Properties

Label 693.2.i.i.100.1
Level $693$
Weight $2$
Character 693.100
Analytic conductor $5.534$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [693,2,Mod(100,693)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(693, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("693.100");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 693.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.53363286007\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.10423593216.5
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 231)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 100.1
Root \(-0.758290 + 1.31340i\) of defining polynomial
Character \(\chi\) \(=\) 693.100
Dual form 693.2.i.i.298.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.758290 + 1.31340i) q^{2} +(-0.150007 - 0.259820i) q^{4} +(-1.16659 + 2.02059i) q^{5} +(-2.28580 - 1.33233i) q^{7} -2.57816 q^{8} +O(q^{10})\) \(q+(-0.758290 + 1.31340i) q^{2} +(-0.150007 - 0.259820i) q^{4} +(-1.16659 + 2.02059i) q^{5} +(-2.28580 - 1.33233i) q^{7} -2.57816 q^{8} +(-1.76922 - 3.06438i) q^{10} +(-0.500000 - 0.866025i) q^{11} -1.53844 q^{13} +(3.48318 - 1.99187i) q^{14} +(2.25501 - 3.90579i) q^{16} +(-0.0583043 - 0.100986i) q^{17} +(1.80566 - 3.12750i) q^{19} +0.699986 q^{20} +1.51658 q^{22} +(3.55502 - 6.15748i) q^{23} +(-0.221850 - 0.384256i) q^{25} +(1.16659 - 2.02059i) q^{26} +(-0.00327987 + 0.793757i) q^{28} -5.05502 q^{29} +(2.18845 + 3.79051i) q^{31} +(0.841739 + 1.45793i) q^{32} +0.176846 q^{34} +(5.35868 - 3.06438i) q^{35} +(0.150007 - 0.259820i) q^{37} +(2.73843 + 4.74310i) q^{38} +(3.00765 - 5.20941i) q^{40} -8.20479 q^{41} -4.18293 q^{43} +(-0.150007 + 0.259820i) q^{44} +(5.39148 + 9.33831i) q^{46} +(1.15001 - 1.99187i) q^{47} +(3.44978 + 6.09089i) q^{49} +0.672908 q^{50} +(0.230778 + 0.399719i) q^{52} +(-5.94346 - 10.2944i) q^{53} +2.33317 q^{55} +(5.89317 + 3.43497i) q^{56} +(3.83317 - 6.63925i) q^{58} +(2.47814 + 4.29226i) q^{59} +(2.28580 - 3.95913i) q^{61} -6.63792 q^{62} +6.46691 q^{64} +(1.79473 - 3.10856i) q^{65} +(-6.14472 - 10.6430i) q^{67} +(-0.0174921 + 0.0302972i) q^{68} +(-0.0386836 + 9.36176i) q^{70} -4.25628 q^{71} +(-5.21900 - 9.03958i) q^{73} +(0.227498 + 0.394038i) q^{74} -1.08345 q^{76} +(-0.0109324 + 2.64573i) q^{77} +(-7.15742 + 12.3970i) q^{79} +(5.26133 + 9.11289i) q^{80} +(6.22161 - 10.7761i) q^{82} +11.1869 q^{83} +0.272068 q^{85} +(3.17187 - 5.49384i) q^{86} +(1.28908 + 2.23276i) q^{88} +(6.96636 - 12.0661i) q^{89} +(3.51658 + 2.04972i) q^{91} -2.13312 q^{92} +(1.74408 + 3.02083i) q^{94} +(4.21292 + 7.29700i) q^{95} -16.4101 q^{97} +(-10.6157 - 0.0877314i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 4 q^{4} + 4 q^{5} + 2 q^{7} - 24 q^{8} - 10 q^{10} - 4 q^{11} - 4 q^{13} + 4 q^{14} - 12 q^{16} + 2 q^{17} - 4 q^{22} + 4 q^{23} - 4 q^{25} - 4 q^{26} - 22 q^{28} - 16 q^{29} + 12 q^{31} + 26 q^{32} - 32 q^{34} + 2 q^{35} + 4 q^{37} + 8 q^{38} + 6 q^{40} - 4 q^{41} + 36 q^{43} - 4 q^{44} + 14 q^{46} + 12 q^{47} - 4 q^{49} - 4 q^{50} + 6 q^{52} - 12 q^{53} - 8 q^{55} - 48 q^{56} + 4 q^{58} + 12 q^{59} - 2 q^{61} + 52 q^{62} + 112 q^{64} - 4 q^{65} - 28 q^{67} - 48 q^{68} - 32 q^{70} - 24 q^{71} - 6 q^{73} - 16 q^{74} - 36 q^{76} - 4 q^{77} - 2 q^{79} + 16 q^{80} + 12 q^{82} + 24 q^{83} + 36 q^{85} + 36 q^{86} + 12 q^{88} + 8 q^{89} + 12 q^{91} + 32 q^{92} - 20 q^{94} + 34 q^{95} - 88 q^{97} - 16 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/693\mathbb{Z}\right)^\times\).

\(n\) \(155\) \(199\) \(442\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.758290 + 1.31340i −0.536192 + 0.928712i 0.462913 + 0.886404i \(0.346804\pi\)
−0.999105 + 0.0423078i \(0.986529\pi\)
\(3\) 0 0
\(4\) −0.150007 0.259820i −0.0750036 0.129910i
\(5\) −1.16659 + 2.02059i −0.521714 + 0.903634i 0.477967 + 0.878378i \(0.341374\pi\)
−0.999681 + 0.0252568i \(0.991960\pi\)
\(6\) 0 0
\(7\) −2.28580 1.33233i −0.863952 0.503574i
\(8\) −2.57816 −0.911519
\(9\) 0 0
\(10\) −1.76922 3.06438i −0.559477 0.969043i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0 0
\(13\) −1.53844 −0.426688 −0.213344 0.976977i \(-0.568435\pi\)
−0.213344 + 0.976977i \(0.568435\pi\)
\(14\) 3.48318 1.99187i 0.930919 0.532350i
\(15\) 0 0
\(16\) 2.25501 3.90579i 0.563753 0.976448i
\(17\) −0.0583043 0.100986i −0.0141409 0.0244927i 0.858868 0.512196i \(-0.171168\pi\)
−0.873009 + 0.487704i \(0.837835\pi\)
\(18\) 0 0
\(19\) 1.80566 3.12750i 0.414247 0.717497i −0.581102 0.813831i \(-0.697378\pi\)
0.995349 + 0.0963336i \(0.0307116\pi\)
\(20\) 0.699986 0.156522
\(21\) 0 0
\(22\) 1.51658 0.323336
\(23\) 3.55502 6.15748i 0.741274 1.28392i −0.210642 0.977563i \(-0.567555\pi\)
0.951916 0.306361i \(-0.0991113\pi\)
\(24\) 0 0
\(25\) −0.221850 0.384256i −0.0443701 0.0768512i
\(26\) 1.16659 2.02059i 0.228787 0.396270i
\(27\) 0 0
