Properties

Label 1152.2.l.a.287.7
Level $1152$
Weight $2$
Character 1152.287
Analytic conductor $9.199$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1152,2,Mod(287,1152)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1152.287");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1152 = 2^{7} \cdot 3^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1152.l (of order \(4\), degree \(2\), 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: \(16\)
Relative dimension: \(8\) over \(\Q(i)\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 4x^{14} + 6x^{12} - 12x^{10} + 33x^{8} - 48x^{6} + 96x^{4} - 256x^{2} + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{18} \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 287.7
Root \(-0.944649 + 1.05244i\) of defining polynomial
Character \(\chi\) \(=\) 1152.287
Dual form 1152.2.l.a.863.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.10489 - 2.10489i) q^{5} -4.40731 q^{7} +O(q^{10})\) \(q+(2.10489 - 2.10489i) q^{5} -4.40731 q^{7} +(-0.215589 - 0.215589i) q^{11} +(2.73544 - 2.73544i) q^{13} +2.36438i q^{17} +(-0.758681 - 0.758681i) q^{19} -1.75549i q^{23} -3.86110i q^{25} +(-5.54221 - 5.54221i) q^{29} -9.01709i q^{31} +(-9.27690 + 9.27690i) q^{35} +(-3.10242 - 3.10242i) q^{37} -10.1014 q^{41} +(3.54621 - 3.54621i) q^{43} -3.90136 q^{47} +12.4244 q^{49} +(-2.71378 + 2.71378i) q^{53} -0.907583 q^{55} +(3.40445 + 3.40445i) q^{59} +(1.75868 - 1.75868i) q^{61} -11.5156i q^{65} +(-9.11951 - 9.11951i) q^{67} +11.8897i q^{71} +0.482639i q^{73} +(0.950169 + 0.950169i) q^{77} +6.88995i q^{79} +(4.79951 - 4.79951i) q^{83} +(4.97676 + 4.97676i) q^{85} +7.00534 q^{89} +(-12.0559 + 12.0559i) q^{91} -3.19387 q^{95} -3.34374 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 16 q^{19} + 32 q^{43} + 16 q^{49} - 64 q^{55} + 32 q^{61} + 16 q^{67} + 32 q^{85} - 48 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(127\) \(641\) \(901\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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
\(5\) 2.10489 2.10489i 0.941334 0.941334i −0.0570377 0.998372i \(-0.518166\pi\)
0.998372 + 0.0570377i \(0.0181655\pi\)
\(6\) 0 0
\(7\) −4.40731 −1.66581 −0.832904 0.553418i \(-0.813323\pi\)
−0.832904 + 0.553418i \(0.813323\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −0.215589 0.215589i −0.0650026 0.0650026i 0.673858 0.738861i \(-0.264636\pi\)
−0.738861 + 0.673858i \(0.764636\pi\)
\(12\) 0 0
\(13\) 2.73544 2.73544i 0.758675 0.758675i −0.217406 0.976081i \(-0.569760\pi\)
0.976081 + 0.217406i \(0.0697597\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 2.36438i 0.573447i 0.958013 + 0.286724i \(0.0925661\pi\)
−0.958013 + 0.286724i \(0.907434\pi\)
\(18\) 0 0
\(19\) −0.758681 0.758681i −0.174053 0.174053i 0.614704 0.788758i \(-0.289275\pi\)
−0.788758 + 0.614704i \(0.789275\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.75549i 0.366045i −0.983109 0.183023i \(-0.941412\pi\)
0.983109 0.183023i \(-0.0585881\pi\)
\(24\) 0 0
\(25\) 3.86110i 0.772221i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −5.54221 5.54221i −1.02916 1.02916i −0.999562 0.0296002i \(-0.990577\pi\)
−0.0296002 0.999562i \(-0.509423\pi\)
\(30\) 0 0
\(31\) 9.01709i 1.61952i −0.586763 0.809759i \(-0.699598\pi\)
0.586763 0.809759i \(-0.300402\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −9.27690 + 9.27690i −1.56808 + 1.56808i
\(36\) 0 0
\(37\) −3.10242 3.10242i −0.510035 0.510035i 0.404502 0.914537i \(-0.367445\pi\)
−0.914537 + 0.404502i \(0.867445\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −10.1014 −1.57757 −0.788785 0.614669i \(-0.789290\pi\)
−0.788785 + 0.614669i \(0.789290\pi\)
\(42\) 0 0
\(43\) 3.54621 3.54621i 0.540792 0.540792i −0.382969 0.923761i \(-0.625099\pi\)
0.923761 + 0.382969i \(0.125099\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.90136 −0.569072 −0.284536 0.958665i \(-0.591840\pi\)
−0.284536 + 0.958665i \(0.591840\pi\)
\(48\) 0 0
\(49\) 12.4244 1.77491
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −2.71378 + 2.71378i −0.372766 + 0.372766i −0.868484 0.495717i \(-0.834905\pi\)
0.495717 + 0.868484i \(0.334905\pi\)
\(54\) 0 0
\(55\) −0.907583 −0.122378
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 3.40445 + 3.40445i 0.443222 + 0.443222i 0.893093 0.449871i \(-0.148530\pi\)
−0.449871 + 0.893093i \(0.648530\pi\)
\(60\) 0 0
\(61\) 1.75868 1.75868i 0.225176 0.225176i −0.585498 0.810674i \(-0.699101\pi\)
0.810674 + 0.585498i \(0.199101\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 11.5156i 1.42833i
\(66\) 0 0
\(67\) −9.11951 9.11951i −1.11413 1.11413i −0.992587 0.121539i \(-0.961217\pi\)
