Properties

Label 980.2.g.a.391.20
Level $980$
Weight $2$
Character 980.391
Analytic conductor $7.825$
Analytic rank $0$
Dimension $32$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [980,2,Mod(391,980)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(980, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("980.391");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 980.g (of order \(2\), degree \(1\), 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: \(7.82533939809\)
Analytic rank: \(0\)
Dimension: \(32\)
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 391.20
Character \(\chi\) \(=\) 980.391
Dual form 980.2.g.a.391.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0982654 + 1.41080i) q^{2} +0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} +1.00000i q^{5} +(0.0650866 + 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +O(q^{10})\) \(q+(0.0982654 + 1.41080i) q^{2} +0.662355 q^{3} +(-1.98069 + 0.277265i) q^{4} +1.00000i q^{5} +(0.0650866 + 0.934447i) q^{6} +(-0.585797 - 2.76710i) q^{8} -2.56129 q^{9} +(-1.41080 + 0.0982654i) q^{10} -3.61296i q^{11} +(-1.31192 + 0.183648i) q^{12} -5.83027i q^{13} +0.662355i q^{15} +(3.84625 - 1.09835i) q^{16} -1.36813i q^{17} +(-0.251686 - 3.61345i) q^{18} -4.09577 q^{19} +(-0.277265 - 1.98069i) q^{20} +(5.09715 - 0.355029i) q^{22} -3.24519i q^{23} +(-0.388005 - 1.83280i) q^{24} -1.00000 q^{25} +(8.22532 - 0.572914i) q^{26} -3.68354 q^{27} +5.19327 q^{29} +(-0.934447 + 0.0650866i) q^{30} -8.86809 q^{31} +(1.92750 + 5.31834i) q^{32} -2.39306i q^{33} +(1.93014 - 0.134439i) q^{34} +(5.07311 - 0.710155i) q^{36} +10.7958 q^{37} +(-0.402472 - 5.77829i) q^{38} -3.86171i q^{39} +(2.76710 - 0.585797i) q^{40} +0.832730i q^{41} +3.10642i q^{43} +(1.00175 + 7.15615i) q^{44} -2.56129i q^{45} +(4.57830 - 0.318890i) q^{46} -6.89601 q^{47} +(2.54758 - 0.727497i) q^{48} +(-0.0982654 - 1.41080i) q^{50} -0.906184i q^{51} +(1.61653 + 11.5479i) q^{52} -7.41752 q^{53} +(-0.361965 - 5.19673i) q^{54} +3.61296 q^{55} -2.71285 q^{57} +(0.510319 + 7.32664i) q^{58} +7.47856 q^{59} +(-0.183648 - 1.31192i) q^{60} -1.48554i q^{61} +(-0.871427 - 12.5111i) q^{62} +(-7.31368 + 3.24192i) q^{64} +5.83027 q^{65} +(3.37612 - 0.235155i) q^{66} -2.53761i q^{67} +(0.379333 + 2.70983i) q^{68} -2.14947i q^{69} -3.52502i q^{71} +(1.50039 + 7.08734i) q^{72} -5.16984i q^{73} +(1.06085 + 15.2306i) q^{74} -0.662355 q^{75} +(8.11244 - 1.13561i) q^{76} +(5.44808 - 0.379472i) q^{78} -11.3401i q^{79} +(1.09835 + 3.84625i) q^{80} +5.24405 q^{81} +(-1.17481 + 0.0818286i) q^{82} -6.49145 q^{83} +1.36813 q^{85} +(-4.38252 + 0.305254i) q^{86} +3.43978 q^{87} +(-9.99743 + 2.11646i) q^{88} -9.39121i q^{89} +(3.61345 - 0.251686i) q^{90} +(0.899777 + 6.42771i) q^{92} -5.87382 q^{93} +(-0.677640 - 9.72886i) q^{94} -4.09577i q^{95} +(1.27669 + 3.52263i) q^{96} +0.343189i q^{97} +9.25383i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 32 q - 4 q^{2} + 4 q^{4} - 4 q^{8} + 32 q^{9} + 28 q^{16} - 8 q^{22} - 32 q^{25} - 40 q^{29} - 4 q^{32} + 60 q^{36} - 16 q^{37} + 36 q^{44} - 4 q^{46} + 4 q^{50} + 16 q^{53} + 48 q^{57} - 4 q^{58} - 28 q^{60} + 4 q^{64} - 8 q^{65} - 8 q^{72} - 76 q^{74} + 120 q^{78} + 72 q^{81} - 56 q^{86} - 8 q^{88} - 4 q^{92} + 16 q^{93}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\) \(491\)
\(\chi(n)\) \(-1\) \(1\) \(-1\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0982654 + 1.41080i 0.0694842 + 0.997583i
\(3\) 0.662355 0.382411 0.191205 0.981550i \(-0.438760\pi\)
0.191205 + 0.981550i \(0.438760\pi\)
\(4\) −1.98069 + 0.277265i −0.990344 + 0.138632i
\(5\) 1.00000i 0.447214i
\(6\) 0.0650866 + 0.934447i 0.0265715 + 0.381486i
\(7\) 0 0
\(8\) −0.585797 2.76710i −0.207111 0.978318i
\(9\) −2.56129 −0.853762
\(10\) −1.41080 + 0.0982654i −0.446133 + 0.0310743i
\(11\) 3.61296i 1.08935i −0.838648 0.544674i \(-0.816653\pi\)
0.838648 0.544674i \(-0.183347\pi\)
\(12\) −1.31192 + 0.183648i −0.378718 + 0.0530145i
\(13\) 5.83027i 1.61703i −0.588478 0.808513i \(-0.700273\pi\)
0.588478 0.808513i \(-0.299727\pi\)
\(14\) 0 0
\(15\) 0.662355i 0.171019i
\(16\) 3.84625 1.09835i 0.961562 0.274588i
\(17\) 1.36813i 0.331819i −0.986141 0.165910i \(-0.946944\pi\)
0.986141 0.165910i \(-0.0530560\pi\)
\(18\) −0.251686 3.61345i −0.0593229 0.851699i
\(19\) −4.09577 −0.939634 −0.469817 0.882764i \(-0.655680\pi\)
−0.469817 + 0.882764i \(0.655680\pi\)
\(20\) −0.277265 1.98069i −0.0619983 0.442895i
\(21\) 0 0
\(22\) 5.09715 0.355029i 1.08672 0.0756925i
\(23\) 3.24519i 0.676669i −0.941026 0.338334i \(-0.890136\pi\)
0.941026 0.338334i \(-0.109864\pi\)
\(24\) −0.388005 1.83280i −0.0792013 0.374119i
\(25\) −1.00000 −0.200000
\(26\) 8.22532 0.572914i 1.61312 0.112358i
\(27\) −3.68354 −0.708898
\(28\) 0 0
\(29\) 5.19327 0.964365 0.482183 0.876071i \(-0.339844\pi\)
0.482183 + 0.876071i \(0.339844\pi\)
\(30\) −0.934447 + 0.0650866i −0.170606 + 0.0118831i
\(31\) −8.86809 −1.59276 −0.796378 0.604799i \(-0.793254\pi\)
−0.796378 + 0.604799i \(0.793254\pi\)
