Properties

Label 729.2.g.b.109.1
Level $729$
Weight $2$
Character 729.109
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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(28,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(54))
 
chi = DirichletCharacter(H, H._module([44]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.28");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.g (of order \(27\), degree \(18\), 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: \(144\)
Relative dimension: \(8\) over \(\Q(\zeta_{27})\)
Twist minimal: no (minimal twist has level 81)
Sato-Tate group: $\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label 109.1
Character \(\chi\) \(=\) 729.109
Dual form 729.2.g.b.622.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.82254 - 1.93178i) q^{2} +(-0.293829 + 5.04485i) q^{4} +(-2.82892 + 0.330653i) q^{5} +(1.70942 + 0.858501i) q^{7} +(6.21207 - 5.21255i) q^{8} +O(q^{10})\) \(q+(-1.82254 - 1.93178i) q^{2} +(-0.293829 + 5.04485i) q^{4} +(-2.82892 + 0.330653i) q^{5} +(1.70942 + 0.858501i) q^{7} +(6.21207 - 5.21255i) q^{8} +(5.79455 + 4.86220i) q^{10} +(0.733735 + 1.70099i) q^{11} +(-0.131251 - 0.0311070i) q^{13} +(-1.45704 - 4.86686i) q^{14} +(-11.3528 - 1.32695i) q^{16} +(-0.193799 + 1.09909i) q^{17} +(-1.05411 - 5.97816i) q^{19} +(-0.836876 - 14.3686i) q^{20} +(1.94867 - 4.51753i) q^{22} +(-0.416930 + 0.209390i) q^{23} +(3.02821 - 0.717699i) q^{25} +(0.179118 + 0.310241i) q^{26} +(-4.83328 + 8.37149i) q^{28} +(0.125753 - 0.420043i) q^{29} +(-2.36480 - 1.55535i) q^{31} +(8.44238 + 11.3401i) q^{32} +(2.47640 - 1.62875i) q^{34} +(-5.11966 - 1.86340i) q^{35} +(-7.77306 + 2.82916i) q^{37} +(-9.62732 + 12.9317i) q^{38} +(-15.8499 + 16.7999i) q^{40} +(3.81865 - 4.04753i) q^{41} +(-4.47917 + 6.01657i) q^{43} +(-8.79682 + 3.20178i) q^{44} +(1.16437 + 0.423795i) q^{46} +(-7.12769 + 4.68795i) q^{47} +(-1.99503 - 2.67979i) q^{49} +(-6.90546 - 4.54179i) q^{50} +(0.195495 - 0.653000i) q^{52} +(2.94278 - 5.09704i) q^{53} +(-2.63811 - 4.56934i) q^{55} +(15.0940 - 3.57734i) q^{56} +(-1.04062 + 0.522618i) q^{58} +(-5.58328 + 12.9435i) q^{59} +(-0.446598 - 7.66779i) q^{61} +(1.30534 + 7.40295i) q^{62} +(2.55035 - 14.4637i) q^{64} +(0.381583 + 0.0446007i) q^{65} +(-3.24125 - 10.8265i) q^{67} +(-5.48779 - 1.30063i) q^{68} +(5.73109 + 13.2862i) q^{70} +(-0.604067 - 0.506872i) q^{71} +(-2.76505 + 2.32015i) q^{73} +(19.6320 + 9.85956i) q^{74} +(30.4687 - 3.56128i) q^{76} +(-0.206042 + 3.53761i) q^{77} +(8.76989 + 9.29554i) q^{79} +32.5547 q^{80} -14.7786 q^{82} +(-11.4722 - 12.1598i) q^{83} +(0.184824 - 3.17331i) q^{85} +(19.7861 - 2.31267i) q^{86} +(13.4245 + 6.74204i) q^{88} +(-8.34578 + 7.00294i) q^{89} +(-0.197657 - 0.165854i) q^{91} +(-0.933836 - 2.16488i) q^{92} +(22.0466 + 5.22513i) q^{94} +(4.95869 + 16.5632i) q^{95} +(-2.28615 - 0.267213i) q^{97} +(-1.54074 + 8.73797i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} + 63 q^{20} + 9 q^{22} - 36 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} + 45 q^{29} + 9 q^{31} - 63 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} + 9 q^{38} + 9 q^{40} + 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} - 63 q^{47} + 9 q^{49} + 225 q^{50} + 27 q^{52} - 45 q^{53} - 9 q^{55} - 99 q^{56} + 9 q^{58} + 117 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} - 81 q^{65} + 36 q^{67} + 18 q^{68} + 63 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} + 90 q^{76} - 81 q^{77} + 63 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} + 63 q^{85} - 81 q^{86} + 90 q^{88} + 81 q^{89} - 18 q^{91} + 63 q^{92} + 63 q^{94} - 153 q^{95} + 36 q^{97} - 81 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{7}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.82254 1.93178i −1.28873 1.36597i −0.894569 0.446930i \(-0.852517\pi\)
−0.394159 0.919042i \(-0.628964\pi\)
\(3\) 0 0
\(4\) −0.293829 + 5.04485i −0.146914 + 2.52242i
\(5\) −2.82892 + 0.330653i −1.26513 + 0.147872i −0.722069 0.691821i \(-0.756809\pi\)
−0.543061 + 0.839693i \(0.682735\pi\)
\(6\) 0 0
\(7\) 1.70942 + 0.858501i 0.646099 + 0.324483i 0.741497 0.670956i \(-0.234116\pi\)
−0.0953983 + 0.995439i \(0.530412\pi\)
\(8\) 6.21207 5.21255i 2.19630 1.84291i
\(9\) 0 0
\(10\) 5.79455 + 4.86220i 1.83240 + 1.53756i
\(11\) 0.733735 + 1.70099i 0.221229 + 0.512867i 0.992296 0.123887i \(-0.0395359\pi\)
−0.771067 + 0.636754i \(0.780277\pi\)
\(12\) 0 0
\(13\) −0.131251 0.0311070i −0.0364024 0.00862753i 0.212374 0.977188i \(-0.431880\pi\)
−0.248777 + 0.968561i \(0.580029\pi\)
\(14\) −1.45704 4.86686i −0.389411 1.30072i
\(15\) 0 0
\(16\) −11.3528 1.32695i −2.83819 0.331737i
\(17\) −0.193799 + 1.09909i −0.0470031 + 0.266568i −0.999248 0.0387665i \(-0.987657\pi\)
0.952245 + 0.305334i \(0.0987683\pi\)
\(18\) 0 0
\(19\) −1.05411 5.97816i −0.241830 1.37148i −0.827741 0.561110i \(-0.810375\pi\)
0.585912 0.810375i \(-0.300737\pi\)
\(20\) −0.836876 14.3686i −0.187131 3.21292i
\(21\) 0 0
\(22\) 1.94867 4.51753i 0.415458 0.963140i