−0.121539 0.992587i \(-0.538783\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 11.8897i 1.41105i 0.708684 + 0.705526i \(0.249289\pi\)
−0.708684 + 0.705526i \(0.750711\pi\)
\(72\) 0 0
\(73\) 0.482639i 0.0564886i 0.999601 + 0.0282443i \(0.00899163\pi\)
−0.999601 + 0.0282443i \(0.991008\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.950169 + 0.950169i 0.108282 + 0.108282i
\(78\) 0 0
\(79\) 6.88995i 0.775180i 0.921832 + 0.387590i \(0.126692\pi\)
−0.921832 + 0.387590i \(0.873308\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 4.79951 4.79951i 0.526814 0.526814i −0.392807 0.919621i \(-0.628496\pi\)
0.919621 + 0.392807i \(0.128496\pi\)
\(84\) 0 0
\(85\) 4.97676 + 4.97676i 0.539805 + 0.539805i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 7.00534 0.742564 0.371282 0.928520i \(-0.378918\pi\)
0.371282 + 0.928520i \(0.378918\pi\)
\(90\) 0 0
\(91\) −12.0559 + 12.0559i −1.26381 + 1.26381i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −3.19387 −0.327685
\(96\) 0 0
\(97\) −3.34374 −0.339506 −0.169753 0.985487i \(-0.554297\pi\)
−0.169753 + 0.985487i \(0.554297\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 1.76361 1.76361i 0.175486 0.175486i −0.613899 0.789385i \(-0.710400\pi\)
0.789385 + 0.613899i \(0.210400\pi\)
\(102\) 0 0
\(103\) −1.01709 −0.100217 −0.0501085 0.998744i \(-0.515957\pi\)
−0.0501085 + 0.998744i \(0.515957\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.33152 2.33152i −0.225396 0.225396i 0.585370 0.810766i \(-0.300949\pi\)
−0.810766 + 0.585370i \(0.800949\pi\)
\(108\) 0 0
\(109\) 8.07918 8.07918i 0.773845 0.773845i −0.204931 0.978776i \(-0.565697\pi\)
0.978776 + 0.204931i \(0.0656970\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 2.09677i 0.197247i −0.995125 0.0986237i \(-0.968556\pi\)
0.995125 0.0986237i \(-0.0314440\pi\)
\(114\) 0 0
\(115\) −3.69511 3.69511i −0.344571 0.344571i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 10.4206i 0.955253i
\(120\) 0 0
\(121\) 10.9070i 0.991549i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 2.39725 + 2.39725i 0.214416 + 0.214416i
\(126\) 0 0
\(127\) 10.2802i 0.912218i −0.889924 0.456109i \(-0.849243\pi\)
0.889924 0.456109i \(-0.150757\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 6.80891 6.80891i 0.594897 0.594897i −0.344053 0.938950i \(-0.611800\pi\)
0.938950 + 0.344053i \(0.111800\pi\)
\(132\) 0 0
\(133\) 3.34374 + 3.34374i 0.289939 + 0.289939i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 13.7922 1.17834 0.589172 0.808008i \(-0.299454\pi\)
0.589172 + 0.808008i \(0.299454\pi\)
\(138\) 0 0
\(139\) 13.1195 13.1195i 1.11278 1.11278i 0.120010 0.992773i \(-0.461707\pi\)
0.992773 0.120010i \(-0.0382927\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −1.17946 −0.0986317
\(144\) 0 0
\(145\) −23.3314 −1.93757
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −7.76174 + 7.76174i −0.635867 + 0.635867i −0.949533 0.313667i \(-0.898443\pi\)
0.313667 + 0.949533i \(0.398443\pi\)
\(150\) 0 0
\(151\) −0.202466 −0.0164765 −0.00823823 0.999966i \(-0.502622\pi\)
−0.00823823 + 0.999966i \(0.502622\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −18.9800 18.9800i −1.52451 1.52451i
\(156\) 0 0
\(157\) −3.75868 + 3.75868i −0.299975 + 0.299975i −0.841004 0.541029i \(-0.818035\pi\)
0.541029 + 0.841004i \(0.318035\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 7.73700i 0.609761i
\(162\) 0 0
\(163\) 13.2684 + 13.2684i 1.03926 + 1.03926i 0.999197 + 0.0400655i \(0.0127567\pi\)
0.0400655 + 0.999197i \(0.487243\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 20.1644i 1.56037i 0.625548 + 0.780186i \(0.284875\pi\)
−0.625548 + 0.780186i \(0.715125\pi\)
\(168\) 0 0
\(169\) 1.96528i 0.151175i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.98315 + 3.98315i 0.302833 + 0.302833i 0.842121 0.539288i \(-0.181307\pi\)
−0.539288 + 0.842121i \(0.681307\pi\)
\(174\) 0 0
\(175\) 17.0171i 1.28637i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 14.7182 14.7182i 1.10009 1.10009i 0.105688 0.994399i \(-0.466296\pi\)
0.994399 0.105688i \(-0.0337044\pi\)
\(180\) 0 0
\(181\) −3.26456 3.26456i −0.242653 0.242653i 0.575294 0.817947i \(-0.304888\pi\)
−0.817947 + 0.575294i \(0.804888\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −13.0605 −0.960227
\(186\) 0 0
\(187\) 0.509736 0.509736i 0.0372756 0.0372756i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 7.69868 0.557057 0.278528 0.960428i \(-0.410153\pi\)
0.278528 + 0.960428i \(0.410153\pi\)
\(192\) 0 0
\(193\) −3.51736 −0.253185 −0.126593 0.991955i \(-0.540404\pi\)
