Properties

Label 700.4.e.a.449.2
Level $700$
Weight $4$
Character 700.449
Analytic conductor $41.301$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [700,4,Mod(449,700)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(700, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("700.449");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 700.e (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: \(41.3013370040\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 28)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 449.2
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 700.449
Dual form 700.4.e.a.449.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+10.0000i q^{3} -7.00000i q^{7} -73.0000 q^{9} +O(q^{10})\) \(q+10.0000i q^{3} -7.00000i q^{7} -73.0000 q^{9} -40.0000 q^{11} +12.0000i q^{13} -58.0000i q^{17} -26.0000 q^{19} +70.0000 q^{21} +64.0000i q^{23} -460.000i q^{27} +62.0000 q^{29} +252.000 q^{31} -400.000i q^{33} +26.0000i q^{37} -120.000 q^{39} +6.00000 q^{41} -416.000i q^{43} -396.000i q^{47} -49.0000 q^{49} +580.000 q^{51} +450.000i q^{53} -260.000i q^{57} -274.000 q^{59} -576.000 q^{61} +511.000i q^{63} -476.000i q^{67} -640.000 q^{69} -448.000 q^{71} +158.000i q^{73} +280.000i q^{77} +936.000 q^{79} +2629.00 q^{81} -530.000i q^{83} +620.000i q^{87} +390.000 q^{89} +84.0000 q^{91} +2520.00i q^{93} +214.000i q^{97} +2920.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 146 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 146 q^{9} - 80 q^{11} - 52 q^{19} + 140 q^{21} + 124 q^{29} + 504 q^{31} - 240 q^{39} + 12 q^{41} - 98 q^{49} + 1160 q^{51} - 548 q^{59} - 1152 q^{61} - 1280 q^{69} - 896 q^{71} + 1872 q^{79} + 5258 q^{81} + 780 q^{89} + 168 q^{91} + 5840 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/700\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(351\) \(477\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) 10.0000i 1.92450i 0.272166 + 0.962250i \(0.412260\pi\)
−0.272166 + 0.962250i \(0.587740\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) − 7.00000i − 0.377964i
\(8\) 0 0
\(9\) −73.0000 −2.70370
\(10\) 0 0
\(11\) −40.0000 −1.09640 −0.548202 0.836346i \(-0.684688\pi\)
−0.548202 + 0.836346i \(0.684688\pi\)
\(12\) 0 0
\(13\) 12.0000i 0.256015i 0.991773 + 0.128008i \(0.0408582\pi\)
−0.991773 + 0.128008i \(0.959142\pi\)
\(14\) 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
\(19\) −26.0000 −0.313937 −0.156969 0.987604i \(-0.550172\pi\)
−0.156969 + 0.987604i \(0.550172\pi\)
\(20\) 0 0
\(21\) 70.0000 0.727393
\(22\) 0 0
\(23\) 64.0000i 0.580214i 0.956994 + 0.290107i \(0.0936909\pi\)
−0.956994 + 0.290107i \(0.906309\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) − 460.000i − 3.27878i
\(28\) 0 0
\(29\) 62.0000 0.397004 0.198502 0.980101i \(-0.436392\pi\)
0.198502 + 0.980101i \(0.436392\pi\)
\(30\) 0 0
\(31\) 252.000 1.46002 0.730009 0.683438i \(-0.239516\pi\)
0.730009 + 0.683438i \(0.239516\pi\)
\(32\) 0 0
\(33\) − 400.000i − 2.11003i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 26.0000i 0.115524i 0.998330 + 0.0577618i \(0.0183964\pi\)
−0.998330 + 0.0577618i \(0.981604\pi\)
\(38\) 0 0
\(39\) −120.000 −0.492702
\(40\) 0 0
\(41\) 6.00000 0.0228547 0.0114273 0.999935i \(-0.496362\pi\)
0.0114273 + 0.999935i \(0.496362\pi\)
\(42\) 0 0
\(43\) − 416.000i − 1.47534i −0.675164 0.737668i \(-0.735927\pi\)
0.675164 0.737668i \(-0.264073\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) − 396.000i − 1.22899i −0.788921 0.614495i \(-0.789360\pi\)
0.788921 0.614495i \(-0.210640\pi\)
\(48\) 0 0
\(49\) −49.0000 −0.142857
\(50\) 0 0
\(51\) 580.000 1.59248
\(52\) 0 0
\(53\) 450.000i 1.16627i 0.812376 + 0.583134i \(0.198174\pi\)
−0.812376 + 0.583134i \(0.801826\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) − 260.000i − 0.604173i
\(58\) 0 0
\(59\) −274.000 −0.604606 −0.302303 0.953212i \(-0.597755\pi\)
−0.302303 + 0.953212i \(0.597755\pi\)
\(60\) 0 0
\(61\) −576.000 −1.20900 −0.604502 0.796604i \(-0.706628\pi\)
−0.604502 + 0.796604i \(0.706628\pi\)
\(62\) 0 0
\(63\) 511.000i 1.02190i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) − 476.000i − 0.867950i −0.900925 0.433975i \(-0.857111\pi\)
0.900925 0.433975i \(-0.142889\pi\)
\(68\) 0 0
\(69\) −640.000 −1.11662
\(70\) 0 0
\(71\) −448.000 −0.748843 −0.374421 0.927259i \(-0.622159\pi\)
