Properties

Label 2200.4.a.a.1.1
Level $2200$
Weight $4$
Character 2200.1
Self dual yes
Analytic conductor $129.804$
Analytic rank $1$
Dimension $1$
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] = [2200,4,Mod(1,2200)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2200, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2200.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2200 = 2^{3} \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 2200.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: \(129.804202013\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 88)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) \(=\) 2200.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-7.00000 q^{3} -2.00000 q^{7} +22.0000 q^{9} +O(q^{10})\) \(q-7.00000 q^{3} -2.00000 q^{7} +22.0000 q^{9} -11.0000 q^{11} +38.0000 q^{17} +44.0000 q^{19} +14.0000 q^{21} -175.000 q^{23} +35.0000 q^{27} -264.000 q^{29} +159.000 q^{31} +77.0000 q^{33} +173.000 q^{37} -220.000 q^{41} +542.000 q^{43} +264.000 q^{47} -339.000 q^{49} -266.000 q^{51} -682.000 q^{53} -308.000 q^{57} +421.000 q^{59} +308.000 q^{61} -44.0000 q^{63} -177.000 q^{67} +1225.00 q^{69} +365.000 q^{71} +528.000 q^{73} +22.0000 q^{77} +686.000 q^{79} -839.000 q^{81} -698.000 q^{83} +1848.00 q^{87} +967.000 q^{89} -1113.00 q^{93} +1127.00 q^{97} -242.000 q^{99} +O(q^{100})\)

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
\(3\) −7.00000 −1.34715 −0.673575 0.739119i \(-0.735242\pi\)
−0.673575 + 0.739119i \(0.735242\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −2.00000 −0.107990 −0.0539949 0.998541i \(-0.517195\pi\)
−0.0539949 + 0.998541i \(0.517195\pi\)
\(8\) 0 0
\(9\) 22.0000 0.814815
\(10\) 0 0
\(11\) −11.0000 −0.301511
\(12\) 0 0
\(13\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 38.0000 0.542138 0.271069 0.962560i \(-0.412623\pi\)
0.271069 + 0.962560i \(0.412623\pi\)
\(18\) 0 0
\(19\) 44.0000 0.531279 0.265639 0.964072i \(-0.414417\pi\)
0.265639 + 0.964072i \(0.414417\pi\)
\(20\) 0 0
\(21\) 14.0000 0.145479
\(22\) 0 0
\(23\) −175.000 −1.58652 −0.793261 0.608881i \(-0.791619\pi\)
−0.793261 + 0.608881i \(0.791619\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 35.0000 0.249472
\(28\) 0 0
\(29\) −264.000 −1.69047 −0.845234 0.534396i \(-0.820539\pi\)
−0.845234 + 0.534396i \(0.820539\pi\)
\(30\) 0 0
\(31\) 159.000 0.921201 0.460601 0.887607i \(-0.347634\pi\)
0.460601 + 0.887607i \(0.347634\pi\)
\(32\) 0 0
\(33\) 77.0000 0.406181
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 173.000 0.768676 0.384338 0.923192i \(-0.374430\pi\)
0.384338 + 0.923192i \(0.374430\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −220.000 −0.838006 −0.419003 0.907985i \(-0.637620\pi\)
−0.419003 + 0.907985i \(0.637620\pi\)
\(42\) 0 0
\(43\) 542.000 1.92219 0.961096 0.276216i \(-0.0890805\pi\)
0.961096 + 0.276216i \(0.0890805\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 264.000 0.819327 0.409663 0.912237i \(-0.365646\pi\)
0.409663 + 0.912237i \(0.365646\pi\)
\(48\) 0 0
\(49\) −339.000 −0.988338
\(50\) 0 0
\(51\) −266.000 −0.730342
\(52\) 0 0
\(53\) −682.000 −1.76755 −0.883773 0.467916i \(-0.845005\pi\)
−0.883773 + 0.467916i \(0.845005\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) −308.000 −0.715712
\(58\) 0 0
\(59\) 421.000 0.928975 0.464488 0.885580i \(-0.346239\pi\)
0.464488 + 0.885580i \(0.346239\pi\)
\(60\) 0 0
\(61\) 308.000 0.646481 0.323241 0.946317i \(-0.395228\pi\)
0.323241 + 0.946317i \(0.395228\pi\)
\(62\) 0 0
\(63\) −44.0000 −0.0879917
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −177.000 −0.322746 −0.161373 0.986893i \(-0.551592\pi\)
−0.161373 + 0.986893i \(0.551592\pi\)
\(68\) 0 0
\(69\) 1225.00 2.13729
\(70\) 0 0
\(71\) 365.000 0.610106 0.305053 0.952335i \(-0.401326\pi\)
0.305053 + 0.952335i \(0.401326\pi\)
\(72\) 0 0
\(73\) 528.000 0.846544 0.423272 0.906003i \(-0.360881\pi\)
0.423272 + 0.906003i \(0.360881\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 22.0000 0.0325602
