Properties

Label 2736.2.cg.c.1151.16
Level $2736$
Weight $2$
Character 2736.1151
Analytic conductor $21.847$
Analytic rank $0$
Dimension $32$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2736,2,Mod(1151,2736)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2736.1151");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2736.cg (of order \(6\), degree \(2\), 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: \(21.8470699930\)
Analytic rank: \(0\)
Dimension: \(32\)
Relative dimension: \(16\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.16
Character \(\chi\) \(=\) 2736.1151
Dual form 2736.2.cg.c.2591.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.37787 + 1.95021i) q^{5} -3.27561i q^{7} +O(q^{10})\) \(q+(3.37787 + 1.95021i) q^{5} -3.27561i q^{7} +5.67850 q^{11} +(-2.34864 - 4.06796i) q^{13} +(1.20495 + 0.695678i) q^{17} +(3.88569 + 1.97520i) q^{19} +(3.59477 + 6.22632i) q^{23} +(5.10665 + 8.84498i) q^{25} +(-4.52822 + 2.61437i) q^{29} -9.36294i q^{31} +(6.38813 - 11.0646i) q^{35} -8.48371 q^{37} +(3.32327 + 1.91869i) q^{41} +(0.584394 + 0.337400i) q^{43} +(-3.54888 - 6.14684i) q^{47} -3.72960 q^{49} +(-4.58282 + 2.64589i) q^{53} +(19.1812 + 11.0743i) q^{55} +(5.63261 - 9.75597i) q^{59} +(0.574458 + 0.994990i) q^{61} -18.3214i q^{65} +(-5.96859 + 3.44597i) q^{67} +(4.92298 - 8.52686i) q^{71} +(5.95529 - 10.3149i) q^{73} -18.6005i q^{77} +(6.25791 + 3.61301i) q^{79} -4.05126 q^{83} +(2.71344 + 4.69981i) q^{85} +(-13.8078 + 7.97196i) q^{89} +(-13.3250 + 7.69321i) q^{91} +(9.27327 + 14.2499i) q^{95} +(4.66740 - 8.08417i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 16 q^{13} + 24 q^{25} - 16 q^{37} - 96 q^{49} - 8 q^{61} - 8 q^{73} + 16 q^{85} + 48 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).

\(n\) \(1009\) \(1217\) \(1711\) \(2053\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(-1\) \(1\)

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
\(5\) 3.37787 + 1.95021i 1.51063 + 0.872161i 0.999923 + 0.0124051i \(0.00394877\pi\)
0.510705 + 0.859756i \(0.329385\pi\)
\(6\) 0 0
\(7\) 3.27561i 1.23806i −0.785366 0.619032i \(-0.787525\pi\)
0.785366 0.619032i \(-0.212475\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 5.67850 1.71213 0.856066 0.516866i \(-0.172902\pi\)
0.856066 + 0.516866i \(0.172902\pi\)
\(12\) 0 0
\(13\) −2.34864 4.06796i −0.651395 1.12825i −0.982785 0.184755i \(-0.940851\pi\)
0.331390 0.943494i \(-0.392482\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.20495 + 0.695678i 0.292243 + 0.168727i 0.638953 0.769246i \(-0.279368\pi\)
−0.346710 + 0.937972i \(0.612701\pi\)
\(18\) 0 0
\(19\) 3.88569 + 1.97520i 0.891438 + 0.453143i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.59477 + 6.22632i 0.749561 + 1.29828i 0.948033 + 0.318171i \(0.103069\pi\)
−0.198472 + 0.980107i \(0.563598\pi\)
\(24\) 0 0
\(25\) 5.10665 + 8.84498i 1.02133 + 1.76900i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −4.52822 + 2.61437i −0.840869 + 0.485476i −0.857560 0.514385i \(-0.828020\pi\)
0.0166905 + 0.999861i \(0.494687\pi\)
\(30\) 0 0
\(31\) 9.36294i 1.68163i −0.541319 0.840817i \(-0.682075\pi\)
0.541319 0.840817i \(-0.317925\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 6.38813 11.0646i 1.07979 1.87025i
\(36\) 0 0
\(37\) −8.48371 −1.39471 −0.697356 0.716725i \(-0.745640\pi\)
−0.697356 + 0.716725i \(0.745640\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 3.32327 + 1.91869i 0.519007 + 0.299649i 0.736528 0.676407i \(-0.236464\pi\)
−0.217521 + 0.976056i \(0.569797\pi\)
\(42\) 0 0
\(43\) 0.584394 + 0.337400i 0.0891192 + 0.0514530i 0.543897 0.839152i \(-0.316948\pi\)
−0.454778 + 0.890605i \(0.650281\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.54888 6.14684i −0.517657 0.896608i −0.999790 0.0205100i \(-0.993471\pi\)
0.482133 0.876098i \(-0.339862\pi\)
\(48\) 0 0
\(49\) −3.72960 −0.532800
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −4.58282 + 2.64589i −0.629498 + 0.363441i −0.780558 0.625084i \(-0.785065\pi\)
0.151060 + 0.988525i \(0.451731\pi\)
\(54\) 0 0
\(55\) 19.1812 + 11.0743i 2.58639 + 1.49326i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.63261 9.75597i 0.733303 1.27012i −0.222160 0.975010i \(-0.571311\pi\)
0.955464 0.295108i \(-0.0953558\pi\)
\(60\) 0 0
\(61\) 0.574458 + 0.994990i 0.0735518 + 0.127395i 0.900456 0.434948i \(-0.143233\pi\)
−0.826904 + 0.562343i \(0.809900\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 18.3214i 2.27249i
\(66\) 0 0
\(67\) −5.96859 + 3.44597i −0.729179 + 0.420992i −0.818122 0.575045i \(-0.804985\pi\)
0.0889425 + 0.996037i \(0.471651\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.92298 8.52686i 0.584251 1.01195i −0.410718 0.911762i \(-0.634722\pi\)
