Properties

Label 2736.2.cg.b.1151.1
Level $2736$
Weight $2$
Character 2736.1151
Analytic conductor $21.847$
Analytic rank $0$
Dimension $24$
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] = [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: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 1151.1
Character \(\chi\) \(=\) 2736.1151
Dual form 2736.2.cg.b.2591.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-3.43403 - 1.98264i) q^{5} -2.01359i q^{7} +O(q^{10})\) \(q+(-3.43403 - 1.98264i) q^{5} -2.01359i q^{7} +3.45028 q^{11} +(0.581638 + 1.00743i) q^{13} +(1.94137 + 1.12085i) q^{17} +(4.27660 - 0.843027i) q^{19} +(1.36603 + 2.36603i) q^{23} +(5.36172 + 9.28677i) q^{25} +(0.0525704 - 0.0303515i) q^{29} -2.92460i q^{31} +(-3.99223 + 6.91474i) q^{35} +10.5602 q^{37} +(-9.71482 - 5.60885i) q^{41} +(6.21445 + 3.58792i) q^{43} +(-5.99139 - 10.3774i) q^{47} +2.94545 q^{49} +(2.31473 - 1.33641i) q^{53} +(-11.8484 - 6.84067i) q^{55} +(-6.08260 + 10.5354i) q^{59} +(-3.76443 - 6.52019i) q^{61} -4.61271i q^{65} +(-2.77551 + 1.60244i) q^{67} +(4.20934 - 7.29079i) q^{71} +(1.71876 - 2.97697i) q^{73} -6.94746i q^{77} +(5.16778 + 2.98362i) q^{79} -12.1548 q^{83} +(-4.44448 - 7.69806i) q^{85} +(12.2015 - 7.04454i) q^{89} +(2.02855 - 1.17118i) q^{91} +(-16.3574 - 5.58397i) q^{95} +(5.03755 - 8.72530i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 12 q^{13} + 12 q^{19} + 8 q^{25} + 16 q^{37} + 12 q^{43} + 16 q^{49} - 12 q^{55} + 60 q^{67} + 8 q^{73} - 12 q^{79} + 16 q^{85} + 12 q^{91} - 32 q^{97}+O(q^{100}) \) 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
\(5\) −3.43403 1.98264i −1.53575 0.886663i −0.999081 0.0428680i \(-0.986351\pi\)
−0.536665 0.843795i \(-0.680316\pi\)
\(6\) 0 0
\(7\) 2.01359i 0.761066i −0.924767 0.380533i \(-0.875741\pi\)
0.924767 0.380533i \(-0.124259\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 3.45028 1.04030 0.520150 0.854075i \(-0.325876\pi\)
0.520150 + 0.854075i \(0.325876\pi\)
\(12\) 0 0
\(13\) 0.581638 + 1.00743i 0.161317 + 0.279410i 0.935341 0.353746i \(-0.115092\pi\)
−0.774024 + 0.633156i \(0.781759\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 1.94137 + 1.12085i 0.470850 + 0.271846i 0.716596 0.697489i \(-0.245699\pi\)
−0.245745 + 0.969334i \(0.579033\pi\)
\(18\) 0 0
\(19\) 4.27660 0.843027i 0.981119 0.193404i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.36603 + 2.36603i 0.284836 + 0.493351i 0.972570 0.232612i \(-0.0747274\pi\)
−0.687733 + 0.725964i \(0.741394\pi\)
\(24\) 0 0
\(25\) 5.36172 + 9.28677i 1.07234 + 1.85735i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.0525704 0.0303515i 0.00976207 0.00563614i −0.495111 0.868830i \(-0.664873\pi\)
0.504873 + 0.863194i \(0.331539\pi\)
\(30\) 0 0
\(31\) 2.92460i 0.525274i −0.964895 0.262637i \(-0.915408\pi\)
0.964895 0.262637i \(-0.0845921\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −3.99223 + 6.91474i −0.674809 + 1.16880i
\(36\) 0 0
\(37\) 10.5602 1.73608 0.868040 0.496494i \(-0.165380\pi\)
0.868040 + 0.496494i \(0.165380\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −9.71482 5.60885i −1.51720 0.875956i −0.999796 0.0202151i \(-0.993565\pi\)
−0.517405 0.855741i \(-0.673102\pi\)
\(42\) 0 0
\(43\) 6.21445 + 3.58792i 0.947695 + 0.547152i 0.892364 0.451316i \(-0.149045\pi\)
0.0553311 + 0.998468i \(0.482379\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −5.99139 10.3774i −0.873934 1.51370i −0.857894 0.513827i \(-0.828227\pi\)
−0.0160399 0.999871i \(-0.505106\pi\)
\(48\) 0 0
\(49\) 2.94545 0.420778
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 2.31473 1.33641i 0.317952 0.183570i −0.332527 0.943094i \(-0.607901\pi\)
0.650479 + 0.759524i \(0.274568\pi\)
\(54\) 0 0
\(55\) −11.8484 6.84067i −1.59764 0.922396i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −6.08260 + 10.5354i −0.791887 + 1.37159i 0.132910 + 0.991128i \(0.457568\pi\)
−0.924797 + 0.380461i \(0.875765\pi\)
\(60\) 0 0
\(61\) −3.76443 6.52019i −0.481986 0.834825i 0.517800 0.855502i \(-0.326751\pi\)
−0.999786 + 0.0206771i \(0.993418\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 4.61271i 0.572137i
\(66\) 0 0
\(67\) −2.77551 + 1.60244i −0.339082 + 0.195769i −0.659866 0.751383i \(-0.729387\pi\)
0.320784 + 0.947152i \(0.396054\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 4.20934 7.29079i 0.499557 0.865258i −0.500443 0.865770i \(-0.666829\pi\)
1.00000 0.000511518i \(0.000162821\pi\)
\(72\) 0 0
\(73\) 1.71876 2.97697i 0.201165 0.348428i −0.747739 0.663993i \(-0.768860\pi\)
0.948904 + 0.315564i \(0.102194\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.94746i 0.791737i
\(78\) 0 0
\(79\) 5.16778 + 2.98362i 0.581421 + 0.335683i 0.761698 0.647932i \(-0.224366\pi\)
