Properties

Label 2736.2.cg.c.1151.6
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 1151.6
Character \(\chi\) \(=\) 2736.1151
Dual form 2736.2.cg.c.2591.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.45856 - 0.842100i) q^{5} -0.172239i q^{7} +O(q^{10})\) \(q+(-1.45856 - 0.842100i) q^{5} -0.172239i q^{7} +2.01814 q^{11} +(-0.109175 - 0.189097i) q^{13} +(5.01452 + 2.89514i) q^{17} +(3.23503 + 2.92140i) q^{19} +(-4.27652 - 7.40715i) q^{23} +(-1.08173 - 1.87362i) q^{25} +(0.957321 - 0.552710i) q^{29} +8.93488i q^{31} +(-0.145042 + 0.251221i) q^{35} -6.80687 q^{37} +(-5.97185 - 3.44785i) q^{41} +(4.91085 + 2.83528i) q^{43} +(1.15411 + 1.99898i) q^{47} +6.97033 q^{49} +(-3.55596 + 2.05304i) q^{53} +(-2.94358 - 1.69948i) q^{55} +(5.14055 - 8.90369i) q^{59} +(5.39443 + 9.34342i) q^{61} +0.367746i q^{65} +(10.6245 - 6.13404i) q^{67} +(7.30373 - 12.6504i) q^{71} +(-2.47256 + 4.28260i) q^{73} -0.347602i q^{77} +(5.20917 + 3.00752i) q^{79} +13.8767 q^{83} +(-4.87599 - 8.44547i) q^{85} +(0.701447 - 0.404980i) q^{89} +(-0.0325699 + 0.0188042i) q^{91} +(-2.25838 - 6.98526i) q^{95} +(-0.990995 + 1.71645i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) 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
\(5\) −1.45856 0.842100i −0.652288 0.376599i 0.137044 0.990565i \(-0.456240\pi\)
−0.789332 + 0.613966i \(0.789573\pi\)
\(6\) 0 0
\(7\) 0.172239i 0.0651001i −0.999470 0.0325501i \(-0.989637\pi\)
0.999470 0.0325501i \(-0.0103628\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 2.01814 0.608492 0.304246 0.952593i \(-0.401595\pi\)
0.304246 + 0.952593i \(0.401595\pi\)
\(12\) 0 0
\(13\) −0.109175 0.189097i −0.0302798 0.0524461i 0.850488 0.525994i \(-0.176306\pi\)
−0.880768 + 0.473548i \(0.842973\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.01452 + 2.89514i 1.21620 + 0.702174i 0.964103 0.265528i \(-0.0855462\pi\)
0.252098 + 0.967702i \(0.418880\pi\)
\(18\) 0 0
\(19\) 3.23503 + 2.92140i 0.742167 + 0.670215i
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.27652 7.40715i −0.891717 1.54450i −0.837816 0.545952i \(-0.816168\pi\)
−0.0539000 0.998546i \(-0.517165\pi\)
\(24\) 0 0
\(25\) −1.08173 1.87362i −0.216347 0.374724i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.957321 0.552710i 0.177770 0.102636i −0.408474 0.912770i \(-0.633939\pi\)
0.586245 + 0.810134i \(0.300606\pi\)
\(30\) 0 0
\(31\) 8.93488i 1.60475i 0.596819 + 0.802376i \(0.296431\pi\)
−0.596819 + 0.802376i \(0.703569\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −0.145042 + 0.251221i −0.0245166 + 0.0424640i
\(36\) 0 0
\(37\) −6.80687 −1.11904 −0.559521 0.828816i \(-0.689015\pi\)
−0.559521 + 0.828816i \(0.689015\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −5.97185 3.44785i −0.932646 0.538463i −0.0449983 0.998987i \(-0.514328\pi\)
−0.887647 + 0.460524i \(0.847662\pi\)
\(42\) 0 0
\(43\) 4.91085 + 2.83528i 0.748897 + 0.432376i 0.825295 0.564702i \(-0.191009\pi\)
−0.0763983 + 0.997077i \(0.524342\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 1.15411 + 1.99898i 0.168345 + 0.291581i 0.937838 0.347073i \(-0.112825\pi\)
−0.769493 + 0.638655i \(0.779491\pi\)
\(48\) 0 0
\(49\) 6.97033 0.995762
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −3.55596 + 2.05304i −0.488449 + 0.282006i −0.723931 0.689872i \(-0.757667\pi\)
0.235482 + 0.971879i \(0.424333\pi\)
\(54\) 0 0
\(55\) −2.94358 1.69948i −0.396912 0.229157i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 5.14055 8.90369i 0.669243 1.15916i −0.308874 0.951103i \(-0.599952\pi\)
0.978116 0.208059i \(-0.0667147\pi\)
\(60\) 0 0
\(61\) 5.39443 + 9.34342i 0.690686 + 1.19630i 0.971614 + 0.236574i \(0.0760245\pi\)
−0.280928 + 0.959729i \(0.590642\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0.367746i 0.0456133i
\(66\) 0 0
\(67\) 10.6245 6.13404i 1.29798 0.749392i 0.317929 0.948115i \(-0.397013\pi\)
0.980056 + 0.198723i \(0.0636794\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 7.30373 12.6504i 0.866794 1.50133i 0.00153867 0.999999i \(-0.499510\pi\)
0.865255 0.501332i \(-0.167156\pi\)
\(72\) 0 0
\(73\) −2.47256 + 4.28260i −0.289391 + 0.501240i −0.973665 0.227985i \(-0.926786\pi\)
0.684273 + 0.729226i \(0.260119\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0.347602i 0.0396129i
\(78\) 0 0
\(79\) 5.20917 + 3.00752i 0.586078 + 0.338372i 0.763545 0.645755i \(-0.223457\pi\)
−0.177467 + 0.984127i \(0.556790\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 13.8767 1.52317 0.761584 0.648066i \(-0.224422\pi\)
0.761584 + 0.648066i \(0.224422\pi\)
\(84\) 0 0
\(85\) −4.87599 8.44547i −0.528876 0.916039i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.701447 0.404980i 0.0743532 0.0429278i −0.462362 0.886691i \(-0.652998\pi\)
