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Properties

Label 6300.2.a.ba.1.1
Level $6300$
Weight $2$
Character 6300.1
Self dual yes
Analytic conductor $50.306$
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] = [6300,2,Mod(1,6300)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(6300, 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("6300.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 6300 = 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 6300.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: \(50.3057532734\)
Analytic rank: \(0\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 2100)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 6300.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{7} +O(q^{10})\) \(q+1.00000 q^{7} +1.00000 q^{11} +2.00000 q^{13} +8.00000 q^{17} -2.00000 q^{19} +1.00000 q^{23} -1.00000 q^{29} +6.00000 q^{31} -9.00000 q^{37} +1.00000 q^{43} +6.00000 q^{47} +1.00000 q^{49} +2.00000 q^{53} +6.00000 q^{59} +8.00000 q^{61} +3.00000 q^{67} -7.00000 q^{71} -16.0000 q^{73} +1.00000 q^{77} +1.00000 q^{79} -6.00000 q^{83} +14.0000 q^{89} +2.00000 q^{91} -14.0000 q^{97} +O(q^{100})\)

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
\(3\) 0 0
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.00000 0.301511 0.150756 − 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) 0 0
\(13\) 2.00000 0.554700 0.277350 − 0.960769i \(-0.410544\pi\)
0.277350 + 0.960769i \(0.410544\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 8.00000 1.94029 0.970143 − 0.242536i \(-0.0779791\pi\)
0.970143 + 0.242536i \(0.0779791\pi\)
\(18\) 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
\(23\) 1.00000 0.208514 0.104257 − 0.994550i \(-0.466753\pi\)
0.104257 + 0.994550i \(0.466753\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −1.00000 −0.185695 −0.0928477 − 0.995680i \(-0.529597\pi\)
−0.0928477 + 0.995680i \(0.529597\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 − 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −9.00000 −1.47959 −0.739795 − 0.672832i \(-0.765078\pi\)
−0.739795 + 0.672832i \(0.765078\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 − 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.00000 0.875190 0.437595 − 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.00000 0.274721 0.137361 − 0.990521i \(-0.456138\pi\)
0.137361 + 0.990521i \(0.456138\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 6.00000 0.781133 0.390567 − 0.920575i \(-0.372279\pi\)
0.390567 + 0.920575i \(0.372279\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 − 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 3.00000 0.366508 0.183254 − 0.983066i \(-0.441337\pi\)
0.183254 + 0.983066i \(0.441337\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −7.00000 −0.830747 −0.415374 − 0.909651i \(-0.636349\pi\)
−0.415374 + 0.909651i \(0.636349\pi\)
\(72\) 0 0
\(73\) −16.0000 −1.87266 −0.936329 − 0.351123i \(-0.885800\pi\)
−0.936329 + 0.351123i \(0.885800\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 1.00000 0.113961
\(78\) 0 0
\(79\) 1.00000 0.112509 0.0562544 − 0.998416i \(-0.482084\pi\)
0.0562544 + 0.998416i \(0.482084\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 − 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 14.0000 1.48400 0.741999 − 0.670402i \(-0.233878\pi\)
0.741999 + 0.670402i \(0.233878\pi\)
\(90\) 0 0
\(91\) 2.00000 0.209657
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 − 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 12.0000 1.19404 0.597022 − 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 0 0
\(103\) −10.0000 −0.985329 −0.492665 − 0.870219i \(-0.663977\pi\)
−0.492665 + 0.870219i \(0.663977\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.0000 1.16008 0.580042 − 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 − 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −9.00000 −0.846649 −0.423324 − 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 8.00000 0.733359
