Properties

Label 1584.2.cd.c.1025.3
Level $1584$
Weight $2$
Character 1584.1025
Analytic conductor $12.648$
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] = [1584,2,Mod(17,1584)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1584, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 5, 9]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1584.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1584 = 2^{4} \cdot 3^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1584.cd (of order \(10\), 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: \(12.6483036802\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 99)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 1025.3
Root \(0.556839 + 1.81878i\) of defining polynomial
Character \(\chi\) \(=\) 1584.1025
Dual form 1584.2.cd.c.17.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0381457 - 0.0123943i) q^{5} +(-0.145094 + 0.199704i) q^{7} +O(q^{10})\) \(q+(0.0381457 - 0.0123943i) q^{5} +(-0.145094 + 0.199704i) q^{7} +(-3.12033 - 1.12407i) q^{11} +(-2.18888 - 0.711209i) q^{13} +(-1.32142 - 4.06692i) q^{17} +(3.64429 + 5.01593i) q^{19} +6.79984i q^{23} +(-4.04378 + 2.93798i) q^{25} +(4.52705 + 3.28909i) q^{29} +(-1.48247 + 4.56258i) q^{31} +(-0.00305951 + 0.00941619i) q^{35} +(3.26102 + 2.36927i) q^{37} +(-7.76893 + 5.64446i) q^{41} +1.03166i q^{43} +(-6.53982 - 9.00129i) q^{47} +(2.14429 + 6.59944i) q^{49} +(-8.52885 - 2.77119i) q^{53} +(-0.132959 - 0.00420408i) q^{55} +(1.63893 - 2.25580i) q^{59} +(8.06923 - 2.62185i) q^{61} -0.0923111 q^{65} -7.94588 q^{67} +(-3.16559 + 1.02856i) q^{71} +(-6.96743 + 9.58984i) q^{73} +(0.677222 - 0.460048i) q^{77} +(2.86363 + 0.930451i) q^{79} +(1.63587 + 5.03470i) q^{83} +(-0.100813 - 0.138757i) q^{85} -8.54422i q^{89} +(0.459624 - 0.333936i) q^{91} +(0.201183 + 0.146168i) q^{95} +(-0.935778 + 2.88003i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q+O(q^{10}) \) Copy content Toggle raw display \( 16 q - 32 q^{25} - 16 q^{31} - 12 q^{37} - 24 q^{49} - 16 q^{55} - 96 q^{67} - 20 q^{73} - 100 q^{85} + 72 q^{91} + 60 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1584\mathbb{Z}\right)^\times\).

\(n\) \(145\) \(353\) \(991\) \(1189\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\) \(-1\) \(1\) \(1\)

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
\(5\) 0.0381457 0.0123943i 0.0170593 0.00554289i −0.300475 0.953790i \(-0.597145\pi\)
0.317534 + 0.948247i \(0.397145\pi\)
\(6\) 0 0
\(7\) −0.145094 + 0.199704i −0.0548403 + 0.0754811i −0.835556 0.549405i \(-0.814855\pi\)
0.780716 + 0.624886i \(0.214855\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −3.12033 1.12407i −0.940815 0.338919i
\(12\) 0 0
\(13\) −2.18888 0.711209i −0.607085 0.197254i −0.0106874 0.999943i \(-0.503402\pi\)
−0.596398 + 0.802689i \(0.703402\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −1.32142 4.06692i −0.320492 0.986372i −0.973435 0.228965i \(-0.926466\pi\)
0.652943 0.757407i \(-0.273534\pi\)
\(18\) 0 0
\(19\) 3.64429 + 5.01593i 0.836057 + 1.15073i 0.986765 + 0.162156i \(0.0518447\pi\)
−0.150708 + 0.988578i \(0.548155\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 6.79984i 1.41786i 0.705277 + 0.708932i \(0.250823\pi\)
−0.705277 + 0.708932i \(0.749177\pi\)
\(24\) 0 0
\(25\) −4.04378 + 2.93798i −0.808757 + 0.587596i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.52705 + 3.28909i 0.840652 + 0.610769i 0.922553 0.385871i \(-0.126099\pi\)
−0.0819007 + 0.996640i \(0.526099\pi\)
\(30\) 0 0
\(31\) −1.48247 + 4.56258i −0.266260 + 0.819463i 0.725141 + 0.688601i \(0.241775\pi\)
−0.991401 + 0.130863i \(0.958225\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.00305951 + 0.00941619i −0.000517151 + 0.00159163i
\(36\) 0 0
\(37\) 3.26102 + 2.36927i 0.536109 + 0.389506i 0.822638 0.568566i \(-0.192502\pi\)
−0.286529 + 0.958072i \(0.592502\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −7.76893 + 5.64446i −1.21330 + 0.881517i −0.995527 0.0944820i \(-0.969881\pi\)
−0.217777 + 0.975999i \(0.569881\pi\)
\(42\) 0 0
\(43\) 1.03166i 0.157327i 0.996901 + 0.0786636i \(0.0250653\pi\)
−0.996901 + 0.0786636i \(0.974935\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −6.53982 9.00129i −0.953931 1.31297i −0.949759 0.312982i \(-0.898672\pi\)
−0.00417211 0.999991i \(-0.501328\pi\)
\(48\) 0 0
\(49\) 2.14429 + 6.59944i 0.306327 + 0.942778i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −8.52885 2.77119i −1.17153 0.380652i −0.342314 0.939585i \(-0.611211\pi\)
−0.829213 + 0.558933i \(0.811211\pi\)
\(54\) 0 0
\(55\) −0.132959 0.00420408i −0.0179282 0.000566878i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.63893 2.25580i 0.213371 0.293680i −0.688894 0.724862i \(-0.741903\pi\)
0.902265 + 0.431182i \(0.141903\pi\)
\(60\) 0 0
\(61\) 8.06923 2.62185i 1.03316 0.335694i 0.257121 0.966379i \(-0.417226\pi\)
0.776039 + 0.630685i \(0.217226\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −0.0923111 −0.0114498
\(66\) 0 0
\(67\) −7.94588 −0.970744 −0.485372 0.874308i \(-0.661316\pi\)