0.994968 0.100189i \(-0.0319448\pi\)
\(72\) 0 0
\(73\) 5.95529 10.3149i 0.697014 1.20726i −0.272483 0.962161i \(-0.587845\pi\)
0.969497 0.245103i \(-0.0788219\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 18.6005i 2.11973i
\(78\) 0 0
\(79\) 6.25791 + 3.61301i 0.704070 + 0.406495i 0.808862 0.587999i \(-0.200084\pi\)
−0.104791 + 0.994494i \(0.533418\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −4.05126 −0.444683 −0.222342 0.974969i \(-0.571370\pi\)
−0.222342 + 0.974969i \(0.571370\pi\)
\(84\) 0 0
\(85\) 2.71344 + 4.69981i 0.294314 + 0.509766i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −13.8078 + 7.97196i −1.46363 + 0.845026i −0.999177 0.0405732i \(-0.987082\pi\)
−0.464451 + 0.885599i \(0.653748\pi\)
\(90\) 0 0
\(91\) −13.3250 + 7.69321i −1.39684 + 0.806468i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 9.27327 + 14.2499i 0.951417 + 1.46201i
\(96\) 0 0
\(97\) 4.66740 8.08417i 0.473902 0.820823i −0.525651 0.850700i \(-0.676178\pi\)
0.999554 + 0.0298774i \(0.00951170\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.65167 1.53094i 0.263851 0.152334i −0.362239 0.932085i \(-0.617988\pi\)
0.626090 + 0.779751i \(0.284654\pi\)
\(102\) 0 0
\(103\) 6.89193i 0.679083i 0.940591 + 0.339541i \(0.110272\pi\)
−0.940591 + 0.339541i \(0.889728\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −2.54022 −0.245573 −0.122786 0.992433i \(-0.539183\pi\)
−0.122786 + 0.992433i \(0.539183\pi\)
\(108\) 0 0
\(109\) −4.44157 + 7.69303i −0.425426 + 0.736859i −0.996460 0.0840672i \(-0.973209\pi\)
0.571034 + 0.820926i \(0.306542\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 17.2092i 1.61890i 0.587186 + 0.809452i \(0.300236\pi\)
−0.587186 + 0.809452i \(0.699764\pi\)
\(114\) 0 0
\(115\) 28.0422i 2.61495i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.27877 3.94694i 0.208894 0.361815i
\(120\) 0 0
\(121\) 21.2454 1.93140
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 20.3341i 1.81874i
\(126\) 0 0
\(127\) 5.10408 2.94684i 0.452914 0.261490i −0.256146 0.966638i \(-0.582453\pi\)
0.709060 + 0.705148i \(0.249120\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −3.64066 + 6.30581i −0.318086 + 0.550941i −0.980089 0.198560i \(-0.936373\pi\)
0.662003 + 0.749501i \(0.269707\pi\)
\(132\) 0 0
\(133\) 6.46999 12.7280i 0.561019 1.10366i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.02007 4.63039i 0.685201 0.395601i −0.116611 0.993178i \(-0.537203\pi\)
0.801812 + 0.597577i \(0.203870\pi\)
\(138\) 0 0
\(139\) −6.37032 + 3.67791i −0.540324 + 0.311956i −0.745210 0.666830i \(-0.767651\pi\)
0.204886 + 0.978786i \(0.434317\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −13.3367 23.0999i −1.11527 1.93171i
\(144\) 0 0
\(145\) −20.3943 −1.69365
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 3.72883 + 2.15284i 0.305478 + 0.176368i 0.644901 0.764266i \(-0.276899\pi\)
−0.339423 + 0.940634i \(0.610232\pi\)
\(150\) 0 0
\(151\) 24.0918i 1.96057i 0.197599 + 0.980283i \(0.436686\pi\)
−0.197599 + 0.980283i \(0.563314\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 18.2597 31.6268i 1.46666 2.54032i
\(156\) 0 0
\(157\) −0.483837 + 0.838030i −0.0386144 + 0.0668821i −0.884687 0.466186i \(-0.845628\pi\)
0.846072 + 0.533068i \(0.178961\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 20.3950 11.7751i 1.60735 0.928004i
\(162\) 0 0
\(163\) 1.13868i 0.0891882i 0.999005 + 0.0445941i \(0.0141994\pi\)
−0.999005 + 0.0445941i \(0.985801\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.11802 8.86467i −0.396044 0.685968i 0.597190 0.802100i \(-0.296284\pi\)
−0.993234 + 0.116132i \(0.962951\pi\)
\(168\) 0 0
\(169\) −4.53220 + 7.84999i −0.348630 + 0.603846i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 6.16300 + 3.55821i 0.468564 + 0.270525i 0.715638 0.698471i \(-0.246136\pi\)
−0.247074 + 0.968996i \(0.579469\pi\)
\(174\) 0 0
\(175\) 28.9727 16.7274i 2.19013 1.26447i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 8.72500 0.652137 0.326068 0.945346i \(-0.394276\pi\)
0.326068 + 0.945346i \(0.394276\pi\)
\(180\) 0 0
\(181\) −9.07811 15.7237i −0.674770 1.16874i −0.976536 0.215355i \(-0.930909\pi\)
0.301765 0.953382i \(-0.402424\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −28.6568 16.5450i −2.10689 1.21641i
\(186\) 0 0
\(187\) 6.84230 + 3.95041i 0.500359 + 0.288882i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −4.16746 −0.301547 −0.150774 0.988568i \(-0.548176\pi\)
−0.150774 + 0.988568i \(0.548176\pi\)
\(192\) 0 0
\(193\) −3.31631 + 5.74402i −0.238713 + 0.413464i −0.960345 0.278813i \(-0.910059\pi\)
0.721632 + 0.692277i \(0.243392\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 15.2595i 1.08719i 0.839347 + 0.543596i \(0.182938\pi\)
−0.839347 + 0.543596i \(0.817062\pi\)
