Properties

Label 5328.2.a.bf.1.1
Level $5328$
Weight $2$
Character 5328.1
Self dual yes
Analytic conductor $42.544$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $1$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [5328,2,Mod(1,5328)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(5328, 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("5328.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 5328 = 2^{4} \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 5328.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: \(42.5442941969\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\sqrt{13}) \)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x - 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 74)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-1.30278\) of defining polynomial
Character \(\chi\) \(=\) 5328.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.30278 q^{5} -4.60555 q^{7} +O(q^{10})\) \(q-1.30278 q^{5} -4.60555 q^{7} +1.30278 q^{11} -2.30278 q^{13} +6.00000 q^{17} -2.00000 q^{19} -6.90833 q^{23} -3.30278 q^{25} -6.90833 q^{29} -3.30278 q^{31} +6.00000 q^{35} +1.00000 q^{37} +0.908327 q^{41} +6.60555 q^{43} -2.60555 q^{47} +14.2111 q^{49} +6.00000 q^{53} -1.69722 q^{55} +3.39445 q^{59} -10.5139 q^{61} +3.00000 q^{65} -14.5139 q^{67} +6.00000 q^{71} -8.69722 q^{73} -6.00000 q^{77} +16.1194 q^{79} +17.2111 q^{83} -7.81665 q^{85} -5.21110 q^{89} +10.6056 q^{91} +2.60555 q^{95} +12.4222 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + q^{5} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + q^{5} - 2 q^{7} - q^{11} - q^{13} + 12 q^{17} - 4 q^{19} - 3 q^{23} - 3 q^{25} - 3 q^{29} - 3 q^{31} + 12 q^{35} + 2 q^{37} - 9 q^{41} + 6 q^{43} + 2 q^{47} + 14 q^{49} + 12 q^{53} - 7 q^{55} + 14 q^{59} - 3 q^{61} + 6 q^{65} - 11 q^{67} + 12 q^{71} - 21 q^{73} - 12 q^{77} + 7 q^{79} + 20 q^{83} + 6 q^{85} + 4 q^{89} + 14 q^{91} - 2 q^{95} - 4 q^{97}+O(q^{100}) \) 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 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.30278 −0.582619 −0.291309 0.956629i \(-0.594091\pi\)
−0.291309 + 0.956629i \(0.594091\pi\)
\(6\) 0 0
\(7\) −4.60555 −1.74073 −0.870367 0.492403i \(-0.836119\pi\)
−0.870367 + 0.492403i \(0.836119\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.30278 0.392802 0.196401 0.980524i \(-0.437075\pi\)
0.196401 + 0.980524i \(0.437075\pi\)
\(12\) 0 0
\(13\) −2.30278 −0.638675 −0.319338 0.947641i \(-0.603460\pi\)
−0.319338 + 0.947641i \(0.603460\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) −2.00000 −0.458831 −0.229416 0.973329i \(-0.573682\pi\)
−0.229416 + 0.973329i \(0.573682\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −6.90833 −1.44049 −0.720243 0.693722i \(-0.755970\pi\)
−0.720243 + 0.693722i \(0.755970\pi\)
\(24\) 0 0
\(25\) −3.30278 −0.660555
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −6.90833 −1.28284 −0.641422 0.767188i \(-0.721655\pi\)
−0.641422 + 0.767188i \(0.721655\pi\)
\(30\) 0 0
\(31\) −3.30278 −0.593196 −0.296598 0.955002i \(-0.595852\pi\)
−0.296598 + 0.955002i \(0.595852\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 6.00000 1.01419
\(36\) 0 0
\(37\) 1.00000 0.164399
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0.908327 0.141857 0.0709284 0.997481i \(-0.477404\pi\)
0.0709284 + 0.997481i \(0.477404\pi\)
\(42\) 0 0
\(43\) 6.60555 1.00734 0.503669 0.863897i \(-0.331983\pi\)
0.503669 + 0.863897i \(0.331983\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −2.60555 −0.380059 −0.190029 0.981778i \(-0.560858\pi\)
−0.190029 + 0.981778i \(0.560858\pi\)
\(48\) 0 0
\(49\) 14.2111 2.03016
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 6.00000 0.824163 0.412082 0.911147i \(-0.364802\pi\)
0.412082 + 0.911147i \(0.364802\pi\)
\(54\) 0 0
\(55\) −1.69722 −0.228854
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.39445 0.441920 0.220960 0.975283i \(-0.429081\pi\)
0.220960 + 0.975283i \(0.429081\pi\)
\(60\) 0 0
\(61\) −10.5139 −1.34616 −0.673082 0.739568i \(-0.735030\pi\)
