Properties

Label 1800.4.f.g.649.2
Level $1800$
Weight $4$
Character 1800.649
Analytic conductor $106.203$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1800,4,Mod(649,1800)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1800.649");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 1800.f (of order \(2\), degree \(1\), not minimal)

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: no
Analytic conductor: \(106.203438010\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 600)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 649.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1800.649
Dual form 1800.4.f.g.649.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+19.0000i q^{7} +O(q^{10})\) \(q+19.0000i q^{7} -22.0000 q^{11} +1.00000i q^{13} -58.0000i q^{17} +53.0000 q^{19} -58.0000i q^{23} +22.0000 q^{29} -35.0000 q^{31} +270.000i q^{37} +468.000 q^{41} -431.000i q^{43} -230.000i q^{47} -18.0000 q^{49} +446.000 q^{59} +127.000 q^{61} +811.000i q^{67} -36.0000 q^{71} +522.000i q^{73} -418.000i q^{77} -1368.00 q^{79} +1138.00i q^{83} +144.000 q^{89} -19.0000 q^{91} +1079.00i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 44 q^{11} + 106 q^{19} + 44 q^{29} - 70 q^{31} + 936 q^{41} - 36 q^{49} + 892 q^{59} + 254 q^{61} - 72 q^{71} - 2736 q^{79} + 288 q^{89} - 38 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1001\) \(1351\)
\(\chi(n)\) \(-1\) \(1\) \(1\) \(1\)

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
\(7\) 19.0000i 1.02590i 0.858417 + 0.512952i \(0.171448\pi\)
−0.858417 + 0.512952i \(0.828552\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −22.0000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) 1.00000i 0.0213346i 0.999943 + 0.0106673i \(0.00339558\pi\)
−0.999943 + 0.0106673i \(0.996604\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) − 58.0000i − 0.827474i −0.910396 0.413737i \(-0.864223\pi\)
0.910396 0.413737i \(-0.135777\pi\)
\(18\) 0 0
\(19\) 53.0000 0.639949 0.319975 0.947426i \(-0.396326\pi\)
0.319975 + 0.947426i \(0.396326\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) − 58.0000i − 0.525819i −0.964821 0.262909i \(-0.915318\pi\)
0.964821 0.262909i \(-0.0846821\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 22.0000 0.140872 0.0704362 0.997516i \(-0.477561\pi\)
0.0704362 + 0.997516i \(0.477561\pi\)
\(30\) 0 0
\(31\) −35.0000 −0.202780 −0.101390 0.994847i \(-0.532329\pi\)
−0.101390 + 0.994847i \(0.532329\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 270.000i 1.19967i 0.800124 + 0.599834i \(0.204767\pi\)
−0.800124 + 0.599834i \(0.795233\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 468.000 1.78267 0.891333 0.453349i \(-0.149771\pi\)
0.891333 + 0.453349i \(0.149771\pi\)
\(42\) 0 0
\(43\) − 431.000i − 1.52853i −0.644901 0.764266i \(-0.723101\pi\)
0.644901 0.764266i \(-0.276899\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 230.000i − 0.713807i −0.934141 0.356904i \(-0.883832\pi\)
0.934141 0.356904i \(-0.116168\pi\)
\(48\) 0 0
\(49\) −18.0000 −0.0524781
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 446.000 0.984140 0.492070 0.870556i \(-0.336240\pi\)
0.492070 + 0.870556i \(0.336240\pi\)
\(60\) 0 0
\(61\) 127.000 0.266569 0.133284 0.991078i \(-0.457448\pi\)
0.133284 + 0.991078i \(0.457448\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 811.000i 1.47880i 0.673268 + 0.739399i \(0.264890\pi\)
−0.673268 + 0.739399i \(0.735110\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −36.0000 −0.0601748 −0.0300874 0.999547i \(-0.509579\pi\)
−0.0300874 + 0.999547i \(0.509579\pi\)
\(72\) 0 0
\(73\) 522.000i 0.836924i 0.908234 + 0.418462i \(0.137431\pi\)
−0.908234 + 0.418462i \(0.862569\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) − 418.000i − 0.618643i