\(32\) 1.92750 + 5.31834i 0.340737 + 0.940159i
\(33\) 2.39306i 0.416579i
\(34\) 1.93014 0.134439i 0.331017 0.0230562i
\(35\) 0 0
\(36\) 5.07311 0.710155i 0.845518 0.118359i
\(37\) 10.7958 1.77482 0.887408 0.460985i \(-0.152504\pi\)
0.887408 + 0.460985i \(0.152504\pi\)
\(38\) −0.402472 5.77829i −0.0652897 0.937363i
\(39\) 3.86171i 0.618368i
\(40\) 2.76710 0.585797i 0.437517 0.0926227i
\(41\) 0.832730i 0.130051i 0.997884 + 0.0650253i \(0.0207128\pi\)
−0.997884 + 0.0650253i \(0.979287\pi\)
\(42\) 0 0
\(43\) 3.10642i 0.473725i 0.971543 + 0.236862i \(0.0761190\pi\)
−0.971543 + 0.236862i \(0.923881\pi\)
\(44\) 1.00175 + 7.15615i 0.151019 + 1.07883i
\(45\) 2.56129i 0.381814i
\(46\) 4.57830 0.318890i 0.675033 0.0470178i
\(47\) −6.89601 −1.00589 −0.502943 0.864319i \(-0.667750\pi\)
−0.502943 + 0.864319i \(0.667750\pi\)
\(48\) 2.54758 0.727497i 0.367712 0.105005i
\(49\) 0 0
\(50\) −0.0982654 1.41080i −0.0138968 0.199517i
\(51\) 0.906184i 0.126891i
\(52\) 1.61653 + 11.5479i 0.224172 + 1.60141i
\(53\) −7.41752 −1.01887 −0.509437 0.860508i \(-0.670146\pi\)
−0.509437 + 0.860508i \(0.670146\pi\)
\(54\) −0.361965 5.19673i −0.0492572 0.707185i
\(55\) 3.61296 0.487172
\(56\) 0 0
\(57\) −2.71285 −0.359326
\(58\) 0.510319 + 7.32664i 0.0670081 + 0.962034i
\(59\) 7.47856 0.973626 0.486813 0.873506i \(-0.338159\pi\)
0.486813 + 0.873506i \(0.338159\pi\)
\(60\) −0.183648 1.31192i −0.0237088 0.169368i
\(61\) 1.48554i 0.190204i −0.995468 0.0951022i \(-0.969682\pi\)
0.995468 0.0951022i \(-0.0303178\pi\)
\(62\) −0.871427 12.5111i −0.110671 1.58891i
\(63\) 0 0
\(64\) −7.31368 + 3.24192i −0.914210 + 0.405240i
\(65\) 5.83027 0.723156
\(66\) 3.37612 0.235155i 0.415572 0.0289456i
\(67\) 2.53761i 0.310018i −0.987913 0.155009i \(-0.950459\pi\)
0.987913 0.155009i \(-0.0495407\pi\)
\(68\) 0.379333 + 2.70983i 0.0460009 + 0.328615i
\(69\) 2.14947i 0.258765i
\(70\) 0 0
\(71\) 3.52502i 0.418342i −0.977879 0.209171i \(-0.932923\pi\)
0.977879 0.209171i \(-0.0670766\pi\)
\(72\) 1.50039 + 7.08734i 0.176823 + 0.835250i
\(73\) 5.16984i 0.605084i −0.953136 0.302542i \(-0.902165\pi\)
0.953136 0.302542i \(-0.0978353\pi\)
\(74\) 1.06085 + 15.2306i 0.123322 + 1.77053i
\(75\) −0.662355 −0.0764821
\(76\) 8.11244 1.13561i 0.930561 0.130264i
\(77\) 0 0
\(78\) 5.44808 0.379472i 0.616873 0.0429668i
\(79\) 11.3401i 1.27586i −0.770094 0.637931i \(-0.779791\pi\)
0.770094 0.637931i \(-0.220209\pi\)
\(80\) 1.09835 + 3.84625i 0.122799 + 0.430024i
\(81\) 5.24405 0.582672
\(82\) −1.17481 + 0.0818286i −0.129736 + 0.00903646i
\(83\) −6.49145 −0.712529 −0.356264 0.934385i \(-0.615950\pi\)
−0.356264 + 0.934385i \(0.615950\pi\)
\(84\) 0 0
\(85\) 1.36813 0.148394
\(86\) −4.38252 + 0.305254i −0.472580 + 0.0329164i
\(87\) 3.43978 0.368783
\(88\) −9.99743 + 2.11646i −1.06573 + 0.225616i
\(89\) 9.39121i 0.995466i −0.867330 0.497733i \(-0.834166\pi\)
0.867330 0.497733i \(-0.165834\pi\)
\(90\) 3.61345 0.251686i 0.380891 0.0265300i
\(91\) 0 0
\(92\) 0.899777 + 6.42771i 0.0938083 + 0.670135i
\(93\) −5.87382 −0.609087
\(94\) −0.677640 9.72886i −0.0698932 1.00346i
\(95\) 4.09577i 0.420217i
\(96\) 1.27669 + 3.52263i 0.130302 + 0.359527i
\(97\) 0.343189i 0.0348455i 0.999848 + 0.0174228i \(0.00554612\pi\)
−0.999848 + 0.0174228i \(0.994454\pi\)
\(98\) 0 0
\(99\) 9.25383i 0.930045i
\(100\) 1.98069 0.277265i 0.198069 0.0277265i
\(101\) 4.53635i 0.451384i 0.974199 + 0.225692i \(0.0724642\pi\)
−0.974199 + 0.225692i \(0.927536\pi\)
\(102\) 1.27844 0.0890466i 0.126584 0.00881693i
\(103\) −6.13812 −0.604807 −0.302404 0.953180i \(-0.597789\pi\)
−0.302404 + 0.953180i \(0.597789\pi\)
\(104\) −16.1329 + 3.41536i −1.58196 + 0.334903i
\(105\) 0 0
\(106\) −0.728886 10.4646i −0.0707957 1.01641i
\(107\) 7.66797i 0.741291i −0.928775 0.370645i \(-0.879137\pi\)
0.928775 0.370645i \(-0.120863\pi\)
\(108\) 7.29595 1.02132i 0.702053 0.0982763i
\(109\) 1.29523 0.124061 0.0620304 0.998074i \(-0.480242\pi\)
0.0620304 + 0.998074i \(0.480242\pi\)
\(110\) 0.355029 + 5.09715i 0.0338507 + 0.485994i
\(111\) 7.15064 0.678709
\(112\) 0 0
\(113\) 7.10591 0.668468 0.334234 0.942490i \(-0.391522\pi\)
0.334234 + 0.942490i \(0.391522\pi\)
\(114\) −0.266580 3.82728i −0.0249675 0.358457i
\(115\) 3.24519 0.302616
\(116\) −10.2862 + 1.43991i −0.955053 + 0.133692i
\(117\) 14.9330i 1.38056i
\(118\) 0.734884 + 10.5507i 0.0676516 + 0.971273i
\(119\) 0 0
\(120\) 1.83280 0.388005i 0.167311 0.0354199i
\(121\) −2.05349 −0.186681
\(122\) 2.09580 0.145978i 0.189745 0.0132162i
\(123\) 0.551563i 0.0497327i
\(124\) 17.5649 2.45881i 1.57738 0.220808i
\(125\) 1.00000i 0.0894427i
\(126\) 0 0
\(127\) 17.0178i 1.51008i 0.655677 + 0.755041i \(0.272383\pi\)
−0.655677 + 0.755041i \(0.727617\pi\)
\(128\) −5.29237 9.99954i −0.467784 0.883843i
\(129\) 2.05755i 0.181157i
\(130\) 0.572914 + 8.22532i 0.0502479 + 0.721408i
\(131\) −1.20613 −0.105380 −0.0526901 0.998611i \(-0.516780\pi\)
−0.0526901 + 0.998611i \(0.516780\pi\)
\(132\) 0.663512 + 4.73991i 0.0577513 + 0.412556i
\(133\) 0 0
\(134\) 3.58005 0.249359i 0.309269 0.0215414i