−0.673082 + 0.739568i \(0.735030\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.00000 0.372104
\(66\) 0 0
\(67\) −14.5139 −1.77315 −0.886576 0.462583i \(-0.846923\pi\)
−0.886576 + 0.462583i \(0.846923\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) −8.69722 −1.01793 −0.508967 0.860786i \(-0.669972\pi\)
−0.508967 + 0.860786i \(0.669972\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −6.00000 −0.683763
\(78\) 0 0
\(79\) 16.1194 1.81358 0.906789 0.421585i \(-0.138526\pi\)
0.906789 + 0.421585i \(0.138526\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 17.2111 1.88916 0.944582 0.328276i \(-0.106467\pi\)
0.944582 + 0.328276i \(0.106467\pi\)
\(84\) 0 0
\(85\) −7.81665 −0.847835
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −5.21110 −0.552376 −0.276188 0.961104i \(-0.589071\pi\)
−0.276188 + 0.961104i \(0.589071\pi\)
\(90\) 0 0
\(91\) 10.6056 1.11176
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 2.60555 0.267324
\(96\) 0 0
\(97\) 12.4222 1.26128 0.630642 0.776074i \(-0.282792\pi\)
0.630642 + 0.776074i \(0.282792\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −16.4222 −1.63407 −0.817035 0.576588i \(-0.804384\pi\)
−0.817035 + 0.576588i \(0.804384\pi\)
\(102\) 0 0
\(103\) −3.30278 −0.325432 −0.162716 0.986673i \(-0.552025\pi\)
−0.162716 + 0.986673i \(0.552025\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 4.30278 0.415965 0.207983 0.978133i \(-0.433310\pi\)
0.207983 + 0.978133i \(0.433310\pi\)
\(108\) 0 0
\(109\) 2.00000 0.191565 0.0957826 0.995402i \(-0.469465\pi\)
0.0957826 + 0.995402i \(0.469465\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −11.2111 −1.05465 −0.527326 0.849663i \(-0.676805\pi\)
−0.527326 + 0.849663i \(0.676805\pi\)
\(114\) 0 0
\(115\) 9.00000 0.839254
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −27.6333 −2.53314
\(120\) 0 0
\(121\) −9.30278 −0.845707
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 10.8167 0.967471
\(126\) 0 0
\(127\) 4.78890 0.424946 0.212473 0.977167i \(-0.431848\pi\)
0.212473 + 0.977167i \(0.431848\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 3.39445 0.296574 0.148287 0.988944i \(-0.452624\pi\)
0.148287 + 0.988944i \(0.452624\pi\)
\(132\) 0 0
\(133\) 9.21110 0.798704
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 9.90833 0.846525 0.423263 0.906007i \(-0.360885\pi\)
0.423263 + 0.906007i \(0.360885\pi\)
\(138\) 0 0
\(139\) −8.90833 −0.755594 −0.377797 0.925888i \(-0.623318\pi\)
−0.377797 + 0.925888i \(0.623318\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −3.00000 −0.250873
\(144\) 0 0
\(145\) 9.00000 0.747409
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.81665 0.148826 0.0744130 0.997228i \(-0.476292\pi\)
0.0744130 + 0.997228i \(0.476292\pi\)
\(150\) 0 0
\(151\) 13.3944 1.09002 0.545012 0.838428i \(-0.316525\pi\)
0.545012 + 0.838428i \(0.316525\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 4.30278 0.345607
\(156\) 0 0
\(157\) 7.21110 0.575509 0.287754 0.957704i \(-0.407091\pi\)
0.287754 + 0.957704i \(0.407091\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 31.8167 2.50750
\(162\) 0 0
\(163\) 20.4222 1.59959 0.799795 0.600273i \(-0.204941\pi\)
0.799795 + 0.600273i \(0.204941\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 12.5139 0.968353 0.484176 0.874970i \(-0.339119\pi\)
0.484176 + 0.874970i \(0.339119\pi\)
\(168\) 0 0
\(169\) −7.69722 −0.592094
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 23.2111 1.76471 0.882354 0.470587i \(-0.155958\pi\)
0.882354 + 0.470587i \(0.155958\pi\)
\(174\) 0 0
\(175\) 15.2111 1.14985
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 7.81665 0.584244 0.292122 0.956381i \(-0.405639\pi\)
0.292122 + 0.956381i \(0.405639\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.30278 −0.0957820
\(186\) 0 0
\(187\) 7.81665 0.571610
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 12.5139 0.905472 0.452736 0.891644i \(-0.350448\pi\)
0.452736 + 0.891644i \(0.350448\pi\)
\(192\) 0 0
\(193\) −4.00000 −0.287926 −0.143963 0.989583i \(-0.545985\pi\)
