Properties

Label 3024.2.k.l.1889.10
Level $3024$
Weight $2$
Character 3024.1889
Analytic conductor $24.147$
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] = [3024,2,Mod(1889,3024)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3024, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3024.1889");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 3024.k (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: \(24.1467615712\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} - 6 x^{15} + 18 x^{14} - 36 x^{13} - 45 x^{12} + 306 x^{11} - 378 x^{10} + 1704 x^{9} + 917 x^{8} - 12522 x^{7} + 27090 x^{6} - 35292 x^{5} + 30948 x^{4} - 18000 x^{3} + \cdots + 256 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{14} \)
Twist minimal: no (minimal twist has level 1512)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 1889.10
Root \(3.41914 - 0.916156i\) of defining polynomial
Character \(\chi\) \(=\) 3024.1889
Dual form 3024.2.k.l.1889.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.933004 q^{5} +(-2.45692 + 0.981597i) q^{7} +O(q^{10})\) \(q+0.933004 q^{5} +(-2.45692 + 0.981597i) q^{7} +1.75675i q^{11} -4.20692i q^{13} -0.231144 q^{17} +5.00597i q^{19} -2.61601i q^{23} -4.12950 q^{25} -3.77311i q^{29} +0.840005i q^{31} +(-2.29232 + 0.915835i) q^{35} +3.01636 q^{37} -8.98174 q^{41} -2.40035 q^{43} -1.03019 q^{47} +(5.07293 - 4.82342i) q^{49} +9.04335i q^{53} +1.63905i q^{55} -6.77898 q^{59} -8.93236i q^{61} -3.92508i q^{65} -1.10252 q^{67} -7.21168i q^{71} -3.44883i q^{73} +(-1.72442 - 4.31619i) q^{77} -5.29783 q^{79} -14.8713 q^{83} -0.215658 q^{85} -15.0053 q^{89} +(4.12950 + 10.3361i) q^{91} +4.67059i q^{95} -1.63905i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 2 q^{7} + 36 q^{25} - 8 q^{37} - 20 q^{43} + 2 q^{49} - 44 q^{67} - 40 q^{79} + 16 q^{85} - 36 q^{91}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).

\(n\) \(757\) \(785\) \(1135\) \(2593\)
\(\chi(n)\) \(1\) \(-1\) \(1\) \(-1\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.933004 0.417252 0.208626 0.977995i \(-0.433101\pi\)
0.208626 + 0.977995i \(0.433101\pi\)
\(6\) 0 0
\(7\) −2.45692 + 0.981597i −0.928629 + 0.371009i
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.75675i 0.529679i 0.964293 + 0.264839i \(0.0853189\pi\)
−0.964293 + 0.264839i \(0.914681\pi\)
\(12\) 0 0
\(13\) 4.20692i 1.16679i −0.812189 0.583395i \(-0.801724\pi\)
0.812189 0.583395i \(-0.198276\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −0.231144 −0.0560606 −0.0280303 0.999607i \(-0.508923\pi\)
−0.0280303 + 0.999607i \(0.508923\pi\)
\(18\) 0 0
\(19\) 5.00597i 1.14845i 0.818698 + 0.574224i \(0.194696\pi\)
−0.818698 + 0.574224i \(0.805304\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 2.61601i 0.545476i −0.962088 0.272738i \(-0.912071\pi\)
0.962088 0.272738i \(-0.0879292\pi\)
\(24\) 0 0
\(25\) −4.12950 −0.825901
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 3.77311i 0.700649i −0.936628 0.350324i \(-0.886071\pi\)
0.936628 0.350324i \(-0.113929\pi\)
\(30\) 0 0
\(31\) 0.840005i 0.150869i 0.997151 + 0.0754347i \(0.0240344\pi\)
−0.997151 + 0.0754347i \(0.975966\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −2.29232 + 0.915835i −0.387473 + 0.154804i
\(36\) 0 0
\(37\) 3.01636 0.495887 0.247944 0.968774i \(-0.420245\pi\)
0.247944 + 0.968774i \(0.420245\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −8.98174 −1.40271 −0.701356 0.712811i \(-0.747422\pi\)
−0.701356 + 0.712811i \(0.747422\pi\)
\(42\) 0 0
\(43\) −2.40035 −0.366050 −0.183025 0.983108i \(-0.558589\pi\)
−0.183025 + 0.983108i \(0.558589\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.03019 −0.150269 −0.0751343 0.997173i \(-0.523939\pi\)
−0.0751343 + 0.997173i \(0.523939\pi\)
\(48\) 0 0
\(49\) 5.07293 4.82342i 0.724705 0.689060i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 9.04335i 1.24220i 0.783732 + 0.621100i \(0.213314\pi\)
−0.783732 + 0.621100i \(0.786686\pi\)
\(54\) 0 0
\(55\) 1.63905i 0.221010i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −6.77898 −0.882548 −0.441274 0.897372i \(-0.645473\pi\)
−0.441274 + 0.897372i \(0.645473\pi\)
\(60\) 0 0
\(61\) 8.93236i 1.14367i −0.820368 0.571836i \(-0.806232\pi\)
0.820368 0.571836i \(-0.193768\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 3.92508i 0.486846i
