8} +1.48998 q^{10} -5.99921 q^{13} -2.63502 q^{14} +1.41712 q^{16} -3.16675 q^{17} +0.530894 q^{19} -3.34363 q^{20} -7.02266 q^{23} -0.244069 q^{25} -4.09881 q^{26} +5.91317 q^{28} +7.62725 q^{29} +0.516471 q^{31} +5.79616 q^{32} -2.16361 q^{34} -8.41082 q^{35} -5.72760 q^{37} +0.362720 q^{38} -5.26441 q^{40} -3.61052 q^{41} -10.9656 q^{43} -4.79806 q^{46} +12.8275 q^{47} +7.87447 q^{49} -0.166754 q^{50} +9.19802 q^{52} -8.02009 q^{53} +9.31007 q^{56} +5.21113 q^{58} +10.6467 q^{59} -4.57377 q^{61} +0.352866 q^{62} +1.12584 q^{64} -13.0831 q^{65} -2.38633 q^{67} +4.85528 q^{68} -5.74648 q^{70} -2.94145 q^{71} -11.4664 q^{73} -3.91324 q^{74} -0.813969 q^{76} +0.254390 q^{79} +3.09047 q^{80} -2.46680 q^{82} +6.81919 q^{83} -6.90609 q^{85} -7.49198 q^{86} +15.5570 q^{89} +23.1374 q^{91} +10.7672 q^{92} +8.76407 q^{94} +1.15778 q^{95} -6.45274 q^{97} +5.38003 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 12 q^{4} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 12 q^{4} - 18 q^{8} + 52 q^{16} - 12 q^{17} + 28 q^{25} - 12 q^{29} + 12 q^{31} - 66 q^{32} + 38 q^{34} - 24 q^{35} - 8 q^{37} + 12 q^{41} + 2 q^{49} + 12 q^{50} - 4 q^{58} + 66 q^{62} + 70 q^{64} - 24 q^{65} - 18 q^{67} + 36 q^{68} + 50 q^{70} + 78 q^{74} - 44 q^{82} - 6 q^{83} + 36 q^{91} + 18 q^{95} - 2 q^{97} - 42 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.683225 0.483113 0.241556 0.970387i \(-0.422342\pi\)
0.241556 + 0.970387i \(0.422342\pi\)
\(3\) 0 0
\(4\) −1.53320 −0.766602
\(5\) 2.18081 0.975288 0.487644 0.873043i \(-0.337856\pi\)
0.487644 + 0.873043i \(0.337856\pi\)
\(6\) 0 0
\(7\) −3.85674 −1.45771 −0.728856 0.684667i \(-0.759948\pi\)
−0.728856 + 0.684667i \(0.759948\pi\)
\(8\) −2.41397 −0.853468
\(9\) 0 0
\(10\) 1.48998 0.471174
\(11\) 0 0
\(12\) 0 0
\(13\) −5.99921 −1.66388 −0.831941 0.554864i \(-0.812770\pi\)
−0.831941 + 0.554864i \(0.812770\pi\)
\(14\) −2.63502 −0.704239
\(15\) 0 0
\(16\) 1.41712 0.354280
\(17\) −3.16675 −0.768051 −0.384025 0.923323i \(-0.625462\pi\)
−0.384025 + 0.923323i \(0.625462\pi\)
\(18\) 0 0
\(19\) 0.530894 0.121795 0.0608977 0.998144i \(-0.480604\pi\)
0.0608977 + 0.998144i \(0.480604\pi\)
\(20\) −3.34363 −0.747657
\(21\) 0 0
\(22\) 0 0
\(23\) −7.02266 −1.46433 −0.732163 0.681129i \(-0.761489\pi\)
−0.732163 + 0.681129i \(0.761489\pi\)
\(24\) 0 0
\(25\) −0.244069 −0.0488139
\(26\) −4.09881 −0.803843
\(27\) 0 0
\(28\) 5.91317 1.11748
\(29\) 7.62725 1.41635 0.708173 0.706039i \(-0.249520\pi\)
0.708173 + 0.706039i \(0.249520\pi\)
\(30\) 0 0
\(31\) 0.516471 0.0927609 0.0463804 0.998924i \(-0.485231\pi\)
0.0463804 + 0.998924i \(0.485231\pi\)
\(32\) 5.79616 1.02463
\(33\) 0 0
\(34\) −2.16361 −0.371055
\(35\) −8.41082 −1.42169
\(36\) 0 0
\(37\) −5.72760 −0.941611 −0.470806 0.882237i \(-0.656037\pi\)
−0.470806 + 0.882237i \(0.656037\pi\)
\(38\) 0.362720 0.0588410
\(39\) 0 0
\(40\) −5.26441 −0.832377
\(41\) −3.61052 −0.563868 −0.281934 0.959434i \(-0.590976\pi\)
−0.281934 + 0.959434i \(0.590976\pi\)
\(42\) 0 0
\(43\) −10.9656 −1.67224 −0.836121 0.548546i \(-0.815182\pi\)
−0.836121 + 0.548546i \(0.815182\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −4.79806 −0.707435
\(47\) 12.8275 1.87108 0.935542 0.353216i \(-0.114912\pi\)
0.935542 + 0.353216i \(0.114912\pi\)
\(48\) 0 0
\(49\) 7.87447 1.12492
\(50\) −0.166754 −0.0235826
\(51\) 0 0
\(52\) 9.19802 1.27554
\(53\) −8.02009 −1.10164 −0.550822 0.834623i \(-0.685686\pi\)
−0.550822 + 0.834623i \(0.685686\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 9.31007 1.24411
\(57\) 0 0
\(58\) 5.21113 0.684255
\(59\) 10.6467 1.38608 0.693041 0.720898i \(-0.256271\pi\)
0.693041 + 0.720898i \(0.256271\pi\)
\(60\) 0 0
\(61\) −4.57377 −0.585611 −0.292805 0.956172i \(-0.594589\pi\)
−0.292805 + 0.956172i \(0.594589\pi\)
\(62\) 0.352866 0.0448140
\(63\) 0 0
\(64\) 1.12584 0.140729
\(65\) −13.0831 −1.62276
\(66\) 0 0
\(67\) −2.38633 −0.291537 −0.145768 0.989319i \(-0.546565\pi\)
−0.145768 + 0.989319i \(0.546565\pi\)
\(68\) 4.85528 0.588789
\(69\) 0 0
\(70\) −5.74648 −0.686836
\(71\) −2.94145 −0.349086 −0.174543 0.984650i \(-0.555845\pi\)
−0.174543 + 0.984650i \(0.555845\pi\)
\(72\) 0 0
\(73\) −11.4664 −1.34204 −0.671021 0.741438i \(-0.734144\pi\)
−0.671021 + 0.741438i \(0.734144\pi\)
\(74\) −3.91324 −0.454905
\(75\) 0 0
\(76\) −0.813969 −0.0933687
\(77\) 0 0
\(78\) 0 0
\(79\) 0.254390 0.0286211 0.0143105 0.999898i \(-0.495445\pi\)