−0.143963 + 0.989583i \(0.545985\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 6.00000 0.427482 0.213741 0.976890i \(-0.431435\pi\)
0.213741 + 0.976890i \(0.431435\pi\)
\(198\) 0 0
\(199\) 2.42221 0.171706 0.0858528 0.996308i \(-0.472639\pi\)
0.0858528 + 0.996308i \(0.472639\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 31.8167 2.23309
\(204\) 0 0
\(205\) −1.18335 −0.0826485
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.60555 −0.180230
\(210\) 0 0
\(211\) −6.69722 −0.461056 −0.230528 0.973066i \(-0.574045\pi\)
−0.230528 + 0.973066i \(0.574045\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −8.60555 −0.586894
\(216\) 0 0
\(217\) 15.2111 1.03260
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −13.8167 −0.929409
\(222\) 0 0
\(223\) −15.8167 −1.05916 −0.529581 0.848260i \(-0.677651\pi\)
−0.529581 + 0.848260i \(0.677651\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −7.81665 −0.518810 −0.259405 0.965769i \(-0.583526\pi\)
−0.259405 + 0.965769i \(0.583526\pi\)
\(228\) 0 0
\(229\) 17.3944 1.14946 0.574729 0.818344i \(-0.305108\pi\)
0.574729 + 0.818344i \(0.305108\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 9.51388 0.623275 0.311637 0.950201i \(-0.399123\pi\)
0.311637 + 0.950201i \(0.399123\pi\)
\(234\) 0 0
\(235\) 3.39445 0.221429
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0.513878 0.0332400 0.0166200 0.999862i \(-0.494709\pi\)
0.0166200 + 0.999862i \(0.494709\pi\)
\(240\) 0 0
\(241\) 8.00000 0.515325 0.257663 0.966235i \(-0.417048\pi\)
0.257663 + 0.966235i \(0.417048\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −18.5139 −1.18281
\(246\) 0 0
\(247\) 4.60555 0.293044
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −6.78890 −0.428511 −0.214256 0.976778i \(-0.568733\pi\)
−0.214256 + 0.976778i \(0.568733\pi\)
\(252\) 0 0
\(253\) −9.00000 −0.565825
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 11.2111 0.699329 0.349665 0.936875i \(-0.386296\pi\)
0.349665 + 0.936875i \(0.386296\pi\)
\(258\) 0 0
\(259\) −4.60555 −0.286175
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −7.81665 −0.481996 −0.240998 0.970526i \(-0.577475\pi\)
−0.240998 + 0.970526i \(0.577475\pi\)
\(264\) 0 0
\(265\) −7.81665 −0.480173
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 6.78890 0.413926 0.206963 0.978349i \(-0.433642\pi\)
0.206963 + 0.978349i \(0.433642\pi\)
\(270\) 0 0
\(271\) −6.42221 −0.390121 −0.195061 0.980791i \(-0.562490\pi\)
−0.195061 + 0.980791i \(0.562490\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −4.30278 −0.259467
\(276\) 0 0
\(277\) −25.1194 −1.50928 −0.754640 0.656139i \(-0.772189\pi\)
−0.754640 + 0.656139i \(0.772189\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 12.0000 0.715860 0.357930 0.933748i \(-0.383483\pi\)
0.357930 + 0.933748i \(0.383483\pi\)
\(282\) 0 0
\(283\) −17.3944 −1.03399 −0.516996 0.855988i \(-0.672950\pi\)
−0.516996 + 0.855988i \(0.672950\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −4.18335 −0.246935
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 25.0278 1.46214 0.731069 0.682304i \(-0.239022\pi\)
0.731069 + 0.682304i \(0.239022\pi\)
\(294\) 0 0
\(295\) −4.42221 −0.257471
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 15.9083 0.920002
\(300\) 0 0
\(301\) −30.4222 −1.75351
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 13.6972 0.784301
\(306\) 0 0
\(307\) −7.09167 −0.404743 −0.202372 0.979309i \(-0.564865\pi\)
−0.202372 + 0.979309i \(0.564865\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 5.09167 0.288722 0.144361 0.989525i \(-0.453887\pi\)
0.144361 + 0.989525i \(0.453887\pi\)
\(312\) 0 0
\(313\) 27.0278 1.52770 0.763850 0.645394i \(-0.223307\pi\)
0.763850 + 0.645394i \(0.223307\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 5.21110 0.292685 0.146342 0.989234i \(-0.453250\pi\)
0.146342 + 0.989234i \(0.453250\pi\)
\(318\) 0 0
\(319\) −9.00000 −0.503903
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −12.0000 −0.667698
\(324\) 0 0
\(325\) 7.60555 0.421880
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 12.0000 0.661581
\(330\) 0 0
