Properties

Label 6525.2.a.cc.1.1
Level $6525$
Weight $2$
Character 6525.1
Self dual yes
Analytic conductor $52.102$
Analytic rank $0$
Dimension $9$
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] = [6525,2,Mod(1,6525)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6525, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("6525.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6525 = 3^{2} \cdot 5^{2} \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6525.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: \(52.1023873189\)
Analytic rank: \(0\)
Dimension: \(9\)
Coefficient field: \(\mathbb{Q}[x]/(x^{9} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{9} - 2x^{8} - 12x^{7} + 21x^{6} + 48x^{5} - 68x^{4} - 73x^{3} + 66x^{2} + 40x - 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-2.21081\) of defining polynomial
Character \(\chi\) \(=\) 6525.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.21081 q^{2} +2.88766 q^{4} +1.31646 q^{7} -1.96245 q^{8} +O(q^{10})\) \(q-2.21081 q^{2} +2.88766 q^{4} +1.31646 q^{7} -1.96245 q^{8} +4.29189 q^{11} +2.97543 q^{13} -2.91044 q^{14} -1.43674 q^{16} +0.642441 q^{17} -5.07923 q^{19} -9.48853 q^{22} +8.84038 q^{23} -6.57809 q^{26} +3.80150 q^{28} -1.00000 q^{29} -6.27016 q^{31} +7.10123 q^{32} -1.42031 q^{34} -0.934054 q^{37} +11.2292 q^{38} +11.0792 q^{41} -2.03981 q^{43} +12.3935 q^{44} -19.5444 q^{46} +9.57178 q^{47} -5.26692 q^{49} +8.59203 q^{52} -13.0891 q^{53} -2.58349 q^{56} +2.21081 q^{58} -2.55069 q^{59} +8.46575 q^{61} +13.8621 q^{62} -12.8260 q^{64} +12.9808 q^{67} +1.85515 q^{68} +5.10419 q^{71} +16.0007 q^{73} +2.06501 q^{74} -14.6671 q^{76} +5.65012 q^{77} -3.30518 q^{79} -24.4939 q^{82} +5.24640 q^{83} +4.50962 q^{86} -8.42260 q^{88} -5.05088 q^{89} +3.91704 q^{91} +25.5280 q^{92} -21.1614 q^{94} +2.04414 q^{97} +11.6441 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 9 q + 2 q^{2} + 10 q^{4} - q^{7} + 9 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 9 q + 2 q^{2} + 10 q^{4} - q^{7} + 9 q^{8} - 2 q^{11} - q^{13} + 3 q^{14} + 4 q^{16} + 12 q^{17} - q^{19} - 3 q^{22} + 16 q^{23} - 6 q^{26} + 4 q^{28} - 9 q^{29} + 5 q^{31} + 20 q^{32} + 3 q^{34} + 30 q^{38} + 10 q^{41} - 3 q^{43} + 13 q^{44} + 4 q^{46} + 26 q^{47} - 8 q^{49} + 9 q^{52} + 22 q^{53} - 22 q^{56} - 2 q^{58} - 4 q^{59} + 7 q^{61} + 28 q^{62} + 9 q^{64} - 5 q^{67} + 39 q^{68} + 10 q^{73} + 34 q^{74} - 2 q^{76} + 34 q^{77} + 10 q^{79} + 8 q^{82} + 46 q^{83} - 28 q^{86} - 2 q^{88} - 4 q^{89} - 21 q^{91} + 20 q^{92} + 5 q^{94} - 7 q^{97} + 51 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.21081 −1.56328 −0.781638 0.623733i \(-0.785615\pi\)
−0.781638 + 0.623733i \(0.785615\pi\)
\(3\) 0 0
\(4\) 2.88766 1.44383
\(5\) 0 0
\(6\) 0 0
\(7\) 1.31646 0.497576 0.248788 0.968558i \(-0.419968\pi\)
0.248788 + 0.968558i \(0.419968\pi\)
\(8\) −1.96245 −0.693830
\(9\) 0 0
\(10\) 0 0
\(11\) 4.29189 1.29405 0.647027 0.762467i \(-0.276012\pi\)
0.647027 + 0.762467i \(0.276012\pi\)
\(12\) 0 0
\(13\) 2.97543 0.825235 0.412617 0.910904i \(-0.364615\pi\)
0.412617 + 0.910904i \(0.364615\pi\)
\(14\) −2.91044 −0.777849
\(15\) 0 0
\(16\) −1.43674 −0.359184
\(17\) 0.642441 0.155815 0.0779074 0.996961i \(-0.475176\pi\)
0.0779074 + 0.996961i \(0.475176\pi\)
\(18\) 0 0
\(19\) −5.07923 −1.16525 −0.582627 0.812740i \(-0.697975\pi\)
−0.582627 + 0.812740i \(0.697975\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −9.48853 −2.02296
\(23\) 8.84038 1.84335 0.921674 0.387966i \(-0.126822\pi\)
0.921674 + 0.387966i \(0.126822\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −6.57809 −1.29007
\(27\) 0 0
\(28\) 3.80150 0.718416
\(29\) −1.00000 −0.185695
\(30\) 0 0
\(31\) −6.27016 −1.12615 −0.563077 0.826404i \(-0.690383\pi\)
−0.563077 + 0.826404i \(0.690383\pi\)
\(32\) 7.10123 1.25533
\(33\) 0 0
\(34\) −1.42031 −0.243582
\(35\) 0 0
\(36\) 0 0
\(37\) −0.934054 −0.153558 −0.0767788 0.997048i \(-0.524464\pi\)
−0.0767788 + 0.997048i \(0.524464\pi\)
\(38\) 11.2292 1.82161
\(39\) 0 0
\(40\) 0 0
\(41\) 11.0792 1.73028 0.865139 0.501533i \(-0.167230\pi\)
0.865139 + 0.501533i \(0.167230\pi\)
\(42\) 0 0
\(43\) −2.03981 −0.311068 −0.155534 0.987831i \(-0.549710\pi\)
−0.155534 + 0.987831i \(0.549710\pi\)
\(44\) 12.3935 1.86839
\(45\) 0 0
\(46\) −19.5444 −2.88166
\(47\) 9.57178 1.39619 0.698094 0.716006i \(-0.254032\pi\)
0.698094 + 0.716006i \(0.254032\pi\)
\(48\) 0 0
