Properties

Label 729.2.c.c.487.1
Level $729$
Weight $2$
Character 729.487
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
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] = [729,2,Mod(244,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.244");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{36})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{6} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 487.1
Root \(0.984808 - 0.173648i\) of defining polynomial
Character \(\chi\) \(=\) 729.487
Dual form 729.2.c.c.244.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.984808 + 1.70574i) q^{2} +(-0.939693 - 1.62760i) q^{4} +(1.85083 + 3.20574i) q^{5} +(1.17365 - 2.03282i) q^{7} -0.237565 q^{8} +O(q^{10})\) \(q+(-0.984808 + 1.70574i) q^{2} +(-0.939693 - 1.62760i) q^{4} +(1.85083 + 3.20574i) q^{5} +(1.17365 - 2.03282i) q^{7} -0.237565 q^{8} -7.29086 q^{10} +(-1.08926 + 1.88666i) q^{11} +(2.35844 + 4.08494i) q^{13} +(2.31164 + 4.00387i) q^{14} +(2.11334 - 3.66041i) q^{16} +2.93512 q^{17} -6.22668 q^{19} +(3.47843 - 6.02481i) q^{20} +(-2.14543 - 3.71599i) q^{22} +(0.259515 + 0.449493i) q^{23} +(-4.35117 + 7.53644i) q^{25} -9.29044 q^{26} -4.41147 q^{28} +(-1.74638 + 3.02481i) q^{29} +(2.15270 + 3.72859i) q^{31} +(3.92490 + 6.79813i) q^{32} +(-2.89053 + 5.00654i) q^{34} +8.68891 q^{35} +2.41147 q^{37} +(6.13208 - 10.6211i) q^{38} +(-0.439693 - 0.761570i) q^{40} +(1.24930 + 2.16385i) q^{41} +(-0.532089 + 0.921605i) q^{43} +4.09429 q^{44} -1.02229 q^{46} +(-0.118782 + 0.205737i) q^{47} +(0.745100 + 1.29055i) q^{49} +(-8.57013 - 14.8439i) q^{50} +(4.43242 - 7.67717i) q^{52} -4.66717 q^{53} -8.06418 q^{55} +(-0.278817 + 0.482926i) q^{56} +(-3.43969 - 5.95772i) q^{58} +(-6.65609 - 11.5287i) q^{59} +(1.83750 - 3.18264i) q^{61} -8.48000 q^{62} -7.00774 q^{64} +(-8.73016 + 15.1211i) q^{65} +(-7.14930 - 12.3830i) q^{67} +(-2.75811 - 4.77719i) q^{68} +(-8.55690 + 14.8210i) q^{70} -1.20307 q^{71} -4.68004 q^{73} +(-2.37484 + 4.11334i) q^{74} +(5.85117 + 10.1345i) q^{76} +(2.55682 + 4.42855i) q^{77} +(6.40033 - 11.0857i) q^{79} +15.6458 q^{80} -4.92127 q^{82} +(-5.65198 + 9.78952i) q^{83} +(5.43242 + 9.40923i) q^{85} +(-1.04801 - 1.81521i) q^{86} +(0.258770 - 0.448204i) q^{88} -0.699287 q^{89} +11.0719 q^{91} +(0.487728 - 0.844770i) q^{92} +(-0.233956 - 0.405223i) q^{94} +(-11.5245 - 19.9611i) q^{95} +(3.54323 - 6.13706i) q^{97} -2.93512 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 12 q^{7} - 24 q^{10} + 12 q^{13} + 12 q^{16} - 48 q^{19} + 6 q^{22} - 12 q^{28} + 30 q^{31} - 12 q^{37} + 6 q^{40} + 12 q^{43} + 12 q^{46} + 6 q^{49} + 6 q^{52} - 60 q^{55} - 30 q^{58} + 12 q^{61} + 12 q^{64} - 6 q^{67} - 30 q^{70} + 24 q^{73} + 18 q^{76} + 48 q^{79} - 24 q^{82} + 18 q^{85} - 42 q^{88} - 12 q^{94} + 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.984808 + 1.70574i −0.696364 + 1.20614i 0.273354 + 0.961913i \(0.411867\pi\)
−0.969719 + 0.244225i \(0.921467\pi\)
\(3\) 0 0
\(4\) −0.939693 1.62760i −0.469846 0.813798i
\(5\) 1.85083 + 3.20574i 0.827718 + 1.43365i 0.899824 + 0.436252i \(0.143694\pi\)
−0.0721067 + 0.997397i \(0.522972\pi\)
\(6\) 0 0
\(7\) 1.17365 2.03282i 0.443597 0.768333i −0.554356 0.832280i \(-0.687035\pi\)
0.997953 + 0.0639466i \(0.0203687\pi\)
\(8\) −0.237565 −0.0839918
\(9\) 0 0
\(10\) −7.29086 −2.30557
\(11\) −1.08926 + 1.88666i −0.328425 + 0.568849i −0.982200 0.187840i \(-0.939851\pi\)
0.653774 + 0.756690i \(0.273185\pi\)
\(12\) 0 0
\(13\) 2.35844 + 4.08494i 0.654114 + 1.13296i 0.982115 + 0.188281i \(0.0602916\pi\)
−0.328001 + 0.944677i \(0.606375\pi\)
\(14\) 2.31164 + 4.00387i 0.617811 + 1.07008i
\(15\) 0 0
\(16\) 2.11334 3.66041i 0.528335 0.915103i
\(17\) 2.93512 0.711871 0.355936 0.934510i \(-0.384162\pi\)
0.355936 + 0.934510i \(0.384162\pi\)
\(18\) 0 0
\(19\) −6.22668 −1.42850 −0.714249 0.699891i \(-0.753232\pi\)
−0.714249 + 0.699891i \(0.753232\pi\)
\(20\) 3.47843 6.02481i 0.777800 1.34719i
\(21\) 0 0
\(22\) −2.14543 3.71599i −0.457407 0.792252i
\(23\) 0.259515 + 0.449493i 0.0541126 + 0.0937257i 0.891813 0.452405i \(-0.149434\pi\)
−0.837700 + 0.546130i \(0.816100\pi\)
\(24\) 0 0
\(25\) −4.35117 + 7.53644i −0.870233 + 1.50729i
\(26\) −9.29044 −1.82201
\(27\) 0 0
\(28\) −4.41147 −0.833690
\(29\) −1.74638 + 3.02481i −0.324294 + 0.561694i −0.981369 0.192131i \(-0.938460\pi\)
0.657075 + 0.753825i \(0.271793\pi\)
\(30\) 0 0
\(31\) 2.15270 + 3.72859i 0.386637 + 0.669675i 0.991995 0.126279i \(-0.0403033\pi\)
−0.605358 + 0.795953i \(0.706970\pi\)
\(32\) 3.92490 + 6.79813i 0.693832 + 1.20175i
\(33\) 0 0
\(34\) −2.89053 + 5.00654i −0.495722 + 0.858615i
\(35\) 8.68891 1.46869
\(36\) 0 0
\(37\) 2.41147 0.396444 0.198222 0.980157i \(-0.436483\pi\)
0.198222 + 0.980157i \(0.436483\pi\)
\(38\) 6.13208 10.6211i 0.994755 1.72297i
\(39\) 0 0
\(40\) −0.439693 0.761570i −0.0695215 0.120415i
\(41\) 1.24930 + 2.16385i 0.195108 + 0.337936i 0.946936 0.321423i \(-0.104161\pi\)
−0.751828 + 0.659359i \(0.770828\pi\)
\(42\) 0 0
\(43\) −0.532089 + 0.921605i −0.0811428 + 0.140543i −0.903741 0.428080i \(-0.859190\pi\)
0.822598 + 0.568623i \(0.192524\pi\)
\(44\) 4.09429 0.617237
\(45\) 0 0
\(46\) −1.02229 −0.150728
\(47\) −0.118782 + 0.205737i −0.0173262 + 0.0300098i −0.874558 0.484920i \(-0.838849\pi\)
0.857232 + 0.514930i \(0.172182\pi\)
\(48\) 0 0
\(49\) 0.745100 + 1.29055i 0.106443 + 0.184364i
\(50\) −8.57013 14.8439i −1.21200 2.09924i
\(51\) 0 0
\(52\) 4.43242 7.67717i 0.614666 1.06463i
\(53\) −4.66717 −0.641085 −0.320543 0.947234i \(-0.603865\pi\)
−0.320543 + 0.947234i \(0.603865\pi\)
\(54\) 0 0
\(55\) −8.06418 −1.08737
\(56\) −0.278817 + 0.482926i −0.0372585 + 0.0645337i
\(57\) 0 0
\(58\) −3.43969 5.95772i −0.451654 0.782287i
\(59\) −6.65609 11.5287i −0.866549 1.50091i −0.865501 0.500908i \(-0.833000\pi\)
−0.00104825 0.999999i \(-0.500334\pi\)
\(60\) 0 0
\(61\) 1.83750 3.18264i 0.235267 0.407495i −0.724083 0.689713i \(-0.757737\pi\)