−0.374421 + 0.927259i \(0.622159\pi\)
\(72\) 0 0
\(73\) 158.000i 0.253322i 0.991946 + 0.126661i \(0.0404260\pi\)
−0.991946 + 0.126661i \(0.959574\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 280.000i 0.414402i
\(78\) 0 0
\(79\) 936.000 1.33302 0.666508 0.745498i \(-0.267788\pi\)
0.666508 + 0.745498i \(0.267788\pi\)
\(80\) 0 0
\(81\) 2629.00 3.60631
\(82\) 0 0
\(83\) − 530.000i − 0.700904i −0.936581 0.350452i \(-0.886028\pi\)
0.936581 0.350452i \(-0.113972\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 620.000i 0.764034i
\(88\) 0 0
\(89\) 390.000 0.464493 0.232247 0.972657i \(-0.425392\pi\)
0.232247 + 0.972657i \(0.425392\pi\)
\(90\) 0 0
\(91\) 84.0000 0.0967648
\(92\) 0 0
\(93\) 2520.00i 2.80980i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 214.000i 0.224004i 0.993708 + 0.112002i \(0.0357263\pi\)
−0.993708 + 0.112002i \(0.964274\pi\)
\(98\) 0 0
\(99\) 2920.00 2.96435
\(100\) 0 0
\(101\) 1432.00 1.41079 0.705393 0.708817i \(-0.250771\pi\)
0.705393 + 0.708817i \(0.250771\pi\)
\(102\) 0 0
\(103\) − 764.000i − 0.730866i −0.930838 0.365433i \(-0.880921\pi\)
0.930838 0.365433i \(-0.119079\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 324.000i 0.292731i 0.989231 + 0.146366i \(0.0467576\pi\)
−0.989231 + 0.146366i \(0.953242\pi\)
\(108\) 0 0
\(109\) 1334.00 1.17224 0.586119 0.810225i \(-0.300655\pi\)
0.586119 + 0.810225i \(0.300655\pi\)
\(110\) 0 0
\(111\) −260.000 −0.222325
\(112\) 0 0
\(113\) − 1798.00i − 1.49683i −0.663232 0.748414i \(-0.730816\pi\)
0.663232 0.748414i \(-0.269184\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) − 876.000i − 0.692190i
\(118\) 0 0
\(119\) −406.000 −0.312756
\(120\) 0 0
\(121\) 269.000 0.202104
\(122\) 0 0
\(123\) 60.0000i 0.0439839i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) − 384.000i − 0.268303i −0.990961 0.134152i \(-0.957169\pi\)
0.990961 0.134152i \(-0.0428309\pi\)
\(128\) 0 0
\(129\) 4160.00 2.83928
\(130\) 0 0
\(131\) −1814.00 −1.20985 −0.604923 0.796284i \(-0.706796\pi\)
−0.604923 + 0.796284i \(0.706796\pi\)
\(132\) 0 0
\(133\) 182.000i 0.118657i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 1666.00i 1.03895i 0.854486 + 0.519474i \(0.173872\pi\)
−0.854486 + 0.519474i \(0.826128\pi\)
\(138\) 0 0
\(139\) −1126.00 −0.687094 −0.343547 0.939135i \(-0.611628\pi\)
−0.343547 + 0.939135i \(0.611628\pi\)
\(140\) 0 0
\(141\) 3960.00 2.36519
\(142\) 0 0
\(143\) − 480.000i − 0.280697i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) − 490.000i − 0.274929i
\(148\) 0 0
\(149\) −2694.00 −1.48122 −0.740608 0.671938i \(-0.765462\pi\)
−0.740608 + 0.671938i \(0.765462\pi\)
\(150\) 0 0
\(151\) −2648.00 −1.42709 −0.713547 0.700607i \(-0.752912\pi\)
−0.713547 + 0.700607i \(0.752912\pi\)
\(152\) 0 0
\(153\) 4234.00i 2.23725i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) − 556.000i − 0.282635i −0.989964 0.141317i \(-0.954866\pi\)
0.989964 0.141317i \(-0.0451338\pi\)
\(158\) 0 0
\(159\) −4500.00 −2.24449
\(160\) 0 0
\(161\) 448.000 0.219300
\(162\) 0 0
\(163\) 328.000i 0.157613i 0.996890 + 0.0788066i \(0.0251109\pi\)
−0.996890 + 0.0788066i \(0.974889\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) − 4268.00i − 1.97765i −0.149077 0.988826i \(-0.547630\pi\)
0.149077 0.988826i \(-0.452370\pi\)
\(168\) 0 0
\(169\) 2053.00 0.934456
\(170\) 0 0
\(171\) 1898.00 0.848793
\(172\) 0 0
\(173\) 3476.00i 1.52760i 0.645451 + 0.763802i \(0.276669\pi\)
−0.645451 + 0.763802i \(0.723331\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) − 2740.00i − 1.16357i
\(178\) 0 0
\(179\) −2268.00 −0.947029 −0.473515 0.880786i \(-0.657015\pi\)
−0.473515 + 0.880786i \(0.657015\pi\)
\(180\) 0 0
\(181\) −276.000 −0.113342 −0.0566710 0.998393i \(-0.518049\pi\)
−0.0566710 + 0.998393i \(0.518049\pi\)
\(182\) 0 0
\(183\) − 5760.00i − 2.32673i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 2320.00i 0.907247i
\(188\) 0 0
\(189\) −3220.00 −1.23926
\(190\) 0 0
\(191\) −3000.00 −1.13650 −0.568252 0.822854i \(-0.692380\pi\)
−0.568252 + 0.822854i \(0.692380\pi\)
\(192\) 0 0
\(193\) − 3278.00i − 1.22257i −0.791411 0.611284i \(-0.790653\pi\)
0.791411 0.611284i \(-0.209347\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) − 2362.00i − 0.854241i −0.904195 0.427121i \(-0.859528\pi\)
0.904195 0.427121i \(-0.140472\pi\)