\(135\) 3.68354i 0.317029i
\(136\) −3.78574 + 0.801444i −0.324624 + 0.0687233i
\(137\) 2.14490 0.183252 0.0916258 0.995794i \(-0.470794\pi\)
0.0916258 + 0.995794i \(0.470794\pi\)
\(138\) 3.03246 0.211218i 0.258140 0.0179801i
\(139\) 3.39555 0.288007 0.144004 0.989577i \(-0.454002\pi\)
0.144004 + 0.989577i \(0.454002\pi\)
\(140\) 0 0
\(141\) −4.56761 −0.384662
\(142\) 4.97308 0.346387i 0.417331 0.0290682i
\(143\) −21.0645 −1.76151
\(144\) −9.85134 + 2.81319i −0.820945 + 0.234432i
\(145\) 5.19327i 0.431277i
\(146\) 7.29359 0.508017i 0.603622 0.0420438i
\(147\) 0 0
\(148\) −21.3831 + 2.99329i −1.75768 + 0.246047i
\(149\) −19.0864 −1.56362 −0.781808 0.623519i \(-0.785703\pi\)
−0.781808 + 0.623519i \(0.785703\pi\)
\(150\) −0.0650866 0.934447i −0.00531430 0.0762973i
\(151\) 9.60595i 0.781721i 0.920450 + 0.390861i \(0.127823\pi\)
−0.920450 + 0.390861i \(0.872177\pi\)
\(152\) 2.39929 + 11.3334i 0.194608 + 0.919260i
\(153\) 3.50416i 0.283295i
\(154\) 0 0
\(155\) 8.86809i 0.712302i
\(156\) 1.07072 + 7.64883i 0.0857258 + 0.612397i
\(157\) 16.4624i 1.31384i 0.753961 + 0.656919i \(0.228141\pi\)
−0.753961 + 0.656919i \(0.771859\pi\)
\(158\) 15.9986 1.11434i 1.27278 0.0886522i
\(159\) −4.91303 −0.389629
\(160\) −5.31834 + 1.92750i −0.420452 + 0.152382i
\(161\) 0 0
\(162\) 0.515309 + 7.39828i 0.0404865 + 0.581264i
\(163\) 7.15612i 0.560510i 0.959926 + 0.280255i \(0.0904191\pi\)
−0.959926 + 0.280255i \(0.909581\pi\)
\(164\) −0.230887 1.64938i −0.0180292 0.128795i
\(165\) 2.39306 0.186300
\(166\) −0.637885 9.15810i −0.0495095 0.710807i
\(167\) −13.7127 −1.06112 −0.530562 0.847646i \(-0.678019\pi\)
−0.530562 + 0.847646i \(0.678019\pi\)
\(168\) 0 0
\(169\) −20.9920 −1.61477
\(170\) 0.134439 + 1.93014i 0.0103110 + 0.148035i
\(171\) 10.4904 0.802224
\(172\) −0.861301 6.15285i −0.0656736 0.469150i
\(173\) 3.92439i 0.298366i −0.988810 0.149183i \(-0.952336\pi\)
0.988810 0.149183i \(-0.0476643\pi\)
\(174\) 0.338012 + 4.85283i 0.0256246 + 0.367892i
\(175\) 0 0
\(176\) −3.96830 13.8963i −0.299122 1.04748i
\(177\) 4.95346 0.372325
\(178\) 13.2491 0.922831i 0.993060 0.0691691i
\(179\) 20.5539i 1.53627i −0.640289 0.768134i \(-0.721185\pi\)
0.640289 0.768134i \(-0.278815\pi\)
\(180\) 0.710155 + 5.07311i 0.0529318 + 0.378127i
\(181\) 13.0603i 0.970762i 0.874303 + 0.485381i \(0.161319\pi\)
−0.874303 + 0.485381i \(0.838681\pi\)
\(182\) 0 0
\(183\) 0.983957i 0.0727362i
\(184\) −8.97976 + 1.90102i −0.661997 + 0.140145i
\(185\) 10.7958i 0.793722i
\(186\) −0.577194 8.28676i −0.0423219 0.607615i
\(187\) −4.94298 −0.361467
\(188\) 13.6588 1.91202i 0.996174 0.139449i
\(189\) 0 0
\(190\) 5.77829 0.402472i 0.419201 0.0291984i
\(191\) 12.4751i 0.902667i −0.892355 0.451334i \(-0.850948\pi\)
0.892355 0.451334i \(-0.149052\pi\)
\(192\) −4.84425 + 2.14730i −0.349604 + 0.154968i
\(193\) 19.0645 1.37229 0.686147 0.727463i \(-0.259301\pi\)
0.686147 + 0.727463i \(0.259301\pi\)
\(194\) −0.484169 + 0.0337236i −0.0347613 + 0.00242121i
\(195\) 3.86171 0.276543
\(196\) 0 0
\(197\) 1.93188 0.137641 0.0688203 0.997629i \(-0.478076\pi\)
0.0688203 + 0.997629i \(0.478076\pi\)
\(198\) −13.0553 + 0.909332i −0.927797 + 0.0646234i
\(199\) 20.5646 1.45778 0.728892 0.684629i \(-0.240036\pi\)
0.728892 + 0.684629i \(0.240036\pi\)
\(200\) 0.585797 + 2.76710i 0.0414221 + 0.195664i
\(201\) 1.68080i 0.118554i
\(202\) −6.39986 + 0.445766i −0.450293 + 0.0313640i
\(203\) 0 0
\(204\) 0.251253 + 1.79487i 0.0175912 + 0.125666i
\(205\) −0.832730 −0.0581604
\(206\) −0.603165 8.65963i −0.0420245 0.603345i
\(207\) 8.31186i 0.577714i
\(208\) −6.40368 22.4247i −0.444015 1.55487i
\(209\) 14.7979i 1.02359i
\(210\) 0 0
\(211\) 9.98398i 0.687326i −0.939093 0.343663i \(-0.888332\pi\)
0.939093 0.343663i \(-0.111668\pi\)
\(212\) 14.6918 2.05662i 1.00904 0.141249i
\(213\) 2.33481i 0.159979i
\(214\) 10.8179 0.753496i 0.739499 0.0515079i
\(215\) −3.10642 −0.211856
\(216\) 2.15781 + 10.1927i 0.146820 + 0.693528i
\(217\) 0 0
\(218\) 0.127277 + 1.82731i 0.00862026 + 0.123761i
\(219\) 3.42427i 0.231391i
\(220\) −7.15615 + 1.00175i −0.482467 + 0.0675378i
\(221\) −7.97654 −0.536560
\(222\) 0.702661 + 10.0881i 0.0471595 + 0.677068i
\(223\) −16.8179 −1.12621 −0.563106 0.826384i \(-0.690394\pi\)
−0.563106 + 0.826384i \(0.690394\pi\)
\(224\) 0 0
\(225\) 2.56129 0.170752
\(226\) 0.698266 + 10.0250i 0.0464479 + 0.666852i
\(227\) −19.8338 −1.31642 −0.658209 0.752835i \(-0.728686\pi\)
−0.658209 + 0.752835i \(0.728686\pi\)
\(228\) 5.37331 0.752178i 0.355856 0.0498142i
\(229\) 13.9331i 0.920725i −0.887731 0.460363i \(-0.847719\pi\)
0.887731 0.460363i \(-0.152281\pi\)
\(230\) 0.318890 + 4.57830i 0.0210270 + 0.301884i
\(231\) 0 0
\(232\) −3.04220 14.3703i −0.199730 0.943455i
\(233\) 10.2257 0.669905 0.334953 0.942235i \(-0.391280\pi\)
0.334953 + 0.942235i \(0.391280\pi\)
\(234\) −21.0674 + 1.46740i −1.37722 + 0.0959267i
\(235\) 6.89601i 0.449846i
\(236\) −14.8127 + 2.07354i −0.964225 + 0.134976i
\(237\) 7.51117i 0.487903i
\(238\) 0 0