\(78\) 0 0
\(79\) −1368.00 −1.94825 −0.974127 0.226002i \(-0.927434\pi\)
−0.974127 + 0.226002i \(0.927434\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1138.00i 1.50496i 0.658615 + 0.752480i \(0.271143\pi\)
−0.658615 + 0.752480i \(0.728857\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 144.000 0.171505 0.0857526 0.996316i \(-0.472671\pi\)
0.0857526 + 0.996316i \(0.472671\pi\)
\(90\) 0 0
\(91\) −19.0000 −0.0218873
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 1079.00i 1.12944i 0.825282 + 0.564721i \(0.191016\pi\)
−0.825282 + 0.564721i \(0.808984\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1440.00 1.41867 0.709333 0.704873i \(-0.248996\pi\)
0.709333 + 0.704873i \(0.248996\pi\)
\(102\) 0 0
\(103\) 124.000i 0.118622i 0.998240 + 0.0593111i \(0.0188904\pi\)
−0.998240 + 0.0593111i \(0.981110\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) − 432.000i − 0.390309i −0.980773 0.195154i \(-0.937479\pi\)
0.980773 0.195154i \(-0.0625208\pi\)
\(108\) 0 0
\(109\) −701.000 −0.615997 −0.307998 0.951387i \(-0.599659\pi\)
−0.307998 + 0.951387i \(0.599659\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 1044.00i 0.869126i 0.900641 + 0.434563i \(0.143097\pi\)
−0.900641 + 0.434563i \(0.856903\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1102.00 0.848909
\(120\) 0 0
\(121\) −847.000 −0.636364
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) − 504.000i − 0.352148i −0.984377 0.176074i \(-0.943660\pi\)
0.984377 0.176074i \(-0.0563398\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −72.0000 −0.0480204 −0.0240102 0.999712i \(-0.507643\pi\)
−0.0240102 + 0.999712i \(0.507643\pi\)
\(132\) 0 0
\(133\) 1007.00i 0.656526i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) − 1850.00i − 1.15369i −0.816852 0.576847i \(-0.804283\pi\)
0.816852 0.576847i \(-0.195717\pi\)
\(138\) 0 0
\(139\) −1836.00 −1.12034 −0.560171 0.828377i \(-0.689265\pi\)
−0.560171 + 0.828377i \(0.689265\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) − 22.0000i − 0.0128653i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −2398.00 −1.31847 −0.659234 0.751938i \(-0.729119\pi\)
−0.659234 + 0.751938i \(0.729119\pi\)
\(150\) 0 0
\(151\) 1871.00 1.00834 0.504172 0.863604i \(-0.331798\pi\)
0.504172 + 0.863604i \(0.331798\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 3293.00i 1.67395i 0.547242 + 0.836975i \(0.315678\pi\)
−0.547242 + 0.836975i \(0.684322\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 1102.00 0.539440
\(162\) 0 0
\(163\) 883.000i 0.424306i 0.977236 + 0.212153i \(0.0680475\pi\)
−0.977236 + 0.212153i \(0.931952\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 4104.00i 1.90166i 0.309715 + 0.950830i \(0.399766\pi\)
−0.309715 + 0.950830i \(0.600234\pi\)
\(168\) 0 0
\(169\) 2196.00 0.999545
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) − 1706.00i − 0.749739i −0.927078 0.374869i \(-0.877688\pi\)
0.927078 0.374869i \(-0.122312\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 662.000 0.276426 0.138213 0.990403i \(-0.455864\pi\)
0.138213 + 0.990403i \(0.455864\pi\)
\(180\) 0 0
\(181\) 4121.00 1.69233 0.846164 0.532922i \(-0.178906\pi\)
0.846164 + 0.532922i \(0.178906\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 1276.00i 0.498986i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 958.000 0.362924 0.181462 0.983398i \(-0.441917\pi\)
0.181462 + 0.983398i \(0.441917\pi\)
\(192\) 0 0
\(193\) 3187.00i 1.18863i 0.804233 + 0.594314i \(0.202576\pi\)
−0.804233 + 0.594314i \(0.797424\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 2282.00i − 0.825308i −0.910888 0.412654i \(-0.864602\pi\)
0.910888 0.412654i \(-0.135398\pi\)
\(198\) 0 0
\(199\) −1043.00 −0.371539 −0.185770 0.982593i \(-0.559478\pi\)