\(28\) −0.00327987 + 0.793757i −0.000619837 + 0.150006i
\(29\) −5.05502 −0.938694 −0.469347 0.883014i \(-0.655511\pi\)
−0.469347 + 0.883014i \(0.655511\pi\)
\(30\) 0 0
\(31\) 2.18845 + 3.79051i 0.393058 + 0.680796i 0.992851 0.119359i \(-0.0380840\pi\)
−0.599794 + 0.800155i \(0.704751\pi\)
\(32\) 0.841739 + 1.45793i 0.148800 + 0.257729i
\(33\) 0 0
\(34\) 0.176846 0.0303289
\(35\) 5.35868 3.06438i 0.905782 0.517975i
\(36\) 0 0
\(37\) 0.150007 0.259820i 0.0246610 0.0427142i −0.853432 0.521205i \(-0.825483\pi\)
0.878093 + 0.478491i \(0.158816\pi\)
\(38\) 2.73843 + 4.74310i 0.444232 + 0.769432i
\(39\) 0 0
\(40\) 3.00765 5.20941i 0.475552 0.823680i
\(41\) −8.20479 −1.28137 −0.640687 0.767802i \(-0.721350\pi\)
−0.640687 + 0.767802i \(0.721350\pi\)
\(42\) 0 0
\(43\) −4.18293 −0.637891 −0.318945 0.947773i \(-0.603329\pi\)
−0.318945 + 0.947773i \(0.603329\pi\)
\(44\) −0.150007 + 0.259820i −0.0226144 + 0.0391693i
\(45\) 0 0
\(46\) 5.39148 + 9.33831i 0.794930 + 1.37686i
\(47\) 1.15001 1.99187i 0.167746 0.290544i −0.769881 0.638187i \(-0.779685\pi\)
0.937627 + 0.347643i \(0.113018\pi\)
\(48\) 0 0
\(49\) 3.44978 + 6.09089i 0.492826 + 0.870128i
\(50\) 0.672908 0.0951635
\(51\) 0 0
\(52\) 0.230778 + 0.399719i 0.0320031 + 0.0554310i
\(53\) −5.94346 10.2944i −0.816397 1.41404i −0.908320 0.418275i \(-0.862635\pi\)
0.0919230 0.995766i \(-0.470699\pi\)
\(54\) 0 0
\(55\) 2.33317 0.314605
\(56\) 5.89317 + 3.43497i 0.787508 + 0.459017i
\(57\) 0 0
\(58\) 3.83317 6.63925i 0.503320 0.871777i
\(59\) 2.47814 + 4.29226i 0.322626 + 0.558804i 0.981029 0.193861i \(-0.0621012\pi\)
−0.658403 + 0.752665i \(0.728768\pi\)
\(60\) 0 0
\(61\) 2.28580 3.95913i 0.292667 0.506914i −0.681773 0.731564i \(-0.738791\pi\)
0.974439 + 0.224650i \(0.0721239\pi\)
\(62\) −6.63792 −0.843017
\(63\) 0 0
\(64\) 6.46691 0.808364
\(65\) 1.79473 3.10856i 0.222609 0.385570i
\(66\) 0 0
\(67\) −6.14472 10.6430i −0.750697 1.30025i −0.947485 0.319800i \(-0.896384\pi\)
0.196788 0.980446i \(-0.436949\pi\)
\(68\) −0.0174921 + 0.0302972i −0.00212123 + 0.00367408i
\(69\) 0 0
\(70\) −0.0386836 + 9.36176i −0.00462357 + 1.11894i
\(71\) −4.25628 −0.505128 −0.252564 0.967580i \(-0.581274\pi\)
−0.252564 + 0.967580i \(0.581274\pi\)
\(72\) 0 0
\(73\) −5.21900 9.03958i −0.610838 1.05800i −0.991099 0.133124i \(-0.957499\pi\)
0.380261 0.924879i \(-0.375834\pi\)
\(74\) 0.227498 + 0.394038i 0.0264461 + 0.0458060i
\(75\) 0 0
\(76\) −1.08345 −0.124280
\(77\) −0.0109324 + 2.64573i −0.00124586 + 0.301509i
\(78\) 0 0
\(79\) −7.15742 + 12.3970i −0.805273 + 1.39477i 0.110834 + 0.993839i \(0.464648\pi\)
−0.916107 + 0.400934i \(0.868686\pi\)
\(80\) 5.26133 + 9.11289i 0.588235 + 1.01885i
\(81\) 0 0
\(82\) 6.22161 10.7761i 0.687062 1.19003i
\(83\) 11.1869 1.22793 0.613963 0.789335i \(-0.289574\pi\)
0.613963 + 0.789335i \(0.289574\pi\)
\(84\) 0 0
\(85\) 0.272068 0.0295099
\(86\) 3.17187 5.49384i 0.342032 0.592416i
\(87\) 0 0
\(88\) 1.28908 + 2.23276i 0.137417 + 0.238013i
\(89\) 6.96636 12.0661i 0.738433 1.27900i −0.214768 0.976665i \(-0.568899\pi\)
0.953201 0.302338i \(-0.0977672\pi\)
\(90\) 0 0
\(91\) 3.51658 + 2.04972i 0.368638 + 0.214869i
\(92\) −2.13312 −0.222393
\(93\) 0 0
\(94\) 1.74408 + 3.02083i 0.179888 + 0.311575i
\(95\) 4.21292 + 7.29700i 0.432237 + 0.748656i
\(96\) 0 0
\(97\) −16.4101 −1.66619 −0.833095 0.553130i \(-0.813433\pi\)
−0.833095 + 0.553130i \(0.813433\pi\)
\(98\) −10.6157 0.0877314i −1.07235 0.00886221i
\(99\) 0 0
\(100\) −0.0665583 + 0.115282i −0.00665583 + 0.0115282i
\(101\) 4.82753 + 8.36152i 0.480357 + 0.832002i 0.999746 0.0225353i \(-0.00717383\pi\)
−0.519389 + 0.854538i \(0.673840\pi\)
\(102\) 0 0
\(103\) −4.41006 + 7.63845i −0.434536 + 0.752639i −0.997258 0.0740075i \(-0.976421\pi\)
0.562721 + 0.826647i \(0.309754\pi\)
\(104\) 3.96636 0.388934
\(105\) 0 0
\(106\) 18.0275 1.75098
\(107\) 5.24207 9.07954i 0.506770 0.877752i −0.493199 0.869917i \(-0.664173\pi\)
0.999969 0.00783538i \(-0.00249410\pi\)
\(108\) 0 0
\(109\) −5.26394 9.11741i −0.504194 0.873289i −0.999988 0.00484932i \(-0.998456\pi\)
0.495794 0.868440i \(-0.334877\pi\)
\(110\) −1.76922 + 3.06438i −0.168689 + 0.292177i
\(111\) 0 0
\(112\) −10.3583 + 5.92345i −0.978769 + 0.559713i
\(113\) −11.4327 −1.07549 −0.537747 0.843106i \(-0.680724\pi\)
−0.537747 + 0.843106i \(0.680724\pi\)
\(114\) 0 0
\(115\) 8.29449 + 14.3665i 0.773465 + 1.33968i
\(116\) 0.758290 + 1.31340i 0.0704055 + 0.121946i
\(117\) 0 0
\(118\) −7.51658 −0.691957
\(119\) −0.00127481 + 0.308514i −0.000116861 + 0.0282815i
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 3.46660 + 6.00433i 0.313851 + 0.543606i
\(123\) 0 0
\(124\) 0.656567 1.13721i 0.0589614 0.102124i
\(125\) −10.6306 −0.950833
\(126\) 0 0
\(127\) 0.234898 0.0208438 0.0104219 0.999946i \(-0.496683\pi\)
0.0104219 + 0.999946i \(0.496683\pi\)
\(128\) −6.58727 + 11.4095i −0.582238 + 1.00847i
