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Properties

Label 5100.2.a.f.1.1
Level $5100$
Weight $2$
Character 5100.1
Self dual yes
Analytic conductor $40.724$
Analytic rank $0$
Dimension $1$
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] = [5100,2,Mod(1,5100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5100, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("5100.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5100.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: \(40.7237050309\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 204)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 5100.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000 q^{3} +1.00000 q^{9} +O(q^{10})\) \(q-1.00000 q^{3} +1.00000 q^{9} +5.00000 q^{11} +5.00000 q^{13} -1.00000 q^{17} +1.00000 q^{19} +3.00000 q^{23} -1.00000 q^{27} +2.00000 q^{29} +2.00000 q^{31} -5.00000 q^{33} +8.00000 q^{37} -5.00000 q^{39} -5.00000 q^{41} +9.00000 q^{43} -6.00000 q^{47} -7.00000 q^{49} +1.00000 q^{51} +6.00000 q^{53} -1.00000 q^{57} +6.00000 q^{59} -4.00000 q^{61} -12.0000 q^{67} -3.00000 q^{69} -12.0000 q^{71} +2.00000 q^{73} +10.0000 q^{79} +1.00000 q^{81} +2.00000 q^{83} -2.00000 q^{87} +12.0000 q^{89} -2.00000 q^{93} -16.0000 q^{97} +5.00000 q^{99} +O(q^{100})\)

Display 100 coefficients 10 coefficients

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 0
\(3\) −1.00000 −0.577350
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 5.00000 1.50756 0.753778 − 0.657129i \(-0.228229\pi\)
0.753778 + 0.657129i \(0.228229\pi\)
\(12\) 0 0
\(13\) 5.00000 1.38675 0.693375 − 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 1.00000 0.229416 0.114708 − 0.993399i \(-0.463407\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 0.625543 0.312772 − 0.949828i \(-0.398743\pi\)
0.312772 + 0.949828i \(0.398743\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) 2.00000 0.371391 0.185695 − 0.982607i \(-0.440546\pi\)
0.185695 + 0.982607i \(0.440546\pi\)
\(30\) 0 0
\(31\) 2.00000 0.359211 0.179605 − 0.983739i \(-0.442518\pi\)
0.179605 + 0.983739i \(0.442518\pi\)
\(32\) 0 0
\(33\) −5.00000 −0.870388
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 8.00000 1.31519 0.657596 − 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 0 0
\(39\) −5.00000 −0.800641
\(40\) 0 0
\(41\) −5.00000 −0.780869 −0.390434 − 0.920631i \(-0.627675\pi\)
−0.390434 + 0.920631i \(0.627675\pi\)
\(42\) 0 0
\(43\) 9.00000 1.37249 0.686244 − 0.727372i \(-0.259258\pi\)
0.686244 + 0.727372i \(0.259258\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.00000 −0.875190 −0.437595 − 0.899172i \(-0.644170\pi\)
−0.437595 + 0.899172i \(0.644170\pi\)
\(48\) 0 0
\(49\) −7.00000 −1.00000
\(50\) 0 0
\(51\) 1.00000 0.140028
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 − 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −1.00000 −0.132453
\(58\) 0 0
\(59\) 6.00000 0.781133 0.390567 − 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) −4.00000 −0.512148 −0.256074 − 0.966657i \(-0.582429\pi\)
−0.256074 + 0.966657i \(0.582429\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −12.0000 −1.46603 −0.733017 − 0.680211i \(-0.761888\pi\)
−0.733017 + 0.680211i \(0.761888\pi\)
\(68\) 0 0
\(69\) −3.00000 −0.361158
\(70\) 0 0
\(71\) −12.0000 −1.42414 −0.712069 − 0.702109i \(-0.752242\pi\)
−0.712069 + 0.702109i \(0.752242\pi\)
\(72\) 0 0
\(73\) 2.00000 0.234082 0.117041 − 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 − 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 2.00000 0.219529 0.109764 − 0.993958i \(-0.464990\pi\)
0.109764 + 0.993958i \(0.464990\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.00000 −0.214423
\(88\) 0 0
\(89\) 12.0000 1.27200 0.635999 − 0.771690i \(-0.280588\pi\)
0.635999 + 0.771690i \(0.280588\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −2.00000 −0.207390