\(78\) 0 0
\(79\) 686.000 0.976975 0.488488 0.872571i \(-0.337549\pi\)
0.488488 + 0.872571i \(0.337549\pi\)
\(80\) 0 0
\(81\) −839.000 −1.15089
\(82\) 0 0
\(83\) −698.000 −0.923078 −0.461539 0.887120i \(-0.652703\pi\)
−0.461539 + 0.887120i \(0.652703\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 1848.00 2.27731
\(88\) 0 0
\(89\) 967.000 1.15171 0.575853 0.817553i \(-0.304670\pi\)
0.575853 + 0.817553i \(0.304670\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −1113.00 −1.24100
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1127.00 1.17969 0.589843 0.807518i \(-0.299190\pi\)
0.589843 + 0.807518i \(0.299190\pi\)
\(98\) 0 0
\(99\) −242.000 −0.245676
\(100\) 0 0
\(101\) 510.000 0.502445 0.251222 0.967929i \(-0.419167\pi\)
0.251222 + 0.967929i \(0.419167\pi\)
\(102\) 0 0
\(103\) 1056.00 1.01020 0.505101 0.863060i \(-0.331455\pi\)
0.505101 + 0.863060i \(0.331455\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1046.00 −0.945053 −0.472526 0.881317i \(-0.656658\pi\)
−0.472526 + 0.881317i \(0.656658\pi\)
\(108\) 0 0
\(109\) 250.000 0.219685 0.109842 0.993949i \(-0.464965\pi\)
0.109842 + 0.993949i \(0.464965\pi\)
\(110\) 0 0
\(111\) −1211.00 −1.03552
\(112\) 0 0
\(113\) −1401.00 −1.16633 −0.583164 0.812355i \(-0.698185\pi\)
−0.583164 + 0.812355i \(0.698185\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −76.0000 −0.0585455
\(120\) 0 0
\(121\) 121.000 0.0909091
\(122\) 0 0
\(123\) 1540.00 1.12892
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 132.000 0.0922292 0.0461146 0.998936i \(-0.485316\pi\)
0.0461146 + 0.998936i \(0.485316\pi\)
\(128\) 0 0
\(129\) −3794.00 −2.58948
\(130\) 0 0
\(131\) −2054.00 −1.36991 −0.684957 0.728583i \(-0.740179\pi\)
−0.684957 + 0.728583i \(0.740179\pi\)
\(132\) 0 0
\(133\) −88.0000 −0.0573727
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −889.000 −0.554397 −0.277199 0.960813i \(-0.589406\pi\)
−0.277199 + 0.960813i \(0.589406\pi\)
\(138\) 0 0
\(139\) 2638.00 1.60973 0.804864 0.593459i \(-0.202238\pi\)
0.804864 + 0.593459i \(0.202238\pi\)
\(140\) 0 0
\(141\) −1848.00 −1.10376
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 2373.00 1.33144
\(148\) 0 0
\(149\) 3338.00 1.83530 0.917650 0.397390i \(-0.130084\pi\)
0.917650 + 0.397390i \(0.130084\pi\)
\(150\) 0 0
\(151\) −430.000 −0.231741 −0.115871 0.993264i \(-0.536966\pi\)
−0.115871 + 0.993264i \(0.536966\pi\)
\(152\) 0 0
\(153\) 836.000 0.441742
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 1159.00 0.589161 0.294580 0.955627i \(-0.404820\pi\)
0.294580 + 0.955627i \(0.404820\pi\)
\(158\) 0 0
\(159\) 4774.00 2.38115
\(160\) 0 0
\(161\) 350.000 0.171328
\(162\) 0 0
\(163\) −1012.00 −0.486294 −0.243147 0.969989i \(-0.578180\pi\)
−0.243147 + 0.969989i \(0.578180\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1584.00 −0.733974 −0.366987 0.930226i \(-0.619611\pi\)
−0.366987 + 0.930226i \(0.619611\pi\)
\(168\) 0 0
\(169\) −2197.00 −1.00000
\(170\) 0 0
\(171\) 968.000 0.432894
\(172\) 0 0
\(173\) −474.000 −0.208310 −0.104155 0.994561i \(-0.533214\pi\)
−0.104155 + 0.994561i \(0.533214\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2947.00 −1.25147
\(178\) 0 0
\(179\) 1665.00 0.695240 0.347620 0.937636i \(-0.386990\pi\)
0.347620 + 0.937636i \(0.386990\pi\)
\(180\) 0 0
\(181\) 2543.00 1.04431 0.522154 0.852851i \(-0.325129\pi\)
0.522154 + 0.852851i \(0.325129\pi\)
\(182\) 0 0
\(183\) −2156.00 −0.870908
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −418.000 −0.163461
\(188\) 0 0
\(189\) −70.0000 −0.0269405
\(190\) 0 0
\(191\) −1631.00 −0.617880 −0.308940 0.951082i \(-0.599974\pi\)
−0.308940 + 0.951082i \(0.599974\pi\)
\(192\) 0 0
\(193\) −484.000 −0.180513 −0.0902567 0.995919i \(-0.528769\pi\)
−0.0902567 + 0.995919i \(0.528769\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −1966.00 −0.711024 −0.355512 0.934672i \(-0.615693\pi\)
−0.355512 + 0.934672i \(0.615693\pi\)
\(198\) 0 0
\(199\) 968.000 0.344823 0.172411 0.985025i \(-0.444844\pi\)
0.172411 + 0.985025i \(0.444844\pi\)