−0.180277 + 0.983616i \(0.557699\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −12.1548 −1.33416 −0.667079 0.744987i \(-0.732455\pi\)
−0.667079 + 0.744987i \(0.732455\pi\)
\(84\) 0 0
\(85\) −4.44448 7.69806i −0.482071 0.834972i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 12.2015 7.04454i 1.29336 0.746720i 0.314109 0.949387i \(-0.398294\pi\)
0.979248 + 0.202667i \(0.0649610\pi\)
\(90\) 0 0
\(91\) 2.02855 1.17118i 0.212649 0.122773i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −16.3574 5.58397i −1.67823 0.572903i
\(96\) 0 0
\(97\) 5.03755 8.72530i 0.511486 0.885920i −0.488425 0.872606i \(-0.662429\pi\)
0.999911 0.0133139i \(-0.00423808\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0.305411 0.176329i 0.0303895 0.0175454i −0.484728 0.874665i \(-0.661082\pi\)
0.515118 + 0.857119i \(0.327748\pi\)
\(102\) 0 0
\(103\) 14.1116i 1.39046i −0.718789 0.695229i \(-0.755303\pi\)
0.718789 0.695229i \(-0.244697\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.568348 0.0549443 0.0274721 0.999623i \(-0.491254\pi\)
0.0274721 + 0.999623i \(0.491254\pi\)
\(108\) 0 0
\(109\) −3.79592 + 6.57472i −0.363583 + 0.629744i −0.988548 0.150909i \(-0.951780\pi\)
0.624965 + 0.780653i \(0.285113\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 7.53420i 0.708758i −0.935102 0.354379i \(-0.884692\pi\)
0.935102 0.354379i \(-0.115308\pi\)
\(114\) 0 0
\(115\) 10.8334i 1.01022i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 2.25693 3.90912i 0.206892 0.358348i
\(120\) 0 0
\(121\) 0.904464 0.0822240
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 22.6950i 2.02990i
\(126\) 0 0
\(127\) −18.9834 + 10.9601i −1.68451 + 0.972550i −0.725906 + 0.687794i \(0.758579\pi\)
−0.958600 + 0.284755i \(0.908088\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −0.400659 + 0.693962i −0.0350057 + 0.0606317i −0.882997 0.469378i \(-0.844478\pi\)
0.847992 + 0.530009i \(0.177812\pi\)
\(132\) 0 0
\(133\) −1.69751 8.61133i −0.147193 0.746697i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 12.2281 7.05989i 1.04472 0.603167i 0.123550 0.992338i \(-0.460572\pi\)
0.921165 + 0.389171i \(0.127239\pi\)
\(138\) 0 0
\(139\) −15.3243 + 8.84752i −1.29979 + 0.750436i −0.980368 0.197175i \(-0.936823\pi\)
−0.319426 + 0.947611i \(0.603490\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.00682 + 3.47591i 0.167818 + 0.290670i
\(144\) 0 0
\(145\) −0.240704 −0.0199894
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −5.11433 2.95276i −0.418982 0.241900i 0.275660 0.961255i \(-0.411104\pi\)
−0.694642 + 0.719356i \(0.744437\pi\)
\(150\) 0 0
\(151\) 4.22190i 0.343573i −0.985134 0.171787i \(-0.945046\pi\)
0.985134 0.171787i \(-0.0549540\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −5.79843 + 10.0432i −0.465741 + 0.806687i
\(156\) 0 0
\(157\) 4.17447 7.23039i 0.333159 0.577048i −0.649970 0.759959i \(-0.725219\pi\)
0.983129 + 0.182911i \(0.0585521\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 4.76422 2.75062i 0.375473 0.216779i
\(162\) 0 0
\(163\) 4.38206i 0.343229i −0.985164 0.171615i \(-0.945102\pi\)
0.985164 0.171615i \(-0.0548984\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.0993411 0.172064i −0.00768724 0.0133147i 0.862156 0.506643i \(-0.169114\pi\)
−0.869843 + 0.493328i \(0.835780\pi\)
\(168\) 0 0
\(169\) 5.82339 10.0864i 0.447953 0.775878i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.74407 + 1.00694i 0.132599 + 0.0765562i 0.564832 0.825206i \(-0.308941\pi\)
−0.432233 + 0.901762i \(0.642274\pi\)
\(174\) 0 0
\(175\) 18.6998 10.7963i 1.41357 0.816124i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 12.2320 0.914265 0.457133 0.889399i \(-0.348876\pi\)
0.457133 + 0.889399i \(0.348876\pi\)
\(180\) 0 0
\(181\) −2.42980 4.20854i −0.180606 0.312818i 0.761481 0.648187i \(-0.224472\pi\)
−0.942087 + 0.335369i \(0.891139\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −36.2639 20.9370i −2.66618 1.53932i
\(186\) 0 0
\(187\) 6.69827 + 3.86725i 0.489826 + 0.282801i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −11.2782 −0.816063 −0.408032 0.912968i \(-0.633785\pi\)
−0.408032 + 0.912968i \(0.633785\pi\)
\(192\) 0 0
\(193\) 3.46037 5.99353i 0.249083 0.431424i −0.714189 0.699953i \(-0.753204\pi\)
0.963272 + 0.268529i \(0.0865376\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.5858i 0.896702i 0.893858 + 0.448351i \(0.147989\pi\)
−0.893858 + 0.448351i \(0.852011\pi\)
\(198\) 0 0
\(199\) 7.34790 4.24231i 0.520879 0.300730i −0.216415 0.976301i \(-0.569436\pi\)
0.737294 + 0.675572i \(0.236103\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.0611156 0.105855i −0.00428947 0.00742958i
\(204\) 0 0