0.536716 + 0.843763i \(0.319665\pi\)
\(90\) 0 0
\(91\) −0.0325699 + 0.0188042i −0.00341425 + 0.00197122i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.25838 6.98526i −0.231705 0.716672i
\(96\) 0 0
\(97\) −0.990995 + 1.71645i −0.100620 + 0.174279i −0.911940 0.410323i \(-0.865416\pi\)
0.811320 + 0.584602i \(0.198749\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 10.6486 6.14795i 1.05957 0.611744i 0.134258 0.990946i \(-0.457135\pi\)
0.925314 + 0.379203i \(0.123802\pi\)
\(102\) 0 0
\(103\) 12.2681i 1.20881i −0.796678 0.604404i \(-0.793411\pi\)
0.796678 0.604404i \(-0.206589\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.30553 0.319558 0.159779 0.987153i \(-0.448922\pi\)
0.159779 + 0.987153i \(0.448922\pi\)
\(108\) 0 0
\(109\) 8.27625 14.3349i 0.792721 1.37303i −0.131556 0.991309i \(-0.541997\pi\)
0.924276 0.381724i \(-0.124669\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 5.44267i 0.512004i −0.966676 0.256002i \(-0.917595\pi\)
0.966676 0.256002i \(-0.0824053\pi\)
\(114\) 0 0
\(115\) 14.4050i 1.34328i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0.498655 0.863695i 0.0457116 0.0791748i
\(120\) 0 0
\(121\) −6.92711 −0.629737
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 12.0647i 1.07910i
\(126\) 0 0
\(127\) 15.4187 8.90200i 1.36819 0.789925i 0.377493 0.926013i \(-0.376786\pi\)
0.990697 + 0.136088i \(0.0434530\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.39893 12.8153i 0.646448 1.11968i −0.337517 0.941319i \(-0.609587\pi\)
0.983965 0.178361i \(-0.0570795\pi\)
\(132\) 0 0
\(133\) 0.503178 0.557198i 0.0436310 0.0483152i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −9.27194 + 5.35315i −0.792155 + 0.457351i −0.840721 0.541469i \(-0.817868\pi\)
0.0485657 + 0.998820i \(0.484535\pi\)
\(138\) 0 0
\(139\) 2.43914 1.40824i 0.206885 0.119445i −0.392978 0.919548i \(-0.628555\pi\)
0.599863 + 0.800103i \(0.295222\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −0.220331 0.381625i −0.0184250 0.0319131i
\(144\) 0 0
\(145\) −1.86175 −0.154610
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 8.18752 + 4.72707i 0.670748 + 0.387256i 0.796360 0.604823i \(-0.206756\pi\)
−0.125612 + 0.992079i \(0.540089\pi\)
\(150\) 0 0
\(151\) 8.56225i 0.696786i 0.937349 + 0.348393i \(0.113272\pi\)
−0.937349 + 0.348393i \(0.886728\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 7.52406 13.0321i 0.604347 1.04676i
\(156\) 0 0
\(157\) −3.59434 + 6.22558i −0.286860 + 0.496856i −0.973058 0.230558i \(-0.925945\pi\)
0.686199 + 0.727414i \(0.259278\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −1.27580 + 0.736583i −0.100547 + 0.0580508i
\(162\) 0 0
\(163\) 15.1222i 1.18446i 0.805770 + 0.592229i \(0.201752\pi\)
−0.805770 + 0.592229i \(0.798248\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −1.50773 2.61146i −0.116671 0.202081i 0.801775 0.597626i \(-0.203889\pi\)
−0.918447 + 0.395545i \(0.870556\pi\)
\(168\) 0 0
\(169\) 6.47616 11.2170i 0.498166 0.862849i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −13.1827 7.61104i −1.00226 0.578657i −0.0933459 0.995634i \(-0.529756\pi\)
−0.908917 + 0.416977i \(0.863090\pi\)
\(174\) 0 0
\(175\) −0.322710 + 0.186317i −0.0243946 + 0.0140842i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 13.5866 1.01551 0.507756 0.861501i \(-0.330475\pi\)
0.507756 + 0.861501i \(0.330475\pi\)
\(180\) 0 0
\(181\) 8.64864 + 14.9799i 0.642848 + 1.11345i 0.984794 + 0.173726i \(0.0555807\pi\)
−0.341946 + 0.939720i \(0.611086\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 9.92822 + 5.73206i 0.729938 + 0.421430i
\(186\) 0 0
\(187\) 10.1200 + 5.84279i 0.740049 + 0.427267i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −12.5893 −0.910932 −0.455466 0.890253i \(-0.650527\pi\)
−0.455466 + 0.890253i \(0.650527\pi\)
\(192\) 0 0
\(193\) −7.29786 + 12.6403i −0.525311 + 0.909866i 0.474254 + 0.880388i \(0.342718\pi\)
−0.999565 + 0.0294780i \(0.990615\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 12.6636i 0.902247i −0.892461 0.451124i \(-0.851023\pi\)
0.892461 0.451124i \(-0.148977\pi\)
\(198\) 0 0
\(199\) 7.38255 4.26232i 0.523335 0.302148i −0.214963 0.976622i \(-0.568963\pi\)
0.738298 + 0.674474i \(0.235630\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −0.0951980 0.164888i −0.00668159 0.0115729i
\(204\) 0 0
\(205\) 5.80687 + 10.0578i 0.405569 + 0.702466i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) 6.52875 + 5.89579i 0.451603 + 0.407820i
\(210\) 0 0
\(211\) −7.73783 4.46744i −0.532694 0.307551i 0.209419 0.977826i \(-0.432843\pi\)