\(200\) 0 0
\(201\) 1239.00 0.434788
\(202\) 0 0
\(203\) 528.000 0.182553
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −3850.00 −1.29272
\(208\) 0 0
\(209\) −484.000 −0.160187
\(210\) 0 0
\(211\) −2948.00 −0.961842 −0.480921 0.876764i \(-0.659698\pi\)
−0.480921 + 0.876764i \(0.659698\pi\)
\(212\) 0 0
\(213\) −2555.00 −0.821905
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −318.000 −0.0994804
\(218\) 0 0
\(219\) −3696.00 −1.14042
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1995.00 −0.599081 −0.299541 0.954084i \(-0.596833\pi\)
−0.299541 + 0.954084i \(0.596833\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6026.00 1.76194 0.880968 0.473175i \(-0.156892\pi\)
0.880968 + 0.473175i \(0.156892\pi\)
\(228\) 0 0
\(229\) −4417.00 −1.27460 −0.637300 0.770615i \(-0.719949\pi\)
−0.637300 + 0.770615i \(0.719949\pi\)
\(230\) 0 0
\(231\) −154.000 −0.0438634
\(232\) 0 0
\(233\) −5808.00 −1.63302 −0.816512 0.577328i \(-0.804095\pi\)
−0.816512 + 0.577328i \(0.804095\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) −4802.00 −1.31613
\(238\) 0 0
\(239\) 626.000 0.169425 0.0847125 0.996405i \(-0.473003\pi\)
0.0847125 + 0.996405i \(0.473003\pi\)
\(240\) 0 0
\(241\) −3520.00 −0.940843 −0.470421 0.882442i \(-0.655898\pi\)
−0.470421 + 0.882442i \(0.655898\pi\)
\(242\) 0 0
\(243\) 4928.00 1.30095
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 4886.00 1.24352
\(250\) 0 0
\(251\) 3921.00 0.986021 0.493011 0.870023i \(-0.335896\pi\)
0.493011 + 0.870023i \(0.335896\pi\)
\(252\) 0 0
\(253\) 1925.00 0.478355
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −4598.00 −1.11601 −0.558007 0.829837i \(-0.688434\pi\)
−0.558007 + 0.829837i \(0.688434\pi\)
\(258\) 0 0
\(259\) −346.000 −0.0830092
\(260\) 0 0
\(261\) −5808.00 −1.37742
\(262\) 0 0
\(263\) 5838.00 1.36877 0.684385 0.729121i \(-0.260071\pi\)
0.684385 + 0.729121i \(0.260071\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −6769.00 −1.55152
\(268\) 0 0
\(269\) −5038.00 −1.14190 −0.570952 0.820983i \(-0.693426\pi\)
−0.570952 + 0.820983i \(0.693426\pi\)
\(270\) 0 0
\(271\) −8096.00 −1.81475 −0.907374 0.420323i \(-0.861917\pi\)
−0.907374 + 0.420323i \(0.861917\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −7014.00 −1.52141 −0.760705 0.649098i \(-0.775146\pi\)
−0.760705 + 0.649098i \(0.775146\pi\)
\(278\) 0 0
\(279\) 3498.00 0.750609
\(280\) 0 0
\(281\) −4362.00 −0.926032 −0.463016 0.886350i \(-0.653233\pi\)
−0.463016 + 0.886350i \(0.653233\pi\)
\(282\) 0 0
\(283\) −4620.00 −0.970426 −0.485213 0.874396i \(-0.661258\pi\)
−0.485213 + 0.874396i \(0.661258\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 440.000 0.0904961
\(288\) 0 0
\(289\) −3469.00 −0.706086
\(290\) 0 0
\(291\) −7889.00 −1.58921
\(292\) 0 0
\(293\) 7172.00 1.43001 0.715005 0.699120i \(-0.246425\pi\)
0.715005 + 0.699120i \(0.246425\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −385.000 −0.0752187
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) −1084.00 −0.207577
\(302\) 0 0
\(303\) −3570.00 −0.676868
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −7348.00 −1.36603 −0.683017 0.730402i \(-0.739333\pi\)
−0.683017 + 0.730402i \(0.739333\pi\)
\(308\) 0 0
\(309\) −7392.00 −1.36089
\(310\) 0 0
\(311\) −5508.00 −1.00428 −0.502138 0.864787i \(-0.667453\pi\)
−0.502138 + 0.864787i \(0.667453\pi\)
\(312\) 0 0
\(313\) 7009.00 1.26573 0.632863 0.774264i \(-0.281880\pi\)
0.632863 + 0.774264i \(0.281880\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −853.000 −0.151133 −0.0755666 0.997141i \(-0.524077\pi\)
−0.0755666 + 0.997141i \(0.524077\pi\)
\(318\) 0 0
\(319\) 2904.00 0.509695
\(320\) 0 0
\(321\) 7322.00 1.27313
\(322\) 0 0
\(323\) 1672.00 0.288027
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1750.00 −0.295949
\(328\) 0 0
\(329\) −528.000 −0.0884790
\(330\) 0 0
\(331\) 3631.00 0.602954 0.301477 0.953473i \(-0.402520\pi\)
0.301477 + 0.953473i \(0.402520\pi\)
\(332\) 0 0
\(333\) 3806.00 0.626329