\(23\) −0.416930 + 0.209390i −0.0869360 + 0.0436609i −0.491736 0.870744i \(-0.663637\pi\)
0.404800 + 0.914405i \(0.367341\pi\)
\(24\) 0 0
\(25\) 3.02821 0.717699i 0.605642 0.143540i
\(26\) 0.179118 + 0.310241i 0.0351279 + 0.0608432i
\(27\) 0 0
\(28\) −4.83328 + 8.37149i −0.913405 + 1.58206i
\(29\) 0.125753 0.420043i 0.0233517 0.0780001i −0.945519 0.325566i \(-0.894445\pi\)
0.968871 + 0.247565i \(0.0796305\pi\)
\(30\) 0 0
\(31\) −2.36480 1.55535i −0.424730 0.279350i 0.319096 0.947722i \(-0.396621\pi\)
−0.743826 + 0.668373i \(0.766991\pi\)
\(32\) 8.44238 + 11.3401i 1.49242 + 2.00466i
\(33\) 0 0
\(34\) 2.47640 1.62875i 0.424699 0.279329i
\(35\) −5.11966 1.86340i −0.865381 0.314973i
\(36\) 0 0
\(37\) −7.77306 + 2.82916i −1.27788 + 0.465112i −0.889732 0.456484i \(-0.849109\pi\)
−0.388152 + 0.921595i \(0.626886\pi\)
\(38\) −9.62732 + 12.9317i −1.56176 + 2.09780i
\(39\) 0 0
\(40\) −15.8499 + 16.7999i −2.50609 + 2.65630i
\(41\) 3.81865 4.04753i 0.596373 0.632118i −0.356931 0.934131i \(-0.616177\pi\)
0.953304 + 0.302012i \(0.0976584\pi\)
\(42\) 0 0
\(43\) −4.47917 + 6.01657i −0.683068 + 0.917519i −0.999517 0.0310906i \(-0.990102\pi\)
0.316449 + 0.948610i \(0.397509\pi\)
\(44\) −8.79682 + 3.20178i −1.32617 + 0.482687i
\(45\) 0 0
\(46\) 1.16437 + 0.423795i 0.171676 + 0.0624851i
\(47\) −7.12769 + 4.68795i −1.03968 + 0.683808i −0.950028 0.312165i \(-0.898946\pi\)
−0.0896522 + 0.995973i \(0.528576\pi\)
\(48\) 0 0
\(49\) −1.99503 2.67979i −0.285004 0.382827i
\(50\) −6.90546 4.54179i −0.976579 0.642306i
\(51\) 0 0
\(52\) 0.195495 0.653000i 0.0271103 0.0905549i
\(53\) 2.94278 5.09704i 0.404222 0.700133i −0.590009 0.807397i \(-0.700876\pi\)
0.994231 + 0.107264i \(0.0342090\pi\)
\(54\) 0 0
\(55\) −2.63811 4.56934i −0.355723 0.616130i
\(56\) 15.0940 3.57734i 2.01702 0.478043i
\(57\) 0 0
\(58\) −1.04062 + 0.522618i −0.136640 + 0.0686231i
\(59\) −5.58328 + 12.9435i −0.726881 + 1.68510i 0.00156855 + 0.999999i \(0.499501\pi\)
−0.728449 + 0.685100i \(0.759759\pi\)
\(60\) 0 0
\(61\) −0.446598 7.66779i −0.0571810 0.981759i −0.897875 0.440250i \(-0.854890\pi\)
0.840694 0.541510i \(-0.182147\pi\)
\(62\) 1.30534 + 7.40295i 0.165778 + 0.940175i
\(63\) 0 0
\(64\) 2.55035 14.4637i 0.318793 1.80797i
\(65\) 0.381583 + 0.0446007i 0.0473296 + 0.00553203i
\(66\) 0 0
\(67\) −3.24125 10.8265i −0.395981 1.32267i −0.891085 0.453836i \(-0.850055\pi\)
0.495104 0.868834i \(-0.335130\pi\)
\(68\) −5.48779 1.30063i −0.665492 0.157725i
\(69\) 0 0
\(70\) 5.73109 + 13.2862i 0.684996 + 1.58800i
\(71\) −0.604067 0.506872i −0.0716895 0.0601547i 0.606239 0.795283i \(-0.292678\pi\)
−0.677928 + 0.735128i \(0.737122\pi\)
\(72\) 0 0
\(73\) −2.76505 + 2.32015i −0.323625 + 0.271553i −0.790096 0.612983i \(-0.789969\pi\)
0.466472 + 0.884536i \(0.345525\pi\)
\(74\) 19.6320 + 9.85956i 2.28217 + 1.14615i
\(75\) 0 0
\(76\) 30.4687 3.56128i 3.49499 0.408506i
\(77\) −0.206042 + 3.53761i −0.0234807 + 0.403148i
\(78\) 0 0
\(79\) 8.76989 + 9.29554i 0.986690 + 1.04583i 0.998946 + 0.0459050i \(0.0146172\pi\)
−0.0122562 + 0.999925i \(0.503901\pi\)
\(80\) 32.5547 3.63973
\(81\) 0 0
\(82\) −14.7786 −1.63202
\(83\) −11.4722 12.1598i −1.25924 1.33472i −0.918940 0.394398i \(-0.870953\pi\)
−0.340299 0.940317i \(-0.610528\pi\)
\(84\) 0 0
\(85\) 0.184824 3.17331i 0.0200470 0.344194i
\(86\) 19.7861 2.31267i 2.13359 0.249381i
\(87\) 0 0
\(88\) 13.4245 + 6.74204i 1.43106 + 0.718704i
\(89\) −8.34578 + 7.00294i −0.884651 + 0.742311i −0.967130 0.254282i \(-0.918161\pi\)
0.0824788 + 0.996593i \(0.473716\pi\)
\(90\) 0 0
\(91\) −0.197657 0.165854i −0.0207201 0.0173862i
\(92\) −0.933836 2.16488i −0.0973592 0.225704i
\(93\) 0 0
\(94\) 22.0466 + 5.22513i 2.27393 + 0.538931i
\(95\) 4.95869 + 16.5632i 0.508751 + 1.69935i
\(96\) 0 0
\(97\) −2.28615 0.267213i −0.232124 0.0271313i −0.000764163 1.00000i \(-0.500243\pi\)
−0.231359 + 0.972868i \(0.574317\pi\)
\(98\) −1.54074 + 8.73797i −0.155638 + 0.882668i
\(99\) 0 0
\(100\) 2.73091 + 15.4877i 0.273091 + 1.54877i
\(101\) −0.500707 8.59680i −0.0498222 0.855414i −0.926957 0.375169i \(-0.877585\pi\)
0.877134 0.480245i \(-0.159452\pi\)
\(102\) 0 0
\(103\) −3.18205 + 7.37683i −0.313537 + 0.726861i −1.00000 0.000304198i \(-0.999903\pi\)
0.686463 + 0.727165i \(0.259162\pi\)
\(104\) −0.977487 + 0.490912i −0.0958505 + 0.0481379i
\(105\) 0 0
\(106\) −15.2097 + 3.60476i −1.47729 + 0.350125i
\(107\) −2.09736 3.63274i −0.202760 0.351190i 0.746657 0.665209i \(-0.231658\pi\)
−0.949417 + 0.314019i \(0.898324\pi\)
\(108\) 0 0
\(109\) −5.69325 + 9.86099i −0.545314 + 0.944512i 0.453273 + 0.891372i \(0.350256\pi\)
−0.998587 + 0.0531401i \(0.983077\pi\)
\(110\) −4.01889 + 13.4240i −0.383186 + 1.27993i
\(111\) 0 0
\(112\) −18.2674 12.0147i −1.72611 1.13528i
\(113\) −8.38939 11.2689i −0.789207 1.06009i −0.996645 0.0818411i \(-0.973920\pi\)
0.207438 0.978248i \(-0.433487\pi\)
\(114\) 0 0
\(115\) 1.11023 0.730207i 0.103529 0.0680921i
\(116\) 2.08211 + 0.757824i 0.193319 + 0.0703622i