\(198\) 0 0
\(199\) 1036.00 0.369046 0.184523 0.982828i \(-0.440926\pi\)
0.184523 + 0.982828i \(0.440926\pi\)
\(200\) 0 0
\(201\) 4760.00 1.67037
\(202\) 0 0
\(203\) − 434.000i − 0.150053i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) − 4672.00i − 1.56873i
\(208\) 0 0
\(209\) 1040.00 0.344202
\(210\) 0 0
\(211\) 3524.00 1.14977 0.574887 0.818233i \(-0.305046\pi\)
0.574887 + 0.818233i \(0.305046\pi\)
\(212\) 0 0
\(213\) − 4480.00i − 1.44115i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) − 1764.00i − 0.551835i
\(218\) 0 0
\(219\) −1580.00 −0.487518
\(220\) 0 0
\(221\) 696.000 0.211846
\(222\) 0 0
\(223\) 1336.00i 0.401189i 0.979674 + 0.200595i \(0.0642874\pi\)
−0.979674 + 0.200595i \(0.935713\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 1290.00i 0.377182i 0.982056 + 0.188591i \(0.0603920\pi\)
−0.982056 + 0.188591i \(0.939608\pi\)
\(228\) 0 0
\(229\) −5524.00 −1.59404 −0.797022 0.603950i \(-0.793593\pi\)
−0.797022 + 0.603950i \(0.793593\pi\)
\(230\) 0 0
\(231\) −2800.00 −0.797517
\(232\) 0 0
\(233\) − 6314.00i − 1.77530i −0.460523 0.887648i \(-0.652338\pi\)
0.460523 0.887648i \(-0.347662\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 9360.00i 2.56539i
\(238\) 0 0
\(239\) 3960.00 1.07176 0.535881 0.844294i \(-0.319980\pi\)
0.535881 + 0.844294i \(0.319980\pi\)
\(240\) 0 0
\(241\) −7018.00 −1.87581 −0.937903 0.346898i \(-0.887235\pi\)
−0.937903 + 0.346898i \(0.887235\pi\)
\(242\) 0 0
\(243\) 13870.0i 3.66157i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) − 312.000i − 0.0803728i
\(248\) 0 0
\(249\) 5300.00 1.34889
\(250\) 0 0
\(251\) −2394.00 −0.602024 −0.301012 0.953620i \(-0.597324\pi\)
−0.301012 + 0.953620i \(0.597324\pi\)
\(252\) 0 0
\(253\) − 2560.00i − 0.636149i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) − 2766.00i − 0.671355i −0.941977 0.335678i \(-0.891035\pi\)
0.941977 0.335678i \(-0.108965\pi\)
\(258\) 0 0
\(259\) 182.000 0.0436638
\(260\) 0 0
\(261\) −4526.00 −1.07338
\(262\) 0 0
\(263\) − 7968.00i − 1.86817i −0.357055 0.934084i \(-0.616219\pi\)
0.357055 0.934084i \(-0.383781\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 3900.00i 0.893918i
\(268\) 0 0
\(269\) 2900.00 0.657309 0.328654 0.944450i \(-0.393405\pi\)
0.328654 + 0.944450i \(0.393405\pi\)
\(270\) 0 0
\(271\) 2640.00 0.591766 0.295883 0.955224i \(-0.404386\pi\)
0.295883 + 0.955224i \(0.404386\pi\)
\(272\) 0 0
\(273\) 840.000i 0.186224i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) − 1522.00i − 0.330138i −0.986282 0.165069i \(-0.947215\pi\)
0.986282 0.165069i \(-0.0527846\pi\)
\(278\) 0 0
\(279\) −18396.0 −3.94745
\(280\) 0 0
\(281\) −4534.00 −0.962547 −0.481274 0.876570i \(-0.659826\pi\)
−0.481274 + 0.876570i \(0.659826\pi\)
\(282\) 0 0
\(283\) − 4834.00i − 1.01538i −0.861541 0.507688i \(-0.830500\pi\)
0.861541 0.507688i \(-0.169500\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) − 42.0000i − 0.00863826i
\(288\) 0 0
\(289\) 1549.00 0.315286
\(290\) 0 0
\(291\) −2140.00 −0.431096
\(292\) 0 0
\(293\) 4656.00i 0.928350i 0.885744 + 0.464175i \(0.153649\pi\)
−0.885744 + 0.464175i \(0.846351\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 18400.0i 3.59487i
\(298\) 0 0
\(299\) −768.000 −0.148544
\(300\) 0 0
\(301\) −2912.00 −0.557624
\(302\) 0 0
\(303\) 14320.0i 2.71506i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) − 7238.00i − 1.34558i −0.739831 0.672792i \(-0.765095\pi\)
0.739831 0.672792i \(-0.234905\pi\)
\(308\) 0 0
\(309\) 7640.00 1.40655
\(310\) 0 0
\(311\) 1096.00 0.199834 0.0999171 0.994996i \(-0.468142\pi\)
0.0999171 + 0.994996i \(0.468142\pi\)
\(312\) 0 0
\(313\) 3818.00i 0.689476i 0.938699 + 0.344738i \(0.112032\pi\)
−0.938699 + 0.344738i \(0.887968\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1998.00i 0.354003i 0.984211 + 0.177001i \(0.0566397\pi\)
−0.984211 + 0.177001i \(0.943360\pi\)
\(318\) 0 0
\(319\) −2480.00 −0.435277
\(320\) 0 0
\(321\) −3240.00 −0.563362
\(322\) 0 0
\(323\) 1508.00i 0.259775i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 13340.0i 2.25597i
\(328\) 0 0
\(329\) −2772.00 −0.464515
\(330\) 0 0
\(331\) −7936.00 −1.31783 −0.658915 0.752217i \(-0.728984\pi\)
−0.658915 + 0.752217i \(0.728984\pi\)
\(332\) 0 0
\(333\) − 1898.00i − 0.312342i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 2766.00i 0.447103i 0.974692 + 0.223551i \(0.0717650\pi\)