\(331\) −1.21110 −0.0665682 −0.0332841 0.999446i \(-0.510597\pi\)
−0.0332841 + 0.999446i \(0.510597\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 18.9083 1.03307
\(336\) 0 0
\(337\) −19.1194 −1.04150 −0.520751 0.853709i \(-0.674348\pi\)
−0.520751 + 0.853709i \(0.674348\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −4.30278 −0.233008
\(342\) 0 0
\(343\) −33.2111 −1.79323
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 31.8167 1.70801 0.854004 0.520267i \(-0.174168\pi\)
0.854004 + 0.520267i \(0.174168\pi\)
\(348\) 0 0
\(349\) −22.2389 −1.19042 −0.595209 0.803571i \(-0.702931\pi\)
−0.595209 + 0.803571i \(0.702931\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −31.8167 −1.69343 −0.846715 0.532047i \(-0.821423\pi\)
−0.846715 + 0.532047i \(0.821423\pi\)
\(354\) 0 0
\(355\) −7.81665 −0.414865
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −11.2111 −0.591699 −0.295850 0.955235i \(-0.595603\pi\)
−0.295850 + 0.955235i \(0.595603\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 11.3305 0.593067
\(366\) 0 0
\(367\) 17.8167 0.930022 0.465011 0.885305i \(-0.346050\pi\)
0.465011 + 0.885305i \(0.346050\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −27.6333 −1.43465
\(372\) 0 0
\(373\) 3.81665 0.197619 0.0988094 0.995106i \(-0.468497\pi\)
0.0988094 + 0.995106i \(0.468497\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 15.9083 0.819321
\(378\) 0 0
\(379\) 15.3305 0.787477 0.393738 0.919223i \(-0.371182\pi\)
0.393738 + 0.919223i \(0.371182\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 20.8444 1.06510 0.532550 0.846399i \(-0.321234\pi\)
0.532550 + 0.846399i \(0.321234\pi\)
\(384\) 0 0
\(385\) 7.81665 0.398374
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 11.8806 0.602369 0.301184 0.953566i \(-0.402618\pi\)
0.301184 + 0.953566i \(0.402618\pi\)
\(390\) 0 0
\(391\) −41.4500 −2.09621
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −21.0000 −1.05662
\(396\) 0 0
\(397\) 27.8167 1.39608 0.698039 0.716060i \(-0.254056\pi\)
0.698039 + 0.716060i \(0.254056\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −13.8167 −0.689971 −0.344985 0.938608i \(-0.612116\pi\)
−0.344985 + 0.938608i \(0.612116\pi\)
\(402\) 0 0
\(403\) 7.60555 0.378859
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.30278 0.0645762
\(408\) 0 0
\(409\) −5.02776 −0.248607 −0.124303 0.992244i \(-0.539670\pi\)
−0.124303 + 0.992244i \(0.539670\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −15.6333 −0.769265
\(414\) 0 0
\(415\) −22.4222 −1.10066
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −25.1472 −1.22852 −0.614260 0.789104i \(-0.710545\pi\)
−0.614260 + 0.789104i \(0.710545\pi\)
\(420\) 0 0
\(421\) 28.7250 1.39997 0.699985 0.714158i \(-0.253190\pi\)
0.699985 + 0.714158i \(0.253190\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −19.8167 −0.961249
\(426\) 0 0
\(427\) 48.4222 2.34331
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −5.21110 −0.251010 −0.125505 0.992093i \(-0.540055\pi\)
−0.125505 + 0.992093i \(0.540055\pi\)
\(432\) 0 0
\(433\) −11.9361 −0.573612 −0.286806 0.957989i \(-0.592593\pi\)
−0.286806 + 0.957989i \(0.592593\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 13.8167 0.660940
\(438\) 0 0
\(439\) 9.33053 0.445322 0.222661 0.974896i \(-0.428526\pi\)
0.222661 + 0.974896i \(0.428526\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.275019 0.0130666 0.00653328 0.999979i \(-0.497920\pi\)
0.00653328 + 0.999979i \(0.497920\pi\)
\(444\) 0 0
\(445\) 6.78890 0.321825
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.788897 0.0372304 0.0186152 0.999827i \(-0.494074\pi\)
0.0186152 + 0.999827i \(0.494074\pi\)
\(450\) 0 0
\(451\) 1.18335 0.0557216
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −13.8167 −0.647735
\(456\) 0 0
\(457\) 4.60555 0.215439 0.107719 0.994181i \(-0.465645\pi\)
0.107719 + 0.994181i \(0.465645\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 16.4222 0.764858 0.382429 0.923985i \(-0.375088\pi\)
0.382429 + 0.923985i \(0.375088\pi\)
\(462\) 0 0
