Properties

Label 1152.2.w.a.719.2
Level $1152$
Weight $2$
Character 1152.719
Analytic conductor $9.199$
Analytic rank $0$
Dimension $32$
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] = [1152,2,Mod(143,1152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1152, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([4, 1, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1152.143");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.w (of order \(8\), degree \(4\), 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: \(9.19876631285\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(8\) over \(\Q(\zeta_{8})\)
Twist minimal: no (minimal twist has level 288)
Sato-Tate group: $\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label 719.2
Character \(\chi\) \(=\) 1152.719
Dual form 1152.2.w.a.431.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.78959 - 0.741273i) q^{5} +(2.33709 - 2.33709i) q^{7} +O(q^{10})\) \(q+(-1.78959 - 0.741273i) q^{5} +(2.33709 - 2.33709i) q^{7} +(-0.683332 - 0.283045i) q^{11} +(2.43602 + 5.88107i) q^{13} -0.967834 q^{17} +(2.52772 - 1.04702i) q^{19} +(5.00283 - 5.00283i) q^{23} +(-0.882385 - 0.882385i) q^{25} +(0.563403 + 1.36018i) q^{29} -7.28582i q^{31} +(-5.91486 + 2.45001i) q^{35} +(3.26572 - 7.88415i) q^{37} +(-6.80014 - 6.80014i) q^{41} +(-1.36517 + 3.29581i) q^{43} -3.69279i q^{47} -3.92399i q^{49} +(-1.85469 + 4.47761i) q^{53} +(1.01307 + 1.01307i) q^{55} +(4.05615 - 9.79242i) q^{59} +(10.8180 - 4.48097i) q^{61} -12.3305i q^{65} +(-1.49290 - 3.60418i) q^{67} +(9.85675 + 9.85675i) q^{71} +(-4.81362 + 4.81362i) q^{73} +(-2.25851 + 0.935506i) q^{77} +11.0160 q^{79} +(-1.15064 - 2.77789i) q^{83} +(1.73203 + 0.717429i) q^{85} +(6.82624 - 6.82624i) q^{89} +(19.4378 + 8.05140i) q^{91} -5.29971 q^{95} +7.67976 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 8 q^{11} + 16 q^{29} + 24 q^{35} + 16 q^{53} + 32 q^{55} + 32 q^{59} + 32 q^{61} + 16 q^{67} + 16 q^{71} + 16 q^{77} + 32 q^{79} - 40 q^{83} + 48 q^{91} - 80 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{5}{8}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −1.78959 0.741273i −0.800329 0.331507i −0.0552409 0.998473i \(-0.517593\pi\)
−0.745088 + 0.666966i \(0.767593\pi\)
\(6\) 0 0
\(7\) 2.33709 2.33709i 0.883337 0.883337i −0.110535 0.993872i \(-0.535256\pi\)
0.993872 + 0.110535i \(0.0352564\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.683332 0.283045i −0.206032 0.0853413i 0.277281 0.960789i \(-0.410567\pi\)
−0.483313 + 0.875448i \(0.660567\pi\)
\(12\) 0 0
\(13\) 2.43602 + 5.88107i 0.675630 + 1.63112i 0.771888 + 0.635759i \(0.219313\pi\)
−0.0962579 + 0.995356i \(0.530687\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.967834 −0.234734 −0.117367 0.993089i \(-0.537445\pi\)
−0.117367 + 0.993089i \(0.537445\pi\)
\(18\) 0 0
\(19\) 2.52772 1.04702i 0.579899 0.240202i −0.0733991 0.997303i \(-0.523385\pi\)
0.653298 + 0.757100i \(0.273385\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 5.00283 5.00283i 1.04316 1.04316i 0.0441370 0.999025i \(-0.485946\pi\)
0.999025 0.0441370i \(-0.0140538\pi\)
\(24\) 0 0
\(25\) −0.882385 0.882385i −0.176477 0.176477i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.563403 + 1.36018i 0.104621 + 0.252578i 0.967518 0.252802i \(-0.0813522\pi\)
−0.862897 + 0.505380i \(0.831352\pi\)
\(30\) 0 0
\(31\) 7.28582i 1.30857i −0.756247 0.654286i \(-0.772969\pi\)
0.756247 0.654286i \(-0.227031\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −5.91486 + 2.45001i −0.999793 + 0.414128i
\(36\) 0 0
\(37\) 3.26572 7.88415i 0.536881 1.29615i −0.390008 0.920812i \(-0.627528\pi\)
0.926889 0.375335i \(-0.122472\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −6.80014 6.80014i −1.06200 1.06200i −0.997946 0.0640576i \(-0.979596\pi\)
−0.0640576 0.997946i \(-0.520404\pi\)
\(42\) 0 0
\(43\) −1.36517 + 3.29581i −0.208187 + 0.502607i −0.993138 0.116951i \(-0.962688\pi\)
0.784951 + 0.619558i \(0.212688\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.69279i 0.538649i −0.963050 0.269324i \(-0.913200\pi\)
0.963050 0.269324i \(-0.0868004\pi\)
\(48\) 0 0
\(49\) 3.92399i 0.560570i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −1.85469 + 4.47761i −0.254761 + 0.615047i −0.998577 0.0533378i \(-0.983014\pi\)
0.743816 + 0.668385i \(0.233014\pi\)
\(54\) 0 0
\(55\) 1.01307 + 1.01307i 0.136602 + 0.136602i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 4.05615 9.79242i 0.528066 1.27486i −0.404722 0.914440i \(-0.632632\pi\)
0.932788 0.360425i \(-0.117368\pi\)
\(60\) 0 0
\(61\) 10.8180 4.48097i 1.38511 0.573730i 0.439265 0.898358i \(-0.355239\pi\)
0.945842 + 0.324628i \(0.105239\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 12.3305i 1.52941i
\(66\) 0 0
\(67\) −1.49290 3.60418i −0.182387 0.440320i 0.806071 0.591819i \(-0.201590\pi\)