\(239\) 17.0835i 1.10504i −0.833501 0.552518i \(-0.813667\pi\)
0.833501 0.552518i \(-0.186333\pi\)
\(240\) 0.727497 + 2.54758i 0.0469598 + 0.164446i
\(241\) 18.4837i 1.19064i −0.803489 0.595320i \(-0.797025\pi\)
0.803489 0.595320i \(-0.202975\pi\)
\(242\) −0.201787 2.89705i −0.0129714 0.186230i
\(243\) 14.5241 0.931718
\(244\) 0.411889 + 2.94240i 0.0263685 + 0.188368i
\(245\) 0 0
\(246\) −0.778142 + 0.0541995i −0.0496125 + 0.00345564i
\(247\) 23.8794i 1.51941i
\(248\) 5.19490 + 24.5389i 0.329877 + 1.55822i
\(249\) −4.29964 −0.272479
\(250\) 1.41080 0.0982654i 0.0892265 0.00621485i
\(251\) −16.5313 −1.04344 −0.521722 0.853116i \(-0.674710\pi\)
−0.521722 + 0.853116i \(0.674710\pi\)
\(252\) 0 0
\(253\) −11.7247 −0.737128
\(254\) −24.0086 + 1.67226i −1.50643 + 0.104927i
\(255\) 0.906184 0.0567475
\(256\) 13.5873 8.44906i 0.849203 0.528066i
\(257\) 6.19499i 0.386433i 0.981156 + 0.193216i \(0.0618919\pi\)
−0.981156 + 0.193216i \(0.938108\pi\)
\(258\) −2.90279 + 0.202186i −0.180720 + 0.0125876i
\(259\) 0 0
\(260\) −11.5479 + 1.61653i −0.716173 + 0.100253i
\(261\) −13.3014 −0.823338
\(262\) −0.118521 1.70161i −0.00732226 0.105126i
\(263\) 21.1536i 1.30439i 0.758053 + 0.652194i \(0.226151\pi\)
−0.758053 + 0.652194i \(0.773849\pi\)
\(264\) −6.62184 + 1.40185i −0.407546 + 0.0862778i
\(265\) 7.41752i 0.455655i
\(266\) 0 0
\(267\) 6.22031i 0.380677i
\(268\) 0.703590 + 5.02621i 0.0429786 + 0.307025i
\(269\) 30.9866i 1.88928i −0.328102 0.944642i \(-0.606409\pi\)
0.328102 0.944642i \(-0.393591\pi\)
\(270\) 5.19673 0.361965i 0.316263 0.0220285i
\(271\) 23.0381 1.39946 0.699732 0.714405i \(-0.253303\pi\)
0.699732 + 0.714405i \(0.253303\pi\)
\(272\) −1.50268 5.26215i −0.0911134 0.319065i
\(273\) 0 0
\(274\) 0.210770 + 3.02602i 0.0127331 + 0.182809i
\(275\) 3.61296i 0.217870i
\(276\) 0.595972 + 4.25742i 0.0358733 + 0.256267i
\(277\) 6.94562 0.417322 0.208661 0.977988i \(-0.433089\pi\)
0.208661 + 0.977988i \(0.433089\pi\)
\(278\) 0.333665 + 4.79043i 0.0200119 + 0.287311i
\(279\) 22.7137 1.35984
\(280\) 0 0
\(281\) −4.24391 −0.253170 −0.126585 0.991956i \(-0.540402\pi\)
−0.126585 + 0.991956i \(0.540402\pi\)
\(282\) −0.448838 6.44396i −0.0267279 0.383732i
\(283\) −8.53198 −0.507174 −0.253587 0.967313i \(-0.581610\pi\)
−0.253587 + 0.967313i \(0.581610\pi\)
\(284\) 0.977363 + 6.98195i 0.0579958 + 0.414303i
\(285\) 2.71285i 0.160695i
\(286\) −2.06992 29.7178i −0.122397 1.75725i
\(287\) 0 0
\(288\) −4.93688 13.6218i −0.290909 0.802672i
\(289\) 15.1282 0.889896
\(290\) −7.32664 + 0.510319i −0.430235 + 0.0299669i
\(291\) 0.227313i 0.0133253i
\(292\) 1.43342 + 10.2398i 0.0838843 + 0.599241i
\(293\) 25.2319i 1.47406i 0.675857 + 0.737032i \(0.263773\pi\)
−0.675857 + 0.737032i \(0.736227\pi\)
\(294\) 0 0
\(295\) 7.47856i 0.435419i
\(296\) −6.32414 29.8730i −0.367583 1.73633i
\(297\) 13.3085i 0.772238i
\(298\) −1.87553 26.9270i −0.108647 1.55984i
\(299\) −18.9203 −1.09419
\(300\) 1.31192 0.183648i 0.0757436 0.0106029i
\(301\) 0 0
\(302\) −13.5520 + 0.943933i −0.779832 + 0.0543172i
\(303\) 3.00467i 0.172614i
\(304\) −15.7533 + 4.49859i −0.903516 + 0.258012i
\(305\) 1.48554 0.0850620
\(306\) −4.94365 + 0.344338i −0.282610 + 0.0196845i
\(307\) 29.2635 1.67016 0.835078 0.550132i \(-0.185423\pi\)
0.835078 + 0.550132i \(0.185423\pi\)
\(308\) 0 0
\(309\) −4.06561 −0.231285
\(310\) 12.5111 0.871427i 0.710581 0.0494937i
\(311\) −22.7461 −1.28981 −0.644906 0.764262i \(-0.723104\pi\)
−0.644906 + 0.764262i \(0.723104\pi\)
\(312\) −10.6857 + 2.26218i −0.604960 + 0.128071i
\(313\) 6.58481i 0.372195i −0.982531 0.186098i \(-0.940416\pi\)
0.982531 0.186098i \(-0.0595841\pi\)
\(314\) −23.2250 + 1.61768i −1.31066 + 0.0912910i
\(315\) 0 0
\(316\) 3.14421 + 22.4612i 0.176876 + 1.26354i
\(317\) −14.1217 −0.793154 −0.396577 0.918001i \(-0.629802\pi\)
−0.396577 + 0.918001i \(0.629802\pi\)
\(318\) −0.482781 6.93128i −0.0270730 0.388687i
\(319\) 18.7631i 1.05053i
\(320\) −3.24192 7.31368i −0.181229 0.408847i
\(321\) 5.07891i 0.283477i
\(322\) 0 0
\(323\) 5.60352i 0.311788i
\(324\) −10.3868 + 1.45399i −0.577046 + 0.0807772i
\(325\) 5.83027i 0.323405i
\(326\) −10.0958 + 0.703199i −0.559155 + 0.0389466i
\(327\) 0.857903 0.0474422
\(328\) 2.30425 0.487811i 0.127231 0.0269349i
\(329\) 0 0
\(330\) 0.235155 + 3.37612i 0.0129449 + 0.185849i
\(331\) 20.3224i 1.11702i 0.829498 + 0.558510i \(0.188627\pi\)
−0.829498 + 0.558510i \(0.811373\pi\)
\(332\) 12.8575 1.79985i 0.705649 0.0987796i
\(333\) −27.6511 −1.51527
\(334\) −1.34749 19.3459i −0.0737313 1.05856i
\(335\) 2.53761 0.138644
\(336\) 0 0
\(337\) 15.7704 0.859067 0.429533 0.903051i \(-0.358678\pi\)
0.429533 + 0.903051i \(0.358678\pi\)
\(338\) −2.06279 29.6155i −0.112201 1.61087i
\(339\) 4.70663 0.255629
\(340\) −2.70983 + 0.379333i −0.146961 + 0.0205722i
\(341\) 32.0401i 1.73507i
\(342\) 1.03085 + 14.7999i 0.0557418 + 0.800285i
\(343\) 0 0
\(344\) 8.59578 1.81973i 0.463453 0.0981134i
\(345\) 2.14947 0.115723
\(346\) 5.53651 0.385632i 0.297644 0.0207317i