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −16.0000 −1.62455 −0.812277 − 0.583272i \(-0.801772\pi\)
−0.812277 + 0.583272i \(0.801772\pi\)
\(98\) 0 0
\(99\) 5.00000 0.502519
\(100\) 0 0
\(101\) 8.00000 0.796030 0.398015 − 0.917379i \(-0.369699\pi\)
0.398015 + 0.917379i \(0.369699\pi\)
\(102\) 0 0
\(103\) −7.00000 −0.689730 −0.344865 − 0.938652i \(-0.612075\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 7.00000 0.676716 0.338358 − 0.941018i \(-0.390129\pi\)
0.338358 + 0.941018i \(0.390129\pi\)
\(108\) 0 0
\(109\) −4.00000 −0.383131 −0.191565 − 0.981480i \(-0.561356\pi\)
−0.191565 + 0.981480i \(0.561356\pi\)
\(110\) 0 0
\(111\) −8.00000 −0.759326
\(112\) 0 0
\(113\) −17.0000 −1.59923 −0.799613 − 0.600516i \(-0.794962\pi\)
−0.799613 + 0.600516i \(0.794962\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 5.00000 0.462250
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 14.0000 1.27273
\(122\) 0 0
\(123\) 5.00000 0.450835
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −9.00000 −0.798621 −0.399310 − 0.916816i \(-0.630750\pi\)
−0.399310 + 0.916816i \(0.630750\pi\)
\(128\) 0 0
\(129\) −9.00000 −0.792406
\(130\) 0 0
\(131\) 3.00000 0.262111 0.131056 − 0.991375i \(-0.458163\pi\)
0.131056 + 0.991375i \(0.458163\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −22.0000 −1.87959 −0.939793 − 0.341743i \(-0.888983\pi\)
−0.939793 + 0.341743i \(0.888983\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 − 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 6.00000 0.505291
\(142\) 0 0
\(143\) 25.0000 2.09061
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 7.00000 0.577350
\(148\) 0 0
\(149\) −22.0000 −1.80231 −0.901155 − 0.433497i \(-0.857280\pi\)
−0.901155 + 0.433497i \(0.857280\pi\)
\(150\) 0 0
\(151\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −1.00000 −0.0808452
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 17.0000 1.35675 0.678374 − 0.734717i \(-0.262685\pi\)
0.678374 + 0.734717i \(0.262685\pi\)
\(158\) 0 0
\(159\) −6.00000 −0.475831
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) 14.0000 1.09656 0.548282 − 0.836293i \(-0.315282\pi\)
0.548282 + 0.836293i \(0.315282\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 23.0000 1.77979 0.889897 − 0.456162i \(-0.150776\pi\)
0.889897 + 0.456162i \(0.150776\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 1.00000 0.0764719
\(172\) 0 0
\(173\) 3.00000 0.228086 0.114043 − 0.993476i \(-0.463620\pi\)
0.114043 + 0.993476i \(0.463620\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −6.00000 −0.450988
\(178\) 0 0
\(179\) −18.0000 −1.34538 −0.672692 − 0.739923i \(-0.734862\pi\)
−0.672692 + 0.739923i \(0.734862\pi\)
\(180\) 0 0
\(181\) 14.0000 1.04061 0.520306 − 0.853980i \(-0.325818\pi\)
0.520306 + 0.853980i \(0.325818\pi\)
\(182\) 0 0
\(183\) 4.00000 0.295689
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −5.00000 −0.365636
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 26.0000 1.88129 0.940647 − 0.339387i \(-0.110219\pi\)
0.940647 + 0.339387i \(0.110219\pi\)
\(192\) 0 0
\(193\) 18.0000 1.29567 0.647834 − 0.761781i \(-0.275675\pi\)
0.647834 + 0.761781i \(0.275675\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −17.0000 −1.21120 −0.605600 − 0.795769i \(-0.707067\pi\)
−0.605600 + 0.795769i \(0.707067\pi\)
\(198\) 0 0
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 12.0000 0.846415
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 3.00000 0.208514
\(208\) 0 0
\(209\) 5.00000 0.345857
\(210\) 0 0
\(211\) −22.0000 −1.51454 −0.757271 − 0.653101i \(-0.773468\pi\)
−0.757271 + 0.653101i \(0.773468\pi\)
\(212\) 0 0
\(213\) 12.0000 0.822226
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −2.00000 −0.135147
\(220\) 0 0
\(221\) −5.00000 −0.336336
\(222\) 0 0
\(223\) 11.0000 0.736614 0.368307 − 0.929704i \(-0.379937\pi\)