\(49\) −5.26692 −0.752418
\(50\) 0 0
\(51\) 0 0
\(52\) 8.59203 1.19150
\(53\) −13.0891 −1.79792 −0.898960 0.438030i \(-0.855676\pi\)
−0.898960 + 0.438030i \(0.855676\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −2.58349 −0.345233
\(57\) 0 0
\(58\) 2.21081 0.290293
\(59\) −2.55069 −0.332071 −0.166036 0.986120i \(-0.553097\pi\)
−0.166036 + 0.986120i \(0.553097\pi\)
\(60\) 0 0
\(61\) 8.46575 1.08393 0.541964 0.840402i \(-0.317681\pi\)
0.541964 + 0.840402i \(0.317681\pi\)
\(62\) 13.8621 1.76049
\(63\) 0 0
\(64\) −12.8260 −1.60325
\(65\) 0 0
\(66\) 0 0
\(67\) 12.9808 1.58586 0.792930 0.609313i \(-0.208555\pi\)
0.792930 + 0.609313i \(0.208555\pi\)
\(68\) 1.85515 0.224970
\(69\) 0 0
\(70\) 0 0
\(71\) 5.10419 0.605756 0.302878 0.953029i \(-0.402053\pi\)
0.302878 + 0.953029i \(0.402053\pi\)
\(72\) 0 0
\(73\) 16.0007 1.87274 0.936372 0.351009i \(-0.114161\pi\)
0.936372 + 0.351009i \(0.114161\pi\)
\(74\) 2.06501 0.240053
\(75\) 0 0
\(76\) −14.6671 −1.68243
\(77\) 5.65012 0.643890
\(78\) 0 0
\(79\) −3.30518 −0.371861 −0.185931 0.982563i \(-0.559530\pi\)
−0.185931 + 0.982563i \(0.559530\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −24.4939 −2.70490
\(83\) 5.24640 0.575867 0.287934 0.957650i \(-0.407032\pi\)
0.287934 + 0.957650i \(0.407032\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.50962 0.486284
\(87\) 0 0
\(88\) −8.42260 −0.897853
\(89\) −5.05088 −0.535392 −0.267696 0.963503i \(-0.586262\pi\)
−0.267696 + 0.963503i \(0.586262\pi\)
\(90\) 0 0
\(91\) 3.91704 0.410617
\(92\) 25.5280 2.66148
\(93\) 0 0
\(94\) −21.1614 −2.18263
\(95\) 0 0
\(96\) 0 0
\(97\) 2.04414 0.207551 0.103776 0.994601i \(-0.466908\pi\)
0.103776 + 0.994601i \(0.466908\pi\)
\(98\) 11.6441 1.17624
\(99\) 0 0
\(100\) 0 0
\(101\) −12.4871 −1.24251 −0.621255 0.783609i \(-0.713377\pi\)
−0.621255 + 0.783609i \(0.713377\pi\)
\(102\) 0 0
\(103\) 10.6723 1.05157 0.525785 0.850617i \(-0.323772\pi\)
0.525785 + 0.850617i \(0.323772\pi\)
\(104\) −5.83912 −0.572572
\(105\) 0 0
\(106\) 28.9374 2.81065
\(107\) −4.85956 −0.469791 −0.234896 0.972021i \(-0.575475\pi\)
−0.234896 + 0.972021i \(0.575475\pi\)
\(108\) 0 0
\(109\) 15.3415 1.46945 0.734723 0.678367i \(-0.237312\pi\)
0.734723 + 0.678367i \(0.237312\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.89141 −0.178721
\(113\) 4.32180 0.406560 0.203280 0.979121i \(-0.434840\pi\)
0.203280 + 0.979121i \(0.434840\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −2.88766 −0.268113
\(117\) 0 0
\(118\) 5.63908 0.519119
\(119\) 0.845750 0.0775298
\(120\) 0 0
\(121\) 7.42032 0.674575
\(122\) −18.7161 −1.69448
\(123\) 0 0
\(124\) −18.1061 −1.62598
\(125\) 0 0
\(126\) 0 0
\(127\) −21.5809 −1.91500 −0.957498 0.288440i \(-0.906863\pi\)
−0.957498 + 0.288440i \(0.906863\pi\)
\(128\) 14.1533 1.25098
\(129\) 0 0
\(130\) 0 0
\(131\) 9.25658 0.808751 0.404376 0.914593i \(-0.367489\pi\)
0.404376 + 0.914593i \(0.367489\pi\)
\(132\) 0 0
\(133\) −6.68661 −0.579803
\(134\) −28.6981 −2.47914
\(135\) 0 0
\(136\) −1.26076 −0.108109
\(137\) −0.843767 −0.0720879 −0.0360439 0.999350i \(-0.511476\pi\)
−0.0360439 + 0.999350i \(0.511476\pi\)
\(138\) 0 0
\(139\) −13.9777 −1.18557 −0.592785 0.805361i \(-0.701972\pi\)
−0.592785 + 0.805361i \(0.701972\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −11.2844 −0.946964
\(143\) 12.7702 1.06790
\(144\) 0 0
\(145\) 0 0
\(146\) −35.3745 −2.92762
\(147\) 0 0
\(148\) −2.69723 −0.221711
\(149\) 19.6274 1.60794 0.803971 0.594669i \(-0.202717\pi\)
0.803971 + 0.594669i \(0.202717\pi\)
\(150\) 0 0
\(151\) −10.7559 −0.875301 −0.437650 0.899145i \(-0.644189\pi\)
−0.437650 + 0.899145i \(0.644189\pi\)
\(152\) 9.96771 0.808488
\(153\) 0 0
\(154\) −12.4913 −1.00658
\(155\) 0 0
\(156\) 0 0
\(157\) −23.5513 −1.87960 −0.939800 0.341724i \(-0.888989\pi\)
−0.939800 + 0.341724i \(0.888989\pi\)
\(158\) 7.30710 0.581322
\(159\) 0 0
\(160\) 0 0
\(161\) 11.6380 0.917206
\(162\) 0 0
\(163\) −9.50148 −0.744213 −0.372107 0.928190i \(-0.621364\pi\)
−0.372107 + 0.928190i \(0.621364\pi\)
\(164\) 31.9929 2.49823
\(165\) 0 0
\(166\) −11.5988 −0.900239
\(167\) −1.82786 −0.141444 −0.0707220 0.997496i \(-0.522530\pi\)
−0.0707220 + 0.997496i \(0.522530\pi\)
\(168\) 0 0
\(169\) −4.14683 −0.318987
\(170\) 0 0
\(171\) 0 0
\(172\) −5.89027 −0.449129
\(173\) 5.50734 0.418715 0.209358 0.977839i \(-0.432863\pi\)
0.209358 + 0.977839i \(0.432863\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −6.16631 −0.464803