\(198\) 0 0
\(199\) 7.53911 4.35271i 0.534433 0.308555i −0.208387 0.978047i \(-0.566821\pi\)
0.742820 + 0.669491i \(0.233488\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 8.56364 + 14.8327i 0.601050 + 1.04105i
\(204\) 0 0
\(205\) 7.48371 + 12.9622i 0.522685 + 0.905316i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 22.0649 + 11.2162i 1.52626 + 0.775840i
\(210\) 0 0
\(211\) 8.10855 + 4.68147i 0.558215 + 0.322286i 0.752429 0.658674i \(-0.228882\pi\)
−0.194214 + 0.980959i \(0.562215\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 1.31600 + 2.27938i 0.0897506 + 0.155453i
\(216\) 0 0
\(217\) −30.6693 −2.08197
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 6.53558i 0.439631i
\(222\) 0 0
\(223\) −14.6062 8.43291i −0.978106 0.564710i −0.0764080 0.997077i \(-0.524345\pi\)
−0.901698 + 0.432367i \(0.857678\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.7763 0.847990 0.423995 0.905665i \(-0.360627\pi\)
0.423995 + 0.905665i \(0.360627\pi\)
\(228\) 0 0
\(229\) 18.0918 1.19554 0.597771 0.801667i \(-0.296053\pi\)
0.597771 + 0.801667i \(0.296053\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −7.17989 4.14531i −0.470370 0.271568i 0.246025 0.969264i \(-0.420876\pi\)
−0.716395 + 0.697695i \(0.754209\pi\)
\(234\) 0 0
\(235\) 27.6843i 1.80592i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 19.5757 1.26625 0.633124 0.774050i \(-0.281772\pi\)
0.633124 + 0.774050i \(0.281772\pi\)
\(240\) 0 0
\(241\) 13.0035 + 22.5228i 0.837630 + 1.45082i 0.891871 + 0.452290i \(0.149393\pi\)
−0.0542404 + 0.998528i \(0.517274\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −12.5981 7.27351i −0.804863 0.464688i
\(246\) 0 0
\(247\) −1.09103 20.4459i −0.0694203 1.30094i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −11.2530 19.4908i −0.710284 1.23025i −0.964751 0.263166i \(-0.915233\pi\)
0.254467 0.967081i \(-0.418100\pi\)
\(252\) 0 0
\(253\) 20.4129 + 35.3562i 1.28335 + 2.22282i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 4.99317 2.88281i 0.311465 0.179825i −0.336117 0.941820i \(-0.609114\pi\)
0.647582 + 0.761996i \(0.275780\pi\)
\(258\) 0 0
\(259\) 27.7893i 1.72674i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −7.85327 + 13.6023i −0.484254 + 0.838752i −0.999836 0.0180879i \(-0.994242\pi\)
0.515583 + 0.856840i \(0.327575\pi\)
\(264\) 0 0
\(265\) −20.6402 −1.26792
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 5.43680 + 3.13894i 0.331488 + 0.191384i 0.656501 0.754325i \(-0.272036\pi\)
−0.325014 + 0.945709i \(0.605369\pi\)
\(270\) 0 0
\(271\) −25.7135 14.8457i −1.56198 0.901812i −0.997056 0.0766706i \(-0.975571\pi\)
−0.564927 0.825141i \(-0.691096\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 28.9981 + 50.2262i 1.74865 + 3.02876i
\(276\) 0 0
\(277\) −30.6970 −1.84440 −0.922202 0.386708i \(-0.873612\pi\)
−0.922202 + 0.386708i \(0.873612\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −7.72370 + 4.45928i −0.460757 + 0.266018i −0.712363 0.701812i \(-0.752375\pi\)
0.251605 + 0.967830i \(0.419042\pi\)
\(282\) 0 0
\(283\) 3.36586 + 1.94328i 0.200079 + 0.115516i 0.596692 0.802470i \(-0.296481\pi\)
−0.396613 + 0.917986i \(0.629815\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 6.28488 10.8857i 0.370984 0.642564i
\(288\) 0 0
\(289\) −7.53207 13.0459i −0.443063 0.767407i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 7.70978i 0.450410i 0.974311 + 0.225205i \(0.0723053\pi\)
−0.974311 + 0.225205i \(0.927695\pi\)
\(294\) 0 0
\(295\) 38.0524 21.9696i 2.21550 1.27912i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 16.8856 29.2467i 0.976520 1.69138i
\(300\) 0 0
\(301\) 1.10519 1.91424i 0.0637020 0.110335i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 4.48126i 0.256596i
\(306\) 0 0
\(307\) −0.310029 0.178995i −0.0176943 0.0102158i 0.491127 0.871088i \(-0.336585\pi\)
−0.508821 + 0.860872i \(0.669919\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −3.68561 −0.208992 −0.104496 0.994525i \(-0.533323\pi\)
−0.104496 + 0.994525i \(0.533323\pi\)
\(312\) 0 0
\(313\) −13.8361 23.9649i −0.782064 1.35457i −0.930737 0.365688i \(-0.880834\pi\)
0.148673 0.988886i \(-0.452500\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9.52139 + 5.49717i −0.534774 + 0.308752i −0.742958 0.669338i \(-0.766578\pi\)
0.208184 + 0.978090i \(0.433245\pi\)
\(318\) 0 0
\(319\) −25.7135 + 14.8457i −1.43968 + 0.831199i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 3.30795 + 5.08321i 0.184059 + 0.282837i
\(324\) 0 0
\(325\) 23.9874 41.5473i 1.33058 2.30463i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −20.1346 + 11.6247i −1.11006 + 0.640892i
\(330\) 0 0
\(331\) 32.7627i 1.80080i −0.435061 0.900401i \(-0.643273\pi\)