0.959350 + 0.282218i \(0.0910701\pi\)
\(62\) −8.48000 −1.07696
\(63\) 0 0
\(64\) −7.00774 −0.875968
\(65\) −8.73016 + 15.1211i −1.08284 + 1.87554i
\(66\) 0 0
\(67\) −7.14930 12.3830i −0.873426 1.51282i −0.858430 0.512931i \(-0.828560\pi\)
−0.0149960 0.999888i \(-0.504774\pi\)
\(68\) −2.75811 4.77719i −0.334470 0.579319i
\(69\) 0 0
\(70\) −8.55690 + 14.8210i −1.02275 + 1.77145i
\(71\) −1.20307 −0.142778 −0.0713891 0.997449i \(-0.522743\pi\)
−0.0713891 + 0.997449i \(0.522743\pi\)
\(72\) 0 0
\(73\) −4.68004 −0.547758 −0.273879 0.961764i \(-0.588307\pi\)
−0.273879 + 0.961764i \(0.588307\pi\)
\(74\) −2.37484 + 4.11334i −0.276069 + 0.478166i
\(75\) 0 0
\(76\) 5.85117 + 10.1345i 0.671175 + 1.16251i
\(77\) 2.55682 + 4.42855i 0.291377 + 0.504680i
\(78\) 0 0
\(79\) 6.40033 11.0857i 0.720093 1.24724i −0.240869 0.970558i \(-0.577432\pi\)
0.960962 0.276681i \(-0.0892344\pi\)
\(80\) 15.6458 1.74925
\(81\) 0 0
\(82\) −4.92127 −0.543464
\(83\) −5.65198 + 9.78952i −0.620385 + 1.07454i 0.369029 + 0.929418i \(0.379690\pi\)
−0.989414 + 0.145121i \(0.953643\pi\)
\(84\) 0 0
\(85\) 5.43242 + 9.40923i 0.589229 + 1.02057i
\(86\) −1.04801 1.81521i −0.113010 0.195739i
\(87\) 0 0
\(88\) 0.258770 0.448204i 0.0275850 0.0477787i
\(89\) −0.699287 −0.0741242 −0.0370621 0.999313i \(-0.511800\pi\)
−0.0370621 + 0.999313i \(0.511800\pi\)
\(90\) 0 0
\(91\) 11.0719 1.16065
\(92\) 0.487728 0.844770i 0.0508492 0.0880734i
\(93\) 0 0
\(94\) −0.233956 0.405223i −0.0241307 0.0417956i
\(95\) −11.5245 19.9611i −1.18239 2.04797i
\(96\) 0 0
\(97\) 3.54323 6.13706i 0.359761 0.623124i −0.628160 0.778084i \(-0.716192\pi\)
0.987921 + 0.154960i \(0.0495250\pi\)
\(98\) −2.93512 −0.296492
\(99\) 0 0
\(100\) 16.3550 1.63550
\(101\) 2.33856 4.05051i 0.232696 0.403041i −0.725905 0.687795i \(-0.758579\pi\)
0.958600 + 0.284755i \(0.0919121\pi\)
\(102\) 0 0
\(103\) 6.81180 + 11.7984i 0.671187 + 1.16253i 0.977568 + 0.210621i \(0.0675486\pi\)
−0.306381 + 0.951909i \(0.599118\pi\)
\(104\) −0.560282 0.970437i −0.0549402 0.0951592i
\(105\) 0 0
\(106\) 4.59627 7.96097i 0.446429 0.773238i
\(107\) −11.6340 −1.12470 −0.562350 0.826900i \(-0.690102\pi\)
−0.562350 + 0.826900i \(0.690102\pi\)
\(108\) 0 0
\(109\) 14.6040 1.39881 0.699405 0.714725i \(-0.253448\pi\)
0.699405 + 0.714725i \(0.253448\pi\)
\(110\) 7.94166 13.7554i 0.757208 1.31152i
\(111\) 0 0
\(112\) −4.96064 8.59208i −0.468736 0.811875i
\(113\) 2.34791 + 4.06670i 0.220873 + 0.382563i 0.955073 0.296370i \(-0.0957760\pi\)
−0.734200 + 0.678933i \(0.762443\pi\)
\(114\) 0 0
\(115\) −0.960637 + 1.66387i −0.0895799 + 0.155157i
\(116\) 6.56423 0.609474
\(117\) 0 0
\(118\) 26.2199 2.41374
\(119\) 3.44480 5.96657i 0.315784 0.546954i
\(120\) 0 0
\(121\) 3.12701 + 5.41614i 0.284274 + 0.492377i
\(122\) 3.61916 + 6.26857i 0.327663 + 0.567530i
\(123\) 0 0
\(124\) 4.04576 7.00746i 0.363320 0.629289i
\(125\) −13.7048 −1.22579
\(126\) 0 0
\(127\) 6.09152 0.540535 0.270267 0.962785i \(-0.412888\pi\)
0.270267 + 0.962785i \(0.412888\pi\)
\(128\) −0.948531 + 1.64290i −0.0838391 + 0.145214i
\(129\) 0 0
\(130\) −17.1951 29.7827i −1.50811 2.61212i
\(131\) 5.17420 + 8.96198i 0.452072 + 0.783012i 0.998515 0.0544847i \(-0.0173516\pi\)
−0.546442 + 0.837497i \(0.684018\pi\)
\(132\) 0 0
\(133\) −7.30793 + 12.6577i −0.633678 + 1.09756i
\(134\) 28.1627 2.43289
\(135\) 0 0
\(136\) −0.697281 −0.0597914
\(137\) 9.54233 16.5278i 0.815257 1.41207i −0.0938868 0.995583i \(-0.529929\pi\)
0.909143 0.416483i \(-0.136737\pi\)
\(138\) 0 0
\(139\) 11.6518 + 20.1816i 0.988295 + 1.71178i 0.626264 + 0.779611i \(0.284583\pi\)
0.362031 + 0.932166i \(0.382083\pi\)
\(140\) −8.16490 14.1420i −0.690060 1.19522i
\(141\) 0 0
\(142\) 1.18479 2.05212i 0.0994256 0.172210i
\(143\) −10.2759 −0.859310
\(144\) 0 0
\(145\) −12.9290 −1.07370
\(146\) 4.60894 7.98293i 0.381439 0.660672i
\(147\) 0 0
\(148\) −2.26604 3.92490i −0.186268 0.322625i
\(149\) 7.75298 + 13.4285i 0.635149 + 1.10011i 0.986484 + 0.163860i \(0.0523945\pi\)
−0.351335 + 0.936250i \(0.614272\pi\)
\(150\) 0 0
\(151\) 2.95084 5.11100i 0.240136 0.415927i −0.720617 0.693333i \(-0.756141\pi\)
0.960753 + 0.277406i \(0.0894747\pi\)
\(152\) 1.47924 0.119982
\(153\) 0 0
\(154\) −10.0719 −0.811618
\(155\) −7.96859 + 13.8020i −0.640053 + 1.10860i
\(156\) 0 0
\(157\) 0.606067 + 1.04974i 0.0483694 + 0.0837783i 0.889196 0.457526i \(-0.151264\pi\)
−0.840827 + 0.541304i \(0.817931\pi\)
\(158\) 12.6062 + 21.8346i 1.00289 + 1.73706i
\(159\) 0 0
\(160\) −14.5287 + 25.1644i −1.14859 + 1.98942i
\(161\) 1.21832 0.0960168
\(162\) 0 0
\(163\) 2.77332 0.217223 0.108612 0.994084i \(-0.465360\pi\)
0.108612 + 0.994084i \(0.465360\pi\)
\(164\) 2.34791 4.06670i 0.183341 0.317556i
\(165\) 0 0
\(166\) −11.1322 19.2816i −0.864028 1.49654i
\(167\) −1.91404 3.31521i −0.148113 0.256538i 0.782417 0.622754i \(-0.213986\pi\)
−0.930530 + 0.366216i \(0.880653\pi\)
\(168\) 0 0
\(169\) −4.62449 + 8.00984i −0.355730 + 0.616142i
\(170\) −21.3996 −1.64127
\(171\) 0 0
\(172\) 2.00000 0.152499
\(173\) −3.51471 + 6.08765i −0.267218 + 0.462835i −0.968142 0.250400i \(-0.919438\pi\)
0.700924 + 0.713236i \(0.252771\pi\)
\(174\) 0 0
\(175\) 10.2135 + 17.6903i 0.772066 + 1.33726i
\(176\) 4.60397 + 7.97431i 0.347037 + 0.601086i
\(177\) 0 0
\(178\) 0.688663 1.19280i 0.0516175 0.0894041i
\(179\) 14.3854 1.07521 0.537607 0.843195i \(-0.319328\pi\)
0.537607 + 0.843195i \(0.319328\pi\)
\(180\) 0 0
\(181\) 13.2003 0.981169 0.490584 0.871394i \(-0.336783\pi\)
0.490584 + 0.871394i \(0.336783\pi\)
\(182\) −10.9037 + 18.8858i −0.808237 + 1.39991i
\(183\) 0 0
\(184\) −0.0616516 0.106784i −0.00454501 0.00787219i
\(185\) 4.46324 + 7.73055i 0.328144 + 0.568361i
\(186\) 0 0
\(187\) −3.19712 + 5.53757i −0.233796 + 0.404947i
\(188\) 0.446476 0.0325626
\(189\) 0 0
\(190\) 45.3979 3.29351
\(191\) 6.71167 11.6250i 0.485639 0.841152i −0.514224 0.857656i \(-0.671920\pi\)
0.999864 + 0.0165036i \(0.00525351\pi\)
\(192\) 0 0