\(66\) 0 0
\(67\) −1.10252 −0.134694 −0.0673471 0.997730i \(-0.521453\pi\)
−0.0673471 + 0.997730i \(0.521453\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.21168i 0.855869i −0.903810 0.427934i \(-0.859241\pi\)
0.903810 0.427934i \(-0.140759\pi\)
\(72\) 0 0
\(73\) 3.44883i 0.403655i −0.979421 0.201828i \(-0.935312\pi\)
0.979421 0.201828i \(-0.0646881\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −1.72442 4.31619i −0.196516 0.491875i
\(78\) 0 0
\(79\) −5.29783 −0.596053 −0.298026 0.954558i \(-0.596328\pi\)
−0.298026 + 0.954558i \(0.596328\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −14.8713 −1.63234 −0.816170 0.577812i \(-0.803907\pi\)
−0.816170 + 0.577812i \(0.803907\pi\)
\(84\) 0 0
\(85\) −0.215658 −0.0233914
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −15.0053 −1.59056 −0.795279 0.606244i \(-0.792675\pi\)
−0.795279 + 0.606244i \(0.792675\pi\)
\(90\) 0 0
\(91\) 4.12950 + 10.3361i 0.432890 + 1.08352i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 4.67059i 0.479192i
\(96\) 0 0
\(97\) 1.63905i 0.166420i −0.996532 0.0832102i \(-0.973483\pi\)
0.996532 0.0832102i \(-0.0265173\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −4.58464 −0.456189 −0.228094 0.973639i \(-0.573249\pi\)
−0.228094 + 0.973639i \(0.573249\pi\)
\(102\) 0 0
\(103\) 16.1411i 1.59043i 0.606328 + 0.795215i \(0.292642\pi\)
−0.606328 + 0.795215i \(0.707358\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 18.4601i 1.78460i −0.451441 0.892301i \(-0.649090\pi\)
0.451441 0.892301i \(-0.350910\pi\)
\(108\) 0 0
\(109\) 8.81132 0.843972 0.421986 0.906602i \(-0.361333\pi\)
0.421986 + 0.906602i \(0.361333\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 13.9026i 1.30785i −0.756560 0.653924i \(-0.773122\pi\)
0.756560 0.653924i \(-0.226878\pi\)
\(114\) 0 0
\(115\) 2.44075i 0.227601i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.567902 0.226890i 0.0520595 0.0207990i
\(120\) 0 0
\(121\) 7.91384 0.719440
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −8.51787 −0.761861
\(126\) 0 0
\(127\) −1.61601 −0.143398 −0.0716989 0.997426i \(-0.522842\pi\)
−0.0716989 + 0.997426i \(0.522842\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −17.7239 −1.54855 −0.774273 0.632852i \(-0.781884\pi\)
−0.774273 + 0.632852i \(0.781884\pi\)
\(132\) 0 0
\(133\) −4.91384 12.2993i −0.426084 1.06648i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 14.9848i 1.28024i −0.768276 0.640118i \(-0.778885\pi\)
0.768276 0.640118i \(-0.221115\pi\)
\(138\) 0 0
\(139\) 1.05435i 0.0894285i 0.999000 + 0.0447143i \(0.0142377\pi\)
−0.999000 + 0.0447143i \(0.985762\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 7.39049 0.618024
\(144\) 0 0
\(145\) 3.52033i 0.292347i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 1.45493i 0.119193i −0.998223 0.0595963i \(-0.981019\pi\)
0.998223 0.0595963i \(-0.0189813\pi\)
\(150\) 0 0
\(151\) −12.6757 −1.03154 −0.515768 0.856728i \(-0.672493\pi\)
−0.515768 + 0.856728i \(0.672493\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.783729i 0.0629506i
\(156\) 0 0
\(157\) 21.7953i 1.73946i 0.493530 + 0.869729i \(0.335706\pi\)
−0.493530 + 0.869729i \(0.664294\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 2.56787 + 6.42734i 0.202376 + 0.506545i
\(162\) 0 0
\(163\) 8.65936 0.678253 0.339127 0.940741i \(-0.389868\pi\)
0.339127 + 0.940741i \(0.389868\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −7.49611 −0.580066 −0.290033 0.957017i \(-0.593666\pi\)
−0.290033 + 0.957017i \(0.593666\pi\)
\(168\) 0 0
\(169\) −4.69819 −0.361399
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −2.71863 −0.206694 −0.103347 0.994645i \(-0.532955\pi\)
−0.103347 + 0.994645i \(0.532955\pi\)
\(174\) 0 0
\(175\) 10.1459 4.05351i 0.766955 0.306416i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 18.3851i 1.37417i −0.726577 0.687085i \(-0.758890\pi\)
0.726577 0.687085i \(-0.241110\pi\)
\(180\) 0 0
\(181\) 8.45745i 0.628638i 0.949317 + 0.314319i \(0.101776\pi\)
−0.949317 + 0.314319i \(0.898224\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.81428 0.206910
\(186\) 0 0
\(187\) 0.406061i 0.0296941i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 25.3412i 1.83362i 0.399320 + 0.916812i \(0.369246\pi\)