−0.988457 + 0.151499i \(0.951590\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 9.85675 + 9.85675i 1.16978 + 1.16978i 0.982261 + 0.187520i \(0.0600450\pi\)
0.187520 + 0.982261i \(0.439955\pi\)
\(72\) 0 0
\(73\) −4.81362 + 4.81362i −0.563391 + 0.563391i −0.930269 0.366878i \(-0.880427\pi\)
0.366878 + 0.930269i \(0.380427\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −2.25851 + 0.935506i −0.257381 + 0.106611i
\(78\) 0 0
\(79\) 11.0160 1.23940 0.619700 0.784839i \(-0.287254\pi\)
0.619700 + 0.784839i \(0.287254\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −1.15064 2.77789i −0.126299 0.304913i 0.848064 0.529894i \(-0.177768\pi\)
−0.974363 + 0.224981i \(0.927768\pi\)
\(84\) 0 0
\(85\) 1.73203 + 0.717429i 0.187865 + 0.0778161i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 6.82624 6.82624i 0.723580 0.723580i −0.245753 0.969333i \(-0.579035\pi\)
0.969333 + 0.245753i \(0.0790352\pi\)
\(90\) 0 0
\(91\) 19.4378 + 8.05140i 2.03763 + 0.844016i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −5.29971 −0.543739
\(96\) 0 0
\(97\) 7.67976 0.779762 0.389881 0.920865i \(-0.372516\pi\)
0.389881 + 0.920865i \(0.372516\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.05030 + 0.435049i 0.104509 + 0.0432890i 0.434325 0.900756i \(-0.356987\pi\)
−0.329816 + 0.944045i \(0.606987\pi\)
\(102\) 0 0
\(103\) −7.06356 + 7.06356i −0.695993 + 0.695993i −0.963544 0.267551i \(-0.913786\pi\)
0.267551 + 0.963544i \(0.413786\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −16.1346 6.68316i −1.55979 0.646086i −0.574737 0.818338i \(-0.694895\pi\)
−0.985053 + 0.172253i \(0.944895\pi\)
\(108\) 0 0
\(109\) 0.771406 + 1.86234i 0.0738873 + 0.178380i 0.956508 0.291706i \(-0.0942230\pi\)
−0.882621 + 0.470086i \(0.844223\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.726213 0.0683163 0.0341582 0.999416i \(-0.489125\pi\)
0.0341582 + 0.999416i \(0.489125\pi\)
\(114\) 0 0
\(115\) −12.6615 + 5.24456i −1.18069 + 0.489058i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) −2.26192 + 2.26192i −0.207350 + 0.207350i
\(120\) 0 0
\(121\) −7.39135 7.39135i −0.671941 0.671941i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 4.63138 + 11.1811i 0.414243 + 1.00007i
\(126\) 0 0
\(127\) 11.5686i 1.02654i −0.858226 0.513272i \(-0.828433\pi\)
0.858226 0.513272i \(-0.171567\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −17.9241 + 7.42442i −1.56604 + 0.648674i −0.986125 0.166004i \(-0.946913\pi\)
−0.579913 + 0.814678i \(0.696913\pi\)
\(132\) 0 0
\(133\) 3.46054 8.35449i 0.300067 0.724426i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 15.9867 + 15.9867i 1.36584 + 1.36584i 0.866283 + 0.499553i \(0.166503\pi\)
0.499553 + 0.866283i \(0.333497\pi\)
\(138\) 0 0
\(139\) −0.0365308 + 0.0881933i −0.00309851 + 0.00748046i −0.925421 0.378940i \(-0.876289\pi\)
0.922323 + 0.386421i \(0.126289\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 4.70822i 0.393721i
\(144\) 0 0
\(145\) 2.85179i 0.236828i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.79476 + 13.9898i −0.474725 + 1.14609i 0.487326 + 0.873220i \(0.337972\pi\)
−0.962051 + 0.272868i \(0.912028\pi\)
\(150\) 0 0
\(151\) −7.47087 7.47087i −0.607971 0.607971i 0.334445 0.942415i \(-0.391451\pi\)
−0.942415 + 0.334445i \(0.891451\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.40078 + 13.0386i −0.433801 + 1.04729i
\(156\) 0 0
\(157\) −11.0372 + 4.57177i −0.880867 + 0.364867i −0.776833 0.629707i \(-0.783175\pi\)
−0.104034 + 0.994574i \(0.533175\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 23.3841i 1.84293i
\(162\) 0 0
\(163\) 3.29972 + 7.96624i 0.258454 + 0.623964i 0.998837 0.0482221i \(-0.0153555\pi\)
−0.740382 + 0.672186i \(0.765356\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.0751100 0.0751100i −0.00581218 0.00581218i 0.704195 0.710007i \(-0.251308\pi\)
−0.710007 + 0.704195i \(0.751308\pi\)
\(168\) 0 0
\(169\) −19.4604 + 19.4604i −1.49695 + 1.49695i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 21.0041 8.70018i 1.59691 0.661463i 0.605937 0.795512i \(-0.292798\pi\)
0.990975 + 0.134050i \(0.0427982\pi\)
\(174\) 0 0
\(175\) −4.12443 −0.311777
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4.35530 + 10.5146i 0.325530 + 0.785900i 0.998913 + 0.0466061i \(0.0148406\pi\)
−0.673383 + 0.739294i \(0.735159\pi\)
\(180\) 0 0
\(181\) −4.28737 1.77589i −0.318677 0.132001i 0.217610 0.976036i \(-0.430174\pi\)
−0.536288 + 0.844035i \(0.680174\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −11.6886 + 11.6886i −0.859364 + 0.859364i
\(186\) 0 0
\(187\) 0.661352 + 0.273941i 0.0483628 + 0.0200325i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 22.2718 1.61153 0.805766 0.592234i \(-0.201754\pi\)
0.805766 + 0.592234i \(0.201754\pi\)
\(192\) 0 0