−0.185770 + 0.982593i \(0.559478\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 418.000i 0.144521i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −1166.00 −0.385904
\(210\) 0 0
\(211\) 4139.00 1.35043 0.675214 0.737621i \(-0.264051\pi\)
0.675214 + 0.737621i \(0.264051\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) − 665.000i − 0.208033i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 58.0000 0.0176539
\(222\) 0 0
\(223\) 413.000i 0.124020i 0.998076 + 0.0620101i \(0.0197511\pi\)
−0.998076 + 0.0620101i \(0.980249\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 5652.00i 1.65258i 0.563242 + 0.826292i \(0.309554\pi\)
−0.563242 + 0.826292i \(0.690446\pi\)
\(228\) 0 0
\(229\) 4391.00 1.26710 0.633549 0.773703i \(-0.281597\pi\)
0.633549 + 0.773703i \(0.281597\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 2052.00i 0.576957i 0.957486 + 0.288479i \(0.0931494\pi\)
−0.957486 + 0.288479i \(0.906851\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −4320.00 −1.16919 −0.584597 0.811324i \(-0.698748\pi\)
−0.584597 + 0.811324i \(0.698748\pi\)
\(240\) 0 0
\(241\) 4265.00 1.13997 0.569985 0.821655i \(-0.306949\pi\)
0.569985 + 0.821655i \(0.306949\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 53.0000i 0.0136531i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 2412.00 0.606550 0.303275 0.952903i \(-0.401920\pi\)
0.303275 + 0.952903i \(0.401920\pi\)
\(252\) 0 0
\(253\) 1276.00i 0.317081i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 6948.00i 1.68640i 0.537601 + 0.843199i \(0.319331\pi\)
−0.537601 + 0.843199i \(0.680669\pi\)
\(258\) 0 0
\(259\) −5130.00 −1.23074
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 3564.00i 0.835611i 0.908537 + 0.417805i \(0.137201\pi\)
−0.908537 + 0.417805i \(0.862799\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1534.00 −0.347694 −0.173847 0.984773i \(-0.555620\pi\)
−0.173847 + 0.984773i \(0.555620\pi\)
\(270\) 0 0
\(271\) 7704.00 1.72688 0.863440 0.504451i \(-0.168305\pi\)
0.863440 + 0.504451i \(0.168305\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 4877.00i − 1.05787i −0.848662 0.528936i \(-0.822591\pi\)
0.848662 0.528936i \(-0.177409\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 3758.00 0.797806 0.398903 0.916993i \(-0.369391\pi\)
0.398903 + 0.916993i \(0.369391\pi\)
\(282\) 0 0
\(283\) 935.000i 0.196396i 0.995167 + 0.0981978i \(0.0313078\pi\)
−0.995167 + 0.0981978i \(0.968692\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 8892.00i 1.82884i
\(288\) 0 0
\(289\) 1549.00 0.315286
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) − 6214.00i − 1.23900i −0.784998 0.619498i \(-0.787336\pi\)
0.784998 0.619498i \(-0.212664\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 58.0000 0.0112181
\(300\) 0 0
\(301\) 8189.00 1.56813
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 3905.00i 0.725961i 0.931797 + 0.362981i \(0.118241\pi\)
−0.931797 + 0.362981i \(0.881759\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −9662.00 −1.76168 −0.880839 0.473416i \(-0.843021\pi\)
−0.880839 + 0.473416i \(0.843021\pi\)
\(312\) 0 0
\(313\) 5147.00i 0.929475i 0.885449 + 0.464737i \(0.153851\pi\)
−0.885449 + 0.464737i \(0.846149\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) − 9216.00i − 1.63288i −0.577432 0.816439i \(-0.695945\pi\)
0.577432 0.816439i \(-0.304055\pi\)
\(318\) 0 0
\(319\) −484.000 −0.0849492
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) − 3074.00i − 0.529542i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 4370.00 0.732298
\(330\) 0 0
\(331\) 2196.00 0.364662 0.182331 0.983237i \(-0.441636\pi\)
0.182331 + 0.983237i \(0.441636\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) − 2521.00i − 0.407500i −0.979023 0.203750i \(-0.934687\pi\)