0.368307 + 0.929704i \(0.379937\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5.00000 0.331862 0.165931 − 0.986137i \(-0.446937\pi\)
0.165931 + 0.986137i \(0.446937\pi\)
\(228\) 0 0
\(229\) 22.0000 1.45380 0.726900 − 0.686743i \(-0.240960\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 13.0000 0.851658 0.425829 − 0.904804i \(-0.359982\pi\)
0.425829 + 0.904804i \(0.359982\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −10.0000 −0.649570
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 − 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −4.00000 −0.257663 −0.128831 − 0.991667i \(-0.541123\pi\)
−0.128831 + 0.991667i \(0.541123\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 5.00000 0.318142
\(248\) 0 0
\(249\) −2.00000 −0.126745
\(250\) 0 0
\(251\) 28.0000 1.76734 0.883672 − 0.468106i \(-0.155064\pi\)
0.883672 + 0.468106i \(0.155064\pi\)
\(252\) 0 0
\(253\) 15.0000 0.943042
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.00000 −0.499026 −0.249513 − 0.968371i \(-0.580271\pi\)
−0.249513 + 0.968371i \(0.580271\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) 0 0
\(263\) −16.0000 −0.986602 −0.493301 − 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) 0 0
\(269\) −21.0000 −1.28039 −0.640196 − 0.768211i \(-0.721147\pi\)
−0.640196 + 0.768211i \(0.721147\pi\)
\(270\) 0 0
\(271\) 25.0000 1.51864 0.759321 − 0.650716i \(-0.225531\pi\)
0.759321 + 0.650716i \(0.225531\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 18.0000 1.08152 0.540758 − 0.841178i \(-0.318138\pi\)
0.540758 + 0.841178i \(0.318138\pi\)
\(278\) 0 0
\(279\) 2.00000 0.119737
\(280\) 0 0
\(281\) 24.0000 1.43172 0.715860 − 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) 0 0
\(283\) 30.0000 1.78331 0.891657 − 0.452711i \(-0.149543\pi\)
0.891657 + 0.452711i \(0.149543\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 16.0000 0.937937
\(292\) 0 0
\(293\) −4.00000 −0.233682 −0.116841 − 0.993151i \(-0.537277\pi\)
−0.116841 + 0.993151i \(0.537277\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −5.00000 −0.290129
\(298\) 0 0
\(299\) 15.0000 0.867472
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) −8.00000 −0.459588
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 − 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 0 0
\(309\) 7.00000 0.398216
\(310\) 0 0
\(311\) 24.0000 1.36092 0.680458 − 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) 0 0
\(313\) −16.0000 −0.904373 −0.452187 − 0.891923i \(-0.649356\pi\)
−0.452187 + 0.891923i \(0.649356\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −30.0000 −1.68497 −0.842484 − 0.538721i \(-0.818908\pi\)
−0.842484 + 0.538721i \(0.818908\pi\)
\(318\) 0 0
\(319\) 10.0000 0.559893
\(320\) 0 0
\(321\) −7.00000 −0.390702
\(322\) 0 0
\(323\) −1.00000 −0.0556415
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 4.00000 0.221201
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −11.0000 −0.604615 −0.302307 − 0.953211i \(-0.597757\pi\)
−0.302307 + 0.953211i \(0.597757\pi\)
\(332\) 0 0
\(333\) 8.00000 0.438397
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2.00000 0.108947 0.0544735 − 0.998515i \(-0.482652\pi\)
0.0544735 + 0.998515i \(0.482652\pi\)
\(338\) 0 0
\(339\) 17.0000 0.923313
\(340\) 0 0
\(341\) 10.0000 0.541530
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −4.00000 −0.214731 −0.107366 − 0.994220i \(-0.534242\pi\)
−0.107366 + 0.994220i \(0.534242\pi\)
\(348\) 0 0
\(349\) −7.00000 −0.374701 −0.187351 − 0.982293i \(-0.559990\pi\)
−0.187351 + 0.982293i \(0.559990\pi\)
\(350\) 0 0
\(351\) −5.00000 −0.266880
\(352\) 0 0
\(353\) 6.00000 0.319348 0.159674 − 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −36.0000 −1.90001 −0.950004 − 0.312239i \(-0.898921\pi\)
−0.950004 + 0.312239i \(0.898921\pi\)
\(360\) 0 0
\(361\) −18.0000 −0.947368