\(193\) 10.8858 0.783575 0.391787 0.920056i \(-0.371857\pi\)
0.391787 + 0.920056i \(0.371857\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.10110 2.52716i −0.434686 0.180053i 0.154601 0.987977i \(-0.450591\pi\)
−0.589286 + 0.807924i \(0.700591\pi\)
\(198\) 0 0
\(199\) −10.1086 + 10.1086i −0.716582 + 0.716582i −0.967904 0.251322i \(-0.919135\pi\)
0.251322 + 0.967904i \(0.419135\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 4.49558 + 1.86213i 0.315528 + 0.130696i
\(204\) 0 0
\(205\) 7.12871 + 17.2102i 0.497891 + 1.20201i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −2.02363 −0.139977
\(210\) 0 0
\(211\) −18.8236 + 7.79698i −1.29587 + 0.536766i −0.920729 0.390202i \(-0.872405\pi\)
−0.375139 + 0.926969i \(0.622405\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 4.88619 4.88619i 0.333236 0.333236i
\(216\) 0 0
\(217\) −17.0276 17.0276i −1.15591 1.15591i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −2.35766 5.69190i −0.158593 0.382879i
\(222\) 0 0
\(223\) 14.8162i 0.992164i −0.868276 0.496082i \(-0.834771\pi\)
0.868276 0.496082i \(-0.165229\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 11.9755 4.96040i 0.794839 0.329233i 0.0519519 0.998650i \(-0.483456\pi\)
0.742887 + 0.669416i \(0.233456\pi\)
\(228\) 0 0
\(229\) −2.65080 + 6.39960i −0.175170 + 0.422897i −0.986942 0.161077i \(-0.948503\pi\)
0.811772 + 0.583975i \(0.198503\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 8.35926 + 8.35926i 0.547634 + 0.547634i 0.925756 0.378122i \(-0.123430\pi\)
−0.378122 + 0.925756i \(0.623430\pi\)
\(234\) 0 0
\(235\) −2.73736 + 6.60858i −0.178566 + 0.431096i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.44122i 0.157909i 0.996878 + 0.0789547i \(0.0251582\pi\)
−0.996878 + 0.0789547i \(0.974842\pi\)
\(240\) 0 0
\(241\) 1.86406i 0.120074i 0.998196 + 0.0600372i \(0.0191219\pi\)
−0.998196 + 0.0600372i \(0.980878\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −2.90874 + 7.02233i −0.185833 + 0.448640i
\(246\) 0 0
\(247\) 12.3152 + 12.3152i 0.783595 + 0.783595i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6.30926 15.2319i 0.398237 0.961430i −0.589847 0.807515i \(-0.700812\pi\)
0.988084 0.153915i \(-0.0491881\pi\)
\(252\) 0 0
\(253\) −4.83462 + 2.00257i −0.303950 + 0.125900i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 5.84660i 0.364701i 0.983234 + 0.182350i \(0.0583705\pi\)
−0.983234 + 0.182350i \(0.941629\pi\)
\(258\) 0 0
\(259\) −10.7937 26.0583i −0.670687 1.61918i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 11.4239 + 11.4239i 0.704427 + 0.704427i 0.965358 0.260930i \(-0.0840293\pi\)
−0.260930 + 0.965358i \(0.584029\pi\)
\(264\) 0 0
\(265\) 6.63826 6.63826i 0.407785 0.407785i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −2.42511 + 1.00451i −0.147862 + 0.0612463i −0.455387 0.890294i \(-0.650499\pi\)
0.307525 + 0.951540i \(0.400499\pi\)
\(270\) 0 0
\(271\) 10.6956 0.649711 0.324856 0.945764i \(-0.394684\pi\)
0.324856 + 0.945764i \(0.394684\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0.353207 + 0.852716i 0.0212992 + 0.0514207i
\(276\) 0 0
\(277\) −13.7497 5.69533i −0.826142 0.342199i −0.0707678 0.997493i \(-0.522545\pi\)
−0.755374 + 0.655294i \(0.772545\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.63475 + 1.63475i −0.0975211 + 0.0975211i −0.754184 0.656663i \(-0.771967\pi\)
0.656663 + 0.754184i \(0.271967\pi\)
\(282\) 0 0
\(283\) 4.75108 + 1.96796i 0.282423 + 0.116983i 0.519398 0.854532i \(-0.326156\pi\)
−0.236976 + 0.971516i \(0.576156\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −31.7851 −1.87622
\(288\) 0 0
\(289\) −16.0633 −0.944900
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −13.0434 5.40274i −0.762001 0.315631i −0.0323737 0.999476i \(-0.510307\pi\)
−0.729628 + 0.683845i \(0.760307\pi\)
\(294\) 0 0
\(295\) −14.5177 + 14.5177i −0.845254 + 0.845254i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 41.6090 + 17.2350i 2.40631 + 0.996726i
\(300\) 0 0
\(301\) 4.51209 + 10.8931i 0.260072 + 0.627870i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −22.6815 −1.29874
\(306\) 0 0
\(307\) −13.7332 + 5.68846i −0.783793 + 0.324658i −0.738445 0.674313i \(-0.764440\pi\)
−0.0453480 + 0.998971i \(0.514440\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −1.93693 + 1.93693i −0.109833 + 0.109833i −0.759888 0.650055i \(-0.774746\pi\)
0.650055 + 0.759888i \(0.274746\pi\)
\(312\) 0 0
\(313\) 20.8065 + 20.8065i 1.17606 + 1.17606i 0.980741 + 0.195315i \(0.0625728\pi\)
0.195315 + 0.980741i \(0.437427\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 6.99169 + 16.8794i 0.392692 + 0.948043i 0.989351 + 0.145548i \(0.0464945\pi\)
−0.596659 + 0.802495i \(0.703505\pi\)
\(318\) 0 0
\(319\) 1.08892i 0.0609678i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) −2.44642 + 1.01334i −0.136122 + 0.0563837i