−0.485372 + 0.874308i \(0.661316\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) −3.16559 + 1.02856i −0.375687 + 0.122068i −0.490773 0.871288i \(-0.663286\pi\)
0.115086 + 0.993355i \(0.463286\pi\)
\(72\) 0 0
\(73\) −6.96743 + 9.58984i −0.815476 + 1.12241i 0.174980 + 0.984572i \(0.444014\pi\)
−0.990455 + 0.137834i \(0.955986\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.677222 0.460048i 0.0771766 0.0524274i
\(78\) 0 0
\(79\) 2.86363 + 0.930451i 0.322184 + 0.104684i 0.465644 0.884972i \(-0.345823\pi\)
−0.143460 + 0.989656i \(0.545823\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 1.63587 + 5.03470i 0.179560 + 0.552630i 0.999812 0.0193724i \(-0.00616680\pi\)
−0.820252 + 0.572002i \(0.806167\pi\)
\(84\) 0 0
\(85\) −0.100813 0.138757i −0.0109347 0.0150503i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 8.54422i 0.905686i −0.891590 0.452843i \(-0.850410\pi\)
0.891590 0.452843i \(-0.149590\pi\)
\(90\) 0 0
\(91\) 0.459624 0.333936i 0.0481817 0.0350060i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0.201183 + 0.146168i 0.0206409 + 0.0149965i
\(96\) 0 0
\(97\) −0.935778 + 2.88003i −0.0950139 + 0.292423i −0.987257 0.159132i \(-0.949130\pi\)
0.892243 + 0.451555i \(0.149130\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) −2.14828 + 6.61172i −0.213762 + 0.657891i 0.785477 + 0.618890i \(0.212417\pi\)
−0.999239 + 0.0390007i \(0.987583\pi\)
\(102\) 0 0
\(103\) 10.6138 + 7.71139i 1.04581 + 0.759826i 0.971411 0.237402i \(-0.0762960\pi\)
0.0743996 + 0.997229i \(0.476296\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 1.10712 0.804368i 0.107029 0.0777612i −0.532983 0.846126i \(-0.678929\pi\)
0.640012 + 0.768365i \(0.278929\pi\)
\(108\) 0 0
\(109\) 7.34454i 0.703480i 0.936098 + 0.351740i \(0.114410\pi\)
−0.936098 + 0.351740i \(0.885590\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.310669 + 0.427600i 0.0292253 + 0.0402252i 0.823380 0.567491i \(-0.192086\pi\)
−0.794154 + 0.607716i \(0.792086\pi\)
\(114\) 0 0
\(115\) 0.0842791 + 0.259385i 0.00785907 + 0.0241877i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 1.00391 + 0.326190i 0.0920284 + 0.0299018i
\(120\) 0 0
\(121\) 8.47294 + 7.01493i 0.770267 + 0.637721i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) −0.235715 + 0.324434i −0.0210830 + 0.0290183i
\(126\) 0 0
\(127\) −12.1468 + 3.94673i −1.07785 + 0.350215i −0.793541 0.608517i \(-0.791765\pi\)
−0.284311 + 0.958732i \(0.591765\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −18.1534 −1.58607 −0.793033 0.609178i \(-0.791499\pi\)
−0.793033 + 0.609178i \(0.791499\pi\)
\(132\) 0 0
\(133\) −1.53047 −0.132708
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −15.2863 + 4.96682i −1.30600 + 0.424344i −0.877664 0.479276i \(-0.840899\pi\)
−0.428334 + 0.903621i \(0.640899\pi\)
\(138\) 0 0
\(139\) −2.26727 + 3.12062i −0.192307 + 0.264688i −0.894272 0.447523i \(-0.852306\pi\)
0.701965 + 0.712211i \(0.252306\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 6.03057 + 4.67966i 0.504302 + 0.391333i
\(144\) 0 0
\(145\) 0.213453 + 0.0693552i 0.0177263 + 0.00575964i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.17360 + 9.76734i 0.259992 + 0.800172i 0.992805 + 0.119742i \(0.0382068\pi\)
−0.732813 + 0.680430i \(0.761793\pi\)
\(150\) 0 0
\(151\) −5.15512 7.09542i −0.419518 0.577417i 0.545990 0.837792i \(-0.316154\pi\)
−0.965508 + 0.260375i \(0.916154\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.192417i 0.0154553i
\(156\) 0 0
\(157\) 10.5422 7.65934i 0.841357 0.611282i −0.0813923 0.996682i \(-0.525937\pi\)
0.922749 + 0.385400i \(0.125937\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.35796 0.986614i −0.107022 0.0777561i
\(162\) 0 0
\(163\) 2.83608 8.72855i 0.222139 0.683673i −0.776431 0.630203i \(-0.782972\pi\)
0.998569 0.0534700i \(-0.0170281\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 2.35141 7.23691i 0.181958 0.560009i −0.817925 0.575325i \(-0.804876\pi\)
0.999883 + 0.0153164i \(0.00487554\pi\)
\(168\) 0 0
\(169\) −6.23186 4.52771i −0.479374 0.348285i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 13.4462 9.76923i 1.02230 0.742741i 0.0555432 0.998456i \(-0.482311\pi\)
0.966752 + 0.255715i \(0.0823109\pi\)
\(174\) 0 0
\(175\) 1.23384i 0.0932698i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 4.14376 + 5.70340i 0.309719 + 0.426292i 0.935294 0.353872i \(-0.115135\pi\)
−0.625574 + 0.780165i \(0.715135\pi\)
\(180\) 0 0
\(181\) −6.52756 20.0898i −0.485189 1.49326i −0.831706 0.555216i \(-0.812636\pi\)
0.346517 0.938044i \(-0.387364\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0.153759 + 0.0499594i 0.0113046 + 0.00367309i
\(186\) 0 0
\(187\) −0.448220 + 14.1755i −0.0327771 + 1.03662i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 8.03400 11.0579i 0.581320 0.800118i −0.412519 0.910949i \(-0.635351\pi\)
0.993839 + 0.110831i \(0.0353511\pi\)
\(192\) 0 0
\(193\) −23.8096 + 7.73620i −1.71385 + 0.556864i −0.990967 0.134105i \(-0.957184\pi\)
