Properties

Label 729.2.c.e.244.1
Level $729$
Weight $2$
Character 729.244
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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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: 12.0.1952986685049.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} - 258 x^{3} + 108 x^{2} - 27 x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 27)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 244.1
Root \(0.500000 - 0.0126039i\) of defining polynomial
Character \(\chi\) \(=\) 729.244
Dual form 729.2.c.e.487.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.840456 - 1.45571i) q^{2} +(-0.412733 + 0.714874i) q^{4} +(0.564772 - 0.978214i) q^{5} +(1.95446 + 3.38523i) q^{7} -1.97429 q^{8} +O(q^{10})\) \(q+(-0.840456 - 1.45571i) q^{2} +(-0.412733 + 0.714874i) q^{4} +(0.564772 - 0.978214i) q^{5} +(1.95446 + 3.38523i) q^{7} -1.97429 q^{8} -1.89866 q^{10} +(0.935228 + 1.61986i) q^{11} +(0.366299 - 0.634448i) q^{13} +(3.28528 - 5.69027i) q^{14} +(2.48477 + 4.30375i) q^{16} +1.88964 q^{17} +2.74286 q^{19} +(0.466200 + 0.807482i) q^{20} +(1.57204 - 2.72285i) q^{22} +(2.91385 - 5.04694i) q^{23} +(1.86207 + 3.22519i) q^{25} -1.23143 q^{26} -3.22668 q^{28} +(2.65997 + 4.60720i) q^{29} +(-0.670300 + 1.16099i) q^{31} +(2.20239 - 3.81465i) q^{32} +(-1.58816 - 2.75078i) q^{34} +4.41530 q^{35} +3.39611 q^{37} +(-2.30525 - 3.99281i) q^{38} +(-1.11502 + 1.93128i) q^{40} +(-0.898166 + 1.55567i) q^{41} +(-2.51508 - 4.35624i) q^{43} -1.54400 q^{44} -9.79585 q^{46} +(-0.854339 - 1.47976i) q^{47} +(-4.13984 + 7.17041i) q^{49} +(3.12997 - 5.42126i) q^{50} +(0.302367 + 0.523715i) q^{52} +2.84494 q^{53} +2.11276 q^{55} +(-3.85867 - 6.68342i) q^{56} +(4.47117 - 7.74430i) q^{58} +(5.63002 - 9.75149i) q^{59} +(-2.61545 - 4.53009i) q^{61} +2.25343 q^{62} +2.53503 q^{64} +(-0.413751 - 0.716637i) q^{65} +(0.944514 - 1.63595i) q^{67} +(-0.779918 + 1.35086i) q^{68} +(-3.71087 - 6.42741i) q^{70} -12.1839 q^{71} +9.88768 q^{73} +(-2.85428 - 4.94376i) q^{74} +(-1.13207 + 1.96080i) q^{76} +(-3.65573 + 6.33192i) q^{77} +(-6.17644 - 10.6979i) q^{79} +5.61331 q^{80} +3.01948 q^{82} +(5.84158 + 10.1179i) q^{83} +(1.06722 - 1.84848i) q^{85} +(-4.22762 + 7.32246i) q^{86} +(-1.84641 - 3.19808i) q^{88} -5.72873 q^{89} +2.86367 q^{91} +(2.40528 + 4.16607i) q^{92} +(-1.43607 + 2.48734i) q^{94} +(1.54909 - 2.68310i) q^{95} +(0.171689 + 0.297374i) q^{97} +13.9174 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 3 q^{2} - 3 q^{4} + 6 q^{5} - 12 q^{8} + 6 q^{10} + 12 q^{11} + 6 q^{14} + 3 q^{16} - 18 q^{17} + 6 q^{19} + 6 q^{20} - 6 q^{22} + 15 q^{23} + 6 q^{25} - 30 q^{26} - 12 q^{28} + 12 q^{29} - 24 q^{35} + 6 q^{37} - 3 q^{38} - 6 q^{40} + 15 q^{41} - 6 q^{44} + 6 q^{46} + 21 q^{47} + 12 q^{49} + 3 q^{50} - 12 q^{52} - 18 q^{53} - 12 q^{55} - 6 q^{56} + 12 q^{58} + 24 q^{59} + 9 q^{61} + 24 q^{62} - 24 q^{64} - 6 q^{65} + 9 q^{67} - 9 q^{68} - 15 q^{70} - 54 q^{71} - 12 q^{73} - 12 q^{74} - 6 q^{76} - 12 q^{77} + 42 q^{80} - 12 q^{82} + 12 q^{83} - 21 q^{86} - 12 q^{88} - 18 q^{89} - 12 q^{91} + 6 q^{92} - 6 q^{94} + 12 q^{95} + 90 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.840456 1.45571i −0.594292 1.02934i −0.993646 0.112548i \(-0.964099\pi\)
0.399354 0.916797i \(-0.369234\pi\)
\(3\) 0 0
\(4\) −0.412733 + 0.714874i −0.206366 + 0.357437i
\(5\) 0.564772 0.978214i 0.252574 0.437471i −0.711660 0.702524i \(-0.752056\pi\)
0.964234 + 0.265054i \(0.0853896\pi\)
\(6\) 0 0
\(7\) 1.95446 + 3.38523i 0.738717 + 1.27950i 0.953073 + 0.302740i \(0.0979013\pi\)
−0.214356 + 0.976756i \(0.568765\pi\)
\(8\) −1.97429 −0.698017
\(9\) 0 0
\(10\) −1.89866 −0.600410
\(11\) 0.935228 + 1.61986i 0.281982 + 0.488407i 0.971873 0.235506i \(-0.0756749\pi\)
−0.689891 + 0.723913i \(0.742342\pi\)
\(12\) 0 0
\(13\) 0.366299 0.634448i 0.101593 0.175964i −0.810748 0.585395i \(-0.800939\pi\)
0.912341 + 0.409431i \(0.134273\pi\)
\(14\) 3.28528 5.69027i 0.878027 1.52079i
\(15\) 0 0
\(16\) 2.48477 + 4.30375i 0.621192 + 1.07594i
\(17\) 1.88964 0.458306 0.229153 0.973390i \(-0.426404\pi\)
0.229153 + 0.973390i \(0.426404\pi\)
\(18\) 0 0
\(19\) 2.74286 0.629254 0.314627 0.949215i \(-0.398121\pi\)
0.314627 + 0.949215i \(0.398121\pi\)
\(20\) 0.466200 + 0.807482i 0.104245 + 0.180558i
\(21\) 0 0
\(22\) 1.57204 2.72285i 0.335159 0.580513i
\(23\) 2.91385 5.04694i 0.607580 1.05236i −0.384058 0.923309i \(-0.625474\pi\)
0.991638 0.129050i \(-0.0411928\pi\)
\(24\) 0 0
\(25\) 1.86207 + 3.22519i 0.372413 + 0.645038i
\(26\) −1.23143 −0.241504
\(27\) 0 0
\(28\) −3.22668 −0.609786
\(29\) 2.65997 + 4.60720i 0.493944 + 0.855535i 0.999976 0.00697928i \(-0.00222159\pi\)
−0.506032 + 0.862515i \(0.668888\pi\)
\(30\) 0 0