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −11574.0 −1.87085 −0.935424 0.353527i \(-0.884982\pi\)
−0.935424 + 0.353527i \(0.884982\pi\)
\(338\) 0 0
\(339\) 9807.00 1.57122
\(340\) 0 0
\(341\) −1749.00 −0.277753
\(342\) 0 0
\(343\) 1364.00 0.214720
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1056.00 0.163369 0.0816845 0.996658i \(-0.473970\pi\)
0.0816845 + 0.996658i \(0.473970\pi\)
\(348\) 0 0
\(349\) 6810.00 1.04450 0.522251 0.852792i \(-0.325093\pi\)
0.522251 + 0.852792i \(0.325093\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −9923.00 −1.49617 −0.748085 0.663603i \(-0.769026\pi\)
−0.748085 + 0.663603i \(0.769026\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 532.000 0.0788695
\(358\) 0 0
\(359\) −2200.00 −0.323431 −0.161715 0.986837i \(-0.551703\pi\)
−0.161715 + 0.986837i \(0.551703\pi\)
\(360\) 0 0
\(361\) −4923.00 −0.717743
\(362\) 0 0
\(363\) −847.000 −0.122468
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −8935.00 −1.27085 −0.635427 0.772161i \(-0.719176\pi\)
−0.635427 + 0.772161i \(0.719176\pi\)
\(368\) 0 0
\(369\) −4840.00 −0.682819
\(370\) 0 0
\(371\) 1364.00 0.190877
\(372\) 0 0
\(373\) −9122.00 −1.26627 −0.633136 0.774041i \(-0.718233\pi\)
−0.633136 + 0.774041i \(0.718233\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 8963.00 1.21477 0.607386 0.794407i \(-0.292218\pi\)
0.607386 + 0.794407i \(0.292218\pi\)
\(380\) 0 0
\(381\) −924.000 −0.124247
\(382\) 0 0
\(383\) 1721.00 0.229606 0.114803 0.993388i \(-0.463376\pi\)
0.114803 + 0.993388i \(0.463376\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 11924.0 1.56623
\(388\) 0 0
\(389\) −7351.00 −0.958125 −0.479062 0.877781i \(-0.659023\pi\)
−0.479062 + 0.877781i \(0.659023\pi\)
\(390\) 0 0
\(391\) −6650.00 −0.860115
\(392\) 0 0
\(393\) 14378.0 1.84548
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 8338.00 1.05409 0.527043 0.849839i \(-0.323301\pi\)
0.527043 + 0.849839i \(0.323301\pi\)
\(398\) 0 0
\(399\) 616.000 0.0772897
\(400\) 0 0
\(401\) −11814.0 −1.47123 −0.735615 0.677400i \(-0.763107\pi\)
−0.735615 + 0.677400i \(0.763107\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1903.00 −0.231765
\(408\) 0 0
\(409\) −7278.00 −0.879887 −0.439944 0.898025i \(-0.645002\pi\)
−0.439944 + 0.898025i \(0.645002\pi\)
\(410\) 0 0
\(411\) 6223.00 0.746856
\(412\) 0 0
\(413\) −842.000 −0.100320
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −18466.0 −2.16855
\(418\) 0 0
\(419\) −3828.00 −0.446325 −0.223162 0.974781i \(-0.571638\pi\)
−0.223162 + 0.974781i \(0.571638\pi\)
\(420\) 0 0
\(421\) −15466.0 −1.79042 −0.895210 0.445645i \(-0.852974\pi\)
−0.895210 + 0.445645i \(0.852974\pi\)
\(422\) 0 0
\(423\) 5808.00 0.667600
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −616.000 −0.0698134
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −2710.00 −0.302868 −0.151434 0.988467i \(-0.548389\pi\)
−0.151434 + 0.988467i \(0.548389\pi\)
\(432\) 0 0
\(433\) 3347.00 0.371470 0.185735 0.982600i \(-0.440533\pi\)
0.185735 + 0.982600i \(0.440533\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −7700.00 −0.842885
\(438\) 0 0
\(439\) 2464.00 0.267882 0.133941 0.990989i \(-0.457237\pi\)
0.133941 + 0.990989i \(0.457237\pi\)
\(440\) 0 0
\(441\) −7458.00 −0.805313
\(442\) 0 0
\(443\) 5955.00 0.638669 0.319335 0.947642i \(-0.396541\pi\)
0.319335 + 0.947642i \(0.396541\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −23366.0 −2.47242
\(448\) 0 0
\(449\) −13173.0 −1.38457 −0.692285 0.721624i \(-0.743396\pi\)
−0.692285 + 0.721624i \(0.743396\pi\)
\(450\) 0 0
\(451\) 2420.00 0.252668
\(452\) 0 0
\(453\) 3010.00 0.312190
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 6292.00 0.644042 0.322021 0.946732i \(-0.395638\pi\)
0.322021 + 0.946732i \(0.395638\pi\)
\(458\) 0 0
\(459\) 1330.00 0.135249
\(460\) 0 0
\(461\) 10164.0 1.02686 0.513432 0.858130i \(-0.328374\pi\)
0.513432 + 0.858130i \(0.328374\pi\)
\(462\) 0 0
\(463\) −5677.00 −0.569833 −0.284916 0.958552i \(-0.591966\pi\)