−0.399320 + 0.916812i \(0.630754\pi\)
\(192\) 0 0
\(193\) −0.404334 −0.0291046 −0.0145523 0.999894i \(-0.504632\pi\)
−0.0145523 + 0.999894i \(0.504632\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 7.58443i 0.540369i 0.962809 + 0.270184i \(0.0870846\pi\)
−0.962809 + 0.270184i \(0.912915\pi\)
\(198\) 0 0
\(199\) 25.7879i 1.82806i −0.405649 0.914029i \(-0.632955\pi\)
0.405649 0.914029i \(-0.367045\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 3.70367 + 9.27024i 0.259947 + 0.650643i
\(204\) 0 0
\(205\) −8.38001 −0.585285
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −8.79421 −0.608308
\(210\) 0 0
\(211\) 3.69819 0.254594 0.127297 0.991865i \(-0.459370\pi\)
0.127297 + 0.991865i \(0.459370\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −2.23954 −0.152735
\(216\) 0 0
\(217\) −0.824547 2.06383i −0.0559739 0.140102i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.972404i 0.0654110i
\(222\) 0 0
\(223\) 8.17692i 0.547567i −0.961791 0.273784i \(-0.911725\pi\)
0.961791 0.273784i \(-0.0882752\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −4.80735 −0.319075 −0.159538 0.987192i \(-0.551000\pi\)
−0.159538 + 0.987192i \(0.551000\pi\)
\(228\) 0 0
\(229\) 3.65010i 0.241205i −0.992701 0.120603i \(-0.961517\pi\)
0.992701 0.120603i \(-0.0384827\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 22.0118i 1.44204i 0.692915 + 0.721020i \(0.256326\pi\)
−0.692915 + 0.721020i \(0.743674\pi\)
\(234\) 0 0
\(235\) −0.961172 −0.0627000
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 5.64361i 0.365055i 0.983201 + 0.182527i \(0.0584278\pi\)
−0.983201 + 0.182527i \(0.941572\pi\)
\(240\) 0 0
\(241\) 24.9479i 1.60704i 0.595280 + 0.803518i \(0.297041\pi\)
−0.595280 + 0.803518i \(0.702959\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 4.73307 4.50027i 0.302385 0.287512i
\(246\) 0 0
\(247\) 21.0597 1.34000
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −16.8598 −1.06418 −0.532089 0.846688i \(-0.678593\pi\)
−0.532089 + 0.846688i \(0.678593\pi\)
\(252\) 0 0
\(253\) 4.59567 0.288927
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −1.13580 −0.0708496 −0.0354248 0.999372i \(-0.511278\pi\)
−0.0354248 + 0.999372i \(0.511278\pi\)
\(258\) 0 0
\(259\) −7.41097 + 2.96085i −0.460495 + 0.183979i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0.485895i 0.0299616i −0.999888 0.0149808i \(-0.995231\pi\)
0.999888 0.0149808i \(-0.00476871\pi\)
\(264\) 0 0
\(265\) 8.43748i 0.518310i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −11.3100 −0.689585 −0.344793 0.938679i \(-0.612051\pi\)
−0.344793 + 0.938679i \(0.612051\pi\)
\(270\) 0 0
\(271\) 5.00862i 0.304252i 0.988361 + 0.152126i \(0.0486119\pi\)
−0.988361 + 0.152126i \(0.951388\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 7.25449i 0.437462i
\(276\) 0 0
\(277\) −20.6717 −1.24204 −0.621022 0.783793i \(-0.713282\pi\)
−0.621022 + 0.783793i \(0.713282\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 13.9448i 0.831878i 0.909393 + 0.415939i \(0.136547\pi\)
−0.909393 + 0.415939i \(0.863453\pi\)
\(282\) 0 0
\(283\) 22.5944i 1.34310i −0.740961 0.671549i \(-0.765629\pi\)
0.740961 0.671549i \(-0.234371\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 22.0674 8.81646i 1.30260 0.520419i
\(288\) 0 0
\(289\) −16.9466 −0.996857
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −6.27838 −0.366787 −0.183394 0.983040i \(-0.558708\pi\)
−0.183394 + 0.983040i \(0.558708\pi\)
\(294\) 0 0
\(295\) −6.32482 −0.368245
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −11.0054 −0.636456
\(300\) 0 0
\(301\) 5.89748 2.35618i 0.339925 0.135808i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 8.33393i 0.477199i
\(306\) 0 0
\(307\) 22.1578i 1.26461i −0.774719 0.632306i \(-0.782109\pi\)
0.774719 0.632306i \(-0.217891\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 20.1295 1.14144 0.570719 0.821145i \(-0.306664\pi\)
0.570719 + 0.821145i \(0.306664\pi\)
\(312\) 0 0
\(313\) 17.2233i 0.973520i −0.873536 0.486760i \(-0.838179\pi\)
0.873536 0.486760i \(-0.161821\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 29.3779i 1.65003i −0.565113 0.825013i \(-0.691168\pi\)
0.565113 0.825013i \(-0.308832\pi\)
\(318\) 0 0
\(319\) 6.62839 0.371119