−0.974692 + 0.223551i \(0.928235\pi\)
\(338\) 0 0
\(339\) 17980.0 2.88065
\(340\) 0 0
\(341\) −10080.0 −1.60077
\(342\) 0 0
\(343\) 343.000i 0.0539949i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8352.00i 1.29210i 0.763295 + 0.646050i \(0.223580\pi\)
−0.763295 + 0.646050i \(0.776420\pi\)
\(348\) 0 0
\(349\) 5924.00 0.908609 0.454304 0.890847i \(-0.349888\pi\)
0.454304 + 0.890847i \(0.349888\pi\)
\(350\) 0 0
\(351\) 5520.00 0.839418
\(352\) 0 0
\(353\) − 2226.00i − 0.335632i −0.985818 0.167816i \(-0.946329\pi\)
0.985818 0.167816i \(-0.0536714\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) − 4060.00i − 0.601899i
\(358\) 0 0
\(359\) −3880.00 −0.570414 −0.285207 0.958466i \(-0.592062\pi\)
−0.285207 + 0.958466i \(0.592062\pi\)
\(360\) 0 0
\(361\) −6183.00 −0.901443
\(362\) 0 0
\(363\) 2690.00i 0.388949i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) − 2584.00i − 0.367531i −0.982970 0.183765i \(-0.941171\pi\)
0.982970 0.183765i \(-0.0588286\pi\)
\(368\) 0 0
\(369\) −438.000 −0.0617923
\(370\) 0 0
\(371\) 3150.00 0.440808
\(372\) 0 0
\(373\) − 10534.0i − 1.46228i −0.682228 0.731139i \(-0.738989\pi\)
0.682228 0.731139i \(-0.261011\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 744.000i 0.101639i
\(378\) 0 0
\(379\) 4472.00 0.606098 0.303049 0.952975i \(-0.401995\pi\)
0.303049 + 0.952975i \(0.401995\pi\)
\(380\) 0 0
\(381\) 3840.00 0.516350
\(382\) 0 0
\(383\) − 2468.00i − 0.329266i −0.986355 0.164633i \(-0.947356\pi\)
0.986355 0.164633i \(-0.0526440\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 30368.0i 3.98887i
\(388\) 0 0
\(389\) 1046.00 0.136335 0.0681675 0.997674i \(-0.478285\pi\)
0.0681675 + 0.997674i \(0.478285\pi\)
\(390\) 0 0
\(391\) 3712.00 0.480112
\(392\) 0 0
\(393\) − 18140.0i − 2.32835i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 2124.00i 0.268515i 0.990946 + 0.134258i \(0.0428649\pi\)
−0.990946 + 0.134258i \(0.957135\pi\)
\(398\) 0 0
\(399\) −1820.00 −0.228356
\(400\) 0 0
\(401\) 11598.0 1.44433 0.722165 0.691721i \(-0.243147\pi\)
0.722165 + 0.691721i \(0.243147\pi\)
\(402\) 0 0
\(403\) 3024.00i 0.373787i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) − 1040.00i − 0.126661i
\(408\) 0 0
\(409\) 2770.00 0.334884 0.167442 0.985882i \(-0.446449\pi\)
0.167442 + 0.985882i \(0.446449\pi\)
\(410\) 0 0
\(411\) −16660.0 −1.99946
\(412\) 0 0
\(413\) 1918.00i 0.228520i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) − 11260.0i − 1.32231i
\(418\) 0 0
\(419\) −9438.00 −1.10042 −0.550211 0.835026i \(-0.685453\pi\)
−0.550211 + 0.835026i \(0.685453\pi\)
\(420\) 0 0
\(421\) 5550.00 0.642495 0.321248 0.946995i \(-0.395898\pi\)
0.321248 + 0.946995i \(0.395898\pi\)
\(422\) 0 0
\(423\) 28908.0i 3.32283i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 4032.00i 0.456961i
\(428\) 0 0
\(429\) 4800.00 0.540201
\(430\) 0 0
\(431\) −3000.00 −0.335278 −0.167639 0.985848i \(-0.553614\pi\)
−0.167639 + 0.985848i \(0.553614\pi\)
\(432\) 0 0
\(433\) − 12926.0i − 1.43460i −0.696762 0.717302i \(-0.745377\pi\)
0.696762 0.717302i \(-0.254623\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) − 1664.00i − 0.182151i
\(438\) 0 0
\(439\) 408.000 0.0443571 0.0221786 0.999754i \(-0.492940\pi\)
0.0221786 + 0.999754i \(0.492940\pi\)
\(440\) 0 0
\(441\) 3577.00 0.386243
\(442\) 0 0
\(443\) 14452.0i 1.54997i 0.631982 + 0.774983i \(0.282242\pi\)
−0.631982 + 0.774983i \(0.717758\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) − 26940.0i − 2.85060i
\(448\) 0 0
\(449\) −10258.0 −1.07818 −0.539092 0.842247i \(-0.681233\pi\)
−0.539092 + 0.842247i \(0.681233\pi\)
\(450\) 0 0
\(451\) −240.000 −0.0250580
\(452\) 0 0
\(453\) − 26480.0i − 2.74644i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) − 5498.00i − 0.562769i −0.959595 0.281385i \(-0.909206\pi\)
0.959595 0.281385i \(-0.0907937\pi\)
\(458\) 0 0
\(459\) −26680.0 −2.71311
\(460\) 0 0
\(461\) −16316.0 −1.64840 −0.824199 0.566300i \(-0.808375\pi\)
−0.824199 + 0.566300i \(0.808375\pi\)
\(462\) 0 0
\(463\) − 8944.00i − 0.897760i −0.893592 0.448880i \(-0.851823\pi\)
0.893592 0.448880i \(-0.148177\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) − 9422.00i − 0.933615i −0.884359 0.466807i \(-0.845404\pi\)
0.884359 0.466807i \(-0.154596\pi\)
\(468\) 0 0
\(469\) −3332.00 −0.328054