\(31\) −0.670300 + 1.16099i −0.120390 + 0.208521i −0.919921 0.392103i \(-0.871748\pi\)
0.799532 + 0.600624i \(0.205081\pi\)
\(32\) 2.20239 3.81465i 0.389331 0.674341i
\(33\) 0 0
\(34\) −1.58816 2.75078i −0.272368 0.471755i
\(35\) 4.41530 0.746322
\(36\) 0 0
\(37\) 3.39611 0.558318 0.279159 0.960245i \(-0.409944\pi\)
0.279159 + 0.960245i \(0.409944\pi\)
\(38\) −2.30525 3.99281i −0.373961 0.647719i
\(39\) 0 0
\(40\) −1.11502 + 1.93128i −0.176301 + 0.305362i
\(41\) −0.898166 + 1.55567i −0.140270 + 0.242955i −0.927598 0.373579i \(-0.878130\pi\)
0.787328 + 0.616534i \(0.211464\pi\)
\(42\) 0 0
\(43\) −2.51508 4.35624i −0.383546 0.664320i 0.608021 0.793921i \(-0.291964\pi\)
−0.991566 + 0.129601i \(0.958630\pi\)
\(44\) −1.54400 −0.232766
\(45\) 0 0
\(46\) −9.79585 −1.44432
\(47\) −0.854339 1.47976i −0.124618 0.215845i 0.796965 0.604025i \(-0.206437\pi\)
−0.921584 + 0.388180i \(0.873104\pi\)
\(48\) 0 0
\(49\) −4.13984 + 7.17041i −0.591405 + 1.02434i
\(50\) 3.12997 5.42126i 0.442644 0.766682i
\(51\) 0 0
\(52\) 0.302367 + 0.523715i 0.0419308 + 0.0726263i
\(53\) 2.84494 0.390783 0.195391 0.980725i \(-0.437402\pi\)
0.195391 + 0.980725i \(0.437402\pi\)
\(54\) 0 0
\(55\) 2.11276 0.284885
\(56\) −3.85867 6.68342i −0.515637 0.893109i
\(57\) 0 0
\(58\) 4.47117 7.74430i 0.587094 1.01688i
\(59\) 5.63002 9.75149i 0.732967 1.26954i −0.222643 0.974900i \(-0.571469\pi\)
0.955610 0.294635i \(-0.0951982\pi\)
\(60\) 0 0
\(61\) −2.61545 4.53009i −0.334874 0.580018i 0.648587 0.761141i \(-0.275360\pi\)
−0.983461 + 0.181122i \(0.942027\pi\)
\(62\) 2.25343 0.286186
\(63\) 0 0
\(64\) 2.53503 0.316879
\(65\) −0.413751 0.716637i −0.0513195 0.0888879i
\(66\) 0 0
\(67\) 0.944514 1.63595i 0.115391 0.199863i −0.802545 0.596591i \(-0.796521\pi\)
0.917936 + 0.396729i \(0.129855\pi\)
\(68\) −0.779918 + 1.35086i −0.0945789 + 0.163816i
\(69\) 0 0
\(70\) −3.71087 6.42741i −0.443533 0.768222i
\(71\) −12.1839 −1.44596 −0.722980 0.690869i \(-0.757228\pi\)
−0.722980 + 0.690869i \(0.757228\pi\)
\(72\) 0 0
\(73\) 9.88768 1.15727 0.578633 0.815588i \(-0.303587\pi\)
0.578633 + 0.815588i \(0.303587\pi\)
\(74\) −2.85428 4.94376i −0.331804 0.574701i
\(75\) 0 0
\(76\) −1.13207 + 1.96080i −0.129857 + 0.224919i
\(77\) −3.65573 + 6.33192i −0.416610 + 0.721589i
\(78\) 0 0
\(79\) −6.17644 10.6979i −0.694904 1.20361i −0.970213 0.242253i \(-0.922114\pi\)
0.275310 0.961356i \(-0.411220\pi\)
\(80\) 5.61331 0.627587
\(81\) 0 0
\(82\) 3.01948 0.333445
\(83\) 5.84158 + 10.1179i 0.641197 + 1.11059i 0.985166 + 0.171605i \(0.0548952\pi\)
−0.343969 + 0.938981i \(0.611772\pi\)
\(84\) 0 0
\(85\) 1.06722 1.84848i 0.115756 0.200495i
\(86\) −4.22762 + 7.32246i −0.455876 + 0.789601i
\(87\) 0 0
\(88\) −1.84641 3.19808i −0.196828 0.340916i
\(89\) −5.72873 −0.607244 −0.303622 0.952793i \(-0.598196\pi\)
−0.303622 + 0.952793i \(0.598196\pi\)
\(90\) 0 0
\(91\) 2.86367 0.300194
\(92\) 2.40528 + 4.16607i 0.250768 + 0.434343i
\(93\) 0 0
\(94\) −1.43607 + 2.48734i −0.148119 + 0.256550i
\(95\) 1.54909 2.68310i 0.158933 0.275280i
\(96\) 0 0
\(97\) 0.171689 + 0.297374i 0.0174324 + 0.0301938i 0.874610 0.484827i \(-0.161117\pi\)
−0.857178 + 0.515021i \(0.827784\pi\)
\(98\) 13.9174 1.40587
\(99\) 0 0
\(100\) −3.07414 −0.307414
\(101\) 8.70113 + 15.0708i 0.865794 + 1.49960i 0.866256 + 0.499600i \(0.166520\pi\)
−0.000461665 1.00000i \(0.500147\pi\)
\(102\) 0 0
\(103\) 7.90650 13.6945i 0.779051 1.34936i −0.153439 0.988158i \(-0.549035\pi\)
0.932489 0.361197i \(-0.117632\pi\)
\(104\) −0.723180 + 1.25258i −0.0709136 + 0.122826i
\(105\) 0 0
\(106\) −2.39105 4.14142i −0.232239 0.402250i
\(107\) −16.5298 −1.59800 −0.798999 0.601332i \(-0.794637\pi\)
−0.798999 + 0.601332i \(0.794637\pi\)
\(108\) 0 0
\(109\) −4.71844 −0.451945 −0.225972 0.974134i \(-0.572556\pi\)
−0.225972 + 0.974134i \(0.572556\pi\)
\(110\) −1.77568 3.07557i −0.169305 0.293245i
\(111\) 0 0
\(112\) −9.71277 + 16.8230i −0.917770 + 1.58963i
\(113\) −9.97241 + 17.2727i −0.938125 + 1.62488i −0.169161 + 0.985588i \(0.554106\pi\)
−0.768964 + 0.639292i \(0.779228\pi\)
\(114\) 0 0
\(115\) −3.29132 5.70074i −0.306917 0.531596i
\(116\) −4.39142 −0.407733
\(117\) 0 0
\(118\) −18.9271 −1.74239
\(119\) 3.69324 + 6.39687i 0.338558 + 0.586400i
\(120\) 0 0
\(121\) 3.75070 6.49640i 0.340972 0.590582i
\(122\) −4.39634 + 7.61468i −0.398026 + 0.689401i
\(123\) 0 0
\(124\) −0.553310 0.958361i −0.0496887 0.0860634i
\(125\) 9.85429 0.881394
\(126\) 0 0
\(127\) 1.06946 0.0948989 0.0474495 0.998874i \(-0.484891\pi\)
0.0474495 + 0.998874i \(0.484891\pi\)
\(128\) −6.53536 11.3196i −0.577650 1.00052i
\(129\) 0 0
\(130\) −0.695479 + 1.20460i −0.0609975 + 0.105651i
\(131\) −3.82015 + 6.61669i −0.333768 + 0.578103i −0.983247 0.182276i \(-0.941654\pi\)