−0.722884 + 0.690969i \(0.757184\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 21.0442 1.49934 0.749668 0.661814i \(-0.230213\pi\)
0.749668 + 0.661814i \(0.230213\pi\)
\(198\) 0 0
\(199\) 10.3709 0.735176 0.367588 0.929989i \(-0.380184\pi\)
0.367588 + 0.929989i \(0.380184\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.31369 + 0.426845i −0.0922031 + 0.0299586i
\(204\) 0 0
\(205\) −0.226392 + 0.311602i −0.0158119 + 0.0217632i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −5.73314 19.7478i −0.396569 1.36598i
\(210\) 0 0
\(211\) 17.8262 + 5.79210i 1.22721 + 0.398744i 0.849702 0.527263i \(-0.176782\pi\)
0.377506 + 0.926007i \(0.376782\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.0127867 + 0.0393535i 0.000872048 + 0.00268389i
\(216\) 0 0
\(217\) −0.696069 0.958057i −0.0472523 0.0650372i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 9.84179i 0.662031i
\(222\) 0 0
\(223\) 7.82233 5.68326i 0.523822 0.380579i −0.294220 0.955738i \(-0.595060\pi\)
0.818042 + 0.575159i \(0.195060\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 9.47859 + 6.88660i 0.629116 + 0.457080i 0.856094 0.516820i \(-0.172884\pi\)
−0.226978 + 0.973900i \(0.572884\pi\)
\(228\) 0 0
\(229\) 6.32872 19.4778i 0.418214 1.28713i −0.491131 0.871086i \(-0.663416\pi\)
0.909345 0.416044i \(-0.136584\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 4.98842 15.3528i 0.326802 1.00579i −0.643818 0.765178i \(-0.722651\pi\)
0.970621 0.240615i \(-0.0773492\pi\)
\(234\) 0 0
\(235\) −0.361031 0.262304i −0.0235510 0.0171108i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −22.9660 + 16.6858i −1.48555 + 1.07931i −0.509830 + 0.860275i \(0.670292\pi\)
−0.975716 + 0.219038i \(0.929708\pi\)
\(240\) 0 0
\(241\) 14.3654i 0.925357i 0.886526 + 0.462679i \(0.153112\pi\)
−0.886526 + 0.462679i \(0.846888\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.163591 + 0.225163i 0.0104514 + 0.0143852i
\(246\) 0 0
\(247\) −4.40952 13.5711i −0.280571 0.863509i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −6.60298 2.14544i −0.416776 0.135419i 0.0931196 0.995655i \(-0.470316\pi\)
−0.509896 + 0.860236i \(0.670316\pi\)
\(252\) 0 0
\(253\) 7.64348 21.2178i 0.480542 1.33395i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −6.12372 + 8.42858i −0.381987 + 0.525760i −0.956110 0.293009i \(-0.905343\pi\)
0.574122 + 0.818769i \(0.305343\pi\)
\(258\) 0 0
\(259\) −0.946307 + 0.307474i −0.0588007 + 0.0191055i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 4.26110 0.262751 0.131375 0.991333i \(-0.458061\pi\)
0.131375 + 0.991333i \(0.458061\pi\)
\(264\) 0 0
\(265\) −0.359686 −0.0220953
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −10.5223 + 3.41889i −0.641553 + 0.208453i −0.611686 0.791101i \(-0.709508\pi\)
−0.0298672 + 0.999554i \(0.509508\pi\)
\(270\) 0 0
\(271\) −9.34327 + 12.8599i −0.567563 + 0.781184i −0.992263 0.124150i \(-0.960379\pi\)
0.424700 + 0.905334i \(0.360379\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 15.9204 4.62198i 0.960038 0.278716i
\(276\) 0 0
\(277\) 10.7860 + 3.50458i 0.648066 + 0.210570i 0.614561 0.788869i \(-0.289333\pi\)
0.0335051 + 0.999439i \(0.489333\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0.482158 + 1.48393i 0.0287631 + 0.0885238i 0.964408 0.264420i \(-0.0851806\pi\)
−0.935644 + 0.352944i \(0.885181\pi\)
\(282\) 0 0
\(283\) −15.6148 21.4919i −0.928202 1.27756i −0.960557 0.278084i \(-0.910301\pi\)
0.0323551 0.999476i \(-0.489699\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 2.37046i 0.139924i
\(288\) 0 0
\(289\) −1.04038 + 0.755878i −0.0611986 + 0.0444634i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 21.3051 + 15.4791i 1.24466 + 0.904296i 0.997900 0.0647811i \(-0.0206349\pi\)
0.246757 + 0.969077i \(0.420635\pi\)
\(294\) 0 0
\(295\) 0.0345592 0.106362i 0.00201211 0.00619265i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.83611 14.8840i 0.279679 0.860765i
\(300\) 0 0
\(301\) −0.206028 0.149688i −0.0118752 0.00862786i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.275310 0.200025i 0.0157642 0.0114534i
\(306\) 0 0
\(307\) 26.0083i 1.48437i −0.670195 0.742185i \(-0.733789\pi\)
0.670195 0.742185i \(-0.266211\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 7.83210 + 10.7800i 0.444118 + 0.611276i 0.971121 0.238588i \(-0.0766844\pi\)
−0.527003 + 0.849863i \(0.676684\pi\)
\(312\) 0 0
\(313\) −3.47592 10.6978i −0.196471 0.604675i −0.999956 0.00935037i \(-0.997024\pi\)
0.803486 0.595324i \(-0.202976\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 10.4166 + 3.38455i 0.585053 + 0.190095i 0.586563 0.809904i \(-0.300481\pi\)
−0.00151019 + 0.999999i \(0.500481\pi\)
\(318\) 0 0
\(319\) −10.4287 15.3518i −0.583897 0.859535i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 15.5837 21.4492i 0.867103 1.19346i
\(324\) 0 0
\(325\) 10.9409 3.55490i 0.606890 0.197191i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 2.74648 0.151419
\(330\) 0 0
\(331\) −4.23285 −0.232659 −0.116329 0.993211i \(-0.537113\pi\)
−0.116329 + 0.993211i \(0.537113\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −0.303101 + 0.0984835i −0.0165602 + 0.00538073i