−0.126593 + 0.991955i \(0.540404\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −6.40456 + 6.40456i −0.456306 + 0.456306i −0.897441 0.441135i \(-0.854576\pi\)
0.441135 + 0.897441i \(0.354576\pi\)
\(198\) 0 0
\(199\) 23.3491 1.65517 0.827586 0.561339i \(-0.189714\pi\)
0.827586 + 0.561339i \(0.189714\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 24.4262 + 24.4262i 1.71439 + 1.71439i
\(204\) 0 0
\(205\) −21.2623 + 21.2623i −1.48502 + 1.48502i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 0.327127i 0.0226278i
\(210\) 0 0
\(211\) 6.63688 + 6.63688i 0.456901 + 0.456901i 0.897637 0.440736i \(-0.145282\pi\)
−0.440736 + 0.897637i \(0.645282\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 14.9287i 1.01813i
\(216\) 0 0
\(217\) 39.7411i 2.69780i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.46763 + 6.46763i 0.435060 + 0.435060i
\(222\) 0 0
\(223\) 13.2219i 0.885406i 0.896668 + 0.442703i \(0.145980\pi\)
−0.896668 + 0.442703i \(0.854020\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −16.4029 + 16.4029i −1.08870 + 1.08870i −0.0930369 + 0.995663i \(0.529657\pi\)
−0.995663 + 0.0930369i \(0.970343\pi\)
\(228\) 0 0
\(229\) 4.98677 + 4.98677i 0.329535 + 0.329535i 0.852410 0.522875i \(-0.175140\pi\)
−0.522875 + 0.852410i \(0.675140\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.05879 −0.0693634 −0.0346817 0.999398i \(-0.511042\pi\)
−0.0346817 + 0.999398i \(0.511042\pi\)
\(234\) 0 0
\(235\) −8.21193 + 8.21193i −0.535687 + 0.535687i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.317107 −0.0205119 −0.0102560 0.999947i \(-0.503265\pi\)
−0.0102560 + 0.999947i \(0.503265\pi\)
\(240\) 0 0
\(241\) 11.7334 0.755816 0.377908 0.925843i \(-0.376644\pi\)
0.377908 + 0.925843i \(0.376644\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 26.1520 26.1520i 1.67079 1.67079i
\(246\) 0 0
\(247\) −4.15065 −0.264100
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 7.02450 + 7.02450i 0.443382 + 0.443382i 0.893147 0.449765i \(-0.148492\pi\)
−0.449765 + 0.893147i \(0.648492\pi\)
\(252\) 0 0
\(253\) −0.378465 + 0.378465i −0.0237939 + 0.0237939i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 23.5830i 1.47107i 0.677487 + 0.735535i \(0.263069\pi\)
−0.677487 + 0.735535i \(0.736931\pi\)
\(258\) 0 0
\(259\) 13.6733 + 13.6733i 0.849621 + 0.849621i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 20.1370i 1.24170i −0.783928 0.620851i \(-0.786787\pi\)
0.783928 0.620851i \(-0.213213\pi\)
\(264\) 0 0
\(265\) 11.4244i 0.701796i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −8.62201 8.62201i −0.525693 0.525693i 0.393592 0.919285i \(-0.371232\pi\)
−0.919285 + 0.393592i \(0.871232\pi\)
\(270\) 0 0
\(271\) 2.18722i 0.132864i −0.997791 0.0664319i \(-0.978838\pi\)
0.997791 0.0664319i \(-0.0211615\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −0.832413 + 0.832413i −0.0501964 + 0.0501964i
\(276\) 0 0
\(277\) −8.64248 8.64248i −0.519277 0.519277i 0.398076 0.917352i \(-0.369678\pi\)
−0.917352 + 0.398076i \(0.869678\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 14.8081 0.883375 0.441688 0.897169i \(-0.354380\pi\)
0.441688 + 0.897169i \(0.354380\pi\)
\(282\) 0 0
\(283\) −6.12714 + 6.12714i −0.364221 + 0.364221i −0.865364 0.501144i \(-0.832913\pi\)
0.501144 + 0.865364i \(0.332913\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 44.5199 2.62793
\(288\) 0 0
\(289\) 11.4097 0.671158
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −11.8979 + 11.8979i −0.695080 + 0.695080i −0.963345 0.268265i \(-0.913550\pi\)
0.268265 + 0.963345i \(0.413550\pi\)
\(294\) 0 0
\(295\) 14.3320 0.834441
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −4.80204 4.80204i −0.277709 0.277709i
\(300\) 0 0
\(301\) −15.6293 + 15.6293i −0.900855 + 0.900855i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 7.40365i 0.423932i
\(306\) 0 0
\(307\) −4.91467 4.91467i −0.280495 0.280495i 0.552811 0.833306i \(-0.313555\pi\)
−0.833306 + 0.552811i \(0.813555\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 20.7712i 1.17783i −0.808195 0.588915i \(-0.799555\pi\)
0.808195 0.588915i \(-0.200445\pi\)
\(312\) 0 0
\(313\) 16.3897i 0.926400i −0.886254 0.463200i \(-0.846701\pi\)
0.886254 0.463200i \(-0.153299\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 22.3592 + 22.3592i 1.25582 + 1.25582i 0.953070 + 0.302749i \(0.0979044\pi\)
0.302749 + 0.953070i \(0.402096\pi\)
\(318\) 0 0
\(319\) 2.38968i 0.133796i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.79381 1.79381i 0.0998103 0.0998103i
\(324\) 0 0
\(325\) −10.5618 10.5618i −0.585865 0.585865i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 17.1945 0.947965
\(330\) 0 0
\(331\) 7.08533 7.08533i 0.389445 0.389445i −0.485044 0.874490i \(-0.661197\pi\)