0.0143105 + 0.999898i \(0.495445\pi\)
\(80\) 3.09047 0.345525
\(81\) 0 0
\(82\) −2.46680 −0.272412
\(83\) 6.81919 0.748503 0.374252 0.927327i \(-0.377900\pi\)
0.374252 + 0.927327i \(0.377900\pi\)
\(84\) 0 0
\(85\) −6.90609 −0.749070
\(86\) −7.49198 −0.807881
\(87\) 0 0
\(88\) 0 0
\(89\) 15.5570 1.64904 0.824519 0.565835i \(-0.191446\pi\)
0.824519 + 0.565835i \(0.191446\pi\)
\(90\) 0 0
\(91\) 23.1374 2.42546
\(92\) 10.7672 1.12256
\(93\) 0 0
\(94\) 8.76407 0.903945
\(95\) 1.15778 0.118786
\(96\) 0 0
\(97\) −6.45274 −0.655176 −0.327588 0.944821i \(-0.606236\pi\)
−0.327588 + 0.944821i \(0.606236\pi\)
\(98\) 5.38003 0.543465
\(99\) 0 0
\(100\) 0.374208 0.0374208
\(101\) −0.974817 −0.0969979 −0.0484990 0.998823i \(-0.515444\pi\)
−0.0484990 + 0.998823i \(0.515444\pi\)
\(102\) 0 0
\(103\) 1.33666 0.131705 0.0658524 0.997829i \(-0.479023\pi\)
0.0658524 + 0.997829i \(0.479023\pi\)
\(104\) 14.4819 1.42007
\(105\) 0 0
\(106\) −5.47952 −0.532218
\(107\) 3.00315 0.290325 0.145163 0.989408i \(-0.453629\pi\)
0.145163 + 0.989408i \(0.453629\pi\)
\(108\) 0 0
\(109\) 1.34628 0.128950 0.0644750 0.997919i \(-0.479463\pi\)
0.0644750 + 0.997919i \(0.479463\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −5.46547 −0.516439
\(113\) 15.4625 1.45459 0.727296 0.686324i \(-0.240777\pi\)
0.727296 + 0.686324i \(0.240777\pi\)
\(114\) 0 0
\(115\) −15.3151 −1.42814
\(116\) −11.6941 −1.08577
\(117\) 0 0
\(118\) 7.27409 0.669634
\(119\) 12.2134 1.11960
\(120\) 0 0
\(121\) 0 0
\(122\) −3.12491 −0.282916
\(123\) 0 0
\(124\) −0.791855 −0.0711107
\(125\) −11.4363 −1.02290
\(126\) 0 0
\(127\) −5.73937 −0.509287 −0.254643 0.967035i \(-0.581958\pi\)
−0.254643 + 0.967035i \(0.581958\pi\)
\(128\) −10.8231 −0.956637
\(129\) 0 0
\(130\) −8.93873 −0.783978
\(131\) 10.9916 0.960336 0.480168 0.877176i \(-0.340576\pi\)
0.480168 + 0.877176i \(0.340576\pi\)
\(132\) 0 0
\(133\) −2.04752 −0.177543
\(134\) −1.63040 −0.140845
\(135\) 0 0
\(136\) 7.64446 0.655507
\(137\) 18.2126 1.55600 0.778002 0.628261i \(-0.216233\pi\)
0.778002 + 0.628261i \(0.216233\pi\)
\(138\) 0 0
\(139\) −20.6108 −1.74819 −0.874093 0.485759i \(-0.838543\pi\)
−0.874093 + 0.485759i \(0.838543\pi\)
\(140\) 12.8955 1.08987
\(141\) 0 0
\(142\) −2.00967 −0.168648
\(143\) 0 0
\(144\) 0 0
\(145\) 16.6336 1.38134
\(146\) −7.83414 −0.648358
\(147\) 0 0
\(148\) 8.78158 0.721841
\(149\) 4.28383 0.350945 0.175473 0.984484i \(-0.443855\pi\)
0.175473 + 0.984484i \(0.443855\pi\)
\(150\) 0 0
\(151\) 11.1954 0.911066 0.455533 0.890219i \(-0.349449\pi\)
0.455533 + 0.890219i \(0.349449\pi\)
\(152\) −1.28156 −0.103949
\(153\) 0 0
\(154\) 0 0
\(155\) 1.12632 0.0904685
\(156\) 0 0
\(157\) 7.31048 0.583440 0.291720 0.956504i \(-0.405773\pi\)
0.291720 + 0.956504i \(0.405773\pi\)
\(158\) 0.173805 0.0138272
\(159\) 0 0
\(160\) 12.6403 0.999305
\(161\) 27.0846 2.13457
\(162\) 0 0
\(163\) −21.9125 −1.71632 −0.858162 0.513380i \(-0.828393\pi\)
−0.858162 + 0.513380i \(0.828393\pi\)
\(164\) 5.53566 0.432263
\(165\) 0 0
\(166\) 4.65904 0.361612
\(167\) 7.22104 0.558781 0.279390 0.960178i \(-0.409868\pi\)
0.279390 + 0.960178i \(0.409868\pi\)
\(168\) 0 0
\(169\) 22.9906 1.76850
\(170\) −4.71841 −0.361886
\(171\) 0 0
\(172\) 16.8125 1.28194
\(173\) −2.40767 −0.183052 −0.0915260 0.995803i \(-0.529174\pi\)
−0.0915260 + 0.995803i \(0.529174\pi\)
\(174\) 0 0
\(175\) 0.941313 0.0711565
\(176\) 0 0
\(177\) 0 0
\(178\) 10.6289 0.796671
\(179\) −14.6200 −1.09275 −0.546375 0.837540i \(-0.683993\pi\)
−0.546375 + 0.837540i \(0.683993\pi\)
\(180\) 0 0
\(181\) 0.900651 0.0669449 0.0334724 0.999440i \(-0.489343\pi\)
0.0334724 + 0.999440i \(0.489343\pi\)
\(182\) 15.8081 1.17177
\(183\) 0 0
\(184\) 16.9525 1.24976
\(185\) −12.4908 −0.918342
\(186\) 0 0
\(187\) 0 0
\(188\) −19.6672 −1.43438
\(189\) 0 0
\(190\) 0.791024 0.0573869
\(191\) 8.05453 0.582805 0.291403 0.956601i \(-0.405878\pi\)
0.291403 + 0.956601i \(0.405878\pi\)
\(192\) 0 0
\(193\) −1.20116 −0.0864611 −0.0432306 0.999065i \(-0.513765\pi\)
−0.0432306 + 0.999065i \(0.513765\pi\)
\(194\) −4.40867 −0.316524
\(195\) 0 0
\(196\) −12.0732 −0.862369
\(197\) 25.9462 1.84859 0.924294 0.381680i \(-0.124655\pi\)
0.924294 + 0.381680i \(0.124655\pi\)
\(198\) 0 0
\(199\) −6.08775 −0.431549 −0.215775 0.976443i \(-0.569228\pi\)
−0.215775 + 0.976443i \(0.569228\pi\)
\(200\) 0.589177 0.0416611
\(201\) 0 0