0.979023 0.203750i \(-0.0653130\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 770.000 0.122281
\(342\) 0 0
\(343\) 6175.00i 0.972066i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 7034.00i 1.08820i 0.839021 + 0.544099i \(0.183129\pi\)
−0.839021 + 0.544099i \(0.816871\pi\)
\(348\) 0 0
\(349\) −7362.00 −1.12917 −0.564583 0.825376i \(-0.690963\pi\)
−0.564583 + 0.825376i \(0.690963\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9382.00i 1.41460i 0.706914 + 0.707300i \(0.250087\pi\)
−0.706914 + 0.707300i \(0.749913\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −10116.0 −1.48719 −0.743596 0.668629i \(-0.766881\pi\)
−0.743596 + 0.668629i \(0.766881\pi\)
\(360\) 0 0
\(361\) −4050.00 −0.590465
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 3277.00i 0.466098i 0.972465 + 0.233049i \(0.0748703\pi\)
−0.972465 + 0.233049i \(0.925130\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 10891.0i 1.51184i 0.654667 + 0.755918i \(0.272809\pi\)
−0.654667 + 0.755918i \(0.727191\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 22.0000i 0.00300546i
\(378\) 0 0
\(379\) 2591.00 0.351163 0.175581 0.984465i \(-0.443819\pi\)
0.175581 + 0.984465i \(0.443819\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 612.000i 0.0816494i 0.999166 + 0.0408247i \(0.0129985\pi\)
−0.999166 + 0.0408247i \(0.987001\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 3708.00 0.483298 0.241649 0.970364i \(-0.422312\pi\)
0.241649 + 0.970364i \(0.422312\pi\)
\(390\) 0 0
\(391\) −3364.00 −0.435102
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 3833.00i 0.484566i 0.970206 + 0.242283i \(0.0778963\pi\)
−0.970206 + 0.242283i \(0.922104\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9288.00 1.15666 0.578330 0.815803i \(-0.303705\pi\)
0.578330 + 0.815803i \(0.303705\pi\)
\(402\) 0 0
\(403\) − 35.0000i − 0.00432624i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 5940.00i − 0.723427i
\(408\) 0 0
\(409\) 755.000 0.0912771 0.0456386 0.998958i \(-0.485468\pi\)
0.0456386 + 0.998958i \(0.485468\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 8474.00i 1.00963i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −9576.00 −1.11651 −0.558256 0.829669i \(-0.688529\pi\)
−0.558256 + 0.829669i \(0.688529\pi\)
\(420\) 0 0
\(421\) 9414.00 1.08981 0.544905 0.838498i \(-0.316566\pi\)
0.544905 + 0.838498i \(0.316566\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 2413.00i 0.273474i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 2254.00 0.251906 0.125953 0.992036i \(-0.459801\pi\)
0.125953 + 0.992036i \(0.459801\pi\)
\(432\) 0 0
\(433\) − 6301.00i − 0.699323i −0.936876 0.349661i \(-0.886297\pi\)
0.936876 0.349661i \(-0.113703\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 3074.00i − 0.336497i
\(438\) 0 0
\(439\) 3779.00 0.410847 0.205423 0.978673i \(-0.434143\pi\)
0.205423 + 0.978673i \(0.434143\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) − 7632.00i − 0.818527i −0.912416 0.409263i \(-0.865786\pi\)
0.912416 0.409263i \(-0.134214\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2988.00 0.314059 0.157029 0.987594i \(-0.449808\pi\)
0.157029 + 0.987594i \(0.449808\pi\)
\(450\) 0 0
\(451\) −10296.0 −1.07499
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1370.00i 0.140232i 0.997539 + 0.0701159i \(0.0223369\pi\)
−0.997539 + 0.0701159i \(0.977663\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 7992.00 0.807429 0.403714 0.914885i \(-0.367719\pi\)
0.403714 + 0.914885i \(0.367719\pi\)
\(462\) 0 0
\(463\) − 3096.00i − 0.310763i −0.987855 0.155382i \(-0.950339\pi\)
0.987855 0.155382i \(-0.0496607\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 8338.00i − 0.826203i −0.910685 0.413101i \(-0.864446\pi\)