0.435061 0.900401i \(-0.356727\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −26.8815 −1.46869
\(336\) 0 0
\(337\) 2.77186 4.80101i 0.150993 0.261528i −0.780600 0.625031i \(-0.785086\pi\)
0.931593 + 0.363504i \(0.118420\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 53.1675i 2.87918i
\(342\) 0 0
\(343\) 10.7125i 0.578423i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −14.0923 + 24.4085i −0.756512 + 1.31032i 0.188107 + 0.982149i \(0.439765\pi\)
−0.944619 + 0.328169i \(0.893569\pi\)
\(348\) 0 0
\(349\) 32.4312 1.73600 0.868002 0.496560i \(-0.165404\pi\)
0.868002 + 0.496560i \(0.165404\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 9.23276i 0.491410i 0.969345 + 0.245705i \(0.0790195\pi\)
−0.969345 + 0.245705i \(0.920981\pi\)
\(354\) 0 0
\(355\) 33.2584 19.2017i 1.76517 1.01912i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −1.28232 + 2.22105i −0.0676784 + 0.117222i −0.897879 0.440242i \(-0.854893\pi\)
0.830201 + 0.557465i \(0.188226\pi\)
\(360\) 0 0
\(361\) 11.1971 + 15.3500i 0.589323 + 0.807897i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 40.2324 23.2282i 2.10586 1.21582i
\(366\) 0 0
\(367\) −24.5597 + 14.1795i −1.28200 + 0.740165i −0.977214 0.212254i \(-0.931919\pi\)
−0.304789 + 0.952420i \(0.598586\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 8.66689 + 15.0115i 0.449963 + 0.779358i
\(372\) 0 0
\(373\) 5.99511 0.310415 0.155207 0.987882i \(-0.450395\pi\)
0.155207 + 0.987882i \(0.450395\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 21.2703 + 12.2804i 1.09548 + 0.632473i
\(378\) 0 0
\(379\) 0.804599i 0.0413295i −0.999786 0.0206647i \(-0.993422\pi\)
0.999786 0.0206647i \(-0.00657826\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 2.07152 3.58798i 0.105850 0.183337i −0.808235 0.588860i \(-0.799577\pi\)
0.914085 + 0.405522i \(0.132910\pi\)
\(384\) 0 0
\(385\) 36.2750 62.8301i 1.84874 3.20212i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −26.5385 + 15.3220i −1.34556 + 0.776857i −0.987616 0.156888i \(-0.949854\pi\)
−0.357939 + 0.933745i \(0.616520\pi\)
\(390\) 0 0
\(391\) 10.0032i 0.505884i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 14.0923 + 24.4085i 0.709058 + 1.22813i
\(396\) 0 0
\(397\) −2.33247 + 4.03996i −0.117064 + 0.202760i −0.918603 0.395182i \(-0.870681\pi\)
0.801539 + 0.597942i \(0.204015\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 8.16733 + 4.71541i 0.407857 + 0.235476i 0.689869 0.723935i \(-0.257668\pi\)
−0.282011 + 0.959411i \(0.591002\pi\)
\(402\) 0 0
\(403\) −38.0881 + 21.9902i −1.89730 + 1.09541i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −48.1747 −2.38793
\(408\) 0 0
\(409\) 10.6228 + 18.3993i 0.525264 + 0.909785i 0.999567 + 0.0294229i \(0.00936695\pi\)
−0.474303 + 0.880362i \(0.657300\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −31.9567 18.4502i −1.57249 0.907876i
\(414\) 0 0
\(415\) −13.6846 7.90081i −0.671751 0.387836i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −2.08467 −0.101843 −0.0509214 0.998703i \(-0.516216\pi\)
−0.0509214 + 0.998703i \(0.516216\pi\)
\(420\) 0 0
\(421\) −2.33625 + 4.04651i −0.113862 + 0.197215i −0.917324 0.398141i \(-0.869656\pi\)
0.803462 + 0.595356i \(0.202989\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 14.2103i 0.689303i
\(426\) 0 0
\(427\) 3.25920 1.88170i 0.157724 0.0910618i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −9.31916 16.1413i −0.448888 0.777497i 0.549426 0.835543i \(-0.314847\pi\)
−0.998314 + 0.0580454i \(0.981513\pi\)
\(432\) 0 0
\(433\) 13.1872 + 22.8409i 0.633737 + 1.09766i 0.986781 + 0.162058i \(0.0518131\pi\)
−0.353044 + 0.935607i \(0.614854\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 1.66990 + 31.2939i 0.0798821 + 1.49699i
\(438\) 0 0
\(439\) −10.3816 5.99383i −0.495488 0.286070i 0.231361 0.972868i \(-0.425682\pi\)
−0.726848 + 0.686798i \(0.759016\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 2.79336 + 4.83824i 0.132717 + 0.229872i 0.924723 0.380641i \(-0.124297\pi\)
−0.792006 + 0.610513i \(0.790963\pi\)
\(444\) 0 0
\(445\) −62.1880 −2.94799
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 18.9428i 0.893964i −0.894543 0.446982i \(-0.852499\pi\)
0.894543 0.446982i \(-0.147501\pi\)
\(450\) 0 0
\(451\) 18.8712 + 10.8953i 0.888610 + 0.513039i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −60.0136 −2.81348
\(456\) 0 0
\(457\) −26.2451 −1.22769 −0.613847 0.789425i \(-0.710379\pi\)
−0.613847 + 0.789425i \(0.710379\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −8.07467 4.66191i −0.376075 0.217127i 0.300034 0.953928i \(-0.403002\pi\)
−0.676109 + 0.736802i \(0.736335\pi\)
\(462\) 0 0
\(463\) 18.6793i 0.868101i −0.900889 0.434050i \(-0.857084\pi\)