\(129\) 0 0
\(130\) 2.72185 + 4.71438i 0.238722 + 0.413479i
\(131\) −2.87927 + 4.98704i −0.251563 + 0.435720i −0.963956 0.266060i \(-0.914278\pi\)
0.712393 + 0.701780i \(0.247611\pi\)
\(132\) 0 0
\(133\) −8.29425 + 4.74310i −0.719203 + 0.411279i
\(134\) 18.6379 1.61007
\(135\) 0 0
\(136\) 0.150318 + 0.260358i 0.0128897 + 0.0223255i
\(137\) 8.04325 + 13.9313i 0.687181 + 1.19023i 0.972746 + 0.231874i \(0.0744856\pi\)
−0.285565 + 0.958359i \(0.592181\pi\)
\(138\) 0 0
\(139\) −14.2930 −1.21231 −0.606157 0.795345i \(-0.707290\pi\)
−0.606157 + 0.795345i \(0.707290\pi\)
\(140\) −1.60003 0.932613i −0.135227 0.0788202i
\(141\) 0 0
\(142\) 3.22750 5.59019i 0.270846 0.469118i
\(143\) 0.769222 + 1.33233i 0.0643256 + 0.111415i
\(144\) 0 0
\(145\) 5.89713 10.2141i 0.489730 0.848237i
\(146\) 15.8301 1.31011
\(147\) 0 0
\(148\) −0.0900086 −0.00739866
\(149\) −0.336454 + 0.582755i −0.0275634 + 0.0477412i −0.879478 0.475939i \(-0.842108\pi\)
0.851915 + 0.523681i \(0.175441\pi\)
\(150\) 0 0
\(151\) −11.8862 20.5875i −0.967285 1.67539i −0.703347 0.710846i \(-0.748312\pi\)
−0.263937 0.964540i \(-0.585021\pi\)
\(152\) −4.65529 + 8.06320i −0.377594 + 0.654012i
\(153\) 0 0
\(154\) −3.46660 2.02059i −0.279347 0.162824i
\(155\) −10.2121 −0.820254
\(156\) 0 0
\(157\) 7.62790 + 13.2119i 0.608773 + 1.05443i 0.991443 + 0.130541i \(0.0416713\pi\)
−0.382670 + 0.923885i \(0.624995\pi\)
\(158\) −10.8548 18.8011i −0.863561 1.49573i
\(159\) 0 0
\(160\) −3.92785 −0.310523
\(161\) −16.3299 + 9.33831i −1.28698 + 0.735962i
\(162\) 0 0
\(163\) −0.210316 + 0.364279i −0.0164733 + 0.0285325i −0.874145 0.485666i \(-0.838577\pi\)
0.857671 + 0.514198i \(0.171911\pi\)
\(164\) 1.23078 + 2.13177i 0.0961076 + 0.166463i
\(165\) 0 0
\(166\) −8.48294 + 14.6929i −0.658404 + 1.14039i
\(167\) −16.4331 −1.27163 −0.635817 0.771840i \(-0.719337\pi\)
−0.635817 + 0.771840i \(0.719337\pi\)
\(168\) 0 0
\(169\) −10.6332 −0.817938
\(170\) −0.206306 + 0.357333i −0.0158230 + 0.0274062i
\(171\) 0 0
\(172\) 0.627469 + 1.08681i 0.0478441 + 0.0828684i
\(173\) 1.93076 3.34418i 0.146793 0.254253i −0.783247 0.621710i \(-0.786438\pi\)
0.930041 + 0.367457i \(0.119771\pi\)
\(174\) 0 0
\(175\) −0.00485070 + 1.17391i −0.000366679 + 0.0887394i
\(176\) −4.51002 −0.339956
\(177\) 0 0
\(178\) 10.5650 + 18.2992i 0.791884 + 1.37158i
\(179\) −6.35480 11.0068i −0.474980 0.822690i 0.524609 0.851343i \(-0.324211\pi\)
−0.999589 + 0.0286535i \(0.990878\pi\)
\(180\) 0 0
\(181\) 16.5196 1.22789 0.613947 0.789347i \(-0.289581\pi\)
0.613947 + 0.789347i \(0.289581\pi\)
\(182\) −5.35868 + 3.06438i −0.397212 + 0.227147i
\(183\) 0 0
\(184\) −9.16544 + 15.8750i −0.675685 + 1.17032i
\(185\) 0.349993 + 0.606205i 0.0257320 + 0.0445691i
\(186\) 0 0
\(187\) −0.0583043 + 0.100986i −0.00426363 + 0.00738482i
\(188\) −0.690037 −0.0503261
\(189\) 0 0
\(190\) −12.7785 −0.927048
\(191\) −8.20479 + 14.2111i −0.593678 + 1.02828i 0.400054 + 0.916492i \(0.368991\pi\)
−0.993732 + 0.111789i \(0.964342\pi\)
\(192\) 0 0
\(193\) −10.3266 17.8862i −0.743326 1.28748i −0.950973 0.309274i \(-0.899914\pi\)
0.207647 0.978204i \(-0.433420\pi\)
\(194\) 12.4436 21.5529i 0.893397 1.54741i
\(195\) 0 0
\(196\) 1.06504 1.81000i 0.0760746 0.129286i
\(197\) −26.3132 −1.87474 −0.937368 0.348342i \(-0.886745\pi\)
−0.937368 + 0.348342i \(0.886745\pi\)
\(198\) 0 0
\(199\) 5.50528 + 9.53543i 0.390259 + 0.675949i 0.992484 0.122378i \(-0.0390520\pi\)
−0.602224 + 0.798327i \(0.705719\pi\)
\(200\) 0.571967 + 0.990675i 0.0404442 + 0.0700513i
\(201\) 0 0
\(202\) −14.6427 −1.03025
\(203\) 11.5548 + 6.73497i 0.810987 + 0.472702i
\(204\) 0 0
\(205\) 9.57160 16.5785i 0.668510 1.15789i
\(206\) −6.68821 11.5843i −0.465990 0.807118i
\(207\) 0 0
\(208\) −3.46921 + 6.00884i −0.240546 + 0.416638i
\(209\) −3.61132 −0.249800
\(210\) 0 0
\(211\) 22.2476 1.53159 0.765793 0.643087i \(-0.222347\pi\)
0.765793 + 0.643087i \(0.222347\pi\)
\(212\) −1.78312 + 3.08846i −0.122465 + 0.212116i
\(213\) 0 0
\(214\) 7.95002 + 13.7698i 0.543452 + 0.941287i
\(215\) 4.87975 8.45197i 0.332796 0.576420i
\(216\) 0 0
\(217\) 0.0478499 11.5801i 0.00324827 0.786108i
\(218\) 15.9664 1.08138
\(219\) 0 0
\(220\) −0.349993 0.606205i −0.0235965 0.0408704i
\(221\) 0.0896979 + 0.155361i 0.00603373 + 0.0104507i
\(222\) 0 0
\(223\) −16.8020 −1.12515 −0.562573 0.826748i \(-0.690188\pi\)
−0.562573 + 0.826748i \(0.690188\pi\)
\(224\) 0.0184044 4.45402i 0.00122970 0.297597i
\(225\) 0 0
\(226\) 8.66927 15.0156i 0.576671 0.998823i
\(227\) 2.71008 + 4.69399i 0.179874 + 0.311551i 0.941837 0.336069i \(-0.109098\pi\)
−0.761963 + 0.647620i \(0.775764\pi\)
\(228\) 0 0
\(229\) −14.1161 + 24.4499i −0.932820 + 1.61569i −0.154345 + 0.988017i \(0.549327\pi\)
−0.778476 + 0.627675i \(0.784007\pi\)
\(230\) −25.1585 −1.65890
\(231\) 0 0
\(232\) 13.0327 0.855637
\(233\) 2.80566 4.85955i 0.183805 0.318360i −0.759368 0.650661i \(-0.774492\pi\)