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −5.00000 −0.443678 −0.221839 − 0.975083i \(-0.571206\pi\)
−0.221839 + 0.975083i \(0.571206\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 16.0000 1.39793 0.698963 − 0.715158i \(-0.253645\pi\)
0.698963 + 0.715158i \(0.253645\pi\)
\(132\) 0 0
\(133\) −2.00000 −0.173422
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 10.0000 0.854358 0.427179 − 0.904167i \(-0.359507\pi\)
0.427179 + 0.904167i \(0.359507\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 − 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.00000 0.167248
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −11.0000 −0.901155 −0.450578 − 0.892737i \(-0.648782\pi\)
−0.450578 + 0.892737i \(0.648782\pi\)
\(150\) 0 0
\(151\) 19.0000 1.54620 0.773099 − 0.634285i \(-0.218706\pi\)
0.773099 + 0.634285i \(0.218706\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 12.0000 0.957704 0.478852 − 0.877896i \(-0.341053\pi\)
0.478852 + 0.877896i \(0.341053\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) 16.0000 1.25322 0.626608 − 0.779334i \(-0.284443\pi\)
0.626608 + 0.779334i \(0.284443\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −2.00000 −0.154765 −0.0773823 − 0.997001i \(-0.524656\pi\)
−0.0773823 + 0.997001i \(0.524656\pi\)
\(168\) 0 0
\(169\) −9.00000 −0.692308
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.00000 0.456172 0.228086 − 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 20.0000 1.49487 0.747435 − 0.664335i \(-0.231285\pi\)
0.747435 + 0.664335i \(0.231285\pi\)
\(180\) 0 0
\(181\) 12.0000 0.891953 0.445976 − 0.895045i \(-0.352856\pi\)
0.445976 + 0.895045i \(0.352856\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 8.00000 0.585018
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −8.00000 −0.578860 −0.289430 − 0.957199i \(-0.593466\pi\)
−0.289430 + 0.957199i \(0.593466\pi\)
\(192\) 0 0
\(193\) −11.0000 −0.791797 −0.395899 − 0.918294i \(-0.629567\pi\)
−0.395899 + 0.918294i \(0.629567\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 27.0000 1.92367 0.961835 − 0.273629i \(-0.0882242\pi\)
0.961835 + 0.273629i \(0.0882242\pi\)
\(198\) 0 0
\(199\) 0 0 − 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.00000 −0.0701862
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.00000 −0.138343
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 − 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 6.00000 0.407307
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 16.0000 1.07628
\(222\) 0 0
\(223\) 4.00000 0.267860 0.133930 − 0.990991i \(-0.457240\pi\)
0.133930 + 0.990991i \(0.457240\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −14.0000 −0.929213 −0.464606 − 0.885517i \(-0.653804\pi\)
−0.464606 + 0.885517i \(0.653804\pi\)
\(228\) 0 0
\(229\) 2.00000 0.132164 0.0660819 − 0.997814i \(-0.478950\pi\)
0.0660819 + 0.997814i \(0.478950\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.00000 −0.458585 −0.229293 − 0.973358i \(-0.573641\pi\)
−0.229293 + 0.973358i \(0.573641\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 12.0000 0.776215 0.388108 − 0.921614i \(-0.373129\pi\)
0.388108 + 0.921614i \(0.373129\pi\)
\(240\) 0 0
\(241\) −14.0000 −0.901819 −0.450910 − 0.892570i \(-0.648900\pi\)
−0.450910 + 0.892570i \(0.648900\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) −4.00000 −0.254514
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 − 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 1.00000 0.0628695
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −2.00000 −0.124757 −0.0623783 − 0.998053i \(-0.519869\pi\)
−0.0623783 + 0.998053i \(0.519869\pi\)
\(258\) 0 0
\(259\) −9.00000 −0.559233
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −25.0000 −1.54157 −0.770783 − 0.637098i \(-0.780135\pi\)