\(347\) 3.04784i 0.163616i 0.996648 + 0.0818082i \(0.0260695\pi\)
−0.996648 + 0.0818082i \(0.973930\pi\)
\(348\) −6.81314 + 0.953731i −0.365222 + 0.0511254i
\(349\) 8.40462i 0.449889i 0.974372 + 0.224944i \(0.0722201\pi\)
−0.974372 + 0.224944i \(0.927780\pi\)
\(350\) 0 0
\(351\) 21.4761i 1.14631i
\(352\) 19.2150 6.96399i 1.02416 0.371182i
\(353\) 0.432821i 0.0230367i 0.999934 + 0.0115184i \(0.00366649\pi\)
−0.999934 + 0.0115184i \(0.996334\pi\)
\(354\) 0.486754 + 6.98832i 0.0258707 + 0.371425i
\(355\) 3.52502 0.187088
\(356\) 2.60385 + 18.6011i 0.138004 + 0.985854i
\(357\) 0 0
\(358\) 28.9973 2.01973i 1.53255 0.106746i
\(359\) 26.9810i 1.42400i 0.702178 + 0.712002i \(0.252211\pi\)
−0.702178 + 0.712002i \(0.747789\pi\)
\(360\) −7.08734 + 1.50039i −0.373535 + 0.0790777i
\(361\) −2.22468 −0.117088
\(362\) −18.4254 + 1.28337i −0.968415 + 0.0674526i
\(363\) −1.36014 −0.0713888
\(364\) 0 0
\(365\) 5.16984 0.270602
\(366\) 1.38816 0.0966889i 0.0725604 0.00505401i
\(367\) 20.8212 1.08686 0.543430 0.839455i \(-0.317125\pi\)
0.543430 + 0.839455i \(0.317125\pi\)
\(368\) −3.56436 12.4818i −0.185805 0.650659i
\(369\) 2.13286i 0.111032i
\(370\) −15.2306 + 1.06085i −0.791804 + 0.0551511i
\(371\) 0 0
\(372\) 11.6342 1.62860i 0.603206 0.0844392i
\(373\) −17.6614 −0.914475 −0.457237 0.889345i \(-0.651161\pi\)
−0.457237 + 0.889345i \(0.651161\pi\)
\(374\) −0.485724 6.97354i −0.0251162 0.360593i
\(375\) 0.662355i 0.0342038i
\(376\) 4.03966 + 19.0820i 0.208330 + 0.984077i
\(377\) 30.2781i 1.55940i
\(378\) 0 0
\(379\) 15.0551i 0.773331i −0.922220 0.386665i \(-0.873627\pi\)
0.922220 0.386665i \(-0.126373\pi\)
\(380\) 1.13561 + 8.11244i 0.0582557 + 0.416159i
\(381\) 11.2718i 0.577472i
\(382\) 17.5998 1.22587i 0.900486 0.0627211i
\(383\) 30.3505 1.55084 0.775420 0.631446i \(-0.217538\pi\)
0.775420 + 0.631446i \(0.217538\pi\)
\(384\) −3.50542 6.62324i −0.178885 0.337991i
\(385\) 0 0
\(386\) 1.87338 + 26.8961i 0.0953527 + 1.36898i
\(387\) 7.95643i 0.404448i
\(388\) −0.0951542 0.679750i −0.00483072 0.0345091i
\(389\) −6.27818 −0.318316 −0.159158 0.987253i \(-0.550878\pi\)
−0.159158 + 0.987253i \(0.550878\pi\)
\(390\) 0.379472 + 5.44808i 0.0192153 + 0.275874i
\(391\) −4.43983 −0.224532
\(392\) 0 0
\(393\) −0.798887 −0.0402985
\(394\) 0.189837 + 2.72549i 0.00956384 + 0.137308i
\(395\) 11.3401 0.570583
\(396\) −2.56576 18.3289i −0.128934 0.921064i
\(397\) 9.72207i 0.487937i 0.969783 + 0.243968i \(0.0784493\pi\)
−0.969783 + 0.243968i \(0.921551\pi\)
\(398\) 2.02079 + 29.0124i 0.101293 + 1.45426i
\(399\) 0 0
\(400\) −3.84625 + 1.09835i −0.192312 + 0.0549175i
\(401\) 6.98744 0.348936 0.174468 0.984663i \(-0.444179\pi\)
0.174468 + 0.984663i \(0.444179\pi\)
\(402\) 2.37126 0.165164i 0.118268 0.00823764i
\(403\) 51.7034i 2.57553i
\(404\) −1.25777 8.98509i −0.0625764 0.447025i
\(405\) 5.24405i 0.260579i
\(406\) 0 0
\(407\) 39.0048i 1.93339i
\(408\) −2.50750 + 0.530840i −0.124140 + 0.0262805i
\(409\) 2.24559i 0.111037i 0.998458 + 0.0555186i \(0.0176812\pi\)
−0.998458 + 0.0555186i \(0.982319\pi\)
\(410\) −0.0818286 1.17481i −0.00404123 0.0580198i
\(411\) 1.42069 0.0700773
\(412\) 12.1577 1.70189i 0.598967 0.0838459i
\(413\) 0 0
\(414\) −11.7263 + 0.816769i −0.576318 + 0.0401420i
\(415\) 6.49145i 0.318653i
\(416\) 31.0074 11.2379i 1.52026 0.550981i
\(417\) 2.24906 0.110137
\(418\) −20.8767 + 1.45412i −1.02111 + 0.0711232i
\(419\) 18.3565 0.896775 0.448388 0.893839i \(-0.351998\pi\)
0.448388 + 0.893839i \(0.351998\pi\)
\(420\) 0 0
\(421\) 2.27310 0.110784 0.0553921 0.998465i \(-0.482359\pi\)
0.0553921 + 0.998465i \(0.482359\pi\)
\(422\) 14.0854 0.981080i 0.685664 0.0477582i
\(423\) 17.6627 0.858788
\(424\) 4.34516 + 20.5250i 0.211020 + 0.996783i
\(425\) 1.36813i 0.0663638i
\(426\) 3.29394 0.229431i 0.159592 0.0111160i
\(427\) 0 0
\(428\) 2.12606 + 15.1879i 0.102767 + 0.734133i
\(429\) −13.9522 −0.673618
\(430\) −0.305254 4.38252i −0.0147206 0.211344i
\(431\) 12.8610i 0.619490i 0.950820 + 0.309745i \(0.100244\pi\)
−0.950820 + 0.309745i \(0.899756\pi\)
\(432\) −14.1678 + 4.04582i −0.681650 + 0.194655i
\(433\) 33.6307i 1.61619i −0.589054 0.808094i \(-0.700499\pi\)
0.589054 0.808094i \(-0.299501\pi\)
\(434\) 0 0
\(435\) 3.43978i 0.164925i
\(436\) −2.56545 + 0.359122i −0.122863 + 0.0171988i
\(437\) 13.2915i 0.635821i
\(438\) 4.83094 0.336487i 0.230831 0.0160780i
\(439\) 24.8870 1.18779 0.593896 0.804542i \(-0.297589\pi\)
0.593896 + 0.804542i \(0.297589\pi\)
\(440\) −2.11646 9.99743i −0.100898 0.476609i
\(441\) 0 0
\(442\) −0.783818 11.2533i −0.0372824 0.535263i
\(443\) 7.94772i 0.377608i 0.982015 + 0.188804i \(0.0604610\pi\)
−0.982015 + 0.188804i \(0.939539\pi\)
\(444\) −14.1632 + 1.98262i −0.672155 + 0.0940910i
\(445\) 9.39121 0.445186
\(446\) −1.65262 23.7267i −0.0782540 1.12349i
\(447\) −12.6420 −0.597944
\(448\) 0 0
\(449\) 14.3027 0.674988 0.337494 0.941328i \(-0.390421\pi\)
0.337494 + 0.941328i \(0.390421\pi\)
\(450\) 0.251686 + 3.61345i 0.0118646 + 0.170340i
\(451\) 3.00862 0.141670
\(452\) −14.0746 + 1.97022i −0.662013 + 0.0926714i