0.943173 + 0.332302i \(0.107825\pi\)
\(234\) 0 0
\(235\) 2.68317 + 4.64738i 0.175031 + 0.303162i
\(236\) 0.743476 1.28774i 0.0483962 0.0838246i
\(237\) 0 0
\(238\) −0.404235 0.235618i −0.0262027 0.0152728i
\(239\) −12.0153 −0.777205 −0.388603 0.921405i \(-0.627042\pi\)
−0.388603 + 0.921405i \(0.627042\pi\)
\(240\) 0 0
\(241\) 10.3663 + 17.9550i 0.667754 + 1.15658i 0.978531 + 0.206101i \(0.0660776\pi\)
−0.310776 + 0.950483i \(0.600589\pi\)
\(242\) −0.758290 1.31340i −0.0487447 0.0844283i
\(243\) 0 0
\(244\) −1.37155 −0.0878043
\(245\) −16.3317 0.134970i −1.04339 0.00862291i
\(246\) 0 0
\(247\) −2.77791 + 4.81148i −0.176754 + 0.306147i
\(248\) −5.64219 9.77256i −0.358279 0.620558i
\(249\) 0 0
\(250\) 8.06111 13.9622i 0.509829 0.883050i
\(251\) 27.2885 1.72243 0.861217 0.508237i \(-0.169703\pi\)
0.861217 + 0.508237i \(0.169703\pi\)
\(252\) 0 0
\(253\) −7.11005 −0.447005
\(254\) −0.178121 + 0.308514i −0.0111763 + 0.0193579i
\(255\) 0 0
\(256\) −3.52321 6.10238i −0.220201 0.381399i
\(257\) 4.45099 7.70933i 0.277645 0.480895i −0.693154 0.720789i \(-0.743779\pi\)
0.970799 + 0.239894i \(0.0771128\pi\)
\(258\) 0 0
\(259\) −0.689053 + 0.394038i −0.0428157 + 0.0244843i
\(260\) −1.07689 −0.0667858
\(261\) 0 0
\(262\) −4.36664 7.56325i −0.269772 0.467259i
\(263\) −1.12790 1.95359i −0.0695495 0.120463i 0.829154 0.559021i \(-0.188823\pi\)
−0.898703 + 0.438558i \(0.855490\pi\)
\(264\) 0 0
\(265\) 27.7343 1.70370
\(266\) 0.0598751 14.4903i 0.00367118 0.888456i
\(267\) 0 0
\(268\) −1.84350 + 3.19304i −0.112610 + 0.195046i
\(269\) 4.18444 + 7.24767i 0.255130 + 0.441898i 0.964931 0.262504i \(-0.0845484\pi\)
−0.709801 + 0.704402i \(0.751215\pi\)
\(270\) 0 0
\(271\) −4.44734 + 7.70302i −0.270157 + 0.467925i −0.968902 0.247445i \(-0.920409\pi\)
0.698745 + 0.715371i \(0.253742\pi\)
\(272\) −0.525907 −0.0318878
\(273\) 0 0
\(274\) −24.3965 −1.47384
\(275\) −0.221850 + 0.384256i −0.0133781 + 0.0231715i
\(276\) 0 0
\(277\) 2.69999 + 4.67651i 0.162226 + 0.280984i 0.935667 0.352885i \(-0.114799\pi\)
−0.773440 + 0.633869i \(0.781466\pi\)
\(278\) 10.8382 18.7723i 0.650033 1.12589i
\(279\) 0 0
\(280\) −13.8156 + 7.90048i −0.825638 + 0.472144i
\(281\) 19.7416 1.17768 0.588841 0.808249i \(-0.299584\pi\)
0.588841 + 0.808249i \(0.299584\pi\)
\(282\) 0 0
\(283\) 5.05259 + 8.75133i 0.300345 + 0.520213i 0.976214 0.216809i \(-0.0695649\pi\)
−0.675869 + 0.737022i \(0.736232\pi\)
\(284\) 0.638473 + 1.10587i 0.0378864 + 0.0656212i
\(285\) 0 0
\(286\) −2.33317 −0.137963
\(287\) 18.7545 + 10.9315i 1.10705 + 0.645267i
\(288\) 0 0
\(289\) 8.49320 14.7107i 0.499600 0.865333i
\(290\) 8.94346 + 15.4905i 0.525178 + 0.909635i
\(291\) 0 0
\(292\) −1.56578 + 2.71200i −0.0916301 + 0.158708i
\(293\) 16.1108 0.941201 0.470601 0.882346i \(-0.344037\pi\)
0.470601 + 0.882346i \(0.344037\pi\)
\(294\) 0 0
\(295\) −11.5638 −0.673273
\(296\) −0.386743 + 0.669859i −0.0224790 + 0.0389347i
\(297\) 0 0
\(298\) −0.510259 0.883795i −0.0295585 0.0511969i
\(299\) −5.46921 + 9.47295i −0.316292 + 0.547835i
\(300\) 0 0
\(301\) 9.56135 + 5.57305i 0.551107 + 0.321225i
\(302\) 36.0527 2.07460
\(303\) 0 0
\(304\) −8.14357 14.1051i −0.467066 0.808982i
\(305\) 5.33317 + 9.23733i 0.305377 + 0.528928i
\(306\) 0 0
\(307\) 27.8168 1.58759 0.793795 0.608185i \(-0.208102\pi\)
0.793795 + 0.608185i \(0.208102\pi\)
\(308\) 0.689053 0.394038i 0.0392625 0.0224524i
\(309\) 0 0
\(310\) 7.74372 13.4125i 0.439813 0.761779i
\(311\) 4.52139 + 7.83127i 0.256384 + 0.444071i 0.965271 0.261252i \(-0.0841354\pi\)
−0.708886 + 0.705323i \(0.750802\pi\)
\(312\) 0 0
\(313\) 8.08842 14.0096i 0.457185 0.791867i −0.541626 0.840619i \(-0.682191\pi\)
0.998811 + 0.0487523i \(0.0155245\pi\)
\(314\) −23.1366 −1.30568
\(315\) 0 0
\(316\) 4.29466 0.241593
\(317\) −2.61685 + 4.53251i −0.146977 + 0.254571i −0.930109 0.367284i \(-0.880288\pi\)
0.783132 + 0.621856i \(0.213621\pi\)
\(318\) 0 0
\(319\) 2.52751 + 4.37778i 0.141514 + 0.245109i
\(320\) −7.54422 + 13.0670i −0.421734 + 0.730466i
\(321\) 0 0
\(322\) 0.117883 28.5288i 0.00656938 1.58985i
\(323\) −0.421111 −0.0234312
\(324\) 0 0
\(325\) 0.341305 + 0.591157i 0.0189322 + 0.0327915i
\(326\) −0.318962 0.552458i −0.0176657 0.0305978i
\(327\) 0 0
\(328\) 21.1533 1.16800
\(329\) −5.28252 + 3.02083i −0.291235 + 0.166544i
\(330\) 0 0
\(331\) 9.76510 16.9137i 0.536739 0.929658i −0.462338 0.886704i \(-0.652989\pi\)
0.999077 0.0429549i \(-0.0136772\pi\)
\(332\) −1.67812 2.90659i −0.0920988 0.159520i
\(333\) 0 0
\(334\) 12.4611 21.5832i 0.681840 1.18098i
\(335\) 28.6734 1.56660
\(336\) 0 0
\(337\) −0.243643 −0.0132721 −0.00663605 0.999978i \(-0.502112\pi\)
−0.00663605 + 0.999978i \(0.502112\pi\)
\(338\) 8.06304 13.9656i 0.438572 0.759628i
\(339\) 0 0
\(340\) −0.0408121 0.0706887i −0.00221335 0.00383363i
\(341\) 2.18845 3.79051i 0.118511 0.205268i