−0.770783 + 0.637098i \(0.780135\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −6.00000 −0.365826 −0.182913 − 0.983129i \(-0.558553\pi\)
−0.182913 + 0.983129i \(0.558553\pi\)
\(270\) 0 0
\(271\) −2.00000 −0.121491 −0.0607457 − 0.998153i \(-0.519348\pi\)
−0.0607457 + 0.998153i \(0.519348\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 14.0000 0.841178 0.420589 − 0.907251i \(-0.361823\pi\)
0.420589 + 0.907251i \(0.361823\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 15.0000 0.894825 0.447412 − 0.894328i \(-0.352346\pi\)
0.447412 + 0.894328i \(0.352346\pi\)
\(282\) 0 0
\(283\) −10.0000 −0.594438 −0.297219 − 0.954809i \(-0.596059\pi\)
−0.297219 + 0.954809i \(0.596059\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) 47.0000 2.76471
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −18.0000 −1.05157 −0.525786 − 0.850617i \(-0.676229\pi\)
−0.525786 + 0.850617i \(0.676229\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 2.00000 0.115663
\(300\) 0 0
\(301\) 1.00000 0.0576390
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 4.00000 0.228292 0.114146 − 0.993464i \(-0.463587\pi\)
0.114146 + 0.993464i \(0.463587\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 20.0000 1.13410 0.567048 − 0.823685i \(-0.308085\pi\)
0.567048 + 0.823685i \(0.308085\pi\)
\(312\) 0 0
\(313\) −18.0000 −1.01742 −0.508710 − 0.860938i \(-0.669877\pi\)
−0.508710 + 0.860938i \(0.669877\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 31.0000 1.74113 0.870567 − 0.492050i \(-0.163752\pi\)
0.870567 + 0.492050i \(0.163752\pi\)
\(318\) 0 0
\(319\) −1.00000 −0.0559893
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −16.0000 −0.890264
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 6.00000 0.330791
\(330\) 0 0
\(331\) 21.0000 1.15426 0.577132 − 0.816651i \(-0.304172\pi\)
0.577132 + 0.816651i \(0.304172\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 − 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 6.00000 0.324918
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −25.0000 −1.34207 −0.671035 − 0.741426i \(-0.734150\pi\)
−0.671035 + 0.741426i \(0.734150\pi\)
\(348\) 0 0
\(349\) 26.0000 1.39175 0.695874 − 0.718164i \(-0.255017\pi\)
0.695874 + 0.718164i \(0.255017\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.0000 0.532246 0.266123 − 0.963939i \(-0.414257\pi\)
0.266123 + 0.963939i \(0.414257\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −3.00000 −0.158334 −0.0791670 − 0.996861i \(-0.525226\pi\)
−0.0791670 + 0.996861i \(0.525226\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −4.00000 −0.208798 −0.104399 − 0.994535i \(-0.533292\pi\)
−0.104399 + 0.994535i \(0.533292\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 2.00000 0.103835
\(372\) 0 0
\(373\) 1.00000 0.0517780 0.0258890 − 0.999665i \(-0.491758\pi\)
0.0258890 + 0.999665i \(0.491758\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −2.00000 −0.103005
\(378\) 0 0
\(379\) 37.0000 1.90056 0.950281 − 0.311393i \(-0.100796\pi\)
0.950281 + 0.311393i \(0.100796\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −2.00000 −0.102195 −0.0510976 − 0.998694i \(-0.516272\pi\)
−0.0510976 + 0.998694i \(0.516272\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −25.0000 −1.26755 −0.633775 − 0.773517i \(-0.718496\pi\)
−0.633775 + 0.773517i \(0.718496\pi\)
\(390\) 0 0
\(391\) 8.00000 0.404577
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 6.00000 0.301131 0.150566 − 0.988600i \(-0.451890\pi\)
0.150566 + 0.988600i \(0.451890\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −1.00000 −0.0499376 −0.0249688 − 0.999688i \(-0.507949\pi\)
−0.0249688 + 0.999688i \(0.507949\pi\)
\(402\) 0 0
\(403\) 12.0000 0.597763
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −9.00000 −0.446113
\(408\) 0 0
\(409\) −26.0000 −1.28562 −0.642809 − 0.766027i \(-0.722231\pi\)
−0.642809 + 0.766027i \(0.722231\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 6.00000 0.295241