\(117\) 0 0
\(118\) 35.1796 12.8043i 3.23855 1.17874i
\(119\) −1.27485 + 1.71242i −0.116865 + 0.156977i
\(120\) 0 0
\(121\) 5.19366 5.50496i 0.472151 0.500451i
\(122\) −13.9985 + 14.8375i −1.26736 + 1.34333i
\(123\) 0 0
\(124\) 8.54136 11.4730i 0.767037 1.03031i
\(125\) 5.05280 1.83907i 0.451936 0.164491i
\(126\) 0 0
\(127\) 6.95520 + 2.53149i 0.617174 + 0.224633i 0.631639 0.775262i \(-0.282382\pi\)
−0.0144652 + 0.999895i \(0.504605\pi\)
\(128\) −8.96524 + 5.89653i −0.792423 + 0.521185i
\(129\) 0 0
\(130\) −0.609291 0.818420i −0.0534383 0.0717801i
\(131\) −6.01389 3.95540i −0.525436 0.345584i 0.258917 0.965900i \(-0.416634\pi\)
−0.784353 + 0.620315i \(0.787005\pi\)
\(132\) 0 0
\(133\) 3.33034 11.1241i 0.288777 0.964584i
\(134\) −15.0071 + 25.9931i −1.29642 + 2.24546i
\(135\) 0 0
\(136\) 4.52516 + 7.83780i 0.388029 + 0.672086i
\(137\) −13.7898 + 3.26824i −1.17814 + 0.279225i −0.772625 0.634863i \(-0.781057\pi\)
−0.405517 + 0.914087i \(0.632909\pi\)
\(138\) 0 0
\(139\) 12.2693 6.16188i 1.04067 0.522644i 0.155462 0.987842i \(-0.450313\pi\)
0.885207 + 0.465198i \(0.154017\pi\)
\(140\) 10.9049 25.2804i 0.921632 2.13658i
\(141\) 0 0
\(142\) 0.121770 + 2.09071i 0.0102187 + 0.175449i
\(143\) −0.0433906 0.246080i −0.00362851 0.0205783i
\(144\) 0 0
\(145\) −0.216855 + 1.22985i −0.0180089 + 0.102133i
\(146\) 9.52142 + 1.11289i 0.787998 + 0.0921038i
\(147\) 0 0
\(148\) −11.9887 40.0452i −0.985469 3.29170i
\(149\) −1.99438 0.472677i −0.163386 0.0387232i 0.148109 0.988971i \(-0.452681\pi\)
−0.311495 + 0.950248i \(0.600830\pi\)
\(150\) 0 0
\(151\) −4.85826 11.2627i −0.395360 0.916547i −0.993360 0.115051i \(-0.963297\pi\)
0.598000 0.801496i \(-0.295962\pi\)
\(152\) −37.7097 31.6422i −3.05866 2.56652i
\(153\) 0 0
\(154\) 7.20939 6.04940i 0.580949 0.487474i
\(155\) 7.20410 + 3.61803i 0.578647 + 0.290607i
\(156\) 0 0
\(157\) −22.6120 + 2.64296i −1.80463 + 0.210931i −0.950840 0.309683i \(-0.899777\pi\)
−0.853792 + 0.520615i \(0.825703\pi\)
\(158\) 1.97346 33.8829i 0.157000 2.69558i
\(159\) 0 0
\(160\) −27.6324 29.2887i −2.18453 2.31547i
\(161\) −0.892470 −0.0703365
\(162\) 0 0
\(163\) −11.4061 −0.893393 −0.446697 0.894685i \(-0.647400\pi\)
−0.446697 + 0.894685i \(0.647400\pi\)
\(164\) 19.2972 + 20.4538i 1.50685 + 1.59717i
\(165\) 0 0
\(166\) −2.58155 + 44.3235i −0.200367 + 3.44017i
\(167\) −5.33283 + 0.623319i −0.412667 + 0.0482338i −0.319894 0.947453i \(-0.603647\pi\)
−0.0927732 + 0.995687i \(0.529573\pi\)
\(168\) 0 0
\(169\) −11.6010 5.82622i −0.892382 0.448171i
\(170\) −6.46697 + 5.42643i −0.495994 + 0.416188i
\(171\) 0 0
\(172\) −29.0366 24.3646i −2.21402 1.85778i
\(173\) 1.35044 + 3.13068i 0.102672 + 0.238021i 0.961807 0.273728i \(-0.0882569\pi\)
−0.859135 + 0.511749i \(0.828998\pi\)
\(174\) 0 0
\(175\) 5.79262 + 1.37288i 0.437881 + 0.103780i
\(176\) −6.07279 20.2845i −0.457754 1.52900i
\(177\) 0 0
\(178\) 28.7386 + 3.35906i 2.15405 + 0.251772i
\(179\) 1.16699 6.61830i 0.0872246 0.494675i −0.909630 0.415420i \(-0.863635\pi\)
0.996854 0.0792553i \(-0.0252542\pi\)
\(180\) 0 0
\(181\) 0.341126 + 1.93462i 0.0253557 + 0.143799i 0.994857 0.101285i \(-0.0322954\pi\)
−0.969502 + 0.245084i \(0.921184\pi\)
\(182\) 0.0398445 + 0.684104i 0.00295347 + 0.0507091i
\(183\) 0 0
\(184\) −1.49855 + 3.47402i −0.110474 + 0.256108i
\(185\) 21.0539 10.5736i 1.54791 0.777390i
\(186\) 0 0
\(187\) −2.01173 + 0.476790i −0.147112 + 0.0348663i
\(188\) −21.5557 37.3356i −1.57211 2.72298i
\(189\) 0 0
\(190\) 22.9590 39.7661i 1.66562 2.88493i
\(191\) 1.34728 4.50022i 0.0974857 0.325625i −0.895310 0.445443i \(-0.853046\pi\)
0.992796 + 0.119819i \(0.0382313\pi\)
\(192\) 0 0
\(193\) 5.27148 + 3.46710i 0.379449 + 0.249568i 0.724878 0.688877i \(-0.241896\pi\)
−0.345429 + 0.938445i \(0.612267\pi\)
\(194\) 3.65040 + 4.90334i 0.262083 + 0.352039i
\(195\) 0 0
\(196\) 14.1053 9.27723i 1.00752 0.662659i
\(197\) 10.1410 + 3.69101i 0.722514 + 0.262973i 0.676992 0.735990i \(-0.263283\pi\)
0.0455211 + 0.998963i \(0.485505\pi\)
\(198\) 0 0
\(199\) −2.20899 + 0.804005i −0.156591 + 0.0569944i −0.419126 0.907928i \(-0.637664\pi\)
0.262535 + 0.964922i \(0.415441\pi\)
\(200\) 15.0704 20.2431i 1.06564 1.43140i
\(201\) 0 0
\(202\) −15.6945 + 16.6352i −1.10426 + 1.17045i
\(203\) 0.575571 0.610070i 0.0403972 0.0428185i
\(204\) 0 0
\(205\) −9.46431 + 12.7128i −0.661016 + 0.887899i
\(206\) 20.0498 7.29753i 1.39694 0.508443i
\(207\) 0 0
\(208\) 1.44878 + 0.527313i 0.100455 + 0.0365626i
\(209\) 9.39535 6.17942i 0.649890 0.427439i
\(210\) 0 0
\(211\) −6.60517 8.87228i −0.454718 0.610793i 0.514351 0.857580i \(-0.328033\pi\)
−0.969070 + 0.246787i \(0.920625\pi\)
\(212\) 24.8491 + 16.3435i 1.70665 + 1.12248i
\(213\) 0 0
\(214\) −3.19512 + 10.6724i −0.218414 + 0.729553i
\(215\) 10.6818 18.5014i 0.728493 1.26179i
\(216\) 0 0
\(217\) −2.70715 4.68893i −0.183774 0.318305i
\(218\) 29.4254 6.97394i 1.99294 0.472335i
\(219\) 0 0
\(220\) 23.8268 11.9663i 1.60640 0.806765i
\(221\) 0.0596256 0.138228i 0.00401085 0.00929820i