\(202\) −0.666019 −0.0468609
\(203\) −29.4164 −2.06462
\(204\) 0 0
\(205\) −7.87385 −0.549934
\(206\) 0.913238 0.0636283
\(207\) 0 0
\(208\) −8.50161 −0.589481
\(209\) 0 0
\(210\) 0 0
\(211\) 8.93130 0.614856 0.307428 0.951571i \(-0.400532\pi\)
0.307428 + 0.951571i \(0.400532\pi\)
\(212\) 12.2964 0.844522
\(213\) 0 0
\(214\) 2.05183 0.140260
\(215\) −23.9139 −1.63092
\(216\) 0 0
\(217\) −1.99189 −0.135219
\(218\) 0.919810 0.0622974
\(219\) 0 0
\(220\) 0 0
\(221\) 18.9980 1.27795
\(222\) 0 0
\(223\) 26.5216 1.77602 0.888009 0.459826i \(-0.152088\pi\)
0.888009 + 0.459826i \(0.152088\pi\)
\(224\) −22.3543 −1.49361
\(225\) 0 0
\(226\) 10.5644 0.702732
\(227\) −2.55624 −0.169663 −0.0848316 0.996395i \(-0.527035\pi\)
−0.0848316 + 0.996395i \(0.527035\pi\)
\(228\) 0 0
\(229\) 22.2984 1.47352 0.736758 0.676156i \(-0.236356\pi\)
0.736758 + 0.676156i \(0.236356\pi\)
\(230\) −10.4636 −0.689952
\(231\) 0 0
\(232\) −18.4120 −1.20881
\(233\) 18.4651 1.20969 0.604845 0.796343i \(-0.293235\pi\)
0.604845 + 0.796343i \(0.293235\pi\)
\(234\) 0 0
\(235\) 27.9743 1.82485
\(236\) −16.3236 −1.06257
\(237\) 0 0
\(238\) 8.34447 0.540892
\(239\) −6.57973 −0.425607 −0.212804 0.977095i \(-0.568259\pi\)
−0.212804 + 0.977095i \(0.568259\pi\)
\(240\) 0 0
\(241\) 6.95830 0.448224 0.224112 0.974563i \(-0.428052\pi\)
0.224112 + 0.974563i \(0.428052\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 7.01251 0.448930
\(245\) 17.1727 1.09712
\(246\) 0 0
\(247\) −3.18495 −0.202653
\(248\) −1.24675 −0.0791684
\(249\) 0 0
\(250\) −7.81358 −0.494174
\(251\) −0.0914931 −0.00577500 −0.00288750 0.999996i \(-0.500919\pi\)
−0.00288750 + 0.999996i \(0.500919\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −3.92128 −0.246043
\(255\) 0 0
\(256\) −9.64629 −0.602893
\(257\) −11.0833 −0.691358 −0.345679 0.938353i \(-0.612351\pi\)
−0.345679 + 0.938353i \(0.612351\pi\)
\(258\) 0 0
\(259\) 22.0899 1.37260
\(260\) 20.0591 1.24401
\(261\) 0 0
\(262\) 7.50970 0.463951
\(263\) −12.5347 −0.772920 −0.386460 0.922306i \(-0.626302\pi\)
−0.386460 + 0.922306i \(0.626302\pi\)
\(264\) 0 0
\(265\) −17.4903 −1.07442
\(266\) −1.39892 −0.0857732
\(267\) 0 0
\(268\) 3.65873 0.223493
\(269\) −17.3696 −1.05904 −0.529522 0.848296i \(-0.677629\pi\)
−0.529522 + 0.848296i \(0.677629\pi\)
\(270\) 0 0
\(271\) −19.5849 −1.18970 −0.594848 0.803838i \(-0.702788\pi\)
−0.594848 + 0.803838i \(0.702788\pi\)
\(272\) −4.48768 −0.272105
\(273\) 0 0
\(274\) 12.4433 0.751726
\(275\) 0 0
\(276\) 0 0
\(277\) 28.2560 1.69774 0.848870 0.528601i \(-0.177283\pi\)
0.848870 + 0.528601i \(0.177283\pi\)
\(278\) −14.0818 −0.844571
\(279\) 0 0
\(280\) 20.3035 1.21337
\(281\) 7.89750 0.471125 0.235563 0.971859i \(-0.424307\pi\)
0.235563 + 0.971859i \(0.424307\pi\)
\(282\) 0 0
\(283\) −26.3792 −1.56808 −0.784039 0.620712i \(-0.786844\pi\)
−0.784039 + 0.620712i \(0.786844\pi\)
\(284\) 4.50984 0.267610
\(285\) 0 0
\(286\) 0 0
\(287\) 13.9248 0.821958
\(288\) 0 0
\(289\) −6.97167 −0.410098
\(290\) 11.3645 0.667345
\(291\) 0 0
\(292\) 17.5804 1.02881
\(293\) −14.8301 −0.866384 −0.433192 0.901302i \(-0.642613\pi\)
−0.433192 + 0.901302i \(0.642613\pi\)
\(294\) 0 0
\(295\) 23.2184 1.35183
\(296\) 13.8263 0.803635
\(297\) 0 0
\(298\) 2.92682 0.169546
\(299\) 42.1304 2.43647
\(300\) 0 0
\(301\) 42.2916 2.43765
\(302\) 7.64895 0.440148
\(303\) 0 0
\(304\) 0.752342 0.0431498
\(305\) −9.97451 −0.571139
\(306\) 0 0
\(307\) −4.86259 −0.277523 −0.138761 0.990326i \(-0.544312\pi\)
−0.138761 + 0.990326i \(0.544312\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.769533 0.0437065
\(311\) 15.2753 0.866182 0.433091 0.901350i \(-0.357423\pi\)
0.433091 + 0.901350i \(0.357423\pi\)
\(312\) 0 0
\(313\) 32.7228 1.84960 0.924800 0.380454i \(-0.124232\pi\)
0.924800 + 0.380454i \(0.124232\pi\)
\(314\) 4.99470 0.281867
\(315\) 0 0
\(316\) −0.390031 −0.0219410
\(317\) −3.08378 −0.173202 −0.0866012 0.996243i \(-0.527601\pi\)
−0.0866012 + 0.996243i \(0.527601\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 2.45523 0.137252
\(321\) 0 0
\(322\) 18.5049 1.03124
\(323\) −1.68121 −0.0935451
\(324\) 0 0
\(325\) 1.46422 0.0812205
\(326\) −14.9712 −0.829178
\(327\) 0 0
\(328\) 8.71569 0.481244
\(329\) −49.4724 −2.72750
\(330\) 0 0
\(331\) 27.1750 1.49367 0.746836 0.665008i \(-0.231572\pi\)
0.746836 + 0.665008i \(0.231572\pi\)
\(332\) −10.4552 −0.573804
\(333\) 0 0