\(205\) 22.2407 + 38.5220i 1.55336 + 2.69049i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 14.7555 2.90868i 1.02066 0.201198i
\(210\) 0 0
\(211\) 8.69295 + 5.01887i 0.598447 + 0.345514i 0.768430 0.639933i \(-0.221038\pi\)
−0.169983 + 0.985447i \(0.554371\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −14.2271 24.6420i −0.970279 1.68057i
\(216\) 0 0
\(217\) −5.88895 −0.399768
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 2.60771i 0.175414i
\(222\) 0 0
\(223\) −21.3326 12.3164i −1.42854 0.824767i −0.431533 0.902097i \(-0.642027\pi\)
−0.997006 + 0.0773302i \(0.975360\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 18.6879 1.24036 0.620180 0.784459i \(-0.287059\pi\)
0.620180 + 0.784459i \(0.287059\pi\)
\(228\) 0 0
\(229\) 21.1273 1.39613 0.698065 0.716034i \(-0.254045\pi\)
0.698065 + 0.716034i \(0.254045\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 11.7091 + 6.76023i 0.767086 + 0.442877i 0.831834 0.555024i \(-0.187291\pi\)
−0.0647482 + 0.997902i \(0.520624\pi\)
\(234\) 0 0
\(235\) 47.5151i 3.09954i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −9.03083 −0.584156 −0.292078 0.956395i \(-0.594347\pi\)
−0.292078 + 0.956395i \(0.594347\pi\)
\(240\) 0 0
\(241\) 6.41260 + 11.1069i 0.413072 + 0.715461i 0.995224 0.0976185i \(-0.0311225\pi\)
−0.582152 + 0.813080i \(0.697789\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −10.1148 5.83976i −0.646209 0.373089i
\(246\) 0 0
\(247\) 3.33672 + 3.81802i 0.212310 + 0.242935i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 3.31032 + 5.73363i 0.208945 + 0.361904i 0.951383 0.308012i \(-0.0996636\pi\)
−0.742437 + 0.669916i \(0.766330\pi\)
\(252\) 0 0
\(253\) 4.71318 + 8.16347i 0.296315 + 0.513233i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −8.26650 + 4.77267i −0.515650 + 0.297711i −0.735153 0.677901i \(-0.762890\pi\)
0.219503 + 0.975612i \(0.429556\pi\)
\(258\) 0 0
\(259\) 21.2639i 1.32127i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 5.80613 10.0565i 0.358022 0.620112i −0.629609 0.776912i \(-0.716785\pi\)
0.987630 + 0.156801i \(0.0501181\pi\)
\(264\) 0 0
\(265\) −10.5985 −0.651058
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 12.4154 + 7.16804i 0.756981 + 0.437043i 0.828211 0.560417i \(-0.189359\pi\)
−0.0712296 + 0.997460i \(0.522692\pi\)
\(270\) 0 0
\(271\) 17.4945 + 10.1004i 1.06271 + 0.613558i 0.926181 0.377078i \(-0.123071\pi\)
0.136532 + 0.990636i \(0.456405\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 18.4995 + 32.0420i 1.11556 + 1.93220i
\(276\) 0 0
\(277\) 3.68936 0.221672 0.110836 0.993839i \(-0.464647\pi\)
0.110836 + 0.993839i \(0.464647\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −9.04933 + 5.22464i −0.539838 + 0.311676i −0.745013 0.667050i \(-0.767557\pi\)
0.205175 + 0.978725i \(0.434224\pi\)
\(282\) 0 0
\(283\) −0.881832 0.509126i −0.0524195 0.0302644i 0.473561 0.880761i \(-0.342968\pi\)
−0.525981 + 0.850497i \(0.676302\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −11.2939 + 19.5617i −0.666660 + 1.15469i
\(288\) 0 0
\(289\) −5.98740 10.3705i −0.352200 0.610028i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 16.1692i 0.944613i −0.881434 0.472307i \(-0.843422\pi\)
0.881434 0.472307i \(-0.156578\pi\)
\(294\) 0 0
\(295\) 41.7757 24.1192i 2.43228 1.40427i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.58907 + 2.75234i −0.0918981 + 0.159172i
\(300\) 0 0
\(301\) 7.22460 12.5134i 0.416419 0.721259i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 29.8541i 1.70944i
\(306\) 0 0
\(307\) −24.2016 13.9728i −1.38126 0.797469i −0.388948 0.921260i \(-0.627161\pi\)
−0.992308 + 0.123791i \(0.960495\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −17.4234 −0.987992 −0.493996 0.869464i \(-0.664464\pi\)
−0.493996 + 0.869464i \(0.664464\pi\)
\(312\) 0 0
\(313\) 13.4149 + 23.2353i 0.758256 + 1.31334i 0.943739 + 0.330690i \(0.107282\pi\)
−0.185483 + 0.982647i \(0.559385\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −27.5318 + 15.8955i −1.54634 + 0.892778i −0.547920 + 0.836531i \(0.684580\pi\)
−0.998417 + 0.0562477i \(0.982086\pi\)
\(318\) 0 0
\(319\) 0.181383 0.104721i 0.0101555 0.00586327i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 9.24735 + 3.15679i 0.514536 + 0.175649i
\(324\) 0 0
\(325\) −6.23716 + 10.8031i −0.345975 + 0.599247i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −20.8958 + 12.0642i −1.15202 + 0.665122i
\(330\) 0 0
\(331\) 12.4861i 0.686299i −0.939281 0.343150i \(-0.888506\pi\)
0.939281 0.343150i \(-0.111494\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 12.7082 0.694326
\(336\) 0 0
\(337\) −11.6772 + 20.2255i −0.636096 + 1.10175i 0.350185 + 0.936680i \(0.386119\pi\)