\(222\) 0 0
\(223\) −0.235968 4.05141i −0.0158016 0.271302i −0.996950 0.0780456i \(-0.975132\pi\)
0.981148 0.193257i \(-0.0619050\pi\)
\(224\) 4.69607 + 26.6327i 0.313769 + 1.77947i
\(225\) 0 0
\(226\) −6.47903 + 36.7444i −0.430979 + 2.44420i
\(227\) −10.7086 1.25166i −0.710756 0.0830755i −0.246971 0.969023i \(-0.579435\pi\)
−0.463786 + 0.885947i \(0.653509\pi\)
\(228\) 0 0
\(229\) 1.63605 + 5.46478i 0.108113 + 0.361123i 0.994876 0.101101i \(-0.0322366\pi\)
−0.886763 + 0.462224i \(0.847051\pi\)
\(230\) −3.43402 0.813878i −0.226433 0.0536656i
\(231\) 0 0
\(232\) −1.40831 3.26483i −0.0924602 0.214347i
\(233\) 20.2690 + 17.0077i 1.32787 + 1.11421i 0.984571 + 0.174987i \(0.0559882\pi\)
0.343297 + 0.939227i \(0.388456\pi\)
\(234\) 0 0
\(235\) 18.6135 15.6186i 1.21421 1.01885i
\(236\) −63.6574 31.9700i −4.14374 2.08107i
\(237\) 0 0
\(238\) 5.63148 0.658226i 0.365035 0.0426664i
\(239\) −0.208731 + 3.58378i −0.0135017 + 0.231816i 0.984806 + 0.173659i \(0.0555592\pi\)
−0.998307 + 0.0581562i \(0.981478\pi\)
\(240\) 0 0
\(241\) 5.82337 + 6.17241i 0.375116 + 0.397600i 0.887237 0.461313i \(-0.152622\pi\)
−0.512121 + 0.858913i \(0.671140\pi\)
\(242\) −20.1000 −1.29208
\(243\) 0 0
\(244\) 38.8140 2.48481
\(245\) 6.52985 + 6.92124i 0.417177 + 0.442182i
\(246\) 0 0
\(247\) −0.0476098 + 0.817429i −0.00302934 + 0.0520118i
\(248\) −22.7977 + 2.66466i −1.44765 + 0.169206i
\(249\) 0 0
\(250\) −12.7616 6.40911i −0.807114 0.405348i
\(251\) 3.14926 2.64255i 0.198780 0.166796i −0.537965 0.842967i \(-0.680807\pi\)
0.736744 + 0.676171i \(0.236362\pi\)
\(252\) 0 0
\(253\) −0.662087 0.555557i −0.0416251 0.0349276i
\(254\) −7.78584 18.0496i −0.488527 1.13253i
\(255\) 0 0
\(256\) −0.851704 0.201858i −0.0532315 0.0126161i
\(257\) −1.65693 5.53454i −0.103357 0.345235i 0.890631 0.454726i \(-0.150263\pi\)
−0.993988 + 0.109492i \(0.965078\pi\)
\(258\) 0 0
\(259\) −15.7162 1.83696i −0.976559 0.114143i
\(260\) −0.337124 + 1.91192i −0.0209075 + 0.118573i
\(261\) 0 0
\(262\) 3.31959 + 18.8263i 0.205085 + 1.16309i
\(263\) 0.836130 + 14.3558i 0.0515580 + 0.885216i 0.920607 + 0.390490i \(0.127695\pi\)
−0.869049 + 0.494726i \(0.835268\pi\)
\(264\) 0 0
\(265\) −6.63952 + 15.3921i −0.407863 + 0.945532i
\(266\) −27.5590 + 13.8406i −1.68975 + 0.848624i
\(267\) 0 0
\(268\) 55.5705 13.1705i 3.39451 0.804514i
\(269\) −4.14565 7.18047i −0.252765 0.437801i 0.711521 0.702664i \(-0.248006\pi\)
−0.964286 + 0.264863i \(0.914673\pi\)
\(270\) 0 0
\(271\) 4.28409 7.42026i 0.260240 0.450748i −0.706066 0.708146i \(-0.749532\pi\)
0.966306 + 0.257398i \(0.0828651\pi\)
\(272\) 3.65858 12.2205i 0.221834 0.740977i
\(273\) 0 0
\(274\) 31.4459 + 20.6823i 1.89972 + 1.24946i
\(275\) 3.44270 + 4.62435i 0.207603 + 0.278859i
\(276\) 0 0
\(277\) −25.6364 + 16.8613i −1.54034 + 1.01310i −0.557171 + 0.830398i \(0.688113\pi\)
−0.983169 + 0.182700i \(0.941516\pi\)
\(278\) −34.2646 12.4713i −2.05506 0.747979i
\(279\) 0 0
\(280\) −41.5168 + 15.1109i −2.48110 + 0.903048i
\(281\) −2.22640 + 2.99057i −0.132816 + 0.178403i −0.863556 0.504253i \(-0.831768\pi\)
0.730740 + 0.682656i \(0.239175\pi\)
\(282\) 0 0
\(283\) −4.88380 + 5.17653i −0.290312 + 0.307713i −0.856071 0.516858i \(-0.827102\pi\)
0.565759 + 0.824570i \(0.308583\pi\)
\(284\) 2.73459 2.89849i 0.162268 0.171994i
\(285\) 0 0
\(286\) −0.396291 + 0.532312i −0.0234332 + 0.0314762i
\(287\) 10.0025 3.64060i 0.590427 0.214898i
\(288\) 0 0
\(289\) 14.8043 + 5.38834i 0.870843 + 0.316961i
\(290\) 2.77102 1.82253i 0.162720 0.107022i
\(291\) 0 0
\(292\) −10.8924 14.6310i −0.637427 0.856214i
\(293\) 7.14612 + 4.70008i 0.417481 + 0.274581i 0.740823 0.671701i \(-0.234436\pi\)
−0.323342 + 0.946282i \(0.604806\pi\)
\(294\) 0 0
\(295\) 11.5148 38.4622i 0.670419 2.23935i
\(296\) −33.5397 + 58.0924i −1.94945 + 3.37655i
\(297\) 0 0
\(298\) 2.72173 + 4.71417i 0.157665 + 0.273085i
\(299\) 0.0612360 0.0145132i 0.00354137 0.000839320i
\(300\) 0 0
\(301\) −12.8220 + 6.43945i −0.739048 + 0.371164i
\(302\) −12.9027 + 29.9118i −0.742466 + 1.72123i
\(303\) 0 0
\(304\) 4.03436 + 69.2674i 0.231387 + 3.97276i
\(305\) 3.79876 + 21.5439i 0.217516 + 1.23360i
\(306\) 0 0
\(307\) 2.00083 11.3473i 0.114194 0.647624i −0.872953 0.487805i \(-0.837798\pi\)
0.987146 0.159819i \(-0.0510911\pi\)
\(308\) −17.7862 2.07890i −1.01346 0.118457i
\(309\) 0 0
\(310\) −6.14050 20.5107i −0.348757 1.16493i
\(311\) 24.9086 + 5.90345i 1.41244 + 0.334754i 0.864865 0.502005i \(-0.167404\pi\)
0.547572 + 0.836759i \(0.315552\pi\)
\(312\) 0 0
\(313\) 0.597467 + 1.38508i 0.0337708 + 0.0782896i 0.934267 0.356575i \(-0.116056\pi\)
−0.900496 + 0.434864i \(0.856796\pi\)
\(314\) 46.3167 + 38.8644i 2.61381 + 2.19324i
\(315\) 0 0
\(316\) −49.4714 + 41.5115i −2.78299 + 2.33520i
\(317\) −6.75232 3.39114i −0.379248 0.190466i 0.248955 0.968515i \(-0.419913\pi\)
−0.628203 + 0.778050i \(0.716209\pi\)
\(318\) 0 0
\(319\) 0.806758 0.0942965i 0.0451698 0.00527959i
\(320\) −2.43224 + 41.7600i −0.135966 + 2.33445i
\(321\) 0 0