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 1.15710i 0.0643827i
\(324\) 0 0
\(325\) 17.3725i 0.963652i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.53110 1.01123i 0.139544 0.0557510i
\(330\) 0 0
\(331\) −13.2550 −0.728562 −0.364281 0.931289i \(-0.618685\pi\)
−0.364281 + 0.931289i \(0.618685\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.02866 −0.0562015
\(336\) 0 0
\(337\) 12.1728 0.663097 0.331549 0.943438i \(-0.392429\pi\)
0.331549 + 0.943438i \(0.392429\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.47568 −0.0799123
\(342\) 0 0
\(343\) −7.72915 + 16.8303i −0.417335 + 0.908753i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 8.55745i 0.459388i −0.973263 0.229694i \(-0.926227\pi\)
0.973263 0.229694i \(-0.0737725\pi\)
\(348\) 0 0
\(349\) 21.3840i 1.14466i 0.820024 + 0.572329i \(0.193960\pi\)
−0.820024 + 0.572329i \(0.806040\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 35.9774 1.91489 0.957443 0.288623i \(-0.0931976\pi\)
0.957443 + 0.288623i \(0.0931976\pi\)
\(354\) 0 0
\(355\) 6.72853i 0.357113i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.864752i 0.0456399i −0.999740 0.0228199i \(-0.992736\pi\)
0.999740 0.0228199i \(-0.00726444\pi\)
\(360\) 0 0
\(361\) −6.05971 −0.318932
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 3.21778i 0.168426i
\(366\) 0 0
\(367\) 28.2287i 1.47352i −0.676152 0.736762i \(-0.736354\pi\)
0.676152 0.736762i \(-0.263646\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −8.87693 22.2188i −0.460867 1.15354i
\(372\) 0 0
\(373\) 22.5074 1.16539 0.582694 0.812691i \(-0.301999\pi\)
0.582694 + 0.812691i \(0.301999\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −15.8732 −0.817510
\(378\) 0 0
\(379\) 15.3306 0.787478 0.393739 0.919222i \(-0.371181\pi\)
0.393739 + 0.919222i \(0.371181\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 31.2215 1.59534 0.797671 0.603093i \(-0.206065\pi\)
0.797671 + 0.603093i \(0.206065\pi\)
\(384\) 0 0
\(385\) −1.60889 4.02702i −0.0819966 0.205236i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 10.4695i 0.530826i −0.964135 0.265413i \(-0.914492\pi\)
0.964135 0.265413i \(-0.0855084\pi\)
\(390\) 0 0
\(391\) 0.604675i 0.0305797i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.94290 −0.248704
\(396\) 0 0
\(397\) 2.27161i 0.114009i −0.998374 0.0570044i \(-0.981845\pi\)
0.998374 0.0570044i \(-0.0181549\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 17.0822i 0.853043i 0.904477 + 0.426522i \(0.140261\pi\)
−0.904477 + 0.426522i \(0.859739\pi\)
\(402\) 0 0
\(403\) 3.53384 0.176033
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 5.29898i 0.262661i
\(408\) 0 0
\(409\) 34.4145i 1.70169i 0.525418 + 0.850844i \(0.323909\pi\)
−0.525418 + 0.850844i \(0.676091\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 16.6554 6.65423i 0.819560 0.327433i
\(414\) 0 0
\(415\) −13.8750 −0.681098
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −35.4899 −1.73380 −0.866898 0.498486i \(-0.833890\pi\)
−0.866898 + 0.498486i \(0.833890\pi\)
\(420\) 0 0
\(421\) −33.1464 −1.61546 −0.807728 0.589555i \(-0.799303\pi\)
−0.807728 + 0.589555i \(0.799303\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0.954509 0.0463005
\(426\) 0 0
\(427\) 8.76798 + 21.9461i 0.424312 + 1.06205i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 6.80071i 0.327578i 0.986495 + 0.163789i \(0.0523717\pi\)
−0.986495 + 0.163789i \(0.947628\pi\)
\(432\) 0 0
\(433\) 15.1067i 0.725982i 0.931793 + 0.362991i \(0.118245\pi\)
−0.931793 + 0.362991i \(0.881755\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 13.0957 0.626451
\(438\) 0 0
\(439\) 8.25619i 0.394046i −0.980399 0.197023i \(-0.936873\pi\)
0.980399 0.197023i \(-0.0631274\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 20.0749i 0.953788i 0.878961 + 0.476894i \(0.158238\pi\)
−0.878961 + 0.476894i \(0.841762\pi\)
\(444\) 0 0
\(445\) −14.0000 −0.663664
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 5.18983i 0.244923i 0.992473 + 0.122462i \(0.0390788\pi\)
−0.992473 + 0.122462i \(0.960921\pi\)
\(450\) 0 0
\(451\) 15.7786i 0.742987i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 3.85284 + 9.64361i 0.180624 + 0.452099i
\(456\) 0 0
\(457\) −19.5074 −0.912517 −0.456259 0.889847i \(-0.650811\pi\)