0.910685 0.413101i \(-0.135554\pi\)
\(468\) 0 0
\(469\) −15409.0 −1.51710
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9482.00i 0.921740i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4918.00 0.469121 0.234561 0.972101i \(-0.424635\pi\)
0.234561 + 0.972101i \(0.424635\pi\)
\(480\) 0 0
\(481\) −270.000 −0.0255945
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 19637.0i 1.82718i 0.406635 + 0.913591i \(0.366702\pi\)
−0.406635 + 0.913591i \(0.633298\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −3096.00 −0.284563 −0.142282 0.989826i \(-0.545444\pi\)
−0.142282 + 0.989826i \(0.545444\pi\)
\(492\) 0 0
\(493\) − 1276.00i − 0.116568i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) − 684.000i − 0.0617336i
\(498\) 0 0
\(499\) −6875.00 −0.616768 −0.308384 0.951262i \(-0.599788\pi\)
−0.308384 + 0.951262i \(0.599788\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) − 11268.0i − 0.998838i −0.866361 0.499419i \(-0.833547\pi\)
0.866361 0.499419i \(-0.166453\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 16078.0 1.40009 0.700044 0.714100i \(-0.253164\pi\)
0.700044 + 0.714100i \(0.253164\pi\)
\(510\) 0 0
\(511\) −9918.00 −0.858604
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 5060.00i 0.430442i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 17366.0 1.46030 0.730152 0.683285i \(-0.239449\pi\)
0.730152 + 0.683285i \(0.239449\pi\)
\(522\) 0 0
\(523\) − 4913.00i − 0.410766i −0.978682 0.205383i \(-0.934156\pi\)
0.978682 0.205383i \(-0.0658440\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 2030.00i 0.167795i
\(528\) 0 0
\(529\) 8803.00 0.723514
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 468.000i 0.0380325i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 396.000 0.0316455
\(540\) 0 0
\(541\) 17605.0 1.39907 0.699536 0.714597i \(-0.253390\pi\)
0.699536 + 0.714597i \(0.253390\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 14560.0i 1.13810i 0.822303 + 0.569050i \(0.192689\pi\)
−0.822303 + 0.569050i \(0.807311\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 1166.00 0.0901511
\(552\) 0 0
\(553\) − 25992.0i − 1.99872i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 20614.0i − 1.56812i −0.620685 0.784060i \(-0.713145\pi\)
0.620685 0.784060i \(-0.286855\pi\)
\(558\) 0 0
\(559\) 431.000 0.0326107
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) − 3442.00i − 0.257661i −0.991667 0.128830i \(-0.958878\pi\)
0.991667 0.128830i \(-0.0411223\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 22082.0 1.62693 0.813467 0.581611i \(-0.197577\pi\)
0.813467 + 0.581611i \(0.197577\pi\)
\(570\) 0 0
\(571\) 451.000 0.0330539 0.0165269 0.999863i \(-0.494739\pi\)
0.0165269 + 0.999863i \(0.494739\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) − 20987.0i − 1.51421i −0.653292 0.757106i \(-0.726613\pi\)
0.653292 0.757106i \(-0.273387\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −21622.0 −1.54394
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 3888.00i 0.273381i 0.990614 + 0.136691i \(0.0436467\pi\)
−0.990614 + 0.136691i \(0.956353\pi\)
\(588\) 0 0
\(589\) −1855.00 −0.129769
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 11268.0i 0.780306i 0.920750 + 0.390153i \(0.127578\pi\)
−0.920750 + 0.390153i \(0.872422\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3996.00 −0.272575 −0.136287 0.990669i \(-0.543517\pi\)
−0.136287 + 0.990669i \(0.543517\pi\)
\(600\) 0 0
\(601\) −24965.0 −1.69442 −0.847208 0.531262i \(-0.821718\pi\)
−0.847208 + 0.531262i \(0.821718\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) − 4176.00i − 0.279240i −0.990205 0.139620i \(-0.955412\pi\)