\(193\) −7.50253 12.9948i −0.540044 0.935383i −0.998901 0.0468730i \(-0.985074\pi\)
0.458857 0.888510i \(-0.348259\pi\)
\(194\) 6.97881 + 12.0876i 0.501049 + 0.867843i
\(195\) 0 0
\(196\) 1.40033 2.42544i 0.100024 0.173246i
\(197\) 22.3212 1.59032 0.795158 0.606402i \(-0.207388\pi\)
0.795158 + 0.606402i \(0.207388\pi\)
\(198\) 0 0
\(199\) −9.10101 −0.645154 −0.322577 0.946543i \(-0.604549\pi\)
−0.322577 + 0.946543i \(0.604549\pi\)
\(200\) 1.03368 1.79039i 0.0730925 0.126600i
\(201\) 0 0
\(202\) 4.60607 + 7.97794i 0.324082 + 0.561326i
\(203\) 4.09927 + 7.10014i 0.287712 + 0.498332i
\(204\) 0 0
\(205\) −4.62449 + 8.00984i −0.322988 + 0.559432i
\(206\) −26.8333 −1.86956
\(207\) 0 0
\(208\) 19.9368 1.38237
\(209\) 6.78250 11.7476i 0.469155 0.812600i
\(210\) 0 0
\(211\) 2.98886 + 5.17685i 0.205761 + 0.356389i 0.950375 0.311107i \(-0.100700\pi\)
−0.744614 + 0.667496i \(0.767366\pi\)
\(212\) 4.38571 + 7.59627i 0.301212 + 0.521714i
\(213\) 0 0
\(214\) 11.4572 19.8445i 0.783200 1.35654i
\(215\) −3.93923 −0.268653
\(216\) 0 0
\(217\) 10.1061 0.686045
\(218\) −14.3821 + 24.9106i −0.974081 + 1.68716i
\(219\) 0 0
\(220\) 7.57785 + 13.1252i 0.510898 + 0.884902i
\(221\) 6.92231 + 11.9898i 0.465645 + 0.806521i
\(222\) 0 0
\(223\) 4.45084 7.70908i 0.298050 0.516238i −0.677640 0.735394i \(-0.736997\pi\)
0.975690 + 0.219156i \(0.0703304\pi\)
\(224\) 18.4258 1.23113
\(225\) 0 0
\(226\) −9.24897 −0.615232
\(227\) −5.33424 + 9.23917i −0.354046 + 0.613225i −0.986954 0.161001i \(-0.948528\pi\)
0.632908 + 0.774227i \(0.281861\pi\)
\(228\) 0 0
\(229\) 4.13563 + 7.16312i 0.273290 + 0.473352i 0.969702 0.244290i \(-0.0785548\pi\)
−0.696412 + 0.717642i \(0.745221\pi\)
\(230\) −1.89209 3.27719i −0.124760 0.216091i
\(231\) 0 0
\(232\) 0.414878 0.718589i 0.0272381 0.0471777i
\(233\) −12.7393 −0.834579 −0.417290 0.908774i \(-0.637020\pi\)
−0.417290 + 0.908774i \(0.637020\pi\)
\(234\) 0 0
\(235\) −0.879385 −0.0573648
\(236\) −12.5094 + 21.6668i −0.814290 + 1.41039i
\(237\) 0 0
\(238\) 6.78493 + 11.7518i 0.439802 + 0.761759i
\(239\) 7.50779 + 13.0039i 0.485638 + 0.841150i 0.999864 0.0165047i \(-0.00525384\pi\)
−0.514225 + 0.857655i \(0.671921\pi\)
\(240\) 0 0
\(241\) −0.397804 + 0.689016i −0.0256248 + 0.0443834i −0.878553 0.477644i \(-0.841491\pi\)
0.852929 + 0.522028i \(0.174824\pi\)
\(242\) −12.3180 −0.791832
\(243\) 0 0
\(244\) −6.90673 −0.442158
\(245\) −2.75811 + 4.77719i −0.176209 + 0.305203i
\(246\) 0 0
\(247\) −14.6853 25.4356i −0.934401 1.61843i
\(248\) −0.511406 0.885782i −0.0324743 0.0562472i
\(249\) 0 0
\(250\) 13.4966 23.3768i 0.853600 1.47848i
\(251\) −8.31499 −0.524837 −0.262419 0.964954i \(-0.584520\pi\)
−0.262419 + 0.964954i \(0.584520\pi\)
\(252\) 0 0
\(253\) −1.13072 −0.0710877
\(254\) −5.99898 + 10.3905i −0.376409 + 0.651960i
\(255\) 0 0
\(256\) −8.87598 15.3737i −0.554749 0.960853i
\(257\) −12.8101 22.1878i −0.799074 1.38404i −0.920220 0.391401i \(-0.871990\pi\)
0.121146 0.992635i \(-0.461343\pi\)
\(258\) 0 0
\(259\) 2.83022 4.90209i 0.175861 0.304601i
\(260\) 32.8147 2.03508
\(261\) 0 0
\(262\) −20.3824 −1.25923
\(263\) 14.0325 24.3050i 0.865281 1.49871i −0.00148730 0.999999i \(-0.500473\pi\)
0.866768 0.498711i \(-0.166193\pi\)
\(264\) 0 0
\(265\) −8.63816 14.9617i −0.530638 0.919091i
\(266\) −14.3938 24.9308i −0.882542 1.52861i
\(267\) 0 0
\(268\) −13.4363 + 23.2723i −0.820752 + 1.42158i
\(269\) 30.1710 1.83956 0.919778 0.392439i \(-0.128369\pi\)
0.919778 + 0.392439i \(0.128369\pi\)
\(270\) 0 0
\(271\) −19.0000 −1.15417 −0.577084 0.816685i \(-0.695809\pi\)
−0.577084 + 0.816685i \(0.695809\pi\)
\(272\) 6.20291 10.7438i 0.376107 0.651436i
\(273\) 0 0
\(274\) 18.7947 + 32.5534i 1.13543 + 1.96662i
\(275\) −9.47913 16.4183i −0.571613 0.990063i
\(276\) 0 0
\(277\) −10.5608 + 18.2918i −0.634535 + 1.09905i 0.352078 + 0.935971i \(0.385475\pi\)
−0.986613 + 0.163077i \(0.947858\pi\)
\(278\) −45.8992 −2.75285
\(279\) 0 0
\(280\) −2.06418 −0.123358
\(281\) −0.873649 + 1.51320i −0.0521175 + 0.0902702i −0.890907 0.454185i \(-0.849930\pi\)
0.838790 + 0.544456i \(0.183264\pi\)
\(282\) 0 0
\(283\) 3.64409 + 6.31174i 0.216618 + 0.375194i 0.953772 0.300531i \(-0.0971639\pi\)
−0.737154 + 0.675725i \(0.763831\pi\)
\(284\) 1.13052 + 1.95811i 0.0670838 + 0.116193i
\(285\) 0 0
\(286\) 10.1197 17.5279i 0.598393 1.03645i
\(287\) 5.86495 0.346197
\(288\) 0 0
\(289\) −8.38507 −0.493239
\(290\) 12.7326 22.0535i 0.747684 1.29503i
\(291\) 0 0
\(292\) 4.39780 + 7.61722i 0.257362 + 0.445764i
\(293\) −7.67545 13.2943i −0.448404 0.776659i 0.549878 0.835245i \(-0.314674\pi\)
−0.998282 + 0.0585858i \(0.981341\pi\)
\(294\) 0 0
\(295\) 24.6386 42.6753i 1.43452 2.48465i
\(296\) −0.572881 −0.0332980
\(297\) 0 0
\(298\) −30.5408 −1.76918
\(299\) −1.22410 + 2.12020i −0.0707916 + 0.122615i
\(300\) 0 0
\(301\) 1.24897 + 2.16328i 0.0719895 + 0.124689i
\(302\) 5.81201 + 10.0667i 0.334444 + 0.579274i
\(303\) 0 0
\(304\) −13.1591 + 22.7922i −0.754726 + 1.30722i
\(305\) 13.6036 0.778940
\(306\) 0 0
\(307\) 16.7638 0.956762 0.478381 0.878152i \(-0.341224\pi\)
0.478381 + 0.878152i \(0.341224\pi\)
\(308\) 4.80526 8.32295i 0.273805 0.474244i
\(309\) 0 0
\(310\) −15.6951 27.1846i −0.891419 1.54398i
\(311\) 8.01157 + 13.8764i 0.454295 + 0.786861i 0.998647 0.0519952i \(-0.0165580\pi\)
−0.544353 + 0.838856i \(0.683225\pi\)
\(312\) 0 0
\(313\) −17.2028 + 29.7961i −0.972360 + 1.68418i −0.283974 + 0.958832i \(0.591653\pi\)
−0.688386 + 0.725344i \(0.741681\pi\)
\(314\) −2.38744 −0.134731
\(315\) 0 0
\(316\) −24.0574 −1.35333
\(317\) 8.15555 14.1258i 0.458061 0.793386i −0.540797 0.841153i \(-0.681877\pi\)
0.998858 + 0.0477675i \(0.0152106\pi\)
\(318\) 0 0
\(319\) −3.80453 6.58964i −0.213013 0.368949i
\(320\) −12.9702 22.4650i −0.725054 1.25583i
\(321\) 0 0
\(322\) −1.19981 + 2.07813i −0.0668626 + 0.115809i
\(323\) −18.2761 −1.01691
\(324\) 0 0
\(325\) −41.0479 −2.27693
\(326\) −2.73119 + 4.73055i −0.151266 + 0.262001i
\(327\) 0 0
\(328\) −0.296789 0.514054i −0.0163874 0.0283839i