−0.986282 + 0.165071i \(0.947215\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 10.0907i 0.546442i
\(342\) 0 0
\(343\) 20.0261i 1.08131i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −5.78797 + 10.0251i −0.310715 + 0.538174i −0.978517 0.206165i \(-0.933902\pi\)
0.667803 + 0.744338i \(0.267235\pi\)
\(348\) 0 0
\(349\) −3.34938 −0.179288 −0.0896441 0.995974i \(-0.528573\pi\)
−0.0896441 + 0.995974i \(0.528573\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 2.21760i 0.118031i −0.998257 0.0590156i \(-0.981204\pi\)
0.998257 0.0590156i \(-0.0187962\pi\)
\(354\) 0 0
\(355\) −28.9100 + 16.6912i −1.53439 + 0.885878i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 13.9153 24.1020i 0.734422 1.27206i −0.220554 0.975375i \(-0.570786\pi\)
0.954976 0.296682i \(-0.0958802\pi\)
\(360\) 0 0
\(361\) 17.5786 7.21058i 0.925190 0.379504i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −11.8045 + 6.81535i −0.617878 + 0.356732i
\(366\) 0 0
\(367\) −15.3348 + 8.85356i −0.800471 + 0.462152i −0.843636 0.536916i \(-0.819589\pi\)
0.0431651 + 0.999068i \(0.486256\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −2.69098 4.66092i −0.139709 0.241983i
\(372\) 0 0
\(373\) −14.5551 −0.753632 −0.376816 0.926288i \(-0.622981\pi\)
−0.376816 + 0.926288i \(0.622981\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.0611538 + 0.0353072i 0.00314958 + 0.00181841i
\(378\) 0 0
\(379\) 29.2376i 1.50184i −0.660396 0.750918i \(-0.729611\pi\)
0.660396 0.750918i \(-0.270389\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −15.0506 + 26.0684i −0.769049 + 1.33203i 0.169030 + 0.985611i \(0.445936\pi\)
−0.938079 + 0.346421i \(0.887397\pi\)
\(384\) 0 0
\(385\) −13.7743 + 23.8578i −0.702004 + 1.21591i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 31.0759 17.9417i 1.57561 0.909678i 0.580148 0.814511i \(-0.302995\pi\)
0.995461 0.0951670i \(-0.0303385\pi\)
\(390\) 0 0
\(391\) 6.12444i 0.309726i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −11.8309 20.4917i −0.595276 1.03105i
\(396\) 0 0
\(397\) −1.45262 + 2.51602i −0.0729051 + 0.126275i −0.900173 0.435532i \(-0.856560\pi\)
0.827268 + 0.561807i \(0.189894\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9.60454 + 5.54519i 0.479628 + 0.276913i 0.720261 0.693703i \(-0.244022\pi\)
−0.240633 + 0.970616i \(0.577355\pi\)
\(402\) 0 0
\(403\) 2.94632 1.70106i 0.146767 0.0847357i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 36.4356 1.80604
\(408\) 0 0
\(409\) −19.7055 34.1309i −0.974375 1.68767i −0.681984 0.731368i \(-0.738882\pi\)
−0.292391 0.956299i \(-0.594451\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 21.2139 + 12.2479i 1.04387 + 0.602679i
\(414\) 0 0
\(415\) 41.7398 + 24.0985i 2.04893 + 1.18295i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 25.6128 1.25127 0.625634 0.780117i \(-0.284840\pi\)
0.625634 + 0.780117i \(0.284840\pi\)
\(420\) 0 0
\(421\) 1.77587 3.07590i 0.0865507 0.149910i −0.819500 0.573079i \(-0.805749\pi\)
0.906051 + 0.423169i \(0.139082\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 24.0387i 1.16605i
\(426\) 0 0
\(427\) −13.1290 + 7.58003i −0.635357 + 0.366823i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −15.2267 26.3734i −0.733444 1.27036i −0.955403 0.295307i \(-0.904578\pi\)
0.221958 0.975056i \(-0.428755\pi\)
\(432\) 0 0
\(433\) −19.8335 34.3527i −0.953140 1.65089i −0.738569 0.674178i \(-0.764498\pi\)
−0.214570 0.976709i \(-0.568835\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.83658 + 8.96696i 0.374875 + 0.428948i
\(438\) 0 0
\(439\) 27.3319 + 15.7801i 1.30448 + 0.753142i 0.981169 0.193151i \(-0.0618708\pi\)
0.323311 + 0.946293i \(0.395204\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −14.5707 25.2371i −0.692273 1.19905i −0.971091 0.238709i \(-0.923276\pi\)
0.278818 0.960344i \(-0.410057\pi\)
\(444\) 0 0
\(445\) −55.8671 −2.64836
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 1.03245i 0.0487241i 0.999703 + 0.0243620i \(0.00775545\pi\)
−0.999703 + 0.0243620i \(0.992245\pi\)
\(450\) 0 0
\(451\) −33.5189 19.3521i −1.57834 0.911257i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −9.28812 −0.435434
\(456\) 0 0
\(457\) −5.59378 −0.261666 −0.130833 0.991404i \(-0.541765\pi\)
−0.130833 + 0.991404i \(0.541765\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 34.5916 + 19.9715i 1.61109 + 0.930165i 0.989117 + 0.147128i \(0.0470029\pi\)
0.621975 + 0.783037i \(0.286330\pi\)
\(462\) 0 0
\(463\) 30.1366i 1.40057i 0.713865 + 0.700283i \(0.246943\pi\)
−0.713865 + 0.700283i \(0.753057\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 21.8956 1.01321 0.506603 0.862179i \(-0.330901\pi\)
0.506603 + 0.862179i \(0.330901\pi\)
\(468\) 0 0
