Properties

Label 729.2.c.c.244.6
Level $729$
Weight $2$
Character 729.244
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 244.6
Root \(-0.984808 - 0.173648i\) of defining polynomial
Character \(\chi\) \(=\) 729.244
Dual form 729.2.c.c.487.6

$q$-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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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 0.969719 + 0.244225i \(0.0785335\pi\)
−0.273354 + 0.961913i \(0.588133\pi\)
\(3\) 0 0
\(4\) −0.939693 + 1.62760i −0.469846 + 0.813798i
\(5\) −1.85083 + 3.20574i −0.827718 + 1.43365i 0.0721067 + 0.997397i \(0.477028\pi\)
−0.899824 + 0.436252i \(0.856306\pi\)
\(6\) 0 0
\(7\) 1.17365 + 2.03282i 0.443597 + 0.768333i 0.997953 0.0639466i \(-0.0203687\pi\)
−0.554356 + 0.832280i \(0.687035\pi\)
\(8\) 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 \(-0.0601488\pi\)
−0.653774 + 0.756690i \(0.726815\pi\)
\(12\) 0 0
\(13\) 2.35844 4.08494i 0.654114 1.13296i −0.328001 0.944677i \(-0.606375\pi\)
0.982115 0.188281i \(-0.0602916\pi\)
\(14\) −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 \(-0.615838\pi\)
−0.355936 + 0.934510i \(0.615838\pi\)
\(18\) 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 \(-0.850566\pi\)
0.837700 + 0.546130i \(0.183900\pi\)
\(24\) 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 \(-0.0615399\pi\)
−0.657075 + 0.753825i \(0.728207\pi\)
\(30\) 0 0
\(31\) 2.15270 3.72859i 0.386637 0.669675i −0.605358 0.795953i \(-0.706970\pi\)
0.991995 + 0.126279i \(0.0403033\pi\)
\(32\) −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 \(-0.895839\pi\)
0.751828 + 0.659359i \(0.229172\pi\)
\(42\) 0 0
\(43\) −0.532089 0.921605i −0.0811428 0.140543i 0.822598 0.568623i \(-0.192524\pi\)
−0.903741 + 0.428080i \(0.859190\pi\)
\(44\) −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 \(-0.161151\pi\)
−0.857232 + 0.514930i \(0.827818\pi\)
\(48\) 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 \(-0.396135\pi\)
0.320543 + 0.947234i \(0.396135\pi\)
\(54\) 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 0.00104825 0.999999i \(-0.499666\pi\)
0.865501 0.500908i \(-0.167000\pi\)
\(60\) 0 0
\(61\) 1.83750 + 3.18264i 0.235267 + 0.407495i 0.959350 0.282218i \(-0.0910701\pi\)
−0.724083 + 0.689713i \(0.757737\pi\)
\(62\) 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 −0.0149960 + 0.999888i \(0.504774\pi\)
−0.858430 + 0.512931i \(0.828560\pi\)
\(68\) 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 \(-0.477257\pi\)
0.0713891 + 0.997449i \(0.477257\pi\)
\(72\) 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 0.960962 + 0.276681i \(0.0892344\pi\)
−0.240869 + 0.970558i \(0.577432\pi\)
\(80\) −15.6458 −1.74925
\(81\) 0 0
\(82\) −4.92127 −0.543464
\(83\) 5.65198 + 9.78952i 0.620385 + 1.07454i 0.989414 + 0.145121i \(0.0463571\pi\)
−0.369029 + 0.929418i \(0.620310\pi\)
\(84\) 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 \(-0.488200\pi\)
0.0370621 + 0.999313i \(0.488200\pi\)
\(90\) 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 0.987921 0.154960i \(-0.0495250\pi\)
−0.628160 + 0.778084i \(0.716192\pi\)
\(98\) 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 \(-0.241421\pi\)
−0.958600 + 0.284755i \(0.908088\pi\)
\(102\) 0 0
\(103\) 6.81180 11.7984i 0.671187 1.16253i −0.306381 0.951909i \(-0.599118\pi\)
0.977568 0.210621i \(-0.0675486\pi\)
\(104\) 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 \(-0.309898\pi\)
0.562350 + 0.826900i \(0.309898\pi\)
\(108\) 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 \(-0.904224\pi\)
0.734200 + 0.678933i \(0.237557\pi\)
\(114\) 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 \(-0.982648\pi\)
0.546442 + 0.837497i \(0.315982\pi\)
\(132\) 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 −0.909143 0.416483i \(-0.863263\pi\)