\(329\) 0.278817 + 0.482926i 0.0153717 + 0.0266246i
\(330\) 0 0
\(331\) 15.7900 27.3491i 0.867896 1.50324i 0.00375320 0.999993i \(-0.498805\pi\)
0.864143 0.503247i \(-0.167861\pi\)
\(332\) 21.2445 1.16594
\(333\) 0 0
\(334\) 7.53983 0.412561
\(335\) 26.4643 45.8376i 1.44590 2.50437i
\(336\) 0 0
\(337\) −3.00253 5.20053i −0.163558 0.283291i 0.772584 0.634912i \(-0.218964\pi\)
−0.936142 + 0.351621i \(0.885630\pi\)
\(338\) −9.10846 15.7763i −0.495435 0.858118i
\(339\) 0 0
\(340\) 10.2096 17.6836i 0.553694 0.959026i
\(341\) −9.37944 −0.507925
\(342\) 0 0
\(343\) 19.9290 1.07607
\(344\) 0.126406 0.218941i 0.00681533 0.0118045i
\(345\) 0 0
\(346\) −6.92262 11.9903i −0.372162 0.644604i
\(347\) −11.5152 19.9449i −0.618168 1.07070i −0.989820 0.142326i \(-0.954542\pi\)
0.371652 0.928372i \(-0.378792\pi\)
\(348\) 0 0
\(349\) 5.78312 10.0167i 0.309563 0.536179i −0.668704 0.743529i \(-0.733150\pi\)
0.978267 + 0.207350i \(0.0664838\pi\)
\(350\) −40.2332 −2.15056
\(351\) 0 0
\(352\) −17.1010 −0.911487
\(353\) 1.06731 1.84864i 0.0568073 0.0983932i −0.836223 0.548389i \(-0.815241\pi\)
0.893031 + 0.449996i \(0.148575\pi\)
\(354\) 0 0
\(355\) −2.22668 3.85673i −0.118180 0.204694i
\(356\) 0.657115 + 1.13816i 0.0348270 + 0.0603221i
\(357\) 0 0
\(358\) −14.1668 + 24.5377i −0.748741 + 1.29686i
\(359\) 24.2235 1.27847 0.639234 0.769012i \(-0.279251\pi\)
0.639234 + 0.769012i \(0.279251\pi\)
\(360\) 0 0
\(361\) 19.7716 1.04061
\(362\) −12.9997 + 22.5162i −0.683251 + 1.18343i
\(363\) 0 0
\(364\) −10.4042 18.0206i −0.545328 0.944536i
\(365\) −8.66198 15.0030i −0.453389 0.785293i
\(366\) 0 0
\(367\) 1.41740 2.45502i 0.0739879 0.128151i −0.826658 0.562705i \(-0.809761\pi\)
0.900646 + 0.434554i \(0.143094\pi\)
\(368\) 2.19377 0.114358
\(369\) 0 0
\(370\) −17.5817 −0.914030
\(371\) −5.47762 + 9.48751i −0.284384 + 0.492567i
\(372\) 0 0
\(373\) 14.4167 + 24.9704i 0.746468 + 1.29292i 0.949506 + 0.313749i \(0.101585\pi\)
−0.203038 + 0.979171i \(0.565081\pi\)
\(374\) −6.29710 10.9069i −0.325615 0.563982i
\(375\) 0 0
\(376\) 0.0282185 0.0488759i 0.00145526 0.00252058i
\(377\) −16.4749 −0.848501
\(378\) 0 0
\(379\) 32.1985 1.65393 0.826963 0.562256i \(-0.190066\pi\)
0.826963 + 0.562256i \(0.190066\pi\)
\(380\) −21.6591 + 37.5146i −1.11109 + 1.92446i
\(381\) 0 0
\(382\) 13.2194 + 22.8967i 0.676364 + 1.17150i
\(383\) −0.336125 0.582186i −0.0171752 0.0297483i 0.857310 0.514800i \(-0.172134\pi\)
−0.874485 + 0.485052i \(0.838801\pi\)
\(384\) 0 0
\(385\) −9.46451 + 16.3930i −0.482356 + 0.835465i
\(386\) 29.5542 1.50427
\(387\) 0 0
\(388\) −13.3182 −0.676129
\(389\) 2.12965 3.68866i 0.107978 0.187023i −0.806973 0.590588i \(-0.798896\pi\)
0.914951 + 0.403565i \(0.132229\pi\)
\(390\) 0 0
\(391\) 0.761707 + 1.31932i 0.0385212 + 0.0667207i
\(392\) −0.177009 0.306589i −0.00894033 0.0154851i
\(393\) 0 0
\(394\) −21.9820 + 38.0740i −1.10744 + 1.91814i
\(395\) 47.3838 2.38414
\(396\) 0 0
\(397\) −8.86484 −0.444913 −0.222457 0.974943i \(-0.571408\pi\)
−0.222457 + 0.974943i \(0.571408\pi\)
\(398\) 8.96275 15.5239i 0.449262 0.778145i
\(399\) 0 0
\(400\) 18.3910 + 31.8541i 0.919550 + 1.59271i
\(401\) −18.5420 32.1156i −0.925941 1.60378i −0.790040 0.613055i \(-0.789940\pi\)
−0.135901 0.990722i \(-0.543393\pi\)
\(402\) 0 0
\(403\) −10.1540 + 17.5873i −0.505809 + 0.876087i
\(404\) −8.79012 −0.437325
\(405\) 0 0
\(406\) −16.1480 −0.801410
\(407\) −2.62673 + 4.54963i −0.130202 + 0.225517i
\(408\) 0 0
\(409\) 1.69459 + 2.93512i 0.0837922 + 0.145132i 0.904876 0.425675i \(-0.139963\pi\)
−0.821084 + 0.570808i \(0.806630\pi\)
\(410\) −9.10846 15.7763i −0.449835 0.779136i
\(411\) 0 0
\(412\) 12.8020 22.1737i 0.630709 1.09242i
\(413\) −31.2476 −1.53760
\(414\) 0 0
\(415\) −41.8435 −2.05402
\(416\) −18.5133 + 32.0660i −0.907690 + 1.57216i
\(417\) 0 0
\(418\) 13.3589 + 23.1383i 0.653406 + 1.13173i
\(419\) 10.3282 + 17.8889i 0.504565 + 0.873932i 0.999986 + 0.00527895i \(0.00168035\pi\)
−0.495421 + 0.868653i \(0.664986\pi\)
\(420\) 0 0
\(421\) −13.7665 + 23.8443i −0.670939 + 1.16210i 0.306700 + 0.951806i \(0.400775\pi\)
−0.977638 + 0.210294i \(0.932558\pi\)
\(422\) −11.7738 −0.573139
\(423\) 0 0
\(424\) 1.10876 0.0538459
\(425\) −12.7712 + 22.1204i −0.619494 + 1.07300i
\(426\) 0 0
\(427\) −4.31315 7.47059i −0.208728 0.361527i
\(428\) 10.9324 + 18.9354i 0.528436 + 0.915278i
\(429\) 0 0
\(430\) 3.87939 6.71929i 0.187081 0.324033i
\(431\) −2.58110 −0.124327 −0.0621636 0.998066i \(-0.519800\pi\)
−0.0621636 + 0.998066i \(0.519800\pi\)
\(432\) 0 0
\(433\) −27.0137 −1.29820 −0.649098 0.760704i \(-0.724854\pi\)
−0.649098 + 0.760704i \(0.724854\pi\)
\(434\) −9.95253 + 17.2383i −0.477737 + 0.827465i
\(435\) 0 0
\(436\) −13.7233 23.7694i −0.657226 1.13835i
\(437\) −1.61592 2.79885i −0.0772997 0.133887i
\(438\) 0 0
\(439\) −5.85504 + 10.1412i −0.279446 + 0.484014i −0.971247 0.238074i \(-0.923484\pi\)
0.691801 + 0.722088i \(0.256817\pi\)
\(440\) 1.91576 0.0913305
\(441\) 0 0
\(442\) −27.2686 −1.29703
\(443\) −1.04039 + 1.80200i −0.0494303 + 0.0856158i −0.889682 0.456581i \(-0.849074\pi\)
0.840252 + 0.542197i \(0.182407\pi\)
\(444\) 0 0
\(445\) −1.29426 2.24173i −0.0613539 0.106268i
\(446\) 8.76644 + 15.1839i 0.415103 + 0.718979i
\(447\) 0 0
\(448\) −8.22462 + 14.2455i −0.388577 + 0.673035i
\(449\) 10.5508 0.497924 0.248962 0.968513i \(-0.419911\pi\)
0.248962 + 0.968513i \(0.419911\pi\)
\(450\) 0 0
\(451\) −5.44326 −0.256313
\(452\) 4.41263 7.64290i 0.207553 0.359492i
\(453\) 0 0
\(454\) −10.5064 18.1976i −0.493090 0.854056i
\(455\) 20.4923 + 35.4937i 0.960693 + 1.66397i
\(456\) 0 0
\(457\) 3.95471 6.84975i 0.184993 0.320418i −0.758581 0.651579i \(-0.774107\pi\)
0.943574 + 0.331161i \(0.107440\pi\)
\(458\) −16.2912 −0.761238
\(459\) 0 0
\(460\) 3.61081 0.168355
\(461\) 19.5464 33.8553i 0.910366 1.57680i 0.0968187 0.995302i \(-0.469133\pi\)
0.813548 0.581498i \(-0.197533\pi\)
\(462\) 0 0
\(463\) −11.8464 20.5186i −0.550550 0.953580i −0.998235 0.0593889i \(-0.981085\pi\)