\(324\) 0 0
\(325\) 3.03986 7.33887i 0.168621 0.407087i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −8.63039 8.63039i −0.475809 0.475809i
\(330\) 0 0
\(331\) −7.57715 + 18.2929i −0.416478 + 1.00547i 0.566882 + 0.823799i \(0.308150\pi\)
−0.983360 + 0.181668i \(0.941850\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 7.55664i 0.412863i
\(336\) 0 0
\(337\) 6.73391i 0.366820i 0.983037 + 0.183410i \(0.0587135\pi\)
−0.983037 + 0.183410i \(0.941286\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −2.06222 + 4.97863i −0.111675 + 0.269608i
\(342\) 0 0
\(343\) 7.18892 + 7.18892i 0.388165 + 0.388165i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 2.79644 6.75121i 0.150121 0.362424i −0.830873 0.556462i \(-0.812158\pi\)
0.980994 + 0.194038i \(0.0621585\pi\)
\(348\) 0 0
\(349\) −3.16816 + 1.31229i −0.169588 + 0.0702455i −0.465862 0.884857i \(-0.654256\pi\)
0.296274 + 0.955103i \(0.404256\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 29.8578i 1.58917i 0.607151 + 0.794586i \(0.292312\pi\)
−0.607151 + 0.794586i \(0.707688\pi\)
\(354\) 0 0
\(355\) −10.3330 24.9461i −0.548419 1.32400i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 9.44266 + 9.44266i 0.498365 + 0.498365i 0.910929 0.412564i \(-0.135367\pi\)
−0.412564 + 0.910929i \(0.635367\pi\)
\(360\) 0 0
\(361\) −8.14189 + 8.14189i −0.428521 + 0.428521i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 12.1826 5.04620i 0.637667 0.264130i
\(366\) 0 0
\(367\) −26.8327 −1.40065 −0.700327 0.713822i \(-0.746962\pi\)
−0.700327 + 0.713822i \(0.746962\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 6.13001 + 14.7991i 0.318254 + 0.768334i
\(372\) 0 0
\(373\) −12.3312 5.10777i −0.638487 0.264470i 0.0398670 0.999205i \(-0.487307\pi\)
−0.678354 + 0.734735i \(0.737307\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −6.62683 + 6.62683i −0.341299 + 0.341299i
\(378\) 0 0
\(379\) 5.26078 + 2.17909i 0.270228 + 0.111932i 0.513683 0.857980i \(-0.328281\pi\)
−0.243455 + 0.969912i \(0.578281\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −8.14683 −0.416283 −0.208142 0.978099i \(-0.566742\pi\)
−0.208142 + 0.978099i \(0.566742\pi\)
\(384\) 0 0
\(385\) 4.73527 0.241332
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 8.22236 + 3.40581i 0.416890 + 0.172682i 0.581261 0.813717i \(-0.302559\pi\)
−0.164371 + 0.986399i \(0.552559\pi\)
\(390\) 0 0
\(391\) −4.84191 + 4.84191i −0.244866 + 0.244866i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −19.7142 8.16588i −0.991927 0.410870i
\(396\) 0 0
\(397\) −0.328403 0.792834i −0.0164821 0.0397912i 0.915424 0.402490i \(-0.131855\pi\)
−0.931906 + 0.362699i \(0.881855\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 17.3098 0.864411 0.432206 0.901775i \(-0.357735\pi\)
0.432206 + 0.901775i \(0.357735\pi\)
\(402\) 0 0
\(403\) 42.8484 17.7484i 2.13443 0.884111i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −4.46314 + 4.46314i −0.221230 + 0.221230i
\(408\) 0 0
\(409\) 5.00972 + 5.00972i 0.247715 + 0.247715i 0.820032 0.572317i \(-0.193955\pi\)
−0.572317 + 0.820032i \(0.693955\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −13.4062 32.3654i −0.659675 1.59260i
\(414\) 0 0
\(415\) 5.82422i 0.285900i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −7.01103 + 2.90406i −0.342511 + 0.141873i −0.547307 0.836932i \(-0.684347\pi\)
0.204796 + 0.978805i \(0.434347\pi\)
\(420\) 0 0
\(421\) 3.94749 9.53009i 0.192389 0.464468i −0.798021 0.602630i \(-0.794119\pi\)
0.990410 + 0.138162i \(0.0441195\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.854002 + 0.854002i 0.0414252 + 0.0414252i
\(426\) 0 0
\(427\) 14.8103 35.7552i 0.716719 1.73031i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 11.8098i 0.568858i −0.958697 0.284429i \(-0.908196\pi\)
0.958697 0.284429i \(-0.0918040\pi\)
\(432\) 0 0
\(433\) 3.26662i 0.156984i 0.996915 + 0.0784919i \(0.0250105\pi\)
−0.996915 + 0.0784919i \(0.974990\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.40772 17.8838i 0.354359 0.855499i
\(438\) 0 0
\(439\) −13.7003 13.7003i −0.653877 0.653877i 0.300047 0.953924i \(-0.402998\pi\)
−0.953924 + 0.300047i \(0.902998\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 7.53737 18.1968i 0.358111 0.864557i −0.637454 0.770488i \(-0.720012\pi\)
0.995566 0.0940692i \(-0.0299875\pi\)
\(444\) 0 0
\(445\) −17.2763 + 7.15607i −0.818974 + 0.339230i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 2.46488i 0.116325i 0.998307 + 0.0581625i \(0.0185241\pi\)
−0.998307 + 0.0581625i \(0.981476\pi\)
\(450\) 0 0
\(451\) 2.72200 + 6.57150i 0.128174 + 0.309440i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −28.8174 28.8174i −1.35098 1.35098i
\(456\) 0 0
\(457\) 3.04617 3.04617i 0.142494 0.142494i −0.632261 0.774755i \(-0.717873\pi\)