−0.284916 + 0.958552i \(0.591966\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 6675.00 0.661418 0.330709 0.943733i \(-0.392712\pi\)
0.330709 + 0.943733i \(0.392712\pi\)
\(468\) 0 0
\(469\) 354.000 0.0348533
\(470\) 0 0
\(471\) −8113.00 −0.793689
\(472\) 0 0
\(473\) −5962.00 −0.579562
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −15004.0 −1.44022
\(478\) 0 0
\(479\) 6424.00 0.612777 0.306388 0.951907i \(-0.400879\pi\)
0.306388 + 0.951907i \(0.400879\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) −2450.00 −0.230805
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 21369.0 1.98834 0.994170 0.107822i \(-0.0343876\pi\)
0.994170 + 0.107822i \(0.0343876\pi\)
\(488\) 0 0
\(489\) 7084.00 0.655112
\(490\) 0 0
\(491\) 1848.00 0.169856 0.0849278 0.996387i \(-0.472934\pi\)
0.0849278 + 0.996387i \(0.472934\pi\)
\(492\) 0 0
\(493\) −10032.0 −0.916468
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −730.000 −0.0658853
\(498\) 0 0
\(499\) −19228.0 −1.72498 −0.862488 0.506077i \(-0.831095\pi\)
−0.862488 + 0.506077i \(0.831095\pi\)
\(500\) 0 0
\(501\) 11088.0 0.988773
\(502\) 0 0
\(503\) −10878.0 −0.964266 −0.482133 0.876098i \(-0.660138\pi\)
−0.482133 + 0.876098i \(0.660138\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 15379.0 1.34715
\(508\) 0 0
\(509\) 10047.0 0.874903 0.437451 0.899242i \(-0.355881\pi\)
0.437451 + 0.899242i \(0.355881\pi\)
\(510\) 0 0
\(511\) −1056.00 −0.0914182
\(512\) 0 0
\(513\) 1540.00 0.132539
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −2904.00 −0.247036
\(518\) 0 0
\(519\) 3318.00 0.280624
\(520\) 0 0
\(521\) −5827.00 −0.489991 −0.244996 0.969524i \(-0.578787\pi\)
−0.244996 + 0.969524i \(0.578787\pi\)
\(522\) 0 0
\(523\) −836.000 −0.0698962 −0.0349481 0.999389i \(-0.511127\pi\)
−0.0349481 + 0.999389i \(0.511127\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6042.00 0.499419
\(528\) 0 0
\(529\) 18458.0 1.51705
\(530\) 0 0
\(531\) 9262.00 0.756943
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −11655.0 −0.936593
\(538\) 0 0
\(539\) 3729.00 0.297995
\(540\) 0 0
\(541\) −7172.00 −0.569960 −0.284980 0.958533i \(-0.591987\pi\)
−0.284980 + 0.958533i \(0.591987\pi\)
\(542\) 0 0
\(543\) −17801.0 −1.40684
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 11264.0 0.880464 0.440232 0.897884i \(-0.354896\pi\)
0.440232 + 0.897884i \(0.354896\pi\)
\(548\) 0 0
\(549\) 6776.00 0.526763
\(550\) 0 0
\(551\) −11616.0 −0.898109
\(552\) 0 0
\(553\) −1372.00 −0.105503
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −306.000 −0.0232776 −0.0116388 0.999932i \(-0.503705\pi\)
−0.0116388 + 0.999932i \(0.503705\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 2926.00 0.220206
\(562\) 0 0
\(563\) −23804.0 −1.78192 −0.890958 0.454085i \(-0.849966\pi\)
−0.890958 + 0.454085i \(0.849966\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 1678.00 0.124285
\(568\) 0 0
\(569\) −4664.00 −0.343629 −0.171815 0.985129i \(-0.554963\pi\)
−0.171815 + 0.985129i \(0.554963\pi\)
\(570\) 0 0
\(571\) 11572.0 0.848114 0.424057 0.905635i \(-0.360606\pi\)
0.424057 + 0.905635i \(0.360606\pi\)
\(572\) 0 0
\(573\) 11417.0 0.832377
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 24407.0 1.76096 0.880482 0.474079i \(-0.157219\pi\)
0.880482 + 0.474079i \(0.157219\pi\)
\(578\) 0 0
\(579\) 3388.00 0.243179
\(580\) 0 0
\(581\) 1396.00 0.0996830
\(582\) 0 0
\(583\) 7502.00 0.532935
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −18436.0 −1.29631 −0.648156 0.761508i \(-0.724460\pi\)
−0.648156 + 0.761508i \(0.724460\pi\)
\(588\) 0 0
\(589\) 6996.00 0.489415
\(590\) 0 0
\(591\) 13762.0 0.957856
\(592\) 0 0
\(593\) 11044.0 0.764794 0.382397 0.923998i \(-0.375099\pi\)
0.382397 + 0.923998i \(0.375099\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −6776.00 −0.464528
\(598\) 0 0
\(599\) 8800.00 0.600264 0.300132 0.953898i \(-0.402969\pi\)
0.300132 + 0.953898i \(0.402969\pi\)
\(600\) 0 0
\(601\) −10826.0 −0.734778 −0.367389 0.930067i \(-0.619748\pi\)
−0.367389 + 0.930067i \(0.619748\pi\)
\(602\) 0 0
\(603\) −3894.00 −0.262978