0.0938868 0.995583i \(-0.470071\pi\)
\(138\) 0 0
\(139\) 11.6518 20.1816i 0.988295 1.71178i 0.362031 0.932166i \(-0.382083\pi\)
0.626264 0.779611i \(-0.284583\pi\)
\(140\) 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 0.351335 + 0.936250i \(0.385728\pi\)
−0.986484 + 0.163860i \(0.947606\pi\)
\(150\) 0 0
\(151\) 2.95084 + 5.11100i 0.240136 + 0.415927i 0.960753 0.277406i \(-0.0894747\pi\)
−0.720617 + 0.693333i \(0.756141\pi\)
\(152\) −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 −0.840827 0.541304i \(-0.817931\pi\)
0.889196 + 0.457526i \(0.151264\pi\)
\(158\) −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 \(-0.786014\pi\)
0.930530 + 0.366216i \(0.119347\pi\)
\(168\) 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 \(-0.0805622\pi\)
−0.700924 + 0.713236i \(0.747229\pi\)
\(174\) 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 \(-0.680672\pi\)
−0.537607 + 0.843195i \(0.680672\pi\)
\(180\) 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 \(-0.328080\pi\)
−0.999864 + 0.0165036i \(0.994746\pi\)
\(192\) 0 0
\(193\) −7.50253 + 12.9948i −0.540044 + 0.935383i 0.458857 + 0.888510i \(0.348259\pi\)
−0.998901 + 0.0468730i \(0.985074\pi\)
\(194\) −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 \(-0.792612\pi\)
−0.795158 + 0.606402i \(0.792612\pi\)
\(198\) 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 −0.744614 0.667496i \(-0.767366\pi\)
0.950375 + 0.311107i \(0.100700\pi\)
\(212\) −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 0.975690 0.219156i \(-0.0703304\pi\)
−0.677640 + 0.735394i \(0.736997\pi\)
\(224\) −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 \(-0.0514724\pi\)
−0.632908 + 0.774227i \(0.718139\pi\)
\(228\) 0 0
\(229\) 4.13563 7.16312i 0.273290 0.473352i −0.696412 0.717642i \(-0.745221\pi\)
0.969702 + 0.244290i \(0.0785548\pi\)
\(230\) 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 \(-0.362980\pi\)
0.417290 + 0.908774i \(0.362980\pi\)
\(234\) 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 \(-0.994746\pi\)
0.514225 + 0.857655i \(0.328079\pi\)
\(240\) 0 0
\(241\) −0.397804 0.689016i −0.0256248 0.0443834i 0.852929 0.522028i \(-0.174824\pi\)
−0.878553 + 0.477644i \(0.841491\pi\)
\(242\) 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 \(-0.415480\pi\)
0.262419 + 0.964954i \(0.415480\pi\)
\(252\) 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 −0.121146 0.992635i \(-0.538657\pi\)
0.920220 0.391401i \(-0.128010\pi\)
\(258\) 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 −0.866768 0.498711i \(-0.833807\pi\)
0.00148730 0.999999i \(-0.499527\pi\)
\(264\) 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 \(-0.871631\pi\)
−0.919778 + 0.392439i \(0.871631\pi\)
\(270\) 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 −0.986613 0.163077i \(-0.947858\pi\)
0.352078 0.935971i \(-0.385475\pi\)
\(278\) 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 \(-0.150070\pi\)
−0.838790 + 0.544456i \(0.816736\pi\)
\(282\) 0 0
\(283\) 3.64409 6.31174i 0.216618 0.375194i −0.737154 0.675725i \(-0.763831\pi\)
0.953772 + 0.300531i \(0.0971639\pi\)
\(284\) −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 \(-0.685326\pi\)
0.998282 + 0.0585858i \(0.0186591\pi\)
\(294\) 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 \(-0.983442\pi\)
0.544353 + 0.838856i \(0.316775\pi\)
\(312\) 0 0
\(313\) −17.2028 29.7961i −0.972360 1.68418i −0.688386 0.725344i \(-0.741681\pi\)
−0.283974 0.958832i \(-0.591653\pi\)
\(314\) 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 \(-0.318123\pi\)
−0.998858 + 0.0477675i \(0.984789\pi\)
\(318\) 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 0.864143 + 0.503247i \(0.167861\pi\)
0.00375320 + 0.999993i \(0.498805\pi\)
\(332\) −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 −0.936142 0.351621i \(-0.885630\pi\)