\(463\) −30.3028 −1.40829 −0.704145 0.710056i \(-0.748669\pi\)
−0.704145 + 0.710056i \(0.748669\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 66.8444 3.08659
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 8.60555 0.395684
\(474\) 0 0
\(475\) 6.60555 0.303083
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 12.1194 0.553751 0.276875 0.960906i \(-0.410701\pi\)
0.276875 + 0.960906i \(0.410701\pi\)
\(480\) 0 0
\(481\) −2.30278 −0.104998
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −16.1833 −0.734848
\(486\) 0 0
\(487\) 22.7889 1.03266 0.516332 0.856389i \(-0.327297\pi\)
0.516332 + 0.856389i \(0.327297\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −14.7250 −0.664529 −0.332265 0.943186i \(-0.607813\pi\)
−0.332265 + 0.943186i \(0.607813\pi\)
\(492\) 0 0
\(493\) −41.4500 −1.86681
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −27.6333 −1.23952
\(498\) 0 0
\(499\) −8.23886 −0.368822 −0.184411 0.982849i \(-0.559038\pi\)
−0.184411 + 0.982849i \(0.559038\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −24.5139 −1.09302 −0.546510 0.837453i \(-0.684044\pi\)
−0.546510 + 0.837453i \(0.684044\pi\)
\(504\) 0 0
\(505\) 21.3944 0.952040
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 25.8167 1.14430 0.572152 0.820148i \(-0.306109\pi\)
0.572152 + 0.820148i \(0.306109\pi\)
\(510\) 0 0
\(511\) 40.0555 1.77195
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 4.30278 0.189603
\(516\) 0 0
\(517\) −3.39445 −0.149288
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 9.63331 0.422043 0.211021 0.977481i \(-0.432321\pi\)
0.211021 + 0.977481i \(0.432321\pi\)
\(522\) 0 0
\(523\) −32.2389 −1.40971 −0.704853 0.709353i \(-0.748987\pi\)
−0.704853 + 0.709353i \(0.748987\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −19.8167 −0.863227
\(528\) 0 0
\(529\) 24.7250 1.07500
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −2.09167 −0.0906004
\(534\) 0 0
\(535\) −5.60555 −0.242349
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 18.5139 0.797449
\(540\) 0 0
\(541\) −20.9361 −0.900113 −0.450056 0.893000i \(-0.648596\pi\)
−0.450056 + 0.893000i \(0.648596\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −2.60555 −0.111610
\(546\) 0 0
\(547\) 13.3944 0.572705 0.286353 0.958124i \(-0.407557\pi\)
0.286353 + 0.958124i \(0.407557\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 13.8167 0.588609
\(552\) 0 0
\(553\) −74.2389 −3.15696
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 6.51388 0.276002 0.138001 0.990432i \(-0.455932\pi\)
0.138001 + 0.990432i \(0.455932\pi\)
\(558\) 0 0
\(559\) −15.2111 −0.643361
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 44.0555 1.85672 0.928359 0.371684i \(-0.121220\pi\)
0.928359 + 0.371684i \(0.121220\pi\)
\(564\) 0 0
\(565\) 14.6056 0.614460
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 10.4222 0.436922 0.218461 0.975846i \(-0.429896\pi\)
0.218461 + 0.975846i \(0.429896\pi\)
\(570\) 0 0
\(571\) 20.3028 0.849645 0.424822 0.905277i \(-0.360337\pi\)
0.424822 + 0.905277i \(0.360337\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 22.8167 0.951520
\(576\) 0 0
\(577\) −28.2389 −1.17560 −0.587800 0.809007i \(-0.700006\pi\)
−0.587800 + 0.809007i \(0.700006\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −79.2666 −3.28853
\(582\) 0 0
\(583\) 7.81665 0.323733
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −2.36669 −0.0976838 −0.0488419 0.998807i \(-0.515553\pi\)
−0.0488419 + 0.998807i \(0.515553\pi\)
\(588\) 0 0
\(589\) 6.60555 0.272177
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −36.5139 −1.49945 −0.749723 0.661752i \(-0.769813\pi\)
−0.749723 + 0.661752i \(0.769813\pi\)
\(594\) 0 0
\(595\) 36.0000 1.47586
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −35.2111 −1.43869 −0.719343 0.694655i \(-0.755557\pi\)
−0.719343 + 0.694655i \(0.755557\pi\)
\(600\) 0 0
\(601\) −20.6972 −0.844257 −0.422129 0.906536i \(-0.638717\pi\)
−0.422129 + 0.906536i \(0.638717\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 12.1194 0.492725
\(606\) 0 0
\(607\) 31.5139 1.27911 0.639554 0.768746i \(-0.279119\pi\)