\(334\) 4.93359 0.269954
\(335\) −5.20414 −0.284332
\(336\) 0 0
\(337\) −36.4605 −1.98613 −0.993066 0.117562i \(-0.962492\pi\)
−0.993066 + 0.117562i \(0.962492\pi\)
\(338\) 15.7077 0.854387
\(339\) 0 0
\(340\) 10.5884 0.574239
\(341\) 0 0
\(342\) 0 0
\(343\) −3.37261 −0.182104
\(344\) 26.4707 1.42720
\(345\) 0 0
\(346\) −1.64498 −0.0884348
\(347\) 18.6220 0.999679 0.499839 0.866118i \(-0.333392\pi\)
0.499839 + 0.866118i \(0.333392\pi\)
\(348\) 0 0
\(349\) −26.6433 −1.42618 −0.713090 0.701072i \(-0.752705\pi\)
−0.713090 + 0.701072i \(0.752705\pi\)
\(350\) 0.643128 0.0343766
\(351\) 0 0
\(352\) 0 0
\(353\) −18.9338 −1.00774 −0.503871 0.863779i \(-0.668091\pi\)
−0.503871 + 0.863779i \(0.668091\pi\)
\(354\) 0 0
\(355\) −6.41474 −0.340459
\(356\) −23.8520 −1.26415
\(357\) 0 0
\(358\) −9.98875 −0.527922
\(359\) 15.7915 0.833446 0.416723 0.909034i \(-0.363178\pi\)
0.416723 + 0.909034i \(0.363178\pi\)
\(360\) 0 0
\(361\) −18.7182 −0.985166
\(362\) 0.615347 0.0323419
\(363\) 0 0
\(364\) −35.4744 −1.85936
\(365\) −25.0061 −1.30888
\(366\) 0 0
\(367\) 4.63255 0.241817 0.120909 0.992664i \(-0.461419\pi\)
0.120909 + 0.992664i \(0.461419\pi\)
\(368\) −9.95196 −0.518782
\(369\) 0 0
\(370\) −8.53403 −0.443663
\(371\) 30.9314 1.60588
\(372\) 0 0
\(373\) −34.6192 −1.79251 −0.896257 0.443535i \(-0.853724\pi\)
−0.896257 + 0.443535i \(0.853724\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −30.9652 −1.59691
\(377\) −45.7575 −2.35663
\(378\) 0 0
\(379\) −4.42388 −0.227240 −0.113620 0.993524i \(-0.536245\pi\)
−0.113620 + 0.993524i \(0.536245\pi\)
\(380\) −1.77511 −0.0910613
\(381\) 0 0
\(382\) 5.50305 0.281561
\(383\) 27.5705 1.40879 0.704394 0.709809i \(-0.251219\pi\)
0.704394 + 0.709809i \(0.251219\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.820660 −0.0417705
\(387\) 0 0
\(388\) 9.89337 0.502260
\(389\) 20.0416 1.01615 0.508074 0.861313i \(-0.330358\pi\)
0.508074 + 0.861313i \(0.330358\pi\)
\(390\) 0 0
\(391\) 22.2390 1.12468
\(392\) −19.0088 −0.960087
\(393\) 0 0
\(394\) 17.7271 0.893077
\(395\) 0.554775 0.0279138
\(396\) 0 0
\(397\) −24.4787 −1.22855 −0.614275 0.789092i \(-0.710552\pi\)
−0.614275 + 0.789092i \(0.710552\pi\)
\(398\) −4.15930 −0.208487
\(399\) 0 0
\(400\) −0.345876 −0.0172938
\(401\) −15.4281 −0.770442 −0.385221 0.922824i \(-0.625875\pi\)
−0.385221 + 0.922824i \(0.625875\pi\)
\(402\) 0 0
\(403\) −3.09842 −0.154343
\(404\) 1.49459 0.0743588
\(405\) 0 0
\(406\) −20.0980 −0.997446
\(407\) 0 0
\(408\) 0 0
\(409\) 8.50534 0.420562 0.210281 0.977641i \(-0.432562\pi\)
0.210281 + 0.977641i \(0.432562\pi\)
\(410\) −5.37961 −0.265680
\(411\) 0 0
\(412\) −2.04937 −0.100965
\(413\) −41.0616 −2.02051
\(414\) 0 0
\(415\) 14.8714 0.730006
\(416\) −34.7724 −1.70486
\(417\) 0 0
\(418\) 0 0
\(419\) −11.2348 −0.548857 −0.274428 0.961608i \(-0.588489\pi\)
−0.274428 + 0.961608i \(0.588489\pi\)
\(420\) 0 0
\(421\) −23.6185 −1.15110 −0.575548 0.817768i \(-0.695211\pi\)
−0.575548 + 0.817768i \(0.695211\pi\)
\(422\) 6.10209 0.297045
\(423\) 0 0
\(424\) 19.3603 0.940218
\(425\) 0.772907 0.0374915
\(426\) 0 0
\(427\) 17.6398 0.853652
\(428\) −4.60444 −0.222564
\(429\) 0 0
\(430\) −16.3386 −0.787917
\(431\) −5.55985 −0.267808 −0.133904 0.990994i \(-0.542751\pi\)
−0.133904 + 0.990994i \(0.542751\pi\)
\(432\) 0 0
\(433\) 21.6137 1.03869 0.519343 0.854566i \(-0.326177\pi\)
0.519343 + 0.854566i \(0.326177\pi\)
\(434\) −1.36091 −0.0653259
\(435\) 0 0
\(436\) −2.06412 −0.0988532
\(437\) −3.72829 −0.178348
\(438\) 0 0
\(439\) 7.66239 0.365706 0.182853 0.983140i \(-0.441467\pi\)
0.182853 + 0.983140i \(0.441467\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.9799 0.617392
\(443\) 23.9011 1.13558 0.567788 0.823175i \(-0.307799\pi\)
0.567788 + 0.823175i \(0.307799\pi\)
\(444\) 0 0
\(445\) 33.9268 1.60829
\(446\) 18.1202 0.858017
\(447\) 0 0
\(448\) −4.34206 −0.205143
\(449\) 33.7817 1.59426 0.797129 0.603810i \(-0.206351\pi\)
0.797129 + 0.603810i \(0.206351\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −23.7072 −1.11509
\(453\) 0 0
\(454\) −1.74648 −0.0819665
\(455\) 50.4583 2.36552
\(456\) 0 0
\(457\) 9.92967 0.464491 0.232245 0.972657i \(-0.425393\pi\)
0.232245 + 0.972657i \(0.425393\pi\)
\(458\) 15.2348 0.711875
\(459\) 0 0
\(460\) 23.4811 1.09481
\(461\) −3.76269 −0.175246 −0.0876230 0.996154i \(-0.527927\pi\)
−0.0876230 + 0.996154i \(0.527927\pi\)
\(462\) 0 0