\(177\) 0 0
\(178\) 11.1665 0.836966
\(179\) 9.36470 0.699950 0.349975 0.936759i \(-0.386190\pi\)
0.349975 + 0.936759i \(0.386190\pi\)
\(180\) 0 0
\(181\) 25.6019 1.90297 0.951487 0.307688i \(-0.0995552\pi\)
0.951487 + 0.307688i \(0.0995552\pi\)
\(182\) −8.65981 −0.641908
\(183\) 0 0
\(184\) −17.3488 −1.27897
\(185\) 0 0
\(186\) 0 0
\(187\) 2.75729 0.201633
\(188\) 27.6401 2.01586
\(189\) 0 0
\(190\) 0 0
\(191\) −12.3658 −0.894756 −0.447378 0.894345i \(-0.647642\pi\)
−0.447378 + 0.894345i \(0.647642\pi\)
\(192\) 0 0
\(193\) 15.7223 1.13172 0.565859 0.824502i \(-0.308545\pi\)
0.565859 + 0.824502i \(0.308545\pi\)
\(194\) −4.51920 −0.324459
\(195\) 0 0
\(196\) −15.2091 −1.08636
\(197\) 21.6728 1.54412 0.772061 0.635549i \(-0.219226\pi\)
0.772061 + 0.635549i \(0.219226\pi\)
\(198\) 0 0
\(199\) −1.23732 −0.0877116 −0.0438558 0.999038i \(-0.513964\pi\)
−0.0438558 + 0.999038i \(0.513964\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 27.6065 1.94238
\(203\) −1.31646 −0.0923976
\(204\) 0 0
\(205\) 0 0
\(206\) −23.5943 −1.64389
\(207\) 0 0
\(208\) −4.27490 −0.296411
\(209\) −21.7995 −1.50790
\(210\) 0 0
\(211\) −5.05346 −0.347895 −0.173947 0.984755i \(-0.555652\pi\)
−0.173947 + 0.984755i \(0.555652\pi\)
\(212\) −37.7968 −2.59589
\(213\) 0 0
\(214\) 10.7435 0.734413
\(215\) 0 0
\(216\) 0 0
\(217\) −8.25444 −0.560348
\(218\) −33.9170 −2.29715
\(219\) 0 0
\(220\) 0 0
\(221\) 1.91154 0.128584
\(222\) 0 0
\(223\) 16.2248 1.08649 0.543245 0.839574i \(-0.317195\pi\)
0.543245 + 0.839574i \(0.317195\pi\)
\(224\) 9.34851 0.624624
\(225\) 0 0
\(226\) −9.55465 −0.635566
\(227\) 6.82690 0.453117 0.226559 0.973998i \(-0.427253\pi\)
0.226559 + 0.973998i \(0.427253\pi\)
\(228\) 0 0
\(229\) −5.87121 −0.387980 −0.193990 0.981003i \(-0.562143\pi\)
−0.193990 + 0.981003i \(0.562143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.96245 0.128841
\(233\) −14.1453 −0.926692 −0.463346 0.886178i \(-0.653351\pi\)
−0.463346 + 0.886178i \(0.653351\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −7.36553 −0.479455
\(237\) 0 0
\(238\) −1.86979 −0.121200
\(239\) −20.6920 −1.33845 −0.669226 0.743059i \(-0.733374\pi\)
−0.669226 + 0.743059i \(0.733374\pi\)
\(240\) 0 0
\(241\) −7.90845 −0.509428 −0.254714 0.967016i \(-0.581981\pi\)
−0.254714 + 0.967016i \(0.581981\pi\)
\(242\) −16.4049 −1.05455
\(243\) 0 0
\(244\) 24.4462 1.56501
\(245\) 0 0
\(246\) 0 0
\(247\) −15.1129 −0.961609
\(248\) 12.3049 0.781359
\(249\) 0 0
\(250\) 0 0
\(251\) 11.8140 0.745691 0.372846 0.927893i \(-0.378382\pi\)
0.372846 + 0.927893i \(0.378382\pi\)
\(252\) 0 0
\(253\) 37.9420 2.38539
\(254\) 47.7112 2.99367
\(255\) 0 0
\(256\) −5.63818 −0.352386
\(257\) −4.35440 −0.271620 −0.135810 0.990735i \(-0.543364\pi\)
−0.135810 + 0.990735i \(0.543364\pi\)
\(258\) 0 0
\(259\) −1.22965 −0.0764066
\(260\) 0 0
\(261\) 0 0
\(262\) −20.4645 −1.26430
\(263\) 27.6727 1.70637 0.853187 0.521605i \(-0.174666\pi\)
0.853187 + 0.521605i \(0.174666\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 14.7828 0.906392
\(267\) 0 0
\(268\) 37.4842 2.28971
\(269\) −6.32037 −0.385360 −0.192680 0.981262i \(-0.561718\pi\)
−0.192680 + 0.981262i \(0.561718\pi\)
\(270\) 0 0
\(271\) 4.37191 0.265575 0.132787 0.991145i \(-0.457607\pi\)
0.132787 + 0.991145i \(0.457607\pi\)
\(272\) −0.923018 −0.0559662
\(273\) 0 0
\(274\) 1.86540 0.112693
\(275\) 0 0
\(276\) 0 0
\(277\) 4.01638 0.241321 0.120660 0.992694i \(-0.461499\pi\)
0.120660 + 0.992694i \(0.461499\pi\)
\(278\) 30.9019 1.85337
\(279\) 0 0
\(280\) 0 0
\(281\) −13.6990 −0.817215 −0.408607 0.912710i \(-0.633985\pi\)
−0.408607 + 0.912710i \(0.633985\pi\)
\(282\) 0 0
\(283\) 14.8058 0.880114 0.440057 0.897970i \(-0.354958\pi\)
0.440057 + 0.897970i \(0.354958\pi\)
\(284\) 14.7392 0.874609
\(285\) 0 0
\(286\) −28.2324 −1.66942
\(287\) 14.5853 0.860945
\(288\) 0 0
\(289\) −16.5873 −0.975722
\(290\) 0 0
\(291\) 0 0
\(292\) 46.2047 2.70393
\(293\) −16.6890 −0.974983 −0.487492 0.873128i \(-0.662088\pi\)
−0.487492 + 0.873128i \(0.662088\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.83303 0.106543
\(297\) 0 0
\(298\) −43.3924 −2.51366
\(299\) 26.3039 1.52119
\(300\) 0 0
\(301\) −2.68533 −0.154780
\(302\) 23.7792 1.36834
\(303\) 0 0
\(304\) 7.29750 0.418540
\(305\) 0 0
\(306\) 0 0
\(307\) −4.97073 −0.283695 −0.141847 0.989889i \(-0.545304\pi\)
−0.141847 + 0.989889i \(0.545304\pi\)
\(308\) 16.3156 0.929669
\(309\) 0 0