−0.742113 + 0.670275i \(0.766176\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −4.77518 8.27085i −0.325664 0.564067i
\(216\) 0 0
\(217\) 1.53893 0.104470
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.26431i 0.0850467i
\(222\) 0 0
\(223\) −2.20595 1.27361i −0.147721 0.0852870i 0.424317 0.905513i \(-0.360514\pi\)
−0.572039 + 0.820226i \(0.693847\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.290085 −0.0192536 −0.00962679 0.999954i \(-0.503064\pi\)
−0.00962679 + 0.999954i \(0.503064\pi\)
\(228\) 0 0
\(229\) 4.65505 0.307614 0.153807 0.988101i \(-0.450847\pi\)
0.153807 + 0.988101i \(0.450847\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −9.69124 5.59524i −0.634894 0.366556i 0.147751 0.989025i \(-0.452797\pi\)
−0.782645 + 0.622468i \(0.786130\pi\)
\(234\) 0 0
\(235\) 3.88751i 0.253593i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 2.74889 0.177811 0.0889054 0.996040i \(-0.471663\pi\)
0.0889054 + 0.996040i \(0.471663\pi\)
\(240\) 0 0
\(241\) −14.3305 24.8212i −0.923111 1.59888i −0.794571 0.607171i \(-0.792304\pi\)
−0.128540 0.991704i \(-0.541029\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −10.1667 5.86972i −0.649524 0.375003i
\(246\) 0 0
\(247\) 0.199242 0.930680i 0.0126775 0.0592178i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 6.07433 + 10.5211i 0.383408 + 0.664083i 0.991547 0.129748i \(-0.0414168\pi\)
−0.608139 + 0.793831i \(0.708084\pi\)
\(252\) 0 0
\(253\) −8.63062 14.9487i −0.542603 0.939815i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 1.83271 1.05811i 0.114321 0.0660033i −0.441749 0.897139i \(-0.645642\pi\)
0.556070 + 0.831135i \(0.312309\pi\)
\(258\) 0 0
\(259\) 1.17241i 0.0728497i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 7.59382 13.1529i 0.468255 0.811041i −0.531087 0.847317i \(-0.678216\pi\)
0.999342 + 0.0362761i \(0.0115496\pi\)
\(264\) 0 0
\(265\) 6.91545 0.424813
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.07559 0.620993i −0.0655800 0.0378626i 0.466851 0.884336i \(-0.345388\pi\)
−0.532431 + 0.846473i \(0.678722\pi\)
\(270\) 0 0
\(271\) 1.93201 + 1.11545i 0.117361 + 0.0677585i 0.557531 0.830156i \(-0.311749\pi\)
−0.440170 + 0.897914i \(0.645082\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −2.18309 3.78123i −0.131645 0.228017i
\(276\) 0 0
\(277\) −16.6434 −1.00000 −0.500002 0.866024i \(-0.666668\pi\)
−0.500002 + 0.866024i \(0.666668\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 14.4047 8.31658i 0.859314 0.496125i −0.00446838 0.999990i \(-0.501422\pi\)
0.863783 + 0.503865i \(0.168089\pi\)
\(282\) 0 0
\(283\) 20.7174 + 11.9612i 1.23152 + 0.711020i 0.967347 0.253455i \(-0.0815670\pi\)
0.264175 + 0.964475i \(0.414900\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.593853 + 1.02858i −0.0350540 + 0.0607153i
\(288\) 0 0
\(289\) 8.26364 + 14.3130i 0.486096 + 0.841944i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 27.6769i 1.61690i 0.588565 + 0.808450i \(0.299693\pi\)
−0.588565 + 0.808450i \(0.700307\pi\)
\(294\) 0 0
\(295\) −14.9956 + 8.65772i −0.873078 + 0.504072i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −0.933782 + 1.61736i −0.0540020 + 0.0935342i
\(300\) 0 0
\(301\) 0.488345 0.845838i 0.0281477 0.0487533i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 18.1706i 1.04045i
\(306\) 0 0
\(307\) −9.10845 5.25876i −0.519846 0.300133i 0.217025 0.976166i \(-0.430365\pi\)
−0.736872 + 0.676032i \(0.763698\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −30.4262 −1.72531 −0.862655 0.505793i \(-0.831200\pi\)
−0.862655 + 0.505793i \(0.831200\pi\)
\(312\) 0 0
\(313\) 7.83955 + 13.5785i 0.443117 + 0.767502i 0.997919 0.0644810i \(-0.0205392\pi\)
−0.554802 + 0.831983i \(0.687206\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −0.875384 + 0.505403i −0.0491665 + 0.0283863i −0.524382 0.851483i \(-0.675704\pi\)
0.475215 + 0.879870i \(0.342370\pi\)
\(318\) 0 0
\(319\) 1.93201 1.11545i 0.108172 0.0624530i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 7.76431 + 24.0153i 0.432017 + 1.33625i
\(324\) 0 0
\(325\) −0.236197 + 0.409106i −0.0131019 + 0.0226931i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0.344302 0.198783i 0.0189820 0.0109593i
\(330\) 0 0
\(331\) 29.1733i 1.60351i 0.597654 + 0.801754i \(0.296099\pi\)
−0.597654 + 0.801754i \(0.703901\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −20.6619 −1.12888
\(336\) 0 0
\(337\) 7.90025 13.6836i 0.430354 0.745396i −0.566549 0.824028i \(-0.691722\pi\)
0.996904 + 0.0786323i \(0.0250553\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 18.0318i 0.976479i
\(342\) 0 0
\(343\) 2.40623i 0.129924i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 5.06526 8.77329i 0.271917 0.470975i −0.697435 0.716648i \(-0.745676\pi\)