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −26.0000 −1.27018 −0.635092 − 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) −17.0000 −0.828529 −0.414265 − 0.910156i \(-0.635961\pi\)
−0.414265 + 0.910156i \(0.635961\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 8.00000 0.387147
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 24.0000 1.15604 0.578020 − 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 0 0
\(433\) −4.00000 −0.192228 −0.0961139 − 0.995370i \(-0.530641\pi\)
−0.0961139 + 0.995370i \(0.530641\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −2.00000 −0.0956730
\(438\) 0 0
\(439\) −26.0000 −1.24091 −0.620456 − 0.784241i \(-0.713053\pi\)
−0.620456 + 0.784241i \(0.713053\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −24.0000 −1.14027 −0.570137 − 0.821549i \(-0.693110\pi\)
−0.570137 + 0.821549i \(0.693110\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −23.0000 −1.08544 −0.542719 − 0.839915i \(-0.682605\pi\)
−0.542719 + 0.839915i \(0.682605\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 17.0000 0.795226 0.397613 − 0.917553i \(-0.369839\pi\)
0.397613 + 0.917553i \(0.369839\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 34.0000 1.58354 0.791769 − 0.610821i \(-0.209160\pi\)
0.791769 + 0.610821i \(0.209160\pi\)
\(462\) 0 0
\(463\) 24.0000 1.11537 0.557687 − 0.830051i \(-0.311689\pi\)
0.557687 + 0.830051i \(0.311689\pi\)
\(464\) 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
\(469\) 3.00000 0.138527
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.00000 0.0459800
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 34.0000 1.55350 0.776750 − 0.629809i \(-0.216867\pi\)
0.776750 + 0.629809i \(0.216867\pi\)
\(480\) 0 0
\(481\) −18.0000 −0.820729
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −7.00000 −0.317200 −0.158600 − 0.987343i \(-0.550698\pi\)
−0.158600 + 0.987343i \(0.550698\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3.00000 −0.135388 −0.0676941 − 0.997706i \(-0.521564\pi\)
−0.0676941 + 0.997706i \(0.521564\pi\)
\(492\) 0 0
\(493\) −8.00000 −0.360302
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −7.00000 −0.313993
\(498\) 0 0
\(499\) 36.0000 1.61158 0.805791 − 0.592200i \(-0.201741\pi\)
0.805791 + 0.592200i \(0.201741\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −38.0000 −1.69434 −0.847168 − 0.531325i \(-0.821694\pi\)
−0.847168 + 0.531325i \(0.821694\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 18.0000 0.797836 0.398918 − 0.916987i \(-0.369386\pi\)
0.398918 + 0.916987i \(0.369386\pi\)
\(510\) 0 0
\(511\) −16.0000 −0.707798
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 6.00000 0.263880
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 − 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 32.0000 1.39926 0.699631 − 0.714504i \(-0.253348\pi\)
0.699631 + 0.714504i \(0.253348\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 48.0000 2.09091
\(528\) 0 0
\(529\) −22.0000 −0.956522
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) 35.0000 1.50477 0.752384 − 0.658725i \(-0.228904\pi\)
0.752384 + 0.658725i \(0.228904\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 27.0000 1.15444 0.577218 − 0.816590i \(-0.304138\pi\)
0.577218 + 0.816590i \(0.304138\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.00000 0.0852029
\(552\) 0 0
\(553\) 1.00000 0.0425243
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −45.0000 −1.90671 −0.953356 − 0.301849i \(-0.902396\pi\)
−0.953356 + 0.301849i \(0.902396\pi\)
\(558\) 0 0
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 26.0000 1.09577 0.547885 − 0.836554i \(-0.315433\pi\)
0.547885 + 0.836554i \(0.315433\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −41.0000 −1.71881 −0.859405 − 0.511296i \(-0.829166\pi\)
−0.859405 + 0.511296i \(0.829166\pi\)
\(570\) 0 0