0.900889 0.434050i \(-0.142916\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 9.63798 0.445992 0.222996 0.974819i \(-0.428416\pi\)
0.222996 + 0.974819i \(0.428416\pi\)
\(468\) 0 0
\(469\) 11.2876 + 19.5508i 0.521215 + 0.902770i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 3.31848 + 1.91592i 0.152584 + 0.0880943i
\(474\) 0 0
\(475\) 2.37222 + 44.4555i 0.108845 + 2.03976i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 2.03784 + 3.52964i 0.0931113 + 0.161274i 0.908819 0.417191i \(-0.136985\pi\)
−0.815707 + 0.578465i \(0.803652\pi\)
\(480\) 0 0
\(481\) 19.9252 + 34.5114i 0.908509 + 1.57358i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 31.5317 18.2048i 1.43178 0.826638i
\(486\) 0 0
\(487\) 7.99607i 0.362337i 0.983452 + 0.181168i \(0.0579879\pi\)
−0.983452 + 0.181168i \(0.942012\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −4.92298 + 8.52686i −0.222171 + 0.384812i −0.955467 0.295098i \(-0.904648\pi\)
0.733296 + 0.679910i \(0.237981\pi\)
\(492\) 0 0
\(493\) −7.27503 −0.327651
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −27.9306 16.1258i −1.25286 0.723339i
\(498\) 0 0
\(499\) −0.416687 0.240574i −0.0186535 0.0107696i 0.490644 0.871360i \(-0.336761\pi\)
−0.509298 + 0.860590i \(0.670095\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −19.9206 34.5036i −0.888218 1.53844i −0.841981 0.539508i \(-0.818610\pi\)
−0.0462369 0.998931i \(-0.514723\pi\)
\(504\) 0 0
\(505\) 11.9426 0.531441
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 19.3040 11.1452i 0.855636 0.494001i −0.00691272 0.999976i \(-0.502200\pi\)
0.862548 + 0.505975i \(0.168867\pi\)
\(510\) 0 0
\(511\) −33.7874 19.5072i −1.49467 0.862947i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −13.4407 + 23.2800i −0.592269 + 1.02584i
\(516\) 0 0
\(517\) −20.1523 34.9048i −0.886297 1.53511i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 7.73125i 0.338712i 0.985555 + 0.169356i \(0.0541688\pi\)
−0.985555 + 0.169356i \(0.945831\pi\)
\(522\) 0 0
\(523\) −0.986124 + 0.569339i −0.0431202 + 0.0248955i −0.521405 0.853309i \(-0.674592\pi\)
0.478285 + 0.878205i \(0.341259\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 6.51359 11.2819i 0.283736 0.491446i
\(528\) 0 0
\(529\) −14.3447 + 24.8458i −0.623684 + 1.08025i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 18.0252i 0.780760i
\(534\) 0 0
\(535\) −8.58053 4.95397i −0.370969 0.214179i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −21.1785 −0.912224
\(540\) 0 0
\(541\) −8.22960 14.2541i −0.353818 0.612831i 0.633097 0.774073i \(-0.281784\pi\)
−0.986915 + 0.161242i \(0.948450\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −30.0061 + 17.3240i −1.28532 + 0.742080i
\(546\) 0 0
\(547\) −10.7926 + 6.23108i −0.461456 + 0.266422i −0.712656 0.701513i \(-0.752508\pi\)
0.251200 + 0.967935i \(0.419175\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) −22.7592 + 1.21447i −0.969573 + 0.0517381i
\(552\) 0 0
\(553\) 11.8348 20.4985i 0.503266 0.871683i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −15.9642 + 9.21695i −0.676426 + 0.390535i −0.798507 0.601985i \(-0.794376\pi\)
0.122081 + 0.992520i \(0.461043\pi\)
\(558\) 0 0
\(559\) 3.16972i 0.134065i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −34.0466 −1.43489 −0.717446 0.696614i \(-0.754689\pi\)
−0.717446 + 0.696614i \(0.754689\pi\)
\(564\) 0 0
\(565\) −33.5616 + 58.1303i −1.41195 + 2.44556i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 25.8995i 1.08576i 0.839809 + 0.542882i \(0.182667\pi\)
−0.839809 + 0.542882i \(0.817333\pi\)
\(570\) 0 0
\(571\) 4.59067i 0.192113i 0.995376 + 0.0960567i \(0.0306230\pi\)
−0.995376 + 0.0960567i \(0.969377\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −36.7145 + 63.5913i −1.53110 + 2.65194i
\(576\) 0 0
\(577\) −20.4295 −0.850493 −0.425247 0.905078i \(-0.639813\pi\)
−0.425247 + 0.905078i \(0.639813\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 13.2703i 0.550546i
\(582\) 0 0
\(583\) −26.0235 + 15.0247i −1.07778 + 0.622259i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 4.95666 8.58519i 0.204583 0.354349i −0.745417 0.666599i \(-0.767749\pi\)
0.950000 + 0.312250i \(0.101083\pi\)
\(588\) 0 0
\(589\) 18.4937 36.3815i 0.762020 1.49907i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 12.3914 7.15420i 0.508856 0.293788i −0.223508 0.974702i \(-0.571751\pi\)
0.732363 + 0.680914i \(0.238417\pi\)
\(594\) 0 0
\(595\) 15.3947 8.88816i 0.631123 0.364379i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −3.35384 5.80903i −0.137034 0.237350i 0.789338 0.613958i \(-0.210424\pi\)
−0.926373 + 0.376608i \(0.877090\pi\)
\(600\) 0 0
\(601\) −3.81850 −0.155760 −0.0778799 0.996963i \(-0.524815\pi\)
−0.0778799 + 0.996963i \(0.524815\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 71.7640 + 41.4330i 2.91762 + 1.68449i