0.969353 + 0.245673i \(0.0790089\pi\)
\(348\) 0 0
\(349\) −16.6980 −0.893821 −0.446910 0.894579i \(-0.647476\pi\)
−0.446910 + 0.894579i \(0.647476\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 25.5505i 1.35991i 0.733252 + 0.679957i \(0.238001\pi\)
−0.733252 + 0.679957i \(0.761999\pi\)
\(354\) 0 0
\(355\) −21.3059 + 12.3010i −1.13080 + 0.652867i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −14.7027 + 25.4658i −0.775977 + 1.34403i 0.158267 + 0.987396i \(0.449409\pi\)
−0.934244 + 0.356635i \(0.883924\pi\)
\(360\) 0 0
\(361\) 1.93087 + 18.9016i 0.101625 + 0.994823i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 7.21275 4.16429i 0.377533 0.217969i
\(366\) 0 0
\(367\) −8.27753 + 4.77904i −0.432084 + 0.249464i −0.700234 0.713913i \(-0.746921\pi\)
0.268150 + 0.963377i \(0.413588\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0.353612 + 0.612475i 0.0183586 + 0.0317981i
\(372\) 0 0
\(373\) 20.7961 1.07678 0.538390 0.842696i \(-0.319033\pi\)
0.538390 + 0.842696i \(0.319033\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.209032 0.120685i −0.0107657 0.00621557i
\(378\) 0 0
\(379\) 3.16095i 0.162367i 0.996699 + 0.0811836i \(0.0258700\pi\)
−0.996699 + 0.0811836i \(0.974130\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −10.0608 + 17.4258i −0.514081 + 0.890415i 0.485785 + 0.874078i \(0.338534\pi\)
−0.999867 + 0.0163367i \(0.994800\pi\)
\(384\) 0 0
\(385\) −0.292716 + 0.506999i −0.0149182 + 0.0258390i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −1.05815 + 0.610921i −0.0536501 + 0.0309749i −0.526585 0.850122i \(-0.676528\pi\)
0.472935 + 0.881097i \(0.343195\pi\)
\(390\) 0 0
\(391\) 49.5245i 2.50456i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −5.06526 8.77329i −0.254861 0.441432i
\(396\) 0 0
\(397\) −3.20352 + 5.54866i −0.160780 + 0.278479i −0.935149 0.354256i \(-0.884734\pi\)
0.774369 + 0.632735i \(0.218068\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) −17.3130 9.99568i −0.864571 0.499160i 0.000969118 1.00000i \(-0.499692\pi\)
−0.865540 + 0.500839i \(0.833025\pi\)
\(402\) 0 0
\(403\) 1.68956 0.975469i 0.0841630 0.0485916i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −13.7372 −0.680928
\(408\) 0 0
\(409\) 1.32392 + 2.29310i 0.0654638 + 0.113387i 0.896900 0.442234i \(-0.145814\pi\)
−0.831436 + 0.555621i \(0.812481\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −1.53356 0.885402i −0.0754616 0.0435678i
\(414\) 0 0
\(415\) −20.2400 11.6856i −0.993544 0.573623i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 34.6528 1.69290 0.846451 0.532467i \(-0.178735\pi\)
0.846451 + 0.532467i \(0.178735\pi\)
\(420\) 0 0
\(421\) 14.5521 25.2049i 0.709224 1.22841i −0.255921 0.966698i \(-0.582379\pi\)
0.965145 0.261715i \(-0.0842880\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 12.5271i 0.607652i
\(426\) 0 0
\(427\) 1.60930 0.929129i 0.0778794 0.0449637i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 5.38079 + 9.31980i 0.259184 + 0.448919i 0.966023 0.258454i \(-0.0832132\pi\)
−0.706840 + 0.707374i \(0.749880\pi\)
\(432\) 0 0
\(433\) −18.1284 31.3993i −0.871195 1.50895i −0.860761 0.509009i \(-0.830012\pi\)
−0.0104340 0.999946i \(-0.503321\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 7.80455 36.4558i 0.373342 1.74392i
\(438\) 0 0
\(439\) 19.2247 + 11.0994i 0.917545 + 0.529745i 0.882851 0.469653i \(-0.155621\pi\)
0.0346940 + 0.999398i \(0.488954\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 4.13148 + 7.15593i 0.196293 + 0.339989i 0.947323 0.320278i \(-0.103776\pi\)
−0.751031 + 0.660267i \(0.770443\pi\)
\(444\) 0 0
\(445\) −1.36414 −0.0646663
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 6.27444i 0.296109i −0.988979 0.148055i \(-0.952699\pi\)
0.988979 0.148055i \(-0.0473012\pi\)
\(450\) 0 0
\(451\) −12.0520 6.95824i −0.567508 0.327651i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0.0633402 0.00296943
\(456\) 0 0
\(457\) 11.5021 0.538044 0.269022 0.963134i \(-0.413300\pi\)
0.269022 + 0.963134i \(0.413300\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 4.75865 + 2.74741i 0.221632 + 0.127960i 0.606706 0.794926i \(-0.292491\pi\)
−0.385073 + 0.922886i \(0.625824\pi\)
\(462\) 0 0
\(463\) 23.3399i 1.08470i −0.840153 0.542349i \(-0.817535\pi\)
0.840153 0.542349i \(-0.182465\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) −5.61376 −0.259774 −0.129887 0.991529i \(-0.541461\pi\)
−0.129887 + 0.991529i \(0.541461\pi\)
\(468\) 0 0
\(469\) −1.05652 1.82994i −0.0487855 0.0844989i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 9.91078 + 5.72199i 0.455698 + 0.263097i
\(474\) 0 0