0.774755 + 0.632261i \(0.217873\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −9.85993 + 4.08412i −0.459223 + 0.190216i −0.600288 0.799784i \(-0.704947\pi\)
0.141065 + 0.990000i \(0.454947\pi\)
\(462\) 0 0
\(463\) 28.1511 1.30829 0.654147 0.756367i \(-0.273028\pi\)
0.654147 + 0.756367i \(0.273028\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −0.133756 0.322916i −0.00618951 0.0149428i 0.920755 0.390142i \(-0.127574\pi\)
−0.926944 + 0.375200i \(0.877574\pi\)
\(468\) 0 0
\(469\) −11.9123 4.93425i −0.550060 0.227842i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.86573 1.86573i 0.0857863 0.0857863i
\(474\) 0 0
\(475\) −3.15430 1.30655i −0.144729 0.0599487i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −25.3551 −1.15850 −0.579251 0.815149i \(-0.696655\pi\)
−0.579251 + 0.815149i \(0.696655\pi\)
\(480\) 0 0
\(481\) 54.3226 2.47690
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −13.7436 5.69280i −0.624066 0.258497i
\(486\) 0 0
\(487\) 15.5211 15.5211i 0.703327 0.703327i −0.261796 0.965123i \(-0.584315\pi\)
0.965123 + 0.261796i \(0.0843149\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 7.79527 + 3.22890i 0.351795 + 0.145718i 0.551581 0.834121i \(-0.314025\pi\)
−0.199786 + 0.979840i \(0.564025\pi\)
\(492\) 0 0
\(493\) −0.545281 1.31642i −0.0245582 0.0592888i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 46.0722 2.06662
\(498\) 0 0
\(499\) 2.14784 0.889664i 0.0961504 0.0398268i −0.334090 0.942541i \(-0.608429\pi\)
0.430240 + 0.902714i \(0.358429\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 10.4975 10.4975i 0.468062 0.468062i −0.433224 0.901286i \(-0.642624\pi\)
0.901286 + 0.433224i \(0.142624\pi\)
\(504\) 0 0
\(505\) −1.55712 1.55712i −0.0692908 0.0692908i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −8.62373 20.8195i −0.382240 0.922810i −0.991532 0.129863i \(-0.958546\pi\)
0.609292 0.792946i \(-0.291454\pi\)
\(510\) 0 0
\(511\) 22.4997i 0.995329i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 17.8769 7.40485i 0.787750 0.326297i
\(516\) 0 0
\(517\) −1.04523 + 2.52340i −0.0459690 + 0.110979i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 23.6260 + 23.6260i 1.03508 + 1.03508i 0.999362 + 0.0357139i \(0.0113705\pi\)
0.0357139 + 0.999362i \(0.488630\pi\)
\(522\) 0 0
\(523\) 0.967311 2.33529i 0.0422975 0.102115i −0.901319 0.433156i \(-0.857400\pi\)
0.943616 + 0.331041i \(0.107400\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 7.05147i 0.307167i
\(528\) 0 0
\(529\) 27.0566i 1.17638i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 23.4268 56.5574i 1.01473 2.44977i
\(534\) 0 0
\(535\) 23.9203 + 23.9203i 1.03416 + 1.03416i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.11067 + 2.68138i −0.0478398 + 0.115495i
\(540\) 0 0
\(541\) 13.3578 5.53299i 0.574298 0.237882i −0.0765813 0.997063i \(-0.524400\pi\)
0.650879 + 0.759181i \(0.274400\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 3.90464i 0.167257i
\(546\) 0 0
\(547\) 16.5682 + 39.9992i 0.708406 + 1.71024i 0.703945 + 0.710254i \(0.251420\pi\)
0.00446097 + 0.999990i \(0.498580\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 2.84825 + 2.84825i 0.121340 + 0.121340i
\(552\) 0 0
\(553\) 25.7454 25.7454i 1.09481 1.09481i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 5.70924 2.36484i 0.241908 0.100202i −0.258436 0.966029i \(-0.583207\pi\)
0.500344 + 0.865827i \(0.333207\pi\)
\(558\) 0 0
\(559\) −22.7085 −0.960467
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −5.89410 14.2296i −0.248407 0.599707i 0.749662 0.661821i \(-0.230216\pi\)
−0.998069 + 0.0621133i \(0.980216\pi\)
\(564\) 0 0
\(565\) −1.29962 0.538322i −0.0546756 0.0226474i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.242674 0.242674i 0.0101734 0.0101734i −0.702002 0.712175i \(-0.747710\pi\)
0.712175 + 0.702002i \(0.247710\pi\)
\(570\) 0 0
\(571\) −25.8985 10.7275i −1.08382 0.448933i −0.231972 0.972722i \(-0.574518\pi\)
−0.851848 + 0.523789i \(0.824518\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −8.82885 −0.368188
\(576\) 0 0
\(577\) 17.7896 0.740589 0.370294 0.928914i \(-0.379257\pi\)
0.370294 + 0.928914i \(0.379257\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −9.18133 3.80303i −0.380906 0.157776i
\(582\) 0 0
\(583\) 2.53473 2.53473i 0.104978 0.104978i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −30.9718 12.8289i −1.27834 0.529507i −0.362852 0.931847i \(-0.618197\pi\)
−0.915490 + 0.402340i \(0.868197\pi\)
\(588\) 0 0
\(589\) −7.62838 18.4165i −0.314322 0.758840i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −41.4635 −1.70270 −0.851351 0.524596i \(-0.824216\pi\)
−0.851351 + 0.524596i \(0.824216\pi\)
\(594\) 0 0
\(595\) 5.72460 2.37121i 0.234686 0.0972100i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −32.9148 + 32.9148i −1.34486 + 1.34486i −0.453719 + 0.891145i \(0.649903\pi\)