\(310\) 0 0
\(311\) −21.0786 −1.19526 −0.597629 0.801773i \(-0.703890\pi\)
−0.597629 + 0.801773i \(0.703890\pi\)
\(312\) 0 0
\(313\) −24.3744 −1.37772 −0.688860 0.724894i \(-0.741889\pi\)
−0.688860 + 0.724894i \(0.741889\pi\)
\(314\) 52.0674 2.93833
\(315\) 0 0
\(316\) −9.54423 −0.536905
\(317\) −13.4102 −0.753194 −0.376597 0.926377i \(-0.622906\pi\)
−0.376597 + 0.926377i \(0.622906\pi\)
\(318\) 0 0
\(319\) −4.29189 −0.240300
\(320\) 0 0
\(321\) 0 0
\(322\) −25.7294 −1.43385
\(323\) −3.26310 −0.181564
\(324\) 0 0
\(325\) 0 0
\(326\) 21.0059 1.16341
\(327\) 0 0
\(328\) −21.7423 −1.20052
\(329\) 12.6009 0.694710
\(330\) 0 0
\(331\) 23.4187 1.28721 0.643603 0.765360i \(-0.277439\pi\)
0.643603 + 0.765360i \(0.277439\pi\)
\(332\) 15.1498 0.831455
\(333\) 0 0
\(334\) 4.04104 0.221116
\(335\) 0 0
\(336\) 0 0
\(337\) −22.7865 −1.24126 −0.620631 0.784103i \(-0.713123\pi\)
−0.620631 + 0.784103i \(0.713123\pi\)
\(338\) 9.16784 0.498665
\(339\) 0 0
\(340\) 0 0
\(341\) −26.9108 −1.45730
\(342\) 0 0
\(343\) −16.1490 −0.871962
\(344\) 4.00301 0.215828
\(345\) 0 0
\(346\) −12.1757 −0.654567
\(347\) 4.98513 0.267616 0.133808 0.991007i \(-0.457279\pi\)
0.133808 + 0.991007i \(0.457279\pi\)
\(348\) 0 0
\(349\) 25.6783 1.37453 0.687264 0.726407i \(-0.258811\pi\)
0.687264 + 0.726407i \(0.258811\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 30.4777 1.62447
\(353\) 20.3160 1.08131 0.540656 0.841244i \(-0.318176\pi\)
0.540656 + 0.841244i \(0.318176\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −14.5852 −0.773016
\(357\) 0 0
\(358\) −20.7035 −1.09422
\(359\) −9.68907 −0.511370 −0.255685 0.966760i \(-0.582301\pi\)
−0.255685 + 0.966760i \(0.582301\pi\)
\(360\) 0 0
\(361\) 6.79854 0.357818
\(362\) −56.6008 −2.97487
\(363\) 0 0
\(364\) 11.3111 0.592862
\(365\) 0 0
\(366\) 0 0
\(367\) −9.16319 −0.478315 −0.239157 0.970981i \(-0.576871\pi\)
−0.239157 + 0.970981i \(0.576871\pi\)
\(368\) −12.7013 −0.662101
\(369\) 0 0
\(370\) 0 0
\(371\) −17.2313 −0.894603
\(372\) 0 0
\(373\) 13.5773 0.703007 0.351504 0.936186i \(-0.385670\pi\)
0.351504 + 0.936186i \(0.385670\pi\)
\(374\) −6.09582 −0.315208
\(375\) 0 0
\(376\) −18.7841 −0.968717
\(377\) −2.97543 −0.153242
\(378\) 0 0
\(379\) 0.0601424 0.00308931 0.00154465 0.999999i \(-0.499508\pi\)
0.00154465 + 0.999999i \(0.499508\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 27.3383 1.39875
\(383\) −9.71642 −0.496486 −0.248243 0.968698i \(-0.579853\pi\)
−0.248243 + 0.968698i \(0.579853\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −34.7590 −1.76919
\(387\) 0 0
\(388\) 5.90279 0.299669
\(389\) 5.68991 0.288490 0.144245 0.989542i \(-0.453925\pi\)
0.144245 + 0.989542i \(0.453925\pi\)
\(390\) 0 0
\(391\) 5.67943 0.287221
\(392\) 10.3361 0.522050
\(393\) 0 0
\(394\) −47.9143 −2.41389
\(395\) 0 0
\(396\) 0 0
\(397\) −6.80729 −0.341648 −0.170824 0.985302i \(-0.554643\pi\)
−0.170824 + 0.985302i \(0.554643\pi\)
\(398\) 2.73548 0.137117
\(399\) 0 0
\(400\) 0 0
\(401\) 11.7255 0.585543 0.292771 0.956182i \(-0.405422\pi\)
0.292771 + 0.956182i \(0.405422\pi\)
\(402\) 0 0
\(403\) −18.6564 −0.929342
\(404\) −36.0584 −1.79397
\(405\) 0 0
\(406\) 2.91044 0.144443
\(407\) −4.00886 −0.198712
\(408\) 0 0
\(409\) −22.2665 −1.10101 −0.550505 0.834832i \(-0.685565\pi\)
−0.550505 + 0.834832i \(0.685565\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 30.8179 1.51829
\(413\) −3.35789 −0.165231
\(414\) 0 0
\(415\) 0 0
\(416\) 21.1292 1.03594
\(417\) 0 0
\(418\) 48.1944 2.35727
\(419\) −28.2149 −1.37839 −0.689194 0.724577i \(-0.742035\pi\)
−0.689194 + 0.724577i \(0.742035\pi\)
\(420\) 0 0
\(421\) −34.5167 −1.68224 −0.841121 0.540847i \(-0.818104\pi\)
−0.841121 + 0.540847i \(0.818104\pi\)
\(422\) 11.1722 0.543855
\(423\) 0 0
\(424\) 25.6866 1.24745
\(425\) 0 0
\(426\) 0 0
\(427\) 11.1449 0.539337
\(428\) −14.0328 −0.678299
\(429\) 0 0
\(430\) 0 0
\(431\) 23.0678 1.11114 0.555568 0.831471i \(-0.312501\pi\)
0.555568 + 0.831471i \(0.312501\pi\)
\(432\) 0 0
\(433\) 17.8519 0.857908 0.428954 0.903326i \(-0.358882\pi\)
0.428954 + 0.903326i \(0.358882\pi\)
\(434\) 18.2490 0.875978
\(435\) 0 0
\(436\) 44.3010 2.12163
\(437\) −44.9023 −2.14797
\(438\) 0 0
\(439\) −3.31655 −0.158290 −0.0791452 0.996863i \(-0.525219\pi\)
−0.0791452 + 0.996863i \(0.525219\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −4.22604 −0.201012
\(443\) 29.8818 1.41973 0.709863 0.704340i \(-0.248757\pi\)