\(571\) −23.0000 −0.962520 −0.481260 − 0.876578i \(-0.659821\pi\)
−0.481260 + 0.876578i \(0.659821\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 2.00000 0.0832611 0.0416305 − 0.999133i \(-0.486745\pi\)
0.0416305 + 0.999133i \(0.486745\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −6.00000 −0.248922
\(582\) 0 0
\(583\) 2.00000 0.0828315
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −36.0000 −1.48588 −0.742940 − 0.669359i \(-0.766569\pi\)
−0.742940 + 0.669359i \(0.766569\pi\)
\(588\) 0 0
\(589\) −12.0000 −0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 24.0000 0.985562 0.492781 − 0.870153i \(-0.335980\pi\)
0.492781 + 0.870153i \(0.335980\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 27.0000 1.10319 0.551595 − 0.834112i \(-0.314019\pi\)
0.551595 + 0.834112i \(0.314019\pi\)
\(600\) 0 0
\(601\) 40.0000 1.63163 0.815817 − 0.578310i \(-0.196288\pi\)
0.815817 + 0.578310i \(0.196288\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 38.0000 1.54237 0.771186 − 0.636610i \(-0.219664\pi\)
0.771186 + 0.636610i \(0.219664\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 12.0000 0.485468
\(612\) 0 0
\(613\) −9.00000 −0.363507 −0.181753 − 0.983344i \(-0.558177\pi\)
−0.181753 + 0.983344i \(0.558177\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 29.0000 1.16750 0.583748 − 0.811935i \(-0.301586\pi\)
0.583748 + 0.811935i \(0.301586\pi\)
\(618\) 0 0
\(619\) −10.0000 −0.401934 −0.200967 − 0.979598i \(-0.564408\pi\)
−0.200967 + 0.979598i \(0.564408\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 14.0000 0.560898
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −72.0000 −2.87083
\(630\) 0 0
\(631\) 29.0000 1.15447 0.577236 − 0.816577i \(-0.304131\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 2.00000 0.0792429
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −13.0000 −0.513469 −0.256735 − 0.966482i \(-0.582647\pi\)
−0.256735 + 0.966482i \(0.582647\pi\)
\(642\) 0 0
\(643\) 4.00000 0.157745 0.0788723 − 0.996885i \(-0.474868\pi\)
0.0788723 + 0.996885i \(0.474868\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.0000 −1.17942 −0.589711 − 0.807614i \(-0.700758\pi\)
−0.589711 + 0.807614i \(0.700758\pi\)
\(648\) 0 0
\(649\) 6.00000 0.235521
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −34.0000 −1.33052 −0.665261 − 0.746611i \(-0.731680\pi\)
−0.665261 + 0.746611i \(0.731680\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 36.0000 1.40236 0.701180 − 0.712984i \(-0.252657\pi\)
0.701180 + 0.712984i \(0.252657\pi\)
\(660\) 0 0
\(661\) −22.0000 −0.855701 −0.427850 − 0.903850i \(-0.640729\pi\)
−0.427850 + 0.903850i \(0.640729\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −1.00000 −0.0387202
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 8.00000 0.308837
\(672\) 0 0
\(673\) −18.0000 −0.693849 −0.346925 − 0.937893i \(-0.612774\pi\)
−0.346925 + 0.937893i \(0.612774\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 22.0000 0.845529 0.422764 − 0.906240i \(-0.361060\pi\)
0.422764 + 0.906240i \(0.361060\pi\)
\(678\) 0 0
\(679\) −14.0000 −0.537271
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 39.0000 1.49229 0.746147 − 0.665782i \(-0.231902\pi\)
0.746147 + 0.665782i \(0.231902\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 4.00000 0.152388
\(690\) 0 0
\(691\) −48.0000 −1.82601 −0.913003 − 0.407953i \(-0.866243\pi\)
−0.913003 + 0.407953i \(0.866243\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 − 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) 18.0000 0.678883
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 12.0000 0.451306
\(708\) 0 0
\(709\) 22.0000 0.826227 0.413114 − 0.910679i \(-0.364441\pi\)
0.413114 + 0.910679i \(0.364441\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.00000 0.224702
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 52.0000 1.93927 0.969636 − 0.244551i \(-0.0786406\pi\)
0.969636 + 0.244551i \(0.0786406\pi\)