0.874490 + 0.485044i \(0.161197\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −38.3911 −2.09753
\(336\) 0 0
\(337\) −23.3314 −1.27094 −0.635472 0.772124i \(-0.719195\pi\)
−0.635472 + 0.772124i \(0.719195\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.94399 + 1.94399i −0.105273 + 0.105273i
\(342\) 0 0
\(343\) −23.9070 −1.29086
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −21.2074 21.2074i −1.13847 1.13847i −0.988724 0.149751i \(-0.952153\pi\)
−0.149751 0.988724i \(-0.547847\pi\)
\(348\) 0 0
\(349\) −5.38022 + 5.38022i −0.287996 + 0.287996i −0.836288 0.548291i \(-0.815279\pi\)
0.548291 + 0.836288i \(0.315279\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 10.5163i 0.559727i 0.960040 + 0.279864i \(0.0902892\pi\)
−0.960040 + 0.279864i \(0.909711\pi\)
\(354\) 0 0
\(355\) 25.0266 + 25.0266i 1.32827 + 1.32827i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.7583i 0.620578i −0.950642 0.310289i \(-0.899574\pi\)
0.950642 0.310289i \(-0.100426\pi\)
\(360\) 0 0
\(361\) 17.8488i 0.939411i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 1.01590 + 1.01590i 0.0531747 + 0.0531747i
\(366\) 0 0
\(367\) 3.49973i 0.182684i −0.995820 0.0913422i \(-0.970884\pi\)
0.995820 0.0913422i \(-0.0291157\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 11.9605 11.9605i 0.620957 0.620957i
\(372\) 0 0
\(373\) −19.1831 19.1831i −0.993262 0.993262i 0.00671500 0.999977i \(-0.497863\pi\)
−0.999977 + 0.00671500i \(0.997863\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −30.3208 −1.56160
\(378\) 0 0
\(379\) 14.9977 14.9977i 0.770381 0.770381i −0.207792 0.978173i \(-0.566628\pi\)
0.978173 + 0.207792i \(0.0666278\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 30.4027 1.55351 0.776754 0.629805i \(-0.216865\pi\)
0.776754 + 0.629805i \(0.216865\pi\)
\(384\) 0 0
\(385\) 4.00000 0.203859
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 19.4571 19.4571i 0.986516 0.986516i −0.0133943 0.999910i \(-0.504264\pi\)
0.999910 + 0.0133943i \(0.00426365\pi\)
\(390\) 0 0
\(391\) 4.15065 0.209908
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 14.5026 + 14.5026i 0.729704 + 0.729704i
\(396\) 0 0
\(397\) 20.4339 20.4339i 1.02555 1.02555i 0.0258815 0.999665i \(-0.491761\pi\)
0.999665 0.0258815i \(-0.00823925\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 22.5671i 1.12695i 0.826133 + 0.563475i \(0.190536\pi\)
−0.826133 + 0.563475i \(0.809464\pi\)
\(402\) 0 0
\(403\) −24.6657 24.6657i −1.22869 1.22869i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 1.33770i 0.0663073i
\(408\) 0 0
\(409\) 9.78286i 0.483731i 0.970310 + 0.241866i \(0.0777593\pi\)
−0.970310 + 0.241866i \(0.922241\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −15.0045 15.0045i −0.738323 0.738323i
\(414\) 0 0
\(415\) 20.2048i 0.991817i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −9.09125 + 9.09125i −0.444137 + 0.444137i −0.893400 0.449263i \(-0.851687\pi\)
0.449263 + 0.893400i \(0.351687\pi\)
\(420\) 0 0
\(421\) 17.9862 + 17.9862i 0.876595 + 0.876595i 0.993181 0.116586i \(-0.0371949\pi\)
−0.116586 + 0.993181i \(0.537195\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 9.12913 0.442828
\(426\) 0 0
\(427\) −7.75106 + 7.75106i −0.375100 + 0.375100i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −30.7707 −1.48217 −0.741085 0.671411i \(-0.765689\pi\)
−0.741085 + 0.671411i \(0.765689\pi\)
\(432\) 0 0
\(433\) 3.49735 0.168072 0.0840360 0.996463i \(-0.473219\pi\)
0.0840360 + 0.996463i \(0.473219\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −1.33186 + 1.33186i −0.0637113 + 0.0637113i
\(438\) 0 0
\(439\) −21.1290 −1.00843 −0.504216 0.863578i \(-0.668218\pi\)
−0.504216 + 0.863578i \(0.668218\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −12.6022 12.6022i −0.598750 0.598750i 0.341230 0.939980i \(-0.389157\pi\)
−0.939980 + 0.341230i \(0.889157\pi\)
\(444\) 0 0
\(445\) 14.7454 14.7454i 0.699001 0.699001i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 9.98731i 0.471330i −0.971834 0.235665i \(-0.924273\pi\)
0.971834 0.235665i \(-0.0757268\pi\)
\(450\) 0 0
\(451\) 2.17775 + 2.17775i 0.102546 + 0.102546i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 50.7528i 2.37933i
\(456\) 0 0
\(457\) 15.2508i 0.713402i 0.934219 + 0.356701i \(0.116098\pi\)
−0.934219 + 0.356701i \(0.883902\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −14.3850 14.3850i −0.669976 0.669976i 0.287734 0.957710i \(-0.407098\pi\)
−0.957710 + 0.287734i \(0.907098\pi\)
\(462\) 0 0
\(463\) 22.1295i 1.02845i 0.857657 + 0.514223i \(0.171920\pi\)