−0.891145 + 0.453719i \(0.850097\pi\)
\(600\) 0 0
\(601\) −12.5748 12.5748i −0.512936 0.512936i 0.402489 0.915425i \(-0.368145\pi\)
−0.915425 + 0.402489i \(0.868145\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.74848 + 18.7065i 0.315021 + 0.760527i
\(606\) 0 0
\(607\) 46.0240i 1.86806i 0.357198 + 0.934029i \(0.383732\pi\)
−0.357198 + 0.934029i \(0.616268\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 21.7176 8.99570i 0.878598 0.363927i
\(612\) 0 0
\(613\) 3.81762 9.21655i 0.154192 0.372253i −0.827841 0.560963i \(-0.810431\pi\)
0.982033 + 0.188711i \(0.0604308\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −9.42700 9.42700i −0.379517 0.379517i 0.491411 0.870928i \(-0.336481\pi\)
−0.870928 + 0.491411i \(0.836481\pi\)
\(618\) 0 0
\(619\) 10.4213 25.1593i 0.418868 1.01124i −0.563808 0.825906i \(-0.690664\pi\)
0.982676 0.185332i \(-0.0593359\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 31.9071i 1.27833i
\(624\) 0 0
\(625\) 17.2034i 0.688136i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −3.16068 + 7.63055i −0.126024 + 0.304250i
\(630\) 0 0
\(631\) −15.7973 15.7973i −0.628879 0.628879i 0.318907 0.947786i \(-0.396684\pi\)
−0.947786 + 0.318907i \(0.896684\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −8.57545 + 20.7030i −0.340307 + 0.821573i
\(636\) 0 0
\(637\) 23.0772 9.55891i 0.914354 0.378738i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 11.2466i 0.444215i 0.975022 + 0.222107i \(0.0712936\pi\)
−0.975022 + 0.222107i \(0.928706\pi\)
\(642\) 0 0
\(643\) −4.46309 10.7749i −0.176007 0.424919i 0.811115 0.584886i \(-0.198861\pi\)
−0.987122 + 0.159968i \(0.948861\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −22.9908 22.9908i −0.903861 0.903861i 0.0919063 0.995768i \(-0.470704\pi\)
−0.995768 + 0.0919063i \(0.970704\pi\)
\(648\) 0 0
\(649\) −5.54340 + 5.54340i −0.217597 + 0.217597i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.731559 + 0.303022i −0.0286281 + 0.0118582i −0.396952 0.917840i \(-0.629932\pi\)
0.368323 + 0.929698i \(0.379932\pi\)
\(654\) 0 0
\(655\) 37.5804 1.46839
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 3.48735 + 8.41921i 0.135848 + 0.327966i 0.977134 0.212624i \(-0.0682010\pi\)
−0.841286 + 0.540590i \(0.818201\pi\)
\(660\) 0 0
\(661\) 22.6551 + 9.38406i 0.881182 + 0.364998i 0.776955 0.629556i \(-0.216763\pi\)
0.104227 + 0.994554i \(0.466763\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −12.3859 + 12.3859i −0.480305 + 0.480305i
\(666\) 0 0
\(667\) 9.62334 + 3.98612i 0.372617 + 0.154343i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −8.66062 −0.334340
\(672\) 0 0
\(673\) −17.3835 −0.670084 −0.335042 0.942203i \(-0.608751\pi\)
−0.335042 + 0.942203i \(0.608751\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 39.4502 + 16.3408i 1.51620 + 0.628029i 0.976825 0.214040i \(-0.0686621\pi\)
0.539371 + 0.842068i \(0.318662\pi\)
\(678\) 0 0
\(679\) 17.9483 17.9483i 0.688793 0.688793i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 40.6471 + 16.8366i 1.55532 + 0.644234i 0.984268 0.176682i \(-0.0565365\pi\)
0.571049 + 0.820916i \(0.306536\pi\)
\(684\) 0 0
\(685\) −16.7591 40.4602i −0.640334 1.54590i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −30.8512 −1.17534
\(690\) 0 0
\(691\) 0.769203 0.318614i 0.0292619 0.0121207i −0.368005 0.929824i \(-0.619959\pi\)
0.397266 + 0.917703i \(0.369959\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.130751 0.130751i 0.00495965 0.00495965i
\(696\) 0 0
\(697\) 6.58141 + 6.58141i 0.249289 + 0.249289i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −10.7572 25.9701i −0.406292 0.980876i −0.986105 0.166126i \(-0.946874\pi\)
0.579812 0.814750i \(-0.303126\pi\)
\(702\) 0 0
\(703\) 23.3482i 0.880595i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 3.47140 1.43790i 0.130555 0.0540778i
\(708\) 0 0
\(709\) −13.7081 + 33.0944i −0.514820 + 1.24289i 0.426229 + 0.904615i \(0.359842\pi\)
−0.941049 + 0.338270i \(0.890158\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −36.4497 36.4497i −1.36505 1.36505i
\(714\) 0 0
\(715\) −3.49008 + 8.42579i −0.130522 + 0.315107i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 24.7319i 0.922345i 0.887311 + 0.461172i \(0.152571\pi\)
−0.887311 + 0.461172i \(0.847429\pi\)
\(720\) 0 0
\(721\) 33.0163i 1.22959i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.703060 1.69734i 0.0261110 0.0630375i
\(726\) 0 0
\(727\) −4.89101 4.89101i −0.181397 0.181397i 0.610567 0.791965i \(-0.290942\pi\)
−0.791965 + 0.610567i \(0.790942\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 1.32126 3.18980i 0.0488685 0.117979i
\(732\) 0 0
\(733\) −10.2058 + 4.22736i −0.376958 + 0.156141i −0.563114 0.826379i \(-0.690397\pi\)
0.186156 + 0.982520i \(0.440397\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 2.88540i 0.106285i