\(720\) 0 0
\(721\) −10.0000 −0.372419
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −44.0000 −1.63187 −0.815935 − 0.578144i \(-0.803777\pi\)
−0.815935 + 0.578144i \(0.803777\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.00000 0.295891
\(732\) 0 0
\(733\) −28.0000 −1.03420 −0.517102 − 0.855924i \(-0.672989\pi\)
−0.517102 + 0.855924i \(0.672989\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.00000 0.110506
\(738\) 0 0
\(739\) −1.00000 −0.0367856 −0.0183928 − 0.999831i \(-0.505855\pi\)
−0.0183928 + 0.999831i \(0.505855\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 36.0000 1.32071 0.660356 − 0.750953i \(-0.270405\pi\)
0.660356 + 0.750953i \(0.270405\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) 4.00000 0.145962 0.0729810 − 0.997333i \(-0.476749\pi\)
0.0729810 + 0.997333i \(0.476749\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −37.0000 −1.34479 −0.672394 − 0.740193i \(-0.734734\pi\)
−0.672394 + 0.740193i \(0.734734\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −40.0000 −1.45000 −0.724999 − 0.688749i \(-0.758160\pi\)
−0.724999 + 0.688749i \(0.758160\pi\)
\(762\) 0 0
\(763\) −7.00000 −0.253417
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 12.0000 0.433295
\(768\) 0 0
\(769\) −20.0000 −0.721218 −0.360609 − 0.932717i \(-0.617431\pi\)
−0.360609 + 0.932717i \(0.617431\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −50.0000 −1.79838 −0.899188 − 0.437564i \(-0.855842\pi\)
−0.899188 + 0.437564i \(0.855842\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) −7.00000 −0.250480
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 28.0000 0.998092 0.499046 − 0.866575i \(-0.333684\pi\)
0.499046 + 0.866575i \(0.333684\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −9.00000 −0.320003
\(792\) 0 0
\(793\) 16.0000 0.568177
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −12.0000 −0.425062 −0.212531 − 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 0 0
\(799\) 48.0000 1.69812
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −16.0000 −0.564628
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 13.0000 0.457056 0.228528 − 0.973537i \(-0.426609\pi\)
0.228528 + 0.973537i \(0.426609\pi\)
\(810\) 0 0
\(811\) −2.00000 −0.0702295 −0.0351147 − 0.999383i \(-0.511180\pi\)
−0.0351147 + 0.999383i \(0.511180\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) −2.00000 −0.0699711
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −34.0000 −1.18661 −0.593304 − 0.804978i \(-0.702177\pi\)
−0.593304 + 0.804978i \(0.702177\pi\)
\(822\) 0 0
\(823\) −57.0000 −1.98690 −0.993448 − 0.114289i \(-0.963541\pi\)
−0.993448 + 0.114289i \(0.963541\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −5.00000 −0.173867 −0.0869335 − 0.996214i \(-0.527707\pi\)
−0.0869335 + 0.996214i \(0.527707\pi\)
\(828\) 0 0
\(829\) −12.0000 −0.416777 −0.208389 − 0.978046i \(-0.566822\pi\)
−0.208389 + 0.978046i \(0.566822\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 8.00000 0.277184
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 16.0000 0.552381 0.276191 − 0.961103i \(-0.410928\pi\)
0.276191 + 0.961103i \(0.410928\pi\)
\(840\) 0 0
\(841\) −28.0000 −0.965517
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −10.0000 −0.343604
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −9.00000 −0.308516
\(852\) 0 0
\(853\) −16.0000 −0.547830 −0.273915 − 0.961754i \(-0.588319\pi\)
−0.273915 + 0.961754i \(0.588319\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −40.0000 −1.36637 −0.683187 − 0.730243i \(-0.739407\pi\)
−0.683187 + 0.730243i \(0.739407\pi\)
\(858\) 0 0
\(859\) −26.0000 −0.887109 −0.443554 − 0.896248i \(-0.646283\pi\)
−0.443554 + 0.896248i \(0.646283\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.00000 −0.0340404 −0.0170202 − 0.999855i \(-0.505418\pi\)
−0.0170202 + 0.999855i \(0.505418\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.00000 0.0339227