0.709863 + 0.704340i \(0.248757\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −35.8698 −1.69848
\(447\) 0 0
\(448\) −16.8849 −0.797738
\(449\) 8.89198 0.419639 0.209819 0.977740i \(-0.432712\pi\)
0.209819 + 0.977740i \(0.432712\pi\)
\(450\) 0 0
\(451\) 47.5506 2.23907
\(452\) 12.4799 0.587004
\(453\) 0 0
\(454\) −15.0929 −0.708347
\(455\) 0 0
\(456\) 0 0
\(457\) 19.8853 0.930194 0.465097 0.885260i \(-0.346019\pi\)
0.465097 + 0.885260i \(0.346019\pi\)
\(458\) 12.9801 0.606520
\(459\) 0 0
\(460\) 0 0
\(461\) −13.5776 −0.632372 −0.316186 0.948697i \(-0.602402\pi\)
−0.316186 + 0.948697i \(0.602402\pi\)
\(462\) 0 0
\(463\) −29.7645 −1.38328 −0.691638 0.722244i \(-0.743111\pi\)
−0.691638 + 0.722244i \(0.743111\pi\)
\(464\) 1.43674 0.0666988
\(465\) 0 0
\(466\) 31.2726 1.44867
\(467\) 6.56767 0.303915 0.151958 0.988387i \(-0.451442\pi\)
0.151958 + 0.988387i \(0.451442\pi\)
\(468\) 0 0
\(469\) 17.0888 0.789086
\(470\) 0 0
\(471\) 0 0
\(472\) 5.00559 0.230401
\(473\) −8.75463 −0.402538
\(474\) 0 0
\(475\) 0 0
\(476\) 2.44224 0.111940
\(477\) 0 0
\(478\) 45.7459 2.09237
\(479\) 36.9147 1.68668 0.843338 0.537383i \(-0.180587\pi\)
0.843338 + 0.537383i \(0.180587\pi\)
\(480\) 0 0
\(481\) −2.77921 −0.126721
\(482\) 17.4840 0.796376
\(483\) 0 0
\(484\) 21.4274 0.973972
\(485\) 0 0
\(486\) 0 0
\(487\) −24.4257 −1.10684 −0.553418 0.832904i \(-0.686677\pi\)
−0.553418 + 0.832904i \(0.686677\pi\)
\(488\) −16.6136 −0.752062
\(489\) 0 0
\(490\) 0 0
\(491\) −0.828059 −0.0373698 −0.0186849 0.999825i \(-0.505948\pi\)
−0.0186849 + 0.999825i \(0.505948\pi\)
\(492\) 0 0
\(493\) −0.642441 −0.0289341
\(494\) 33.4116 1.50326
\(495\) 0 0
\(496\) 9.00856 0.404496
\(497\) 6.71948 0.301410
\(498\) 0 0
\(499\) 32.7413 1.46570 0.732850 0.680390i \(-0.238189\pi\)
0.732850 + 0.680390i \(0.238189\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −26.1184 −1.16572
\(503\) 3.04972 0.135980 0.0679901 0.997686i \(-0.478341\pi\)
0.0679901 + 0.997686i \(0.478341\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −83.8823 −3.72902
\(507\) 0 0
\(508\) −62.3183 −2.76493
\(509\) 11.2666 0.499384 0.249692 0.968325i \(-0.419671\pi\)
0.249692 + 0.968325i \(0.419671\pi\)
\(510\) 0 0
\(511\) 21.0644 0.931833
\(512\) −15.8416 −0.700107
\(513\) 0 0
\(514\) 9.62673 0.424617
\(515\) 0 0
\(516\) 0 0
\(517\) 41.0810 1.80674
\(518\) 2.71851 0.119445
\(519\) 0 0
\(520\) 0 0
\(521\) −1.39366 −0.0610573 −0.0305287 0.999534i \(-0.509719\pi\)
−0.0305287 + 0.999534i \(0.509719\pi\)
\(522\) 0 0
\(523\) 10.6212 0.464434 0.232217 0.972664i \(-0.425402\pi\)
0.232217 + 0.972664i \(0.425402\pi\)
\(524\) 26.7299 1.16770
\(525\) 0 0
\(526\) −61.1791 −2.66753
\(527\) −4.02821 −0.175472
\(528\) 0 0
\(529\) 55.1524 2.39793
\(530\) 0 0
\(531\) 0 0
\(532\) −19.3087 −0.837137
\(533\) 32.9653 1.42789
\(534\) 0 0
\(535\) 0 0
\(536\) −25.4742 −1.10032
\(537\) 0 0
\(538\) 13.9731 0.602424
\(539\) −22.6051 −0.973669
\(540\) 0 0
\(541\) 31.1071 1.33740 0.668698 0.743534i \(-0.266852\pi\)
0.668698 + 0.743534i \(0.266852\pi\)
\(542\) −9.66544 −0.415166
\(543\) 0 0
\(544\) 4.56212 0.195599
\(545\) 0 0
\(546\) 0 0
\(547\) 17.0828 0.730408 0.365204 0.930927i \(-0.380999\pi\)
0.365204 + 0.930927i \(0.380999\pi\)
\(548\) −2.43651 −0.104083
\(549\) 0 0
\(550\) 0 0
\(551\) 5.07923 0.216382
\(552\) 0 0
\(553\) −4.35114 −0.185029
\(554\) −8.87942 −0.377251
\(555\) 0 0
\(556\) −40.3628 −1.71176
\(557\) −15.1831 −0.643329 −0.321665 0.946854i \(-0.604242\pi\)
−0.321665 + 0.946854i \(0.604242\pi\)
\(558\) 0 0
\(559\) −6.06930 −0.256704
\(560\) 0 0
\(561\) 0 0
\(562\) 30.2859 1.27753
\(563\) −34.9344 −1.47231 −0.736154 0.676814i \(-0.763360\pi\)
−0.736154 + 0.676814i \(0.763360\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −32.7328 −1.37586
\(567\) 0 0
\(568\) −10.0167 −0.420291
\(569\) −2.51836 −0.105575 −0.0527875 0.998606i \(-0.516811\pi\)
−0.0527875 + 0.998606i \(0.516811\pi\)
\(570\) 0 0
\(571\) 18.9130 0.791485 0.395742 0.918362i \(-0.370487\pi\)
0.395742 + 0.918362i \(0.370487\pi\)
\(572\) 36.8760 1.54186
\(573\) 0 0
\(574\) −32.2453 −1.34589
\(575\) 0 0
\(576\) 0 0
\(577\) 4.64049 0.193186 0.0965930 0.995324i \(-0.469205\pi\)
0.0965930 + 0.995324i \(0.469205\pi\)
\(578\) 36.6712 1.52532
\(579\) 0 0
\(580\) 0 0
\(581\) 6.90669 0.286538
\(582\) 0 0
\(583\) −56.1768 −2.32661
\(584\) −31.4006 −1.29937
\(585\) 0 0
\(586\) 36.8962 1.52417
\(587\) 25.7669 1.06351 0.531756 0.846897i \(-0.321532\pi\)