−0.456259 + 0.889847i \(0.650811\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −34.1566 −1.59083 −0.795416 0.606064i \(-0.792748\pi\)
−0.795416 + 0.606064i \(0.792748\pi\)
\(462\) 0 0
\(463\) 9.23866 0.429357 0.214678 0.976685i \(-0.431130\pi\)
0.214678 + 0.976685i \(0.431130\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16.4374 −0.760630 −0.380315 0.924857i \(-0.624184\pi\)
−0.380315 + 0.924857i \(0.624184\pi\)
\(468\) 0 0
\(469\) 2.70881 1.08223i 0.125081 0.0499728i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 4.21681i 0.193889i
\(474\) 0 0
\(475\) 20.6722i 0.948504i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 33.1011 1.51243 0.756215 0.654323i \(-0.227046\pi\)
0.756215 + 0.654323i \(0.227046\pi\)
\(480\) 0 0
\(481\) 12.6896i 0.578596i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 1.52924i 0.0694393i
\(486\) 0 0
\(487\) 35.1137 1.59115 0.795576 0.605853i \(-0.207168\pi\)
0.795576 + 0.605853i \(0.207168\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 10.9560i 0.494439i 0.968959 + 0.247220i \(0.0795169\pi\)
−0.968959 + 0.247220i \(0.920483\pi\)
\(492\) 0 0
\(493\) 0.872131i 0.0392788i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 7.07896 + 17.7185i 0.317535 + 0.794785i
\(498\) 0 0
\(499\) 12.0985 0.541605 0.270802 0.962635i \(-0.412711\pi\)
0.270802 + 0.962635i \(0.412711\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 17.5594 0.782936 0.391468 0.920192i \(-0.371967\pi\)
0.391468 + 0.920192i \(0.371967\pi\)
\(504\) 0 0
\(505\) −4.27749 −0.190346
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 2.06881 0.0916984 0.0458492 0.998948i \(-0.485401\pi\)
0.0458492 + 0.998948i \(0.485401\pi\)
\(510\) 0 0
\(511\) 3.38537 + 8.47352i 0.149760 + 0.374846i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 15.0597i 0.663610i
\(516\) 0 0
\(517\) 1.80978i 0.0795941i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 27.9440 1.22425 0.612123 0.790762i \(-0.290316\pi\)
0.612123 + 0.790762i \(0.290316\pi\)
\(522\) 0 0
\(523\) 31.2026i 1.36439i 0.731168 + 0.682197i \(0.238976\pi\)
−0.731168 + 0.682197i \(0.761024\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0.194162i 0.00845783i
\(528\) 0 0
\(529\) 16.1565 0.702456
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 37.7855i 1.63667i
\(534\) 0 0
\(535\) 17.2233i 0.744629i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 8.47352 + 8.91185i 0.364980 + 0.383861i
\(540\) 0 0
\(541\) 37.9905 1.63334 0.816669 0.577107i \(-0.195818\pi\)
0.816669 + 0.577107i \(0.195818\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 8.22101 0.352149
\(546\) 0 0
\(547\) −31.4173 −1.34330 −0.671652 0.740866i \(-0.734415\pi\)
−0.671652 + 0.740866i \(0.734415\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 18.8881 0.804659
\(552\) 0 0
\(553\) 13.0164 5.20034i 0.553512 0.221141i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 32.8158i 1.39045i 0.718791 + 0.695226i \(0.244696\pi\)
−0.718791 + 0.695226i \(0.755304\pi\)
\(558\) 0 0
\(559\) 10.0981i 0.427104i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 23.4092 0.986579 0.493289 0.869865i \(-0.335794\pi\)
0.493289 + 0.869865i \(0.335794\pi\)
\(564\) 0 0
\(565\) 12.9712i 0.545702i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 33.2320i 1.39316i −0.717480 0.696579i \(-0.754704\pi\)
0.717480 0.696579i \(-0.245296\pi\)
\(570\) 0 0
\(571\) −19.5996 −0.820220 −0.410110 0.912036i \(-0.634510\pi\)
−0.410110 + 0.912036i \(0.634510\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 10.8028i 0.450509i
\(576\) 0 0
\(577\) 11.3337i 0.471830i 0.971774 + 0.235915i \(0.0758086\pi\)
−0.971774 + 0.235915i \(0.924191\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 36.5377 14.5977i 1.51584 0.605613i
\(582\) 0 0
\(583\) −15.8869 −0.657967
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.6923 −0.523866 −0.261933 0.965086i \(-0.584360\pi\)
−0.261933 + 0.965086i \(0.584360\pi\)
\(588\) 0 0
\(589\) −4.20504 −0.173266
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 13.2663 0.544783 0.272392 0.962186i \(-0.412185\pi\)
0.272392 + 0.962186i \(0.412185\pi\)
\(594\) 0 0
\(595\) 0.529856 0.211690i 0.0217220 0.00867843i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 4.74613i 0.193921i 0.995288 + 0.0969607i \(0.0309121\pi\)