\(342\) 0 0
\(343\) 0.229575 18.5188i 0.0123959 0.999923i
\(344\) 10.7843 0.581449
\(345\) 0 0
\(346\) 2.92816 + 5.07172i 0.157419 + 0.272657i
\(347\) 11.0805 + 19.1920i 0.594834 + 1.03028i 0.993570 + 0.113217i \(0.0361156\pi\)
−0.398736 + 0.917066i \(0.630551\pi\)
\(348\) 0 0
\(349\) −16.1822 −0.866213 −0.433107 0.901343i \(-0.642583\pi\)
−0.433107 + 0.901343i \(0.642583\pi\)
\(350\) −1.53813 0.896537i −0.0822167 0.0479219i
\(351\) 0 0
\(352\) 0.841739 1.45793i 0.0448648 0.0777082i
\(353\) −3.88844 6.73497i −0.206961 0.358466i 0.743795 0.668408i \(-0.233024\pi\)
−0.950756 + 0.309941i \(0.899691\pi\)
\(354\) 0 0
\(355\) 4.96533 8.60020i 0.263532 0.456451i
\(356\) −4.18002 −0.221540
\(357\) 0 0
\(358\) 19.2751 1.01872
\(359\) 5.40642 9.36420i 0.285340 0.494223i −0.687352 0.726325i \(-0.741227\pi\)
0.972692 + 0.232102i \(0.0745602\pi\)
\(360\) 0 0
\(361\) 2.97917 + 5.16008i 0.156798 + 0.271583i
\(362\) −12.5267 + 21.6968i −0.658387 + 1.14036i
\(363\) 0 0
\(364\) 0.00504590 1.22115i 0.000264477 0.0640057i
\(365\) 24.3537 1.27473
\(366\) 0 0
\(367\) 0.878346 + 1.52134i 0.0458493 + 0.0794133i 0.888039 0.459768i \(-0.152067\pi\)
−0.842190 + 0.539181i \(0.818734\pi\)
\(368\) −16.0332 27.7704i −0.835790 1.44763i
\(369\) 0 0
\(370\) −1.06158 −0.0551891
\(371\) −0.129952 + 31.4496i −0.00674679 + 1.63278i
\(372\) 0 0
\(373\) 4.63683 8.03123i 0.240086 0.415841i −0.720653 0.693296i \(-0.756158\pi\)
0.960739 + 0.277455i \(0.0894910\pi\)
\(374\) −0.0884231 0.153153i −0.00457225 0.00791936i
\(375\) 0 0
\(376\) −2.96491 + 5.13537i −0.152903 + 0.264836i
\(377\) 7.77687 0.400529
\(378\) 0 0
\(379\) −11.5130 −0.591386 −0.295693 0.955283i \(-0.595550\pi\)
−0.295693 + 0.955283i \(0.595550\pi\)
\(380\) 1.26394 2.18920i 0.0648386 0.112304i
\(381\) 0 0
\(382\) −12.4432 21.5523i −0.636651 1.10271i
\(383\) −11.2392 + 19.4669i −0.574298 + 0.994713i 0.421820 + 0.906680i \(0.361391\pi\)
−0.996118 + 0.0880331i \(0.971942\pi\)
\(384\) 0 0
\(385\) −5.33317 3.10856i −0.271804 0.158427i
\(386\) 31.3223 1.59426
\(387\) 0 0
\(388\) 2.46163 + 4.26366i 0.124970 + 0.216455i
\(389\) −17.1663 29.7329i −0.870365 1.50752i −0.861620 0.507554i \(-0.830550\pi\)
−0.00874493 0.999962i \(-0.502784\pi\)
\(390\) 0 0
\(391\) −0.829092 −0.0419290
\(392\) −8.89410 15.7033i −0.449220 0.793138i
\(393\) 0 0
\(394\) 19.9530 34.5596i 1.00522 1.74109i
\(395\) −16.6995 28.9244i −0.840243 1.45534i
\(396\) 0 0
\(397\) 4.89980 8.48671i 0.245914 0.425936i −0.716474 0.697614i \(-0.754245\pi\)
0.962388 + 0.271678i \(0.0875785\pi\)
\(398\) −16.6984 −0.837016
\(399\) 0 0
\(400\) −2.00110 −0.100055
\(401\) 1.73819 3.01064i 0.0868011 0.150344i −0.819356 0.573285i \(-0.805669\pi\)
0.906157 + 0.422941i \(0.139002\pi\)
\(402\) 0 0
\(403\) −3.36681 5.83149i −0.167713 0.290487i
\(404\) 1.44833 2.50858i 0.0720570 0.124806i
\(405\) 0 0
\(406\) −17.6076 + 10.0690i −0.873849 + 0.499714i
\(407\) −0.300014 −0.0148712
\(408\) 0 0
\(409\) −17.5609 30.4164i −0.868332 1.50399i −0.863700 0.504006i \(-0.831859\pi\)
−0.00463138 0.999989i \(-0.501474\pi\)
\(410\) 14.5161 + 25.1426i 0.716899 + 1.24171i
\(411\) 0 0
\(412\) 2.64616 0.130367
\(413\) 0.0541838 13.1129i 0.00266621 0.645246i
\(414\) 0 0
\(415\) −13.0505 + 22.6042i −0.640626 + 1.10960i
\(416\) −1.29497 2.24295i −0.0634911 0.109970i
\(417\) 0 0
\(418\) 2.73843 4.74310i 0.133941 0.231993i
\(419\) −13.8100 −0.674664 −0.337332 0.941386i \(-0.609525\pi\)
−0.337332 + 0.941386i \(0.609525\pi\)
\(420\) 0 0
\(421\) 9.72050 0.473748 0.236874 0.971540i \(-0.423877\pi\)
0.236874 + 0.971540i \(0.423877\pi\)
\(422\) −16.8701 + 29.2199i −0.821224 + 1.42240i
\(423\) 0 0
\(424\) 15.3232 + 26.5406i 0.744161 + 1.28893i
\(425\) −0.0258696 + 0.0448075i −0.00125486 + 0.00217348i
\(426\) 0 0
\(427\) −10.4998 + 6.00433i −0.508119 + 0.290570i
\(428\) −3.14539 −0.152038
\(429\) 0 0
\(430\) 7.40053 + 12.8181i 0.356885 + 0.618143i
\(431\) −5.09584 8.82625i −0.245458 0.425145i 0.716802 0.697276i \(-0.245605\pi\)
−0.962260 + 0.272131i \(0.912272\pi\)
\(432\) 0 0
\(433\) −21.0101 −1.00968 −0.504840 0.863213i \(-0.668449\pi\)
−0.504840 + 0.863213i \(0.668449\pi\)
\(434\) 15.1730 + 8.84392i 0.728326 + 0.424522i
\(435\) 0 0
\(436\) −1.57926 + 2.73535i −0.0756327 + 0.131000i
\(437\) −12.8383 22.2367i −0.614141 1.06372i
\(438\) 0 0
\(439\) −4.92336 + 8.52751i −0.234979 + 0.406996i −0.959267 0.282502i \(-0.908836\pi\)
0.724287 + 0.689498i \(0.242169\pi\)
\(440\) −6.01531 −0.286768
\(441\) 0 0
\(442\) −0.272068 −0.0129410
\(443\) 7.77560 13.4677i 0.369430 0.639871i −0.620047 0.784565i \(-0.712886\pi\)
0.989477 + 0.144694i \(0.0462197\pi\)
\(444\) 0 0
\(445\) 16.2537 + 28.1523i 0.770501 + 1.33455i
\(446\) 12.7408 22.0677i 0.603294 1.04494i
\(447\) 0 0
\(448\) −14.7821 8.61607i −0.698388 0.407071i
\(449\) −2.62021 −0.123655 −0.0618277 0.998087i \(-0.519693\pi\)