\(362\) 0 0
\(363\) −14.0000 −0.734809
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −12.0000 −0.626395 −0.313197 − 0.949688i \(-0.601400\pi\)
−0.313197 + 0.949688i \(0.601400\pi\)
\(368\) 0 0
\(369\) −5.00000 −0.260290
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 6.00000 0.310668 0.155334 − 0.987862i \(-0.450355\pi\)
0.155334 + 0.987862i \(0.450355\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 10.0000 0.515026
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 − 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) 9.00000 0.461084
\(382\) 0 0
\(383\) −20.0000 −1.02195 −0.510976 − 0.859595i \(-0.670716\pi\)
−0.510976 + 0.859595i \(0.670716\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 9.00000 0.457496
\(388\) 0 0
\(389\) −8.00000 −0.405616 −0.202808 − 0.979219i \(-0.565007\pi\)
−0.202808 + 0.979219i \(0.565007\pi\)
\(390\) 0 0
\(391\) −3.00000 −0.151717
\(392\) 0 0
\(393\) −3.00000 −0.151330
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 − 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −17.0000 −0.848939 −0.424470 − 0.905442i \(-0.639539\pi\)
−0.424470 + 0.905442i \(0.639539\pi\)
\(402\) 0 0
\(403\) 10.0000 0.498135
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 40.0000 1.98273
\(408\) 0 0
\(409\) 5.00000 0.247234 0.123617 − 0.992330i \(-0.460551\pi\)
0.123617 + 0.992330i \(0.460551\pi\)
\(410\) 0 0
\(411\) 22.0000 1.08518
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −14.0000 −0.685583
\(418\) 0 0
\(419\) 28.0000 1.36789 0.683945 − 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) −29.0000 −1.41337 −0.706687 − 0.707527i \(-0.749811\pi\)
−0.706687 + 0.707527i \(0.749811\pi\)
\(422\) 0 0
\(423\) −6.00000 −0.291730
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) −25.0000 −1.20701
\(430\) 0 0
\(431\) −32.0000 −1.54139 −0.770693 − 0.637207i \(-0.780090\pi\)
−0.770693 + 0.637207i \(0.780090\pi\)
\(432\) 0 0
\(433\) 41.0000 1.97033 0.985167 − 0.171598i \(-0.0548929\pi\)
0.985167 + 0.171598i \(0.0548929\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 3.00000 0.143509
\(438\) 0 0
\(439\) 28.0000 1.33637 0.668184 − 0.743996i \(-0.267072\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) 0 0
\(441\) −7.00000 −0.333333
\(442\) 0 0
\(443\) −2.00000 −0.0950229 −0.0475114 − 0.998871i \(-0.515129\pi\)
−0.0475114 + 0.998871i \(0.515129\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 22.0000 1.04056
\(448\) 0 0
\(449\) −10.0000 −0.471929 −0.235965 − 0.971762i \(-0.575825\pi\)
−0.235965 + 0.971762i \(0.575825\pi\)
\(450\) 0 0
\(451\) −25.0000 −1.17720
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −13.0000 −0.608114 −0.304057 − 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) 0 0
\(459\) 1.00000 0.0466760
\(460\) 0 0
\(461\) −6.00000 −0.279448 −0.139724 − 0.990190i \(-0.544622\pi\)
−0.139724 + 0.990190i \(0.544622\pi\)
\(462\) 0 0
\(463\) −8.00000 −0.371792 −0.185896 − 0.982569i \(-0.559519\pi\)
−0.185896 + 0.982569i \(0.559519\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −18.0000 −0.832941 −0.416470 − 0.909149i \(-0.636733\pi\)
−0.416470 + 0.909149i \(0.636733\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −17.0000 −0.783319
\(472\) 0 0
\(473\) 45.0000 2.06910
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 0 0
\(479\) 9.00000 0.411220 0.205610 − 0.978634i \(-0.434082\pi\)
0.205610 + 0.978634i \(0.434082\pi\)
\(480\) 0 0
\(481\) 40.0000 1.82384
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 34.0000 1.54069 0.770344 − 0.637629i \(-0.220085\pi\)
0.770344 + 0.637629i \(0.220085\pi\)
\(488\) 0 0
\(489\) −14.0000 −0.633102
\(490\) 0 0
\(491\) 30.0000 1.35388 0.676941 − 0.736038i \(-0.263305\pi\)
0.676941 + 0.736038i \(0.263305\pi\)
\(492\) 0 0
\(493\) −2.00000 −0.0900755
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 10.0000 0.447661 0.223831 − 0.974628i \(-0.428144\pi\)