\(475\) 1.97414 9.22139i 0.0905797 0.423107i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 9.41707 + 16.3108i 0.430277 + 0.745262i 0.996897 0.0787176i \(-0.0250825\pi\)
−0.566620 + 0.823979i \(0.691749\pi\)
\(480\) 0 0
\(481\) 0.743142 + 1.28716i 0.0338844 + 0.0586894i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.89085 1.66903i 0.131267 0.0757869i
\(486\) 0 0
\(487\) 43.4061i 1.96692i −0.181135 0.983458i \(-0.557977\pi\)
0.181135 0.983458i \(-0.442023\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −7.30373 + 12.6504i −0.329613 + 0.570906i −0.982435 0.186605i \(-0.940252\pi\)
0.652822 + 0.757511i \(0.273585\pi\)
\(492\) 0 0
\(493\) 6.40068 0.288272
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −2.17890 1.25799i −0.0977368 0.0564284i
\(498\) 0 0
\(499\) −28.2166 16.2908i −1.26315 0.729278i −0.289464 0.957189i \(-0.593477\pi\)
−0.973682 + 0.227911i \(0.926811\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −3.94108 6.82616i −0.175724 0.304363i 0.764687 0.644401i \(-0.222893\pi\)
−0.940412 + 0.340038i \(0.889560\pi\)
\(504\) 0 0
\(505\) −20.7088 −0.921528
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −13.1464 + 7.59006i −0.582703 + 0.336424i −0.762207 0.647334i \(-0.775884\pi\)
0.179504 + 0.983757i \(0.442551\pi\)
\(510\) 0 0
\(511\) 0.737629 + 0.425870i 0.0326308 + 0.0188394i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −10.3309 + 17.8937i −0.455236 + 0.788492i
\(516\) 0 0
\(517\) 2.32916 + 4.03423i 0.102436 + 0.177425i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 25.8859i 1.13408i 0.823689 + 0.567041i \(0.191912\pi\)
−0.823689 + 0.567041i \(0.808088\pi\)
\(522\) 0 0
\(523\) −13.0962 + 7.56108i −0.572655 + 0.330623i −0.758209 0.652011i \(-0.773925\pi\)
0.185554 + 0.982634i \(0.440592\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −25.8677 + 44.8042i −1.12681 + 1.95170i
\(528\) 0 0
\(529\) −25.0773 + 43.4351i −1.09032 + 1.88848i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.50568i 0.0652182i
\(534\) 0 0
\(535\) −4.82132 2.78359i −0.208444 0.120345i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 14.0671 0.605914
\(540\) 0 0
\(541\) 2.47033 + 4.27874i 0.106208 + 0.183958i 0.914231 0.405193i \(-0.132796\pi\)
−0.808023 + 0.589151i \(0.799462\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −24.1428 + 13.9389i −1.03416 + 0.597075i
\(546\) 0 0
\(547\) −35.7483 + 20.6393i −1.52849 + 0.882472i −0.529060 + 0.848584i \(0.677455\pi\)
−0.999426 + 0.0338872i \(0.989211\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 4.71165 + 1.00868i 0.200723 + 0.0429713i
\(552\) 0 0
\(553\) 0.518011 0.897221i 0.0220281 0.0381537i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 28.7555 16.6020i 1.21841 0.703449i 0.253831 0.967249i \(-0.418309\pi\)
0.964577 + 0.263800i \(0.0849759\pi\)
\(558\) 0 0
\(559\) 1.23817i 0.0523690i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 20.6020 0.868272 0.434136 0.900847i \(-0.357054\pi\)
0.434136 + 0.900847i \(0.357054\pi\)
\(564\) 0 0
\(565\) −4.58328 + 7.93847i −0.192820 + 0.333974i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 35.2258i 1.47674i 0.674394 + 0.738371i \(0.264405\pi\)
−0.674394 + 0.738371i \(0.735595\pi\)
\(570\) 0 0
\(571\) 34.7468i 1.45411i −0.686580 0.727054i \(-0.740889\pi\)
0.686580 0.727054i \(-0.259111\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −9.25212 + 16.0251i −0.385840 + 0.668295i
\(576\) 0 0
\(577\) 15.4671 0.643904 0.321952 0.946756i \(-0.395661\pi\)
0.321952 + 0.946756i \(0.395661\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 2.39011i 0.0991584i
\(582\) 0 0
\(583\) −7.17644 + 4.14332i −0.297218 + 0.171599i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −12.1741 + 21.0862i −0.502479 + 0.870320i 0.497517 + 0.867454i \(0.334245\pi\)
−0.999996 + 0.00286514i \(0.999088\pi\)
\(588\) 0 0
\(589\) −26.1023 + 28.9046i −1.07553 + 1.19099i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 29.5771 17.0763i 1.21459 0.701241i 0.250831 0.968031i \(-0.419296\pi\)
0.963755 + 0.266790i \(0.0859630\pi\)
\(594\) 0 0
\(595\) −1.45464 + 0.839835i −0.0596343 + 0.0344299i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −4.64190 8.04000i −0.189663 0.328505i 0.755475 0.655177i \(-0.227406\pi\)
−0.945138 + 0.326672i \(0.894073\pi\)
\(600\) 0 0
\(601\) 9.17512 0.374261 0.187131 0.982335i \(-0.440081\pi\)
0.187131 + 0.982335i \(0.440081\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 10.1036 + 5.83332i 0.410770 + 0.237158i
\(606\) 0 0
\(607\) 25.2294i 1.02403i −0.858976 0.512016i \(-0.828899\pi\)
0.858976 0.512016i \(-0.171101\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0.252001 0.436479i 0.0101949 0.0176581i
\(612\) 0 0