−0.995288 + 0.0969607i \(0.969088\pi\)
\(600\) 0 0
\(601\) 23.0666i 0.940908i −0.882425 0.470454i \(-0.844090\pi\)
0.882425 0.470454i \(-0.155910\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 7.38365 0.300188
\(606\) 0 0
\(607\) 35.6212i 1.44582i 0.690942 + 0.722910i \(0.257196\pi\)
−0.690942 + 0.722910i \(0.742804\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 4.33393i 0.175332i
\(612\) 0 0
\(613\) 33.8931 1.36893 0.684466 0.729045i \(-0.260036\pi\)
0.684466 + 0.729045i \(0.260036\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 1.09014i 0.0438872i −0.999759 0.0219436i \(-0.993015\pi\)
0.999759 0.0219436i \(-0.00698543\pi\)
\(618\) 0 0
\(619\) 21.1907i 0.851725i −0.904788 0.425862i \(-0.859971\pi\)
0.904788 0.425862i \(-0.140029\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 36.8668 14.7291i 1.47704 0.590111i
\(624\) 0 0
\(625\) 12.7003 0.508012
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −0.697214 −0.0277997
\(630\) 0 0
\(631\) 14.9020 0.593239 0.296620 0.954996i \(-0.404141\pi\)
0.296620 + 0.954996i \(0.404141\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.50775 −0.0598331
\(636\) 0 0
\(637\) −20.2917 21.3414i −0.803988 0.845578i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 24.3260i 0.960818i 0.877045 + 0.480409i \(0.159512\pi\)
−0.877045 + 0.480409i \(0.840488\pi\)
\(642\) 0 0
\(643\) 22.4341i 0.884714i 0.896839 + 0.442357i \(0.145858\pi\)
−0.896839 + 0.442357i \(0.854142\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 37.5251 1.47526 0.737631 0.675204i \(-0.235944\pi\)
0.737631 + 0.675204i \(0.235944\pi\)
\(648\) 0 0
\(649\) 11.9089i 0.467467i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 29.4549i 1.15266i 0.817217 + 0.576330i \(0.195516\pi\)
−0.817217 + 0.576330i \(0.804484\pi\)
\(654\) 0 0
\(655\) −16.5365 −0.646134
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 43.8012i 1.70625i −0.521703 0.853127i \(-0.674703\pi\)
0.521703 0.853127i \(-0.325297\pi\)
\(660\) 0 0
\(661\) 8.90182i 0.346241i −0.984901 0.173120i \(-0.944615\pi\)
0.984901 0.173120i \(-0.0553850\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −4.58464 11.4753i −0.177785 0.444992i
\(666\) 0 0
\(667\) −9.87050 −0.382187
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15.6919 0.605778
\(672\) 0 0
\(673\) 21.0761 0.812423 0.406211 0.913779i \(-0.366850\pi\)
0.406211 + 0.913779i \(0.366850\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 31.1464 1.19705 0.598526 0.801103i \(-0.295753\pi\)
0.598526 + 0.801103i \(0.295753\pi\)
\(678\) 0 0
\(679\) 1.60889 + 4.02702i 0.0617435 + 0.154543i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 19.5805i 0.749225i 0.927181 + 0.374613i \(0.122224\pi\)
−0.927181 + 0.374613i \(0.877776\pi\)
\(684\) 0 0
\(685\) 13.9809i 0.534182i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 38.0446 1.44939
\(690\) 0 0
\(691\) 34.1739i 1.30004i 0.759919 + 0.650018i \(0.225239\pi\)
−0.759919 + 0.650018i \(0.774761\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0.983710i 0.0373143i
\(696\) 0 0
\(697\) 2.07608 0.0786370
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 42.1904i 1.59351i −0.604304 0.796754i \(-0.706549\pi\)
0.604304 0.796754i \(-0.293451\pi\)
\(702\) 0 0
\(703\) 15.0998i 0.569501i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 11.2641 4.50027i 0.423630 0.169250i
\(708\) 0 0
\(709\) −37.4937 −1.40810 −0.704052 0.710148i \(-0.748628\pi\)
−0.704052 + 0.710148i \(0.748628\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.19746 0.0822956
\(714\) 0 0
\(715\) 6.89536 0.257872
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −3.26820 −0.121883 −0.0609416 0.998141i \(-0.519410\pi\)
−0.0609416 + 0.998141i \(0.519410\pi\)
\(720\) 0 0
\(721\) −15.8441 39.6574i −0.590063 1.47692i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 15.5811i 0.578666i
\(726\) 0 0
\(727\) 21.3997i 0.793671i 0.917890 + 0.396836i \(0.129892\pi\)
−0.917890 + 0.396836i \(0.870108\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.554827 0.0205210
\(732\) 0 0
\(733\) 39.3611i 1.45384i −0.686724 0.726919i \(-0.740952\pi\)
0.686724 0.726919i \(-0.259048\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 1.93685i 0.0713447i
\(738\) 0 0