0.223831 + 0.974628i \(0.428144\pi\)
\(500\) 0 0
\(501\) −23.0000 −1.02756
\(502\) 0 0
\(503\) −27.0000 −1.20387 −0.601935 − 0.798545i \(-0.705603\pi\)
−0.601935 + 0.798545i \(0.705603\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −12.0000 −0.532939
\(508\) 0 0
\(509\) −36.0000 −1.59567 −0.797836 − 0.602875i \(-0.794022\pi\)
−0.797836 + 0.602875i \(0.794022\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) −1.00000 −0.0441511
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −30.0000 −1.31940
\(518\) 0 0
\(519\) −3.00000 −0.131685
\(520\) 0 0
\(521\) −13.0000 −0.569540 −0.284770 − 0.958596i \(-0.591917\pi\)
−0.284770 + 0.958596i \(0.591917\pi\)
\(522\) 0 0
\(523\) −20.0000 −0.874539 −0.437269 − 0.899331i \(-0.644054\pi\)
−0.437269 + 0.899331i \(0.644054\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −2.00000 −0.0871214
\(528\) 0 0
\(529\) −14.0000 −0.608696
\(530\) 0 0
\(531\) 6.00000 0.260378
\(532\) 0 0
\(533\) −25.0000 −1.08287
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 18.0000 0.776757
\(538\) 0 0
\(539\) −35.0000 −1.50756
\(540\) 0 0
\(541\) 44.0000 1.89171 0.945854 − 0.324593i \(-0.105227\pi\)
0.945854 + 0.324593i \(0.105227\pi\)
\(542\) 0 0
\(543\) −14.0000 −0.600798
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 12.0000 0.513083 0.256541 − 0.966533i \(-0.417417\pi\)
0.256541 + 0.966533i \(0.417417\pi\)
\(548\) 0 0
\(549\) −4.00000 −0.170716
\(550\) 0 0
\(551\) 2.00000 0.0852029
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −14.0000 −0.593199 −0.296600 − 0.955002i \(-0.595853\pi\)
−0.296600 + 0.955002i \(0.595853\pi\)
\(558\) 0 0
\(559\) 45.0000 1.90330
\(560\) 0 0
\(561\) 5.00000 0.211100
\(562\) 0 0
\(563\) 18.0000 0.758610 0.379305 − 0.925272i \(-0.376163\pi\)
0.379305 + 0.925272i \(0.376163\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −24.0000 −1.00613 −0.503066 − 0.864248i \(-0.667795\pi\)
−0.503066 + 0.864248i \(0.667795\pi\)
\(570\) 0 0
\(571\) 16.0000 0.669579 0.334790 − 0.942293i \(-0.391335\pi\)
0.334790 + 0.942293i \(0.391335\pi\)
\(572\) 0 0
\(573\) −26.0000 −1.08617
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 7.00000 0.291414 0.145707 − 0.989328i \(-0.453454\pi\)
0.145707 + 0.989328i \(0.453454\pi\)
\(578\) 0 0
\(579\) −18.0000 −0.748054
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 30.0000 1.24247
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −4.00000 −0.165098 −0.0825488 − 0.996587i \(-0.526306\pi\)
−0.0825488 + 0.996587i \(0.526306\pi\)
\(588\) 0 0
\(589\) 2.00000 0.0824086
\(590\) 0 0
\(591\) 17.0000 0.699287
\(592\) 0 0
\(593\) −22.0000 −0.903432 −0.451716 − 0.892162i \(-0.649188\pi\)
−0.451716 + 0.892162i \(0.649188\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 10.0000 0.408589 0.204294 − 0.978909i \(-0.434510\pi\)
0.204294 + 0.978909i \(0.434510\pi\)
\(600\) 0 0
\(601\) 42.0000 1.71322 0.856608 − 0.515968i \(-0.172568\pi\)
0.856608 + 0.515968i \(0.172568\pi\)
\(602\) 0 0
\(603\) −12.0000 −0.488678
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 6.00000 0.243532 0.121766 − 0.992559i \(-0.461144\pi\)
0.121766 + 0.992559i \(0.461144\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −30.0000 −1.21367
\(612\) 0 0
\(613\) 25.0000 1.00974 0.504870 − 0.863195i \(-0.331540\pi\)
0.504870 + 0.863195i \(0.331540\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 18.0000 0.724653 0.362326 − 0.932051i \(-0.381983\pi\)
0.362326 + 0.932051i \(0.381983\pi\)
\(618\) 0 0
\(619\) 34.0000 1.36658 0.683288 − 0.730149i \(-0.260549\pi\)
0.683288 + 0.730149i \(0.260549\pi\)
\(620\) 0 0
\(621\) −3.00000 −0.120386
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −5.00000 −0.199681
\(628\) 0 0
\(629\) −8.00000 −0.318981
\(630\) 0 0
\(631\) 9.00000 0.358284 0.179142 − 0.983823i \(-0.442668\pi\)
0.179142 + 0.983823i \(0.442668\pi\)