0.990205 0.139620i \(-0.0445881\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 230.000 0.0152288
\(612\) 0 0
\(613\) − 9558.00i − 0.629762i −0.949131 0.314881i \(-0.898035\pi\)
0.949131 0.314881i \(-0.101965\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) − 9000.00i − 0.587239i −0.955922 0.293619i \(-0.905140\pi\)
0.955922 0.293619i \(-0.0948598\pi\)
\(618\) 0 0
\(619\) 15625.0 1.01457 0.507287 0.861777i \(-0.330648\pi\)
0.507287 + 0.861777i \(0.330648\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2736.00i 0.175948i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 15660.0 0.992695
\(630\) 0 0
\(631\) −31175.0 −1.96681 −0.983405 0.181424i \(-0.941929\pi\)
−0.983405 + 0.181424i \(0.941929\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) − 18.0000i − 0.00111960i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 6732.00 0.414817 0.207409 0.978254i \(-0.433497\pi\)
0.207409 + 0.978254i \(0.433497\pi\)
\(642\) 0 0
\(643\) − 6228.00i − 0.381973i −0.981593 0.190986i \(-0.938831\pi\)
0.981593 0.190986i \(-0.0611686\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) − 396.000i − 0.0240624i −0.999928 0.0120312i \(-0.996170\pi\)
0.999928 0.0120312i \(-0.00382974\pi\)
\(648\) 0 0
\(649\) −9812.00 −0.593459
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 4702.00i 0.281782i 0.990025 + 0.140891i \(0.0449967\pi\)
−0.990025 + 0.140891i \(0.955003\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −22140.0 −1.30873 −0.654364 0.756180i \(-0.727064\pi\)
−0.654364 + 0.756180i \(0.727064\pi\)
\(660\) 0 0
\(661\) −13518.0 −0.795445 −0.397723 0.917506i \(-0.630199\pi\)
−0.397723 + 0.917506i \(0.630199\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) − 1276.00i − 0.0740733i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −2794.00 −0.160747
\(672\) 0 0
\(673\) − 11250.0i − 0.644362i −0.946678 0.322181i \(-0.895584\pi\)
0.946678 0.322181i \(-0.104416\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) − 15170.0i − 0.861197i −0.902544 0.430599i \(-0.858302\pi\)
0.902544 0.430599i \(-0.141698\pi\)
\(678\) 0 0
\(679\) −20501.0 −1.15870
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) − 22680.0i − 1.27061i −0.772262 0.635305i \(-0.780875\pi\)
0.772262 0.635305i \(-0.219125\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 128.000 0.00704682 0.00352341 0.999994i \(-0.498878\pi\)
0.00352341 + 0.999994i \(0.498878\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) − 27144.0i − 1.47511i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −25682.0 −1.38373 −0.691866 0.722026i \(-0.743211\pi\)
−0.691866 + 0.722026i \(0.743211\pi\)
\(702\) 0 0
\(703\) 14310.0i 0.767727i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 27360.0i 1.45542i
\(708\) 0 0
\(709\) 4951.00 0.262255 0.131127 0.991366i \(-0.458140\pi\)
0.131127 + 0.991366i \(0.458140\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2030.00i 0.106626i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −22190.0 −1.15097 −0.575485 0.817812i \(-0.695187\pi\)
−0.575485 + 0.817812i \(0.695187\pi\)
\(720\) 0 0
\(721\) −2356.00 −0.121695
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 7685.00i − 0.392051i −0.980599 0.196025i \(-0.937197\pi\)
0.980599 0.196025i \(-0.0628035\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −24998.0 −1.26482
\(732\) 0 0
\(733\) 29574.0i 1.49023i 0.666934 + 0.745116i \(0.267606\pi\)
−0.666934 + 0.745116i \(0.732394\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) − 17842.0i − 0.891748i
\(738\) 0 0
\(739\) 32580.0 1.62175 0.810876 0.585218i \(-0.198991\pi\)
0.810876 + 0.585218i \(0.198991\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3060.00i 0.151091i 0.997142 + 0.0755454i \(0.0240698\pi\)
−0.997142 + 0.0755454i \(0.975930\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8208.00 0.400419