−0.857657 + 0.514223i \(0.828080\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 4.79951 4.79951i 0.222095 0.222095i −0.587285 0.809380i \(-0.699803\pi\)
0.809380 + 0.587285i \(0.199803\pi\)
\(468\) 0 0
\(469\) 40.1926 + 40.1926i 1.85592 + 1.85592i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −1.52905 −0.0703058
\(474\) 0 0
\(475\) −2.92934 + 2.92934i −0.134408 + 0.134408i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −23.2801 −1.06369 −0.531847 0.846840i \(-0.678502\pi\)
−0.531847 + 0.846840i \(0.678502\pi\)
\(480\) 0 0
\(481\) −16.9730 −0.773902
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −7.03820 + 7.03820i −0.319588 + 0.319588i
\(486\) 0 0
\(487\) 21.0748 0.954990 0.477495 0.878635i \(-0.341545\pi\)
0.477495 + 0.878635i \(0.341545\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 26.1459 + 26.1459i 1.17995 + 1.17995i 0.979756 + 0.200194i \(0.0641571\pi\)
0.200194 + 0.979756i \(0.435843\pi\)
\(492\) 0 0
\(493\) 13.1039 13.1039i 0.590170 0.590170i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 52.4018i 2.35054i
\(498\) 0 0
\(499\) −21.0195 21.0195i −0.940961 0.940961i 0.0573910 0.998352i \(-0.481722\pi\)
−0.998352 + 0.0573910i \(0.981722\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 44.4925i 1.98382i 0.126929 + 0.991912i \(0.459488\pi\)
−0.126929 + 0.991912i \(0.540512\pi\)
\(504\) 0 0
\(505\) 7.42440i 0.330382i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −11.7664 11.7664i −0.521536 0.521536i 0.396499 0.918035i \(-0.370225\pi\)
−0.918035 + 0.396499i \(0.870225\pi\)
\(510\) 0 0
\(511\) 2.12714i 0.0940991i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −2.14086 + 2.14086i −0.0943377 + 0.0943377i
\(516\) 0 0
\(517\) 0.841092 + 0.841092i 0.0369912 + 0.0369912i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −29.6216 −1.29775 −0.648873 0.760897i \(-0.724759\pi\)
−0.648873 + 0.760897i \(0.724759\pi\)
\(522\) 0 0
\(523\) −4.96353 + 4.96353i −0.217040 + 0.217040i −0.807250 0.590210i \(-0.799045\pi\)
0.590210 + 0.807250i \(0.299045\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 21.3199 0.928708
\(528\) 0 0
\(529\) 19.9183 0.866011
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −27.6317 + 27.6317i −1.19686 + 1.19686i
\(534\) 0 0
\(535\) −9.81517 −0.424347
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −2.67857 2.67857i −0.115374 0.115374i
\(540\) 0 0
\(541\) −10.0792 + 10.0792i −0.433338 + 0.433338i −0.889762 0.456424i \(-0.849130\pi\)
0.456424 + 0.889762i \(0.349130\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 34.0115i 1.45689i
\(546\) 0 0
\(547\) −2.48797 2.48797i −0.106378 0.106378i 0.651914 0.758293i \(-0.273966\pi\)
−0.758293 + 0.651914i \(0.773966\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 8.40953i 0.358258i
\(552\) 0 0
\(553\) 30.3662i 1.29130i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 24.2575 + 24.2575i 1.02782 + 1.02782i 0.999602 + 0.0282205i \(0.00898407\pi\)
0.0282205 + 0.999602i \(0.491016\pi\)
\(558\) 0 0
\(559\) 19.4009i 0.820570i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −14.4061 + 14.4061i −0.607143 + 0.607143i −0.942198 0.335055i \(-0.891245\pi\)
0.335055 + 0.942198i \(0.391245\pi\)
\(564\) 0 0
\(565\) −4.41346 4.41346i −0.185676 0.185676i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 33.5254 1.40546 0.702729 0.711457i \(-0.251964\pi\)
0.702729 + 0.711457i \(0.251964\pi\)
\(570\) 0 0
\(571\) −14.5368 + 14.5368i −0.608348 + 0.608348i −0.942514 0.334167i \(-0.891545\pi\)
0.334167 + 0.942514i \(0.391545\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6.77813 −0.282668
\(576\) 0 0
\(577\) 20.3662 0.847855 0.423927 0.905696i \(-0.360651\pi\)
0.423927 + 0.905696i \(0.360651\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −21.1529 + 21.1529i −0.877571 + 0.877571i
\(582\) 0 0
\(583\) 1.17012 0.0484616
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −17.4809 17.4809i −0.721512 0.721512i 0.247401 0.968913i \(-0.420424\pi\)
−0.968913 + 0.247401i \(0.920424\pi\)
\(588\) 0 0
\(589\) −6.84109 + 6.84109i −0.281882 + 0.281882i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 25.6632i 1.05386i 0.849908 + 0.526930i \(0.176657\pi\)
−0.849908 + 0.526930i \(0.823343\pi\)
\(594\) 0 0
\(595\) −21.9341 21.9341i −0.899212 0.899212i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 22.4652i 0.917902i −0.888461 0.458951i \(-0.848225\pi\)
0.888461 0.458951i \(-0.151775\pi\)
\(600\) 0 0
\(601\) 31.8106i 1.29758i −0.760967 0.648790i \(-0.775275\pi\)
0.760967 0.648790i \(-0.224725\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −22.9581 22.9581i −0.933379 0.933379i
\(606\) 0 0
\(607\) 14.9829i 0.608138i −0.952650 0.304069i \(-0.901655\pi\)