−0.0618277 + 0.998087i \(0.519693\pi\)
\(450\) 0 0
\(451\) 4.10240 + 7.10556i 0.193174 + 0.334588i
\(452\) 1.71498 + 2.97043i 0.0806659 + 0.139717i
\(453\) 0 0
\(454\) −8.22010 −0.385788
\(455\) −8.24403 + 4.71438i −0.386486 + 0.221014i
\(456\) 0 0
\(457\) −3.81295 + 6.60423i −0.178362 + 0.308933i −0.941320 0.337516i \(-0.890413\pi\)
0.762957 + 0.646449i \(0.223747\pi\)
\(458\) −21.4082 37.0802i −1.00034 1.73264i
\(459\) 0 0
\(460\) 2.48847 4.31015i 0.116025 0.200962i
\(461\) 12.7392 0.593325 0.296662 0.954982i \(-0.404126\pi\)
0.296662 + 0.954982i \(0.404126\pi\)
\(462\) 0 0
\(463\) −8.76838 −0.407501 −0.203751 0.979023i \(-0.565313\pi\)
−0.203751 + 0.979023i \(0.565313\pi\)
\(464\) −11.3991 + 19.7439i −0.529191 + 0.916586i
\(465\) 0 0
\(466\) 4.25501 + 7.36989i 0.197110 + 0.341404i
\(467\) −9.68413 + 16.7734i −0.448128 + 0.776181i −0.998264 0.0588943i \(-0.981243\pi\)
0.550136 + 0.835075i \(0.314576\pi\)
\(468\) 0 0
\(469\) −0.134353 + 32.5145i −0.00620384 + 1.50138i
\(470\) −8.13847 −0.375400
\(471\) 0 0
\(472\) −6.38904 11.0661i −0.294079 0.509360i
\(473\) 2.09146 + 3.62252i 0.0961656 + 0.166564i
\(474\) 0 0
\(475\) −1.60235 −0.0735207
\(476\) 0.0803495 0.0459482i 0.00368281 0.00210603i
\(477\) 0 0
\(478\) 9.11108 15.7809i 0.416731 0.721800i
\(479\) 12.0995 + 20.9569i 0.552839 + 0.957546i 0.998068 + 0.0621289i \(0.0197890\pi\)
−0.445229 + 0.895417i \(0.646878\pi\)
\(480\) 0 0
\(481\) −0.230778 + 0.399719i −0.0105226 + 0.0182256i
\(482\) −31.4427 −1.43218
\(483\) 0 0
\(484\) 0.300014 0.0136370
\(485\) 19.1438 33.1580i 0.869274 1.50563i
\(486\) 0 0
\(487\) 10.6093 + 18.3759i 0.480755 + 0.832692i 0.999756 0.0220818i \(-0.00702942\pi\)
−0.519001 + 0.854773i \(0.673696\pi\)
\(488\) −5.89317 + 10.2073i −0.266771 + 0.462062i
\(489\) 0 0
\(490\) 12.5614 21.3476i 0.567466 0.964386i
\(491\) 28.2038 1.27282 0.636411 0.771350i \(-0.280418\pi\)
0.636411 + 0.771350i \(0.280418\pi\)
\(492\) 0 0
\(493\) 0.294729 + 0.510486i 0.0132739 + 0.0229911i
\(494\) −4.21292 7.29700i −0.189548 0.328307i
\(495\) 0 0
\(496\) 19.7399 0.886349
\(497\) 9.72902 + 5.67078i 0.436406 + 0.254369i
\(498\) 0 0
\(499\) 17.7490 30.7422i 0.794555 1.37621i −0.128567 0.991701i \(-0.541038\pi\)
0.923122 0.384508i \(-0.125629\pi\)
\(500\) 1.59467 + 2.76205i 0.0713159 + 0.123523i
\(501\) 0 0
\(502\) −20.6926 + 35.8406i −0.923555 + 1.59964i
\(503\) −16.0477 −0.715529 −0.357765 0.933812i \(-0.616461\pi\)
−0.357765 + 0.933812i \(0.616461\pi\)
\(504\) 0 0
\(505\) −22.5269 −1.00243
\(506\) 5.39148 9.33831i 0.239680 0.415139i
\(507\) 0 0
\(508\) −0.0352364 0.0610313i −0.00156336 0.00270782i
\(509\) 4.10652 7.11270i 0.182018 0.315265i −0.760550 0.649280i \(-0.775070\pi\)
0.942568 + 0.334015i \(0.108404\pi\)
\(510\) 0 0
\(511\) −0.114112 + 27.6161i −0.00504803 + 1.22167i
\(512\) −15.6626 −0.692197
\(513\) 0 0
\(514\) 6.75027 + 11.6918i 0.297742 + 0.515704i
\(515\) −10.2894 17.8218i −0.453407 0.785324i
\(516\) 0 0
\(517\) −2.30001 −0.101155
\(518\) 0.00497418 1.20380i 0.000218553 0.0528917i
\(519\) 0 0
\(520\) −4.62711 + 8.01438i −0.202912 + 0.351454i
\(521\) −4.27767 7.40914i −0.187408 0.324601i 0.756977 0.653441i \(-0.226675\pi\)
−0.944385 + 0.328841i \(0.893342\pi\)
\(522\) 0 0
\(523\) −15.0185 + 26.0128i −0.656712 + 1.13746i 0.324750 + 0.945800i \(0.394720\pi\)
−0.981462 + 0.191658i \(0.938613\pi\)
\(524\) 1.72765 0.0754725
\(525\) 0 0
\(526\) 3.42111 0.149168
\(527\) 0.255192 0.442006i 0.0111163 0.0192541i
\(528\) 0 0
\(529\) −13.7764 23.8614i −0.598974 1.03745i
\(530\) −21.0306 + 36.4261i −0.913511 + 1.58225i
\(531\) 0 0
\(532\) 2.47655 + 1.44351i 0.107372 + 0.0625843i
\(533\) 12.6226 0.546746
\(534\) 0 0
\(535\) 12.2307 + 21.1841i 0.528778 + 0.915870i
\(536\) 15.8421 + 27.4393i 0.684275 + 1.18520i
\(537\) 0 0
\(538\) −12.6921 −0.547194
\(539\) 3.54998 6.03305i 0.152908 0.259862i
\(540\) 0 0
\(541\) −9.50845 + 16.4691i −0.408800 + 0.708063i −0.994756 0.102281i \(-0.967386\pi\)
0.585955 + 0.810343i \(0.300719\pi\)
\(542\) −6.74475 11.6823i −0.289712 0.501796i
\(543\) 0 0
\(544\) 0.0981539 0.170008i 0.00420831 0.00728901i
\(545\) 24.5634 1.05218
\(546\) 0 0
\(547\) 34.4968 1.47498 0.737489 0.675360i \(-0.236012\pi\)
0.737489 + 0.675360i \(0.236012\pi\)
\(548\) 2.41309 4.17960i 0.103082 0.178543i
\(549\) 0 0
\(550\) −0.336454 0.582755i −0.0143464 0.0248488i
\(551\) −9.12766 + 15.8096i −0.388852 + 0.673511i
\(552\) 0 0
\(553\) 32.8774 18.8011i 1.39809 0.799503i
\(554\) −8.18949 −0.347938
\(555\) 0 0
\(556\) 2.14405 + 3.71360i 0.0909279 + 0.157492i
\(557\) 2.71456 + 4.70176i 0.115020 + 0.199220i 0.917788 0.397072i \(-0.129974\pi\)
−0.802768 + 0.596292i \(0.796640\pi\)
\(558\) 0 0
\(559\) 6.43520 0.272180
\(560\) 0.115038 27.8401i 0.00486123 1.17646i
\(561\) 0 0
\(562\) −14.9698 + 25.9285i −0.631464 + 1.09373i