\(470\) 0 0
\(471\) 5560.00 0.543931
\(472\) 0 0
\(473\) 16640.0i 1.61756i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) − 32850.0i − 3.15325i
\(478\) 0 0
\(479\) −13820.0 −1.31827 −0.659136 0.752024i \(-0.729078\pi\)
−0.659136 + 0.752024i \(0.729078\pi\)
\(480\) 0 0
\(481\) −312.000 −0.0295758
\(482\) 0 0
\(483\) 4480.00i 0.422044i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) − 13264.0i − 1.23419i −0.786890 0.617094i \(-0.788310\pi\)
0.786890 0.617094i \(-0.211690\pi\)
\(488\) 0 0
\(489\) −3280.00 −0.303327
\(490\) 0 0
\(491\) −5940.00 −0.545964 −0.272982 0.962019i \(-0.588010\pi\)
−0.272982 + 0.962019i \(0.588010\pi\)
\(492\) 0 0
\(493\) − 3596.00i − 0.328511i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 3136.00i 0.283036i
\(498\) 0 0
\(499\) 8252.00 0.740301 0.370151 0.928972i \(-0.379306\pi\)
0.370151 + 0.928972i \(0.379306\pi\)
\(500\) 0 0
\(501\) 42680.0 3.80599
\(502\) 0 0
\(503\) − 4704.00i − 0.416980i −0.978024 0.208490i \(-0.933145\pi\)
0.978024 0.208490i \(-0.0668549\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 20530.0i 1.79836i
\(508\) 0 0
\(509\) 10788.0 0.939430 0.469715 0.882818i \(-0.344357\pi\)
0.469715 + 0.882818i \(0.344357\pi\)
\(510\) 0 0
\(511\) 1106.00 0.0957467
\(512\) 0 0
\(513\) 11960.0i 1.02933i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 15840.0i 1.34747i
\(518\) 0 0
\(519\) −34760.0 −2.93987
\(520\) 0 0
\(521\) −14586.0 −1.22653 −0.613267 0.789876i \(-0.710145\pi\)
−0.613267 + 0.789876i \(0.710145\pi\)
\(522\) 0 0
\(523\) − 26.0000i − 0.00217381i −0.999999 0.00108690i \(-0.999654\pi\)
0.999999 0.00108690i \(-0.000345972\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) − 14616.0i − 1.20813i
\(528\) 0 0
\(529\) 8071.00 0.663352
\(530\) 0 0
\(531\) 20002.0 1.63468
\(532\) 0 0
\(533\) 72.0000i 0.00585116i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) − 22680.0i − 1.82256i
\(538\) 0 0
\(539\) 1960.00 0.156629
\(540\) 0 0
\(541\) 11214.0 0.891178 0.445589 0.895238i \(-0.352994\pi\)
0.445589 + 0.895238i \(0.352994\pi\)
\(542\) 0 0
\(543\) − 2760.00i − 0.218127i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) − 5424.00i − 0.423973i −0.977273 0.211987i \(-0.932007\pi\)
0.977273 0.211987i \(-0.0679934\pi\)
\(548\) 0 0
\(549\) 42048.0 3.26879
\(550\) 0 0
\(551\) −1612.00 −0.124634
\(552\) 0 0
\(553\) − 6552.00i − 0.503833i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) − 17618.0i − 1.34021i −0.742265 0.670106i \(-0.766248\pi\)
0.742265 0.670106i \(-0.233752\pi\)
\(558\) 0 0
\(559\) 4992.00 0.377709
\(560\) 0 0
\(561\) −23200.0 −1.74600
\(562\) 0 0
\(563\) 3562.00i 0.266644i 0.991073 + 0.133322i \(0.0425644\pi\)
−0.991073 + 0.133322i \(0.957436\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) − 18403.0i − 1.36306i
\(568\) 0 0
\(569\) −2838.00 −0.209095 −0.104548 0.994520i \(-0.533339\pi\)
−0.104548 + 0.994520i \(0.533339\pi\)
\(570\) 0 0
\(571\) −360.000 −0.0263845 −0.0131922 0.999913i \(-0.504199\pi\)
−0.0131922 + 0.999913i \(0.504199\pi\)
\(572\) 0 0
\(573\) − 30000.0i − 2.18720i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 22018.0i 1.58860i 0.607527 + 0.794299i \(0.292162\pi\)
−0.607527 + 0.794299i \(0.707838\pi\)
\(578\) 0 0
\(579\) 32780.0 2.35283
\(580\) 0 0
\(581\) −3710.00 −0.264917
\(582\) 0 0
\(583\) − 18000.0i − 1.27870i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1454.00i 0.102237i 0.998693 + 0.0511184i \(0.0162786\pi\)
−0.998693 + 0.0511184i \(0.983721\pi\)
\(588\) 0 0
\(589\) −6552.00 −0.458354
\(590\) 0 0
\(591\) 23620.0 1.64399
\(592\) 0 0
\(593\) − 13818.0i − 0.956892i −0.878117 0.478446i \(-0.841200\pi\)
0.878117 0.478446i \(-0.158800\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 10360.0i 0.710229i
\(598\) 0 0
\(599\) −6696.00 −0.456746 −0.228373 0.973574i \(-0.573341\pi\)
−0.228373 + 0.973574i \(0.573341\pi\)
\(600\) 0 0
\(601\) 10010.0 0.679395 0.339698 0.940535i \(-0.389675\pi\)
0.339698 + 0.940535i \(0.389675\pi\)
\(602\) 0 0
\(603\) 34748.0i 2.34668i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 2880.00i 0.192579i 0.995353 + 0.0962896i \(0.0306975\pi\)
−0.995353 + 0.0962896i \(0.969303\pi\)
\(608\) 0 0
\(609\) 4340.00 0.288778
\(610\) 0 0
\(611\) 4752.00 0.314640
\(612\) 0 0
\(613\) − 6522.00i − 0.429724i −0.976644 0.214862i \(-0.931070\pi\)