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −4066.00 −0.271884 −0.135942 0.990717i \(-0.543406\pi\)
−0.135942 + 0.990717i \(0.543406\pi\)
\(608\) 0 0
\(609\) −3696.00 −0.245927
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −4752.00 −0.313102 −0.156551 0.987670i \(-0.550038\pi\)
−0.156551 + 0.987670i \(0.550038\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 3806.00 0.248337 0.124168 0.992261i \(-0.460374\pi\)
0.124168 + 0.992261i \(0.460374\pi\)
\(618\) 0 0
\(619\) −5185.00 −0.336676 −0.168338 0.985729i \(-0.553840\pi\)
−0.168338 + 0.985729i \(0.553840\pi\)
\(620\) 0 0
\(621\) −6125.00 −0.395794
\(622\) 0 0
\(623\) −1934.00 −0.124373
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 3388.00 0.215795
\(628\) 0 0
\(629\) 6574.00 0.416729
\(630\) 0 0
\(631\) −13049.0 −0.823253 −0.411626 0.911353i \(-0.635039\pi\)
−0.411626 + 0.911353i \(0.635039\pi\)
\(632\) 0 0
\(633\) 20636.0 1.29575
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 8030.00 0.497123
\(640\) 0 0
\(641\) 9959.00 0.613661 0.306831 0.951764i \(-0.400731\pi\)
0.306831 + 0.951764i \(0.400731\pi\)
\(642\) 0 0
\(643\) −12197.0 −0.748060 −0.374030 0.927417i \(-0.622024\pi\)
−0.374030 + 0.927417i \(0.622024\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 5759.00 0.349938 0.174969 0.984574i \(-0.444018\pi\)
0.174969 + 0.984574i \(0.444018\pi\)
\(648\) 0 0
\(649\) −4631.00 −0.280097
\(650\) 0 0
\(651\) 2226.00 0.134015
\(652\) 0 0
\(653\) 25209.0 1.51073 0.755363 0.655306i \(-0.227460\pi\)
0.755363 + 0.655306i \(0.227460\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 11616.0 0.689777
\(658\) 0 0
\(659\) −4062.00 −0.240111 −0.120055 0.992767i \(-0.538307\pi\)
−0.120055 + 0.992767i \(0.538307\pi\)
\(660\) 0 0
\(661\) 31173.0 1.83433 0.917163 0.398513i \(-0.130474\pi\)
0.917163 + 0.398513i \(0.130474\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 46200.0 2.68197
\(668\) 0 0
\(669\) 13965.0 0.807052
\(670\) 0 0
\(671\) −3388.00 −0.194921
\(672\) 0 0
\(673\) 26690.0 1.52871 0.764357 0.644794i \(-0.223057\pi\)
0.764357 + 0.644794i \(0.223057\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 7398.00 0.419983 0.209991 0.977703i \(-0.432656\pi\)
0.209991 + 0.977703i \(0.432656\pi\)
\(678\) 0 0
\(679\) −2254.00 −0.127394
\(680\) 0 0
\(681\) −42182.0 −2.37359
\(682\) 0 0
\(683\) −27960.0 −1.56641 −0.783206 0.621762i \(-0.786417\pi\)
−0.783206 + 0.621762i \(0.786417\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 30919.0 1.71708
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 19465.0 1.07161 0.535806 0.844341i \(-0.320008\pi\)
0.535806 + 0.844341i \(0.320008\pi\)
\(692\) 0 0
\(693\) 484.000 0.0265305
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −8360.00 −0.454315
\(698\) 0 0
\(699\) 40656.0 2.19993
\(700\) 0 0
\(701\) 13518.0 0.728342 0.364171 0.931332i \(-0.381352\pi\)
0.364171 + 0.931332i \(0.381352\pi\)
\(702\) 0 0
\(703\) 7612.00 0.408381
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1020.00 −0.0542589
\(708\) 0 0
\(709\) 14727.0 0.780090 0.390045 0.920796i \(-0.372459\pi\)
0.390045 + 0.920796i \(0.372459\pi\)
\(710\) 0 0
\(711\) 15092.0 0.796054
\(712\) 0 0
\(713\) −27825.0 −1.46151
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −4382.00 −0.228241
\(718\) 0 0
\(719\) 15711.0 0.814912 0.407456 0.913225i \(-0.366416\pi\)
0.407456 + 0.913225i \(0.366416\pi\)
\(720\) 0 0
\(721\) −2112.00 −0.109092
\(722\) 0 0
\(723\) 24640.0 1.26746
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −12099.0 −0.617231 −0.308616 0.951187i \(-0.599866\pi\)
−0.308616 + 0.951187i \(0.599866\pi\)
\(728\) 0 0
\(729\) −11843.0 −0.601687
\(730\) 0 0
\(731\) 20596.0 1.04209
\(732\) 0 0
\(733\) −9812.00 −0.494426 −0.247213 0.968961i \(-0.579515\pi\)
−0.247213 + 0.968961i \(0.579515\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1947.00 0.0973116
\(738\) 0 0
\(739\) −11854.0 −0.590063 −0.295031 0.955488i \(-0.595330\pi\)