\(453\) 6.36255i 0.298939i
\(454\) −1.94898 27.9815i −0.0914702 1.31324i
\(455\) 0 0
\(456\) 1.58918 + 7.50673i 0.0744202 + 0.351535i
\(457\) 22.1786 1.03747 0.518737 0.854934i \(-0.326403\pi\)
0.518737 + 0.854934i \(0.326403\pi\)
\(458\) 19.6568 1.36914i 0.918500 0.0639758i
\(459\) 5.03955i 0.235226i
\(460\) −6.42771 + 0.899777i −0.299693 + 0.0419523i
\(461\) 32.8587i 1.53038i −0.643803 0.765192i \(-0.722644\pi\)
0.643803 0.765192i \(-0.277356\pi\)
\(462\) 0 0
\(463\) 3.31392i 0.154011i 0.997031 + 0.0770055i \(0.0245359\pi\)
−0.997031 + 0.0770055i \(0.975464\pi\)
\(464\) 19.9746 5.70402i 0.927297 0.264803i
\(465\) 5.87382i 0.272392i
\(466\) 1.00483 + 14.4263i 0.0465478 + 0.668286i
\(467\) 35.1334 1.62578 0.812890 0.582417i \(-0.197893\pi\)
0.812890 + 0.582417i \(0.197893\pi\)
\(468\) −4.14039 29.5776i −0.191390 1.36722i
\(469\) 0 0
\(470\) 9.72886 0.677640i 0.448759 0.0312572i
\(471\) 10.9039i 0.502426i
\(472\) −4.38092 20.6939i −0.201648 0.952516i
\(473\) 11.2234 0.516051
\(474\) 10.5967 0.738088i 0.486724 0.0339015i
\(475\) 4.09577 0.187927
\(476\) 0 0
\(477\) 18.9984 0.869877
\(478\) 24.1013 1.67871i 1.10237 0.0767825i
\(479\) 22.3266 1.02013 0.510065 0.860136i \(-0.329621\pi\)
0.510065 + 0.860136i \(0.329621\pi\)
\(480\) −3.52263 + 1.27669i −0.160785 + 0.0582726i
\(481\) 62.9423i 2.86992i
\(482\) 26.0767 1.81631i 1.18776 0.0827306i
\(483\) 0 0
\(484\) 4.06732 0.569361i 0.184878 0.0258800i
\(485\) −0.343189 −0.0155834
\(486\) 1.42721 + 20.4905i 0.0647397 + 0.929466i
\(487\) 7.18519i 0.325592i 0.986660 + 0.162796i \(0.0520512\pi\)
−0.986660 + 0.162796i \(0.947949\pi\)
\(488\) −4.11065 + 0.870227i −0.186080 + 0.0393933i
\(489\) 4.73989i 0.214345i
\(490\) 0 0
\(491\) 5.80059i 0.261777i 0.991397 + 0.130889i \(0.0417830\pi\)
−0.991397 + 0.130889i \(0.958217\pi\)
\(492\) −0.152929 1.09247i −0.00689457 0.0492525i
\(493\) 7.10504i 0.319995i
\(494\) −33.6890 + 2.34652i −1.51574 + 0.105575i
\(495\) −9.25383 −0.415929
\(496\) −34.1089 + 9.74027i −1.53153 + 0.437351i
\(497\) 0 0
\(498\) −0.422506 6.06591i −0.0189329 0.271820i
\(499\) 39.6601i 1.77543i −0.460394 0.887715i \(-0.652292\pi\)
0.460394 0.887715i \(-0.347708\pi\)
\(500\) 0.277265 + 1.98069i 0.0123997 + 0.0885791i
\(501\) −9.08270 −0.405785
\(502\) −1.62445 23.3222i −0.0725028 1.04092i
\(503\) −8.22384 −0.366683 −0.183341 0.983049i \(-0.558691\pi\)
−0.183341 + 0.983049i \(0.558691\pi\)
\(504\) 0 0
\(505\) −4.53635 −0.201865
\(506\) −1.15214 16.5412i −0.0512187 0.735347i
\(507\) −13.9042 −0.617506
\(508\) −4.71843 33.7069i −0.209346 1.49550i
\(509\) 32.5719i 1.44373i 0.692036 + 0.721863i \(0.256714\pi\)
−0.692036 + 0.721863i \(0.743286\pi\)
\(510\) 0.0890466 + 1.27844i 0.00394305 + 0.0566103i
\(511\) 0 0
\(512\) 13.2550 + 18.3386i 0.585796 + 0.810459i
\(513\) 15.0869 0.666105
\(514\) −8.73986 + 0.608753i −0.385499 + 0.0268509i
\(515\) 6.13812i 0.270478i
\(516\) −0.570487 4.07537i −0.0251143 0.179408i
\(517\) 24.9150i 1.09576i
\(518\) 0 0
\(519\) 2.59934i 0.114098i
\(520\) −3.41536 16.1329i −0.149773 0.707476i
\(521\) 5.64398i 0.247267i −0.992328 0.123634i \(-0.960545\pi\)
0.992328 0.123634i \(-0.0394547\pi\)
\(522\) −1.30707 18.7656i −0.0572090 0.821348i
\(523\) 2.73410 0.119554 0.0597770 0.998212i \(-0.480961\pi\)
0.0597770 + 0.998212i \(0.480961\pi\)
\(524\) 2.38897 0.334418i 0.104363 0.0146091i
\(525\) 0 0
\(526\) −29.8434 + 2.07867i −1.30123 + 0.0906342i
\(527\) 12.1327i 0.528507i
\(528\) −2.62842 9.20431i −0.114387 0.400566i
\(529\) 12.4687 0.542119
\(530\) 10.4646 0.728886i 0.454553 0.0316608i
\(531\) −19.1547 −0.831245
\(532\) 0 0
\(533\) 4.85504 0.210295
\(534\) 8.77559 0.611242i 0.379757 0.0264510i
\(535\) 7.66797 0.331515
\(536\) −7.02182 + 1.48652i −0.303296 + 0.0642081i
\(537\) 13.6139i 0.587485i
\(538\) 43.7157 3.04491i 1.88472 0.131275i
\(539\) 0 0
\(540\) 1.02132 + 7.29595i 0.0439505 + 0.313968i
\(541\) 28.2999 1.21671 0.608355 0.793665i \(-0.291830\pi\)
0.608355 + 0.793665i \(0.291830\pi\)
\(542\) 2.26385 + 32.5020i 0.0972406 + 1.39608i
\(543\) 8.65052i 0.371230i
\(544\) 7.27616 2.63706i 0.311963 0.113063i
\(545\) 1.29523i 0.0554817i
\(546\) 0 0
\(547\) 20.7596i 0.887616i 0.896122 + 0.443808i \(0.146373\pi\)
−0.896122 + 0.443808i \(0.853627\pi\)
\(548\) −4.24839 + 0.594707i −0.181482 + 0.0254046i
\(549\) 3.80490i 0.162389i
\(550\) −5.09715 + 0.355029i −0.217343 + 0.0151385i
\(551\) −21.2704 −0.906150
\(552\) −5.94779 + 1.25915i −0.253155 + 0.0535930i
\(553\) 0 0
\(554\) 0.682514 + 9.79885i 0.0289973 + 0.416313i
\(555\) 7.15064i 0.303528i
\(556\) −6.72553 + 0.941468i −0.285226 + 0.0399271i
\(557\) −18.7575 −0.794781 −0.397391 0.917650i \(-0.630084\pi\)
−0.397391 + 0.917650i \(0.630084\pi\)
\(558\) 2.23197 + 32.0444i 0.0944870 + 1.35655i
\(559\) 18.1113 0.766025
\(560\) 0 0
\(561\) −3.27401 −0.138229
\(562\) −0.417029 5.98728i −0.0175913 0.252558i
\(563\) −33.3740 −1.40655 −0.703274 0.710919i \(-0.748279\pi\)
−0.703274 + 0.710919i \(0.748279\pi\)
\(564\) 9.04700 1.26644i 0.380947 0.0533266i