0.772584 + 0.634912i \(0.218964\pi\)
\(338\) 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 −0.371652 0.928372i \(-0.621208\pi\)
0.989820 0.142326i \(-0.0454583\pi\)
\(348\) 0 0
\(349\) 5.78312 + 10.0167i 0.309563 + 0.536179i 0.978267 0.207350i \(-0.0664838\pi\)
−0.668704 + 0.743529i \(0.733150\pi\)
\(350\) 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 \(-0.184759\pi\)
−0.893031 + 0.449996i \(0.851425\pi\)
\(354\) 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 \(-0.720749\pi\)
−0.639234 + 0.769012i \(0.720749\pi\)
\(360\) 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 0.900646 0.434554i \(-0.143094\pi\)
−0.826658 + 0.562705i \(0.809761\pi\)
\(368\) −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 −0.203038 0.979171i \(-0.565081\pi\)
0.949506 0.313749i \(-0.101585\pi\)
\(374\) 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 \(-0.827866\pi\)
0.874485 + 0.485052i \(0.161199\pi\)
\(384\) 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 \(-0.201104\pi\)
−0.914951 + 0.403565i \(0.867771\pi\)
\(390\) 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 0.135901 0.990722i \(-0.456607\pi\)
0.790040 0.613055i \(-0.210060\pi\)
\(402\) 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 −0.821084 0.570808i \(-0.806630\pi\)
0.904876 + 0.425675i \(0.139963\pi\)
\(410\) 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 0.495421 + 0.868653i \(0.335014\pi\)
−0.999986 + 0.00527895i \(0.998320\pi\)
\(420\) 0 0
\(421\) −13.7665 23.8443i −0.670939 1.16210i −0.977638 0.210294i \(-0.932558\pi\)
0.306700 0.951806i \(-0.400775\pi\)
\(422\) 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 \(-0.480200\pi\)
0.0621636 + 0.998066i \(0.480200\pi\)
\(432\) 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 0.691801 0.722088i \(-0.256817\pi\)
−0.971247 + 0.238074i \(0.923484\pi\)
\(440\) −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 \(-0.150926\pi\)
−0.840252 + 0.542197i \(0.817593\pi\)
\(444\) 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 \(-0.580089\pi\)
−0.248962 + 0.968513i \(0.580089\pi\)
\(450\) 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 0.943574 0.331161i \(-0.107440\pi\)
−0.758581 + 0.651579i \(0.774107\pi\)
\(458\) 16.2912 0.761238
\(459\) 0 0
\(460\) 3.61081 0.168355
\(461\) −19.5464 33.8553i −0.910366 1.57680i −0.813548 0.581498i \(-0.802467\pi\)
−0.0968187 0.995302i \(-0.530867\pi\)
\(462\) 0 0
\(463\) −11.8464 + 20.5186i −0.550550 + 0.953580i 0.447685 + 0.894191i \(0.352249\pi\)
−0.998235 + 0.0593889i \(0.981085\pi\)
\(464\) −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 \(-0.203122\pi\)
0.803214 + 0.595691i \(0.203122\pi\)
\(468\) 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 \(-0.213976\pi\)
−0.930517 + 0.366248i \(0.880642\pi\)
\(480\) 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 0.402183 + 0.915559i \(0.368251\pi\)
−0.993989 + 0.109478i \(0.965082\pi\)
\(492\) 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 −0.928024 0.372520i \(-0.878494\pi\)
0.786624 + 0.617432i \(0.211827\pi\)
\(500\) −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 \(-0.338241\pi\)
0.486589 + 0.873631i \(0.338241\pi\)
\(504\) 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 −0.339591 0.940573i \(-0.610289\pi\)
0.984356 0.176192i \(-0.0563779\pi\)
\(510\) 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 \(-0.403016\pi\)
0.299991 + 0.953942i \(0.403016\pi\)
\(522\) 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 0.977672 + 0.210135i \(0.0673905\pi\)
−0.306854 + 0.951757i \(0.599276\pi\)
\(548\) 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 \(-0.127953\pi\)
0.920290 + 0.391237i \(0.127953\pi\)
\(558\) 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 0.301868 + 0.953350i \(0.402390\pi\)
−0.976559 + 0.215250i \(0.930944\pi\)