0.649479 + 0.760379i \(0.274987\pi\)
\(132\) 0 0
\(133\) 5.36081 + 9.28519i 0.464841 + 0.805128i
\(134\) −3.17529 −0.274303
\(135\) 0 0
\(136\) −3.73070 −0.319905
\(137\) −7.82525 13.5537i −0.668556 1.15797i −0.978308 0.207156i \(-0.933579\pi\)
0.309752 0.950818i \(-0.399754\pi\)
\(138\) 0 0
\(139\) −4.32847 + 7.49712i −0.367136 + 0.635898i −0.989116 0.147135i \(-0.952995\pi\)
0.621981 + 0.783033i \(0.286328\pi\)
\(140\) −1.82234 + 3.15638i −0.154016 + 0.266763i
\(141\) 0 0
\(142\) 10.2400 + 17.7362i 0.859322 + 1.48839i
\(143\) 1.37029 0.114590
\(144\) 0 0
\(145\) 6.00910 0.499029
\(146\) −8.31016 14.3936i −0.687754 1.19122i
\(147\) 0 0
\(148\) −1.40169 + 2.42779i −0.115218 + 0.199563i
\(149\) 1.23191 2.13373i 0.100922 0.174802i −0.811143 0.584848i \(-0.801154\pi\)
0.912065 + 0.410046i \(0.134487\pi\)
\(150\) 0 0
\(151\) 5.25670 + 9.10488i 0.427785 + 0.740945i 0.996676 0.0814681i \(-0.0259609\pi\)
−0.568891 + 0.822413i \(0.692628\pi\)
\(152\) −5.41519 −0.439230
\(153\) 0 0
\(154\) 12.2899 0.990351
\(155\) 0.757134 + 1.31139i 0.0608145 + 0.105334i
\(156\) 0 0
\(157\) −0.179974 + 0.311725i −0.0143635 + 0.0248783i −0.873118 0.487509i \(-0.837906\pi\)
0.858754 + 0.512388i \(0.171239\pi\)
\(158\) −10.3820 + 17.9822i −0.825951 + 1.43059i
\(159\) 0 0
\(160\) −2.48770 4.30882i −0.196670 0.340642i
\(161\) 22.7800 1.79532
\(162\) 0 0
\(163\) 14.6186 1.14502 0.572508 0.819899i \(-0.305971\pi\)
0.572508 + 0.819899i \(0.305971\pi\)
\(164\) −0.741405 1.28415i −0.0578940 0.100275i
\(165\) 0 0
\(166\) 9.81919 17.0073i 0.762117 1.32002i
\(167\) −1.08792 + 1.88434i −0.0841861 + 0.145815i −0.905044 0.425318i \(-0.860162\pi\)
0.820858 + 0.571132i \(0.193496\pi\)
\(168\) 0 0
\(169\) 6.23165 + 10.7935i 0.479358 + 0.830272i
\(170\) −3.58780 −0.275172
\(171\) 0 0
\(172\) 4.15222 0.316604
\(173\) 8.78351 + 15.2135i 0.667798 + 1.15666i 0.978519 + 0.206159i \(0.0660963\pi\)
−0.310721 + 0.950501i \(0.600570\pi\)
\(174\) 0 0
\(175\) −7.27867 + 12.6070i −0.550216 + 0.953001i
\(176\) −4.64765 + 8.04997i −0.350330 + 0.606789i
\(177\) 0 0
\(178\) 4.81475 + 8.33939i 0.360881 + 0.625064i
\(179\) 1.00447 0.0750777 0.0375388 0.999295i \(-0.488048\pi\)
0.0375388 + 0.999295i \(0.488048\pi\)
\(180\) 0 0
\(181\) −21.1732 −1.57380 −0.786898 0.617084i \(-0.788314\pi\)
−0.786898 + 0.617084i \(0.788314\pi\)
\(182\) −2.40679 4.16868i −0.178403 0.309003i
\(183\) 0 0
\(184\) −5.75278 + 9.96411i −0.424101 + 0.734564i
\(185\) 1.91803 3.32212i 0.141016 0.244247i
\(186\) 0 0
\(187\) 1.76725 + 3.06096i 0.129234 + 0.223840i
\(188\) 1.41045 0.102868
\(189\) 0 0
\(190\) −5.20776 −0.377811
\(191\) 4.91419 + 8.51163i 0.355578 + 0.615880i 0.987217 0.159383i \(-0.0509506\pi\)
−0.631638 + 0.775263i \(0.717617\pi\)
\(192\) 0 0
\(193\) 5.57804 9.66145i 0.401516 0.695447i −0.592393 0.805649i \(-0.701817\pi\)
0.993909 + 0.110203i \(0.0351500\pi\)
\(194\) 0.288594 0.499860i 0.0207199 0.0358879i
\(195\) 0 0
\(196\) −3.41729 5.91893i −0.244092 0.422781i
\(197\) 9.08994 0.647631 0.323816 0.946120i \(-0.395034\pi\)
0.323816 + 0.946120i \(0.395034\pi\)
\(198\) 0 0
\(199\) −14.6939 −1.04162 −0.520811 0.853672i \(-0.674370\pi\)
−0.520811 + 0.853672i \(0.674370\pi\)
\(200\) −3.67625 6.36746i −0.259950 0.450247i
\(201\) 0 0
\(202\) 14.6258 25.3327i 1.02907 1.78240i
\(203\) −10.3976 + 18.0092i −0.729769 + 1.26400i
\(204\) 0 0
\(205\) 1.01452 + 1.75720i 0.0708570 + 0.122728i
\(206\) −26.5803 −1.85194
\(207\) 0 0
\(208\) 3.64067 0.252435
\(209\) 2.56520 + 4.44305i 0.177438 + 0.307332i
\(210\) 0 0
\(211\) −3.92915 + 6.80549i −0.270494 + 0.468509i −0.968988 0.247106i \(-0.920520\pi\)
0.698495 + 0.715615i \(0.253854\pi\)
\(212\) −1.17420 + 2.03378i −0.0806445 + 0.139680i
\(213\) 0 0
\(214\) 13.8926 + 24.0627i 0.949678 + 1.64489i
\(215\) −5.68178 −0.387494
\(216\) 0 0
\(217\) −5.24030 −0.355735
\(218\) 3.96564 + 6.86869i 0.268587 + 0.465207i
\(219\) 0 0
\(220\) −0.872006 + 1.51036i −0.0587907 + 0.101828i
\(221\) 0.692174 1.19888i 0.0465607 0.0806455i
\(222\) 0 0
\(223\) 4.37044 + 7.56983i 0.292666 + 0.506913i 0.974439 0.224651i \(-0.0721241\pi\)
−0.681773 + 0.731564i \(0.738791\pi\)
\(224\) 17.2179 1.15042
\(225\) 0 0
\(226\) 33.5255 2.23008
\(227\) −2.03421 3.52335i −0.135015 0.233853i 0.790588 0.612348i \(-0.209775\pi\)
−0.925603 + 0.378495i \(0.876442\pi\)
\(228\) 0 0
\(229\) −8.07794 + 13.9914i −0.533805 + 0.924577i 0.465415 + 0.885093i \(0.345905\pi\)
−0.999220 + 0.0394849i \(0.987428\pi\)
\(230\) −5.53242 + 9.58244i −0.364797 + 0.631847i
\(231\) 0 0
\(232\) −5.25154 9.09594i −0.344781 0.597178i
\(233\) 17.2132 1.12767 0.563836 0.825887i \(-0.309325\pi\)
0.563836 + 0.825887i \(0.309325\pi\)
\(234\) 0 0
\(235\) −1.93003 −0.125901
\(236\) 4.64739 + 8.04952i 0.302519 + 0.523979i