\(469\) 3.22666 + 5.58874i 0.148993 + 0.258064i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 21.4416 + 12.3793i 0.985887 + 0.569202i
\(474\) 0 0
\(475\) 30.7589 + 35.1957i 1.41132 + 1.61489i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 5.01871 + 8.69266i 0.229311 + 0.397178i 0.957604 0.288088i \(-0.0930195\pi\)
−0.728293 + 0.685266i \(0.759686\pi\)
\(480\) 0 0
\(481\) 6.14219 + 10.6386i 0.280060 + 0.485078i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −34.5982 + 19.9753i −1.57102 + 0.907032i
\(486\) 0 0
\(487\) 4.09614i 0.185614i 0.995684 + 0.0928070i \(0.0295840\pi\)
−0.995684 + 0.0928070i \(0.970416\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 16.8753 29.2288i 0.761570 1.31908i −0.180472 0.983580i \(-0.557762\pi\)
0.942041 0.335497i \(-0.108904\pi\)
\(492\) 0 0
\(493\) 0.136078 0.00612863
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −14.6807 8.47590i −0.658519 0.380196i
\(498\) 0 0
\(499\) −18.9048 10.9147i −0.846296 0.488609i 0.0131035 0.999914i \(-0.495829\pi\)
−0.859399 + 0.511305i \(0.829162\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0.689494 + 1.19424i 0.0307430 + 0.0532485i 0.880988 0.473139i \(-0.156879\pi\)
−0.850245 + 0.526388i \(0.823546\pi\)
\(504\) 0 0
\(505\) −1.39839 −0.0622275
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 12.5531 7.24751i 0.556404 0.321240i −0.195297 0.980744i \(-0.562567\pi\)
0.751701 + 0.659504i \(0.229234\pi\)
\(510\) 0 0
\(511\) −5.99441 3.46087i −0.265177 0.153100i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −27.9782 + 48.4597i −1.23287 + 2.13539i
\(516\) 0 0
\(517\) −20.6720 35.8050i −0.909153 1.57470i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 15.9019i 0.696673i −0.937370 0.348336i \(-0.886747\pi\)
0.937370 0.348336i \(-0.113253\pi\)
\(522\) 0 0
\(523\) −32.0835 + 18.5234i −1.40291 + 0.809971i −0.994690 0.102912i \(-0.967184\pi\)
−0.408221 + 0.912883i \(0.633851\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 3.27803 5.67772i 0.142793 0.247325i
\(528\) 0 0
\(529\) 7.76794 13.4545i 0.337736 0.584977i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 13.0493i 0.565227i
\(534\) 0 0
\(535\) −1.95172 1.12683i −0.0843804 0.0487171i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 10.1626 0.437736
\(540\) 0 0
\(541\) −15.1041 26.1611i −0.649376 1.12475i −0.983272 0.182143i \(-0.941697\pi\)
0.333896 0.942610i \(-0.391637\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 26.0706 15.0519i 1.11674 0.644751i
\(546\) 0 0
\(547\) −38.0038 + 21.9415i −1.62492 + 0.938151i −0.639349 + 0.768917i \(0.720796\pi\)
−0.985576 + 0.169234i \(0.945871\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0.199235 0.174120i 0.00848771 0.00741774i
\(552\) 0 0
\(553\) 6.00779 10.4058i 0.255477 0.442500i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 1.14237 0.659549i 0.0484039 0.0279460i −0.475603 0.879660i \(-0.657770\pi\)
0.524007 + 0.851714i \(0.324437\pi\)
\(558\) 0 0
\(559\) 8.34747i 0.353060i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 27.8925 1.17553 0.587765 0.809032i \(-0.300008\pi\)
0.587765 + 0.809032i \(0.300008\pi\)
\(564\) 0 0
\(565\) −14.9376 + 25.8727i −0.628429 + 1.08847i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.1984i 0.762918i 0.924386 + 0.381459i \(0.124578\pi\)
−0.924386 + 0.381459i \(0.875422\pi\)
\(570\) 0 0
\(571\) 16.6385i 0.696299i 0.937439 + 0.348150i \(0.113190\pi\)
−0.937439 + 0.348150i \(0.886810\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −14.6485 + 25.3720i −0.610885 + 1.05808i
\(576\) 0 0
\(577\) 21.7146 0.903990 0.451995 0.892021i \(-0.350713\pi\)
0.451995 + 0.892021i \(0.350713\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 24.4747i 1.01538i
\(582\) 0 0
\(583\) 7.98647 4.61099i 0.330766 0.190968i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −3.12021 + 5.40437i −0.128785 + 0.223062i −0.923206 0.384305i \(-0.874441\pi\)
0.794421 + 0.607367i \(0.207774\pi\)
\(588\) 0 0
\(589\) −2.46552 12.5073i −0.101590 0.515356i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −14.1517 + 8.17048i −0.581140 + 0.335522i −0.761586 0.648063i \(-0.775579\pi\)
0.180446 + 0.983585i \(0.442246\pi\)
\(594\) 0 0
\(595\) −15.5007 + 8.94936i −0.635469 + 0.366888i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −17.8274 30.8780i −0.728408 1.26164i −0.957556 0.288248i \(-0.906927\pi\)
0.229148 0.973392i \(-0.426406\pi\)
\(600\) 0 0
\(601\) −33.6218 −1.37146 −0.685732 0.727855i \(-0.740518\pi\)
−0.685732 + 0.727855i \(0.740518\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −3.10596 1.79323i −0.126275 0.0729050i
\(606\) 0 0
\(607\) 9.30198i 0.377556i 0.982020 + 0.188778i \(0.0604526\pi\)