0.447685 0.894191i \(-0.352249\pi\)
\(464\) 7.38138 + 12.7849i 0.342672 + 0.593525i
\(465\) 0 0
\(466\) 12.5458 21.7299i 0.581171 1.00662i
\(467\) −34.7152 −1.60643 −0.803214 0.595691i \(-0.796878\pi\)
−0.803214 + 0.595691i \(0.796878\pi\)
\(468\) 0 0
\(469\) −33.5631 −1.54980
\(470\) 0.866025 1.50000i 0.0399468 0.0691898i
\(471\) 0 0
\(472\) 1.58125 + 2.73881i 0.0727830 + 0.126064i
\(473\) −1.15917 2.00774i −0.0532987 0.0923160i
\(474\) 0 0
\(475\) 27.0933 46.9270i 1.24313 2.15316i
\(476\) −12.9482 −0.593480
\(477\) 0 0
\(478\) −29.5749 −1.35272
\(479\) 3.24086 5.61334i 0.148079 0.256480i −0.782439 0.622728i \(-0.786024\pi\)
0.930517 + 0.366248i \(0.119358\pi\)
\(480\) 0 0
\(481\) 5.68732 + 9.85073i 0.259319 + 0.449154i
\(482\) −0.783520 1.35710i −0.0356884 0.0618141i
\(483\) 0 0
\(484\) 5.87686 10.1790i 0.267130 0.462683i
\(485\) 26.2317 1.19112
\(486\) 0 0
\(487\) 19.9828 0.905505 0.452753 0.891636i \(-0.350442\pi\)
0.452753 + 0.891636i \(0.350442\pi\)
\(488\) −0.436524 + 0.756082i −0.0197605 + 0.0342262i
\(489\) 0 0
\(490\) −5.43242 9.40923i −0.245412 0.425065i
\(491\) 13.1135 + 22.7133i 0.591806 + 1.02504i 0.993989 + 0.109478i \(0.0349181\pi\)
−0.402183 + 0.915559i \(0.631749\pi\)
\(492\) 0 0
\(493\) −5.12583 + 8.87820i −0.230856 + 0.399854i
\(494\) 57.8486 2.60273
\(495\) 0 0
\(496\) 18.1976 0.817096
\(497\) −1.41198 + 2.44562i −0.0633360 + 0.109701i
\(498\) 0 0
\(499\) −3.15863 5.47091i −0.141400 0.244912i 0.786624 0.617432i \(-0.211827\pi\)
−0.928024 + 0.372520i \(0.878494\pi\)
\(500\) 12.8783 + 22.3059i 0.575935 + 0.997549i
\(501\) 0 0
\(502\) 8.18866 14.1832i 0.365478 0.633026i
\(503\) −21.8261 −0.973179 −0.486589 0.873631i \(-0.661759\pi\)
−0.486589 + 0.873631i \(0.661759\pi\)
\(504\) 0 0
\(505\) 17.3131 0.770425
\(506\) 1.11354 1.92871i 0.0495030 0.0857416i
\(507\) 0 0
\(508\) −5.72416 9.91453i −0.253968 0.439886i
\(509\) −14.5466 25.1954i −0.644765 1.11676i −0.984356 0.176192i \(-0.943622\pi\)
0.339591 0.940573i \(-0.389711\pi\)
\(510\) 0 0
\(511\) −5.49273 + 9.51368i −0.242984 + 0.420860i
\(512\) 31.1704 1.37755
\(513\) 0 0
\(514\) 50.4620 2.22579
\(515\) −25.2150 + 43.6737i −1.11111 + 1.92449i
\(516\) 0 0
\(517\) −0.258770 0.448204i −0.0113807 0.0197120i
\(518\) 5.57445 + 9.65523i 0.244927 + 0.424226i
\(519\) 0 0
\(520\) 2.07398 3.59224i 0.0909499 0.157530i
\(521\) −13.6949 −0.599982 −0.299991 0.953942i \(-0.596984\pi\)
−0.299991 + 0.953942i \(0.596984\pi\)
\(522\) 0 0
\(523\) 13.1506 0.575038 0.287519 0.957775i \(-0.407170\pi\)
0.287519 + 0.957775i \(0.407170\pi\)
\(524\) 9.72432 16.8430i 0.424809 0.735791i
\(525\) 0 0
\(526\) 27.6386 + 47.8715i 1.20510 + 2.08730i
\(527\) 6.31844 + 10.9439i 0.275236 + 0.476722i
\(528\) 0 0
\(529\) 11.3653 19.6853i 0.494144 0.855882i
\(530\) 34.0277 1.47807
\(531\) 0 0
\(532\) 27.4688 1.19093
\(533\) −5.89279 + 10.2066i −0.255245 + 0.442098i
\(534\) 0 0
\(535\) −21.5326 37.2955i −0.930934 1.61242i
\(536\) 1.69842 + 2.94175i 0.0733606 + 0.127064i
\(537\) 0 0
\(538\) −29.7126 + 51.4637i −1.28100 + 2.21876i
\(539\) −3.24644 −0.139834
\(540\) 0 0
\(541\) 6.26083 0.269174 0.134587 0.990902i \(-0.457029\pi\)
0.134587 + 0.990902i \(0.457029\pi\)
\(542\) 18.7113 32.4090i 0.803721 1.39209i
\(543\) 0 0
\(544\) 11.5201 + 19.9533i 0.493919 + 0.855492i
\(545\) 27.0296 + 46.8166i 1.15782 + 2.00540i
\(546\) 0 0
\(547\) 15.6891 27.1744i 0.670819 1.16189i −0.306854 0.951757i \(-0.599276\pi\)
0.977672 0.210135i \(-0.0673905\pi\)
\(548\) −35.8674 −1.53218
\(549\) 0 0
\(550\) 37.3405 1.59220
\(551\) 10.8741 18.8346i 0.463254 0.802379i
\(552\) 0 0
\(553\) −15.0235 26.0214i −0.638863 1.10654i
\(554\) −20.8007 36.0278i −0.883736 1.53067i
\(555\) 0 0
\(556\) 21.8983 37.9289i 0.928694 1.60854i
\(557\) −43.4392 −1.84058 −0.920290 0.391237i \(-0.872047\pi\)
−0.920290 + 0.391237i \(0.872047\pi\)
\(558\) 0 0
\(559\) −5.01960 −0.212306
\(560\) 18.3626 31.8050i 0.775962 1.34401i
\(561\) 0 0
\(562\) −1.72075 2.98043i −0.0725855 0.125722i
\(563\) 16.0088 + 27.7281i 0.674691 + 1.16860i 0.976559 + 0.215250i \(0.0690565\pi\)
−0.301868 + 0.953350i \(0.597610\pi\)
\(564\) 0 0
\(565\) −8.69119 + 15.0536i −0.365641 + 0.633309i
\(566\) −14.3549 −0.603381
\(567\) 0 0
\(568\) 0.285807 0.0119922
\(569\) 3.38597 5.86468i 0.141947 0.245860i −0.786283 0.617867i \(-0.787997\pi\)
0.928230 + 0.372007i \(0.121330\pi\)
\(570\) 0 0
\(571\) 10.5765 + 18.3190i 0.442613 + 0.766628i 0.997883 0.0650424i \(-0.0207182\pi\)
−0.555270 + 0.831670i \(0.687385\pi\)
\(572\) 9.65614 + 16.7249i 0.403744 + 0.699304i
\(573\) 0 0
\(574\) −5.77584 + 10.0041i −0.241079 + 0.417561i
\(575\) −4.51677 −0.188362
\(576\) 0 0
\(577\) 11.9162 0.496079 0.248039 0.968750i \(-0.420214\pi\)
0.248039 + 0.968750i \(0.420214\pi\)
\(578\) 8.25768 14.3027i 0.343474 0.594915i
\(579\) 0 0
\(580\) 12.1493 + 21.0432i 0.504472 + 0.873772i
\(581\) 13.2669 + 22.9789i 0.550403 + 0.953325i
\(582\) 0 0
\(583\) 5.08378 8.80536i 0.210549 0.364681i
\(584\) 1.11181 0.0460072
\(585\) 0 0
\(586\) 30.2354 1.24901
\(587\) 0.0649308 0.112463i 0.00267998 0.00464186i −0.864682 0.502319i \(-0.832480\pi\)
0.867362 + 0.497677i \(0.165814\pi\)
\(588\) 0 0
\(589\) −13.4042 23.2168i −0.552310 0.956630i
\(590\) 48.5286 + 84.0540i 1.99789 + 3.46045i
\(591\) 0 0
\(592\) 5.09627 8.82699i 0.209455 0.362787i
\(593\) 26.2622 1.07846 0.539230 0.842158i \(-0.318715\pi\)
0.539230 + 0.842158i \(0.318715\pi\)
\(594\) 0 0
\(595\) 25.5030 1.04552
\(596\) 14.5708 25.2374i 0.596844 1.03376i
\(597\) 0 0
\(598\) −2.41101 4.17599i −0.0985934 0.170769i
\(599\) −13.7976 23.8981i −0.563754 0.976450i −0.997164 0.0752537i \(-0.976023\pi\)
0.433411 0.901197i \(-0.357310\pi\)
\(600\) 0 0
\(601\) −0.666374 + 1.15419i −0.0271820 + 0.0470806i −0.879296 0.476275i \(-0.841987\pi\)
0.852114 + 0.523356i \(0.175320\pi\)
\(602\) −4.91998 −0.200524
\(603\) 0 0
\(604\) −11.0915 −0.451308
\(605\) −11.5752 + 20.0488i −0.470597 + 0.815098i