\(237\) 0 0
\(238\) 6.20800 10.7526i 0.402405 0.696986i
\(239\) 0.767720 1.32973i 0.0496597 0.0860131i −0.840127 0.542390i \(-0.817520\pi\)
0.889787 + 0.456377i \(0.150853\pi\)
\(240\) 0 0
\(241\) 2.76084 + 4.78191i 0.177841 + 0.308030i 0.941141 0.338015i \(-0.109755\pi\)
−0.763300 + 0.646045i \(0.776422\pi\)
\(242\) −12.6092 −0.810549
\(243\) 0 0
\(244\) 4.31792 0.276427
\(245\) 4.67613 + 8.09929i 0.298747 + 0.517445i
\(246\) 0 0
\(247\) 1.00471 1.74020i 0.0639279 0.110726i
\(248\) 1.32337 2.29214i 0.0840339 0.145551i
\(249\) 0 0
\(250\) −8.28210 14.3450i −0.523806 0.907258i
\(251\) −21.4409 −1.35334 −0.676668 0.736288i \(-0.736577\pi\)
−0.676668 + 0.736288i \(0.736577\pi\)
\(252\) 0 0
\(253\) 10.9005 0.685306
\(254\) −0.898831 1.55682i −0.0563977 0.0976837i
\(255\) 0 0
\(256\) −8.45034 + 14.6364i −0.528146 + 0.914776i
\(257\) 7.39324 12.8055i 0.461177 0.798783i −0.537843 0.843045i \(-0.680761\pi\)
0.999020 + 0.0442626i \(0.0140938\pi\)
\(258\) 0 0
\(259\) 6.63757 + 11.4966i 0.412439 + 0.714365i
\(260\) 0.683074 0.0423625
\(261\) 0 0
\(262\) 12.8427 0.793423
\(263\) −1.40138 2.42726i −0.0864127 0.149671i 0.819580 0.572965i \(-0.194207\pi\)
−0.905992 + 0.423294i \(0.860874\pi\)
\(264\) 0 0
\(265\) 1.60674 2.78296i 0.0987015 0.170956i
\(266\) 9.01104 15.6076i 0.552503 0.956963i
\(267\) 0 0
\(268\) 0.779664 + 1.35042i 0.0476256 + 0.0824899i
\(269\) −0.356528 −0.0217379 −0.0108689 0.999941i \(-0.503460\pi\)
−0.0108689 + 0.999941i \(0.503460\pi\)
\(270\) 0 0
\(271\) −12.1467 −0.737857 −0.368928 0.929458i \(-0.620275\pi\)
−0.368928 + 0.929458i \(0.620275\pi\)
\(272\) 4.69533 + 8.13255i 0.284696 + 0.493108i
\(273\) 0 0
\(274\) −13.1536 + 22.7826i −0.794636 + 1.37635i
\(275\) −3.48291 + 6.03258i −0.210027 + 0.363778i
\(276\) 0 0
\(277\) −12.4950 21.6419i −0.750751 1.30034i −0.947459 0.319876i \(-0.896359\pi\)
0.196709 0.980462i \(-0.436975\pi\)
\(278\) 14.5515 0.872744
\(279\) 0 0
\(280\) −8.71708 −0.520945
\(281\) −3.66143 6.34179i −0.218423 0.378319i 0.735903 0.677087i \(-0.236758\pi\)
−0.954326 + 0.298767i \(0.903425\pi\)
\(282\) 0 0
\(283\) 7.19404 12.4604i 0.427641 0.740697i −0.569022 0.822323i \(-0.692678\pi\)
0.996663 + 0.0816258i \(0.0260112\pi\)
\(284\) 5.02868 8.70993i 0.298397 0.516839i
\(285\) 0 0
\(286\) −1.15167 1.99475i −0.0680997 0.117952i
\(287\) −7.02172 −0.414479
\(288\) 0 0
\(289\) −13.4292 −0.789956
\(290\) −5.05039 8.74752i −0.296569 0.513672i
\(291\) 0 0
\(292\) −4.08097 + 7.06845i −0.238821 + 0.413650i
\(293\) 7.20776 12.4842i 0.421082 0.729335i −0.574964 0.818179i \(-0.694984\pi\)
0.996046 + 0.0888441i \(0.0283173\pi\)
\(294\) 0 0
\(295\) −6.35936 11.0147i −0.370256 0.641303i
\(296\) −6.70491 −0.389715
\(297\) 0 0
\(298\) −4.14147 −0.239909
\(299\) −2.13468 3.69737i −0.123452 0.213825i
\(300\) 0 0
\(301\) 9.83124 17.0282i 0.566663 0.981489i
\(302\) 8.83606 15.3045i 0.508458 0.880675i
\(303\) 0 0
\(304\) 6.81536 + 11.8046i 0.390888 + 0.677038i
\(305\) −5.90853 −0.338321
\(306\) 0 0
\(307\) −30.4326 −1.73688 −0.868440 0.495795i \(-0.834877\pi\)
−0.868440 + 0.495795i \(0.834877\pi\)
\(308\) −3.01768 5.22678i −0.171948 0.297823i
\(309\) 0 0
\(310\) 1.27268 2.20434i 0.0722831 0.125198i
\(311\) 6.99780 12.1206i 0.396809 0.687293i −0.596521 0.802597i \(-0.703451\pi\)
0.993330 + 0.115304i \(0.0367842\pi\)
\(312\) 0 0
\(313\) −11.0438 19.1284i −0.624231 1.08120i −0.988689 0.149981i \(-0.952079\pi\)
0.364457 0.931220i \(-0.381254\pi\)
\(314\) 0.605042 0.0341445
\(315\) 0 0
\(316\) 10.1969 0.573619
\(317\) −8.69436 15.0591i −0.488324 0.845802i 0.511586 0.859232i \(-0.329058\pi\)
−0.999910 + 0.0134302i \(0.995725\pi\)
\(318\) 0 0
\(319\) −4.97535 + 8.61756i −0.278566 + 0.482491i
\(320\) 1.43171 2.47980i 0.0800352 0.138625i
\(321\) 0 0
\(322\) −19.1456 33.1612i −1.06694 1.84800i
\(323\) 5.18302 0.288391
\(324\) 0 0
\(325\) 2.72829 0.151338
\(326\) −12.2863 21.2804i −0.680474 1.17861i
\(327\) 0 0
\(328\) 1.77324 3.07134i 0.0979108 0.169586i
\(329\) 3.33954 5.78426i 0.184115 0.318897i
\(330\) 0 0
\(331\) −0.432074 0.748374i −0.0237489 0.0411343i 0.853907 0.520426i \(-0.174227\pi\)
−0.877656 + 0.479292i \(0.840894\pi\)
\(332\) −9.64405 −0.529286
\(333\) 0 0
\(334\) 3.65741 0.200124
\(335\) −1.06687 1.84787i −0.0582893 0.100960i
\(336\) 0 0
\(337\) −0.209264 + 0.362457i −0.0113994 + 0.0197443i −0.871669 0.490095i \(-0.836962\pi\)
0.860269 + 0.509840i \(0.170295\pi\)
\(338\) 10.4749 18.1430i 0.569757 0.986848i
\(339\) 0 0
\(340\) 0.880952 + 1.52585i 0.0477763 + 0.0827510i
\(341\) −2.50753 −0.135791
\(342\) 0 0
\(343\) −5.00216 −0.270091
\(344\) 4.96549 + 8.60048i 0.267721 + 0.463707i
\(345\) 0 0
\(346\) 14.7643 25.5725i 0.793734 1.37479i