\(463\) 29.4887 1.37045 0.685227 0.728329i \(-0.259703\pi\)
0.685227 + 0.728329i \(0.259703\pi\)
\(464\) 10.8087 0.501783
\(465\) 0 0
\(466\) 12.6158 0.584417
\(467\) −12.2272 −0.565809 −0.282904 0.959148i \(-0.591298\pi\)
−0.282904 + 0.959148i \(0.591298\pi\)
\(468\) 0 0
\(469\) 9.20347 0.424977
\(470\) 19.1128 0.881606
\(471\) 0 0
\(472\) −25.7008 −1.18298
\(473\) 0 0
\(474\) 0 0
\(475\) −0.129575 −0.00594531
\(476\) −18.7256 −0.858285
\(477\) 0 0
\(478\) −4.49543 −0.205616
\(479\) 31.0255 1.41759 0.708795 0.705414i \(-0.249239\pi\)
0.708795 + 0.705414i \(0.249239\pi\)
\(480\) 0 0
\(481\) 34.3611 1.56673
\(482\) 4.75408 0.216543
\(483\) 0 0
\(484\) 0 0
\(485\) −14.0722 −0.638986
\(486\) 0 0
\(487\) 13.7298 0.622154 0.311077 0.950385i \(-0.399310\pi\)
0.311077 + 0.950385i \(0.399310\pi\)
\(488\) 11.0409 0.499800
\(489\) 0 0
\(490\) 11.7328 0.530035
\(491\) 8.43140 0.380504 0.190252 0.981735i \(-0.439070\pi\)
0.190252 + 0.981735i \(0.439070\pi\)
\(492\) 0 0
\(493\) −24.1536 −1.08782
\(494\) −2.17604 −0.0979045
\(495\) 0 0
\(496\) 0.731902 0.0328634
\(497\) 11.3444 0.508867
\(498\) 0 0
\(499\) −24.7395 −1.10749 −0.553746 0.832686i \(-0.686802\pi\)
−0.553746 + 0.832686i \(0.686802\pi\)
\(500\) 17.5342 0.784153
\(501\) 0 0
\(502\) −0.0625104 −0.00278997
\(503\) −16.3439 −0.728740 −0.364370 0.931254i \(-0.618716\pi\)
−0.364370 + 0.931254i \(0.618716\pi\)
\(504\) 0 0
\(505\) −2.12589 −0.0946009
\(506\) 0 0
\(507\) 0 0
\(508\) 8.79962 0.390420
\(509\) −20.4702 −0.907327 −0.453664 0.891173i \(-0.649883\pi\)
−0.453664 + 0.891173i \(0.649883\pi\)
\(510\) 0 0
\(511\) 44.2230 1.95631
\(512\) 15.0556 0.665372
\(513\) 0 0
\(514\) −7.57239 −0.334004
\(515\) 2.91500 0.128450
\(516\) 0 0
\(517\) 0 0
\(518\) 15.0924 0.663120
\(519\) 0 0
\(520\) 31.5823 1.38498
\(521\) −40.1151 −1.75747 −0.878737 0.477306i \(-0.841613\pi\)
−0.878737 + 0.477306i \(0.841613\pi\)
\(522\) 0 0
\(523\) 17.6107 0.770064 0.385032 0.922903i \(-0.374190\pi\)
0.385032 + 0.922903i \(0.374190\pi\)
\(524\) −16.8523 −0.736196
\(525\) 0 0
\(526\) −8.56399 −0.373408
\(527\) −1.63554 −0.0712450
\(528\) 0 0
\(529\) 26.3178 1.14425
\(530\) −11.9498 −0.519066
\(531\) 0 0
\(532\) 3.13927 0.136105
\(533\) 21.6603 0.938210
\(534\) 0 0
\(535\) 6.54930 0.283151
\(536\) 5.76054 0.248817
\(537\) 0 0
\(538\) −11.8674 −0.511638
\(539\) 0 0
\(540\) 0 0
\(541\) 20.5537 0.883675 0.441837 0.897095i \(-0.354327\pi\)
0.441837 + 0.897095i \(0.354327\pi\)
\(542\) −13.3809 −0.574757
\(543\) 0 0
\(544\) −18.3550 −0.786964
\(545\) 2.93597 0.125763
\(546\) 0 0
\(547\) 16.0069 0.684407 0.342204 0.939626i \(-0.388827\pi\)
0.342204 + 0.939626i \(0.388827\pi\)
\(548\) −27.9236 −1.19284
\(549\) 0 0
\(550\) 0 0
\(551\) 4.04926 0.172504
\(552\) 0 0
\(553\) −0.981115 −0.0417213
\(554\) 19.3052 0.820200
\(555\) 0 0
\(556\) 31.6006 1.34016
\(557\) 12.2300 0.518202 0.259101 0.965850i \(-0.416574\pi\)
0.259101 + 0.965850i \(0.416574\pi\)
\(558\) 0 0
\(559\) 65.7851 2.78241
\(560\) −11.9192 −0.503676
\(561\) 0 0
\(562\) 5.39577 0.227607
\(563\) 31.6605 1.33433 0.667165 0.744910i \(-0.267507\pi\)
0.667165 + 0.744910i \(0.267507\pi\)
\(564\) 0 0
\(565\) 33.7208 1.41865
\(566\) −18.0229 −0.757559
\(567\) 0 0
\(568\) 7.10058 0.297934
\(569\) 28.6418 1.20073 0.600364 0.799727i \(-0.295022\pi\)
0.600364 + 0.799727i \(0.295022\pi\)
\(570\) 0 0
\(571\) −13.7649 −0.576044 −0.288022 0.957624i \(-0.592998\pi\)
−0.288022 + 0.957624i \(0.592998\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 9.51380 0.397098
\(575\) 1.71402 0.0714794
\(576\) 0 0
\(577\) 12.9997 0.541184 0.270592 0.962694i \(-0.412781\pi\)
0.270592 + 0.962694i \(0.412781\pi\)
\(578\) −4.76322 −0.198124
\(579\) 0 0
\(580\) −25.5027 −1.05894
\(581\) −26.2999 −1.09110
\(582\) 0 0
\(583\) 0 0
\(584\) 27.6796 1.14539
\(585\) 0 0
\(586\) −10.1323 −0.418561
\(587\) −22.4701 −0.927439 −0.463720 0.885982i \(-0.653486\pi\)
−0.463720 + 0.885982i \(0.653486\pi\)
\(588\) 0 0
\(589\) 0.274191 0.0112979
\(590\) 15.8634 0.653086
\(591\) 0 0
\(592\) −8.11670 −0.333594
\(593\) 8.07538 0.331616 0.165808 0.986158i \(-0.446977\pi\)
0.165808 + 0.986158i \(0.446977\pi\)
\(594\) 0 0
\(595\) 26.6350 1.09193
\(596\) −6.56799 −0.269035
\(597\) 0 0
\(598\) 28.7846 1.17709
\(599\) 34.7973 1.42178 0.710889 0.703304i \(-0.248293\pi\)
0.710889 + 0.703304i \(0.248293\pi\)
\(600\) 0 0