−0.295031 + 0.955488i \(0.595330\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −18788.0 −0.927678 −0.463839 0.885919i \(-0.653528\pi\)
−0.463839 + 0.885919i \(0.653528\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −15356.0 −0.752137
\(748\) 0 0
\(749\) 2092.00 0.102056
\(750\) 0 0
\(751\) −16559.0 −0.804589 −0.402295 0.915510i \(-0.631787\pi\)
−0.402295 + 0.915510i \(0.631787\pi\)
\(752\) 0 0
\(753\) −27447.0 −1.32832
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −26610.0 −1.27762 −0.638809 0.769365i \(-0.720573\pi\)
−0.638809 + 0.769365i \(0.720573\pi\)
\(758\) 0 0
\(759\) −13475.0 −0.644416
\(760\) 0 0
\(761\) 7040.00 0.335348 0.167674 0.985843i \(-0.446374\pi\)
0.167674 + 0.985843i \(0.446374\pi\)
\(762\) 0 0
\(763\) −500.000 −0.0237237
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −18128.0 −0.850081 −0.425041 0.905174i \(-0.639740\pi\)
−0.425041 + 0.905174i \(0.639740\pi\)
\(770\) 0 0
\(771\) 32186.0 1.50344
\(772\) 0 0
\(773\) −9570.00 −0.445290 −0.222645 0.974900i \(-0.571469\pi\)
−0.222645 + 0.974900i \(0.571469\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 2422.00 0.111826
\(778\) 0 0
\(779\) −9680.00 −0.445214
\(780\) 0 0
\(781\) −4015.00 −0.183954
\(782\) 0 0
\(783\) −9240.00 −0.421725
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 16280.0 0.737382 0.368691 0.929552i \(-0.379806\pi\)
0.368691 + 0.929552i \(0.379806\pi\)
\(788\) 0 0
\(789\) −40866.0 −1.84394
\(790\) 0 0
\(791\) 2802.00 0.125952
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 603.000 0.0267997 0.0133998 0.999910i \(-0.495735\pi\)
0.0133998 + 0.999910i \(0.495735\pi\)
\(798\) 0 0
\(799\) 10032.0 0.444189
\(800\) 0 0
\(801\) 21274.0 0.938427
\(802\) 0 0
\(803\) −5808.00 −0.255243
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 35266.0 1.53832
\(808\) 0 0
\(809\) 23276.0 1.01155 0.505773 0.862667i \(-0.331207\pi\)
0.505773 + 0.862667i \(0.331207\pi\)
\(810\) 0 0
\(811\) −45662.0 −1.97708 −0.988539 0.150968i \(-0.951761\pi\)
−0.988539 + 0.150968i \(0.951761\pi\)
\(812\) 0 0
\(813\) 56672.0 2.44474
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 23848.0 1.02122
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 33222.0 1.41225 0.706124 0.708088i \(-0.250442\pi\)
0.706124 + 0.708088i \(0.250442\pi\)
\(822\) 0 0
\(823\) 3569.00 0.151163 0.0755817 0.997140i \(-0.475919\pi\)
0.0755817 + 0.997140i \(0.475919\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 41008.0 1.72429 0.862145 0.506662i \(-0.169121\pi\)
0.862145 + 0.506662i \(0.169121\pi\)
\(828\) 0 0
\(829\) −17839.0 −0.747375 −0.373688 0.927555i \(-0.621907\pi\)
−0.373688 + 0.927555i \(0.621907\pi\)
\(830\) 0 0
\(831\) 49098.0 2.04957
\(832\) 0 0
\(833\) −12882.0 −0.535816
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 5565.00 0.229814
\(838\) 0 0
\(839\) 20731.0 0.853056 0.426528 0.904474i \(-0.359737\pi\)
0.426528 + 0.904474i \(0.359737\pi\)
\(840\) 0 0
\(841\) 45307.0 1.85768
\(842\) 0 0
\(843\) 30534.0 1.24751
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) −242.000 −0.00981726
\(848\) 0 0
\(849\) 32340.0 1.30731
\(850\) 0 0
\(851\) −30275.0 −1.21952
\(852\) 0 0
\(853\) −9102.00 −0.365354 −0.182677 0.983173i \(-0.558476\pi\)
−0.182677 + 0.983173i \(0.558476\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −12936.0 −0.515619 −0.257809 0.966196i \(-0.583001\pi\)
−0.257809 + 0.966196i \(0.583001\pi\)
\(858\) 0 0
\(859\) 15113.0 0.600290 0.300145 0.953894i \(-0.402965\pi\)
0.300145 + 0.953894i \(0.402965\pi\)
\(860\) 0 0
\(861\) −3080.00 −0.121912
\(862\) 0 0
\(863\) −29216.0 −1.15240 −0.576202 0.817308i \(-0.695466\pi\)
−0.576202 + 0.817308i \(0.695466\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 24283.0 0.951204
\(868\) 0 0
\(869\) −7546.00 −0.294569
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 24794.0 0.961225
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −29304.0 −1.12831 −0.564154 0.825670i \(-0.690798\pi\)
−0.564154 + 0.825670i \(0.690798\pi\)
\(878\) 0 0
\(879\) −50204.0 −1.92644
\(880\) 0 0