\(613\) 5.71776 9.90345i 0.230938 0.399997i −0.727146 0.686483i \(-0.759154\pi\)
0.958084 + 0.286486i \(0.0924871\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −28.5273 + 16.4703i −1.14847 + 0.663067i −0.948513 0.316738i \(-0.897412\pi\)
−0.199953 + 0.979805i \(0.564079\pi\)
\(618\) 0 0
\(619\) 37.8796i 1.52251i 0.648453 + 0.761255i \(0.275416\pi\)
−0.648453 + 0.761255i \(0.724584\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −0.0697533 0.120816i −0.00279461 0.00484040i
\(624\) 0 0
\(625\) 4.75103 8.22903i 0.190041 0.329161i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) −34.1332 19.7068i −1.36098 0.785762i
\(630\) 0 0
\(631\) 21.7897 12.5803i 0.867434 0.500813i 0.000939347 1.00000i \(-0.499701\pi\)
0.866495 + 0.499186i \(0.166368\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −29.9855 −1.18994
\(636\) 0 0
\(637\) −0.760989 1.31807i −0.0301515 0.0522239i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −33.1330 19.1294i −1.30868 0.755565i −0.326801 0.945093i \(-0.605971\pi\)
−0.981875 + 0.189528i \(0.939304\pi\)
\(642\) 0 0
\(643\) 0.504443 + 0.291240i 0.0198933 + 0.0114854i 0.509914 0.860226i \(-0.329677\pi\)
−0.490020 + 0.871711i \(0.663011\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −45.7409 −1.79826 −0.899129 0.437683i \(-0.855799\pi\)
−0.899129 + 0.437683i \(0.855799\pi\)
\(648\) 0 0
\(649\) 10.3744 17.9689i 0.407229 0.705341i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 23.7797i 0.930570i −0.885161 0.465285i \(-0.845952\pi\)
0.885161 0.465285i \(-0.154048\pi\)
\(654\) 0 0
\(655\) −21.5836 + 12.4613i −0.843340 + 0.486903i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.85047 + 8.40125i 0.188947 + 0.327266i 0.944900 0.327360i \(-0.106159\pi\)
−0.755952 + 0.654627i \(0.772826\pi\)
\(660\) 0 0
\(661\) −3.80687 6.59368i −0.148070 0.256465i 0.782444 0.622721i \(-0.213973\pi\)
−0.930514 + 0.366256i \(0.880639\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −1.20313 + 0.388981i −0.0466554 + 0.0150840i
\(666\) 0 0
\(667\) −8.18801 4.72735i −0.317041 0.183044i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 10.8867 + 18.8563i 0.420277 + 0.727941i
\(672\) 0 0
\(673\) 42.8822 1.65299 0.826493 0.562946i \(-0.190332\pi\)
0.826493 + 0.562946i \(0.190332\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 33.8674i 1.30163i 0.759236 + 0.650815i \(0.225573\pi\)
−0.759236 + 0.650815i \(0.774427\pi\)
\(678\) 0 0
\(679\) 0.295640 + 0.170688i 0.0113456 + 0.00655039i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −9.32361 −0.356758 −0.178379 0.983962i \(-0.557085\pi\)
−0.178379 + 0.983962i \(0.557085\pi\)
\(684\) 0 0
\(685\) 18.0316 0.688951
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.776447 + 0.448282i 0.0295803 + 0.0170782i
\(690\) 0 0
\(691\) 47.2936i 1.79913i 0.436784 + 0.899566i \(0.356117\pi\)
−0.436784 + 0.899566i \(0.643883\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) −4.74351 −0.179931
\(696\) 0 0
\(697\) −19.9640 34.5786i −0.756190 1.30976i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 15.3169 + 8.84321i 0.578511 + 0.334004i 0.760541 0.649289i \(-0.224934\pi\)
−0.182030 + 0.983293i \(0.558267\pi\)
\(702\) 0 0
\(703\) −22.0204 19.8856i −0.830516 0.749998i
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.05891 1.83409i −0.0398246 0.0689782i
\(708\) 0 0
\(709\) −0.212948 0.368836i −0.00799742 0.0138519i 0.861999 0.506910i \(-0.169212\pi\)
−0.869996 + 0.493058i \(0.835879\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 66.1820 38.2102i 2.47854 1.43098i
\(714\) 0 0
\(715\) 0.742164i 0.0277554i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −7.08340 + 12.2688i −0.264166 + 0.457550i −0.967345 0.253464i \(-0.918430\pi\)
0.703179 + 0.711013i \(0.251763\pi\)
\(720\) 0 0
\(721\) −2.11304 −0.0786936
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.07113 1.19577i −0.0769200 0.0444098i
\(726\) 0 0
\(727\) −2.79442 1.61336i −0.103639 0.0598361i 0.447285 0.894392i \(-0.352391\pi\)
−0.550924 + 0.834556i \(0.685724\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 16.4170 + 28.4351i 0.607206 + 1.05171i
\(732\) 0 0
\(733\) −27.9587 −1.03268 −0.516339 0.856384i \(-0.672705\pi\)
−0.516339 + 0.856384i \(0.672705\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 21.4417 12.3793i 0.789814 0.455999i
\(738\) 0 0
\(739\) −22.4433 12.9576i −0.825590 0.476655i 0.0267502 0.999642i \(-0.491484\pi\)
−0.852340 + 0.522987i \(0.824817\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −20.9220 + 36.2380i −0.767555 + 1.32944i 0.171330 + 0.985214i \(0.445194\pi\)
−0.938885 + 0.344231i \(0.888140\pi\)
\(744\) 0 0