0.531756 + 0.846897i \(0.321532\pi\)
\(588\) 0 0
\(589\) 31.8476 1.31226
\(590\) 0 0
\(591\) 0 0
\(592\) 1.34199 0.0551554
\(593\) −3.02524 −0.124232 −0.0621158 0.998069i \(-0.519785\pi\)
−0.0621158 + 0.998069i \(0.519785\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 56.6774 2.32160
\(597\) 0 0
\(598\) −58.1529 −2.37805
\(599\) 0.521774 0.0213191 0.0106596 0.999943i \(-0.496607\pi\)
0.0106596 + 0.999943i \(0.496607\pi\)
\(600\) 0 0
\(601\) −34.7237 −1.41641 −0.708204 0.706008i \(-0.750494\pi\)
−0.708204 + 0.706008i \(0.750494\pi\)
\(602\) 5.93674 0.241964
\(603\) 0 0
\(604\) −31.0593 −1.26379
\(605\) 0 0
\(606\) 0 0
\(607\) −14.0480 −0.570190 −0.285095 0.958499i \(-0.592025\pi\)
−0.285095 + 0.958499i \(0.592025\pi\)
\(608\) −36.0688 −1.46278
\(609\) 0 0
\(610\) 0 0
\(611\) 28.4801 1.15218
\(612\) 0 0
\(613\) 15.3819 0.621269 0.310635 0.950529i \(-0.399458\pi\)
0.310635 + 0.950529i \(0.399458\pi\)
\(614\) 10.9893 0.443493
\(615\) 0 0
\(616\) −11.0880 −0.446750
\(617\) 15.6734 0.630988 0.315494 0.948928i \(-0.397830\pi\)
0.315494 + 0.948928i \(0.397830\pi\)
\(618\) 0 0
\(619\) 36.1380 1.45251 0.726254 0.687427i \(-0.241260\pi\)
0.726254 + 0.687427i \(0.241260\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 46.6007 1.86852
\(623\) −6.64930 −0.266399
\(624\) 0 0
\(625\) 0 0
\(626\) 53.8870 2.15376
\(627\) 0 0
\(628\) −68.0083 −2.71383
\(629\) −0.600075 −0.0239265
\(630\) 0 0
\(631\) −5.20523 −0.207217 −0.103608 0.994618i \(-0.533039\pi\)
−0.103608 + 0.994618i \(0.533039\pi\)
\(632\) 6.48623 0.258008
\(633\) 0 0
\(634\) 29.6474 1.17745
\(635\) 0 0
\(636\) 0 0
\(637\) −15.6714 −0.620921
\(638\) 9.48853 0.375655
\(639\) 0 0
\(640\) 0 0
\(641\) 28.6342 1.13098 0.565492 0.824754i \(-0.308686\pi\)
0.565492 + 0.824754i \(0.308686\pi\)
\(642\) 0 0
\(643\) −35.6717 −1.40676 −0.703378 0.710816i \(-0.748326\pi\)
−0.703378 + 0.710816i \(0.748326\pi\)
\(644\) 33.6067 1.32429
\(645\) 0 0
\(646\) 7.21409 0.283834
\(647\) 6.14445 0.241563 0.120782 0.992679i \(-0.461460\pi\)
0.120782 + 0.992679i \(0.461460\pi\)
\(648\) 0 0
\(649\) −10.9473 −0.429718
\(650\) 0 0
\(651\) 0 0
\(652\) −27.4371 −1.07452
\(653\) 8.62982 0.337711 0.168855 0.985641i \(-0.445993\pi\)
0.168855 + 0.985641i \(0.445993\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −15.9178 −0.621488
\(657\) 0 0
\(658\) −27.8581 −1.08602
\(659\) −35.4336 −1.38030 −0.690148 0.723668i \(-0.742455\pi\)
−0.690148 + 0.723668i \(0.742455\pi\)
\(660\) 0 0
\(661\) 12.7938 0.497622 0.248811 0.968552i \(-0.419960\pi\)
0.248811 + 0.968552i \(0.419960\pi\)
\(662\) −51.7741 −2.01226
\(663\) 0 0
\(664\) −10.2958 −0.399554
\(665\) 0 0
\(666\) 0 0
\(667\) −8.84038 −0.342301
\(668\) −5.27824 −0.204221
\(669\) 0 0
\(670\) 0 0
\(671\) 36.3341 1.40266
\(672\) 0 0
\(673\) 39.0602 1.50566 0.752830 0.658215i \(-0.228688\pi\)
0.752830 + 0.658215i \(0.228688\pi\)
\(674\) 50.3766 1.94043
\(675\) 0 0
\(676\) −11.9747 −0.460564
\(677\) 51.8790 1.99387 0.996936 0.0782187i \(-0.0249233\pi\)
0.996936 + 0.0782187i \(0.0249233\pi\)
\(678\) 0 0
\(679\) 2.69104 0.103272
\(680\) 0 0
\(681\) 0 0
\(682\) 59.4946 2.27817
\(683\) 27.2220 1.04162 0.520811 0.853672i \(-0.325630\pi\)
0.520811 + 0.853672i \(0.325630\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 35.7022 1.36312
\(687\) 0 0
\(688\) 2.93066 0.111730
\(689\) −38.9455 −1.48371
\(690\) 0 0
\(691\) 21.7474 0.827309 0.413655 0.910434i \(-0.364252\pi\)
0.413655 + 0.910434i \(0.364252\pi\)
\(692\) 15.9033 0.604554
\(693\) 0 0
\(694\) −11.0212 −0.418357
\(695\) 0 0
\(696\) 0 0
\(697\) 7.11772 0.269603
\(698\) −56.7698 −2.14877
\(699\) 0 0
\(700\) 0 0
\(701\) 35.4994 1.34079 0.670397 0.742003i \(-0.266124\pi\)
0.670397 + 0.742003i \(0.266124\pi\)
\(702\) 0 0
\(703\) 4.74427 0.178934
\(704\) −55.0477 −2.07469
\(705\) 0 0
\(706\) −44.9148 −1.69039
\(707\) −16.4388 −0.618243
\(708\) 0 0
\(709\) 33.4325 1.25558 0.627792 0.778381i \(-0.283959\pi\)
0.627792 + 0.778381i \(0.283959\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 9.91208 0.371471
\(713\) −55.4306 −2.07589
\(714\) 0 0
\(715\) 0 0
\(716\) 27.0421 1.01061
\(717\) 0 0
\(718\) 21.4207 0.799412
\(719\) 44.5343 1.66085 0.830425 0.557130i \(-0.188098\pi\)
0.830425 + 0.557130i \(0.188098\pi\)
\(720\) 0 0
\(721\) 14.0497 0.523237
\(722\) −15.0302 −0.559368
\(723\) 0 0
\(724\) 73.9296 2.74757
\(725\) 0 0
\(726\) 0 0