\(601\) 6.58485 0.268602 0.134301 0.990941i \(-0.457121\pi\)
0.134301 + 0.990941i \(0.457121\pi\)
\(602\) 28.8947 1.17766
\(603\) 0 0
\(604\) −17.1648 −0.698425
\(605\) 0 0
\(606\) 0 0
\(607\) −1.62390 −0.0659119 −0.0329560 0.999457i \(-0.510492\pi\)
−0.0329560 + 0.999457i \(0.510492\pi\)
\(608\) 3.07715 0.124795
\(609\) 0 0
\(610\) −6.81483 −0.275925
\(611\) −76.9549 −3.11326
\(612\) 0 0
\(613\) 9.80435 0.395994 0.197997 0.980203i \(-0.436556\pi\)
0.197997 + 0.980203i \(0.436556\pi\)
\(614\) −3.32224 −0.134075
\(615\) 0 0
\(616\) 0 0
\(617\) −25.7948 −1.03846 −0.519230 0.854635i \(-0.673781\pi\)
−0.519230 + 0.854635i \(0.673781\pi\)
\(618\) 0 0
\(619\) 27.9268 1.12247 0.561237 0.827655i \(-0.310326\pi\)
0.561237 + 0.827655i \(0.310326\pi\)
\(620\) −1.72688 −0.0693534
\(621\) 0 0
\(622\) 10.4365 0.418464
\(623\) −59.9993 −2.40382
\(624\) 0 0
\(625\) −23.7201 −0.948803
\(626\) 22.3570 0.893566
\(627\) 0 0
\(628\) −11.2085 −0.447266
\(629\) 18.1379 0.723205
\(630\) 0 0
\(631\) −26.0594 −1.03741 −0.518705 0.854954i \(-0.673586\pi\)
−0.518705 + 0.854954i \(0.673586\pi\)
\(632\) −0.614089 −0.0244272
\(633\) 0 0
\(634\) −2.10692 −0.0836763
\(635\) −12.5165 −0.496701
\(636\) 0 0
\(637\) −47.2406 −1.87174
\(638\) 0 0
\(639\) 0 0
\(640\) −23.6032 −0.932997
\(641\) −22.9474 −0.906367 −0.453184 0.891417i \(-0.649712\pi\)
−0.453184 + 0.891417i \(0.649712\pi\)
\(642\) 0 0
\(643\) −31.2843 −1.23373 −0.616866 0.787068i \(-0.711598\pi\)
−0.616866 + 0.787068i \(0.711598\pi\)
\(644\) −41.5262 −1.63636
\(645\) 0 0
\(646\) −1.14865 −0.0451929
\(647\) −14.9853 −0.589131 −0.294566 0.955631i \(-0.595175\pi\)
−0.294566 + 0.955631i \(0.595175\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 1.00039 0.0392387
\(651\) 0 0
\(652\) 33.5964 1.31574
\(653\) −4.90689 −0.192021 −0.0960107 0.995380i \(-0.530608\pi\)
−0.0960107 + 0.995380i \(0.530608\pi\)
\(654\) 0 0
\(655\) 23.9705 0.936604
\(656\) −5.11654 −0.199768
\(657\) 0 0
\(658\) −33.8008 −1.31769
\(659\) −3.66895 −0.142922 −0.0714610 0.997443i \(-0.522766\pi\)
−0.0714610 + 0.997443i \(0.522766\pi\)
\(660\) 0 0
\(661\) 22.1469 0.861413 0.430707 0.902492i \(-0.358264\pi\)
0.430707 + 0.902492i \(0.358264\pi\)
\(662\) 18.5666 0.721612
\(663\) 0 0
\(664\) −16.4613 −0.638824
\(665\) −4.46526 −0.173155
\(666\) 0 0
\(667\) −53.5636 −2.07399
\(668\) −11.0713 −0.428362
\(669\) 0 0
\(670\) −3.55559 −0.137365
\(671\) 0 0
\(672\) 0 0
\(673\) −22.0420 −0.849657 −0.424828 0.905274i \(-0.639666\pi\)
−0.424828 + 0.905274i \(0.639666\pi\)
\(674\) −24.9107 −0.959526
\(675\) 0 0
\(676\) −35.2492 −1.35574
\(677\) −28.7363 −1.10443 −0.552214 0.833703i \(-0.686217\pi\)
−0.552214 + 0.833703i \(0.686217\pi\)
\(678\) 0 0
\(679\) 24.8866 0.955059
\(680\) 16.6711 0.639308
\(681\) 0 0
\(682\) 0 0
\(683\) 46.4334 1.77672 0.888362 0.459143i \(-0.151843\pi\)
0.888362 + 0.459143i \(0.151843\pi\)
\(684\) 0 0
\(685\) 39.7182 1.51755
\(686\) −2.30425 −0.0879767
\(687\) 0 0
\(688\) −15.5396 −0.592442
\(689\) 48.1142 1.83301
\(690\) 0 0
\(691\) −7.83156 −0.297926 −0.148963 0.988843i \(-0.547594\pi\)
−0.148963 + 0.988843i \(0.547594\pi\)
\(692\) 3.69146 0.140328
\(693\) 0 0
\(694\) 12.7230 0.482958
\(695\) −44.9482 −1.70498
\(696\) 0 0
\(697\) 11.4336 0.433079
\(698\) −18.2033 −0.689006
\(699\) 0 0
\(700\) −1.44322 −0.0545487
\(701\) −27.6808 −1.04549 −0.522746 0.852489i \(-0.675092\pi\)
−0.522746 + 0.852489i \(0.675092\pi\)
\(702\) 0 0
\(703\) −3.04075 −0.114684
\(704\) 0 0
\(705\) 0 0
\(706\) −12.9360 −0.486853
\(707\) 3.75962 0.141395
\(708\) 0 0
\(709\) −30.4153 −1.14227 −0.571135 0.820856i \(-0.693497\pi\)
−0.571135 + 0.820856i \(0.693497\pi\)
\(710\) −4.38271 −0.164480
\(711\) 0 0
\(712\) −37.5541 −1.40740
\(713\) −3.62700 −0.135832
\(714\) 0 0
\(715\) 0 0
\(716\) 22.4155 0.837705
\(717\) 0 0
\(718\) 10.7892 0.402649
\(719\) −37.3869 −1.39430 −0.697148 0.716927i \(-0.745548\pi\)
−0.697148 + 0.716927i \(0.745548\pi\)
\(720\) 0 0
\(721\) −5.15515 −0.191988
\(722\) −12.7887 −0.475946
\(723\) 0 0
\(724\) −1.38088 −0.0513201
\(725\) −1.86158 −0.0691373
\(726\) 0 0
\(727\) 16.3288 0.605603 0.302802 0.953054i \(-0.402078\pi\)
0.302802 + 0.953054i \(0.402078\pi\)
\(728\) −55.8531 −2.07005
\(729\) 0 0
\(730\) −17.0848 −0.632336
\(731\) 34.7254 1.28437
\(732\) 0 0
\(733\) 22.5505 0.832921 0.416461 0.909154i \(-0.363270\pi\)
0.416461 + 0.909154i \(0.363270\pi\)
\(734\) 3.16508 0.116825