\(347\) −11.7049 + 20.2734i −0.628351 + 1.08834i 0.359532 + 0.933133i \(0.382936\pi\)
−0.987883 + 0.155202i \(0.950397\pi\)
\(348\) 0 0
\(349\) −10.5882 18.3393i −0.566773 0.981680i −0.996882 0.0789033i \(-0.974858\pi\)
0.430109 0.902777i \(-0.358475\pi\)
\(350\) 24.4696 1.30796
\(351\) 0 0
\(352\) 8.23894 0.439137
\(353\) −11.7722 20.3901i −0.626573 1.08526i −0.988235 0.152946i \(-0.951124\pi\)
0.361662 0.932309i \(-0.382209\pi\)
\(354\) 0 0
\(355\) −6.88111 + 11.9184i −0.365211 + 0.632565i
\(356\) 2.36444 4.09532i 0.125315 0.217052i
\(357\) 0 0
\(358\) −0.844214 1.46222i −0.0446181 0.0772808i
\(359\) −10.4609 −0.552107 −0.276053 0.961142i \(-0.589027\pi\)
−0.276053 + 0.961142i \(0.589027\pi\)
\(360\) 0 0
\(361\) −11.4767 −0.604039
\(362\) 17.7952 + 30.8222i 0.935294 + 1.61998i
\(363\) 0 0
\(364\) −1.18193 + 2.04716i −0.0619500 + 0.107301i
\(365\) 5.58428 9.67227i 0.292295 0.506269i
\(366\) 0 0
\(367\) −10.6291 18.4102i −0.554836 0.961005i −0.997916 0.0645226i \(-0.979448\pi\)
0.443080 0.896482i \(-0.353886\pi\)
\(368\) 28.9610 1.50970
\(369\) 0 0
\(370\) −6.44808 −0.335220
\(371\) 5.56033 + 9.63077i 0.288678 + 0.500005i
\(372\) 0 0
\(373\) −1.15504 + 2.00059i −0.0598059 + 0.103587i −0.894378 0.447312i \(-0.852381\pi\)
0.834572 + 0.550898i \(0.185715\pi\)
\(374\) 2.97059 5.14521i 0.153605 0.266052i
\(375\) 0 0
\(376\) 1.68671 + 2.92147i 0.0869855 + 0.150663i
\(377\) 3.89737 0.200725
\(378\) 0 0
\(379\) 12.5539 0.644850 0.322425 0.946595i \(-0.395502\pi\)
0.322425 + 0.946595i \(0.395502\pi\)
\(380\) 1.27872 + 2.21481i 0.0655969 + 0.113617i
\(381\) 0 0
\(382\) 8.26032 14.3073i 0.422635 0.732025i
\(383\) 9.82727 17.0213i 0.502150 0.869749i −0.497847 0.867265i \(-0.665876\pi\)
0.999997 0.00248418i \(-0.000790741\pi\)
\(384\) 0 0
\(385\) 4.12931 + 7.15218i 0.210449 + 0.364509i
\(386\) −18.7524 −0.954472
\(387\) 0 0
\(388\) −0.283447 −0.0143898
\(389\) 9.42129 + 16.3182i 0.477679 + 0.827364i 0.999673 0.0255856i \(-0.00814502\pi\)
−0.521994 + 0.852949i \(0.674812\pi\)
\(390\) 0 0
\(391\) 5.50614 9.53691i 0.278457 0.482302i
\(392\) 8.17324 14.1565i 0.412811 0.715009i
\(393\) 0 0
\(394\) −7.63969 13.2323i −0.384882 0.666636i
\(395\) −13.9531 −0.702058
\(396\) 0 0
\(397\) 20.1178 1.00968 0.504841 0.863212i \(-0.331551\pi\)
0.504841 + 0.863212i \(0.331551\pi\)
\(398\) 12.3496 + 21.3901i 0.619028 + 1.07219i
\(399\) 0 0
\(400\) −9.25360 + 16.0277i −0.462680 + 0.801385i
\(401\) 15.4028 26.6785i 0.769181 1.33226i −0.168826 0.985646i \(-0.553998\pi\)
0.938007 0.346615i \(-0.112669\pi\)
\(402\) 0 0
\(403\) 0.491061 + 0.850542i 0.0244615 + 0.0423685i
\(404\) −14.3650 −0.714684
\(405\) 0 0
\(406\) 34.9549 1.73478
\(407\) 3.17614 + 5.50124i 0.157435 + 0.272686i
\(408\) 0 0
\(409\) −19.8460 + 34.3743i −0.981323 + 1.69970i −0.324067 + 0.946034i \(0.605050\pi\)
−0.657256 + 0.753667i \(0.728283\pi\)
\(410\) 1.70532 2.95369i 0.0842196 0.145873i
\(411\) 0 0
\(412\) 6.52655 + 11.3043i 0.321540 + 0.556923i
\(413\) 44.0146 2.16582
\(414\) 0 0
\(415\) 13.1966 0.647798
\(416\) −1.61347 2.79460i −0.0791067 0.137017i
\(417\) 0 0
\(418\) 4.31187 7.46838i 0.210900 0.365290i
\(419\) −7.72057 + 13.3724i −0.377174 + 0.653285i −0.990650 0.136429i \(-0.956438\pi\)
0.613476 + 0.789714i \(0.289771\pi\)
\(420\) 0 0
\(421\) 9.04682 + 15.6696i 0.440915 + 0.763687i 0.997758 0.0669307i \(-0.0213206\pi\)
−0.556843 + 0.830618i \(0.687987\pi\)
\(422\) 13.2091 0.643009
\(423\) 0 0
\(424\) −5.61674 −0.272773
\(425\) 3.51864 + 6.09446i 0.170679 + 0.295625i
\(426\) 0 0
\(427\) 10.2236 17.7078i 0.494754 0.856939i
\(428\) 6.82240 11.8167i 0.329773 0.571184i
\(429\) 0 0
\(430\) 4.77529 + 8.27104i 0.230285 + 0.398865i
\(431\) −28.9683 −1.39535 −0.697677 0.716412i \(-0.745783\pi\)
−0.697677 + 0.716412i \(0.745783\pi\)
\(432\) 0 0
\(433\) −37.5902 −1.80647 −0.903235 0.429146i \(-0.858815\pi\)
−0.903235 + 0.429146i \(0.858815\pi\)
\(434\) 4.40425 + 7.62838i 0.211411 + 0.366174i
\(435\) 0 0
\(436\) 1.94746 3.37309i 0.0932662 0.161542i
\(437\) 7.99227 13.8430i 0.382322 0.662201i
\(438\) 0 0
\(439\) −5.13177 8.88848i −0.244926 0.424224i 0.717185 0.696883i \(-0.245430\pi\)
−0.962111 + 0.272659i \(0.912097\pi\)
\(440\) −4.17120 −0.198854
\(441\) 0 0
\(442\) −2.32697 −0.110683
\(443\) −10.9543 18.9733i −0.520452 0.901450i −0.999717 0.0237794i \(-0.992430\pi\)
0.479265 0.877670i \(-0.340903\pi\)
\(444\) 0 0
\(445\) −3.23543 + 5.60393i −0.153374 + 0.265652i
\(446\) 7.34633 12.7242i 0.347859 0.602509i
\(447\) 0 0
\(448\) 4.95462 + 8.58165i 0.234084 + 0.405445i
\(449\) 9.97130 0.470575 0.235287 0.971926i \(-0.424397\pi\)
0.235287 + 0.971926i \(0.424397\pi\)
\(450\) 0 0
\(451\) −3.35996 −0.158214
\(452\) −8.23188 14.2580i −0.387195 0.670642i
\(453\) 0 0
\(454\) −3.41932 + 5.92244i −0.160477 + 0.277954i