\(336\) 0 0
\(337\) −1.56491 + 2.15391i −0.0852460 + 0.117331i −0.849510 0.527572i \(-0.823102\pi\)
0.764264 + 0.644903i \(0.223102\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 9.75446 12.5704i 0.528233 0.680723i
\(342\) 0 0
\(343\) −3.27243 1.06328i −0.176694 0.0574115i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5.13066 + 15.7905i 0.275428 + 0.847681i 0.989106 + 0.147207i \(0.0470282\pi\)
−0.713678 + 0.700474i \(0.752972\pi\)
\(348\) 0 0
\(349\) −8.09660 11.1440i −0.433401 0.596525i 0.535329 0.844644i \(-0.320188\pi\)
−0.968730 + 0.248118i \(0.920188\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 11.0249i 0.586795i 0.955990 + 0.293398i \(0.0947860\pi\)
−0.955990 + 0.293398i \(0.905214\pi\)
\(354\) 0 0
\(355\) −0.108005 + 0.0784705i −0.00573233 + 0.00416478i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 15.3828 + 11.1763i 0.811875 + 0.589862i 0.914374 0.404871i \(-0.132684\pi\)
−0.102499 + 0.994733i \(0.532684\pi\)
\(360\) 0 0
\(361\) −6.00743 + 18.4890i −0.316180 + 0.973103i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −0.146918 + 0.452167i −0.00769004 + 0.0236675i
\(366\) 0 0
\(367\) −4.60911 3.34872i −0.240594 0.174802i 0.460954 0.887424i \(-0.347507\pi\)
−0.701548 + 0.712622i \(0.747507\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.79090 1.30117i 0.0929789 0.0675531i
\(372\) 0 0
\(373\) 22.1594i 1.14737i −0.819076 0.573684i \(-0.805514\pi\)
0.819076 0.573684i \(-0.194486\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −7.56992 10.4191i −0.389871 0.536611i
\(378\) 0 0
\(379\) 0.117844 + 0.362687i 0.00605325 + 0.0186300i 0.954038 0.299687i \(-0.0968823\pi\)
−0.947984 + 0.318317i \(0.896882\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 12.0446 + 3.91352i 0.615450 + 0.199972i 0.600119 0.799911i \(-0.295120\pi\)
0.0153308 + 0.999882i \(0.495120\pi\)
\(384\) 0 0
\(385\) 0.0201311 0.0259425i 0.00102598 0.00132215i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 13.9885 19.2535i 0.709243 0.976190i −0.290570 0.956854i \(-0.593845\pi\)
0.999813 0.0193359i \(-0.00615519\pi\)
\(390\) 0 0
\(391\) 27.6544 8.98546i 1.39854 0.454414i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0.120768 0.00607647
\(396\) 0 0
\(397\) 5.00497 0.251192 0.125596 0.992081i \(-0.459916\pi\)
0.125596 + 0.992081i \(0.459916\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −4.03643 + 1.31151i −0.201570 + 0.0654939i −0.408062 0.912954i \(-0.633795\pi\)
0.206492 + 0.978448i \(0.433795\pi\)
\(402\) 0 0
\(403\) 6.48990 8.93258i 0.323285 0.444963i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −7.51225 11.0585i −0.372368 0.548151i
\(408\) 0 0
\(409\) −11.2278 3.64812i −0.555177 0.180388i 0.0179728 0.999838i \(-0.494279\pi\)
−0.573150 + 0.819450i \(0.694279\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0.212694 + 0.654604i 0.0104660 + 0.0322109i
\(414\) 0 0
\(415\) 0.124803 + 0.171777i 0.00612634 + 0.00843218i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 20.9795i 1.02492i 0.858712 + 0.512459i \(0.171265\pi\)
−0.858712 + 0.512459i \(0.828735\pi\)
\(420\) 0 0
\(421\) 2.24889 1.63391i 0.109604 0.0796320i −0.531633 0.846975i \(-0.678421\pi\)
0.641237 + 0.767343i \(0.278421\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 17.2921 + 12.5634i 0.838789 + 0.609416i
\(426\) 0 0
\(427\) −0.647200 + 1.99188i −0.0313202 + 0.0963936i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 8.63060 26.5623i 0.415722 1.27946i −0.495882 0.868390i \(-0.665155\pi\)
0.911604 0.411070i \(-0.134845\pi\)
\(432\) 0 0
\(433\) 7.41714 + 5.38887i 0.356445 + 0.258973i 0.751568 0.659656i \(-0.229298\pi\)
−0.395123 + 0.918628i \(0.629298\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −34.1075 + 24.7806i −1.63159 + 1.18542i
\(438\) 0 0
\(439\) 2.93111i 0.139894i −0.997551 0.0699472i \(-0.977717\pi\)
0.997551 0.0699472i \(-0.0222831\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −21.0670 28.9963i −1.00093 1.37766i −0.924756 0.380561i \(-0.875731\pi\)
−0.0761695 0.997095i \(-0.524269\pi\)
\(444\) 0 0
\(445\) −0.105900 0.325925i −0.00502012 0.0154503i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −13.5184 4.39241i −0.637974 0.207290i −0.0278700 0.999612i \(-0.508872\pi\)
−0.610104 + 0.792321i \(0.708872\pi\)
\(450\) 0 0
\(451\) 30.5864 8.87978i 1.44026 0.418132i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.0133938 0.0184349i 0.000627909 0.000864243i
\(456\) 0 0
\(457\) 19.4009 6.30372i 0.907534 0.294876i 0.182191 0.983263i \(-0.441681\pi\)
0.725343 + 0.688387i \(0.241681\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −0.770354 −0.0358790 −0.0179395 0.999839i \(-0.505711\pi\)
−0.0179395 + 0.999839i \(0.505711\pi\)
\(462\) 0 0
\(463\) −37.7948 −1.75647 −0.878236 0.478228i \(-0.841279\pi\)
−0.878236 + 0.478228i \(0.841279\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −16.7411 + 5.43950i −0.774684 + 0.251710i −0.669569 0.742750i \(-0.733521\pi\)
−0.105115 + 0.994460i \(0.533521\pi\)