\(745\) −7.96133 13.7894i −0.291681 0.505205i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0.569341i 0.0208033i
\(750\) 0 0
\(751\) −0.0270700 + 0.0156289i −0.000987799 + 0.000570306i −0.500494 0.865740i \(-0.666848\pi\)
0.499506 + 0.866310i \(0.333515\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 7.21027 12.4886i 0.262409 0.454505i
\(756\) 0 0
\(757\) −13.6270 + 23.6027i −0.495283 + 0.857855i −0.999985 0.00543871i \(-0.998269\pi\)
0.504703 + 0.863293i \(0.331602\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 13.4135i 0.486237i −0.969997 0.243119i \(-0.921830\pi\)
0.969997 0.243119i \(-0.0781704\pi\)
\(762\) 0 0
\(763\) −2.46902 1.42549i −0.0893846 0.0516062i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −2.24489 −0.0810581
\(768\) 0 0
\(769\) −5.88817 10.1986i −0.212333 0.367772i 0.740111 0.672484i \(-0.234773\pi\)
−0.952444 + 0.304713i \(0.901439\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −29.4951 + 17.0290i −1.06087 + 0.612492i −0.925672 0.378327i \(-0.876499\pi\)
−0.135195 + 0.990819i \(0.543166\pi\)
\(774\) 0 0
\(775\) 16.7406 9.66517i 0.601339 0.347183i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −9.24659 28.6000i −0.331293 1.02470i
\(780\) 0 0
\(781\) 14.7400 25.5304i 0.527437 0.913548i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 10.4851 6.05359i 0.374230 0.216062i
\(786\) 0 0
\(787\) 32.5159i 1.15907i −0.814948 0.579533i \(-0.803235\pi\)
0.814948 0.579533i \(-0.196765\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −0.937439 −0.0333315
\(792\) 0 0
\(793\) 1.17788 2.04014i 0.0418276 0.0724476i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 12.8868i 0.456474i 0.973606 + 0.228237i \(0.0732962\pi\)
−0.973606 + 0.228237i \(0.926704\pi\)
\(798\) 0 0
\(799\) 13.3653i 0.472829i
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −4.98997 + 8.64289i −0.176092 + 0.305001i
\(804\) 0 0
\(805\) 2.48111 0.0874475
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 22.2442i 0.782063i 0.920377 + 0.391031i \(0.127882\pi\)
−0.920377 + 0.391031i \(0.872118\pi\)
\(810\) 0 0
\(811\) 11.1859 6.45816i 0.392789 0.226777i −0.290579 0.956851i \(-0.593848\pi\)
0.683368 + 0.730074i \(0.260515\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 12.7344 22.0566i 0.446065 0.772608i
\(816\) 0 0
\(817\) 7.60377 + 23.5187i 0.266022 + 0.822817i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −10.7950 + 6.23249i −0.376748 + 0.217515i −0.676402 0.736532i \(-0.736462\pi\)
0.299655 + 0.954048i \(0.403129\pi\)
\(822\) 0 0
\(823\) −7.13742 + 4.12079i −0.248795 + 0.143642i −0.619212 0.785224i \(-0.712548\pi\)
0.370417 + 0.928865i \(0.379215\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −0.902111 1.56250i −0.0313695 0.0543335i 0.849914 0.526921i \(-0.176654\pi\)
−0.881284 + 0.472587i \(0.843320\pi\)
\(828\) 0 0
\(829\) 15.8057 0.548954 0.274477 0.961594i \(-0.411495\pi\)
0.274477 + 0.961594i \(0.411495\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 34.9529 + 20.1801i 1.21105 + 0.699198i
\(834\) 0 0
\(835\) 5.07862i 0.175753i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −5.00727 + 8.67284i −0.172870 + 0.299420i −0.939422 0.342762i \(-0.888637\pi\)
0.766552 + 0.642182i \(0.221971\pi\)
\(840\) 0 0
\(841\) −13.8890 + 24.0565i −0.478932 + 0.829534i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −18.8917 + 10.9072i −0.649896 + 0.375218i
\(846\) 0 0
\(847\) 1.19312i 0.0409960i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 29.1097 + 50.4195i 0.997868 + 1.72836i
\(852\) 0 0
\(853\) −10.2794 + 17.8045i −0.351961 + 0.609614i −0.986593 0.163200i \(-0.947818\pi\)
0.634632 + 0.772814i \(0.281152\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) −41.3464 23.8714i −1.41237 0.815430i −0.416755 0.909019i \(-0.636833\pi\)
−0.995611 + 0.0935891i \(0.970166\pi\)
\(858\) 0 0
\(859\) −18.0965 + 10.4480i −0.617446 + 0.356483i −0.775874 0.630888i \(-0.782691\pi\)
0.158428 + 0.987371i \(0.449357\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −9.49946 −0.323366 −0.161683 0.986843i \(-0.551692\pi\)
−0.161683 + 0.986843i \(0.551692\pi\)
\(864\) 0 0
\(865\) 12.8185 + 22.2023i 0.435843 + 0.754902i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 10.5128 + 6.06959i 0.356624 + 0.205897i
\(870\) 0 0
\(871\) −2.31986 1.33937i −0.0786054 0.0453828i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 2.07801 0.0702496
\(876\) 0 0
\(877\) 16.0799 27.8513i 0.542981 0.940470i −0.455750 0.890108i \(-0.650629\pi\)
0.998731 0.0503626i \(-0.0160377\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 31.5821i 1.06403i 0.846736 + 0.532014i \(0.178565\pi\)
−0.846736 + 0.532014i \(0.821435\pi\)
\(882\) 0 0