−0.982020 + 0.188778i \(0.939547\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 6.96964 12.0718i 0.281961 0.488371i
\(612\) 0 0
\(613\) 13.6974 23.7245i 0.553232 0.958225i −0.444807 0.895626i \(-0.646728\pi\)
0.998039 0.0625989i \(-0.0199389\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.43300 + 2.55939i −0.178466 + 0.103037i −0.586572 0.809897i \(-0.699523\pi\)
0.408106 + 0.912935i \(0.366189\pi\)
\(618\) 0 0
\(619\) 35.5902i 1.43049i 0.698874 + 0.715245i \(0.253685\pi\)
−0.698874 + 0.715245i \(0.746315\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −14.1848 24.5688i −0.568303 0.984330i
\(624\) 0 0
\(625\) −18.1875 + 31.5016i −0.727498 + 1.26006i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 20.5011 + 11.8363i 0.817434 + 0.471946i
\(630\) 0 0
\(631\) 29.2225 16.8716i 1.16333 0.671648i 0.211229 0.977437i \(-0.432253\pi\)
0.952099 + 0.305789i \(0.0989201\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 86.9195 3.44930
\(636\) 0 0
\(637\) 1.71318 + 2.96732i 0.0678788 + 0.117570i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 14.8223 + 8.55766i 0.585446 + 0.338007i 0.763295 0.646051i \(-0.223581\pi\)
−0.177849 + 0.984058i \(0.556914\pi\)
\(642\) 0 0
\(643\) 31.7033 + 18.3039i 1.25025 + 0.721835i 0.971160 0.238429i \(-0.0766325\pi\)
0.279094 + 0.960264i \(0.409966\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −20.1390 −0.791746 −0.395873 0.918305i \(-0.629558\pi\)
−0.395873 + 0.918305i \(0.629558\pi\)
\(648\) 0 0
\(649\) −20.9867 + 36.3500i −0.823800 + 1.42686i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 20.6576i 0.808394i 0.914672 + 0.404197i \(0.132449\pi\)
−0.914672 + 0.404197i \(0.867551\pi\)
\(654\) 0 0
\(655\) 2.75175 1.58872i 0.107520 0.0620766i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 10.9945 + 19.0431i 0.428285 + 0.741812i 0.996721 0.0809156i \(-0.0257844\pi\)
−0.568435 + 0.822728i \(0.692451\pi\)
\(660\) 0 0
\(661\) 3.94593 + 6.83455i 0.153479 + 0.265833i 0.932504 0.361159i \(-0.117619\pi\)
−0.779025 + 0.626993i \(0.784286\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −11.2438 + 32.9371i −0.436017 + 1.27725i
\(666\) 0 0
\(667\) 0.143625 + 0.0829220i 0.00556119 + 0.00321075i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) −12.9884 22.4965i −0.501410 0.868468i
\(672\) 0 0
\(673\) 29.9434 1.15423 0.577117 0.816662i \(-0.304178\pi\)
0.577117 + 0.816662i \(0.304178\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 23.5765i 0.906120i 0.891480 + 0.453060i \(0.149668\pi\)
−0.891480 + 0.453060i \(0.850332\pi\)
\(678\) 0 0
\(679\) −17.5692 10.1436i −0.674243 0.389275i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 32.9586 1.26112 0.630562 0.776139i \(-0.282824\pi\)
0.630562 + 0.776139i \(0.282824\pi\)
\(684\) 0 0
\(685\) −55.9888 −2.13922
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 2.69267 + 1.55461i 0.102582 + 0.0592260i
\(690\) 0 0
\(691\) 35.8385i 1.36336i −0.731651 0.681680i \(-0.761250\pi\)
0.731651 0.681680i \(-0.238750\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 70.1657 2.66154
\(696\) 0 0
\(697\) −12.5733 21.7777i −0.476250 0.824888i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −22.8861 13.2133i −0.864395 0.499059i 0.00108645 0.999999i \(-0.499654\pi\)
−0.865482 + 0.500941i \(0.832988\pi\)
\(702\) 0 0
\(703\) 45.1616 8.90251i 1.70330 0.335764i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −0.355055 0.614973i −0.0133532 0.0231285i
\(708\) 0 0
\(709\) 25.8389 + 44.7543i 0.970401 + 1.68078i 0.694346 + 0.719641i \(0.255694\pi\)
0.276055 + 0.961142i \(0.410973\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 6.91969 3.99508i 0.259144 0.149617i
\(714\) 0 0
\(715\) 15.9152i 0.595194i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −12.6038 + 21.8305i −0.470043 + 0.814139i −0.999413 0.0342525i \(-0.989095\pi\)
0.529370 + 0.848391i \(0.322428\pi\)
\(720\) 0 0
\(721\) −28.4150 −1.05823
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 0.563735 + 0.325473i 0.0209366 + 0.0120877i
\(726\) 0 0
\(727\) 3.35763 + 1.93853i 0.124528 + 0.0718960i 0.560970 0.827836i \(-0.310428\pi\)
−0.436442 + 0.899732i \(0.643762\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 8.04302 + 13.9309i 0.297482 + 0.515254i
\(732\) 0 0
\(733\) 27.0229 0.998115 0.499057 0.866569i \(-0.333680\pi\)
0.499057 + 0.866569i \(0.333680\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −9.57629 + 5.52887i −0.352747 + 0.203659i
\(738\) 0 0
\(739\) −11.6140 6.70537i −0.427229 0.246661i 0.270936 0.962597i \(-0.412667\pi\)
−0.698166 + 0.715936i \(0.746000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 3.30822 5.73000i 0.121367 0.210213i −0.798940 0.601411i \(-0.794606\pi\)