\(735\) 0 0
\(736\) −40.7044 −1.50039
\(737\) 0 0
\(738\) 0 0
\(739\) 13.7185 0.504641 0.252321 0.967644i \(-0.418806\pi\)
0.252321 + 0.967644i \(0.418806\pi\)
\(740\) 19.1509 0.704003
\(741\) 0 0
\(742\) 21.1331 0.775821
\(743\) 41.0233 1.50500 0.752499 0.658594i \(-0.228848\pi\)
0.752499 + 0.658594i \(0.228848\pi\)
\(744\) 0 0
\(745\) 9.34223 0.342273
\(746\) −23.6527 −0.865987
\(747\) 0 0
\(748\) 0 0
\(749\) −11.5824 −0.423211
\(750\) 0 0
\(751\) 37.9309 1.38412 0.692059 0.721841i \(-0.256704\pi\)
0.692059 + 0.721841i \(0.256704\pi\)
\(752\) 18.1781 0.662888
\(753\) 0 0
\(754\) −31.2627 −1.13852
\(755\) 24.4150 0.888551
\(756\) 0 0
\(757\) −22.7700 −0.827589 −0.413794 0.910370i \(-0.635797\pi\)
−0.413794 + 0.910370i \(0.635797\pi\)
\(758\) −3.02251 −0.109782
\(759\) 0 0
\(760\) −2.79485 −0.101380
\(761\) 4.64031 0.168211 0.0841056 0.996457i \(-0.473197\pi\)
0.0841056 + 0.996457i \(0.473197\pi\)
\(762\) 0 0
\(763\) −5.19224 −0.187972
\(764\) −12.3492 −0.446780
\(765\) 0 0
\(766\) 18.8369 0.680604
\(767\) −63.8718 −2.30628
\(768\) 0 0
\(769\) −2.74051 −0.0988253 −0.0494127 0.998778i \(-0.515735\pi\)
−0.0494127 + 0.998778i \(0.515735\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.84162 0.0662813
\(773\) 11.0421 0.397158 0.198579 0.980085i \(-0.436367\pi\)
0.198579 + 0.980085i \(0.436367\pi\)
\(774\) 0 0
\(775\) −0.126055 −0.00452802
\(776\) 15.5767 0.559172
\(777\) 0 0
\(778\) 13.6929 0.490914
\(779\) −1.91680 −0.0686766
\(780\) 0 0
\(781\) 0 0
\(782\) 15.1943 0.543346
\(783\) 0 0
\(784\) 11.1591 0.398539
\(785\) 15.9428 0.569021
\(786\) 0 0
\(787\) −29.3886 −1.04759 −0.523795 0.851844i \(-0.675484\pi\)
−0.523795 + 0.851844i \(0.675484\pi\)
\(788\) −39.7808 −1.41713
\(789\) 0 0
\(790\) 0.379036 0.0134855
\(791\) −59.6350 −2.12038
\(792\) 0 0
\(793\) 27.4390 0.974387
\(794\) −16.7244 −0.593529
\(795\) 0 0
\(796\) 9.33376 0.330826
\(797\) −1.11623 −0.0395390 −0.0197695 0.999805i \(-0.506293\pi\)
−0.0197695 + 0.999805i \(0.506293\pi\)
\(798\) 0 0
\(799\) −40.6216 −1.43709
\(800\) −1.41466 −0.0500159
\(801\) 0 0
\(802\) −10.5409 −0.372210
\(803\) 0 0
\(804\) 0 0
\(805\) 59.0664 2.08182
\(806\) −2.11692 −0.0745652
\(807\) 0 0
\(808\) 2.35318 0.0827846
\(809\) 43.3724 1.52489 0.762445 0.647053i \(-0.223999\pi\)
0.762445 + 0.647053i \(0.223999\pi\)
\(810\) 0 0
\(811\) 33.0062 1.15900 0.579502 0.814971i \(-0.303247\pi\)
0.579502 + 0.814971i \(0.303247\pi\)
\(812\) 45.1013 1.58274
\(813\) 0 0
\(814\) 0 0
\(815\) −47.7871 −1.67391
\(816\) 0 0
\(817\) −5.82158 −0.203671
\(818\) 5.81106 0.203179
\(819\) 0 0
\(820\) 12.0722 0.421580
\(821\) −27.0131 −0.942762 −0.471381 0.881930i \(-0.656244\pi\)
−0.471381 + 0.881930i \(0.656244\pi\)
\(822\) 0 0
\(823\) 2.23678 0.0779694 0.0389847 0.999240i \(-0.487588\pi\)
0.0389847 + 0.999240i \(0.487588\pi\)
\(824\) −3.22665 −0.112406
\(825\) 0 0
\(826\) −28.0543 −0.976133
\(827\) −24.0696 −0.836980 −0.418490 0.908221i \(-0.637441\pi\)
−0.418490 + 0.908221i \(0.637441\pi\)
\(828\) 0 0
\(829\) −7.42634 −0.257927 −0.128964 0.991649i \(-0.541165\pi\)
−0.128964 + 0.991649i \(0.541165\pi\)
\(830\) 10.1605 0.352675
\(831\) 0 0
\(832\) −6.75413 −0.234157
\(833\) −24.9365 −0.863999
\(834\) 0 0
\(835\) 15.7477 0.544972
\(836\) 0 0
\(837\) 0 0
\(838\) −7.67591 −0.265160
\(839\) 11.3704 0.392550 0.196275 0.980549i \(-0.437115\pi\)
0.196275 + 0.980549i \(0.437115\pi\)
\(840\) 0 0
\(841\) 29.1750 1.00603
\(842\) −16.1367 −0.556109
\(843\) 0 0
\(844\) −13.6935 −0.471350
\(845\) 50.1380 1.72480
\(846\) 0 0
\(847\) 0 0
\(848\) −11.3654 −0.390291
\(849\) 0 0
\(850\) 0.528070 0.0181126
\(851\) 40.2230 1.37883
\(852\) 0 0
\(853\) −3.35595 −0.114905 −0.0574527 0.998348i \(-0.518298\pi\)
−0.0574527 + 0.998348i \(0.518298\pi\)
\(854\) 12.0520 0.412410
\(855\) 0 0
\(856\) −7.24952 −0.247783
\(857\) −18.5664 −0.634215 −0.317107 0.948390i \(-0.602712\pi\)
−0.317107 + 0.948390i \(0.602712\pi\)
\(858\) 0 0
\(859\) 14.1518 0.482853 0.241426 0.970419i \(-0.422385\pi\)
0.241426 + 0.970419i \(0.422385\pi\)
\(860\) 36.6649 1.25026
\(861\) 0 0
\(862\) −3.79863 −0.129382
\(863\) 52.4715 1.78615 0.893076 0.449906i \(-0.148542\pi\)
0.893076 + 0.449906i \(0.148542\pi\)
\(864\) 0 0
\(865\) −5.25068 −0.178528
\(866\) 14.7670 0.501803
\(867\) 0 0
\(868\) 3.05398 0.103659
\(869\) 0 0
\(870\) 0 0
\(871\) 14.3161 0.485083
\(872\) −3.24987 −0.110055
\(873\) 0 0