\(738\) 0 0
\(739\) −1.71029 4.12900i −0.0629139 0.151888i 0.889296 0.457332i \(-0.151195\pi\)
−0.952210 + 0.305445i \(0.901195\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −12.6977 12.6977i −0.465832 0.465832i 0.434729 0.900561i \(-0.356844\pi\)
−0.900561 + 0.434729i \(0.856844\pi\)
\(744\) 0 0
\(745\) 20.7405 20.7405i 0.759873 0.759873i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −53.3272 + 22.0888i −1.94853 + 0.807108i
\(750\) 0 0
\(751\) 25.3864 0.926362 0.463181 0.886264i \(-0.346708\pi\)
0.463181 + 0.886264i \(0.346708\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 7.83185 + 18.9078i 0.285030 + 0.688123i
\(756\) 0 0
\(757\) 48.9351 + 20.2696i 1.77858 + 0.736711i 0.993023 + 0.117918i \(0.0376220\pi\)
0.785554 + 0.618793i \(0.212378\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 7.18378 7.18378i 0.260412 0.260412i −0.564809 0.825221i \(-0.691050\pi\)
0.825221 + 0.564809i \(0.191050\pi\)
\(762\) 0 0
\(763\) 6.15530 + 2.54961i 0.222837 + 0.0923020i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 67.4708 2.43623
\(768\) 0 0
\(769\) −48.6570 −1.75462 −0.877309 0.479926i \(-0.840663\pi\)
−0.877309 + 0.479926i \(0.840663\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 7.43579 + 3.08000i 0.267447 + 0.110780i 0.512377 0.858761i \(-0.328765\pi\)
−0.244930 + 0.969541i \(0.578765\pi\)
\(774\) 0 0
\(775\) −6.42890 + 6.42890i −0.230933 + 0.230933i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −24.3087 10.0690i −0.870951 0.360760i
\(780\) 0 0
\(781\) −3.94552 9.52534i −0.141182 0.340843i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 23.1411 0.825940
\(786\) 0 0
\(787\) −14.9915 + 6.20966i −0.534388 + 0.221351i −0.633524 0.773723i \(-0.718392\pi\)
0.0991360 + 0.995074i \(0.468392\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 1.69722 1.69722i 0.0603464 0.0603464i
\(792\) 0 0
\(793\) 52.7058 + 52.7058i 1.87164 + 1.87164i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 2.43692 + 5.88325i 0.0863202 + 0.208395i 0.961145 0.276044i \(-0.0890236\pi\)
−0.874825 + 0.484439i \(0.839024\pi\)
\(798\) 0 0
\(799\) 3.57401i 0.126439i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 4.65177 1.92682i 0.164157 0.0679962i
\(804\) 0 0
\(805\) −17.3340 + 41.8480i −0.610944 + 1.47495i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 9.30765 + 9.30765i 0.327240 + 0.327240i 0.851536 0.524296i \(-0.175672\pi\)
−0.524296 + 0.851536i \(0.675672\pi\)
\(810\) 0 0
\(811\) 8.10599 19.5696i 0.284640 0.687181i −0.715292 0.698825i \(-0.753706\pi\)
0.999932 + 0.0116440i \(0.00370648\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 16.7023i 0.585056i
\(816\) 0 0
\(817\) 9.76026i 0.341468i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 3.81353 9.20668i 0.133093 0.321315i −0.843257 0.537511i \(-0.819365\pi\)
0.976350 + 0.216195i \(0.0693648\pi\)
\(822\) 0 0
\(823\) 16.5761 + 16.5761i 0.577808 + 0.577808i 0.934299 0.356491i \(-0.116027\pi\)
−0.356491 + 0.934299i \(0.616027\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 11.1677 26.9613i 0.388340 0.937537i −0.601951 0.798533i \(-0.705610\pi\)
0.990292 0.139004i \(-0.0443901\pi\)
\(828\) 0 0
\(829\) 8.82768 3.65654i 0.306598 0.126997i −0.224080 0.974571i \(-0.571938\pi\)
0.530678 + 0.847574i \(0.321938\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 3.79777i 0.131585i
\(834\) 0 0
\(835\) 0.0787391 + 0.190093i 0.00272488 + 0.00657844i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 4.55814 + 4.55814i 0.157364 + 0.157364i 0.781398 0.624033i \(-0.214507\pi\)
−0.624033 + 0.781398i \(0.714507\pi\)
\(840\) 0 0
\(841\) 18.9734 18.9734i 0.654257 0.654257i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 49.2516 20.4007i 1.69431 0.701805i
\(846\) 0 0
\(847\) −34.5485 −1.18710
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −23.1052 55.7809i −0.792037 1.91215i
\(852\) 0 0
\(853\) 13.7268 + 5.68583i 0.469997 + 0.194679i 0.605095 0.796153i \(-0.293135\pi\)
−0.135098 + 0.990832i \(0.543135\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 11.1744 11.1744i 0.381711 0.381711i −0.490007 0.871718i \(-0.663006\pi\)
0.871718 + 0.490007i \(0.163006\pi\)
\(858\) 0 0
\(859\) −39.1836 16.2304i −1.33693 0.553773i −0.404304 0.914625i \(-0.632486\pi\)
−0.932623 + 0.360851i \(0.882486\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −22.2298 −0.756710 −0.378355 0.925661i \(-0.623510\pi\)
−0.378355 + 0.925661i \(0.623510\pi\)
\(864\) 0 0
\(865\) −44.0379 −1.49733
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −7.52760 3.11803i −0.255356 0.105772i
\(870\) 0 0
\(871\) 17.5597 17.5597i 0.594987 0.594987i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 36.9553 + 15.3074i 1.24932 + 0.517484i
\(876\) 0 0
\(877\) 3.13025 + 7.55709i 0.105701 + 0.255185i 0.967877 0.251424i \(-0.0808989\pi\)