0.920307 + 0.391197i \(0.127939\pi\)
\(744\) 0 0
\(745\) 11.7085 + 20.2797i 0.428967 + 0.742992i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 1.14442i 0.0418162i
\(750\) 0 0
\(751\) 3.29369 1.90162i 0.120189 0.0693909i −0.438700 0.898633i \(-0.644561\pi\)
0.558889 + 0.829242i \(0.311228\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) −8.37050 + 14.4981i −0.304634 + 0.527641i
\(756\) 0 0
\(757\) −1.06155 + 1.83865i −0.0385826 + 0.0668270i −0.884672 0.466214i \(-0.845618\pi\)
0.846089 + 0.533041i \(0.178951\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 4.72565i 0.171305i 0.996325 + 0.0856523i \(0.0272974\pi\)
−0.996325 + 0.0856523i \(0.972703\pi\)
\(762\) 0 0
\(763\) 13.2388 + 7.64343i 0.479277 + 0.276711i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −14.1515 −0.510981
\(768\) 0 0
\(769\) 3.04662 + 5.27690i 0.109864 + 0.190290i 0.915715 0.401828i \(-0.131625\pi\)
−0.805851 + 0.592118i \(0.798292\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −11.7456 + 6.78132i −0.422460 + 0.243907i −0.696129 0.717917i \(-0.745096\pi\)
0.273669 + 0.961824i \(0.411763\pi\)
\(774\) 0 0
\(775\) 27.1601 15.6809i 0.975619 0.563274i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −46.2748 15.7970i −1.65797 0.565985i
\(780\) 0 0
\(781\) 14.5234 25.1553i 0.519689 0.900128i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −28.6705 + 16.5529i −1.02330 + 0.590800i
\(786\) 0 0
\(787\) 16.6702i 0.594228i −0.954842 0.297114i \(-0.903976\pi\)
0.954842 0.297114i \(-0.0960241\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −15.1708 −0.539411
\(792\) 0 0
\(793\) 4.37907 7.58478i 0.155505 0.269343i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 29.7438i 1.05358i 0.849996 + 0.526790i \(0.176604\pi\)
−0.849996 + 0.526790i \(0.823396\pi\)
\(798\) 0 0
\(799\) 26.8617i 0.950300i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 5.93020 10.2714i 0.209272 0.362470i
\(804\) 0 0
\(805\) −21.8140 −0.768841
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 54.3612i 1.91124i −0.294608 0.955618i \(-0.595189\pi\)
0.294608 0.955618i \(-0.404811\pi\)
\(810\) 0 0
\(811\) −32.4006 + 18.7065i −1.13774 + 0.656874i −0.945870 0.324547i \(-0.894788\pi\)
−0.191869 + 0.981421i \(0.561455\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −8.68804 + 15.0481i −0.304329 + 0.527113i
\(816\) 0 0
\(817\) 29.6014 + 10.1051i 1.03562 + 0.353534i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −22.6396 + 13.0710i −0.790128 + 0.456180i −0.840007 0.542575i \(-0.817450\pi\)
0.0498798 + 0.998755i \(0.484116\pi\)
\(822\) 0 0
\(823\) −30.1146 + 17.3867i −1.04973 + 0.606062i −0.922574 0.385821i \(-0.873918\pi\)
−0.127156 + 0.991883i \(0.540585\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 8.10335 + 14.0354i 0.281781 + 0.488059i 0.971823 0.235710i \(-0.0757415\pi\)
−0.690042 + 0.723769i \(0.742408\pi\)
\(828\) 0 0
\(829\) 1.59194 0.0552905 0.0276453 0.999618i \(-0.491199\pi\)
0.0276453 + 0.999618i \(0.491199\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 5.71819 + 3.30140i 0.198124 + 0.114387i
\(834\) 0 0
\(835\) 0.787830i 0.0272640i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 4.40972 7.63785i 0.152240 0.263688i −0.779810 0.626016i \(-0.784685\pi\)
0.932051 + 0.362328i \(0.118018\pi\)
\(840\) 0 0
\(841\) −14.4982 + 25.1115i −0.499936 + 0.865915i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −39.9955 + 23.0914i −1.37589 + 0.794368i
\(846\) 0 0
\(847\) 1.82122i 0.0625779i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 14.4255 + 24.9856i 0.494499 + 0.856497i
\(852\) 0 0
\(853\) −17.3911 + 30.1223i −0.595460 + 1.03137i 0.398022 + 0.917376i \(0.369697\pi\)
−0.993482 + 0.113991i \(0.963637\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 42.9864 + 24.8182i 1.46839 + 0.847773i 0.999373 0.0354174i \(-0.0112761\pi\)
0.469014 + 0.883191i \(0.344609\pi\)
\(858\) 0 0
\(859\) 18.9914 10.9647i 0.647978 0.374110i −0.139703 0.990193i \(-0.544615\pi\)
0.787681 + 0.616083i \(0.211282\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 17.4011 0.592340 0.296170 0.955135i \(-0.404290\pi\)
0.296170 + 0.955135i \(0.404290\pi\)
\(864\) 0 0
\(865\) −3.99279 6.91572i −0.135759 0.235142i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 17.8303 + 10.2943i 0.604852 + 0.349212i
\(870\) 0 0
\(871\) −3.22868 1.86408i −0.109400 0.0631619i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −45.6985 −1.54489
\(876\) 0 0
\(877\) 11.9056 20.6212i 0.402025 0.696328i −0.591945 0.805978i \(-0.701640\pi\)
0.993970 + 0.109651i \(0.0349732\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 38.8172i 1.30779i 0.756587 + 0.653893i \(0.226865\pi\)