\(468\) 0 0
\(469\) 1.15290 1.58683i 0.0532358 0.0732728i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 1.15966 3.21913i 0.0533212 0.148016i
\(474\) 0 0
\(475\) −29.4734 9.57650i −1.35233 0.439400i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.743452 2.28811i −0.0339692 0.104546i 0.932634 0.360823i \(-0.117504\pi\)
−0.966603 + 0.256277i \(0.917504\pi\)
\(480\) 0 0
\(481\) −5.45293 7.50531i −0.248632 0.342213i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0.121459i 0.00551517i
\(486\) 0 0
\(487\) 11.8099 8.58039i 0.535157 0.388815i −0.287126 0.957893i \(-0.592700\pi\)
0.822283 + 0.569078i \(0.192700\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 20.2597 + 14.7195i 0.914307 + 0.664283i 0.942101 0.335331i \(-0.108848\pi\)
−0.0277932 + 0.999614i \(0.508848\pi\)
\(492\) 0 0
\(493\) 7.39433 22.7574i 0.333024 1.02494i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0.253899 0.781420i 0.0113889 0.0350515i
\(498\) 0 0
\(499\) 18.3740 + 13.3495i 0.822535 + 0.597607i 0.917438 0.397880i \(-0.130254\pi\)
−0.0949025 + 0.995487i \(0.530254\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 8.41953 6.11715i 0.375408 0.272750i −0.384042 0.923316i \(-0.625468\pi\)
0.759450 + 0.650566i \(0.225468\pi\)
\(504\) 0 0
\(505\) 0.278835i 0.0124080i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 4.75254 + 6.54130i 0.210652 + 0.289938i 0.901249 0.433302i \(-0.142652\pi\)
−0.690596 + 0.723241i \(0.742652\pi\)
\(510\) 0 0
\(511\) −0.904203 2.78285i −0.0399996 0.123106i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.500449 + 0.162606i 0.0220524 + 0.00716526i
\(516\) 0 0
\(517\) 10.2883 + 35.4382i 0.452481 + 1.55857i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 20.5846 28.3323i 0.901828 1.24126i −0.0680535 0.997682i \(-0.521679\pi\)
0.969881 0.243578i \(-0.0783211\pi\)
\(522\) 0 0
\(523\) −41.1766 + 13.3791i −1.80052 + 0.585026i −0.999900 0.0141400i \(-0.995499\pi\)
−0.800625 + 0.599166i \(0.795499\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 20.5146 0.893630
\(528\) 0 0
\(529\) −23.2378 −1.01034
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 21.0196 6.82969i 0.910461 0.295827i
\(534\) 0 0
\(535\) 0.0322622 0.0444051i 0.00139482 0.00191980i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.727333 23.0028i 0.0313284 0.990800i
\(540\) 0 0
\(541\) −0.215252 0.0699396i −0.00925440 0.00300694i 0.304386 0.952549i \(-0.401549\pi\)
−0.313641 + 0.949542i \(0.601549\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0.0910303 + 0.280163i 0.00389931 + 0.0120008i
\(546\) 0 0
\(547\) 9.67686 + 13.3191i 0.413753 + 0.569482i 0.964129 0.265435i \(-0.0855157\pi\)
−0.550376 + 0.834917i \(0.685516\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 34.6938i 1.47801i
\(552\) 0 0
\(553\) −0.601310 + 0.436877i −0.0255703 + 0.0185779i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 21.2624 + 15.4481i 0.900919 + 0.654556i 0.938702 0.344730i \(-0.112030\pi\)
−0.0377832 + 0.999286i \(0.512030\pi\)
\(558\) 0 0
\(559\) 0.733729 2.25818i 0.0310334 0.0955110i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −11.2376 + 34.5859i −0.473610 + 1.45762i 0.374213 + 0.927343i \(0.377913\pi\)
−0.847823 + 0.530279i \(0.822087\pi\)
\(564\) 0 0
\(565\) 0.0171505 + 0.0124606i 0.000721527 + 0.000524220i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −16.3670 + 11.8913i −0.686138 + 0.498509i −0.875388 0.483420i \(-0.839394\pi\)
0.189250 + 0.981929i \(0.439394\pi\)
\(570\) 0 0
\(571\) 24.4002i 1.02112i 0.859843 + 0.510558i \(0.170561\pi\)
−0.859843 + 0.510558i \(0.829439\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −19.9778 27.4971i −0.833132 1.14671i
\(576\) 0 0
\(577\) −5.96494 18.3582i −0.248324 0.764262i −0.995072 0.0991553i \(-0.968386\pi\)
0.746748 0.665107i \(-0.231614\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.24281 0.403812i −0.0515603 0.0167530i
\(582\) 0 0
\(583\) 23.4978 + 18.2340i 0.973180 + 0.755177i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −11.2480 + 15.4816i −0.464256 + 0.638994i −0.975385 0.220510i \(-0.929228\pi\)
0.511128 + 0.859504i \(0.329228\pi\)
\(588\) 0 0
\(589\) −28.2882 + 9.19138i −1.16559 + 0.378724i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −14.9885 −0.615503 −0.307751 0.951467i \(-0.599577\pi\)
−0.307751 + 0.951467i \(0.599577\pi\)
\(594\) 0 0
\(595\) 0.0423378 0.00173568
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −31.7090 + 10.3029i −1.29560 + 0.420965i −0.874047 0.485841i \(-0.838513\pi\)
−0.421549 + 0.906806i \(0.638513\pi\)
\(600\) 0 0
\(601\) −24.8474 + 34.1996i −1.01355 + 1.39503i −0.0969178 + 0.995292i \(0.530898\pi\)
−0.916630 + 0.399737i \(0.869102\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0.410151 + 0.162573i 0.0166750 + 0.00660955i
\(606\) 0 0
\(607\) 29.3742 + 9.54427i 1.19226 + 0.387390i 0.836909 0.547342i \(-0.184360\pi\)
0.355354 + 0.934732i \(0.384360\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 7.91306 + 24.3539i 0.320128 + 0.985254i
\(612\) 0 0