−0.862176 + 0.506609i \(0.830899\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 4.77921 0.161016 0.0805078 0.996754i \(-0.474346\pi\)
0.0805078 + 0.996754i \(0.474346\pi\)
\(882\) 0 0
\(883\) 45.1752 18.7122i 1.52027 0.629716i 0.542622 0.839977i \(-0.317431\pi\)
0.977645 + 0.210261i \(0.0674314\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 6.92890 6.92890i 0.232650 0.232650i −0.581148 0.813798i \(-0.697396\pi\)
0.813798 + 0.581148i \(0.197396\pi\)
\(888\) 0 0
\(889\) −27.0368 27.0368i −0.906784 0.906784i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −3.86641 9.33435i −0.129385 0.312362i
\(894\) 0 0
\(895\) 22.0453i 0.736894i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 9.91000 4.10486i 0.330517 0.136905i
\(900\) 0 0
\(901\) 1.79503 4.33358i 0.0598011 0.144373i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 6.35622 + 6.35622i 0.211288 + 0.211288i
\(906\) 0 0
\(907\) −14.4242 + 34.8230i −0.478946 + 1.15628i 0.481157 + 0.876634i \(0.340217\pi\)
−0.960104 + 0.279644i \(0.909783\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 44.7402i 1.48231i 0.671335 + 0.741154i \(0.265721\pi\)
−0.671335 + 0.741154i \(0.734279\pi\)
\(912\) 0 0
\(913\) 2.22390i 0.0736004i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −24.5388 + 59.2418i −0.810342 + 1.95634i
\(918\) 0 0
\(919\) −25.4709 25.4709i −0.840207 0.840207i 0.148678 0.988886i \(-0.452498\pi\)
−0.988886 + 0.148678i \(0.952498\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −33.9570 + 81.9795i −1.11771 + 2.69839i
\(924\) 0 0
\(925\) −9.83848 + 4.07523i −0.323487 + 0.133993i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 23.0747i 0.757058i 0.925589 + 0.378529i \(0.123570\pi\)
−0.925589 + 0.378529i \(0.876430\pi\)
\(930\) 0 0
\(931\) −4.10848 9.91875i −0.134650 0.325074i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −0.980484 0.980484i −0.0320652 0.0320652i
\(936\) 0 0
\(937\) 6.57961 6.57961i 0.214947 0.214947i −0.591418 0.806365i \(-0.701432\pi\)
0.806365 + 0.591418i \(0.201432\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −40.5076 + 16.7788i −1.32051 + 0.546973i −0.927934 0.372746i \(-0.878416\pi\)
−0.392577 + 0.919719i \(0.628416\pi\)
\(942\) 0 0
\(943\) −68.0399 −2.21569
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −21.7966 52.6218i −0.708296 1.70998i −0.704216 0.709986i \(-0.748701\pi\)
−0.00407986 0.999992i \(-0.501299\pi\)
\(948\) 0 0
\(949\) −40.0353 16.5831i −1.29960 0.538312i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 24.5821 24.5821i 0.796293 0.796293i −0.186216 0.982509i \(-0.559622\pi\)
0.982509 + 0.186216i \(0.0596224\pi\)
\(954\) 0 0
\(955\) −39.8574 16.5095i −1.28976 0.534234i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 74.7248 2.41299
\(960\) 0 0
\(961\) −22.0832 −0.712362
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −19.4811 8.06932i −0.627118 0.259761i
\(966\) 0 0
\(967\) 19.1878 19.1878i 0.617037 0.617037i −0.327734 0.944770i \(-0.606285\pi\)
0.944770 + 0.327734i \(0.106285\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −35.5982 14.7453i −1.14240 0.473198i −0.270422 0.962742i \(-0.587163\pi\)
−0.871979 + 0.489544i \(0.837163\pi\)
\(972\) 0 0
\(973\) 0.120740 + 0.291492i 0.00387074 + 0.00934479i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 10.7488 0.343885 0.171943 0.985107i \(-0.444996\pi\)
0.171943 + 0.985107i \(0.444996\pi\)
\(978\) 0 0
\(979\) −6.59672 + 2.73245i −0.210832 + 0.0873295i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 15.2745 15.2745i 0.487181 0.487181i −0.420234 0.907416i \(-0.638052\pi\)
0.907416 + 0.420234i \(0.138052\pi\)
\(984\) 0 0
\(985\) 9.04516 + 9.04516i 0.288203 + 0.288203i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 9.65868 + 23.3181i 0.307128 + 0.741473i
\(990\) 0 0
\(991\) 15.5708i 0.494622i 0.968936 + 0.247311i \(0.0795469\pi\)
−0.968936 + 0.247311i \(0.920453\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 25.5836 10.5971i 0.811053 0.335949i
\(996\) 0 0
\(997\) −1.71754 + 4.14652i −0.0543951 + 0.131321i −0.948741 0.316055i \(-0.897642\pi\)
0.894346 + 0.447376i \(0.147642\pi\)
\(998\) 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 1152.2.w.a.719.2 32
3.2 odd 2 1152.2.w.b.719.7 32
4.3 odd 2 288.2.w.b.107.3 yes 32
12.11 even 2 288.2.w.a.107.6 yes 32
32.3 odd 8 1152.2.w.b.431.7 32
32.29 even 8 288.2.w.a.35.6 32
96.29 odd 8 288.2.w.b.35.3 yes 32
96.35 even 8 inner 1152.2.w.a.431.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
288.2.w.a.35.6 32 32.29 even 8
288.2.w.a.107.6 yes 32 12.11 even 2
288.2.w.b.35.3 yes 32 96.29 odd 8
288.2.w.b.107.3 yes 32 4.3 odd 2
1152.2.w.a.431.2 32 96.35 even 8 inner
1152.2.w.a.719.2 32 1.1 even 1 trivial
1152.2.w.b.431.7 32 32.3 odd 8
1152.2.w.b.719.7 32 3.2 odd 2