0.952650 0.304069i \(-0.0983453\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −10.6720 + 10.6720i −0.431741 + 0.431741i
\(612\) 0 0
\(613\) −25.6734 25.6734i −1.03694 1.03694i −0.999291 0.0376494i \(-0.988013\pi\)
−0.0376494 0.999291i \(-0.511987\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −27.1598 −1.09341 −0.546705 0.837325i \(-0.684118\pi\)
−0.546705 + 0.837325i \(0.684118\pi\)
\(618\) 0 0
\(619\) 29.4244 29.4244i 1.18267 1.18267i 0.203616 0.979051i \(-0.434731\pi\)
0.979051 0.203616i \(-0.0652693\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −30.8747 −1.23697
\(624\) 0 0
\(625\) 29.3974 1.17590
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 7.33532 7.33532i 0.292478 0.292478i
\(630\) 0 0
\(631\) −7.84697 −0.312383 −0.156191 0.987727i \(-0.549922\pi\)
−0.156191 + 0.987727i \(0.549922\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −21.6386 21.6386i −0.858702 0.858702i
\(636\) 0 0
\(637\) 33.9862 33.9862i 1.34658 1.34658i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 37.7956i 1.49284i −0.665477 0.746418i \(-0.731772\pi\)
0.665477 0.746418i \(-0.268228\pi\)
\(642\) 0 0
\(643\) −27.3026 27.3026i −1.07671 1.07671i −0.996802 0.0799071i \(-0.974538\pi\)
−0.0799071 0.996802i \(-0.525462\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.100686i 0.00395836i 0.999998 + 0.00197918i \(0.000629993\pi\)
−0.999998 + 0.00197918i \(0.999370\pi\)
\(648\) 0 0
\(649\) 1.46793i 0.0576212i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −9.10477 9.10477i −0.356297 0.356297i 0.506149 0.862446i \(-0.331069\pi\)
−0.862446 + 0.506149i \(0.831069\pi\)
\(654\) 0 0
\(655\) 28.6640i 1.11999i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 14.6141 14.6141i 0.569285 0.569285i −0.362643 0.931928i \(-0.618126\pi\)
0.931928 + 0.362643i \(0.118126\pi\)
\(660\) 0 0
\(661\) −5.87057 5.87057i −0.228339 0.228339i 0.583660 0.811998i \(-0.301620\pi\)
−0.811998 + 0.583660i \(0.801620\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 14.0764 0.545860
\(666\) 0 0
\(667\) −9.72929 + 9.72929i −0.376720 + 0.376720i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −0.758305 −0.0292741
\(672\) 0 0
\(673\) −27.3515 −1.05432 −0.527161 0.849766i \(-0.676743\pi\)
−0.527161 + 0.849766i \(0.676743\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 31.2462 31.2462i 1.20089 1.20089i 0.226992 0.973897i \(-0.427111\pi\)
0.973897 0.226992i \(-0.0728891\pi\)
\(678\) 0 0
\(679\) 14.7369 0.565551
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 15.0378 + 15.0378i 0.575406 + 0.575406i 0.933634 0.358228i \(-0.116619\pi\)
−0.358228 + 0.933634i \(0.616619\pi\)
\(684\) 0 0
\(685\) 29.0310 29.0310i 1.10922 1.10922i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 14.8468i 0.565617i
\(690\) 0 0
\(691\) −4.24894 4.24894i −0.161637 0.161637i 0.621654 0.783292i \(-0.286461\pi\)
−0.783292 + 0.621654i \(0.786461\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 55.2302i 2.09500i
\(696\) 0 0
\(697\) 23.8835i 0.904653i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 23.4629 + 23.4629i 0.886183 + 0.886183i 0.994154 0.107971i \(-0.0344354\pi\)
−0.107971 + 0.994154i \(0.534435\pi\)
\(702\) 0 0
\(703\) 4.70750i 0.177547i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −7.77278 + 7.77278i −0.292326 + 0.292326i
\(708\) 0 0
\(709\) −2.79314 2.79314i −0.104898 0.104898i 0.652710 0.757608i \(-0.273632\pi\)
−0.757608 + 0.652710i \(0.773632\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −15.8294 −0.592816
\(714\) 0 0
\(715\) −2.48264 + 2.48264i −0.0928454 + 0.0928454i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −33.8130 −1.26101 −0.630507 0.776184i \(-0.717153\pi\)
−0.630507 + 0.776184i \(0.717153\pi\)
\(720\) 0 0
\(721\) 4.48264 0.166942
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −21.3990 + 21.3990i −0.794740 + 0.794740i
\(726\) 0 0
\(727\) −2.42732 −0.0900245 −0.0450122 0.998986i \(-0.514333\pi\)
−0.0450122 + 0.998986i \(0.514333\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.38460 + 8.38460i 0.310115 + 0.310115i
\(732\) 0 0
\(733\) −16.8596 + 16.8596i −0.622725 + 0.622725i −0.946227 0.323503i \(-0.895140\pi\)
0.323503 + 0.946227i \(0.395140\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 3.93214i 0.144842i
\(738\) 0 0
\(739\) −25.2243 25.2243i −0.927892 0.927892i 0.0696780 0.997570i \(-0.477803\pi\)
−0.997570 + 0.0696780i \(0.977803\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 33.4926i 1.22872i 0.789025 + 0.614361i \(0.210586\pi\)
−0.789025 + 0.614361i \(0.789414\pi\)
\(744\) 0 0
\(745\) 32.6752i 1.19713i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 10.2757 + 10.2757i 0.375467 + 0.375467i