\(455\) 1.61732 2.80128i 0.0758211 0.131326i
\(456\) 0 0
\(457\) 3.80905 + 6.59747i 0.178180 + 0.308617i 0.941257 0.337691i \(-0.109646\pi\)
−0.763077 + 0.646307i \(0.776312\pi\)
\(458\) 27.1566 1.26894
\(459\) 0 0
\(460\) 5.43375 0.253350
\(461\) 11.4003 + 19.7458i 0.530963 + 0.919656i 0.999347 + 0.0361304i \(0.0115032\pi\)
−0.468384 + 0.883525i \(0.655164\pi\)
\(462\) 0 0
\(463\) 4.39787 7.61733i 0.204386 0.354007i −0.745551 0.666449i \(-0.767813\pi\)
0.949937 + 0.312442i \(0.101147\pi\)
\(464\) −13.2188 + 22.8956i −0.613668 + 1.06290i
\(465\) 0 0
\(466\) −14.4669 25.0574i −0.670166 1.16076i
\(467\) −10.9976 −0.508906 −0.254453 0.967085i \(-0.581895\pi\)
−0.254453 + 0.967085i \(0.581895\pi\)
\(468\) 0 0
\(469\) 7.38406 0.340964
\(470\) 1.62210 + 2.80956i 0.0748220 + 0.129596i
\(471\) 0 0
\(472\) −11.1153 + 19.2523i −0.511623 + 0.886157i
\(473\) 4.70434 8.14816i 0.216306 0.374653i
\(474\) 0 0
\(475\) 5.10738 + 8.84624i 0.234343 + 0.405893i
\(476\) −6.09728 −0.279468
\(477\) 0 0
\(478\) −2.58094 −0.118049
\(479\) −12.8463 22.2504i −0.586961 1.01665i −0.994628 0.103515i \(-0.966991\pi\)
0.407667 0.913131i \(-0.366342\pi\)
\(480\) 0 0
\(481\) 1.24399 2.15466i 0.0567212 0.0982440i
\(482\) 4.64072 8.03797i 0.211379 0.366119i
\(483\) 0 0
\(484\) 3.09607 + 5.36255i 0.140731 + 0.243752i
\(485\) 0.387861 0.0176119
\(486\) 0 0
\(487\) −30.3800 −1.37665 −0.688325 0.725402i \(-0.741654\pi\)
−0.688325 + 0.725402i \(0.741654\pi\)
\(488\) 5.16365 + 8.94370i 0.233747 + 0.404862i
\(489\) 0 0
\(490\) 7.86016 13.6142i 0.355086 0.615027i
\(491\) −4.35414 + 7.54159i −0.196499 + 0.340347i −0.947391 0.320078i \(-0.896291\pi\)
0.750892 + 0.660425i \(0.229624\pi\)
\(492\) 0 0
\(493\) 5.02639 + 8.70596i 0.226377 + 0.392097i
\(494\) −3.37764 −0.151967
\(495\) 0 0
\(496\) −6.66217 −0.299140
\(497\) −23.8129 41.2451i −1.06815 1.85010i
\(498\) 0 0
\(499\) −5.81774 + 10.0766i −0.260438 + 0.451091i −0.966358 0.257200i \(-0.917200\pi\)
0.705921 + 0.708291i \(0.250534\pi\)
\(500\) −4.06719 + 7.04458i −0.181890 + 0.315043i
\(501\) 0 0
\(502\) 18.0201 + 31.2118i 0.804277 + 1.39305i
\(503\) −37.7991 −1.68538 −0.842689 0.538400i \(-0.819029\pi\)
−0.842689 + 0.538400i \(0.819029\pi\)
\(504\) 0 0
\(505\) 19.6566 0.874708
\(506\) −9.16135 15.8679i −0.407272 0.705416i
\(507\) 0 0
\(508\) −0.441400 + 0.764527i −0.0195840 + 0.0339204i
\(509\) −11.7868 + 20.4154i −0.522442 + 0.904896i 0.477217 + 0.878785i \(0.341645\pi\)
−0.999659 + 0.0261103i \(0.991688\pi\)
\(510\) 0 0
\(511\) 19.3251 + 33.4720i 0.854891 + 1.48072i
\(512\) 2.26711 0.100193
\(513\) 0 0
\(514\) −24.8548 −1.09630
\(515\) −8.93074 15.4685i −0.393536 0.681623i
\(516\) 0 0
\(517\) 1.59800 2.76782i 0.0702801 0.121729i
\(518\) 11.1572 19.3248i 0.490218 0.849083i
\(519\) 0 0
\(520\) 0.816864 + 1.41485i 0.0358218 + 0.0620453i
\(521\) 7.86948 0.344768 0.172384 0.985030i \(-0.444853\pi\)
0.172384 + 0.985030i \(0.444853\pi\)
\(522\) 0 0
\(523\) 33.2935 1.45582 0.727911 0.685672i \(-0.240491\pi\)
0.727911 + 0.685672i \(0.240491\pi\)
\(524\) −3.15340 5.46185i −0.137757 0.238602i
\(525\) 0 0
\(526\) −2.35559 + 4.08001i −0.102709 + 0.177897i
\(527\) −1.26663 + 2.19387i −0.0551752 + 0.0955663i
\(528\) 0 0
\(529\) −5.48104 9.49344i −0.238306 0.412758i
\(530\) −5.40159 −0.234630
\(531\) 0 0
\(532\) −8.85032 −0.383710
\(533\) 0.657995 + 1.13968i 0.0285009 + 0.0493650i
\(534\) 0 0
\(535\) −9.33558 + 16.1697i −0.403612 + 0.699077i
\(536\) −1.86474 + 3.22983i −0.0805447 + 0.139507i
\(537\) 0 0
\(538\) 0.299646 + 0.519002i 0.0129186 + 0.0223758i
\(539\) −15.4868 −0.667062
\(540\) 0 0
\(541\) 22.4283 0.964266 0.482133 0.876098i \(-0.339862\pi\)
0.482133 + 0.876098i \(0.339862\pi\)
\(542\) 10.2087 + 17.6820i 0.438503 + 0.759509i
\(543\) 0 0
\(544\) 4.16173 7.20833i 0.178433 0.309055i
\(545\) −2.66484 + 4.61564i −0.114149 + 0.197712i
\(546\) 0 0
\(547\) 10.4456 + 18.0923i 0.446621 + 0.773570i 0.998164 0.0605770i \(-0.0192941\pi\)
−0.551543 + 0.834146i \(0.685961\pi\)
\(548\) 12.9190 0.551870
\(549\) 0 0
\(550\) 11.7089 0.499271
\(551\) 7.29591 + 12.6369i 0.310816 + 0.538349i
\(552\) 0 0
\(553\) 24.1432 41.8173i 1.02667 1.77825i
\(554\) −21.0030 + 36.3782i −0.892330 + 1.54556i
\(555\) 0 0
\(556\) −3.57300 6.18862i −0.151529 0.262456i
\(557\) 8.57840 0.363478 0.181739 0.983347i \(-0.441827\pi\)
0.181739 + 0.983347i \(0.441827\pi\)
\(558\) 0 0
\(559\) −3.68508 −0.155862
\(560\) 10.9710 + 19.0023i 0.463609 + 0.802995i
\(561\) 0 0
\(562\) −6.15455 + 10.6600i −0.259614 + 0.449665i
\(563\) 7.85744 13.6095i 0.331152 0.573571i −0.651586 0.758574i \(-0.725896\pi\)
0.982738 + 0.185003i \(0.0592295\pi\)
\(564\) 0 0
\(565\) 11.2643 + 19.5103i 0.473892 + 0.820804i
\(566\) −24.1851 −1.01658