\(632\) 0 0
\(633\) 22.0000 0.874421
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −35.0000 −1.38675
\(638\) 0 0
\(639\) −12.0000 −0.474713
\(640\) 0 0
\(641\) −7.00000 −0.276483 −0.138242 − 0.990399i \(-0.544145\pi\)
−0.138242 + 0.990399i \(0.544145\pi\)
\(642\) 0 0
\(643\) −8.00000 −0.315489 −0.157745 − 0.987480i \(-0.550422\pi\)
−0.157745 + 0.987480i \(0.550422\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 22.0000 0.864909 0.432455 − 0.901656i \(-0.357648\pi\)
0.432455 + 0.901656i \(0.357648\pi\)
\(648\) 0 0
\(649\) 30.0000 1.17760
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −33.0000 −1.29139 −0.645695 − 0.763596i \(-0.723432\pi\)
−0.645695 + 0.763596i \(0.723432\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) 30.0000 1.16863 0.584317 − 0.811525i \(-0.301362\pi\)
0.584317 + 0.811525i \(0.301362\pi\)
\(660\) 0 0
\(661\) −3.00000 −0.116686 −0.0583432 − 0.998297i \(-0.518582\pi\)
−0.0583432 + 0.998297i \(0.518582\pi\)
\(662\) 0 0
\(663\) 5.00000 0.194184
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 6.00000 0.232321
\(668\) 0 0
\(669\) −11.0000 −0.425285
\(670\) 0 0
\(671\) −20.0000 −0.772091
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 − 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 41.0000 1.57576 0.787879 − 0.615830i \(-0.211179\pi\)
0.787879 + 0.615830i \(0.211179\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −5.00000 −0.191600
\(682\) 0 0
\(683\) 5.00000 0.191320 0.0956598 − 0.995414i \(-0.469504\pi\)
0.0956598 + 0.995414i \(0.469504\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −22.0000 −0.839352
\(688\) 0 0
\(689\) 30.0000 1.14291
\(690\) 0 0
\(691\) −28.0000 −1.06517 −0.532585 − 0.846376i \(-0.678779\pi\)
−0.532585 + 0.846376i \(0.678779\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 5.00000 0.189389
\(698\) 0 0
\(699\) −13.0000 −0.491705
\(700\) 0 0
\(701\) 40.0000 1.51078 0.755390 − 0.655276i \(-0.227448\pi\)
0.755390 + 0.655276i \(0.227448\pi\)
\(702\) 0 0
\(703\) 8.00000 0.301726
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) 10.0000 0.375558 0.187779 − 0.982211i \(-0.439871\pi\)
0.187779 + 0.982211i \(0.439871\pi\)
\(710\) 0 0
\(711\) 10.0000 0.375029
\(712\) 0 0
\(713\) 6.00000 0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −12.0000 −0.448148
\(718\) 0 0
\(719\) 7.00000 0.261056 0.130528 − 0.991445i \(-0.458333\pi\)
0.130528 + 0.991445i \(0.458333\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 4.00000 0.148762
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −16.0000 −0.593407 −0.296704 − 0.954970i \(-0.595887\pi\)
−0.296704 + 0.954970i \(0.595887\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −9.00000 −0.332877
\(732\) 0 0
\(733\) −10.0000 −0.369358 −0.184679 − 0.982799i \(-0.559125\pi\)
−0.184679 + 0.982799i \(0.559125\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −60.0000 −2.21013
\(738\) 0 0
\(739\) −23.0000 −0.846069 −0.423034 − 0.906114i \(-0.639035\pi\)
−0.423034 + 0.906114i \(0.639035\pi\)
\(740\) 0 0
\(741\) −5.00000 −0.183680
\(742\) 0 0
\(743\) 16.0000 0.586983 0.293492 − 0.955962i \(-0.405183\pi\)
0.293492 + 0.955962i \(0.405183\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 2.00000 0.0731762
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) −22.0000 −0.802791 −0.401396 − 0.915905i \(-0.631475\pi\)
−0.401396 + 0.915905i \(0.631475\pi\)
\(752\) 0 0
\(753\) −28.0000 −1.02038
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −41.0000 −1.49017 −0.745085 − 0.666969i \(-0.767591\pi\)
−0.745085 + 0.666969i \(0.767591\pi\)
\(758\) 0 0
\(759\) −15.0000 −0.544466
\(760\) 0 0
\(761\) −42.0000 −1.52250 −0.761249 − 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 30.0000 1.08324
\(768\) 0 0
\(769\) −39.0000 −1.40638 −0.703188 − 0.711004i \(-0.748241\pi\)
−0.703188 + 0.711004i \(0.748241\pi\)