0.639554 + 0.768746i \(0.279119\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.00000 0.242734
\(612\) 0 0
\(613\) −8.18335 −0.330522 −0.165261 0.986250i \(-0.552847\pi\)
−0.165261 + 0.986250i \(0.552847\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −47.5694 −1.91507 −0.957536 0.288314i \(-0.906905\pi\)
−0.957536 + 0.288314i \(0.906905\pi\)
\(618\) 0 0
\(619\) 2.69722 0.108411 0.0542053 0.998530i \(-0.482737\pi\)
0.0542053 + 0.998530i \(0.482737\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 24.0000 0.961540
\(624\) 0 0
\(625\) 2.42221 0.0968882
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 6.00000 0.239236
\(630\) 0 0
\(631\) −18.3028 −0.728622 −0.364311 0.931277i \(-0.618695\pi\)
−0.364311 + 0.931277i \(0.618695\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −6.23886 −0.247582
\(636\) 0 0
\(637\) −32.7250 −1.29661
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 2.48612 0.0981959 0.0490980 0.998794i \(-0.484365\pi\)
0.0490980 + 0.998794i \(0.484365\pi\)
\(642\) 0 0
\(643\) 29.8167 1.17585 0.587927 0.808914i \(-0.299944\pi\)
0.587927 + 0.808914i \(0.299944\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −25.9361 −1.01965 −0.509826 0.860277i \(-0.670290\pi\)
−0.509826 + 0.860277i \(0.670290\pi\)
\(648\) 0 0
\(649\) 4.42221 0.173587
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −6.90833 −0.270344 −0.135172 0.990822i \(-0.543159\pi\)
−0.135172 + 0.990822i \(0.543159\pi\)
\(654\) 0 0
\(655\) −4.42221 −0.172790
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −42.1194 −1.64074 −0.820370 0.571833i \(-0.806233\pi\)
−0.820370 + 0.571833i \(0.806233\pi\)
\(660\) 0 0
\(661\) −12.4861 −0.485654 −0.242827 0.970070i \(-0.578075\pi\)
−0.242827 + 0.970070i \(0.578075\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −12.0000 −0.465340
\(666\) 0 0
\(667\) 47.7250 1.84792
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −13.6972 −0.528775
\(672\) 0 0
\(673\) 24.3028 0.936803 0.468402 0.883516i \(-0.344830\pi\)
0.468402 + 0.883516i \(0.344830\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 36.2389 1.39277 0.696386 0.717667i \(-0.254790\pi\)
0.696386 + 0.717667i \(0.254790\pi\)
\(678\) 0 0
\(679\) −57.2111 −2.19556
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 12.0000 0.459167 0.229584 0.973289i \(-0.426264\pi\)
0.229584 + 0.973289i \(0.426264\pi\)
\(684\) 0 0
\(685\) −12.9083 −0.493202
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −13.8167 −0.526373
\(690\) 0 0
\(691\) −8.00000 −0.304334 −0.152167 0.988355i \(-0.548625\pi\)
−0.152167 + 0.988355i \(0.548625\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 11.6056 0.440224
\(696\) 0 0
\(697\) 5.44996 0.206432
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −14.8806 −0.562031 −0.281016 0.959703i \(-0.590671\pi\)
−0.281016 + 0.959703i \(0.590671\pi\)
\(702\) 0 0
\(703\) −2.00000 −0.0754314
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 75.6333 2.84448
\(708\) 0 0
\(709\) −1.66947 −0.0626982 −0.0313491 0.999508i \(-0.509980\pi\)
−0.0313491 + 0.999508i \(0.509980\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 22.8167 0.854490
\(714\) 0 0
\(715\) 3.90833 0.146163
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −8.36669 −0.312025 −0.156012 0.987755i \(-0.549864\pi\)
−0.156012 + 0.987755i \(0.549864\pi\)
\(720\) 0 0
\(721\) 15.2111 0.566491
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 22.8167 0.847389
\(726\) 0 0
\(727\) −29.9083 −1.10924 −0.554619 0.832104i \(-0.687136\pi\)
−0.554619 + 0.832104i \(0.687136\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 39.6333 1.46589
\(732\) 0 0
\(733\) 29.6333 1.09453 0.547266 0.836959i \(-0.315669\pi\)
0.547266 + 0.836959i \(0.315669\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −18.9083 −0.696497
\(738\) 0 0
\(739\) 42.3305 1.55715 0.778577 0.627549i \(-0.215942\pi\)
0.778577 + 0.627549i \(0.215942\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 35.4500 1.30053 0.650266 0.759706i \(-0.274657\pi\)
0.650266 + 0.759706i \(0.274657\pi\)