\(727\) −15.6700 −0.581170 −0.290585 0.956849i \(-0.593850\pi\)
−0.290585 + 0.956849i \(0.593850\pi\)
\(728\) −7.68698 −0.284898
\(729\) 0 0
\(730\) 0 0
\(731\) −1.31046 −0.0484689
\(732\) 0 0
\(733\) −29.7350 −1.09829 −0.549143 0.835728i \(-0.685046\pi\)
−0.549143 + 0.835728i \(0.685046\pi\)
\(734\) 20.2580 0.747738
\(735\) 0 0
\(736\) 62.7776 2.31401
\(737\) 55.7123 2.05219
\(738\) 0 0
\(739\) 42.9178 1.57876 0.789379 0.613906i \(-0.210403\pi\)
0.789379 + 0.613906i \(0.210403\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 38.0950 1.39851
\(743\) 10.9064 0.400117 0.200058 0.979784i \(-0.435887\pi\)
0.200058 + 0.979784i \(0.435887\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −30.0168 −1.09899
\(747\) 0 0
\(748\) 7.96211 0.291124
\(749\) −6.39743 −0.233757
\(750\) 0 0
\(751\) 47.2977 1.72592 0.862960 0.505273i \(-0.168608\pi\)
0.862960 + 0.505273i \(0.168608\pi\)
\(752\) −13.7521 −0.501488
\(753\) 0 0
\(754\) 6.57809 0.239560
\(755\) 0 0
\(756\) 0 0
\(757\) −33.3406 −1.21179 −0.605893 0.795546i \(-0.707184\pi\)
−0.605893 + 0.795546i \(0.707184\pi\)
\(758\) −0.132963 −0.00482944
\(759\) 0 0
\(760\) 0 0
\(761\) −45.9707 −1.66644 −0.833219 0.552944i \(-0.813504\pi\)
−0.833219 + 0.552944i \(0.813504\pi\)
\(762\) 0 0
\(763\) 20.1965 0.731162
\(764\) −35.7082 −1.29188
\(765\) 0 0
\(766\) 21.4811 0.776144
\(767\) −7.58939 −0.274037
\(768\) 0 0
\(769\) −9.21048 −0.332138 −0.166069 0.986114i \(-0.553108\pi\)
−0.166069 + 0.986114i \(0.553108\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 45.4007 1.63401
\(773\) 28.6595 1.03081 0.515405 0.856947i \(-0.327642\pi\)
0.515405 + 0.856947i \(0.327642\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −4.01152 −0.144005
\(777\) 0 0
\(778\) −12.5793 −0.450989
\(779\) −56.2737 −2.01621
\(780\) 0 0
\(781\) 21.9066 0.783881
\(782\) −12.5561 −0.449005
\(783\) 0 0
\(784\) 7.56718 0.270256
\(785\) 0 0
\(786\) 0 0
\(787\) −20.8195 −0.742136 −0.371068 0.928606i \(-0.621008\pi\)
−0.371068 + 0.928606i \(0.621008\pi\)
\(788\) 62.5837 2.22945
\(789\) 0 0
\(790\) 0 0
\(791\) 5.68948 0.202295
\(792\) 0 0
\(793\) 25.1892 0.894496
\(794\) 15.0496 0.534090
\(795\) 0 0
\(796\) −3.57298 −0.126641
\(797\) 44.8656 1.58922 0.794610 0.607120i \(-0.207675\pi\)
0.794610 + 0.607120i \(0.207675\pi\)
\(798\) 0 0
\(799\) 6.14931 0.217547
\(800\) 0 0
\(801\) 0 0
\(802\) −25.9228 −0.915365
\(803\) 68.6734 2.42343
\(804\) 0 0
\(805\) 0 0
\(806\) 41.2457 1.45282
\(807\) 0 0
\(808\) 24.5052 0.862090
\(809\) −26.6975 −0.938633 −0.469317 0.883030i \(-0.655500\pi\)
−0.469317 + 0.883030i \(0.655500\pi\)
\(810\) 0 0
\(811\) −21.6414 −0.759934 −0.379967 0.925000i \(-0.624065\pi\)
−0.379967 + 0.925000i \(0.624065\pi\)
\(812\) −3.80150 −0.133406
\(813\) 0 0
\(814\) 8.86281 0.310641
\(815\) 0 0
\(816\) 0 0
\(817\) 10.3606 0.362473
\(818\) 49.2270 1.72118
\(819\) 0 0
\(820\) 0 0
\(821\) 36.0374 1.25771 0.628857 0.777521i \(-0.283523\pi\)
0.628857 + 0.777521i \(0.283523\pi\)
\(822\) 0 0
\(823\) 23.4577 0.817684 0.408842 0.912605i \(-0.365933\pi\)
0.408842 + 0.912605i \(0.365933\pi\)
\(824\) −20.9438 −0.729611
\(825\) 0 0
\(826\) 7.42364 0.258301
\(827\) −14.7623 −0.513334 −0.256667 0.966500i \(-0.582624\pi\)
−0.256667 + 0.966500i \(0.582624\pi\)
\(828\) 0 0
\(829\) 5.63801 0.195816 0.0979081 0.995195i \(-0.468785\pi\)
0.0979081 + 0.995195i \(0.468785\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −38.1628 −1.32306
\(833\) −3.38369 −0.117238
\(834\) 0 0
\(835\) 0 0
\(836\) −62.9495 −2.17715
\(837\) 0 0
\(838\) 62.3776 2.15480
\(839\) −56.4632 −1.94932 −0.974662 0.223681i \(-0.928193\pi\)
−0.974662 + 0.223681i \(0.928193\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 76.3098 2.62981
\(843\) 0 0
\(844\) −14.5927 −0.502301
\(845\) 0 0
\(846\) 0 0
\(847\) 9.76858 0.335652
\(848\) 18.8055 0.645784
\(849\) 0 0
\(850\) 0 0
\(851\) −8.25740 −0.283060
\(852\) 0 0
\(853\) −38.2731 −1.31045 −0.655223 0.755436i \(-0.727425\pi\)
−0.655223 + 0.755436i \(0.727425\pi\)
\(854\) −24.6391 −0.843133
\(855\) 0 0
\(856\) 9.53663 0.325955
\(857\) 47.5891 1.62561 0.812806 0.582534i \(-0.197939\pi\)
0.812806 + 0.582534i \(0.197939\pi\)
\(858\) 0 0
\(859\) −19.4348 −0.663108 −0.331554 0.943436i \(-0.607573\pi\)
−0.331554 + 0.943436i \(0.607573\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −50.9984 −1.73701
\(863\) 24.3695 0.829546 0.414773 0.909925i \(-0.363861\pi\)