\(750\) 0 0
\(751\) 17.9247i 0.654081i 0.945010 + 0.327040i \(0.106051\pi\)
−0.945010 + 0.327040i \(0.893949\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.426168 + 0.426168i −0.0155099 + 0.0155099i
\(756\) 0 0
\(757\) −3.10619 3.10619i −0.112896 0.112896i 0.648402 0.761298i \(-0.275438\pi\)
−0.761298 + 0.648402i \(0.775438\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.10917 0.0402073 0.0201037 0.999798i \(-0.493600\pi\)
0.0201037 + 0.999798i \(0.493600\pi\)
\(762\) 0 0
\(763\) −35.6075 + 35.6075i −1.28908 + 1.28908i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 18.6254 0.672523
\(768\) 0 0
\(769\) 22.4591 0.809897 0.404948 0.914340i \(-0.367289\pi\)
0.404948 + 0.914340i \(0.367289\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 22.6327 22.6327i 0.814041 0.814041i −0.171196 0.985237i \(-0.554763\pi\)
0.985237 + 0.171196i \(0.0547631\pi\)
\(774\) 0 0
\(775\) −34.8159 −1.25062
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 7.66372 + 7.66372i 0.274581 + 0.274581i
\(780\) 0 0
\(781\) 2.56330 2.56330i 0.0917221 0.0917221i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 15.8232i 0.564754i
\(786\) 0 0
\(787\) 38.6505 + 38.6505i 1.37774 + 1.37774i 0.848425 + 0.529315i \(0.177551\pi\)
0.529315 + 0.848425i \(0.322449\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 9.24111i 0.328576i
\(792\) 0 0
\(793\) 9.62153i 0.341671i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −37.8969 37.8969i −1.34238 1.34238i −0.893689 0.448686i \(-0.851892\pi\)
−0.448686 0.893689i \(-0.648108\pi\)
\(798\) 0 0
\(799\) 9.22432i 0.326333i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0.104052 0.104052i 0.00367191 0.00367191i
\(804\) 0 0
\(805\) 16.2855 + 16.2855i 0.573989 + 0.573989i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 27.0719 0.951799 0.475899 0.879500i \(-0.342123\pi\)
0.475899 + 0.879500i \(0.342123\pi\)
\(810\) 0 0
\(811\) 19.0554 19.0554i 0.669126 0.669126i −0.288388 0.957514i \(-0.593119\pi\)
0.957514 + 0.288388i \(0.0931193\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 55.8571 1.95659
\(816\) 0 0
\(817\) −5.38088 −0.188253
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 37.5393 37.5393i 1.31013 1.31013i 0.388817 0.921315i \(-0.372884\pi\)
0.921315 0.388817i \(-0.127116\pi\)
\(822\) 0 0
\(823\) −27.9589 −0.974584 −0.487292 0.873239i \(-0.662015\pi\)
−0.487292 + 0.873239i \(0.662015\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 2.04182 + 2.04182i 0.0710011 + 0.0710011i 0.741716 0.670715i \(-0.234012\pi\)
−0.670715 + 0.741716i \(0.734012\pi\)
\(828\) 0 0
\(829\) −34.5808 + 34.5808i −1.20104 + 1.20104i −0.227188 + 0.973851i \(0.572953\pi\)
−0.973851 + 0.227188i \(0.927047\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 29.3760i 1.01782i
\(834\) 0 0
\(835\) 42.4439 + 42.4439i 1.46883 + 1.46883i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0.865723i 0.0298881i 0.999888 + 0.0149440i \(0.00475701\pi\)
−0.999888 + 0.0149440i \(0.995243\pi\)
\(840\) 0 0
\(841\) 32.4321i 1.11835i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.13669 4.13669i −0.142306 0.142306i
\(846\) 0 0
\(847\) 48.0707i 1.65173i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −5.44628 + 5.44628i −0.186696 + 0.186696i
\(852\) 0 0
\(853\) 14.4262 + 14.4262i 0.493942 + 0.493942i 0.909546 0.415604i \(-0.136430\pi\)
−0.415604 + 0.909546i \(0.636430\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −37.6532 −1.28621 −0.643105 0.765778i \(-0.722354\pi\)
−0.643105 + 0.765778i \(0.722354\pi\)
\(858\) 0 0
\(859\) 38.7470 38.7470i 1.32203 1.32203i 0.409901 0.912130i \(-0.365563\pi\)
0.912130 0.409901i \(-0.134437\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 14.8672 0.506085 0.253043 0.967455i \(-0.418569\pi\)
0.253043 + 0.967455i \(0.418569\pi\)
\(864\) 0 0
\(865\) 16.7681 0.570134
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 1.48540 1.48540i 0.0503887 0.0503887i
\(870\) 0 0
\(871\) −49.8918 −1.69052
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −10.5654 10.5654i −0.357176 0.357176i
\(876\) 0 0
\(877\) 13.7699 13.7699i 0.464976 0.464976i −0.435306 0.900283i \(-0.643360\pi\)
0.900283 + 0.435306i \(0.143360\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 20.6232i 0.694812i 0.937715 + 0.347406i \(0.112937\pi\)
−0.937715 + 0.347406i \(0.887063\pi\)
\(882\) 0 0
\(883\) 41.5416 + 41.5416i 1.39799 + 1.39799i 0.805802 + 0.592185i \(0.201735\pi\)
0.592185 + 0.805802i \(0.298265\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 7.44312i 0.249916i −0.992162 0.124958i \(-0.960120\pi\)