\(606\) 0 0
\(607\) 19.5650i 0.794120i −0.917793 0.397060i \(-0.870031\pi\)
0.917793 0.397060i \(-0.129969\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −16.6701 + 28.8734i −0.674398 + 1.16809i
\(612\) 0 0
\(613\) −21.2753 + 36.8498i −0.859299 + 1.48835i 0.0132989 + 0.999912i \(0.495767\pi\)
−0.872598 + 0.488439i \(0.837567\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −13.5604 + 7.82909i −0.545921 + 0.315187i −0.747475 0.664290i \(-0.768734\pi\)
0.201554 + 0.979477i \(0.435401\pi\)
\(618\) 0 0
\(619\) 34.6107i 1.39112i 0.718467 + 0.695561i \(0.244844\pi\)
−0.718467 + 0.695561i \(0.755156\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 26.1130 + 45.2290i 1.04620 + 1.81206i
\(624\) 0 0
\(625\) −14.1226 + 24.4610i −0.564902 + 0.978439i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −10.2224 5.90193i −0.407595 0.235325i
\(630\) 0 0
\(631\) 6.11091 3.52814i 0.243272 0.140453i −0.373408 0.927667i \(-0.621811\pi\)
0.616679 + 0.787214i \(0.288477\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 22.9879 0.912246
\(636\) 0 0
\(637\) 8.75948 + 15.1719i 0.347063 + 0.601131i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −16.9743 9.80009i −0.670443 0.387080i 0.125802 0.992055i \(-0.459850\pi\)
−0.796244 + 0.604975i \(0.793183\pi\)
\(642\) 0 0
\(643\) −12.8109 7.39637i −0.505212 0.291685i 0.225651 0.974208i \(-0.427549\pi\)
−0.730863 + 0.682524i \(0.760882\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.8654 −1.21344 −0.606721 0.794915i \(-0.707516\pi\)
−0.606721 + 0.794915i \(0.707516\pi\)
\(648\) 0 0
\(649\) 31.9848 55.3993i 1.25551 2.17461i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 27.6677i 1.08272i 0.840791 + 0.541360i \(0.182090\pi\)
−0.840791 + 0.541360i \(0.817910\pi\)
\(654\) 0 0
\(655\) −24.5953 + 14.2001i −0.961019 + 0.554845i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 18.4089 + 31.8851i 0.717108 + 1.24207i 0.962141 + 0.272552i \(0.0878677\pi\)
−0.245033 + 0.969515i \(0.578799\pi\)
\(660\) 0 0
\(661\) −5.48371 9.49806i −0.213291 0.369432i 0.739451 0.673210i \(-0.235085\pi\)
−0.952743 + 0.303778i \(0.901752\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 46.6770 30.3756i 1.81006 1.17791i
\(666\) 0 0
\(667\) −32.5558 18.7961i −1.26057 0.727788i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 3.26206 + 5.65005i 0.125930 + 0.218118i
\(672\) 0 0
\(673\) −17.0122 −0.655772 −0.327886 0.944717i \(-0.606336\pi\)
−0.327886 + 0.944717i \(0.606336\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 3.69536i 0.142024i −0.997475 0.0710120i \(-0.977377\pi\)
0.997475 0.0710120i \(-0.0226229\pi\)
\(678\) 0 0
\(679\) −26.4805 15.2886i −1.01623 0.586721i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 49.8693 1.90820 0.954099 0.299493i \(-0.0968175\pi\)
0.954099 + 0.299493i \(0.0968175\pi\)
\(684\) 0 0
\(685\) 36.1210 1.38011
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 21.5267 + 12.4285i 0.820104 + 0.473487i
\(690\) 0 0
\(691\) 19.6882i 0.748974i 0.927232 + 0.374487i \(0.122181\pi\)
−0.927232 + 0.374487i \(0.877819\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −28.6908 −1.08830
\(696\) 0 0
\(697\) 2.66958 + 4.62385i 0.101118 + 0.175141i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −19.0808 11.0163i −0.720673 0.416081i 0.0943271 0.995541i \(-0.469930\pi\)
−0.815000 + 0.579460i \(0.803263\pi\)
\(702\) 0 0
\(703\) −32.9650 16.7570i −1.24330 0.632004i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −5.01476 8.68583i −0.188600 0.326664i
\(708\) 0 0
\(709\) 3.54702 + 6.14363i 0.133211 + 0.230729i 0.924913 0.380179i \(-0.124138\pi\)
−0.791701 + 0.610908i \(0.790804\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 58.2967 33.6576i 2.18323 1.26049i
\(714\) 0 0
\(715\) 104.038i 3.89080i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 8.41376 14.5731i 0.313780 0.543483i −0.665397 0.746489i \(-0.731738\pi\)
0.979177 + 0.203006i \(0.0650712\pi\)
\(720\) 0 0
\(721\) 22.5753 0.840747
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −46.2481 26.7013i −1.71761 0.991663i
\(726\) 0 0
\(727\) 22.0180 + 12.7121i 0.816602 + 0.471465i 0.849243 0.528002i \(-0.177059\pi\)
−0.0326416 + 0.999467i \(0.510392\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0.469443 + 0.813099i 0.0173630 + 0.0300736i
\(732\) 0 0
\(733\) −17.8756 −0.660250 −0.330125 0.943937i \(-0.607091\pi\)
−0.330125 + 0.943937i \(0.607091\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −33.8926 + 19.5679i −1.24845 + 0.720794i
\(738\) 0 0
\(739\) 3.86322 + 2.23043i 0.142111 + 0.0820478i 0.569370 0.822082i \(-0.307187\pi\)
−0.427259 + 0.904129i \(0.640521\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 16.3588 28.3343i 0.600147 1.03948i −0.392652 0.919687i \(-0.628442\pi\)