\(564\) 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 \(-0.212003\pi\)
−0.928230 + 0.372007i \(0.878670\pi\)
\(570\) 0 0
\(571\) 10.5765 18.3190i 0.442613 0.766628i −0.555270 0.831670i \(-0.687385\pi\)
0.997883 + 0.0650424i \(0.0207182\pi\)
\(572\) −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 \(-0.167520\pi\)
−0.867362 + 0.497677i \(0.834186\pi\)
\(588\) 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 \(-0.681285\pi\)
−0.539230 + 0.842158i \(0.681285\pi\)
\(594\) 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 −0.433411 0.901197i \(-0.642690\pi\)
0.997164 0.0752537i \(-0.0239767\pi\)
\(600\) 0 0
\(601\) −0.666374 1.15419i −0.0271820 0.0470806i 0.852114 0.523356i \(-0.175320\pi\)
−0.879296 + 0.476275i \(0.841987\pi\)
\(602\) 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 −0.709904 0.704298i \(-0.751262\pi\)
0.964892 + 0.262646i \(0.0845950\pi\)
\(608\) 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 \(-0.672501\pi\)
0.999832 + 0.0183296i \(0.00583482\pi\)
\(618\) 0 0
\(619\) −3.43582 5.95102i −0.138097 0.239192i 0.788679 0.614805i \(-0.210765\pi\)
−0.926776 + 0.375614i \(0.877432\pi\)
\(620\) −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 \(-0.290281\pi\)
−0.990867 + 0.134842i \(0.956947\pi\)
\(642\) 0 0
\(643\) −9.68820 + 16.7804i −0.382065 + 0.661756i −0.991357 0.131190i \(-0.958120\pi\)
0.609292 + 0.792946i \(0.291454\pi\)
\(644\) 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 \(-0.555159\pi\)
−0.172420 + 0.985024i \(0.555159\pi\)
\(648\) 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 −0.343029 0.939325i \(-0.611453\pi\)
0.984994 0.172591i \(-0.0552139\pi\)
\(654\) 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 \(-0.0483230\pi\)
−0.625217 + 0.780451i \(0.714990\pi\)
\(660\) 0 0
\(661\) −18.2037 + 31.5297i −0.708041 + 1.22636i 0.257542 + 0.966267i \(0.417087\pi\)
−0.965583 + 0.260096i \(0.916246\pi\)
\(662\) −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 −0.943265 0.332041i \(-0.892263\pi\)
0.184076 0.982912i \(-0.441071\pi\)
\(674\) −11.8276 −0.455584
\(675\) 0 0
\(676\) 17.3824 0.668553
\(677\) 15.8377 + 27.4317i 0.608692 + 1.05429i 0.991456 + 0.130440i \(0.0416389\pi\)
−0.382764 + 0.923846i \(0.625028\pi\)
\(678\) 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 \(-0.312304\pi\)
0.556083 + 0.831127i \(0.312304\pi\)
\(684\) 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 0.810566 0.585647i \(-0.199160\pi\)
−0.912468 + 0.409147i \(0.865826\pi\)
\(692\) −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 \(-0.339016\pi\)
0.484461 + 0.874813i \(0.339016\pi\)
\(702\) 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 0.906698 0.421780i \(-0.138594\pi\)
−0.818621 + 0.574334i \(0.805261\pi\)
\(710\) −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 \(-0.759771\pi\)
−0.728476 + 0.685072i \(0.759771\pi\)
\(720\) 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 0.948768 0.315972i \(-0.102331\pi\)
−0.748024 + 0.663672i \(0.768997\pi\)
\(728\) 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 −0.832794 0.553583i \(-0.813260\pi\)
0.895814 + 0.444429i \(0.146593\pi\)
\(734\) −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 −0.468424 0.883504i \(-0.655178\pi\)
0.999349 0.0360843i \(-0.0114885\pi\)
\(744\) 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 −0.632251 0.774764i \(-0.717869\pi\)
0.987090 + 0.160164i \(0.0512022\pi\)
\(752\) −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 \(-0.773384\pi\)
0.944324 + 0.329016i \(0.106717\pi\)
\(762\) 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 0.104848 + 0.994488i \(0.466564\pi\)
−0.913676 + 0.406443i \(0.866769\pi\)
\(770\) 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 \(-0.780814\pi\)
−0.772141 + 0.635452i \(0.780814\pi\)
\(774\) 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