\(563\) −17.0841 29.5905i −0.720007 1.24709i −0.960996 0.276562i \(-0.910805\pi\)
0.240989 0.970528i \(-0.422528\pi\)
\(564\) 0 0
\(565\) 13.3372 23.1007i 0.561100 0.971853i
\(566\) −15.3253 −0.644170
\(567\) 0 0
\(568\) 10.9734 0.460434
\(569\) −8.29626 + 14.3695i −0.347797 + 0.602402i −0.985858 0.167584i \(-0.946404\pi\)
0.638061 + 0.769986i \(0.279737\pi\)
\(570\) 0 0
\(571\) −6.96720 12.0675i −0.291568 0.505011i 0.682612 0.730781i \(-0.260844\pi\)
−0.974181 + 0.225769i \(0.927510\pi\)
\(572\) 0.230778 0.399719i 0.00964930 0.0167131i
\(573\) 0 0
\(574\) −28.5788 + 16.3429i −1.19286 + 0.682139i
\(575\) −3.15473 −0.131562
\(576\) 0 0
\(577\) −22.8387 39.5578i −0.950788 1.64681i −0.743726 0.668485i \(-0.766943\pi\)
−0.207062 0.978328i \(-0.566390\pi\)
\(578\) 12.8806 + 22.3099i 0.535763 + 0.927969i
\(579\) 0 0
\(580\) −3.53844 −0.146926
\(581\) −25.5711 14.9047i −1.06087 0.618352i
\(582\) 0 0
\(583\) −5.94346 + 10.2944i −0.246153 + 0.426350i
\(584\) 13.4554 + 23.3055i 0.556790 + 0.964389i
\(585\) 0 0
\(586\) −12.2166 + 21.1598i −0.504665 + 0.874105i
\(587\) −29.3966 −1.21333 −0.606664 0.794958i \(-0.707493\pi\)
−0.606664 + 0.794958i \(0.707493\pi\)
\(588\) 0 0
\(589\) 15.8064 0.651292
\(590\) 8.76874 15.1879i 0.361003 0.625276i
\(591\) 0 0
\(592\) −0.676535 1.17179i −0.0278054 0.0481604i
\(593\) −0.912178 + 1.57994i −0.0374587 + 0.0648803i −0.884147 0.467209i \(-0.845260\pi\)
0.846688 + 0.532089i \(0.178593\pi\)
\(594\) 0 0
\(595\) −0.621893 0.362485i −0.0254951 0.0148604i
\(596\) 0.201882 0.00826941
\(597\) 0 0
\(598\) −8.29449 14.3665i −0.339187 0.587489i
\(599\) −11.2497 19.4851i −0.459651 0.796139i 0.539291 0.842119i \(-0.318692\pi\)
−0.998942 + 0.0459800i \(0.985359\pi\)
\(600\) 0 0
\(601\) −10.3352 −0.421583 −0.210792 0.977531i \(-0.567604\pi\)
−0.210792 + 0.977531i \(0.567604\pi\)
\(602\) −14.5699 + 8.33185i −0.593825 + 0.339581i
\(603\) 0 0
\(604\) −3.56603 + 6.17654i −0.145100 + 0.251320i
\(605\) −1.16659 2.02059i −0.0474285 0.0821486i
\(606\) 0 0
\(607\) 16.3137 28.2562i 0.662155 1.14689i −0.317894 0.948126i \(-0.602976\pi\)
0.980048 0.198759i \(-0.0636911\pi\)
\(608\) 6.07958 0.246560
\(609\) 0 0
\(610\) −16.1764 −0.654962
\(611\) −1.76922 + 3.06438i −0.0715751 + 0.123972i
\(612\) 0 0
\(613\) 3.19350 + 5.53130i 0.128984 + 0.223407i 0.923283 0.384120i \(-0.125495\pi\)
−0.794299 + 0.607527i \(0.792162\pi\)
\(614\) −21.0932 + 36.5345i −0.851253 + 1.47441i
\(615\) 0 0
\(616\) 0.0281855 6.82112i 0.00113562 0.274831i
\(617\) −4.14609 −0.166915 −0.0834577 0.996511i \(-0.526596\pi\)
−0.0834577 + 0.996511i \(0.526596\pi\)
\(618\) 0 0
\(619\) 19.2980 + 33.4252i 0.775653 + 1.34347i 0.934427 + 0.356155i \(0.115913\pi\)
−0.158774 + 0.987315i \(0.550754\pi\)
\(620\) 1.53188 + 2.65330i 0.0615220 + 0.106559i
\(621\) 0 0
\(622\) −13.7141 −0.549885
\(623\) −31.9998 + 18.2992i −1.28204 + 0.733142i
\(624\) 0 0
\(625\) 13.5108 23.4014i 0.540433 0.936057i
\(626\) 12.2667 + 21.2466i 0.490278 + 0.849186i
\(627\) 0 0
\(628\) 2.28848 3.96376i 0.0913203 0.158171i
\(629\) −0.0349842 −0.00139491
\(630\) 0 0
\(631\) −8.89990 −0.354299 −0.177150 0.984184i \(-0.556688\pi\)
−0.177150 + 0.984184i \(0.556688\pi\)
\(632\) 18.4530 31.9615i 0.734021 1.27136i
\(633\) 0 0
\(634\) −3.96866 6.87392i −0.157616 0.272998i
\(635\) −0.274029 + 0.474632i −0.0108745 + 0.0188352i
\(636\) 0 0
\(637\) −5.30730 9.37050i −0.210283 0.371273i
\(638\) −7.66635 −0.303514
\(639\) 0 0
\(640\) −15.3693 26.6203i −0.607523 1.05226i
\(641\) 18.6648 + 32.3284i 0.737217 + 1.27690i 0.953744 + 0.300620i \(0.0971936\pi\)
−0.216527 + 0.976277i \(0.569473\pi\)
\(642\) 0 0
\(643\) 15.9206 0.627846 0.313923 0.949449i \(-0.398357\pi\)
0.313923 + 0.949449i \(0.398357\pi\)
\(644\) 4.87588 + 2.84202i 0.192137 + 0.111991i
\(645\) 0 0
\(646\) 0.319324 0.553086i 0.0125636 0.0217609i
\(647\) 8.77640 + 15.2012i 0.345036 + 0.597619i 0.985360 0.170485i \(-0.0545335\pi\)
−0.640325 + 0.768105i \(0.721200\pi\)
\(648\) 0 0
\(649\) 2.47814 4.29226i 0.0972753 0.168486i
\(650\) −1.03523 −0.0406051
\(651\) 0 0
\(652\) 0.126196 0.00494221
\(653\) −11.9829 + 20.7549i −0.468926 + 0.812204i −0.999369 0.0355170i \(-0.988692\pi\)
0.530443 + 0.847721i \(0.322026\pi\)
\(654\) 0 0
\(655\) −6.71784 11.6356i −0.262488 0.454642i
\(656\) −18.5019 + 32.0462i −0.722377 + 1.25119i
\(657\) 0 0
\(658\) 0.0381338 9.22871i 0.00148661 0.359773i
\(659\) 38.6166 1.50429 0.752144 0.658999i \(-0.229020\pi\)
0.752144 + 0.658999i \(0.229020\pi\)
\(660\) 0 0
\(661\) −5.18942 8.98833i −0.201845 0.349606i 0.747278 0.664512i \(-0.231360\pi\)
−0.949123 + 0.314906i \(0.898027\pi\)
\(662\) 14.8096 + 25.6509i 0.575590 + 0.996951i
\(663\) 0 0
\(664\) −28.8418 −1.11928
\(665\) 0.0921145 22.2925i 0.00357205 0.864466i
\(666\) 0 0
\(667\) −17.9707 + 31.1262i −0.695830 + 1.20521i
\(668\) 2.46509 + 4.26966i 0.0953771 + 0.165198i
\(669\) 0 0