\(881\) −23715.0 −0.906900 −0.453450 0.891282i \(-0.649807\pi\)
−0.453450 + 0.891282i \(0.649807\pi\)
\(882\) 0 0
\(883\) −6028.00 −0.229738 −0.114869 0.993381i \(-0.536645\pi\)
−0.114869 + 0.993381i \(0.536645\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −18786.0 −0.711130 −0.355565 0.934652i \(-0.615712\pi\)
−0.355565 + 0.934652i \(0.615712\pi\)
\(888\) 0 0
\(889\) −264.000 −0.00995982
\(890\) 0 0
\(891\) 9229.00 0.347007
\(892\) 0 0
\(893\) 11616.0 0.435291
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −41976.0 −1.55726
\(900\) 0 0
\(901\) −25916.0 −0.958254
\(902\) 0 0
\(903\) 7588.00 0.279638
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 2156.00 0.0789292 0.0394646 0.999221i \(-0.487435\pi\)
0.0394646 + 0.999221i \(0.487435\pi\)
\(908\) 0 0
\(909\) 11220.0 0.409399
\(910\) 0 0
\(911\) −51732.0 −1.88140 −0.940701 0.339236i \(-0.889831\pi\)
−0.940701 + 0.339236i \(0.889831\pi\)
\(912\) 0 0
\(913\) 7678.00 0.278318
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 4108.00 0.147937
\(918\) 0 0
\(919\) −18254.0 −0.655216 −0.327608 0.944814i \(-0.606243\pi\)
−0.327608 + 0.944814i \(0.606243\pi\)
\(920\) 0 0
\(921\) 51436.0 1.84025
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 23232.0 0.823127
\(928\) 0 0
\(929\) 5610.00 0.198125 0.0990625 0.995081i \(-0.468416\pi\)
0.0990625 + 0.995081i \(0.468416\pi\)
\(930\) 0 0
\(931\) −14916.0 −0.525083
\(932\) 0 0
\(933\) 38556.0 1.35291
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 37180.0 1.29628 0.648142 0.761520i \(-0.275546\pi\)
0.648142 + 0.761520i \(0.275546\pi\)
\(938\) 0 0
\(939\) −49063.0 −1.70512
\(940\) 0 0
\(941\) −31278.0 −1.08356 −0.541782 0.840519i \(-0.682250\pi\)
−0.541782 + 0.840519i \(0.682250\pi\)
\(942\) 0 0
\(943\) 38500.0 1.32951
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 47475.0 1.62907 0.814535 0.580114i \(-0.196992\pi\)
0.814535 + 0.580114i \(0.196992\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 5971.00 0.203599
\(952\) 0 0
\(953\) −20462.0 −0.695519 −0.347759 0.937584i \(-0.613057\pi\)
−0.347759 + 0.937584i \(0.613057\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) −20328.0 −0.686636
\(958\) 0 0
\(959\) 1778.00 0.0598693
\(960\) 0 0
\(961\) −4510.00 −0.151388
\(962\) 0 0
\(963\) −23012.0 −0.770043
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −52360.0 −1.74125 −0.870623 0.491952i \(-0.836284\pi\)
−0.870623 + 0.491952i \(0.836284\pi\)
\(968\) 0 0
\(969\) −11704.0 −0.388015
\(970\) 0 0
\(971\) 56247.0 1.85896 0.929481 0.368870i \(-0.120255\pi\)
0.929481 + 0.368870i \(0.120255\pi\)
\(972\) 0 0
\(973\) −5276.00 −0.173834
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 18155.0 0.594503 0.297252 0.954799i \(-0.403930\pi\)
0.297252 + 0.954799i \(0.403930\pi\)
\(978\) 0 0
\(979\) −10637.0 −0.347252
\(980\) 0 0
\(981\) 5500.00 0.179003
\(982\) 0 0
\(983\) −1191.00 −0.0386439 −0.0193220 0.999813i \(-0.506151\pi\)
−0.0193220 + 0.999813i \(0.506151\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 3696.00 0.119195
\(988\) 0 0
\(989\) −94850.0 −3.04960
\(990\) 0 0
\(991\) 28864.0 0.925222 0.462611 0.886561i \(-0.346913\pi\)
0.462611 + 0.886561i \(0.346913\pi\)
\(992\) 0 0
\(993\) −25417.0 −0.812270
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −51610.0 −1.63942 −0.819712 0.572776i \(-0.805866\pi\)
−0.819712 + 0.572776i \(0.805866\pi\)
\(998\) 0 0
\(999\) 6055.00 0.191763
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 2200.4.a.a.1.1 1
5.4 even 2 88.4.a.b.1.1 1
15.14 odd 2 792.4.a.b.1.1 1
20.19 odd 2 176.4.a.a.1.1 1
40.19 odd 2 704.4.a.k.1.1 1
40.29 even 2 704.4.a.a.1.1 1
55.54 odd 2 968.4.a.e.1.1 1
60.59 even 2 1584.4.a.g.1.1 1
220.219 even 2 1936.4.a.b.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
88.4.a.b.1.1 1 5.4 even 2
176.4.a.a.1.1 1 20.19 odd 2
704.4.a.a.1.1 1 40.29 even 2
704.4.a.k.1.1 1 40.19 odd 2
792.4.a.b.1.1 1 15.14 odd 2
968.4.a.e.1.1 1 55.54 odd 2
1584.4.a.g.1.1 1 60.59 even 2
1936.4.a.b.1.1 1 220.219 even 2
2200.4.a.a.1.1 1 1.1 even 1 trivial