\(606\) 0 0
\(607\) 6.28224 + 10.8812i 0.254988 + 0.441653i 0.964892 0.262646i \(-0.0845950\pi\)
−0.709904 + 0.704298i \(0.751262\pi\)
\(608\) −24.4391 42.3298i −0.991138 1.71670i
\(609\) 0 0
\(610\) −13.3969 + 23.2042i −0.542426 + 0.939509i
\(611\) −1.12056 −0.0453332
\(612\) 0 0
\(613\) −13.9982 −0.565384 −0.282692 0.959211i \(-0.591227\pi\)
−0.282692 + 0.959211i \(0.591227\pi\)
\(614\) −16.5091 + 28.5947i −0.666255 + 1.15399i
\(615\) 0 0
\(616\) −0.607411 1.05207i −0.0244733 0.0423890i
\(617\) −12.0234 20.8251i −0.484042 0.838386i 0.515790 0.856715i \(-0.327499\pi\)
−0.999832 + 0.0183296i \(0.994165\pi\)
\(618\) 0 0
\(619\) −3.43582 + 5.95102i −0.138097 + 0.239192i −0.926776 0.375614i \(-0.877432\pi\)
0.788679 + 0.614805i \(0.210765\pi\)
\(620\) 29.9521 1.20291
\(621\) 0 0
\(622\) −31.5594 −1.26542
\(623\) −0.820717 + 1.42152i −0.0328813 + 0.0569521i
\(624\) 0 0
\(625\) −3.60947 6.25179i −0.144379 0.250071i
\(626\) −33.8829 58.6869i −1.35423 2.34560i
\(627\) 0 0
\(628\) 1.13903 1.97286i 0.0454524 0.0787258i
\(629\) 7.07797 0.282217
\(630\) 0 0
\(631\) −35.3773 −1.40835 −0.704175 0.710027i \(-0.748683\pi\)
−0.704175 + 0.710027i \(0.748683\pi\)
\(632\) −1.52049 + 2.63357i −0.0604819 + 0.104758i
\(633\) 0 0
\(634\) 16.0633 + 27.8225i 0.637955 + 1.10497i
\(635\) 11.2744 + 19.5278i 0.447410 + 0.774937i
\(636\) 0 0
\(637\) −3.51455 + 6.08738i −0.139251 + 0.241191i
\(638\) 14.9869 0.593338
\(639\) 0 0
\(640\) −7.02229 −0.277580
\(641\) 9.58683 16.6049i 0.378657 0.655854i −0.612210 0.790695i \(-0.709719\pi\)
0.990867 + 0.134842i \(0.0430526\pi\)
\(642\) 0 0
\(643\) −9.68820 16.7804i −0.382065 0.661756i 0.609292 0.792946i \(-0.291454\pi\)
−0.991357 + 0.131190i \(0.958120\pi\)
\(644\) −1.14484 1.98293i −0.0451131 0.0781382i
\(645\) 0 0
\(646\) 17.9984 31.1742i 0.708138 1.22653i
\(647\) 8.77141 0.344840 0.172420 0.985024i \(-0.444841\pi\)
0.172420 + 0.985024i \(0.444841\pi\)
\(648\) 0 0
\(649\) 29.0009 1.13839
\(650\) 40.4243 70.0169i 1.58557 2.74629i
\(651\) 0 0
\(652\) −2.60607 4.51384i −0.102061 0.176776i
\(653\) −16.4047 28.4138i −0.641965 1.11192i −0.984994 0.172591i \(-0.944786\pi\)
0.343029 0.939325i \(-0.388547\pi\)
\(654\) 0 0
\(655\) −19.1532 + 33.1743i −0.748376 + 1.29623i
\(656\) 10.5608 0.412329
\(657\) 0 0
\(658\) −1.09833 −0.0428172
\(659\) −9.32580 + 16.1528i −0.363282 + 0.629222i −0.988499 0.151229i \(-0.951677\pi\)
0.625217 + 0.780451i \(0.285010\pi\)
\(660\) 0 0
\(661\) −18.2037 31.5297i −0.708041 1.22636i −0.965583 0.260096i \(-0.916246\pi\)
0.257542 0.966267i \(-0.417087\pi\)
\(662\) 31.1002 + 53.8671i 1.20874 + 2.09360i
\(663\) 0 0
\(664\) 1.34271 2.32564i 0.0521073 0.0902525i
\(665\) −54.1031 −2.09803
\(666\) 0 0
\(667\) −1.81284 −0.0701936
\(668\) −3.59721 + 6.23055i −0.139180 + 0.241067i
\(669\) 0 0
\(670\) 52.1245 + 90.2824i 2.01375 + 3.48791i
\(671\) 4.00303 + 6.93346i 0.154535 + 0.267663i
\(672\) 0 0
\(673\) −19.6951 + 34.1128i −0.759189 + 1.31495i 0.184076 + 0.982912i \(0.441071\pi\)
−0.943265 + 0.332041i \(0.892263\pi\)
\(674\) 11.8276 0.455584
\(675\) 0 0
\(676\) 17.3824 0.668553
\(677\) −15.8377 + 27.4317i −0.608692 + 1.05429i 0.382764 + 0.923846i \(0.374972\pi\)
−0.991456 + 0.130440i \(0.958361\pi\)
\(678\) 0 0
\(679\) −8.31702 14.4055i −0.319178 0.552832i
\(680\) −1.29055 2.23530i −0.0494904 0.0857198i
\(681\) 0 0
\(682\) 9.23695 15.9989i 0.353701 0.612628i
\(683\) −29.0656 −1.11217 −0.556083 0.831127i \(-0.687696\pi\)
−0.556083 + 0.831127i \(0.687696\pi\)
\(684\) 0 0
\(685\) 70.6451 2.69921
\(686\) −19.6262 + 33.9937i −0.749334 + 1.29788i
\(687\) 0 0
\(688\) 2.24897 + 3.89533i 0.0857412 + 0.148508i
\(689\) −11.0072 19.0651i −0.419343 0.726323i
\(690\) 0 0
\(691\) −2.67870 + 4.63965i −0.101903 + 0.176500i −0.912468 0.409147i \(-0.865826\pi\)
0.810566 + 0.585647i \(0.199160\pi\)
\(692\) 13.2110 0.502206
\(693\) 0 0
\(694\) 45.3610 1.72188
\(695\) −43.1312 + 74.7054i −1.63606 + 2.83374i
\(696\) 0 0
\(697\) 3.66684 + 6.35115i 0.138892 + 0.240567i
\(698\) 11.3905 + 19.7290i 0.431138 + 0.746752i
\(699\) 0 0
\(700\) 19.1951 33.2468i 0.725505 1.25661i
\(701\) −25.6536 −0.968922 −0.484461 0.874813i \(-0.660984\pi\)
−0.484461 + 0.874813i \(0.660984\pi\)
\(702\) 0 0
\(703\) −15.0155 −0.566320
\(704\) 7.63327 13.2212i 0.287690 0.498293i
\(705\) 0 0
\(706\) 2.10220 + 3.64111i 0.0791172 + 0.137035i
\(707\) −5.48930 9.50774i −0.206446 0.357575i
\(708\) 0 0
\(709\) 2.34524 4.06207i 0.0880772 0.152554i −0.818621 0.574334i \(-0.805261\pi\)
0.906698 + 0.421780i \(0.138594\pi\)
\(710\) 8.77141 0.329185
\(711\) 0 0
\(712\) 0.166126 0.00622583
\(713\) −1.11732 + 1.93525i −0.0418438 + 0.0724757i
\(714\) 0 0
\(715\) −19.0189 32.9417i −0.711266 1.23195i
\(716\) −13.5178 23.4136i −0.505185 0.875007i
\(717\) 0 0
\(718\) −23.8555 + 41.3189i −0.890280 + 1.54201i
\(719\) 39.0669 1.45695 0.728476 0.685072i \(-0.240229\pi\)
0.728476 + 0.685072i \(0.240229\pi\)
\(720\) 0 0
\(721\) 31.9786 1.19095
\(722\) −19.4712 + 33.7251i −0.724643 + 1.25512i
\(723\) 0 0
\(724\) −12.4042 21.4847i −0.460998 0.798473i
\(725\) −15.1976 26.3229i −0.564423 0.977610i
\(726\) 0 0
\(727\) 5.41266 9.37500i 0.200744 0.347699i −0.748024 0.663672i \(-0.768997\pi\)
0.948768 + 0.315972i \(0.102331\pi\)
\(728\) −2.63030 −0.0974853
\(729\) 0 0
\(730\) 34.1215 1.26290
\(731\) −1.56175 + 2.70502i −0.0577632 + 0.100049i
\(732\) 0 0
\(733\) 1.70620 + 2.95523i 0.0630201 + 0.109154i 0.895814 0.444429i \(-0.146593\pi\)
−0.832794 + 0.553583i \(0.813260\pi\)
\(734\) 2.79174 + 4.83544i 0.103045 + 0.178479i
\(735\) 0 0
\(736\) −2.03714 + 3.52843i −0.0750900 + 0.130060i
\(737\) 31.1499 1.14742
\(738\) 0 0
\(739\) 26.3010 0.967497 0.483748 0.875207i \(-0.339275\pi\)
0.483748 + 0.875207i \(0.339275\pi\)
\(740\) 8.38814 14.5287i 0.308354 0.534085i
\(741\) 0 0
\(742\) −10.7888 18.6867i −0.396069 0.686012i
\(743\) −14.4719 25.0662i −0.530924 0.919588i −0.999349 0.0360843i \(-0.988512\pi\)
0.468424 0.883504i \(-0.344822\pi\)