\(322\) 1.62656 + 1.72405i 0.0906446 + 0.0960776i
\(323\) 6.77481 0.376961
\(324\) 0 0
\(325\) −0.419780 −0.0232852
\(326\) 20.7880 + 22.0340i 1.15134 + 1.22035i
\(327\) 0 0
\(328\) 2.62377 45.0485i 0.144874 2.48739i
\(329\) −16.2088 + 1.89454i −0.893620 + 0.104449i
\(330\) 0 0
\(331\) 27.0102 + 13.5650i 1.48461 + 0.745601i 0.992188 0.124753i \(-0.0398137\pi\)
0.492427 + 0.870354i \(0.336110\pi\)
\(332\) 64.7154 54.3027i 3.55172 2.98025i
\(333\) 0 0
\(334\) 10.9234 + 9.16582i 0.597701 + 0.501531i
\(335\) 12.7490 + 29.5556i 0.696554 + 1.61479i
\(336\) 0 0
\(337\) 21.9824 + 5.20993i 1.19746 + 0.283803i 0.780520 0.625131i \(-0.214955\pi\)
0.416940 + 0.908934i \(0.363103\pi\)
\(338\) 9.88823 + 33.0290i 0.537849 + 1.79654i
\(339\) 0 0
\(340\) 15.9545 + 1.86482i 0.865257 + 0.101134i
\(341\) 0.910502 5.16371i 0.0493064 0.279631i
\(342\) 0 0
\(343\) −3.43492 19.4804i −0.185468 1.05184i
\(344\) 3.53673 + 60.7233i 0.190688 + 3.27398i
\(345\) 0 0
\(346\) 3.58653 8.31452i 0.192813 0.446991i
\(347\) 16.0215 8.04632i 0.860082 0.431949i 0.0366256 0.999329i \(-0.488339\pi\)
0.823456 + 0.567380i \(0.192043\pi\)
\(348\) 0 0
\(349\) −26.1088 + 6.18789i −1.39757 + 0.331230i −0.859269 0.511523i \(-0.829081\pi\)
−0.538300 + 0.842753i \(0.680933\pi\)
\(350\) −7.90517 13.6921i −0.422549 0.731876i
\(351\) 0 0
\(352\) −13.0949 + 22.6810i −0.697960 + 1.20890i
\(353\) 5.99125 20.0122i 0.318882 1.06514i −0.636871 0.770970i \(-0.719772\pi\)
0.955753 0.294170i \(-0.0950431\pi\)
\(354\) 0 0
\(355\) 1.87645 + 1.23416i 0.0995918 + 0.0655025i
\(356\) −32.8766 44.1609i −1.74245 2.34052i
\(357\) 0 0
\(358\) −14.9119 + 9.80774i −0.788121 + 0.518355i
\(359\) 12.6815 + 4.61568i 0.669303 + 0.243606i 0.654248 0.756280i \(-0.272985\pi\)
0.0150553 + 0.999887i \(0.495208\pi\)
\(360\) 0 0
\(361\) −16.7731 + 6.10492i −0.882796 + 0.321311i
\(362\) 3.11554 4.18490i 0.163749 0.219953i
\(363\) 0 0
\(364\) 0.894785 0.948416i 0.0468995 0.0497105i
\(365\) 7.05493 7.47779i 0.369272 0.391405i
\(366\) 0 0
\(367\) −5.89270 + 7.91527i −0.307596 + 0.413173i −0.928862 0.370427i \(-0.879211\pi\)
0.621265 + 0.783600i \(0.286619\pi\)
\(368\) 5.01116 1.82391i 0.261225 0.0950780i
\(369\) 0 0
\(370\) −58.7974 21.4005i −3.05673 1.11256i
\(371\) 9.40625 6.18659i 0.488348 0.321192i
\(372\) 0 0
\(373\) 6.44396 + 8.65574i 0.333655 + 0.448177i 0.937013 0.349293i \(-0.113578\pi\)
−0.603358 + 0.797471i \(0.706171\pi\)
\(374\) 4.58751 + 3.01725i 0.237214 + 0.156018i
\(375\) 0 0
\(376\) −19.8415 + 66.2753i −1.02325 + 3.41789i
\(377\) −0.0295714 + 0.0512192i −0.00152301 + 0.00263792i
\(378\) 0 0
\(379\) −6.41085 11.1039i −0.329303 0.570370i 0.653071 0.757297i \(-0.273480\pi\)
−0.982374 + 0.186927i \(0.940147\pi\)
\(380\) −85.0157 + 20.1491i −4.36121 + 1.03363i
\(381\) 0 0
\(382\) −11.1489 + 5.59918i −0.570427 + 0.286479i
\(383\) 5.50565 12.7635i 0.281326 0.652186i −0.717699 0.696354i \(-0.754804\pi\)
0.999024 + 0.0441680i \(0.0140637\pi\)
\(384\) 0 0
\(385\) −0.586844 10.0757i −0.0299084 0.513507i
\(386\) −2.90979 16.5022i −0.148104 0.839942i
\(387\) 0 0
\(388\) 2.01979 11.4548i 0.102539 0.581528i
\(389\) 34.5433 + 4.03753i 1.75141 + 0.204711i 0.930488 0.366324i \(-0.119384\pi\)
0.820926 + 0.571034i \(0.193458\pi\)
\(390\) 0 0
\(391\) −0.149338 0.498823i −0.00755234 0.0252266i
\(392\) −26.3618 6.24787i −1.33147 0.315565i
\(393\) 0 0
\(394\) −11.3521 26.3171i −0.571909 1.32583i
\(395\) −27.8829 23.3965i −1.40294 1.17721i
\(396\) 0 0
\(397\) 11.3325 9.50911i 0.568763 0.477249i −0.312472 0.949927i \(-0.601157\pi\)
0.881235 + 0.472678i \(0.156713\pi\)
\(398\) 5.57911 + 2.80194i 0.279656 + 0.140448i
\(399\) 0 0
\(400\) −35.3309 + 4.12958i −1.76654 + 0.206479i
\(401\) −1.50994 + 25.9247i −0.0754029 + 1.29462i 0.722305 + 0.691574i \(0.243083\pi\)
−0.797708 + 0.603044i \(0.793954\pi\)
\(402\) 0 0
\(403\) 0.261999 + 0.277703i 0.0130511 + 0.0138334i
\(404\) 43.5167 2.16504
\(405\) 0 0
\(406\) −2.22752 −0.110550
\(407\) −10.5157 11.1460i −0.521246 0.552488i
\(408\) 0 0
\(409\) −1.20574 + 20.7018i −0.0596200 + 1.02364i 0.827314 + 0.561740i \(0.189868\pi\)
−0.886934 + 0.461896i \(0.847169\pi\)
\(410\) 41.8073 4.88657i 2.06471 0.241331i
\(411\) 0 0
\(412\) −36.2800 18.2205i −1.78739 0.897660i
\(413\) −20.6561 + 17.3326i −1.01642 + 0.852880i
\(414\) 0 0
\(415\) 36.4746 + 30.6058i 1.79047 + 1.50238i
\(416\) −0.755313 1.75101i −0.0370323 0.0858505i
\(417\) 0 0
\(418\) −29.0606 6.88749i −1.42140 0.336878i
\(419\) −2.60357 8.69653i −0.127193 0.424853i 0.870544 0.492090i \(-0.163767\pi\)
−0.997737 + 0.0672367i \(0.978582\pi\)
\(420\) 0 0
\(421\) 25.6584 + 2.99904i 1.25051 + 0.146164i 0.715460 0.698654i \(-0.246217\pi\)
0.535054 + 0.844818i \(0.320291\pi\)
\(422\) −5.10110 + 28.9298i −0.248318 + 1.40828i
\(423\) 0 0
\(424\) −8.28783 47.0026i −0.402492 2.28265i
\(425\) 0.201951 + 3.46736i 0.00979604 + 0.168192i
\(426\) 0 0
\(427\) 5.81938 13.4908i 0.281620 0.652868i
\(428\) 18.9429 9.51347i 0.915639 0.459851i
\(429\) 0 0
\(430\) −55.2086 + 13.0847i −2.66240 + 0.630999i