\(770\) 0 0
\(771\) 8.00000 0.288113
\(772\) 0 0
\(773\) 16.0000 0.575480 0.287740 − 0.957709i \(-0.407096\pi\)
0.287740 + 0.957709i \(0.407096\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −5.00000 −0.179144
\(780\) 0 0
\(781\) −60.0000 −2.14697
\(782\) 0 0
\(783\) −2.00000 −0.0714742
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 32.0000 1.14068 0.570338 − 0.821410i \(-0.306812\pi\)
0.570338 + 0.821410i \(0.306812\pi\)
\(788\) 0 0
\(789\) 16.0000 0.569615
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −20.0000 −0.710221
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.00000 −0.283375 −0.141687 − 0.989911i \(-0.545253\pi\)
−0.141687 + 0.989911i \(0.545253\pi\)
\(798\) 0 0
\(799\) 6.00000 0.212265
\(800\) 0 0
\(801\) 12.0000 0.423999
\(802\) 0 0
\(803\) 10.0000 0.352892
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 21.0000 0.739235
\(808\) 0 0
\(809\) 11.0000 0.386739 0.193370 − 0.981126i \(-0.438058\pi\)
0.193370 + 0.981126i \(0.438058\pi\)
\(810\) 0 0
\(811\) −26.0000 −0.912983 −0.456492 − 0.889728i \(-0.650894\pi\)
−0.456492 + 0.889728i \(0.650894\pi\)
\(812\) 0 0
\(813\) −25.0000 −0.876788
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 9.00000 0.314870
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −31.0000 −1.08191 −0.540954 − 0.841052i \(-0.681937\pi\)
−0.540954 + 0.841052i \(0.681937\pi\)
\(822\) 0 0
\(823\) −8.00000 −0.278862 −0.139431 − 0.990232i \(-0.544527\pi\)
−0.139431 + 0.990232i \(0.544527\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 5.00000 0.173867 0.0869335 − 0.996214i \(-0.472293\pi\)
0.0869335 + 0.996214i \(0.472293\pi\)
\(828\) 0 0
\(829\) −10.0000 −0.347314 −0.173657 − 0.984806i \(-0.555558\pi\)
−0.173657 + 0.984806i \(0.555558\pi\)
\(830\) 0 0
\(831\) −18.0000 −0.624413
\(832\) 0 0
\(833\) 7.00000 0.242536
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −2.00000 −0.0691301
\(838\) 0 0
\(839\) −21.0000 −0.725001 −0.362500 − 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(840\) 0 0
\(841\) −25.0000 −0.862069
\(842\) 0 0
\(843\) −24.0000 −0.826604
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) −30.0000 −1.02960
\(850\) 0 0
\(851\) 24.0000 0.822709
\(852\) 0 0
\(853\) −58.0000 −1.98588 −0.992941 − 0.118609i \(-0.962157\pi\)
−0.992941 + 0.118609i \(0.962157\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 6.00000 0.204956 0.102478 − 0.994735i \(-0.467323\pi\)
0.102478 + 0.994735i \(0.467323\pi\)
\(858\) 0 0
\(859\) 36.0000 1.22830 0.614152 − 0.789188i \(-0.289498\pi\)
0.614152 + 0.789188i \(0.289498\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −4.00000 −0.136162 −0.0680808 − 0.997680i \(-0.521688\pi\)
−0.0680808 + 0.997680i \(0.521688\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −1.00000 −0.0339618
\(868\) 0 0
\(869\) 50.0000 1.69613
\(870\) 0 0
\(871\) −60.0000 −2.03302
\(872\) 0 0
\(873\) −16.0000 −0.541518
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 26.0000 0.877958 0.438979 − 0.898497i \(-0.355340\pi\)
0.438979 + 0.898497i \(0.355340\pi\)
\(878\) 0 0
\(879\) 4.00000 0.134917
\(880\) 0 0
\(881\) 14.0000 0.471672 0.235836 − 0.971793i \(-0.424217\pi\)
0.235836 + 0.971793i \(0.424217\pi\)
\(882\) 0 0
\(883\) 27.0000 0.908622 0.454311 − 0.890843i \(-0.349885\pi\)
0.454311 + 0.890843i \(0.349885\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −27.0000 −0.906571 −0.453286 − 0.891365i \(-0.649748\pi\)
−0.453286 + 0.891365i \(0.649748\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 5.00000 0.167506
\(892\) 0 0
\(893\) −6.00000 −0.200782
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −15.0000 −0.500835
\(898\) 0 0
\(899\) 4.00000 0.133407
\(900\) 0 0
\(901\) −6.00000 −0.199889
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 2.00000 0.0664089 0.0332045 − 0.999449i \(-0.489429\pi\)
0.0332045 + 0.999449i \(0.489429\pi\)