0.992798 0.119797i \(-0.0382245\pi\)
\(744\) 0 0
\(745\) 8.39700 + 14.5440i 0.307642 + 0.532852i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 8.32077i 0.304034i
\(750\) 0 0
\(751\) 2.49214 1.43884i 0.0909395 0.0525040i −0.453841 0.891083i \(-0.649946\pi\)
0.544780 + 0.838579i \(0.316613\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −46.9842 + 81.3790i −1.70993 + 2.96169i
\(756\) 0 0
\(757\) 12.8360 22.2326i 0.466532 0.808057i −0.532737 0.846281i \(-0.678837\pi\)
0.999269 + 0.0382235i \(0.0121699\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 17.9352i 0.650150i −0.945688 0.325075i \(-0.894610\pi\)
0.945688 0.325075i \(-0.105390\pi\)
\(762\) 0 0
\(763\) 25.1994 + 14.5489i 0.912278 + 0.526704i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −52.9158 −1.91068
\(768\) 0 0
\(769\) −9.92395 17.1888i −0.357867 0.619843i 0.629738 0.776808i \(-0.283162\pi\)
−0.987604 + 0.156965i \(0.949829\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −26.4410 + 15.2657i −0.951018 + 0.549071i −0.893397 0.449268i \(-0.851685\pi\)
−0.0576213 + 0.998339i \(0.518352\pi\)
\(774\) 0 0
\(775\) 82.8151 47.8133i 2.97481 1.71750i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 9.12338 + 14.0196i 0.326879 + 0.502303i
\(780\) 0 0
\(781\) 27.9552 48.4198i 1.00031 1.73260i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −3.26867 + 1.88717i −0.116664 + 0.0673559i
\(786\) 0 0
\(787\) 25.1007i 0.894744i −0.894348 0.447372i \(-0.852360\pi\)
0.894348 0.447372i \(-0.147640\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 56.3705 2.00430
\(792\) 0 0
\(793\) 2.69839 4.67374i 0.0958225 0.165970i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 24.4922i 0.867560i 0.901019 + 0.433780i \(0.142820\pi\)
−0.901019 + 0.433780i \(0.857180\pi\)
\(798\) 0 0
\(799\) 9.87550i 0.349370i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 33.8171 58.5730i 1.19338 2.06700i
\(804\) 0 0
\(805\) 91.8554 3.23748
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 4.71435i 0.165748i −0.996560 0.0828738i \(-0.973590\pi\)
0.996560 0.0828738i \(-0.0264098\pi\)
\(810\) 0 0
\(811\) −40.1007 + 23.1521i −1.40812 + 0.812981i −0.995207 0.0977875i \(-0.968823\pi\)
−0.412917 + 0.910769i \(0.635490\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −2.22066 + 3.84630i −0.0777865 + 0.134730i
\(816\) 0 0
\(817\) 1.60434 + 2.46533i 0.0561287 + 0.0862508i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −6.52776 + 3.76881i −0.227821 + 0.131532i −0.609566 0.792735i \(-0.708656\pi\)
0.381746 + 0.924267i \(0.375323\pi\)
\(822\) 0 0
\(823\) 36.9895 21.3559i 1.28937 0.744420i 0.310831 0.950465i \(-0.399393\pi\)
0.978543 + 0.206045i \(0.0660592\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −13.1212 22.7265i −0.456268 0.790279i 0.542492 0.840061i \(-0.317481\pi\)
−0.998760 + 0.0497815i \(0.984147\pi\)
\(828\) 0 0
\(829\) −45.4613 −1.57894 −0.789469 0.613791i \(-0.789644\pi\)
−0.789469 + 0.613791i \(0.789644\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) −4.49398 2.59460i −0.155707 0.0898976i
\(834\) 0 0
\(835\) 39.9249i 1.38166i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −10.3025 + 17.8444i −0.355680 + 0.616056i −0.987234 0.159276i \(-0.949084\pi\)
0.631554 + 0.775332i \(0.282417\pi\)
\(840\) 0 0
\(841\) −0.830158 + 1.43788i −0.0286262 + 0.0495820i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −30.6183 + 17.6775i −1.05330 + 0.608124i
\(846\) 0 0
\(847\) 69.5915i 2.39119i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) −30.4970 52.8223i −1.04542 1.81072i
\(852\) 0 0
\(853\) −3.52842 + 6.11139i −0.120811 + 0.209250i −0.920088 0.391713i \(-0.871883\pi\)
0.799277 + 0.600963i \(0.205216\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −16.4352 9.48889i −0.561417 0.324134i 0.192297 0.981337i \(-0.438406\pi\)
−0.753714 + 0.657203i \(0.771740\pi\)
\(858\) 0 0
\(859\) 6.42562 3.70983i 0.219239 0.126578i −0.386359 0.922349i \(-0.626267\pi\)
0.605598 + 0.795771i \(0.292934\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 37.7307 1.28437 0.642184 0.766550i \(-0.278028\pi\)
0.642184 + 0.766550i \(0.278028\pi\)
\(864\) 0 0
\(865\) 13.8785 + 24.0383i 0.471884 + 0.817327i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 35.5356 + 20.5165i 1.20546 + 0.695973i
\(870\) 0 0
\(871\) 28.0361 + 16.1867i 0.949967 + 0.548464i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 66.6066 2.25171
\(876\) 0 0
\(877\) −0.927858 + 1.60710i −0.0313315 + 0.0542678i −0.881266 0.472621i \(-0.843308\pi\)
0.849934 + 0.526888i \(0.176641\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 13.9367i 0.469539i −0.972051 0.234770i \(-0.924566\pi\)