0.414773 + 0.909925i \(0.363861\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −39.4671 −1.34115
\(867\) 0 0
\(868\) −23.8360 −0.809047
\(869\) −14.1855 −0.481209
\(870\) 0 0
\(871\) 38.6235 1.30871
\(872\) −30.1068 −1.01955
\(873\) 0 0
\(874\) 99.2703 3.35787
\(875\) 0 0
\(876\) 0 0
\(877\) −23.4009 −0.790193 −0.395097 0.918640i \(-0.629289\pi\)
−0.395097 + 0.918640i \(0.629289\pi\)
\(878\) 7.33225 0.247451
\(879\) 0 0
\(880\) 0 0
\(881\) 49.1434 1.65568 0.827841 0.560963i \(-0.189569\pi\)
0.827841 + 0.560963i \(0.189569\pi\)
\(882\) 0 0
\(883\) 42.0245 1.41424 0.707118 0.707095i \(-0.249995\pi\)
0.707118 + 0.707095i \(0.249995\pi\)
\(884\) 5.51987 0.185653
\(885\) 0 0
\(886\) −66.0628 −2.21942
\(887\) 38.7280 1.30036 0.650179 0.759781i \(-0.274694\pi\)
0.650179 + 0.759781i \(0.274694\pi\)
\(888\) 0 0
\(889\) −28.4105 −0.952857
\(890\) 0 0
\(891\) 0 0
\(892\) 46.8516 1.56871
\(893\) −48.6173 −1.62691
\(894\) 0 0
\(895\) 0 0
\(896\) 18.6323 0.622460
\(897\) 0 0
\(898\) −19.6584 −0.656011
\(899\) 6.27016 0.209122
\(900\) 0 0
\(901\) −8.40895 −0.280143
\(902\) −105.125 −3.50029
\(903\) 0 0
\(904\) −8.48129 −0.282084
\(905\) 0 0
\(906\) 0 0
\(907\) −22.7366 −0.754956 −0.377478 0.926019i \(-0.623209\pi\)
−0.377478 + 0.926019i \(0.623209\pi\)
\(908\) 19.7138 0.654224
\(909\) 0 0
\(910\) 0 0
\(911\) 5.74791 0.190437 0.0952183 0.995456i \(-0.469645\pi\)
0.0952183 + 0.995456i \(0.469645\pi\)
\(912\) 0 0
\(913\) 22.5170 0.745203
\(914\) −43.9625 −1.45415
\(915\) 0 0
\(916\) −16.9541 −0.560178
\(917\) 12.1859 0.402415
\(918\) 0 0
\(919\) 52.1835 1.72137 0.860687 0.509135i \(-0.170035\pi\)
0.860687 + 0.509135i \(0.170035\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 30.0175 0.988572
\(923\) 15.1871 0.499891
\(924\) 0 0
\(925\) 0 0
\(926\) 65.8036 2.16244
\(927\) 0 0
\(928\) −7.10123 −0.233109
\(929\) −4.61899 −0.151544 −0.0757721 0.997125i \(-0.524142\pi\)
−0.0757721 + 0.997125i \(0.524142\pi\)
\(930\) 0 0
\(931\) 26.7519 0.876758
\(932\) −40.8469 −1.33799
\(933\) 0 0
\(934\) −14.5198 −0.475104
\(935\) 0 0
\(936\) 0 0
\(937\) 22.8991 0.748082 0.374041 0.927412i \(-0.377972\pi\)
0.374041 + 0.927412i \(0.377972\pi\)
\(938\) −37.7800 −1.23356
\(939\) 0 0
\(940\) 0 0
\(941\) 24.1297 0.786604 0.393302 0.919409i \(-0.371333\pi\)
0.393302 + 0.919409i \(0.371333\pi\)
\(942\) 0 0
\(943\) 97.9442 3.18950
\(944\) 3.66466 0.119275
\(945\) 0 0
\(946\) 19.3548 0.629278
\(947\) −13.6427 −0.443329 −0.221665 0.975123i \(-0.571149\pi\)
−0.221665 + 0.975123i \(0.571149\pi\)
\(948\) 0 0
\(949\) 47.6090 1.54545
\(950\) 0 0
\(951\) 0 0
\(952\) −1.65974 −0.0537925
\(953\) −45.3303 −1.46839 −0.734196 0.678937i \(-0.762441\pi\)
−0.734196 + 0.678937i \(0.762441\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −59.7514 −1.93250
\(957\) 0 0
\(958\) −81.6113 −2.63674
\(959\) −1.11079 −0.0358692
\(960\) 0 0
\(961\) 8.31492 0.268223
\(962\) 6.14429 0.198100
\(963\) 0 0
\(964\) −22.8369 −0.735528
\(965\) 0 0
\(966\) 0 0
\(967\) 45.2638 1.45558 0.727792 0.685798i \(-0.240547\pi\)
0.727792 + 0.685798i \(0.240547\pi\)
\(968\) −14.5620 −0.468040
\(969\) 0 0
\(970\) 0 0
\(971\) −47.1089 −1.51180 −0.755899 0.654688i \(-0.772800\pi\)
−0.755899 + 0.654688i \(0.772800\pi\)
\(972\) 0 0
\(973\) −18.4011 −0.589912
\(974\) 54.0006 1.73029
\(975\) 0 0
\(976\) −12.1630 −0.389330
\(977\) 2.89922 0.0927542 0.0463771 0.998924i \(-0.485232\pi\)
0.0463771 + 0.998924i \(0.485232\pi\)
\(978\) 0 0
\(979\) −21.6778 −0.692826
\(980\) 0 0
\(981\) 0 0
\(982\) 1.83068 0.0584193
\(983\) −37.0610 −1.18206 −0.591031 0.806649i \(-0.701279\pi\)
−0.591031 + 0.806649i \(0.701279\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 1.42031 0.0452320
\(987\) 0 0
\(988\) −43.6408 −1.38840
\(989\) −18.0327 −0.573406
\(990\) 0 0
\(991\) 17.4669 0.554854 0.277427 0.960747i \(-0.410518\pi\)
0.277427 + 0.960747i \(0.410518\pi\)
\(992\) −44.5259 −1.41370
\(993\) 0 0
\(994\) −14.8555 −0.471187
\(995\) 0 0
\(996\) 0 0
\(997\) 19.4726 0.616703 0.308352 0.951272i \(-0.400223\pi\)
0.308352 + 0.951272i \(0.400223\pi\)
\(998\) −72.3846 −2.29129
\(999\) 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 6525.2.a.cc.1.1 yes 9
3.2 odd 2 6525.2.a.ca.1.9 9
5.4 even 2 6525.2.a.cb.1.9 yes 9
15.14 odd 2 6525.2.a.cd.1.1 yes 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
6525.2.a.ca.1.9 9 3.2 odd 2
6525.2.a.cb.1.9 yes 9 5.4 even 2
6525.2.a.cc.1.1 yes 9 1.1 even 1 trivial
6525.2.a.cd.1.1 yes 9 15.14 odd 2