\(750\) 0 0
\(751\) −7992.00 −0.388325 −0.194163 0.980969i \(-0.562199\pi\)
−0.194163 + 0.980969i \(0.562199\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) − 22841.0i − 1.09666i −0.836263 0.548329i \(-0.815264\pi\)
0.836263 0.548329i \(-0.184736\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17172.0 0.817982 0.408991 0.912538i \(-0.365881\pi\)
0.408991 + 0.912538i \(0.365881\pi\)
\(762\) 0 0
\(763\) − 13319.0i − 0.631953i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 446.000i 0.0209963i
\(768\) 0 0
\(769\) 30869.0 1.44755 0.723774 0.690037i \(-0.242406\pi\)
0.723774 + 0.690037i \(0.242406\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) − 34884.0i − 1.62314i −0.584252 0.811572i \(-0.698612\pi\)
0.584252 0.811572i \(-0.301388\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 24804.0 1.14082
\(780\) 0 0
\(781\) 792.000 0.0362868
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 5039.00i − 0.228235i −0.993467 0.114118i \(-0.963596\pi\)
0.993467 0.114118i \(-0.0364040\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −19836.0 −0.891640
\(792\) 0 0
\(793\) 127.000i 0.00568714i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 540.000i 0.0239997i 0.999928 + 0.0119999i \(0.00381977\pi\)
−0.999928 + 0.0119999i \(0.996180\pi\)
\(798\) 0 0
\(799\) −13340.0 −0.590657
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) − 11484.0i − 0.504684i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −41328.0 −1.79606 −0.898032 0.439931i \(-0.855003\pi\)
−0.898032 + 0.439931i \(0.855003\pi\)
\(810\) 0 0
\(811\) −12853.0 −0.556510 −0.278255 0.960507i \(-0.589756\pi\)
−0.278255 + 0.960507i \(0.589756\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) − 22843.0i − 0.978183i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −29470.0 −1.25275 −0.626376 0.779521i \(-0.715463\pi\)
−0.626376 + 0.779521i \(0.715463\pi\)
\(822\) 0 0
\(823\) − 24407.0i − 1.03375i −0.856062 0.516874i \(-0.827096\pi\)
0.856062 0.516874i \(-0.172904\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 15048.0i 0.632733i 0.948637 + 0.316367i \(0.102463\pi\)
−0.948637 + 0.316367i \(0.897537\pi\)
\(828\) 0 0
\(829\) 28406.0 1.19009 0.595043 0.803694i \(-0.297135\pi\)
0.595043 + 0.803694i \(0.297135\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 1044.00i 0.0434243i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −26914.0 −1.10748 −0.553739 0.832690i \(-0.686800\pi\)
−0.553739 + 0.832690i \(0.686800\pi\)
\(840\) 0 0
\(841\) −23905.0 −0.980155
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 16093.0i − 0.652848i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 15660.0 0.630808
\(852\) 0 0
\(853\) 21275.0i 0.853977i 0.904257 + 0.426988i \(0.140425\pi\)
−0.904257 + 0.426988i \(0.859575\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 39132.0i 1.55977i 0.625922 + 0.779885i \(0.284723\pi\)
−0.625922 + 0.779885i \(0.715277\pi\)
\(858\) 0 0
\(859\) 448.000 0.0177946 0.00889730 0.999960i \(-0.497168\pi\)
0.00889730 + 0.999960i \(0.497168\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 26856.0i 1.05932i 0.848212 + 0.529658i \(0.177680\pi\)
−0.848212 + 0.529658i \(0.822320\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 30096.0 1.17484
\(870\) 0 0
\(871\) −811.000 −0.0315496
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 3653.00i 0.140653i 0.997524 + 0.0703267i \(0.0224042\pi\)
−0.997524 + 0.0703267i \(0.977596\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 6552.00 0.250559 0.125280 0.992121i \(-0.460017\pi\)
0.125280 + 0.992121i \(0.460017\pi\)
\(882\) 0 0
\(883\) 4481.00i 0.170779i 0.996348 + 0.0853894i \(0.0272134\pi\)