\(431\) 10.5319 + 18.2418i 0.507305 + 0.878678i 0.999964 + 0.00845587i \(0.00269162\pi\)
−0.492659 + 0.870222i \(0.663975\pi\)
\(432\) 0 0
\(433\) −14.6179 + 25.3190i −0.702493 + 1.21675i 0.265095 + 0.964222i \(0.414597\pi\)
−0.967589 + 0.252532i \(0.918737\pi\)
\(434\) −4.12407 + 13.7754i −0.197962 + 0.661238i
\(435\) 0 0
\(436\) −48.0744 31.6190i −2.30235 1.51428i
\(437\) 1.69126 + 2.27176i 0.0809040 + 0.108673i
\(438\) 0 0
\(439\) 20.4577 13.4553i 0.976394 0.642185i 0.0422600 0.999107i \(-0.486544\pi\)
0.934134 + 0.356922i \(0.116174\pi\)
\(440\) −40.2061 14.6338i −1.91675 0.697640i
\(441\) 0 0
\(442\) −0.375695 + 0.136742i −0.0178700 + 0.00650414i
\(443\) 12.1100 16.2665i 0.575363 0.772846i −0.415226 0.909718i \(-0.636297\pi\)
0.990589 + 0.136872i \(0.0437049\pi\)
\(444\) 0 0
\(445\) 21.2940 22.5703i 1.00943 1.06993i
\(446\) −7.39635 + 7.83967i −0.350227 + 0.371219i
\(447\) 0 0
\(448\) 16.7767 22.5351i 0.792627 1.06468i
\(449\) −29.1855 + 10.6227i −1.37735 + 0.501314i −0.921374 0.388678i \(-0.872932\pi\)
−0.455976 + 0.889992i \(0.650710\pi\)
\(450\) 0 0
\(451\) 9.68668 + 3.52566i 0.456128 + 0.166017i
\(452\) 59.3150 39.0121i 2.78994 1.83497i
\(453\) 0 0
\(454\) 17.0989 + 22.9679i 0.802493 + 1.07793i
\(455\) 0.613995 + 0.403831i 0.0287845 + 0.0189319i
\(456\) 0 0
\(457\) 1.55375 5.18989i 0.0726815 0.242773i −0.913927 0.405878i \(-0.866966\pi\)
0.986609 + 0.163105i \(0.0521509\pi\)
\(458\) 7.57498 13.1202i 0.353956 0.613069i
\(459\) 0 0
\(460\) 3.35757 + 5.81548i 0.156547 + 0.271148i
\(461\) 16.3680 3.87929i 0.762335 0.180677i 0.168982 0.985619i \(-0.445952\pi\)
0.593353 + 0.804942i \(0.297804\pi\)
\(462\) 0 0
\(463\) 5.82307 2.92446i 0.270621 0.135911i −0.308314 0.951285i \(-0.599765\pi\)
0.578935 + 0.815374i \(0.303468\pi\)
\(464\) −1.98501 + 4.60178i −0.0921520 + 0.213632i
\(465\) 0 0
\(466\) −4.08591 70.1524i −0.189276 3.24975i
\(467\) 1.70237 + 9.65460i 0.0787761 + 0.446761i 0.998527 + 0.0542586i \(0.0172795\pi\)
−0.919751 + 0.392503i \(0.871609\pi\)
\(468\) 0 0
\(469\) 3.75394 21.2896i 0.173341 0.983064i
\(470\) −64.0955 7.49169i −2.95651 0.345566i
\(471\) 0 0
\(472\) 32.7848 + 109.509i 1.50904 + 5.04056i
\(473\) −13.5207 3.20445i −0.621680 0.147341i
\(474\) 0 0
\(475\) −7.48259 17.3466i −0.343325 0.795916i
\(476\) −8.26432 6.93459i −0.378795 0.317846i
\(477\) 0 0
\(478\) 7.30348 6.12835i 0.334054 0.280304i
\(479\) −3.29029 1.65245i −0.150337 0.0755022i 0.372040 0.928217i \(-0.378658\pi\)
−0.522377 + 0.852715i \(0.674955\pi\)
\(480\) 0 0
\(481\) 1.10823 0.129533i 0.0505308 0.00590621i
\(482\) 1.31041 22.4989i 0.0596876 1.02480i
\(483\) 0 0
\(484\) 26.2456 + 27.8188i 1.19298 + 1.26449i
\(485\) 6.55569 0.297678
\(486\) 0 0
\(487\) 21.6887 0.982808 0.491404 0.870932i \(-0.336484\pi\)
0.491404 + 0.870932i \(0.336484\pi\)
\(488\) −42.7430 45.3049i −1.93489 2.05086i
\(489\) 0 0
\(490\) 1.46939 25.2284i 0.0663802 1.13970i
\(491\) −13.4650 + 1.57383i −0.607666 + 0.0710259i −0.414361 0.910113i \(-0.635995\pi\)
−0.193305 + 0.981139i \(0.561921\pi\)
\(492\) 0 0
\(493\) 0.437294 + 0.219617i 0.0196947 + 0.00989106i
\(494\) 1.66586 1.39782i 0.0749506 0.0628910i
\(495\) 0 0
\(496\) 24.7831 + 20.7955i 1.11279 + 0.933745i
\(497\) −0.597451 1.38505i −0.0267993 0.0621279i
\(498\) 0 0
\(499\) 5.14154 + 1.21857i 0.230167 + 0.0545506i 0.344081 0.938940i \(-0.388191\pi\)
−0.113914 + 0.993491i \(0.536339\pi\)
\(500\) 7.79317 + 26.0310i 0.348521 + 1.16414i
\(501\) 0 0
\(502\) −10.8445 1.26754i −0.484012 0.0565729i
\(503\) 3.77163 21.3900i 0.168169 0.953731i −0.777568 0.628798i \(-0.783547\pi\)
0.945737 0.324933i \(-0.105342\pi\)
\(504\) 0 0
\(505\) 4.25901 + 24.1541i 0.189524 + 1.07484i
\(506\) 0.133466 + 2.29153i 0.00593330 + 0.101871i
\(507\) 0 0
\(508\) −14.8146 + 34.3441i −0.657292 + 1.52377i
\(509\) −18.1154 + 9.09792i −0.802953 + 0.403258i −0.802433 0.596742i \(-0.796462\pi\)
−0.000519625 1.00000i \(0.500165\pi\)
\(510\) 0 0
\(511\) −6.71847 + 1.59231i −0.297208 + 0.0704395i
\(512\) 11.8929 + 20.5990i 0.525595 + 0.910358i
\(513\) 0 0
\(514\) −7.67167 + 13.2877i −0.338383 + 0.586096i
\(515\) 6.56259 21.9206i 0.289182 0.965936i
\(516\) 0 0
\(517\) −13.2040 8.68440i −0.580711 0.381940i
\(518\) 25.0948 + 33.7082i 1.10260 + 1.48105i
\(519\) 0 0
\(520\) 2.60291 1.71196i 0.114145 0.0750743i
\(521\) −14.6420 5.32927i −0.641479 0.233479i 0.000740713 1.00000i \(-0.499764\pi\)
−0.642220 + 0.766520i \(0.721986\pi\)
\(522\) 0 0
\(523\) −12.3756 + 4.50436i −0.541148 + 0.196962i −0.598109 0.801415i \(-0.704081\pi\)
0.0569613 + 0.998376i \(0.481859\pi\)
\(524\) 21.7214 29.1769i 0.948905 1.27460i
\(525\) 0 0
\(526\) 26.2083 27.7792i 1.14274 1.21123i
\(527\) 2.16776 2.29770i 0.0944293 0.100089i
\(528\) 0 0
\(529\) −13.6047 + 18.2742i −0.591507 + 0.794532i
\(530\) 41.8350 15.2267i 1.81719 0.661405i
\(531\) 0 0
\(532\) 55.1410 + 20.0697i 2.39066 + 0.870131i
\(533\) −0.627108 + 0.412455i −0.0271630 + 0.0178654i
\(534\) 0 0