\(613\) −9.38958 12.9237i −0.379242 0.521981i 0.576142 0.817350i \(-0.304558\pi\)
−0.955383 + 0.295368i \(0.904558\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 2.63374i 0.106030i −0.998594 0.0530151i \(-0.983117\pi\)
0.998594 0.0530151i \(-0.0168831\pi\)
\(618\) 0 0
\(619\) 16.3822 11.9023i 0.658454 0.478395i −0.207686 0.978196i \(-0.566593\pi\)
0.866141 + 0.499800i \(0.166593\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 1.70632 + 1.23971i 0.0683622 + 0.0496680i
\(624\) 0 0
\(625\) 7.71797 23.7535i 0.308719 0.950139i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 5.32645 16.3931i 0.212379 0.653636i
\(630\) 0 0
\(631\) 6.82846 + 4.96116i 0.271837 + 0.197501i 0.715349 0.698767i \(-0.246268\pi\)
−0.443512 + 0.896268i \(0.646268\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.414430 + 0.301101i −0.0164462 + 0.0119488i
\(636\) 0 0
\(637\) 15.9704i 0.632771i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −18.9940 26.1429i −0.750216 1.03258i −0.997965 0.0637599i \(-0.979691\pi\)
0.247749 0.968824i \(-0.420309\pi\)
\(642\) 0 0
\(643\) −4.25724 13.1024i −0.167889 0.516709i 0.831349 0.555751i \(-0.187569\pi\)
−0.999238 + 0.0390421i \(0.987569\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −8.11003 2.63511i −0.318838 0.103597i 0.145226 0.989399i \(-0.453609\pi\)
−0.464064 + 0.885802i \(0.653609\pi\)
\(648\) 0 0
\(649\) −7.64968 + 5.19656i −0.300276 + 0.203983i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0.710037 0.977282i 0.0277859 0.0382440i −0.794898 0.606743i \(-0.792476\pi\)
0.822684 + 0.568499i \(0.192476\pi\)
\(654\) 0 0
\(655\) −0.692472 + 0.224998i −0.0270571 + 0.00879139i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 9.41054 0.366583 0.183291 0.983059i \(-0.441325\pi\)
0.183291 + 0.983059i \(0.441325\pi\)
\(660\) 0 0
\(661\) 15.1027 0.587425 0.293713 0.955894i \(-0.405109\pi\)
0.293713 + 0.955894i \(0.405109\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −0.0583807 + 0.0189690i −0.00226391 + 0.000735588i
\(666\) 0 0
\(667\) −22.3653 + 30.7832i −0.865988 + 1.19193i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −28.1258 0.889320i −1.08579 0.0343318i
\(672\) 0 0
\(673\) 39.5629 + 12.8548i 1.52504 + 0.495514i 0.947201 0.320639i \(-0.103898\pi\)
0.577835 + 0.816153i \(0.303898\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −1.39693 4.29931i −0.0536884 0.165236i 0.920617 0.390467i \(-0.127686\pi\)
−0.974305 + 0.225231i \(0.927686\pi\)
\(678\) 0 0
\(679\) −0.439379 0.604753i −0.0168618 0.0232083i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 34.7783i 1.33075i −0.746507 0.665377i \(-0.768271\pi\)
0.746507 0.665377i \(-0.231729\pi\)
\(684\) 0 0
\(685\) −0.521547 + 0.378926i −0.0199273 + 0.0144780i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 16.6977 + 12.1316i 0.636132 + 0.462177i
\(690\) 0 0
\(691\) 5.52630 17.0082i 0.210230 0.647023i −0.789228 0.614101i \(-0.789519\pi\)
0.999458 0.0329217i \(-0.0104812\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −0.0478085 + 0.147139i −0.00181348 + 0.00558132i
\(696\) 0 0
\(697\) 33.2216 + 24.1369i 1.25836 + 0.914250i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −14.1345 + 10.2693i −0.533852 + 0.387866i −0.821797 0.569781i \(-0.807028\pi\)
0.287945 + 0.957647i \(0.407028\pi\)
\(702\) 0 0
\(703\) 24.9914i 0.942568i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.00869 1.38834i −0.0379356 0.0522139i
\(708\) 0 0
\(709\) 2.57673 + 7.93037i 0.0967713 + 0.297831i 0.987711 0.156290i \(-0.0499533\pi\)
−0.890940 + 0.454121i \(0.849953\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −31.0248 10.0806i −1.16189 0.377520i
\(714\) 0 0
\(715\) 0.288041 + 0.103764i 0.0107721 + 0.00388056i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 13.8736 19.0953i 0.517397 0.712136i −0.467748 0.883862i \(-0.654934\pi\)
0.985145 + 0.171726i \(0.0549344\pi\)
\(720\) 0 0
\(721\) −3.08000 + 1.00075i −0.114705 + 0.0372699i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −27.9697 −1.03877
\(726\) 0 0
\(727\) −1.90462 −0.0706386 −0.0353193 0.999376i \(-0.511245\pi\)
−0.0353193 + 0.999376i \(0.511245\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 4.19569 1.36326i 0.155183 0.0504221i
\(732\) 0 0
\(733\) −10.3520 + 14.2482i −0.382358 + 0.526271i −0.956207 0.292690i \(-0.905450\pi\)
0.573849 + 0.818961i \(0.305450\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 24.7938 + 8.93171i 0.913291 + 0.329004i
\(738\) 0 0
\(739\) 4.54355 + 1.47629i 0.167137 + 0.0543062i 0.391390 0.920225i \(-0.371994\pi\)
−0.224253 + 0.974531i \(0.571994\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.567901 1.74782i −0.0208343 0.0641212i 0.940099 0.340902i \(-0.110732\pi\)
−0.960933 + 0.276781i \(0.910732\pi\)
\(744\) 0 0
\(745\) 0.242118 + 0.333247i 0.00887053 + 0.0122092i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.337805i 0.0123431i
\(750\) 0 0
\(751\) −30.6978 + 22.3033i −1.12018 + 0.813857i −0.984236 0.176859i \(-0.943406\pi\)