−0.996348 + 0.0853894i \(0.972787\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 14666.0i − 0.555170i −0.960701 0.277585i \(-0.910466\pi\)
0.960701 0.277585i \(-0.0895341\pi\)
\(888\) 0 0
\(889\) 9576.00 0.361270
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) − 12190.0i − 0.456800i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −770.000 −0.0285661
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) − 51804.0i − 1.89650i −0.317528 0.948249i \(-0.602853\pi\)
0.317528 0.948249i \(-0.397147\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −31198.0 −1.13462 −0.567308 0.823505i \(-0.692015\pi\)
−0.567308 + 0.823505i \(0.692015\pi\)
\(912\) 0 0
\(913\) − 25036.0i − 0.907525i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) − 1368.00i − 0.0492643i
\(918\) 0 0
\(919\) 27001.0 0.969185 0.484592 0.874740i \(-0.338968\pi\)
0.484592 + 0.874740i \(0.338968\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) − 36.0000i − 0.00128381i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −22694.0 −0.801470 −0.400735 0.916194i \(-0.631245\pi\)
−0.400735 + 0.916194i \(0.631245\pi\)
\(930\) 0 0
\(931\) −954.000 −0.0335833
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) − 29503.0i − 1.02862i −0.857603 0.514312i \(-0.828047\pi\)
0.857603 0.514312i \(-0.171953\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −14566.0 −0.504610 −0.252305 0.967648i \(-0.581189\pi\)
−0.252305 + 0.967648i \(0.581189\pi\)
\(942\) 0 0
\(943\) − 27144.0i − 0.937360i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 42322.0i 1.45225i 0.687563 + 0.726125i \(0.258681\pi\)
−0.687563 + 0.726125i \(0.741319\pi\)
\(948\) 0 0
\(949\) −522.000 −0.0178555
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) − 43416.0i − 1.47574i −0.674942 0.737871i \(-0.735831\pi\)
0.674942 0.737871i \(-0.264169\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 35150.0 1.18358
\(960\) 0 0
\(961\) −28566.0 −0.958880
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 21528.0i − 0.715919i −0.933737 0.357960i \(-0.883473\pi\)
0.933737 0.357960i \(-0.116527\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −27050.0 −0.894002 −0.447001 0.894533i \(-0.647508\pi\)
−0.447001 + 0.894533i \(0.647508\pi\)
\(972\) 0 0
\(973\) − 34884.0i − 1.14936i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 24934.0i − 0.816489i −0.912873 0.408244i \(-0.866141\pi\)
0.912873 0.408244i \(-0.133859\pi\)
\(978\) 0 0
\(979\) −3168.00 −0.103422
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) − 8388.00i − 0.272162i −0.990698 0.136081i \(-0.956549\pi\)
0.990698 0.136081i \(-0.0434508\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −24998.0 −0.803731
\(990\) 0 0
\(991\) 29033.0 0.930639 0.465320 0.885143i \(-0.345939\pi\)
0.465320 + 0.885143i \(0.345939\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 25326.0i 0.804496i 0.915531 + 0.402248i \(0.131771\pi\)
−0.915531 + 0.402248i \(0.868229\pi\)
\(998\) 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 1800.4.f.g.649.2 2
3.2 odd 2 600.4.f.h.49.2 2
5.2 odd 4 1800.4.a.g.1.1 1
5.3 odd 4 1800.4.a.bf.1.1 1
5.4 even 2 inner 1800.4.f.g.649.1 2
12.11 even 2 1200.4.f.f.49.1 2
15.2 even 4 600.4.a.j.1.1 yes 1
15.8 even 4 600.4.a.g.1.1 1
15.14 odd 2 600.4.f.h.49.1 2
60.23 odd 4 1200.4.a.x.1.1 1
60.47 odd 4 1200.4.a.n.1.1 1
60.59 even 2 1200.4.f.f.49.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
600.4.a.g.1.1 1 15.8 even 4
600.4.a.j.1.1 yes 1 15.2 even 4
600.4.f.h.49.1 2 15.14 odd 2
600.4.f.h.49.2 2 3.2 odd 2
1200.4.a.n.1.1 1 60.47 odd 4
1200.4.a.x.1.1 1 60.23 odd 4
1200.4.f.f.49.1 2 12.11 even 2
1200.4.f.f.49.2 2 60.59 even 2
1800.4.a.g.1.1 1 5.2 odd 4
1800.4.a.bf.1.1 1 5.3 odd 4
1800.4.f.g.649.1 2 5.4 even 2 inner
1800.4.f.g.649.2 2 1.1 even 1 trivial