\(535\) 7.13444 + 9.58321i 0.308449 + 0.414318i
\(536\) −76.5686 50.3600i −3.30726 2.17522i
\(537\) 0 0
\(538\) −6.31547 + 21.0951i −0.272279 + 0.909476i
\(539\) 3.09447 5.35978i 0.133288 0.230862i
\(540\) 0 0
\(541\) 12.1790 + 21.0947i 0.523618 + 0.906933i 0.999622 + 0.0274896i \(0.00875133\pi\)
−0.476004 + 0.879443i \(0.657915\pi\)
\(542\) −22.1422 + 5.24779i −0.951088 + 0.225412i
\(543\) 0 0
\(544\) −14.0999 + 7.08123i −0.604527 + 0.303605i
\(545\) 12.8452 29.7784i 0.550226 1.27557i
\(546\) 0 0
\(547\) 0.838665 + 14.3993i 0.0358587 + 0.615671i 0.967591 + 0.252524i \(0.0812606\pi\)
−0.931732 + 0.363147i \(0.881702\pi\)
\(548\) −12.4359 70.5278i −0.531237 3.01280i
\(549\) 0 0
\(550\) 2.65876 15.0786i 0.113370 0.642952i
\(551\) −2.64364 0.308998i −0.112623 0.0131637i
\(552\) 0 0
\(553\) 7.01116 + 23.4189i 0.298145 + 0.995873i
\(554\) 79.2955 + 18.7934i 3.36894 + 0.798454i
\(555\) 0 0
\(556\) 27.4807 + 63.7073i 1.16544 + 2.70179i
\(557\) −17.7225 14.8710i −0.750928 0.630103i 0.184821 0.982772i \(-0.440830\pi\)
−0.935748 + 0.352669i \(0.885274\pi\)
\(558\) 0 0
\(559\) 0.775053 0.650347i 0.0327812 0.0275067i
\(560\) 55.6496 + 27.9483i 2.35162 + 1.18103i
\(561\) 0 0
\(562\) 9.83481 1.14952i 0.414857 0.0484898i
\(563\) 0.0302164 0.518796i 0.00127347 0.0218647i −0.997612 0.0690737i \(-0.977996\pi\)
0.998885 + 0.0472090i \(0.0150327\pi\)
\(564\) 0 0
\(565\) 27.4590 + 29.1048i 1.15521 + 1.22445i
\(566\) 18.9008 0.794460
\(567\) 0 0
\(568\) −6.39460 −0.268312
\(569\) −2.27935 2.41597i −0.0955553 0.101283i 0.677831 0.735218i \(-0.262920\pi\)
−0.773386 + 0.633935i \(0.781439\pi\)
\(570\) 0 0
\(571\) 1.38043 23.7011i 0.0577693 0.991861i −0.837529 0.546394i \(-0.816000\pi\)
0.895298 0.445468i \(-0.146963\pi\)
\(572\) 1.25419 0.146594i 0.0524402 0.00612939i
\(573\) 0 0
\(574\) −25.2627 12.6874i −1.05444 0.529562i
\(575\) −1.11227 + 0.933308i −0.0463850 + 0.0389216i
\(576\) 0 0
\(577\) −30.1749 25.3198i −1.25620 1.05408i −0.996076 0.0885007i \(-0.971792\pi\)
−0.260123 0.965576i \(-0.583763\pi\)
\(578\) −16.5724 38.4191i −0.689320 1.59802i
\(579\) 0 0
\(580\) −6.14068 1.45537i −0.254978 0.0604308i
\(581\) −9.17155 30.6351i −0.380500 1.27096i
\(582\) 0 0
\(583\) 10.8292 + 1.26576i 0.448501 + 0.0524223i
\(584\) −5.08279 + 28.8259i −0.210327 + 1.19282i
\(585\) 0 0
\(586\) −3.94457 22.3708i −0.162949 0.924128i
\(587\) 0.576562 + 9.89918i 0.0237972 + 0.408583i 0.989080 + 0.147377i \(0.0470831\pi\)
−0.965283 + 0.261206i \(0.915880\pi\)
\(588\) 0 0
\(589\) −6.80539 + 15.7767i −0.280411 + 0.650066i
\(590\) −95.2865 + 47.8547i −3.92288 + 1.97015i
\(591\) 0 0
\(592\) 91.9998 21.8044i 3.78117 0.896153i
\(593\) −5.22061 9.04237i −0.214385 0.371326i 0.738697 0.674037i \(-0.235441\pi\)
−0.953082 + 0.302712i \(0.902108\pi\)
\(594\) 0 0
\(595\) 3.04023 5.26583i 0.124637 0.215878i
\(596\) 2.97059 9.92247i 0.121680 0.406440i
\(597\) 0 0
\(598\) −0.139641 0.0918434i −0.00571035 0.00375575i
\(599\) 27.1659 + 36.4901i 1.10997 + 1.49095i 0.851078 + 0.525039i \(0.175949\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(600\) 0 0
\(601\) 7.83707 5.15452i 0.319681 0.210257i −0.379518 0.925184i \(-0.623910\pi\)
0.699199 + 0.714927i \(0.253540\pi\)
\(602\) 35.8082 + 13.0331i 1.45943 + 0.531190i
\(603\) 0 0
\(604\) 58.2462 21.1999i 2.37000 0.862611i
\(605\) −12.8722 + 17.2904i −0.523329 + 0.702953i
\(606\) 0 0
\(607\) −21.8779 + 23.1892i −0.887997 + 0.941221i −0.998613 0.0526417i \(-0.983236\pi\)
0.110617 + 0.993863i \(0.464717\pi\)
\(608\) 58.8937 62.4237i 2.38845 2.53161i
\(609\) 0 0
\(610\) 34.6945 46.6028i 1.40474 1.88689i
\(611\) 1.08134 0.393577i 0.0437465 0.0159224i
\(612\) 0 0
\(613\) −23.7444 8.64224i −0.959025 0.349057i −0.185374 0.982668i \(-0.559350\pi\)
−0.773652 + 0.633611i \(0.781572\pi\)
\(614\) −25.5670 + 16.8157i −1.03180 + 0.678626i
\(615\) 0 0
\(616\) 17.1600 + 23.0499i 0.691397 + 0.928707i
\(617\) −6.63890 4.36647i −0.267272 0.175788i 0.408798 0.912625i \(-0.365948\pi\)
−0.676070 + 0.736837i \(0.736318\pi\)
\(618\) 0 0
\(619\) 10.2509 34.2405i 0.412019 1.37624i −0.460500 0.887660i \(-0.652330\pi\)
0.872519 0.488580i \(-0.162485\pi\)
\(620\) −20.3692 + 35.2805i −0.818047 + 1.41690i
\(621\) 0 0
\(622\) −33.9927 58.8771i −1.36298 2.36076i
\(623\) −20.2785 + 4.80608i −0.812439 + 0.192552i
\(624\) 0 0
\(625\) −27.5912 + 13.8568i −1.10365 + 0.554273i
\(626\) 1.58677 3.67854i 0.0634200 0.147024i
\(627\) 0 0
\(628\) −6.68928 114.851i −0.266931 4.58304i
\(629\) −1.60309 9.09157i −0.0639193 0.362504i
\(630\) 0 0
\(631\) −3.64311 + 20.6611i −0.145030 + 0.822506i 0.822313 + 0.569035i \(0.192683\pi\)
−0.967343 + 0.253471i \(0.918428\pi\)
\(632\) 102.933 + 12.0311i 4.09444 + 0.478572i
\(633\) 0 0
\(634\) 5.75542 + 19.2245i 0.228577 + 0.763501i
\(635\) −20.5127 4.86160i −0.814022 0.192927i
\(636\) 0 0
\(637\) 0.178489 + 0.413784i 0.00707199 + 0.0163947i
\(638\) −1.65251 1.38662i −0.0654233 0.0548967i
\(639\) 0 0
\(640\) 23.4122 19.6452i 0.925449 0.776544i