−0.135942 + 0.990717i \(0.543406\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −0.284588 0.206765i −0.0103572 0.00752497i
\(756\) 0 0
\(757\) −9.46409 + 29.1275i −0.343978 + 1.05866i 0.618150 + 0.786060i \(0.287882\pi\)
−0.962128 + 0.272596i \(0.912118\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −9.53788 + 29.3546i −0.345748 + 1.06410i 0.615434 + 0.788188i \(0.288981\pi\)
−0.961182 + 0.275914i \(0.911019\pi\)
\(762\) 0 0
\(763\) −1.46674 1.06565i −0.0530994 0.0385790i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −5.19177 + 3.77204i −0.187464 + 0.136200i
\(768\) 0 0
\(769\) 19.3154i 0.696532i 0.937396 + 0.348266i \(0.113229\pi\)
−0.937396 + 0.348266i \(0.886771\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −1.72928 2.38015i −0.0621980 0.0856082i 0.776785 0.629766i \(-0.216849\pi\)
−0.838983 + 0.544158i \(0.816849\pi\)
\(774\) 0 0
\(775\) −7.40997 22.8056i −0.266174 0.819200i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −56.6245 18.3984i −2.02878 0.659191i
\(780\) 0 0
\(781\) 11.0339 + 0.348884i 0.394823 + 0.0124840i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0.307206 0.422833i 0.0109647 0.0150916i
\(786\) 0 0
\(787\) 7.65190 2.48625i 0.272761 0.0886254i −0.169443 0.985540i \(-0.554197\pi\)
0.442204 + 0.896915i \(0.354197\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −0.130470 −0.00463897
\(792\) 0 0
\(793\) −19.5272 −0.693433
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −52.2338 + 16.9718i −1.85022 + 0.601172i −0.853418 + 0.521227i \(0.825474\pi\)
−0.996799 + 0.0799446i \(0.974526\pi\)
\(798\) 0 0
\(799\) −27.9657 + 38.4914i −0.989354 + 1.36173i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 32.5203 22.0916i 1.14762 0.779596i
\(804\) 0 0
\(805\) −0.0640286 0.0208041i −0.00225671 0.000733250i
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 7.52538 + 23.1607i 0.264578 + 0.814288i 0.991790 + 0.127875i \(0.0408156\pi\)
−0.727212 + 0.686413i \(0.759184\pi\)
\(810\) 0 0
\(811\) 12.2026 + 16.7955i 0.428493 + 0.589770i 0.967607 0.252463i \(-0.0812407\pi\)
−0.539114 + 0.842233i \(0.681241\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0.368107i 0.0128942i
\(816\) 0 0
\(817\) −5.17476 + 3.75968i −0.181042 + 0.131535i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −23.1681 16.8326i −0.808571 0.587461i 0.104845 0.994489i \(-0.466565\pi\)
−0.913416 + 0.407027i \(0.866565\pi\)
\(822\) 0 0
\(823\) −0.768785 + 2.36608i −0.0267982 + 0.0824763i −0.963561 0.267488i \(-0.913806\pi\)
0.936763 + 0.349964i \(0.113806\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 7.36490 22.6668i 0.256103 0.788202i −0.737508 0.675338i \(-0.763998\pi\)
0.993610 0.112864i \(-0.0360024\pi\)
\(828\) 0 0
\(829\) 32.8736 + 23.8841i 1.14175 + 0.829528i 0.987362 0.158482i \(-0.0506601\pi\)
0.154386 + 0.988011i \(0.450660\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 24.0059 17.4413i 0.831755 0.604305i
\(834\) 0 0
\(835\) 0.305201i 0.0105619i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 33.6349 + 46.2945i 1.16121 + 1.59826i 0.706683 + 0.707531i \(0.250191\pi\)
0.454525 + 0.890734i \(0.349809\pi\)
\(840\) 0 0
\(841\) 0.714546 + 2.19915i 0.0246395 + 0.0758327i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −0.293836 0.0954731i −0.0101083 0.00328438i
\(846\) 0 0
\(847\) −2.63028 + 0.674260i −0.0903776 + 0.0231679i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −16.1107 + 22.1744i −0.552266 + 0.760130i
\(852\) 0 0
\(853\) −29.0464 + 9.43774i −0.994529 + 0.323142i −0.760677 0.649130i \(-0.775133\pi\)
−0.233852 + 0.972272i \(0.575133\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −6.14781 −0.210005 −0.105003 0.994472i \(-0.533485\pi\)
−0.105003 + 0.994472i \(0.533485\pi\)
\(858\) 0 0
\(859\) 27.5988 0.941660 0.470830 0.882224i \(-0.343955\pi\)
0.470830 + 0.882224i \(0.343955\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −40.7061 + 13.2262i −1.38565 + 0.450226i −0.904523 0.426424i \(-0.859773\pi\)
−0.481129 + 0.876650i \(0.659773\pi\)
\(864\) 0 0
\(865\) 0.391832 0.539310i 0.0133227 0.0183371i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −7.88960 6.12224i −0.267636 0.207683i
\(870\) 0 0
\(871\) 17.3926 + 5.65118i 0.589324 + 0.191483i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −0.0305901 0.0941467i −0.00103414 0.00318274i
\(876\) 0 0
\(877\) 6.60112 + 9.08566i 0.222904 + 0.306801i 0.905792 0.423722i \(-0.139277\pi\)
−0.682889 + 0.730523i \(0.739277\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 47.3136i 1.59403i 0.603957 + 0.797017i \(0.293590\pi\)
−0.603957 + 0.797017i \(0.706410\pi\)
\(882\) 0 0
\(883\) 14.7740 10.7340i 0.497186 0.361227i −0.310755 0.950490i \(-0.600582\pi\)
0.807941 + 0.589263i \(0.200582\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 32.9354 + 23.9289i 1.10586 + 0.803455i 0.982007 0.188845i \(-0.0604744\pi\)
0.123854 + 0.992300i \(0.460474\pi\)
\(888\) 0 0
\(889\) 0.974242 2.99841i 0.0326750 0.100563i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 21.3169 65.6066i 0.713342 2.19544i
\(894\) 0 0