\(565\) 7.10591i 0.298948i
\(566\) −0.838399 12.0369i −0.0352405 0.505948i
\(567\) 0 0
\(568\) −9.75407 + 2.06494i −0.409272 + 0.0866431i
\(569\) 13.0300 0.546247 0.273124 0.961979i \(-0.411943\pi\)
0.273124 + 0.961979i \(0.411943\pi\)
\(570\) 3.82728 0.266580i 0.160307 0.0111658i
\(571\) 32.9558i 1.37916i 0.724211 + 0.689579i \(0.242204\pi\)
−0.724211 + 0.689579i \(0.757796\pi\)
\(572\) 41.7223 5.84046i 1.74450 0.244202i
\(573\) 8.26295i 0.345190i
\(574\) 0 0
\(575\) 3.24519i 0.135334i
\(576\) 18.7324 8.30348i 0.780518 0.345978i
\(577\) 36.3874i 1.51483i −0.652935 0.757414i \(-0.726462\pi\)
0.652935 0.757414i \(-0.273538\pi\)
\(578\) 1.48658 + 21.3428i 0.0618337 + 0.887745i
\(579\) 12.6275 0.524780
\(580\) −1.43991 10.2862i −0.0597890 0.427113i
\(581\) 0 0
\(582\) −0.320692 + 0.0223370i −0.0132931 + 0.000925898i
\(583\) 26.7992i 1.10991i
\(584\) −14.3055 + 3.02848i −0.591964 + 0.125319i
\(585\) −14.9330 −0.617403
\(586\) −35.5971 + 2.47943i −1.47050 + 0.102424i
\(587\) 28.4245 1.17321 0.586603 0.809875i \(-0.300465\pi\)
0.586603 + 0.809875i \(0.300465\pi\)
\(588\) 0 0
\(589\) 36.3217 1.49661
\(590\) −10.5507 + 0.734884i −0.434366 + 0.0302547i
\(591\) 1.27959 0.0526352
\(592\) 41.5233 11.8576i 1.70660 0.487342i
\(593\) 7.57149i 0.310924i −0.987842 0.155462i \(-0.950313\pi\)
0.987842 0.155462i \(-0.0496866\pi\)
\(594\) −18.7756 + 1.30777i −0.770371 + 0.0536583i
\(595\) 0 0
\(596\) 37.8042 5.29198i 1.54852 0.216768i
\(597\) 13.6210 0.557472
\(598\) −1.85921 26.6927i −0.0760289 1.09155i
\(599\) 47.4510i 1.93879i −0.245499 0.969397i \(-0.578952\pi\)
0.245499 0.969397i \(-0.421048\pi\)
\(600\) 0.388005 + 1.83280i 0.0158403 + 0.0748238i
\(601\) 13.3242i 0.543506i 0.962367 + 0.271753i \(0.0876034\pi\)
−0.962367 + 0.271753i \(0.912397\pi\)
\(602\) 0 0
\(603\) 6.49954i 0.264682i
\(604\) −2.66339 19.0264i −0.108372 0.774173i
\(605\) 2.05349i 0.0834862i
\(606\) −4.23898 + 0.295255i −0.172197 + 0.0119939i
\(607\) 15.0816 0.612143 0.306072 0.952008i \(-0.400985\pi\)
0.306072 + 0.952008i \(0.400985\pi\)
\(608\) −7.89460 21.7827i −0.320168 0.883405i
\(609\) 0 0
\(610\) 0.145978 + 2.09580i 0.00591046 + 0.0848564i
\(611\) 40.2056i 1.62654i
\(612\) −0.971581 6.94065i −0.0392738 0.280559i
\(613\) −5.20469 −0.210215 −0.105108 0.994461i \(-0.533519\pi\)
−0.105108 + 0.994461i \(0.533519\pi\)
\(614\) 2.87559 + 41.2848i 0.116049 + 1.66612i
\(615\) −0.551563 −0.0222412
\(616\) 0 0
\(617\) −35.7404 −1.43885 −0.719426 0.694569i \(-0.755595\pi\)
−0.719426 + 0.694569i \(0.755595\pi\)
\(618\) −0.399509 5.73575i −0.0160706 0.230726i
\(619\) 38.2437 1.53715 0.768573 0.639762i \(-0.220967\pi\)
0.768573 + 0.639762i \(0.220967\pi\)
\(620\) 2.45881 + 17.5649i 0.0987482 + 0.705424i
\(621\) 11.9538i 0.479689i
\(622\) −2.23515 32.0901i −0.0896215 1.28670i
\(623\) 0 0
\(624\) −4.24151 14.8531i −0.169796 0.594599i
\(625\) 1.00000 0.0400000
\(626\) 9.28981 0.647059i 0.371296 0.0258617i
\(627\) 9.80143i 0.391431i
\(628\) −4.56443 32.6068i −0.182141 1.30115i
\(629\) 14.7700i 0.588918i
\(630\) 0 0
\(631\) 12.0334i 0.479042i 0.970891 + 0.239521i \(0.0769904\pi\)
−0.970891 + 0.239521i \(0.923010\pi\)
\(632\) −31.3792 + 6.64300i −1.24820 + 0.264244i
\(633\) 6.61294i 0.262841i
\(634\) −1.38768 19.9229i −0.0551117 0.791237i
\(635\) −17.0178 −0.675329
\(636\) 9.73118 1.36221i 0.385866 0.0540152i
\(637\) 0 0
\(638\) 26.4709 1.84376i 1.04799 0.0729952i
\(639\) 9.02857i 0.357165i
\(640\) 9.99954 5.29237i 0.395267 0.209199i
\(641\) 22.9352 0.905888 0.452944 0.891539i \(-0.350374\pi\)
0.452944 + 0.891539i \(0.350374\pi\)
\(642\) 7.16531 0.499082i 0.282792 0.0196972i
\(643\) 1.23955 0.0488833 0.0244416 0.999701i \(-0.492219\pi\)
0.0244416 + 0.999701i \(0.492219\pi\)
\(644\) 0 0
\(645\) −2.05755 −0.0810160
\(646\) −7.90543 + 0.550633i −0.311035 + 0.0216644i
\(647\) −14.1415 −0.555962 −0.277981 0.960587i \(-0.589665\pi\)
−0.277981 + 0.960587i \(0.589665\pi\)
\(648\) −3.07195 14.5108i −0.120678 0.570038i
\(649\) 27.0198i 1.06062i
\(650\) −8.22532 + 0.572914i −0.322624 + 0.0224715i
\(651\) 0 0
\(652\) −1.98414 14.1740i −0.0777049 0.555098i
\(653\) −17.0916 −0.668845 −0.334423 0.942423i \(-0.608541\pi\)
−0.334423 + 0.942423i \(0.608541\pi\)
\(654\) 0.0843022 + 1.21033i 0.00329648 + 0.0473275i
\(655\) 1.20613i 0.0471275i
\(656\) 0.914629 + 3.20289i 0.0357103 + 0.125052i
\(657\) 13.2414i 0.516598i
\(658\) 0 0
\(659\) 3.45765i 0.134691i −0.997730 0.0673455i \(-0.978547\pi\)
0.997730 0.0673455i \(-0.0214530\pi\)
\(660\) −4.73991 + 0.663512i −0.184501 + 0.0258272i
\(661\) 15.1632i 0.589780i 0.955531 + 0.294890i \(0.0952830\pi\)
−0.955531 + 0.294890i \(0.904717\pi\)
\(662\) −28.6707 + 1.99699i −1.11432 + 0.0776152i
\(663\) −5.28330 −0.205186
\(664\) 3.80267 + 17.9625i 0.147572 + 0.697079i
\(665\) 0 0
\(666\) −2.71715 39.0100i −0.105287 1.51161i
\(667\) 16.8531i 0.652556i
\(668\) 27.1607 3.80206i 1.05088 0.147106i
\(669\) −11.1394 −0.430676
\(670\) 0.249359 + 3.58005i 0.00963359 + 0.138309i
\(671\) −5.36721 −0.207199