\(870\) 0 0
\(871\) 6.00000 0.203302
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −14.0000 −0.472746 −0.236373 − 0.971662i \(-0.575959\pi\)
−0.236373 + 0.971662i \(0.575959\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −14.0000 −0.471672 −0.235836 − 0.971793i \(-0.575783\pi\)
−0.235836 + 0.971793i \(0.575783\pi\)
\(882\) 0 0
\(883\) 19.0000 0.639401 0.319700 − 0.947519i \(-0.396418\pi\)
0.319700 + 0.947519i \(0.396418\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 8.00000 0.268614 0.134307 − 0.990940i \(-0.457119\pi\)
0.134307 + 0.990940i \(0.457119\pi\)
\(888\) 0 0
\(889\) −5.00000 −0.167695
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −12.0000 −0.401565
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −6.00000 −0.200111
\(900\) 0 0
\(901\) 16.0000 0.533037
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −28.0000 −0.929725 −0.464862 − 0.885383i \(-0.653896\pi\)
−0.464862 + 0.885383i \(0.653896\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −53.0000 −1.75597 −0.877984 − 0.478690i \(-0.841112\pi\)
−0.877984 + 0.478690i \(0.841112\pi\)
\(912\) 0 0
\(913\) −6.00000 −0.198571
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 16.0000 0.528367
\(918\) 0 0
\(919\) 25.0000 0.824674 0.412337 − 0.911031i \(-0.364713\pi\)
0.412337 + 0.911031i \(0.364713\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −14.0000 −0.460816
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −28.0000 −0.918650 −0.459325 − 0.888268i \(-0.651909\pi\)
−0.459325 + 0.888268i \(0.651909\pi\)
\(930\) 0 0
\(931\) −2.00000 −0.0655474
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −40.0000 −1.30674 −0.653372 − 0.757037i \(-0.726646\pi\)
−0.653372 + 0.757037i \(0.726646\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −30.0000 −0.977972 −0.488986 − 0.872292i \(-0.662633\pi\)
−0.488986 + 0.872292i \(0.662633\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 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
\(949\) −32.0000 −1.03876
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 11.0000 0.356325 0.178162 − 0.984001i \(-0.442985\pi\)
0.178162 + 0.984001i \(0.442985\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 10.0000 0.322917
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −16.0000 −0.514525 −0.257263 − 0.966342i \(-0.582821\pi\)
−0.257263 + 0.966342i \(0.582821\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 14.0000 0.449281 0.224641 − 0.974442i \(-0.427879\pi\)
0.224641 + 0.974442i \(0.427879\pi\)
\(972\) 0 0
\(973\) −4.00000 −0.128234
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −3.00000 −0.0959785 −0.0479893 − 0.998848i \(-0.515281\pi\)
−0.0479893 + 0.998848i \(0.515281\pi\)
\(978\) 0 0
\(979\) 14.0000 0.447442
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 54.0000 1.72233 0.861166 − 0.508323i \(-0.169735\pi\)
0.861166 + 0.508323i \(0.169735\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 1.00000 0.0317982
\(990\) 0 0
\(991\) 61.0000 1.93773 0.968864 − 0.247592i \(-0.0796392\pi\)
0.968864 + 0.247592i \(0.0796392\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 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
\(999\) 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 6300.2.a.ba.1.1 1
3.2 odd 2 2100.2.a.f.1.1 ✓ 1
5.2 odd 4 6300.2.k.l.6049.2 2
5.3 odd 4 6300.2.k.l.6049.1 2
5.4 even 2 6300.2.a.j.1.1 1
12.11 even 2 8400.2.a.by.1.1 1
15.2 even 4 2100.2.k.e.1849.2 2
15.8 even 4 2100.2.k.e.1849.1 2
15.14 odd 2 2100.2.a.l.1.1 yes 1
60.59 even 2 8400.2.a.ba.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2100.2.a.f.1.1 ✓ 1 3.2 odd 2
2100.2.a.l.1.1 yes 1 15.14 odd 2
2100.2.k.e.1849.1 2 15.8 even 4
2100.2.k.e.1849.2 2 15.2 even 4
6300.2.a.j.1.1 1 5.4 even 2
6300.2.a.ba.1.1 1 1.1 even 1 trivial
6300.2.k.l.6049.1 2 5.3 odd 4
6300.2.k.l.6049.2 2 5.2 odd 4
8400.2.a.ba.1.1 1 60.59 even 2
8400.2.a.by.1.1 1 12.11 even 2