\(744\) 0 0
\(745\) −28.6989 + 49.7080i −1.05145 + 1.82116i
\(746\) −56.7907 −2.07925
\(747\) 0 0
\(748\) 12.0172 0.439394
\(749\) −13.6542 + 23.6498i −0.498914 + 0.864144i
\(750\) 0 0
\(751\) 9.72416 + 16.8427i 0.354839 + 0.614600i 0.987090 0.160164i \(-0.0512022\pi\)
−0.632251 + 0.774764i \(0.717869\pi\)
\(752\) 0.502055 + 0.869585i 0.0183081 + 0.0317105i
\(753\) 0 0
\(754\) 16.2246 28.1019i 0.590866 1.02341i
\(755\) 21.8460 0.795058
\(756\) 0 0
\(757\) 6.59627 0.239745 0.119873 0.992789i \(-0.461751\pi\)
0.119873 + 0.992789i \(0.461751\pi\)
\(758\) −31.7094 + 54.9222i −1.15174 + 1.99486i
\(759\) 0 0
\(760\) 2.73783 + 4.74205i 0.0993114 + 0.172012i
\(761\) −5.16485 8.94578i −0.187226 0.324284i 0.757099 0.653301i \(-0.226616\pi\)
−0.944324 + 0.329016i \(0.893283\pi\)
\(762\) 0 0
\(763\) 17.1400 29.6873i 0.620508 1.07475i
\(764\) −25.2276 −0.912703
\(765\) 0 0
\(766\) 1.32407 0.0478407
\(767\) 31.3960 54.3794i 1.13364 1.96353i
\(768\) 0 0
\(769\) −22.4295 38.8490i −0.808828 1.40093i −0.913676 0.406443i \(-0.866769\pi\)
0.104848 0.994488i \(-0.466564\pi\)
\(770\) −18.6414 32.2879i −0.671791 1.16358i
\(771\) 0 0
\(772\) −14.1001 + 24.4222i −0.507475 + 0.878973i
\(773\) 42.9355 1.54428 0.772141 0.635452i \(-0.219186\pi\)
0.772141 + 0.635452i \(0.219186\pi\)
\(774\) 0 0
\(775\) −37.4671 −1.34586
\(776\) −0.841747 + 1.45795i −0.0302170 + 0.0523373i
\(777\) 0 0
\(778\) 4.19459 + 7.26525i 0.150383 + 0.260472i
\(779\) −7.77898 13.4736i −0.278711 0.482742i
\(780\) 0 0
\(781\) 1.31046 2.26978i 0.0468919 0.0812192i
\(782\) −3.00054 −0.107299
\(783\) 0 0
\(784\) 6.29860 0.224950
\(785\) −2.24346 + 3.88578i −0.0800724 + 0.138690i
\(786\) 0 0
\(787\) −0.238703 0.413446i −0.00850885 0.0147378i 0.861740 0.507351i \(-0.169375\pi\)
−0.870248 + 0.492613i \(0.836042\pi\)
\(788\) −20.9750 36.3298i −0.747204 1.29420i
\(789\) 0 0
\(790\) −46.6639 + 80.8243i −1.66023 + 2.87560i
\(791\) 11.0225 0.391915
\(792\) 0 0
\(793\) 17.3345 0.615566
\(794\) 8.73016 15.1211i 0.309822 0.536627i
\(795\) 0 0
\(796\) 8.55216 + 14.8128i 0.303123 + 0.525025i
\(797\) −5.73448 9.93242i −0.203126 0.351824i 0.746408 0.665488i \(-0.231777\pi\)
−0.949534 + 0.313664i \(0.898443\pi\)
\(798\) 0 0
\(799\) −0.348641 + 0.603863i −0.0123340 + 0.0213631i
\(800\) −68.3116 −2.41518
\(801\) 0 0
\(802\) 73.0411 2.57917
\(803\) 5.09780 8.82965i 0.179897 0.311592i
\(804\) 0 0
\(805\) 2.25490 + 3.90560i 0.0794748 + 0.137654i
\(806\) −19.9996 34.6403i −0.704455 1.22015i
\(807\) 0 0
\(808\) −0.555560 + 0.962258i −0.0195445 + 0.0338521i
\(809\) 42.7873 1.50432 0.752161 0.658979i \(-0.229012\pi\)
0.752161 + 0.658979i \(0.229012\pi\)
\(810\) 0 0
\(811\) −31.2098 −1.09592 −0.547962 0.836503i \(-0.684596\pi\)
−0.547962 + 0.836503i \(0.684596\pi\)
\(812\) 7.70410 13.3439i 0.270361 0.468279i
\(813\) 0 0
\(814\) −5.17365 8.96102i −0.181336 0.314084i
\(815\) 5.13295 + 8.89053i 0.179799 + 0.311422i
\(816\) 0 0
\(817\) 3.31315 5.73854i 0.115912 0.200766i
\(818\) −6.67539 −0.233400
\(819\) 0 0
\(820\) 17.3824 0.607019
\(821\) −13.6255 + 23.6001i −0.475535 + 0.823650i −0.999607 0.0280232i \(-0.991079\pi\)
0.524072 + 0.851674i \(0.324412\pi\)
\(822\) 0 0
\(823\) 7.22028 + 12.5059i 0.251683 + 0.435928i 0.963989 0.265941i \(-0.0856825\pi\)
−0.712306 + 0.701869i \(0.752349\pi\)
\(824\) −1.61824 2.80288i −0.0563742 0.0976430i
\(825\) 0 0
\(826\) 30.7729 53.3002i 1.07073 1.85455i
\(827\) 7.02757 0.244373 0.122186 0.992507i \(-0.461009\pi\)
0.122186 + 0.992507i \(0.461009\pi\)
\(828\) 0 0
\(829\) −42.0806 −1.46152 −0.730760 0.682635i \(-0.760834\pi\)
−0.730760 + 0.682635i \(0.760834\pi\)
\(830\) 41.2078 71.3740i 1.43034 2.47743i
\(831\) 0 0
\(832\) −16.5273 28.6262i −0.572982 0.992435i
\(833\) 2.18696 + 3.78792i 0.0757736 + 0.131244i
\(834\) 0 0
\(835\) 7.08512 12.2718i 0.245191 0.424683i
\(836\) −25.4938 −0.881723
\(837\) 0 0
\(838\) −40.6851 −1.40544
\(839\) 19.9606 34.5729i 0.689118 1.19359i −0.283006 0.959118i \(-0.591331\pi\)
0.972124 0.234469i \(-0.0753352\pi\)
\(840\) 0 0
\(841\) 8.40033 + 14.5498i 0.289667 + 0.501717i
\(842\) −27.1147 46.9641i −0.934435 1.61849i
\(843\) 0 0
\(844\) 5.61721 9.72930i 0.193352 0.334896i
\(845\) −34.2366 −1.17777
\(846\) 0 0
\(847\) 14.6800 0.504412
\(848\) −9.86332 + 17.0838i −0.338708 + 0.586659i
\(849\) 0 0
\(850\) −25.1544 43.5686i −0.862787 1.49439i
\(851\) 0.625813 + 1.08394i 0.0214526 + 0.0371570i
\(852\) 0 0
\(853\) 11.7405 20.3352i 0.401988 0.696263i −0.591978 0.805954i \(-0.701653\pi\)
0.993966 + 0.109691i \(0.0349862\pi\)
\(854\) 16.9905 0.581402
\(855\) 0 0
\(856\) 2.76382 0.0944655
\(857\) 4.01736 6.95827i 0.137230 0.237690i −0.789217 0.614115i \(-0.789513\pi\)
0.926447 + 0.376425i \(0.122847\pi\)
\(858\) 0 0
\(859\) 12.1480 + 21.0409i 0.414483 + 0.717905i 0.995374 0.0960758i \(-0.0306291\pi\)
−0.580891 + 0.813981i \(0.697296\pi\)
\(860\) 3.70167 + 6.41147i 0.126226 + 0.218629i
\(861\) 0 0
\(862\) 2.54189 4.40268i 0.0865771 0.149956i
\(863\) 10.2828 0.350029 0.175015 0.984566i \(-0.444003\pi\)
0.175015 + 0.984566i \(0.444003\pi\)
\(864\) 0 0
\(865\) −26.0205 −0.884725
\(866\) 26.6033 46.0783i 0.904018 1.56580i
\(867\) 0 0
\(868\) −9.49660 16.4486i −0.322335 0.558301i
\(869\) 13.9433 + 24.1505i 0.472994 + 0.819249i
\(870\) 0 0
\(871\) 33.7224 58.4089i 1.14264 1.97911i
\(872\) −3.46940 −0.117489
\(873\) 0 0
\(874\) 6.36547 0.215315
\(875\) −16.0846 + 27.8594i −0.543759 + 0.941819i
\(876\) 0 0
\(877\) 13.1138 + 22.7138i 0.442822 + 0.766990i 0.997898 0.0648099i \(-0.0206441\pi\)
−0.555076 + 0.831800i \(0.687311\pi\)
\(878\) −11.5322 19.9743i −0.389192 0.674100i
\(879\) 0 0
\(880\) −17.0424 + 29.5182i −0.574498 + 0.995059i
\(881\) 39.2326 1.32178 0.660890 0.750483i \(-0.270179\pi\)
0.660890 + 0.750483i \(0.270179\pi\)
\(882\) 0 0
\(883\) 7.79830 0.262434 0.131217 0.991354i \(-0.458112\pi\)
0.131217 + 0.991354i \(0.458112\pi\)
\(884\) 13.0097 22.5334i 0.437563 0.757881i
\(885\) 0 0