0.976644 0.214862i \(-0.0689303\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 6614.00i 0.431555i 0.976443 + 0.215778i \(0.0692286\pi\)
−0.976443 + 0.215778i \(0.930771\pi\)
\(618\) 0 0
\(619\) −5266.00 −0.341936 −0.170968 0.985277i \(-0.554689\pi\)
−0.170968 + 0.985277i \(0.554689\pi\)
\(620\) 0 0
\(621\) 29440.0 1.90239
\(622\) 0 0
\(623\) − 2730.00i − 0.175562i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 10400.0i 0.662418i
\(628\) 0 0
\(629\) 1508.00 0.0955928
\(630\) 0 0
\(631\) 3344.00 0.210971 0.105485 0.994421i \(-0.466360\pi\)
0.105485 + 0.994421i \(0.466360\pi\)
\(632\) 0 0
\(633\) 35240.0i 2.21274i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) − 588.000i − 0.0365736i
\(638\) 0 0
\(639\) 32704.0 2.02465
\(640\) 0 0
\(641\) −4882.00 −0.300823 −0.150411 0.988623i \(-0.548060\pi\)
−0.150411 + 0.988623i \(0.548060\pi\)
\(642\) 0 0
\(643\) 15898.0i 0.975048i 0.873110 + 0.487524i \(0.162100\pi\)
−0.873110 + 0.487524i \(0.837900\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 6132.00i 0.372602i 0.982493 + 0.186301i \(0.0596500\pi\)
−0.982493 + 0.186301i \(0.940350\pi\)
\(648\) 0 0
\(649\) 10960.0 0.662893
\(650\) 0 0
\(651\) 17640.0 1.06201
\(652\) 0 0
\(653\) 24198.0i 1.45014i 0.688676 + 0.725070i \(0.258192\pi\)
−0.688676 + 0.725070i \(0.741808\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) − 11534.0i − 0.684907i
\(658\) 0 0
\(659\) −17456.0 −1.03185 −0.515925 0.856634i \(-0.672552\pi\)
−0.515925 + 0.856634i \(0.672552\pi\)
\(660\) 0 0
\(661\) −656.000 −0.0386013 −0.0193006 0.999814i \(-0.506144\pi\)
−0.0193006 + 0.999814i \(0.506144\pi\)
\(662\) 0 0
\(663\) 6960.00i 0.407698i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 3968.00i 0.230347i
\(668\) 0 0
\(669\) −13360.0 −0.772089
\(670\) 0 0
\(671\) 23040.0 1.32556
\(672\) 0 0
\(673\) 18214.0i 1.04324i 0.853179 + 0.521618i \(0.174671\pi\)
−0.853179 + 0.521618i \(0.825329\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 30252.0i 1.71740i 0.512480 + 0.858699i \(0.328727\pi\)
−0.512480 + 0.858699i \(0.671273\pi\)
\(678\) 0 0
\(679\) 1498.00 0.0846656
\(680\) 0 0
\(681\) −12900.0 −0.725887
\(682\) 0 0
\(683\) 10836.0i 0.607069i 0.952820 + 0.303534i \(0.0981667\pi\)
−0.952820 + 0.303534i \(0.901833\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) − 55240.0i − 3.06774i
\(688\) 0 0
\(689\) −5400.00 −0.298583
\(690\) 0 0
\(691\) 9578.00 0.527300 0.263650 0.964618i \(-0.415074\pi\)
0.263650 + 0.964618i \(0.415074\pi\)
\(692\) 0 0
\(693\) − 20440.0i − 1.12042i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) − 348.000i − 0.0189117i
\(698\) 0 0
\(699\) 63140.0 3.41656
\(700\) 0 0
\(701\) 12442.0 0.670368 0.335184 0.942153i \(-0.391202\pi\)
0.335184 + 0.942153i \(0.391202\pi\)
\(702\) 0 0
\(703\) − 676.000i − 0.0362672i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) − 10024.0i − 0.533227i
\(708\) 0 0
\(709\) 25174.0 1.33347 0.666734 0.745295i \(-0.267692\pi\)
0.666734 + 0.745295i \(0.267692\pi\)
\(710\) 0 0
\(711\) −68328.0 −3.60408
\(712\) 0 0
\(713\) 16128.0i 0.847123i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 39600.0i 2.06261i
\(718\) 0 0
\(719\) −34188.0 −1.77329 −0.886646 0.462448i \(-0.846971\pi\)
−0.886646 + 0.462448i \(0.846971\pi\)
\(720\) 0 0
\(721\) −5348.00 −0.276241
\(722\) 0 0
\(723\) − 70180.0i − 3.60999i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) − 5204.00i − 0.265482i −0.991151 0.132741i \(-0.957622\pi\)
0.991151 0.132741i \(-0.0423779\pi\)
\(728\) 0 0
\(729\) −67717.0 −3.44038
\(730\) 0 0
\(731\) −24128.0 −1.22080
\(732\) 0 0
\(733\) 32880.0i 1.65682i 0.560121 + 0.828411i \(0.310755\pi\)
−0.560121 + 0.828411i \(0.689245\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 19040.0i 0.951625i
\(738\) 0 0
\(739\) 3912.00 0.194730 0.0973648 0.995249i \(-0.468959\pi\)
0.0973648 + 0.995249i \(0.468959\pi\)
\(740\) 0 0
\(741\) 3120.00 0.154678
\(742\) 0 0
\(743\) 16008.0i 0.790413i 0.918592 + 0.395206i \(0.129327\pi\)
−0.918592 + 0.395206i \(0.870673\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 38690.0i 1.89504i
\(748\) 0 0
\(749\) 2268.00 0.110642
\(750\) 0 0
\(751\) 9960.00 0.483949 0.241974 0.970283i \(-0.422205\pi\)
0.241974 + 0.970283i \(0.422205\pi\)
\(752\) 0 0
\(753\) − 23940.0i − 1.15860i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 12378.0i 0.594301i 0.954831 + 0.297151i \(0.0960364\pi\)