\(908\) 0 0
\(909\) 8.00000 0.265343
\(910\) 0 0
\(911\) 17.0000 0.563235 0.281618 − 0.959527i \(-0.409129\pi\)
0.281618 + 0.959527i \(0.409129\pi\)
\(912\) 0 0
\(913\) 10.0000 0.330952
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) −15.0000 −0.494804 −0.247402 − 0.968913i \(-0.579577\pi\)
−0.247402 + 0.968913i \(0.579577\pi\)
\(920\) 0 0
\(921\) −12.0000 −0.395413
\(922\) 0 0
\(923\) −60.0000 −1.97492
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −7.00000 −0.229910
\(928\) 0 0
\(929\) −31.0000 −1.01708 −0.508539 − 0.861039i \(-0.669814\pi\)
−0.508539 + 0.861039i \(0.669814\pi\)
\(930\) 0 0
\(931\) −7.00000 −0.229416
\(932\) 0 0
\(933\) −24.0000 −0.785725
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 22.0000 0.718709 0.359354 − 0.933201i \(-0.382997\pi\)
0.359354 + 0.933201i \(0.382997\pi\)
\(938\) 0 0
\(939\) 16.0000 0.522140
\(940\) 0 0
\(941\) −34.0000 −1.10837 −0.554184 − 0.832394i \(-0.686970\pi\)
−0.554184 + 0.832394i \(0.686970\pi\)
\(942\) 0 0
\(943\) −15.0000 −0.488467
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 28.0000 0.909878 0.454939 − 0.890523i \(-0.349661\pi\)
0.454939 + 0.890523i \(0.349661\pi\)
\(948\) 0 0
\(949\) 10.0000 0.324614
\(950\) 0 0
\(951\) 30.0000 0.972817
\(952\) 0 0
\(953\) −36.0000 −1.16615 −0.583077 − 0.812417i \(-0.698151\pi\)
−0.583077 + 0.812417i \(0.698151\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −10.0000 −0.323254
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −27.0000 −0.870968
\(962\) 0 0
\(963\) 7.00000 0.225572
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −19.0000 −0.610999 −0.305499 − 0.952192i \(-0.598823\pi\)
−0.305499 + 0.952192i \(0.598823\pi\)
\(968\) 0 0
\(969\) 1.00000 0.0321246
\(970\) 0 0
\(971\) −22.0000 −0.706014 −0.353007 − 0.935621i \(-0.614841\pi\)
−0.353007 + 0.935621i \(0.614841\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −14.0000 −0.447900 −0.223950 − 0.974601i \(-0.571895\pi\)
−0.223950 + 0.974601i \(0.571895\pi\)
\(978\) 0 0
\(979\) 60.0000 1.91761
\(980\) 0 0
\(981\) −4.00000 −0.127710
\(982\) 0 0
\(983\) −51.0000 −1.62665 −0.813324 − 0.581811i \(-0.802344\pi\)
−0.813324 + 0.581811i \(0.802344\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 27.0000 0.858550
\(990\) 0 0
\(991\) 20.0000 0.635321 0.317660 − 0.948205i \(-0.397103\pi\)
0.317660 + 0.948205i \(0.397103\pi\)
\(992\) 0 0
\(993\) 11.0000 0.349074
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 2.00000 0.0633406 0.0316703 − 0.999498i \(-0.489917\pi\)
0.0316703 + 0.999498i \(0.489917\pi\)
\(998\) 0 0
\(999\) −8.00000 −0.253109
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 5100.2.a.f.1.1 1
5.2 odd 4 5100.2.g.l.2449.2 2
5.3 odd 4 5100.2.g.l.2449.1 2
5.4 even 2 204.2.a.b.1.1 ✓ 1
15.14 odd 2 612.2.a.b.1.1 1
20.19 odd 2 816.2.a.e.1.1 1
35.34 odd 2 9996.2.a.b.1.1 1
40.19 odd 2 3264.2.a.u.1.1 1
40.29 even 2 3264.2.a.f.1.1 1
60.59 even 2 2448.2.a.e.1.1 1
85.4 even 4 3468.2.b.a.577.1 2
85.9 even 8 3468.2.j.f.829.2 4
85.19 even 8 3468.2.j.f.3217.2 4
85.49 even 8 3468.2.j.f.3217.1 4
85.59 even 8 3468.2.j.f.829.1 4
85.64 even 4 3468.2.b.a.577.2 2
85.84 even 2 3468.2.a.a.1.1 1
120.29 odd 2 9792.2.a.bo.1.1 1
120.59 even 2 9792.2.a.bn.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
204.2.a.b.1.1 ✓ 1 5.4 even 2
612.2.a.b.1.1 1 15.14 odd 2
816.2.a.e.1.1 1 20.19 odd 2
2448.2.a.e.1.1 1 60.59 even 2
3264.2.a.f.1.1 1 40.29 even 2
3264.2.a.u.1.1 1 40.19 odd 2
3468.2.a.a.1.1 1 85.84 even 2
3468.2.b.a.577.1 2 85.4 even 4
3468.2.b.a.577.2 2 85.64 even 4
3468.2.j.f.829.1 4 85.59 even 8
3468.2.j.f.829.2 4 85.9 even 8
3468.2.j.f.3217.1 4 85.49 even 8
3468.2.j.f.3217.2 4 85.19 even 8
5100.2.a.f.1.1 1 1.1 even 1 trivial
5100.2.g.l.2449.1 2 5.3 odd 4
5100.2.g.l.2449.2 2 5.2 odd 4
9792.2.a.bn.1.1 1 120.59 even 2
9792.2.a.bo.1.1 1 120.29 odd 2
9996.2.a.b.1.1 1 35.34 odd 2