\(886\) −2.04916 3.54925i −0.0688430 0.119240i
\(887\) −11.4285 19.7948i −0.383732 0.664644i 0.607860 0.794044i \(-0.292028\pi\)
−0.991592 + 0.129400i \(0.958695\pi\)
\(888\) 0 0
\(889\) 7.14930 12.3830i 0.239780 0.415311i
\(890\) 5.09840 0.170899
\(891\) 0 0
\(892\) −16.7297 −0.560151
\(893\) 0.739620 1.28106i 0.0247504 0.0428690i
\(894\) 0 0
\(895\) 26.6250 + 46.1158i 0.889974 + 1.54148i
\(896\) 2.22648 + 3.85638i 0.0743816 + 0.128833i
\(897\) 0 0
\(898\) −10.3905 + 17.9969i −0.346736 + 0.600565i
\(899\) −15.0377 −0.501537
\(900\) 0 0
\(901\) −13.6987 −0.456370
\(902\) 5.36056 9.28477i 0.178487 0.309149i
\(903\) 0 0
\(904\) −0.557781 0.966105i −0.0185515 0.0321322i
\(905\) 24.4315 + 42.3166i 0.812131 + 1.40665i
\(906\) 0 0
\(907\) 18.9243 32.7778i 0.628370 1.08837i −0.359509 0.933142i \(-0.617056\pi\)
0.987879 0.155227i \(-0.0496109\pi\)
\(908\) 20.0502 0.665388
\(909\) 0 0
\(910\) −80.7238 −2.67597
\(911\) −26.3522 + 45.6434i −0.873089 + 1.51223i −0.0143040 + 0.999898i \(0.504553\pi\)
−0.858785 + 0.512336i \(0.828780\pi\)
\(912\) 0 0
\(913\) −12.3130 21.3267i −0.407500 0.705811i
\(914\) 7.78925 + 13.4914i 0.257646 + 0.446255i
\(915\) 0 0
\(916\) 7.77244 13.4623i 0.256809 0.444806i
\(917\) 24.2908 0.802152
\(918\) 0 0
\(919\) −49.1052 −1.61983 −0.809916 0.586545i \(-0.800488\pi\)
−0.809916 + 0.586545i \(0.800488\pi\)
\(920\) 0.228213 0.395277i 0.00752398 0.0130319i
\(921\) 0 0
\(922\) 38.4989 + 66.6820i 1.26789 + 2.19605i
\(923\) −2.83737 4.91447i −0.0933931 0.161762i
\(924\) 0 0
\(925\) −10.4927 + 18.1739i −0.344999 + 0.597555i
\(926\) 46.6658 1.53353
\(927\) 0 0
\(928\) −27.4175 −0.900022
\(929\) −8.97535 + 15.5458i −0.294472 + 0.510040i −0.974862 0.222810i \(-0.928477\pi\)
0.680390 + 0.732850i \(0.261810\pi\)
\(930\) 0 0
\(931\) −4.63950 8.03585i −0.152053 0.263364i
\(932\) 11.9710 + 20.7344i 0.392124 + 0.679179i
\(933\) 0 0
\(934\) 34.1878 59.2150i 1.11866 1.93757i
\(935\) −23.6693 −0.774070
\(936\) 0 0
\(937\) −29.7980 −0.973457 −0.486729 0.873553i \(-0.661810\pi\)
−0.486729 + 0.873553i \(0.661810\pi\)
\(938\) 33.0532 57.2497i 1.07922 1.86927i
\(939\) 0 0
\(940\) 0.826352 + 1.43128i 0.0269526 + 0.0466833i
\(941\) 15.0056 + 25.9905i 0.489169 + 0.847266i 0.999922 0.0124613i \(-0.00396665\pi\)
−0.510753 + 0.859728i \(0.670633\pi\)
\(942\) 0 0
\(943\) −0.648423 + 1.12310i −0.0211155 + 0.0365732i
\(944\) −56.2663 −1.83131
\(945\) 0 0
\(946\) 4.56624 0.148461
\(947\) −22.8007 + 39.4919i −0.740922 + 1.28331i 0.211154 + 0.977453i \(0.432278\pi\)
−0.952076 + 0.305862i \(0.901055\pi\)
\(948\) 0 0
\(949\) −11.0376 19.1177i −0.358296 0.620587i
\(950\) 53.3634 + 92.4282i 1.73134 + 2.99877i
\(951\) 0 0
\(952\) −0.818363 + 1.41745i −0.0265233 + 0.0459397i
\(953\) −13.1957 −0.427451 −0.213726 0.976894i \(-0.568560\pi\)
−0.213726 + 0.976894i \(0.568560\pi\)
\(954\) 0 0
\(955\) 49.6887 1.60789
\(956\) 14.1100 24.4393i 0.456351 0.790423i
\(957\) 0 0
\(958\) 6.38326 + 11.0561i 0.206234 + 0.357207i
\(959\) −22.3987 38.7957i −0.723291 1.25278i
\(960\) 0 0
\(961\) 6.23173 10.7937i 0.201024 0.348183i
\(962\) −22.4037 −0.722323
\(963\) 0 0
\(964\) 1.49525 0.0481588
\(965\) 27.7718 48.1023i 0.894007 1.54847i
\(966\) 0 0
\(967\) 10.0774 + 17.4545i 0.324067 + 0.561300i 0.981323 0.192367i \(-0.0616164\pi\)
−0.657256 + 0.753667i \(0.728283\pi\)
\(968\) −0.742868 1.28668i −0.0238767 0.0413556i
\(969\) 0 0
\(970\) −25.8332 + 44.7444i −0.829455 + 1.43666i
\(971\) −26.5839 −0.853118 −0.426559 0.904460i \(-0.640274\pi\)
−0.426559 + 0.904460i \(0.640274\pi\)
\(972\) 0 0
\(973\) 54.7006 1.75362
\(974\) −19.6792 + 34.0853i −0.630562 + 1.09216i
\(975\) 0 0
\(976\) −7.76651 13.4520i −0.248600 0.430588i
\(977\) −7.20204 12.4743i −0.230414 0.399088i 0.727516 0.686091i \(-0.240675\pi\)
−0.957930 + 0.287002i \(0.907341\pi\)
\(978\) 0 0
\(979\) 0.761707 1.31932i 0.0243443 0.0421655i
\(980\) 10.3671 0.331165
\(981\) 0 0
\(982\) −51.6573 −1.64845
\(983\) 21.4941 37.2288i 0.685554 1.18741i −0.287708 0.957718i \(-0.592893\pi\)
0.973262 0.229696i \(-0.0737733\pi\)
\(984\) 0 0
\(985\) 41.3127 + 71.5558i 1.31633 + 2.27996i
\(986\) −10.0959 17.4866i −0.321519 0.556888i
\(987\) 0 0
\(988\) −27.5993 + 47.8033i −0.878049 + 1.52083i
\(989\) −0.552340 −0.0175634
\(990\) 0 0
\(991\) −15.5794 −0.494895 −0.247447 0.968901i \(-0.579592\pi\)
−0.247447 + 0.968901i \(0.579592\pi\)
\(992\) −16.8983 + 29.2687i −0.536522 + 0.929283i
\(993\) 0 0
\(994\) −2.78106 4.81694i −0.0882098 0.152784i
\(995\) −16.8445 29.1755i −0.534005 0.924924i
\(996\) 0 0
\(997\) −20.3093 + 35.1767i −0.643201 + 1.11406i 0.341513 + 0.939877i \(0.389061\pi\)
−0.984714 + 0.174180i \(0.944273\pi\)
\(998\) 12.4426 0.393863
\(999\) 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 729.2.c.c.487.1 12
3.2 odd 2 inner 729.2.c.c.487.6 12
9.2 odd 6 729.2.a.c.1.1 6
9.4 even 3 inner 729.2.c.c.244.1 12
9.5 odd 6 inner 729.2.c.c.244.6 12
9.7 even 3 729.2.a.c.1.6 yes 6
27.2 odd 18 729.2.e.q.325.1 12
27.4 even 9 729.2.e.r.163.1 12
27.5 odd 18 729.2.e.q.406.1 12
27.7 even 9 729.2.e.m.82.2 12
27.11 odd 18 729.2.e.r.568.2 12
27.13 even 9 729.2.e.m.649.2 12
27.14 odd 18 729.2.e.m.649.1 12
27.16 even 9 729.2.e.r.568.1 12
27.20 odd 18 729.2.e.m.82.1 12
27.22 even 9 729.2.e.q.406.2 12
27.23 odd 18 729.2.e.r.163.2 12
27.25 even 9 729.2.e.q.325.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
729.2.a.c.1.1 6 9.2 odd 6
729.2.a.c.1.6 yes 6 9.7 even 3
729.2.c.c.244.1 12 9.4 even 3 inner
729.2.c.c.244.6 12 9.5 odd 6 inner
729.2.c.c.487.1 12 1.1 even 1 trivial
729.2.c.c.487.6 12 3.2 odd 2 inner
729.2.e.m.82.1 12 27.20 odd 18
729.2.e.m.82.2 12 27.7 even 9
729.2.e.m.649.1 12 27.14 odd 18
729.2.e.m.649.2 12 27.13 even 9
729.2.e.q.325.1 12 27.2 odd 18
729.2.e.q.325.2 12 27.25 even 9
729.2.e.q.406.1 12 27.5 odd 18
729.2.e.q.406.2 12 27.22 even 9
729.2.e.r.163.1 12 27.4 even 9
729.2.e.r.163.2 12 27.23 odd 18
729.2.e.r.568.1 12 27.16 even 9
729.2.e.r.568.2 12 27.11 odd 18