−0.954831 + 0.297151i \(0.903964\pi\)
\(758\) 0 0
\(759\) 25600.0 1.22427
\(760\) 0 0
\(761\) 34670.0 1.65149 0.825747 0.564041i \(-0.190754\pi\)
0.825747 + 0.564041i \(0.190754\pi\)
\(762\) 0 0
\(763\) − 9338.00i − 0.443065i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) − 3288.00i − 0.154789i
\(768\) 0 0
\(769\) 10898.0 0.511043 0.255521 0.966803i \(-0.417753\pi\)
0.255521 + 0.966803i \(0.417753\pi\)
\(770\) 0 0
\(771\) 27660.0 1.29202
\(772\) 0 0
\(773\) 25808.0i 1.20084i 0.799685 + 0.600420i \(0.205000\pi\)
−0.799685 + 0.600420i \(0.795000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1820.00i 0.0840311i
\(778\) 0 0
\(779\) −156.000 −0.00717494
\(780\) 0 0
\(781\) 17920.0 0.821035
\(782\) 0 0
\(783\) − 28520.0i − 1.30169i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) − 21054.0i − 0.953614i −0.879008 0.476807i \(-0.841794\pi\)
0.879008 0.476807i \(-0.158206\pi\)
\(788\) 0 0
\(789\) 79680.0 3.59529
\(790\) 0 0
\(791\) −12586.0 −0.565748
\(792\) 0 0
\(793\) − 6912.00i − 0.309524i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) − 24276.0i − 1.07892i −0.842011 0.539461i \(-0.818628\pi\)
0.842011 0.539461i \(-0.181372\pi\)
\(798\) 0 0
\(799\) −22968.0 −1.01696
\(800\) 0 0
\(801\) −28470.0 −1.25585
\(802\) 0 0
\(803\) − 6320.00i − 0.277743i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 29000.0i 1.26499i
\(808\) 0 0
\(809\) −21526.0 −0.935493 −0.467747 0.883863i \(-0.654934\pi\)
−0.467747 + 0.883863i \(0.654934\pi\)
\(810\) 0 0
\(811\) −12806.0 −0.554475 −0.277238 0.960801i \(-0.589419\pi\)
−0.277238 + 0.960801i \(0.589419\pi\)
\(812\) 0 0
\(813\) 26400.0i 1.13885i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 10816.0i 0.463163i
\(818\) 0 0
\(819\) −6132.00 −0.261623
\(820\) 0 0
\(821\) 13214.0 0.561720 0.280860 0.959749i \(-0.409380\pi\)
0.280860 + 0.959749i \(0.409380\pi\)
\(822\) 0 0
\(823\) − 32248.0i − 1.36585i −0.730488 0.682925i \(-0.760708\pi\)
0.730488 0.682925i \(-0.239292\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) − 14316.0i − 0.601954i −0.953631 0.300977i \(-0.902687\pi\)
0.953631 0.300977i \(-0.0973128\pi\)
\(828\) 0 0
\(829\) −25168.0 −1.05443 −0.527214 0.849733i \(-0.676763\pi\)
−0.527214 + 0.849733i \(0.676763\pi\)
\(830\) 0 0
\(831\) 15220.0 0.635350
\(832\) 0 0
\(833\) 2842.00i 0.118211i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) − 115920.i − 4.78707i
\(838\) 0 0
\(839\) −9356.00 −0.384988 −0.192494 0.981298i \(-0.561658\pi\)
−0.192494 + 0.981298i \(0.561658\pi\)
\(840\) 0 0
\(841\) −20545.0 −0.842388
\(842\) 0 0
\(843\) − 45340.0i − 1.85242i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) − 1883.00i − 0.0763880i
\(848\) 0 0
\(849\) 48340.0 1.95409
\(850\) 0 0
\(851\) −1664.00 −0.0670284
\(852\) 0 0
\(853\) − 2372.00i − 0.0952119i −0.998866 0.0476059i \(-0.984841\pi\)
0.998866 0.0476059i \(-0.0151592\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 11694.0i 0.466114i 0.972463 + 0.233057i \(0.0748728\pi\)
−0.972463 + 0.233057i \(0.925127\pi\)
\(858\) 0 0
\(859\) 20506.0 0.814500 0.407250 0.913317i \(-0.366488\pi\)
0.407250 + 0.913317i \(0.366488\pi\)
\(860\) 0 0
\(861\) 420.000 0.0166243
\(862\) 0 0
\(863\) 28136.0i 1.10980i 0.831916 + 0.554902i \(0.187244\pi\)
−0.831916 + 0.554902i \(0.812756\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 15490.0i 0.606768i
\(868\) 0 0
\(869\) −37440.0 −1.46152
\(870\) 0 0
\(871\) 5712.00 0.222209
\(872\) 0 0
\(873\) − 15622.0i − 0.605641i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) − 37070.0i − 1.42733i −0.700489 0.713663i \(-0.747035\pi\)
0.700489 0.713663i \(-0.252965\pi\)
\(878\) 0 0
\(879\) −46560.0 −1.78661
\(880\) 0 0
\(881\) −6198.00 −0.237021 −0.118511 0.992953i \(-0.537812\pi\)
−0.118511 + 0.992953i \(0.537812\pi\)
\(882\) 0 0
\(883\) 31876.0i 1.21485i 0.794377 + 0.607425i \(0.207798\pi\)
−0.794377 + 0.607425i \(0.792202\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) − 132.000i − 0.00499676i −0.999997 0.00249838i \(-0.999205\pi\)
0.999997 0.00249838i \(-0.000795260\pi\)
\(888\) 0 0
\(889\) −2688.00 −0.101409
\(890\) 0 0
\(891\) −105160. −3.95398
\(892\) 0 0
\(893\) 10296.0i 0.385826i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) − 7680.00i − 0.285873i
\(898\) 0 0