\(883\) −10.7492 + 6.20608i −0.361741 + 0.208851i −0.669844 0.742502i \(-0.733639\pi\)
0.308103 + 0.951353i \(0.400306\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) −23.8795 41.3605i −0.801795 1.38875i −0.918434 0.395575i \(-0.870545\pi\)
0.116638 0.993174i \(-0.462788\pi\)
\(888\) 0 0
\(889\) −1.53327 2.65570i −0.0514242 0.0890693i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −2.10623 + 9.83839i −0.0704822 + 0.329229i
\(894\) 0 0
\(895\) −19.8169 11.4413i −0.662407 0.382441i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 4.93839 + 8.55355i 0.164705 + 0.285277i
\(900\) 0 0
\(901\) −23.7753 −0.792070
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 29.1321i 0.968383i
\(906\) 0 0
\(907\) 37.0023 + 21.3633i 1.22864 + 0.709356i 0.966746 0.255740i \(-0.0823191\pi\)
0.261895 + 0.965096i \(0.415652\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −23.3000 −0.771964 −0.385982 0.922506i \(-0.626137\pi\)
−0.385982 + 0.922506i \(0.626137\pi\)
\(912\) 0 0
\(913\) 28.0052 0.926836
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) −2.20730 1.27438i −0.0728913 0.0420838i
\(918\) 0 0
\(919\) 14.2297i 0.469395i 0.972069 + 0.234697i \(0.0754099\pi\)
−0.972069 + 0.234697i \(0.924590\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) −3.18955 −0.104985
\(924\) 0 0
\(925\) 7.36322 + 12.7535i 0.242101 + 0.419332i
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) −44.0463 25.4301i −1.44511 0.834336i −0.446928 0.894570i \(-0.647482\pi\)
−0.998184 + 0.0602338i \(0.980815\pi\)
\(930\) 0 0
\(931\) 22.5493 + 20.3631i 0.739022 + 0.667374i
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) −9.84044 17.0441i −0.321817 0.557403i
\(936\) 0 0
\(937\) 5.13439 + 8.89303i 0.167733 + 0.290523i 0.937623 0.347655i \(-0.113022\pi\)
−0.769889 + 0.638177i \(0.779689\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 7.13944 4.12196i 0.232739 0.134372i −0.379096 0.925357i \(-0.623765\pi\)
0.611835 + 0.790985i \(0.290432\pi\)
\(942\) 0 0
\(943\) 58.9792i 1.92063i
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −15.4715 + 26.7974i −0.502756 + 0.870799i 0.497239 + 0.867614i \(0.334347\pi\)
−0.999995 + 0.00318534i \(0.998986\pi\)
\(948\) 0 0
\(949\) 1.07977 0.0350508
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −34.3702 19.8436i −1.11336 0.642798i −0.173662 0.984805i \(-0.555560\pi\)
−0.939697 + 0.342007i \(0.888893\pi\)
\(954\) 0 0
\(955\) 18.3623 + 10.6015i 0.594190 + 0.343056i
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0.922020 + 1.59699i 0.0297736 + 0.0515694i
\(960\) 0 0
\(961\) −48.8321 −1.57523
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 21.2887 12.2911i 0.685309 0.395663i
\(966\) 0 0
\(967\) −31.2876 18.0639i −1.00614 0.580896i −0.0960818 0.995373i \(-0.530631\pi\)
−0.910060 + 0.414477i \(0.863964\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 27.7154 48.0044i 0.889428 1.54053i 0.0488755 0.998805i \(-0.484436\pi\)
0.840553 0.541730i \(-0.182230\pi\)
\(972\) 0 0
\(973\) −0.242553 0.420114i −0.00777589 0.0134682i
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 53.3001i 1.70522i 0.522546 + 0.852611i \(0.324982\pi\)
−0.522546 + 0.852611i \(0.675018\pi\)
\(978\) 0 0
\(979\) 1.41562 0.817308i 0.0452434 0.0261213i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 21.5159 37.2666i 0.686250 1.18862i −0.286792 0.957993i \(-0.592589\pi\)
0.973042 0.230628i \(-0.0740779\pi\)
\(984\) 0 0
\(985\) −10.6641 + 18.4707i −0.339785 + 0.588525i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 48.5005i 1.54223i
\(990\) 0 0
\(991\) −4.57619 2.64206i −0.145367 0.0839279i 0.425552 0.904934i \(-0.360080\pi\)
−0.570920 + 0.821006i \(0.693413\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) −14.3572 −0.455154
\(996\) 0 0
\(997\) −6.36964 11.0325i −0.201728 0.349404i 0.747357 0.664423i \(-0.231322\pi\)
−0.949085 + 0.315019i \(0.897989\pi\)
\(998\) 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.1151.6 yes 32
3.2 odd 2 inner 2736.2.cg.c.1151.12 yes 32
4.3 odd 2 inner 2736.2.cg.c.1151.5 32
12.11 even 2 inner 2736.2.cg.c.1151.11 yes 32
19.7 even 3 inner 2736.2.cg.c.2591.12 yes 32
57.26 odd 6 inner 2736.2.cg.c.2591.6 yes 32
76.7 odd 6 inner 2736.2.cg.c.2591.11 yes 32
228.83 even 6 inner 2736.2.cg.c.2591.5 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
2736.2.cg.c.1151.5 32 4.3 odd 2 inner
2736.2.cg.c.1151.6 yes 32 1.1 even 1 trivial
2736.2.cg.c.1151.11 yes 32 12.11 even 2 inner
2736.2.cg.c.1151.12 yes 32 3.2 odd 2 inner
2736.2.cg.c.2591.5 yes 32 228.83 even 6 inner
2736.2.cg.c.2591.6 yes 32 57.26 odd 6 inner
2736.2.cg.c.2591.11 yes 32 76.7 odd 6 inner
2736.2.cg.c.2591.12 yes 32 19.7 even 3 inner