\(739\) 9.40433 0.345944 0.172972 0.984927i \(-0.444663\pi\)
0.172972 + 0.984927i \(0.444663\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 32.8880i 1.20654i 0.797535 + 0.603272i \(0.206137\pi\)
−0.797535 + 0.603272i \(0.793863\pi\)
\(744\) 0 0
\(745\) 1.35746i 0.0497334i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 18.1203 + 45.3549i 0.662103 + 1.65723i
\(750\) 0 0
\(751\) 23.9081 0.872419 0.436209 0.899845i \(-0.356321\pi\)
0.436209 + 0.899845i \(0.356321\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −11.8265 −0.430411
\(756\) 0 0
\(757\) 48.2944 1.75529 0.877645 0.479312i \(-0.159114\pi\)
0.877645 + 0.479312i \(0.159114\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −34.5737 −1.25330 −0.626648 0.779302i \(-0.715574\pi\)
−0.626648 + 0.779302i \(0.715574\pi\)
\(762\) 0 0
\(763\) −21.6487 + 8.64917i −0.783737 + 0.313121i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 28.5186i 1.02975i
\(768\) 0 0
\(769\) 33.1831i 1.19661i 0.801267 + 0.598307i \(0.204160\pi\)
−0.801267 + 0.598307i \(0.795840\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 37.5014 1.34883 0.674415 0.738352i \(-0.264396\pi\)
0.674415 + 0.738352i \(0.264396\pi\)
\(774\) 0 0
\(775\) 3.46880i 0.124603i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 44.9623i 1.61094i
\(780\) 0 0
\(781\) 12.6691 0.453335
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 20.3352i 0.725793i
\(786\) 0 0
\(787\) 9.33842i 0.332879i 0.986052 + 0.166439i \(0.0532270\pi\)
−0.986052 + 0.166439i \(0.946773\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 13.6468 + 34.1576i 0.485223 + 1.21451i
\(792\) 0 0
\(793\) −37.5777 −1.33442
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −31.6239 −1.12018 −0.560089 0.828433i \(-0.689233\pi\)
−0.560089 + 0.828433i \(0.689233\pi\)
\(798\) 0 0
\(799\) 0.238122 0.00842416
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 6.05872 0.213808
\(804\) 0 0
\(805\) 2.39583 + 5.99673i 0.0844420 + 0.211357i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 27.7318i 0.974998i −0.873123 0.487499i \(-0.837909\pi\)
0.873123 0.487499i \(-0.162091\pi\)
\(810\) 0 0
\(811\) 8.45321i 0.296832i 0.988925 + 0.148416i \(0.0474175\pi\)
−0.988925 + 0.148416i \(0.952582\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 8.07922 0.283003
\(816\) 0 0
\(817\) 12.0161i 0.420390i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0.496589i 0.0173311i −0.999962 0.00866554i \(-0.997242\pi\)
0.999962 0.00866554i \(-0.00275836\pi\)
\(822\) 0 0
\(823\) −48.0721 −1.67569 −0.837844 0.545910i \(-0.816184\pi\)
−0.837844 + 0.545910i \(0.816184\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 11.6211i 0.404107i 0.979375 + 0.202053i \(0.0647614\pi\)
−0.979375 + 0.202053i \(0.935239\pi\)
\(828\) 0 0
\(829\) 39.4221i 1.36919i 0.728926 + 0.684593i \(0.240020\pi\)
−0.728926 + 0.684593i \(0.759980\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −1.17258 + 1.11490i −0.0406274 + 0.0386291i
\(834\) 0 0
\(835\) −6.99390 −0.242034
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −23.9656 −0.827384 −0.413692 0.910417i \(-0.635761\pi\)
−0.413692 + 0.910417i \(0.635761\pi\)
\(840\) 0 0
\(841\) 14.7636 0.509091
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −4.38343 −0.150795
\(846\) 0 0
\(847\) −19.4437 + 7.76821i −0.668093 + 0.266919i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 7.89084i 0.270495i
\(852\) 0 0
\(853\) 17.9030i 0.612988i −0.951873 0.306494i \(-0.900844\pi\)
0.951873 0.306494i \(-0.0991559\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −15.1623 −0.517934 −0.258967 0.965886i \(-0.583382\pi\)
−0.258967 + 0.965886i \(0.583382\pi\)
\(858\) 0 0
\(859\) 19.8862i 0.678508i −0.940695 0.339254i \(-0.889825\pi\)
0.940695 0.339254i \(-0.110175\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 21.1813i 0.721018i 0.932756 + 0.360509i \(0.117397\pi\)
−0.932756 + 0.360509i \(0.882603\pi\)
\(864\) 0 0
\(865\) −2.53649 −0.0862434
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 9.30695i 0.315717i
\(870\) 0 0
\(871\) 4.63821i 0.157160i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 20.9277 8.36112i 0.707487 0.282657i
\(876\) 0 0
\(877\) −4.89802 −0.165394 −0.0826972 0.996575i \(-0.526353\pi\)