\(899\) 15624.0 0.579632
\(900\) 0 0
\(901\) 26100.0 0.965058
\(902\) 0 0
\(903\) − 29120.0i − 1.07315i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 38244.0i 1.40008i 0.714104 + 0.700039i \(0.246834\pi\)
−0.714104 + 0.700039i \(0.753166\pi\)
\(908\) 0 0
\(909\) −104536. −3.81435
\(910\) 0 0
\(911\) −7008.00 −0.254869 −0.127434 0.991847i \(-0.540674\pi\)
−0.127434 + 0.991847i \(0.540674\pi\)
\(912\) 0 0
\(913\) 21200.0i 0.768475i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 12698.0i 0.457279i
\(918\) 0 0
\(919\) −36664.0 −1.31603 −0.658016 0.753004i \(-0.728604\pi\)
−0.658016 + 0.753004i \(0.728604\pi\)
\(920\) 0 0
\(921\) 72380.0 2.58958
\(922\) 0 0
\(923\) − 5376.00i − 0.191715i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 55772.0i 1.97604i
\(928\) 0 0
\(929\) −45510.0 −1.60725 −0.803625 0.595136i \(-0.797098\pi\)
−0.803625 + 0.595136i \(0.797098\pi\)
\(930\) 0 0
\(931\) 1274.00 0.0448482
\(932\) 0 0
\(933\) 10960.0i 0.384581i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) − 3838.00i − 0.133812i −0.997759 0.0669061i \(-0.978687\pi\)
0.997759 0.0669061i \(-0.0213128\pi\)
\(938\) 0 0
\(939\) −38180.0 −1.32690
\(940\) 0 0
\(941\) −16832.0 −0.583111 −0.291556 0.956554i \(-0.594173\pi\)
−0.291556 + 0.956554i \(0.594173\pi\)
\(942\) 0 0
\(943\) 384.000i 0.0132606i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) − 40928.0i − 1.40442i −0.711972 0.702208i \(-0.752198\pi\)
0.711972 0.702208i \(-0.247802\pi\)
\(948\) 0 0
\(949\) −1896.00 −0.0648543
\(950\) 0 0
\(951\) −19980.0 −0.681279
\(952\) 0 0
\(953\) 24070.0i 0.818157i 0.912499 + 0.409079i \(0.134150\pi\)
−0.912499 + 0.409079i \(0.865850\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) − 24800.0i − 0.837691i
\(958\) 0 0
\(959\) 11662.0 0.392686
\(960\) 0 0
\(961\) 33713.0 1.13165
\(962\) 0 0
\(963\) − 23652.0i − 0.791459i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) − 17152.0i − 0.570394i −0.958469 0.285197i \(-0.907941\pi\)
0.958469 0.285197i \(-0.0920590\pi\)
\(968\) 0 0
\(969\) −15080.0 −0.499937
\(970\) 0 0
\(971\) −32910.0 −1.08767 −0.543837 0.839191i \(-0.683029\pi\)
−0.543837 + 0.839191i \(0.683029\pi\)
\(972\) 0 0
\(973\) 7882.00i 0.259697i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) − 6822.00i − 0.223393i −0.993742 0.111697i \(-0.964372\pi\)
0.993742 0.111697i \(-0.0356285\pi\)
\(978\) 0 0
\(979\) −15600.0 −0.509273
\(980\) 0 0
\(981\) −97382.0 −3.16939
\(982\) 0 0
\(983\) 48420.0i 1.57107i 0.618820 + 0.785533i \(0.287611\pi\)
−0.618820 + 0.785533i \(0.712389\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) − 27720.0i − 0.893959i
\(988\) 0 0
\(989\) 26624.0 0.856010
\(990\) 0 0
\(991\) −49216.0 −1.57760 −0.788798 0.614652i \(-0.789296\pi\)
−0.788798 + 0.614652i \(0.789296\pi\)
\(992\) 0 0
\(993\) − 79360.0i − 2.53617i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 35264.0i 1.12018i 0.828431 + 0.560091i \(0.189234\pi\)
−0.828431 + 0.560091i \(0.810766\pi\)
\(998\) 0 0
\(999\) 11960.0 0.378776
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 700.4.e.a.449.2 2
5.2 odd 4 700.4.a.n.1.1 1
5.3 odd 4 28.4.a.a.1.1 1
5.4 even 2 inner 700.4.e.a.449.1 2
15.8 even 4 252.4.a.d.1.1 1
20.3 even 4 112.4.a.g.1.1 1
35.3 even 12 196.4.e.a.177.1 2
35.13 even 4 196.4.a.d.1.1 1
35.18 odd 12 196.4.e.f.177.1 2
35.23 odd 12 196.4.e.f.165.1 2
35.33 even 12 196.4.e.a.165.1 2
40.3 even 4 448.4.a.a.1.1 1
40.13 odd 4 448.4.a.p.1.1 1
60.23 odd 4 1008.4.a.o.1.1 1
105.23 even 12 1764.4.k.d.361.1 2
105.38 odd 12 1764.4.k.m.1549.1 2
105.53 even 12 1764.4.k.d.1549.1 2
105.68 odd 12 1764.4.k.m.361.1 2
105.83 odd 4 1764.4.a.c.1.1 1
140.83 odd 4 784.4.a.a.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
28.4.a.a.1.1 1 5.3 odd 4
112.4.a.g.1.1 1 20.3 even 4
196.4.a.d.1.1 1 35.13 even 4
196.4.e.a.165.1 2 35.33 even 12
196.4.e.a.177.1 2 35.3 even 12
196.4.e.f.165.1 2 35.23 odd 12
196.4.e.f.177.1 2 35.18 odd 12
252.4.a.d.1.1 1 15.8 even 4
448.4.a.a.1.1 1 40.3 even 4
448.4.a.p.1.1 1 40.13 odd 4
700.4.a.n.1.1 1 5.2 odd 4
700.4.e.a.449.1 2 5.4 even 2 inner
700.4.e.a.449.2 2 1.1 even 1 trivial
784.4.a.a.1.1 1 140.83 odd 4
1008.4.a.o.1.1 1 60.23 odd 4
1764.4.a.c.1.1 1 105.83 odd 4
1764.4.k.d.361.1 2 105.23 even 12
1764.4.k.d.1549.1 2 105.53 even 12
1764.4.k.m.361.1 2 105.68 odd 12
1764.4.k.m.1549.1 2 105.38 odd 12