\(672\) 0 0
\(673\) −11.2116 −0.432175 −0.216087 0.976374i \(-0.569330\pi\)
−0.216087 + 0.976374i \(0.569330\pi\)
\(674\) 1.54968 + 22.2488i 0.0596915 + 0.856991i
\(675\) 3.68354 0.141780
\(676\) 41.5787 5.82036i 1.59918 0.223860i
\(677\) 3.67637i 0.141294i −0.997501 0.0706471i \(-0.977494\pi\)
0.997501 0.0706471i \(-0.0225064\pi\)
\(678\) 0.462500 + 6.64010i 0.0177622 + 0.255011i
\(679\) 0 0
\(680\) −0.801444 3.78574i −0.0307340 0.145176i
\(681\) −13.1370 −0.503412
\(682\) −45.2020 + 3.14843i −1.73087 + 0.120560i
\(683\) 42.1877i 1.61427i −0.590369 0.807133i \(-0.701018\pi\)
0.590369 0.807133i \(-0.298982\pi\)
\(684\) −20.7783 + 2.90863i −0.794477 + 0.111214i
\(685\) 2.14490i 0.0819526i
\(686\) 0 0
\(687\) 9.22865i 0.352095i
\(688\) 3.41194 + 11.9481i 0.130079 + 0.455516i
\(689\) 43.2461i 1.64755i
\(690\) 0.211218 + 3.03246i 0.00804094 + 0.115444i
\(691\) −23.1230 −0.879640 −0.439820 0.898086i \(-0.644958\pi\)
−0.439820 + 0.898086i \(0.644958\pi\)
\(692\) 1.08809 + 7.77298i 0.0413631 + 0.295485i
\(693\) 0 0
\(694\) −4.29987 + 0.299497i −0.163221 + 0.0113688i
\(695\) 3.39555i 0.128801i
\(696\) −2.01502 9.51822i −0.0763790 0.360787i
\(697\) 1.13928 0.0431533
\(698\) −11.8572 + 0.825884i −0.448802 + 0.0312602i
\(699\) 6.77301 0.256179
\(700\) 0 0
\(701\) 29.3192 1.10737 0.553686 0.832725i \(-0.313221\pi\)
0.553686 + 0.832725i \(0.313221\pi\)
\(702\) −30.2983 + 2.11035i −1.14354 + 0.0796502i
\(703\) −44.2170 −1.66768
\(704\) 11.7129 + 26.4241i 0.441448 + 0.995894i
\(705\) 4.56761i 0.172026i
\(706\) −0.610622 + 0.0425314i −0.0229811 + 0.00160069i
\(707\) 0 0
\(708\) −9.81126 + 1.37342i −0.368730 + 0.0516163i
\(709\) 3.35439 0.125977 0.0629884 0.998014i \(-0.479937\pi\)
0.0629884 + 0.998014i \(0.479937\pi\)
\(710\) 0.346387 + 4.97308i 0.0129997 + 0.186636i
\(711\) 29.0453i 1.08928i
\(712\) −25.9864 + 5.50134i −0.973882 + 0.206172i
\(713\) 28.7786i 1.07777i
\(714\) 0 0
\(715\) 21.0645i 0.787769i
\(716\) 5.69886 + 40.7108i 0.212977 + 1.52143i
\(717\) 11.3153i 0.422578i
\(718\) −38.0647 + 2.65130i −1.42056 + 0.0989457i
\(719\) −31.0284 −1.15717 −0.578583 0.815624i \(-0.696394\pi\)
−0.578583 + 0.815624i \(0.696394\pi\)
\(720\) −2.81319 9.85134i −0.104841 0.367138i
\(721\) 0 0
\(722\) −0.218609 3.13857i −0.00813579 0.116805i
\(723\) 12.2428i 0.455313i
\(724\) −3.62115 25.8683i −0.134579 0.961388i
\(725\) −5.19327 −0.192873
\(726\) −0.133655 1.91888i −0.00496039 0.0712162i
\(727\) −37.9906 −1.40899 −0.704497 0.709707i \(-0.748827\pi\)
−0.704497 + 0.709707i \(0.748827\pi\)
\(728\) 0 0
\(729\) −6.11207 −0.226373
\(730\) 0.508017 + 7.29359i 0.0188025 + 0.269948i
\(731\) 4.24997 0.157191
\(732\) 0.272817 + 1.94891i 0.0100836 + 0.0720338i
\(733\) 30.9751i 1.14409i 0.820222 + 0.572046i \(0.193850\pi\)
−0.820222 + 0.572046i \(0.806150\pi\)
\(734\) 2.04601 + 29.3745i 0.0755195 + 1.08423i
\(735\) 0 0
\(736\) 17.2590 6.25511i 0.636176 0.230566i
\(737\) −9.16828 −0.337718
\(738\) 3.00903 0.209586i 0.110764 0.00771498i
\(739\) 2.92228i 0.107498i −0.998554 0.0537488i \(-0.982883\pi\)
0.998554 0.0537488i \(-0.0171170\pi\)
\(740\) −2.99329 21.3831i −0.110036 0.786058i
\(741\) 15.8167i 0.581039i
\(742\) 0 0
\(743\) 36.6505i 1.34457i −0.740290 0.672287i \(-0.765312\pi\)
0.740290 0.672287i \(-0.234688\pi\)
\(744\) 3.44087 + 16.2535i 0.126148 + 0.595881i
\(745\) 19.0864i 0.699271i
\(746\) −1.73551 24.9167i −0.0635415 0.912265i
\(747\) 16.6265 0.608330
\(748\) 9.79051 1.37052i 0.357976 0.0501110i
\(749\) 0 0
\(750\) 0.934447 0.0650866i 0.0341212 0.00237663i
\(751\) 36.1831i 1.32034i −0.751116 0.660170i \(-0.770484\pi\)
0.751116 0.660170i \(-0.229516\pi\)
\(752\) −26.5238 + 7.57424i −0.967223 + 0.276204i
\(753\) −10.9496 −0.399024
\(754\) 42.7163 2.97529i 1.55563 0.108354i
\(755\) −9.60595 −0.349596
\(756\) 0 0
\(757\) −1.44394 −0.0524807 −0.0262404 0.999656i \(-0.508354\pi\)
−0.0262404 + 0.999656i \(0.508354\pi\)
\(758\) 21.2397 1.47940i 0.771462 0.0537342i
\(759\) −7.76594 −0.281886
\(760\) −11.3334 + 2.39929i −0.411106 + 0.0870314i
\(761\) 28.2334i 1.02346i 0.859146 + 0.511730i \(0.170995\pi\)
−0.859146 + 0.511730i \(0.829005\pi\)
\(762\) −15.9022 + 1.10763i −0.576076 + 0.0401251i
\(763\) 0 0
\(764\) 3.45891 + 24.7093i 0.125139 + 0.893951i
\(765\) −3.50416 −0.126693
\(766\) 2.98241 + 42.8184i 0.107759 + 1.54709i
\(767\) 43.6020i 1.57438i
\(768\) 8.99958 5.59627i 0.324744 0.201938i
\(769\) 38.3866i 1.38426i −0.721774 0.692129i \(-0.756673\pi\)
0.721774 0.692129i \(-0.243327\pi\)
\(770\) 0 0
\(771\) 4.10328i 0.147776i
\(772\) −37.7608 + 5.28592i −1.35904 + 0.190244i
\(773\) 19.0817i 0.686322i 0.939277 + 0.343161i \(0.111498\pi\)
−0.939277 + 0.343161i \(0.888502\pi\)
\(774\) 11.2249 0.781842i 0.403471 0.0281027i
\(775\) 8.86809 0.318551
\(776\) 0.949638 0.201039i 0.0340900 0.00721688i
\(777\) 0 0
\(778\) −0.616928 8.85722i −0.0221179 0.317547i
\(779\) 3.41067i 0.122200i
\(780\) −7.64883 + 1.07072i −0.273872 + 0.0383378i
\(781\) −12.7357 −0.455721
\(782\) −0.436281 6.26369i −0.0156014