−0.756587 + 0.653893i \(0.773135\pi\)
\(882\) 0 0
\(883\) 18.1788 10.4955i 0.611765 0.353203i −0.161891 0.986809i \(-0.551759\pi\)
0.773656 + 0.633606i \(0.218426\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 18.5521 + 32.1331i 0.622918 + 1.07893i 0.988940 + 0.148319i \(0.0473862\pi\)
−0.366022 + 0.930606i \(0.619280\pi\)
\(888\) 0 0
\(889\) 22.0691 + 38.2249i 0.740175 + 1.28202i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −34.3712 39.3290i −1.15019 1.31610i
\(894\) 0 0
\(895\) −42.0052 24.2517i −1.40408 0.810645i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) −0.0887661 0.153747i −0.00296051 0.00512776i
\(900\) 0 0
\(901\) 5.99164 0.199611
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 19.2697i 0.640546i
\(906\) 0 0
\(907\) 23.8981 + 13.7976i 0.793522 + 0.458140i 0.841201 0.540722i \(-0.181849\pi\)
−0.0476787 + 0.998863i \(0.515182\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 40.3906 1.33820 0.669100 0.743173i \(-0.266680\pi\)
0.669100 + 0.743173i \(0.266680\pi\)
\(912\) 0 0
\(913\) −41.9373 −1.38792
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 1.39736 + 0.806764i 0.0461448 + 0.0266417i
\(918\) 0 0
\(919\) 37.5875i 1.23990i 0.784642 + 0.619949i \(0.212847\pi\)
−0.784642 + 0.619949i \(0.787153\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 9.79325 0.322349
\(924\) 0 0
\(925\) 56.6206 + 98.0698i 1.86167 + 3.22451i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −12.1824 7.03353i −0.399693 0.230763i 0.286659 0.958033i \(-0.407455\pi\)
−0.686351 + 0.727270i \(0.740789\pi\)
\(930\) 0 0
\(931\) 12.5965 2.48309i 0.412834 0.0813801i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −15.3347 26.5605i −0.501498 0.868621i
\(936\) 0 0
\(937\) −29.6943 51.4321i −0.970071 1.68021i −0.695324 0.718696i \(-0.744739\pi\)
−0.274747 0.961517i \(-0.588594\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 24.3591 14.0637i 0.794083 0.458464i −0.0473147 0.998880i \(-0.515066\pi\)
0.841398 + 0.540416i \(0.181733\pi\)
\(942\) 0 0
\(943\) 30.6474i 0.998017i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −12.2582 + 21.2319i −0.398339 + 0.689944i −0.993521 0.113647i \(-0.963747\pi\)
0.595182 + 0.803591i \(0.297080\pi\)
\(948\) 0 0
\(949\) 3.99878 0.129806
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 35.7222 + 20.6242i 1.15716 + 0.668085i 0.950621 0.310354i \(-0.100448\pi\)
0.206536 + 0.978439i \(0.433781\pi\)
\(954\) 0 0
\(955\) 38.7298 + 22.3606i 1.25327 + 0.723573i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) −14.2157 24.6224i −0.459050 0.795098i
\(960\) 0 0
\(961\) 22.4467 0.724088
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −23.7660 + 13.7213i −0.765055 + 0.441705i
\(966\) 0 0
\(967\) 3.07230 + 1.77379i 0.0987985 + 0.0570414i 0.548585 0.836095i \(-0.315167\pi\)
−0.449787 + 0.893136i \(0.648500\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −18.2213 + 31.5602i −0.584749 + 1.01282i 0.410158 + 0.912015i \(0.365474\pi\)
−0.994907 + 0.100800i \(0.967860\pi\)
\(972\) 0 0
\(973\) 17.8153 + 30.8570i 0.571132 + 0.989229i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 14.7328i 0.471345i 0.971833 + 0.235672i \(0.0757292\pi\)
−0.971833 + 0.235672i \(0.924271\pi\)
\(978\) 0 0
\(979\) 42.0987 24.3057i 1.34548 0.776813i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 13.5873 23.5340i 0.433369 0.750617i −0.563792 0.825917i \(-0.690658\pi\)
0.997161 + 0.0752996i \(0.0239913\pi\)
\(984\) 0 0
\(985\) 24.9531 43.2201i 0.795073 1.37711i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 19.6048i 0.623395i
\(990\) 0 0
\(991\) −27.8950 16.1052i −0.886113 0.511598i −0.0134440 0.999910i \(-0.504279\pi\)
−0.872669 + 0.488312i \(0.837613\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −33.6439 −1.06658
\(996\) 0 0
\(997\) −7.81673 13.5390i −0.247558 0.428783i 0.715290 0.698828i \(-0.246295\pi\)
−0.962848 + 0.270045i \(0.912961\pi\)
\(998\) 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.b.1151.1 yes 24
3.2 odd 2 inner 2736.2.cg.b.1151.12 yes 24
4.3 odd 2 2736.2.cg.a.1151.1 24
12.11 even 2 2736.2.cg.a.1151.12 yes 24
19.7 even 3 2736.2.cg.a.2591.12 yes 24
57.26 odd 6 2736.2.cg.a.2591.1 yes 24
76.7 odd 6 inner 2736.2.cg.b.2591.12 yes 24
228.83 even 6 inner 2736.2.cg.b.2591.1 yes 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2736.2.cg.a.1151.1 24 4.3 odd 2
2736.2.cg.a.1151.12 yes 24 12.11 even 2
2736.2.cg.a.2591.1 yes 24 57.26 odd 6
2736.2.cg.a.2591.12 yes 24 19.7 even 3
2736.2.cg.b.1151.1 yes 24 1.1 even 1 trivial
2736.2.cg.b.1151.12 yes 24 3.2 odd 2 inner
2736.2.cg.b.2591.1 yes 24 228.83 even 6 inner
2736.2.cg.b.2591.12 yes 24 76.7 odd 6 inner