\(874\) −2.54726 −0.0861624
\(875\) 44.1069 1.49109
\(876\) 0 0
\(877\) −31.8136 −1.07427 −0.537135 0.843496i \(-0.680494\pi\)
−0.537135 + 0.843496i \(0.680494\pi\)
\(878\) 5.23513 0.176677
\(879\) 0 0
\(880\) 0 0
\(881\) −29.3806 −0.989858 −0.494929 0.868933i \(-0.664806\pi\)
−0.494929 + 0.868933i \(0.664806\pi\)
\(882\) 0 0
\(883\) −0.606382 −0.0204064 −0.0102032 0.999948i \(-0.503248\pi\)
−0.0102032 + 0.999948i \(0.503248\pi\)
\(884\) −29.1279 −0.979676
\(885\) 0 0
\(886\) 16.3298 0.548611
\(887\) −7.56882 −0.254136 −0.127068 0.991894i \(-0.540557\pi\)
−0.127068 + 0.991894i \(0.540557\pi\)
\(888\) 0 0
\(889\) 22.1353 0.742393
\(890\) 23.1796 0.776984
\(891\) 0 0
\(892\) −40.6630 −1.36150
\(893\) 6.81005 0.227890
\(894\) 0 0
\(895\) −31.8835 −1.06575
\(896\) 41.7420 1.39450
\(897\) 0 0
\(898\) 23.0805 0.770206
\(899\) 3.93925 0.131381
\(900\) 0 0
\(901\) 25.3977 0.846119
\(902\) 0 0
\(903\) 0 0
\(904\) −37.3261 −1.24145
\(905\) 1.96415 0.0652905
\(906\) 0 0
\(907\) −30.7730 −1.02180 −0.510900 0.859640i \(-0.670688\pi\)
−0.510900 + 0.859640i \(0.670688\pi\)
\(908\) 3.91923 0.130064
\(909\) 0 0
\(910\) 34.4744 1.14281
\(911\) −11.6236 −0.385106 −0.192553 0.981287i \(-0.561677\pi\)
−0.192553 + 0.981287i \(0.561677\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 6.78420 0.224401
\(915\) 0 0
\(916\) −34.1879 −1.12960
\(917\) −42.3916 −1.39989
\(918\) 0 0
\(919\) 32.0118 1.05597 0.527986 0.849253i \(-0.322947\pi\)
0.527986 + 0.849253i \(0.322947\pi\)
\(920\) 36.9702 1.21887
\(921\) 0 0
\(922\) −2.57076 −0.0846636
\(923\) 17.6464 0.580838
\(924\) 0 0
\(925\) 1.39793 0.0459637
\(926\) 20.1474 0.662084
\(927\) 0 0
\(928\) 44.2088 1.45122
\(929\) −16.0439 −0.526384 −0.263192 0.964744i \(-0.584775\pi\)
−0.263192 + 0.964744i \(0.584775\pi\)
\(930\) 0 0
\(931\) 4.18051 0.137011
\(932\) −28.3108 −0.927350
\(933\) 0 0
\(934\) −8.35395 −0.273350
\(935\) 0 0
\(936\) 0 0
\(937\) −28.7829 −0.940296 −0.470148 0.882588i \(-0.655799\pi\)
−0.470148 + 0.882588i \(0.655799\pi\)
\(938\) 6.28804 0.205312
\(939\) 0 0
\(940\) −42.8904 −1.39893
\(941\) 32.0887 1.04606 0.523032 0.852313i \(-0.324801\pi\)
0.523032 + 0.852313i \(0.324801\pi\)
\(942\) 0 0
\(943\) 25.3554 0.825687
\(944\) 15.0877 0.491062
\(945\) 0 0
\(946\) 0 0
\(947\) 31.8805 1.03598 0.517989 0.855387i \(-0.326681\pi\)
0.517989 + 0.855387i \(0.326681\pi\)
\(948\) 0 0
\(949\) 68.7895 2.23300
\(950\) −0.0885288 −0.00287225
\(951\) 0 0
\(952\) −29.4827 −0.955540
\(953\) −33.5509 −1.08682 −0.543410 0.839468i \(-0.682867\pi\)
−0.543410 + 0.839468i \(0.682867\pi\)
\(954\) 0 0
\(955\) 17.5654 0.568403
\(956\) 10.0881 0.326271
\(957\) 0 0
\(958\) 21.1974 0.684856
\(959\) −70.2412 −2.26821
\(960\) 0 0
\(961\) −30.7333 −0.991395
\(962\) 23.4763 0.756908
\(963\) 0 0
\(964\) −10.6685 −0.343609
\(965\) −2.61949 −0.0843245
\(966\) 0 0
\(967\) 17.3428 0.557708 0.278854 0.960333i \(-0.410045\pi\)
0.278854 + 0.960333i \(0.410045\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) −9.61447 −0.308702
\(971\) 42.3522 1.35915 0.679573 0.733608i \(-0.262165\pi\)
0.679573 + 0.733608i \(0.262165\pi\)
\(972\) 0 0
\(973\) 79.4906 2.54835
\(974\) 9.38051 0.300571
\(975\) 0 0
\(976\) −6.48158 −0.207470
\(977\) 0.820225 0.0262413 0.0131207 0.999914i \(-0.495823\pi\)
0.0131207 + 0.999914i \(0.495823\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −26.3293 −0.841058
\(981\) 0 0
\(982\) 5.76054 0.183826
\(983\) 31.2508 0.996747 0.498374 0.866962i \(-0.333931\pi\)
0.498374 + 0.866962i \(0.333931\pi\)
\(984\) 0 0
\(985\) 56.5837 1.80291
\(986\) −16.5024 −0.525542
\(987\) 0 0
\(988\) 4.88317 0.155354
\(989\) 77.0078 2.44871
\(990\) 0 0
\(991\) 4.89850 0.155606 0.0778030 0.996969i \(-0.475209\pi\)
0.0778030 + 0.996969i \(0.475209\pi\)
\(992\) 2.99355 0.0950452
\(993\) 0 0
\(994\) 7.75079 0.245840
\(995\) −13.2762 −0.420885
\(996\) 0 0
\(997\) −21.6834 −0.686721 −0.343360 0.939204i \(-0.611565\pi\)
−0.343360 + 0.939204i \(0.611565\pi\)
\(998\) −16.9026 −0.535044
\(999\) 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 9801.2.a.bx.1.6 yes 8
3.2 odd 2 9801.2.a.by.1.3 yes 8
11.10 odd 2 9801.2.a.by.1.4 yes 8
33.32 even 2 inner 9801.2.a.bx.1.5 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
9801.2.a.bx.1.5 8 33.32 even 2 inner
9801.2.a.bx.1.6 yes 8 1.1 even 1 trivial
9801.2.a.by.1.3 yes 8 3.2 odd 2
9801.2.a.by.1.4 yes 8 11.10 odd 2