\(895\) 0.228756 + 0.166201i 0.00764648 + 0.00555549i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −21.7180 + 15.7790i −0.724335 + 0.526260i
\(900\) 0 0
\(901\) 38.3480i 1.27756i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −0.497996 0.685433i −0.0165540 0.0227846i
\(906\) 0 0
\(907\) −0.365168 1.12387i −0.0121252 0.0373176i 0.944811 0.327616i \(-0.106245\pi\)
−0.956936 + 0.290299i \(0.906245\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −20.1283 6.54007i −0.666879 0.216682i −0.0440370 0.999030i \(-0.514022\pi\)
−0.622842 + 0.782348i \(0.714022\pi\)
\(912\) 0 0
\(913\) 0.554880 17.5488i 0.0183639 0.580779i
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 2.63394 3.62530i 0.0869803 0.119718i
\(918\) 0 0
\(919\) 13.4009 4.35422i 0.442055 0.143633i −0.0795283 0.996833i \(-0.525341\pi\)
0.521584 + 0.853200i \(0.325341\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 7.66061 0.252152
\(924\) 0 0
\(925\) −20.1477 −0.662454
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −32.4174 + 10.5331i −1.06358 + 0.345578i −0.787985 0.615695i \(-0.788875\pi\)
−0.275596 + 0.961273i \(0.588875\pi\)
\(930\) 0 0
\(931\) −25.2880 + 34.8059i −0.828780 + 1.14072i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0.158598 + 0.546290i 0.00518669 + 0.0178656i
\(936\) 0 0
\(937\) 6.41974 + 2.08590i 0.209724 + 0.0681434i 0.411995 0.911186i \(-0.364832\pi\)
−0.202271 + 0.979330i \(0.564832\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 10.2896 + 31.6682i 0.335432 + 1.03235i 0.966509 + 0.256633i \(0.0826131\pi\)
−0.631077 + 0.775720i \(0.717387\pi\)
\(942\) 0 0
\(943\) −38.3814 52.8275i −1.24987 1.72030i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0.751232i 0.0244117i −0.999926 0.0122059i \(-0.996115\pi\)
0.999926 0.0122059i \(-0.00388535\pi\)
\(948\) 0 0
\(949\) 22.0712 16.0357i 0.716462 0.520540i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −3.76491 2.73537i −0.121957 0.0886073i 0.525134 0.851019i \(-0.324015\pi\)
−0.647092 + 0.762412i \(0.724015\pi\)
\(954\) 0 0
\(955\) 0.169408 0.521385i 0.00548192 0.0168716i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 1.22605 3.77340i 0.0395913 0.121849i
\(960\) 0 0
\(961\) 6.46012 + 4.69355i 0.208391 + 0.151405i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −0.812348 + 0.590205i −0.0261504 + 0.0189994i
\(966\) 0 0
\(967\) 21.7529i 0.699525i 0.936838 + 0.349763i \(0.113738\pi\)
−0.936838 + 0.349763i \(0.886262\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −3.45215 4.75147i −0.110785 0.152482i 0.750024 0.661410i \(-0.230042\pi\)
−0.860809 + 0.508928i \(0.830042\pi\)
\(972\) 0 0
\(973\) −0.294236 0.905565i −0.00943277 0.0290311i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −0.874965 0.284293i −0.0279926 0.00909535i 0.294987 0.955501i \(-0.404685\pi\)
−0.322980 + 0.946406i \(0.604685\pi\)
\(978\) 0 0
\(979\) −9.60429 + 26.6608i −0.306954 + 0.852083i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 27.4119 37.7293i 0.874304 1.20338i −0.103662 0.994613i \(-0.533056\pi\)
0.977966 0.208764i \(-0.0669440\pi\)
\(984\) 0 0
\(985\) 0.802745 0.260828i 0.0255776 0.00831066i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) −7.01515 −0.223069
\(990\) 0 0
\(991\) −6.21090 −0.197296 −0.0986478 0.995122i \(-0.531452\pi\)
−0.0986478 + 0.995122i \(0.531452\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0.395607 0.128540i 0.0125416 0.00407500i
\(996\) 0 0
\(997\) −16.7911 + 23.1110i −0.531781 + 0.731933i −0.987400 0.158241i \(-0.949418\pi\)
0.455620 + 0.890174i \(0.349418\pi\)
\(998\) 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 1584.2.cd.c.1025.3 16
3.2 odd 2 inner 1584.2.cd.c.1025.2 16
4.3 odd 2 99.2.j.a.35.2 yes 16
11.6 odd 10 inner 1584.2.cd.c.17.2 16
12.11 even 2 99.2.j.a.35.3 yes 16
33.17 even 10 inner 1584.2.cd.c.17.3 16
36.7 odd 6 891.2.u.c.134.3 32
36.11 even 6 891.2.u.c.134.2 32
36.23 even 6 891.2.u.c.431.3 32
36.31 odd 6 891.2.u.c.431.2 32
44.7 even 10 1089.2.d.g.1088.11 16
44.15 odd 10 1089.2.d.g.1088.5 16
44.39 even 10 99.2.j.a.17.3 yes 16
132.59 even 10 1089.2.d.g.1088.12 16
132.83 odd 10 99.2.j.a.17.2 16
132.95 odd 10 1089.2.d.g.1088.6 16
396.83 odd 30 891.2.u.c.215.2 32
396.259 even 30 891.2.u.c.215.3 32
396.347 odd 30 891.2.u.c.512.3 32
396.391 even 30 891.2.u.c.512.2 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.j.a.17.2 16 132.83 odd 10
99.2.j.a.17.3 yes 16 44.39 even 10
99.2.j.a.35.2 yes 16 4.3 odd 2
99.2.j.a.35.3 yes 16 12.11 even 2
891.2.u.c.134.2 32 36.11 even 6
891.2.u.c.134.3 32 36.7 odd 6
891.2.u.c.215.2 32 396.83 odd 30
891.2.u.c.215.3 32 396.259 even 30
891.2.u.c.431.2 32 36.31 odd 6
891.2.u.c.431.3 32 36.23 even 6
891.2.u.c.512.2 32 396.391 even 30
891.2.u.c.512.3 32 396.347 odd 30
1089.2.d.g.1088.5 16 44.15 odd 10
1089.2.d.g.1088.6 16 132.95 odd 10
1089.2.d.g.1088.11 16 44.7 even 10
1089.2.d.g.1088.12 16 132.59 even 10
1584.2.cd.c.17.2 16 11.6 odd 10 inner
1584.2.cd.c.17.3 16 33.17 even 10 inner
1584.2.cd.c.1025.2 16 3.2 odd 2 inner
1584.2.cd.c.1025.3 16 1.1 even 1 trivial