\(567\) 0 0
\(568\) 24.0545 1.00930
\(569\) −6.33639 10.9750i −0.265635 0.460094i 0.702094 0.712084i \(-0.252248\pi\)
−0.967730 + 0.251990i \(0.918915\pi\)
\(570\) 0 0
\(571\) 13.1613 22.7961i 0.550785 0.953988i −0.447433 0.894317i \(-0.647662\pi\)
0.998218 0.0596704i \(-0.0190050\pi\)
\(572\) −0.565565 + 0.979587i −0.0236474 + 0.0409586i
\(573\) 0 0
\(574\) 5.90145 + 10.2216i 0.246322 + 0.426642i
\(575\) 21.7031 0.905082
\(576\) 0 0
\(577\) −22.1154 −0.920676 −0.460338 0.887744i \(-0.652272\pi\)
−0.460338 + 0.887744i \(0.652272\pi\)
\(578\) 11.2867 + 19.5491i 0.469465 + 0.813136i
\(579\) 0 0
\(580\) −2.48015 + 4.29575i −0.102983 + 0.178371i
\(581\) −22.8343 + 39.5502i −0.947326 + 1.64082i
\(582\) 0 0
\(583\) 2.66067 + 4.60842i 0.110194 + 0.190861i
\(584\) −19.5211 −0.807790
\(585\) 0 0
\(586\) −24.2312 −1.00098
\(587\) −7.15157 12.3869i −0.295177 0.511261i 0.679849 0.733352i \(-0.262045\pi\)
−0.975026 + 0.222091i \(0.928712\pi\)
\(588\) 0 0
\(589\) −1.83854 + 3.18444i −0.0757556 + 0.131213i
\(590\) −10.6895 + 18.5148i −0.440081 + 0.762242i
\(591\) 0 0
\(592\) 8.43856 + 14.6160i 0.346823 + 0.600714i
\(593\) 47.7300 1.96004 0.980018 0.198908i \(-0.0637397\pi\)
0.980018 + 0.198908i \(0.0637397\pi\)
\(594\) 0 0
\(595\) 8.34334 0.342044
\(596\) 1.01690 + 1.76132i 0.0416539 + 0.0721466i
\(597\) 0 0
\(598\) −3.58821 + 6.21496i −0.146733 + 0.254149i
\(599\) 0.249785 0.432640i 0.0102059 0.0176772i −0.860877 0.508813i \(-0.830085\pi\)
0.871083 + 0.491135i \(0.163418\pi\)
\(600\) 0 0
\(601\) 8.46354 + 14.6593i 0.345235 + 0.597965i 0.985396 0.170276i \(-0.0544659\pi\)
−0.640161 + 0.768240i \(0.721133\pi\)
\(602\) −33.0509 −1.34705
\(603\) 0 0
\(604\) −8.67846 −0.353121
\(605\) −4.23658 7.33797i −0.172241 0.298331i
\(606\) 0 0
\(607\) −0.347316 + 0.601569i −0.0140971 + 0.0244170i −0.872988 0.487742i \(-0.837821\pi\)
0.858891 + 0.512159i \(0.171154\pi\)
\(608\) 6.04084 10.4630i 0.244988 0.424332i
\(609\) 0 0
\(610\) 4.96586 + 8.60112i 0.201062 + 0.348249i
\(611\) −1.25177 −0.0506413
\(612\) 0 0
\(613\) −32.6633 −1.31926 −0.659630 0.751590i \(-0.729287\pi\)
−0.659630 + 0.751590i \(0.729287\pi\)
\(614\) 25.5772 + 44.3011i 1.03221 + 1.78785i
\(615\) 0 0
\(616\) 7.21747 12.5010i 0.290800 0.503681i
\(617\) −11.4422 + 19.8185i −0.460646 + 0.797863i −0.998993 0.0448606i \(-0.985716\pi\)
0.538347 + 0.842723i \(0.319049\pi\)
\(618\) 0 0
\(619\) −4.24287 7.34886i −0.170535 0.295376i 0.768072 0.640364i \(-0.221216\pi\)
−0.938607 + 0.344988i \(0.887883\pi\)
\(620\) −1.24998 −0.0502002
\(621\) 0 0
\(622\) −23.5254 −0.943282
\(623\) −11.1966 19.3931i −0.448582 0.776966i
\(624\) 0 0
\(625\) −3.74490 + 6.48635i −0.149796 + 0.259454i
\(626\) −18.5636 + 32.1531i −0.741952 + 1.28510i
\(627\) 0 0
\(628\) −0.148563 0.257318i −0.00592829 0.0102681i
\(629\) 6.41744 0.255880
\(630\) 0 0
\(631\) 1.59173 0.0633657 0.0316829 0.999498i \(-0.489913\pi\)
0.0316829 + 0.999498i \(0.489913\pi\)
\(632\) 12.1941 + 21.1208i 0.485054 + 0.840138i
\(633\) 0 0
\(634\) −14.6145 + 25.3130i −0.580414 + 1.00531i
\(635\) 0.603999 1.04616i 0.0239690 0.0415155i
\(636\) 0 0
\(637\) 3.03284 + 5.25303i 0.120165 + 0.208133i
\(638\) 16.7263 0.662199
\(639\) 0 0
\(640\) −14.7640 −0.583597
\(641\) −10.8373 18.7708i −0.428049 0.741402i 0.568651 0.822579i \(-0.307466\pi\)
−0.996700 + 0.0811767i \(0.974132\pi\)
\(642\) 0 0
\(643\) 3.45103 5.97736i 0.136095 0.235724i −0.789920 0.613210i \(-0.789878\pi\)
0.926015 + 0.377486i \(0.123211\pi\)
\(644\) −9.40207 + 16.2849i −0.370493 + 0.641713i
\(645\) 0 0
\(646\) −4.35610 7.54499i −0.171388 0.296854i
\(647\) −6.18972 −0.243343 −0.121671 0.992570i \(-0.538825\pi\)
−0.121671 + 0.992570i \(0.538825\pi\)
\(648\) 0 0
\(649\) 21.0614 0.826733
\(650\) −2.29301 3.97161i −0.0899392 0.155779i
\(651\) 0 0
\(652\) −6.03357 + 10.4504i −0.236293 + 0.409271i
\(653\) 13.6072 23.5684i 0.532492 0.922304i −0.466788 0.884369i \(-0.654589\pi\)
0.999280 0.0379345i \(-0.0120778\pi\)
\(654\) 0 0
\(655\) 4.31503 + 7.47385i 0.168602 + 0.292027i
\(656\) −8.92694 −0.348539
\(657\) 0 0
\(658\) −11.2270 −0.437672
\(659\) −2.64100 4.57434i −0.102879 0.178191i 0.809991 0.586443i \(-0.199472\pi\)
−0.912870 + 0.408251i \(0.866139\pi\)
\(660\) 0 0
\(661\) −5.83252 + 10.1022i −0.226859 + 0.392931i −0.956875 0.290498i \(-0.906179\pi\)
0.730017 + 0.683429i \(0.239512\pi\)
\(662\) −0.726278 + 1.25795i −0.0282276 + 0.0488916i
\(663\) 0 0
\(664\) −11.5330 19.9757i −0.447566 0.775207i
\(665\) 12.1105 0.469626
\(666\) 0 0
\(667\) 31.0030 1.20044
\(668\) −0.898044 1.55546i −0.0347464 0.0601824i
\(669\) 0 0
\(670\) −1.79332 + 3.10611i −0.0692818 + 0.120000i
\(671\) 4.89208 8.47333i 0.188857 0.327109i
\(672\) 0 0