\(744\) 0 0
\(745\) −2.36669 −0.0867089
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −19.8167 −0.724085
\(750\) 0 0
\(751\) −14.0000 −0.510867 −0.255434 0.966827i \(-0.582218\pi\)
−0.255434 + 0.966827i \(0.582218\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −17.4500 −0.635069
\(756\) 0 0
\(757\) 9.30278 0.338115 0.169058 0.985606i \(-0.445928\pi\)
0.169058 + 0.985606i \(0.445928\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −42.1194 −1.52683 −0.763414 0.645909i \(-0.776478\pi\)
−0.763414 + 0.645909i \(0.776478\pi\)
\(762\) 0 0
\(763\) −9.21110 −0.333464
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −7.81665 −0.282243
\(768\) 0 0
\(769\) −22.0000 −0.793340 −0.396670 0.917961i \(-0.629834\pi\)
−0.396670 + 0.917961i \(0.629834\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 50.0555 1.80037 0.900186 0.435506i \(-0.143431\pi\)
0.900186 + 0.435506i \(0.143431\pi\)
\(774\) 0 0
\(775\) 10.9083 0.391839
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −1.81665 −0.0650884
\(780\) 0 0
\(781\) 7.81665 0.279702
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −9.39445 −0.335302
\(786\) 0 0
\(787\) −25.2111 −0.898679 −0.449339 0.893361i \(-0.648341\pi\)
−0.449339 + 0.893361i \(0.648341\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 51.6333 1.83587
\(792\) 0 0
\(793\) 24.2111 0.859761
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 17.3305 0.613879 0.306939 0.951729i \(-0.400695\pi\)
0.306939 + 0.951729i \(0.400695\pi\)
\(798\) 0 0
\(799\) −15.6333 −0.553067
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −11.3305 −0.399846
\(804\) 0 0
\(805\) −41.4500 −1.46092
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −29.4500 −1.03541 −0.517703 0.855561i \(-0.673213\pi\)
−0.517703 + 0.855561i \(0.673213\pi\)
\(810\) 0 0
\(811\) −54.1472 −1.90136 −0.950682 0.310166i \(-0.899615\pi\)
−0.950682 + 0.310166i \(0.899615\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −26.6056 −0.931952
\(816\) 0 0
\(817\) −13.2111 −0.462198
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −11.2111 −0.391270 −0.195635 0.980677i \(-0.562677\pi\)
−0.195635 + 0.980677i \(0.562677\pi\)
\(822\) 0 0
\(823\) 12.8444 0.447728 0.223864 0.974620i \(-0.428133\pi\)
0.223864 + 0.974620i \(0.428133\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 27.3944 0.952598 0.476299 0.879283i \(-0.341978\pi\)
0.476299 + 0.879283i \(0.341978\pi\)
\(828\) 0 0
\(829\) 4.72498 0.164105 0.0820527 0.996628i \(-0.473852\pi\)
0.0820527 + 0.996628i \(0.473852\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 85.2666 2.95431
\(834\) 0 0
\(835\) −16.3028 −0.564181
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −49.0278 −1.69263 −0.846313 0.532686i \(-0.821183\pi\)
−0.846313 + 0.532686i \(0.821183\pi\)
\(840\) 0 0
\(841\) 18.7250 0.645689
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 10.0278 0.344965
\(846\) 0 0
\(847\) 42.8444 1.47215
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −6.90833 −0.236814
\(852\) 0 0
\(853\) −11.5416 −0.395178 −0.197589 0.980285i \(-0.563311\pi\)
−0.197589 + 0.980285i \(0.563311\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 14.8444 0.507075 0.253538 0.967326i \(-0.418406\pi\)
0.253538 + 0.967326i \(0.418406\pi\)
\(858\) 0 0
\(859\) 24.0555 0.820764 0.410382 0.911914i \(-0.365395\pi\)
0.410382 + 0.911914i \(0.365395\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 12.0000 0.408485 0.204242 0.978920i \(-0.434527\pi\)
0.204242 + 0.978920i \(0.434527\pi\)
\(864\) 0 0
\(865\) −30.2389 −1.02815
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 21.0000 0.712376
\(870\) 0 0
\(871\) 33.4222 1.13247
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −49.8167 −1.68411
\(876\) 0 0
\(877\) 7.21110 0.243502 0.121751 0.992561i \(-0.461149\pi\)
0.121751 + 0.992561i \(0.461149\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −25.5416 −0.860520 −0.430260 0.902705i \(-0.641578\pi\)
−0.430260 + 0.902705i \(0.641578\pi\)
\(882\) 0 0
\(883\) 2.42221 0.0815137 0.0407568 0.999169i \(-0.487023\pi\)