0.992162 0.124958i \(-0.0398795\pi\)
\(888\) 0 0
\(889\) 45.3079i 1.51958i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 2.95989 + 2.95989i 0.0990489 + 0.0990489i
\(894\) 0 0
\(895\) 61.9602i 2.07110i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −49.9746 + 49.9746i −1.66675 + 1.66675i
\(900\) 0 0
\(901\) −6.41642 6.41642i −0.213762 0.213762i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −13.7431 −0.456835
\(906\) 0 0
\(907\) −3.75106 + 3.75106i −0.124552 + 0.124552i −0.766635 0.642083i \(-0.778070\pi\)
0.642083 + 0.766635i \(0.278070\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 29.9816 0.993334 0.496667 0.867941i \(-0.334557\pi\)
0.496667 + 0.867941i \(0.334557\pi\)
\(912\) 0 0
\(913\) −2.06944 −0.0684886
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −30.0090 + 30.0090i −0.990984 + 0.990984i
\(918\) 0 0
\(919\) 38.1402 1.25813 0.629064 0.777353i \(-0.283438\pi\)
0.629064 + 0.777353i \(0.283438\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 32.5237 + 32.5237i 1.07053 + 1.07053i
\(924\) 0 0
\(925\) −11.9788 + 11.9788i −0.393860 + 0.393860i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 13.8738i 0.455183i 0.973757 + 0.227592i \(0.0730851\pi\)
−0.973757 + 0.227592i \(0.926915\pi\)
\(930\) 0 0
\(931\) −9.42615 9.42615i −0.308930 0.308930i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 2.14587i 0.0701775i
\(936\) 0 0
\(937\) 26.4097i 0.862767i −0.902169 0.431384i \(-0.858026\pi\)
0.902169 0.431384i \(-0.141974\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 4.91123 + 4.91123i 0.160102 + 0.160102i 0.782612 0.622510i \(-0.213887\pi\)
−0.622510 + 0.782612i \(0.713887\pi\)
\(942\) 0 0
\(943\) 17.7329i 0.577462i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 6.84386 6.84386i 0.222396 0.222396i −0.587111 0.809507i \(-0.699735\pi\)
0.809507 + 0.587111i \(0.199735\pi\)
\(948\) 0 0
\(949\) 1.32023 + 1.32023i 0.0428565 + 0.0428565i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 4.33045 0.140277 0.0701386 0.997537i \(-0.477656\pi\)
0.0701386 + 0.997537i \(0.477656\pi\)
\(954\) 0 0
\(955\) 16.2048 16.2048i 0.524377 0.524377i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −60.7864 −1.96289
\(960\) 0 0
\(961\) −50.3079 −1.62284
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −7.40365 + 7.40365i −0.238332 + 0.238332i
\(966\) 0 0
\(967\) 40.6664 1.30774 0.653871 0.756606i \(-0.273144\pi\)
0.653871 + 0.756606i \(0.273144\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −24.0742 24.0742i −0.772577 0.772577i 0.205979 0.978556i \(-0.433962\pi\)
−0.978556 + 0.205979i \(0.933962\pi\)
\(972\) 0 0
\(973\) −57.8218 + 57.8218i −1.85368 + 1.85368i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 21.0381i 0.673068i −0.941671 0.336534i \(-0.890745\pi\)
0.941671 0.336534i \(-0.109255\pi\)
\(978\) 0 0
\(979\) −1.51028 1.51028i −0.0482686 0.0482686i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 14.1206i 0.450376i −0.974315 0.225188i \(-0.927700\pi\)
0.974315 0.225188i \(-0.0722997\pi\)
\(984\) 0 0
\(985\) 26.9618i 0.859074i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −6.22534 6.22534i −0.197954 0.197954i
\(990\) 0 0
\(991\) 33.3338i 1.05888i 0.848346 + 0.529442i \(0.177599\pi\)
−0.848346 + 0.529442i \(0.822401\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 49.1472 49.1472i 1.55807 1.55807i
\(996\) 0 0
\(997\) −24.8358 24.8358i −0.786559 0.786559i 0.194369 0.980928i \(-0.437734\pi\)
−0.980928 + 0.194369i \(0.937734\pi\)
\(998\) 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.l.a.287.7 16
3.2 odd 2 inner 1152.2.l.a.287.2 16
4.3 odd 2 1152.2.l.b.287.7 16
8.3 odd 2 576.2.l.a.143.2 16
8.5 even 2 144.2.l.a.107.1 yes 16
12.11 even 2 1152.2.l.b.287.2 16
16.3 odd 4 inner 1152.2.l.a.863.2 16
16.5 even 4 576.2.l.a.431.7 16
16.11 odd 4 144.2.l.a.35.8 yes 16
16.13 even 4 1152.2.l.b.863.2 16
24.5 odd 2 144.2.l.a.107.8 yes 16
24.11 even 2 576.2.l.a.143.7 16
48.5 odd 4 576.2.l.a.431.2 16
48.11 even 4 144.2.l.a.35.1 16
48.29 odd 4 1152.2.l.b.863.7 16
48.35 even 4 inner 1152.2.l.a.863.7 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
144.2.l.a.35.1 16 48.11 even 4
144.2.l.a.35.8 yes 16 16.11 odd 4
144.2.l.a.107.1 yes 16 8.5 even 2
144.2.l.a.107.8 yes 16 24.5 odd 2
576.2.l.a.143.2 16 8.3 odd 2
576.2.l.a.143.7 16 24.11 even 2
576.2.l.a.431.2 16 48.5 odd 4
576.2.l.a.431.7 16 16.5 even 4
1152.2.l.a.287.2 16 3.2 odd 2 inner
1152.2.l.a.287.7 16 1.1 even 1 trivial
1152.2.l.a.863.2 16 16.3 odd 4 inner
1152.2.l.a.863.7 16 48.35 even 4 inner
1152.2.l.b.287.2 16 12.11 even 2
1152.2.l.b.287.7 16 4.3 odd 2
1152.2.l.b.863.2 16 16.13 even 4
1152.2.l.b.863.7 16 48.29 odd 4