\(670\) −21.7428 + 37.6596i −0.839996 + 1.45492i
\(671\) −4.57160 −0.176485
\(672\) 0 0
\(673\) −11.8103 −0.455253 −0.227627 0.973748i \(-0.573097\pi\)
−0.227627 + 0.973748i \(0.573097\pi\)
\(674\) 0.184752 0.320000i 0.00711640 0.0123260i
\(675\) 0 0
\(676\) 1.59505 + 2.76272i 0.0613483 + 0.106258i
\(677\) 20.9845 36.3462i 0.806499 1.39690i −0.108776 0.994066i \(-0.534693\pi\)
0.915275 0.402830i \(-0.131974\pi\)
\(678\) 0 0
\(679\) 37.5102 + 21.8637i 1.43951 + 0.839050i
\(680\) −0.701436 −0.0268988
\(681\) 0 0
\(682\) 3.31896 + 5.74861i 0.127090 + 0.220126i
\(683\) 12.0767 + 20.9174i 0.462100 + 0.800381i 0.999065 0.0432234i \(-0.0137627\pi\)
−0.536965 + 0.843604i \(0.680429\pi\)
\(684\) 0 0
\(685\) −37.5326 −1.43405
\(686\) 24.1485 + 14.3442i 0.921994 + 0.547663i
\(687\) 0 0
\(688\) −9.43254 + 16.3376i −0.359612 + 0.622867i
\(689\) 9.14369 + 15.8373i 0.348347 + 0.603354i
\(690\) 0 0
\(691\) 2.63720 4.56776i 0.100324 0.173766i −0.811494 0.584360i \(-0.801345\pi\)
0.911818 + 0.410595i \(0.134679\pi\)
\(692\) −1.15851 −0.0440401
\(693\) 0 0
\(694\) −33.6090 −1.27578
\(695\) 16.6740 28.8802i 0.632481 1.09549i
\(696\) 0 0
\(697\) 0.478374 + 0.828569i 0.0181197 + 0.0313843i
\(698\) 12.2708 21.2537i 0.464457 0.804463i
\(699\) 0 0
\(700\) 0.305733 0.174835i 0.0115556 0.00660814i
\(701\) −26.9166 −1.01662 −0.508312 0.861173i \(-0.669730\pi\)
−0.508312 + 0.861173i \(0.669730\pi\)
\(702\) 0 0
\(703\) −0.541724 0.938294i −0.0204315 0.0353884i
\(704\) −3.23346 5.60051i −0.121865 0.211077i
\(705\) 0 0
\(706\) 11.7943 0.443883
\(707\) 0.105553 25.5447i 0.00396972 0.960705i
\(708\) 0 0
\(709\) −5.87138 + 10.1695i −0.220504 + 0.381925i −0.954961 0.296731i \(-0.904104\pi\)
0.734457 + 0.678655i \(0.237437\pi\)
\(710\) 7.53031 + 13.0429i 0.282608 + 0.489491i
\(711\) 0 0
\(712\) −17.9604 + 31.1084i −0.673095 + 1.16584i
\(713\) 31.1200 1.16545
\(714\) 0 0
\(715\) −3.58946 −0.134238
\(716\) −1.90653 + 3.30221i −0.0712504 + 0.123409i
\(717\) 0 0
\(718\) 8.19927 + 14.2015i 0.305994 + 0.529997i
\(719\) 14.0839 24.3941i 0.525242 0.909746i −0.474326 0.880349i \(-0.657308\pi\)
0.999568 0.0293966i \(-0.00935859\pi\)
\(720\) 0 0
\(721\) 20.2575 11.5843i 0.754428 0.431423i
\(722\) −9.03630 −0.336296
\(723\) 0 0
\(724\) −2.47806 4.29213i −0.0920965 0.159516i
\(725\) 1.12146 + 1.94242i 0.0416499 + 0.0721398i
\(726\) 0 0
\(727\) 32.9885 1.22347 0.611737 0.791061i \(-0.290471\pi\)
0.611737 + 0.791061i \(0.290471\pi\)
\(728\) −9.06632 5.28451i −0.336020 0.195857i
\(729\) 0 0
\(730\) −18.4672 + 31.9861i −0.683500 + 1.18386i
\(731\) 0.243882 + 0.422417i 0.00902032 + 0.0156237i
\(732\) 0 0
\(733\) −0.953106 + 1.65083i −0.0352038 + 0.0609747i −0.883090 0.469203i \(-0.844541\pi\)
0.847887 + 0.530177i \(0.177875\pi\)
\(734\) −2.66416 −0.0983360
\(735\) 0 0
\(736\) 11.9696 0.441206
\(737\) −6.14472 + 10.6430i −0.226344 + 0.392039i
\(738\) 0 0
\(739\) 18.9136 + 32.7594i 0.695749 + 1.20507i 0.969927 + 0.243394i \(0.0782609\pi\)
−0.274178 + 0.961679i \(0.588406\pi\)
\(740\) 0.105003 0.181870i 0.00385998 0.00668569i
\(741\) 0 0
\(742\) −41.2072 24.0186i −1.51276 0.881750i
\(743\) −46.4995 −1.70590 −0.852950 0.521993i \(-0.825189\pi\)
−0.852950 + 0.521993i \(0.825189\pi\)
\(744\) 0 0
\(745\) −0.785005 1.35967i −0.0287604 0.0498144i
\(746\) 7.03212 + 12.1800i 0.257464 + 0.445941i
\(747\) 0 0
\(748\) 0.0349842 0.00127915
\(749\) −24.0793 + 13.7698i −0.879838 + 0.503139i
\(750\) 0 0
\(751\) −2.07408 + 3.59242i −0.0756843 + 0.131089i −0.901384 0.433021i \(-0.857447\pi\)
0.825699 + 0.564110i \(0.190781\pi\)
\(752\) −5.18656 8.98338i −0.189134 0.327590i
\(753\) 0 0
\(754\) −5.89713 + 10.2141i −0.214761 + 0.371976i
\(755\) 55.4651 2.01858
\(756\) 0 0
\(757\) 4.56418 0.165888 0.0829439 0.996554i \(-0.473568\pi\)
0.0829439 + 0.996554i \(0.473568\pi\)
\(758\) 8.73023 15.1212i 0.317096 0.549227i
\(759\) 0 0
\(760\) −10.8616 18.8129i −0.393992 0.682414i
\(761\) −6.52544 + 11.3024i −0.236547 + 0.409711i −0.959721 0.280954i \(-0.909349\pi\)
0.723174 + 0.690666i \(0.242682\pi\)
\(762\) 0 0
\(763\) −0.115095 + 27.8539i −0.00416671 + 1.00838i
\(764\) 4.92311 0.178112
\(765\) 0 0
\(766\) −17.0452 29.5231i −0.615868 1.06671i
\(767\) −3.81247 6.60340i −0.137660 0.238435i
\(768\) 0 0
\(769\) −4.40156 −0.158724 −0.0793622 0.996846i \(-0.525288\pi\)
−0.0793622 + 0.996846i \(0.525288\pi\)
\(770\) 8.12687 4.64738i 0.292872 0.167480i
\(771\) 0 0
\(772\) −3.09813 + 5.36612i −0.111504 + 0.193131i
\(773\) 11.2048 + 19.4073i 0.403008 + 0.698031i 0.994087 0.108583i \(-0.0346312\pi\)
−0.591079 + 0.806614i \(0.701298\pi\)
\(774\) 0 0
\(775\) 0.971018 1.68185i 0.0348800 0.0604139i
\(776\) 42.3078 1.51876
\(777\) 0 0
\(778\) 52.0681 1.86673
\(779\) −14.8151 + 25.6605i −0.530805 + 0.919382i
\(780\) 0 0
\(781\) 2.12814 + 3.68605i 0.0761509 + 0.131897i
\(782\) 0.628692 1.08893i