0.0407568 + 0.999169i \(0.487023\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 28.4222 0.954324 0.477162 0.878815i \(-0.341665\pi\)
0.477162 + 0.878815i \(0.341665\pi\)
\(888\) 0 0
\(889\) −22.0555 −0.739718
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 5.21110 0.174383
\(894\) 0 0
\(895\) −10.1833 −0.340392
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 22.8167 0.760978
\(900\) 0 0
\(901\) 36.0000 1.19933
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −26.0555 −0.866115
\(906\) 0 0
\(907\) −26.0000 −0.863316 −0.431658 0.902037i \(-0.642071\pi\)
−0.431658 + 0.902037i \(0.642071\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −46.4222 −1.53804 −0.769018 0.639227i \(-0.779254\pi\)
−0.769018 + 0.639227i \(0.779254\pi\)
\(912\) 0 0
\(913\) 22.4222 0.742067
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −15.6333 −0.516257
\(918\) 0 0
\(919\) 38.4222 1.26743 0.633716 0.773566i \(-0.281529\pi\)
0.633716 + 0.773566i \(0.281529\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −13.8167 −0.454781
\(924\) 0 0
\(925\) −3.30278 −0.108595
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 36.5139 1.19798 0.598991 0.800756i \(-0.295569\pi\)
0.598991 + 0.800756i \(0.295569\pi\)
\(930\) 0 0
\(931\) −28.4222 −0.931500
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −10.1833 −0.333031
\(936\) 0 0
\(937\) −28.9083 −0.944394 −0.472197 0.881493i \(-0.656539\pi\)
−0.472197 + 0.881493i \(0.656539\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 7.81665 0.254816 0.127408 0.991850i \(-0.459334\pi\)
0.127408 + 0.991850i \(0.459334\pi\)
\(942\) 0 0
\(943\) −6.27502 −0.204343
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 39.6333 1.28791 0.643955 0.765064i \(-0.277293\pi\)
0.643955 + 0.765064i \(0.277293\pi\)
\(948\) 0 0
\(949\) 20.0278 0.650128
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 18.7527 0.607461 0.303730 0.952758i \(-0.401768\pi\)
0.303730 + 0.952758i \(0.401768\pi\)
\(954\) 0 0
\(955\) −16.3028 −0.527545
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −45.6333 −1.47358
\(960\) 0 0
\(961\) −20.0917 −0.648118
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 5.21110 0.167751
\(966\) 0 0
\(967\) −25.7250 −0.827260 −0.413630 0.910445i \(-0.635739\pi\)
−0.413630 + 0.910445i \(0.635739\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 31.5416 1.01222 0.506110 0.862469i \(-0.331083\pi\)
0.506110 + 0.862469i \(0.331083\pi\)
\(972\) 0 0
\(973\) 41.0278 1.31529
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −18.0000 −0.575871 −0.287936 0.957650i \(-0.592969\pi\)
−0.287936 + 0.957650i \(0.592969\pi\)
\(978\) 0 0
\(979\) −6.78890 −0.216974
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −12.0000 −0.382741 −0.191370 0.981518i \(-0.561293\pi\)
−0.191370 + 0.981518i \(0.561293\pi\)
\(984\) 0 0
\(985\) −7.81665 −0.249059
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −45.6333 −1.45105
\(990\) 0 0
\(991\) −54.3028 −1.72498 −0.862492 0.506070i \(-0.831098\pi\)
−0.862492 + 0.506070i \(0.831098\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −3.15559 −0.100039
\(996\) 0 0
\(997\) −23.5778 −0.746716 −0.373358 0.927687i \(-0.621794\pi\)
−0.373358 + 0.927687i \(0.621794\pi\)
\(998\) 0 0
\(999\) 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 5328.2.a.bf.1.1 2
3.2 odd 2 592.2.a.f.1.2 2
4.3 odd 2 666.2.a.j.1.1 2
12.11 even 2 74.2.a.a.1.1 2
24.5 odd 2 2368.2.a.ba.1.1 2
24.11 even 2 2368.2.a.s.1.2 2
60.23 odd 4 1850.2.b.i.149.3 4
60.47 odd 4 1850.2.b.i.149.2 4
60.59 even 2 1850.2.a.u.1.2 2
84.83 odd 2 3626.2.a.a.1.2 2
132.131 odd 2 8954.2.a.p.1.1 2
444.443 even 2 2738.2.a.l.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
74.2.a.a.1.1 2 12.11 even 2
592.2.a.f.1.2 2 3.2 odd 2
666.2.a.j.1.1 2 4.3 odd 2
1850.2.a.u.1.2 2 60.59 even 2
1850.2.b.i.149.2 4 60.47 odd 4
1850.2.b.i.149.3 4 60.23 odd 4
2368.2.a.s.1.2 2 24.11 even 2
2368.2.a.ba.1.1 2 24.5 odd 2
2738.2.a.l.1.1 2 444.443 even 2
3626.2.a.a.1.2 2 84.83 odd 2
5328.2.a.bf.1.1 2 1.1 even 1 trivial
8954.2.a.p.1.1 2 132.131 odd 2