−0.0826972 + 0.996575i \(0.526353\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 14.0502 0.473362 0.236681 0.971587i \(-0.423940\pi\)
0.236681 + 0.971587i \(0.423940\pi\)
\(882\) 0 0
\(883\) −17.4928 −0.588679 −0.294340 0.955701i \(-0.595100\pi\)
−0.294340 + 0.955701i \(0.595100\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −0.286309 −0.00961331 −0.00480665 0.999988i \(-0.501530\pi\)
−0.00480665 + 0.999988i \(0.501530\pi\)
\(888\) 0 0
\(889\) 3.97041 1.58627i 0.133163 0.0532019i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 5.15710i 0.172576i
\(894\) 0 0
\(895\) 17.1534i 0.573376i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 3.16943 0.105706
\(900\) 0 0
\(901\) 2.09031i 0.0696385i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 7.89084i 0.262300i
\(906\) 0 0
\(907\) 16.5299 0.548865 0.274432 0.961606i \(-0.411510\pi\)
0.274432 + 0.961606i \(0.411510\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 48.8889i 1.61976i −0.586594 0.809881i \(-0.699532\pi\)
0.586594 0.809881i \(-0.300468\pi\)
\(912\) 0 0
\(913\) 26.1251i 0.864616i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 43.5463 17.3977i 1.43803 0.574524i
\(918\) 0 0
\(919\) 8.24441 0.271958 0.135979 0.990712i \(-0.456582\pi\)
0.135979 + 0.990712i \(0.456582\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −30.3390 −0.998619
\(924\) 0 0
\(925\) −12.4561 −0.409553
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −19.4613 −0.638504 −0.319252 0.947670i \(-0.603432\pi\)
−0.319252 + 0.947670i \(0.603432\pi\)
\(930\) 0 0
\(931\) 24.1459 + 25.3949i 0.791349 + 0.832286i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0.378857i 0.0123899i
\(936\) 0 0
\(937\) 19.2022i 0.627310i −0.949537 0.313655i \(-0.898446\pi\)
0.949537 0.313655i \(-0.101554\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −32.3809 −1.05559 −0.527794 0.849373i \(-0.676981\pi\)
−0.527794 + 0.849373i \(0.676981\pi\)
\(942\) 0 0
\(943\) 23.4963i 0.765146i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 54.5365i 1.77220i 0.463496 + 0.886099i \(0.346595\pi\)
−0.463496 + 0.886099i \(0.653405\pi\)
\(948\) 0 0
\(949\) −14.5090 −0.470981
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 41.5158i 1.34483i −0.740175 0.672414i \(-0.765257\pi\)
0.740175 0.672414i \(-0.234743\pi\)
\(954\) 0 0
\(955\) 23.6434i 0.765084i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 14.7090 + 36.8165i 0.474979 + 1.18887i
\(960\) 0 0
\(961\) 30.2944 0.977238
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −0.377245 −0.0121439
\(966\) 0 0
\(967\) −33.7358 −1.08487 −0.542435 0.840098i \(-0.682497\pi\)
−0.542435 + 0.840098i \(0.682497\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −36.5369 −1.17253 −0.586263 0.810121i \(-0.699401\pi\)
−0.586263 + 0.810121i \(0.699401\pi\)
\(972\) 0 0
\(973\) −1.03494 2.59045i −0.0331788 0.0830460i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 44.7254i 1.43089i 0.698669 + 0.715445i \(0.253776\pi\)
−0.698669 + 0.715445i \(0.746224\pi\)
\(978\) 0 0
\(979\) 26.3605i 0.842484i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 43.7614 1.39577 0.697885 0.716209i \(-0.254124\pi\)
0.697885 + 0.716209i \(0.254124\pi\)
\(984\) 0 0
\(985\) 7.07631i 0.225470i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 6.27935i 0.199672i
\(990\) 0 0
\(991\) 17.4844 0.555410 0.277705 0.960666i \(-0.410426\pi\)
0.277705 + 0.960666i \(0.410426\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 24.0602i 0.762761i
\(996\) 0 0
\(997\) 23.3062i 0.738115i −0.929407 0.369058i \(-0.879680\pi\)
0.929407 0.369058i \(-0.120320\pi\)
\(998\) 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 3024.2.k.l.1889.10 16
3.2 odd 2 inner 3024.2.k.l.1889.8 16
4.3 odd 2 1512.2.k.b.377.9 yes 16
7.6 odd 2 inner 3024.2.k.l.1889.7 16
12.11 even 2 1512.2.k.b.377.7 16
21.20 even 2 inner 3024.2.k.l.1889.9 16
28.27 even 2 1512.2.k.b.377.8 yes 16
84.83 odd 2 1512.2.k.b.377.10 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1512.2.k.b.377.7 16 12.11 even 2
1512.2.k.b.377.8 yes 16 28.27 even 2
1512.2.k.b.377.9 yes 16 4.3 odd 2
1512.2.k.b.377.10 yes 16 84.83 odd 2
3024.2.k.l.1889.7 16 7.6 odd 2 inner
3024.2.k.l.1889.8 16 3.2 odd 2 inner
3024.2.k.l.1889.9 16 21.20 even 2 inner
3024.2.k.l.1889.10 16 1.1 even 1 trivial