\(673\) −24.5512 42.5239i −0.946380 1.63918i −0.752965 0.658061i \(-0.771377\pi\)
−0.193415 0.981117i \(-0.561956\pi\)
\(674\) 0.703510 0.0270982
\(675\) 0 0
\(676\) −10.2880 −0.395693
\(677\) 11.3095 + 19.5887i 0.434660 + 0.752854i 0.997268 0.0738704i \(-0.0235351\pi\)
−0.562608 + 0.826724i \(0.690202\pi\)
\(678\) 0 0
\(679\) −0.671120 + 1.16241i −0.0257552 + 0.0446093i
\(680\) −2.10700 + 3.64942i −0.0807996 + 0.139949i
\(681\) 0 0
\(682\) 2.10747 + 3.65025i 0.0806993 + 0.139775i
\(683\) −17.1386 −0.655791 −0.327896 0.944714i \(-0.606339\pi\)
−0.327896 + 0.944714i \(0.606339\pi\)
\(684\) 0 0
\(685\) −17.6779 −0.675439
\(686\) 4.20409 + 7.28170i 0.160513 + 0.278017i
\(687\) 0 0
\(688\) 12.4988 21.6485i 0.476511 0.825341i
\(689\) 1.04210 1.80497i 0.0397008 0.0687639i
\(690\) 0 0
\(691\) −9.12796 15.8101i −0.347244 0.601444i 0.638515 0.769609i \(-0.279549\pi\)
−0.985759 + 0.168165i \(0.946216\pi\)
\(692\) −14.5010 −0.551244
\(693\) 0 0
\(694\) 39.3497 1.49370
\(695\) 4.88919 + 8.46833i 0.185458 + 0.321222i
\(696\) 0 0
\(697\) −1.69721 + 2.93966i −0.0642866 + 0.111348i
\(698\) −17.7978 + 30.8268i −0.673658 + 1.16681i
\(699\) 0 0
\(700\) −6.00829 10.4067i −0.227092 0.393335i
\(701\) −2.92075 −0.110315 −0.0551575 0.998478i \(-0.517566\pi\)
−0.0551575 + 0.998478i \(0.517566\pi\)
\(702\) 0 0
\(703\) 9.31505 0.351324
\(704\) 2.37083 + 4.10640i 0.0893540 + 0.154766i
\(705\) 0 0
\(706\) −19.7881 + 34.2740i −0.744734 + 1.28992i
\(707\) −34.0120 + 58.9106i −1.27915 + 2.21556i
\(708\) 0 0
\(709\) −15.0137 26.0044i −0.563850 0.976617i −0.997156 0.0753698i \(-0.975986\pi\)
0.433306 0.901247i \(-0.357347\pi\)
\(710\) 23.1331 0.868169
\(711\) 0 0
\(712\) 11.3102 0.423867
\(713\) 3.90631 + 6.76593i 0.146292 + 0.253386i
\(714\) 0 0
\(715\) 0.773903 1.34044i 0.0289423 0.0501296i
\(716\) −0.414578 + 0.718071i −0.0154935 + 0.0268356i
\(717\) 0 0
\(718\) 8.79195 + 15.2281i 0.328113 + 0.568308i
\(719\) 40.0569 1.49387 0.746936 0.664896i \(-0.231524\pi\)
0.746936 + 0.664896i \(0.231524\pi\)
\(720\) 0 0
\(721\) 61.8118 2.30199
\(722\) 9.64570 + 16.7068i 0.358976 + 0.621764i
\(723\) 0 0
\(724\) 8.73890 15.1362i 0.324779 0.562533i
\(725\) −9.90607 + 17.1578i −0.367902 + 0.637225i
\(726\) 0 0
\(727\) 0.769390 + 1.33262i 0.0285351 + 0.0494243i 0.879940 0.475084i \(-0.157582\pi\)
−0.851405 + 0.524509i \(0.824249\pi\)
\(728\) −5.65371 −0.209540
\(729\) 0 0
\(730\) −18.7734 −0.694834
\(731\) −4.75260 8.23174i −0.175781 0.304462i
\(732\) 0 0
\(733\) 0.755947 1.30934i 0.0279215 0.0483615i −0.851727 0.523986i \(-0.824444\pi\)
0.879649 + 0.475624i \(0.157778\pi\)
\(734\) −17.8666 + 30.9459i −0.659470 + 1.14224i
\(735\) 0 0
\(736\) −12.8349 22.2306i −0.473099 0.819432i
\(737\) 3.53334 0.130152
\(738\) 0 0
\(739\) 21.3558 0.785584 0.392792 0.919627i \(-0.371509\pi\)
0.392792 + 0.919627i \(0.371509\pi\)
\(740\) 1.58327 + 2.74230i 0.0582021 + 0.100809i
\(741\) 0 0
\(742\) 9.34643 16.1885i 0.343118 0.594298i
\(743\) 10.1644 17.6052i 0.372895 0.645872i −0.617115 0.786873i \(-0.711699\pi\)
0.990009 + 0.141001i \(0.0450320\pi\)
\(744\) 0 0
\(745\) −1.39150 2.41015i −0.0509806 0.0883009i
\(746\) 3.88305 0.142169
\(747\) 0 0
\(748\) −2.91760 −0.106678
\(749\) −32.3069 55.9572i −1.18047 2.04463i
\(750\) 0 0
\(751\) −2.13158 + 3.69200i −0.0777824 + 0.134723i −0.902293 0.431124i \(-0.858117\pi\)
0.824510 + 0.565847i \(0.191451\pi\)
\(752\) 4.24567 7.35371i 0.154824 0.268162i
\(753\) 0 0
\(754\) −3.27557 5.67346i −0.119289 0.206615i
\(755\) 11.8754 0.432189
\(756\) 0 0
\(757\) 54.3419 1.97509 0.987546 0.157332i \(-0.0502892\pi\)
0.987546 + 0.157332i \(0.0502892\pi\)
\(758\) −10.5510 18.2748i −0.383229 0.663772i
\(759\) 0 0
\(760\) −3.05835 + 5.29721i −0.110938 + 0.192150i
\(761\) −9.08056 + 15.7280i −0.329170 + 0.570139i −0.982347 0.187066i \(-0.940102\pi\)
0.653177 + 0.757205i \(0.273436\pi\)
\(762\) 0 0
\(763\) −9.22201 15.9730i −0.333859 0.578261i
\(764\) −8.11299 −0.293518
\(765\) 0 0
\(766\) −33.0375 −1.19369
\(767\) −4.12454 7.14392i −0.148929 0.257952i
\(768\) 0 0
\(769\) −12.4274 + 21.5248i −0.448142 + 0.776205i −0.998265 0.0588785i \(-0.981248\pi\)
0.550123 + 0.835084i \(0.314581\pi\)
\(770\) 6.94101 12.0222i 0.250137 0.433249i
\(771\) 0 0
\(772\) 4.60448 + 7.97520i 0.165719 + 0.287034i
\(773\) 38.4832 1.38414 0.692071 0.721829i \(-0.256698\pi\)
0.692071 + 0.721829i \(0.256698\pi\)
\(774\) 0 0
\(775\) −4.99257 −0.179338
\(776\) −0.338964 0.587103i −0.0121681 0.0210758i
\(777\) 0 0
\(778\) 15.8364 27.4294i 0.567761 0.983391i
\(779\) −2.46354 + 4.26698i −0.0882655 + 0.152880i
\(780\) 0 0
\(781\) −11.3947 19.7362i −0.407734 0.706216i
\(782\) −18.5107 −0.661940
\(783\) 0 0
\(784\) −41.1462 −1.46951
\(785\) 0.203289 + 0.352107i 0.00725569 + 0.0125672i
\(786\) 0 0