0.972051 0.234770i \(-0.0754336\pi\)
\(882\) 0 0
\(883\) −31.5144 + 18.1948i −1.06054 + 0.612305i −0.925582 0.378546i \(-0.876424\pi\)
−0.134961 + 0.990851i \(0.543091\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −18.2719 31.6479i −0.613511 1.06263i −0.990644 0.136474i \(-0.956423\pi\)
0.377132 0.926159i \(-0.376910\pi\)
\(888\) 0 0
\(889\) −9.65270 16.7190i −0.323741 0.560736i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.64858 30.8944i −0.0551676 1.03384i
\(894\) 0 0
\(895\) 29.4719 + 17.0156i 0.985136 + 0.568769i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 24.4782 + 42.3974i 0.816393 + 1.41403i
\(900\) 0 0
\(901\) −7.36275 −0.245289
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 70.8169i 2.35403i
\(906\) 0 0
\(907\) 29.6994 + 17.1470i 0.986153 + 0.569355i 0.904122 0.427274i \(-0.140526\pi\)
0.0820306 + 0.996630i \(0.473859\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 49.5696 1.64231 0.821156 0.570703i \(-0.193329\pi\)
0.821156 + 0.570703i \(0.193329\pi\)
\(912\) 0 0
\(913\) −23.0051 −0.761357
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 20.6553 + 11.9254i 0.682100 + 0.393810i
\(918\) 0 0
\(919\) 12.3617i 0.407774i −0.978994 0.203887i \(-0.934642\pi\)
0.978994 0.203887i \(-0.0653575\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −46.2492 −1.52231
\(924\) 0 0
\(925\) −43.3233 75.0382i −1.42446 2.46724i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −22.5934 13.0443i −0.741267 0.427971i 0.0812629 0.996693i \(-0.474105\pi\)
−0.822530 + 0.568722i \(0.807438\pi\)
\(930\) 0 0
\(931\) −14.4921 7.36672i −0.474958 0.241435i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 15.4083 + 26.6879i 0.503904 + 0.872787i
\(936\) 0 0
\(937\) 13.5296 + 23.4340i 0.441993 + 0.765555i 0.997837 0.0657317i \(-0.0209381\pi\)
−0.555844 + 0.831287i \(0.687605\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 28.6188 16.5230i 0.932945 0.538636i 0.0452031 0.998978i \(-0.485607\pi\)
0.887742 + 0.460342i \(0.152273\pi\)
\(942\) 0 0
\(943\) 27.5890i 0.898421i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −19.0733 + 33.0360i −0.619800 + 1.07353i 0.369721 + 0.929143i \(0.379453\pi\)
−0.989522 + 0.144383i \(0.953880\pi\)
\(948\) 0 0
\(949\) −55.9473 −1.81613
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 25.6143 + 14.7884i 0.829728 + 0.479044i 0.853759 0.520668i \(-0.174317\pi\)
−0.0240316 + 0.999711i \(0.507650\pi\)
\(954\) 0 0
\(955\) −14.0771 8.12744i −0.455525 0.262998i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −15.1673 26.2706i −0.489779 0.848322i
\(960\) 0 0
\(961\) −56.6647 −1.82789
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −22.4041 + 12.9350i −0.721214 + 0.416393i
\(966\) 0 0
\(967\) −50.8725 29.3713i −1.63595 0.944516i −0.982208 0.187798i \(-0.939865\pi\)
−0.653742 0.756718i \(-0.726802\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −11.9963 + 20.7782i −0.384980 + 0.666805i −0.991766 0.128060i \(-0.959125\pi\)
0.606786 + 0.794865i \(0.292458\pi\)
\(972\) 0 0
\(973\) 12.0474 + 20.8667i 0.386221 + 0.668955i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 51.3764i 1.64368i −0.569721 0.821838i \(-0.692949\pi\)
0.569721 0.821838i \(-0.307051\pi\)
\(978\) 0 0
\(979\) −78.4078 + 45.2688i −2.50592 + 1.44680i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) −22.6437 + 39.2200i −0.722222 + 1.25092i 0.237886 + 0.971293i \(0.423546\pi\)
−0.960107 + 0.279631i \(0.909788\pi\)
\(984\) 0 0
\(985\) −29.7592 + 51.5445i −0.948208 + 1.64234i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 4.85150i 0.154269i
\(990\) 0 0
\(991\) 35.9481 + 20.7547i 1.14193 + 0.659293i 0.946908 0.321506i \(-0.104189\pi\)
0.195022 + 0.980799i \(0.437522\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 33.9548 1.07644
\(996\) 0 0
\(997\) 13.1534 + 22.7824i 0.416573 + 0.721525i 0.995592 0.0937884i \(-0.0298977\pi\)
−0.579019 + 0.815314i \(0.696564\pi\)
\(998\) 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 2736.2.cg.c.1151.16 yes 32
3.2 odd 2 inner 2736.2.cg.c.1151.2 yes 32
4.3 odd 2 inner 2736.2.cg.c.1151.15 yes 32
12.11 even 2 inner 2736.2.cg.c.1151.1 32
19.7 even 3 inner 2736.2.cg.c.2591.1 yes 32
57.26 odd 6 inner 2736.2.cg.c.2591.15 yes 32
76.7 odd 6 inner 2736.2.cg.c.2591.2 yes 32
228.83 even 6 inner 2736.2.cg.c.2591.16 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2736.2.cg.c.1151.1 32 12.11 even 2 inner
2736.2.cg.c.1151.2 yes 32 3.2 odd 2 inner
2736.2.cg.c.1151.15 yes 32 4.3 odd 2 inner
2736.2.cg.c.1151.16 yes 32 1.1 even 1 trivial
2736.2.cg.c.2591.1 yes 32 19.7 even 3 inner
2736.2.cg.c.2591.2 yes 32 76.7 odd 6 inner
2736.2.cg.c.2591.15 yes 32 57.26 odd 6 inner
2736.2.cg.c.2591.16 yes 32 228.83 even 6 inner