\(641\) 4.26195 + 2.14043i 0.168337 + 0.0845420i 0.530973 0.847389i \(-0.321827\pi\)
−0.362636 + 0.931931i \(0.618123\pi\)
\(642\) 0 0
\(643\) 8.05217 0.941164i 0.317547 0.0371159i 0.0441733 0.999024i \(-0.485935\pi\)
0.273373 + 0.961908i \(0.411861\pi\)
\(644\) 0.262233 4.50237i 0.0103334 0.177418i
\(645\) 0 0
\(646\) −12.3473 13.0874i −0.485800 0.514918i
\(647\) −10.4984 −0.412736 −0.206368 0.978474i \(-0.566164\pi\)
−0.206368 + 0.978474i \(0.566164\pi\)
\(648\) 0 0
\(649\) −26.1134 −1.02504
\(650\) 0.765065 + 0.810922i 0.0300083 + 0.0318070i
\(651\) 0 0
\(652\) 3.35144 57.5420i 0.131252 2.25352i
\(653\) −46.4167 + 5.42533i −1.81642 + 0.212310i −0.955209 0.295931i \(-0.904370\pi\)
−0.861215 + 0.508240i \(0.830296\pi\)
\(654\) 0 0
\(655\) 18.3206 + 9.20097i 0.715847 + 0.359512i
\(656\) −48.7230 + 40.8835i −1.90231 + 1.59623i
\(657\) 0 0
\(658\) 33.2010 + 27.8589i 1.29431 + 1.08605i
\(659\) −6.00323 13.9170i −0.233852 0.542131i 0.760368 0.649493i \(-0.225019\pi\)
−0.994220 + 0.107362i \(0.965760\pi\)
\(660\) 0 0
\(661\) −46.7631 11.0831i −1.81888 0.431081i −0.827426 0.561575i \(-0.810196\pi\)
−0.991449 + 0.130494i \(0.958344\pi\)
\(662\) −23.0225 76.9004i −0.894794 2.98882i
\(663\) 0 0
\(664\) −134.650 15.7383i −5.22543 0.610765i
\(665\) −5.74304 + 32.5704i −0.222706 + 1.26303i
\(666\) 0 0
\(667\) 0.0355229 + 0.201460i 0.00137545 + 0.00780057i
\(668\) −1.57761 27.0865i −0.0610395 1.04801i
\(669\) 0 0
\(670\) 33.8592 78.4944i 1.30809 3.03250i
\(671\) 12.7151 6.38578i 0.490862 0.246520i
\(672\) 0 0
\(673\) −25.8107 + 6.11725i −0.994930 + 0.235803i −0.695664 0.718367i \(-0.744890\pi\)
−0.299266 + 0.954170i \(0.596742\pi\)
\(674\) −29.9994 51.9604i −1.15553 2.00144i
\(675\) 0 0
\(676\) 32.8011 56.8132i 1.26158 2.18512i
\(677\) −13.5662 + 45.3143i −0.521392 + 1.74157i 0.138649 + 0.990342i \(0.455724\pi\)
−0.660041 + 0.751230i \(0.729461\pi\)
\(678\) 0 0
\(679\) −3.67858 2.41944i −0.141171 0.0928496i
\(680\) −15.3929 20.6762i −0.590290 0.792897i
\(681\) 0 0
\(682\) −11.6346 + 7.65217i −0.445510 + 0.293017i
\(683\) −14.6776 5.34220i −0.561622 0.204414i 0.0455809 0.998961i \(-0.485486\pi\)
−0.607203 + 0.794547i \(0.707708\pi\)
\(684\) 0 0
\(685\) 37.9295 13.8052i 1.44921 0.527470i
\(686\) −31.3715 + 42.1392i −1.19777 + 1.60888i
\(687\) 0 0
\(688\) 58.8346 62.3611i 2.24305 2.37749i
\(689\) −0.544796 + 0.577450i −0.0207551 + 0.0219991i
\(690\) 0 0
\(691\) 3.91734 5.26190i 0.149023 0.200172i −0.721343 0.692578i \(-0.756475\pi\)
0.870366 + 0.492406i \(0.163882\pi\)
\(692\) −16.1906 + 5.89289i −0.615474 + 0.224014i
\(693\) 0 0
\(694\) −44.7436 16.2853i −1.69844 0.618182i
\(695\) −32.6714 + 21.4883i −1.23930 + 0.815098i
\(696\) 0 0
\(697\) 3.70854 + 4.98144i 0.140471 + 0.188685i
\(698\) 59.5378 + 39.1586i 2.25354 + 1.48218i
\(699\) 0 0
\(700\) −8.62799 + 28.8195i −0.326107 + 1.08927i
\(701\) −11.9474 + 20.6936i −0.451249 + 0.781586i −0.998464 0.0554061i \(-0.982355\pi\)
0.547215 + 0.836992i \(0.315688\pi\)
\(702\) 0 0
\(703\) 25.1069 + 43.4864i 0.946924 + 1.64012i
\(704\) 26.4739 6.27444i 0.997774 0.236477i
\(705\) 0 0
\(706\) −49.5783 + 24.8992i −1.86590 + 0.937092i
\(707\) 6.52445 15.1254i 0.245377 0.568848i
\(708\) 0 0
\(709\) 2.69978 + 46.3535i 0.101393 + 1.74084i 0.539558 + 0.841948i \(0.318591\pi\)
−0.438165 + 0.898894i \(0.644372\pi\)
\(710\) −1.03578 5.87419i −0.0388721 0.220455i
\(711\) 0 0
\(712\) −15.3414 + 87.0056i −0.574945 + 3.26067i
\(713\) 1.31163 + 0.153308i 0.0491210 + 0.00574142i
\(714\) 0 0
\(715\) 0.204116 + 0.681794i 0.00763349 + 0.0254976i
\(716\) 33.0454 + 7.83191i 1.23497 + 0.292692i
\(717\) 0 0
\(718\) −14.1960 32.9100i −0.529790 1.22819i
\(719\) −3.57771 3.00206i −0.133426 0.111958i 0.573632 0.819113i \(-0.305534\pi\)
−0.707059 + 0.707155i \(0.749978\pi\)
\(720\) 0 0
\(721\) −11.7725 + 9.87828i −0.438430 + 0.367886i
\(722\) 42.3630 + 21.2755i 1.57659 + 0.791791i
\(723\) 0 0
\(724\) −9.86011 + 1.15248i −0.366448 + 0.0428316i
\(725\) 0.0793410 1.36223i 0.00294665 0.0505920i
\(726\) 0 0
\(727\) 23.7620 + 25.1863i 0.881285 + 0.934107i 0.998256 0.0590282i \(-0.0188002\pi\)
−0.116972 + 0.993135i \(0.537319\pi\)
\(728\) −2.09238 −0.0775488
\(729\) 0 0
\(730\) −27.3033 −1.01054
\(731\) −5.74469 6.08901i −0.212475 0.225210i
\(732\) 0 0
\(733\) 2.61871 44.9615i 0.0967242 1.66069i −0.505846 0.862624i \(-0.668820\pi\)
0.602570 0.798066i \(-0.294143\pi\)
\(734\) 26.0302 3.04249i 0.960791 0.112300i
\(735\) 0 0
\(736\) −5.89439 2.96027i −0.217270 0.109117i
\(737\) 16.0376 13.4571i 0.590752 0.495699i
\(738\) 0 0
\(739\) −38.9851 32.7123i −1.43409 1.20334i −0.943246 0.332094i \(-0.892245\pi\)
−0.490842 0.871249i \(-0.663311\pi\)
\(740\) 47.1562 + 109.320i 1.73350 + 4.01870i
\(741\) 0 0
\(742\) −29.0943 6.89549i −1.06809 0.253141i
\(743\) 5.23961 + 17.5015i 0.192222 + 0.642068i 0.998708 + 0.0508142i \(0.0161816\pi\)
−0.806486 + 0.591254i \(0.798633\pi\)
\(744\) 0 0
\(745\) 5.79823 + 0.677716i 0.212431 + 0.0248296i
\(746\) 4.97660 28.2237i 0.182206 1.03334i
\(747\) 0 0
\(748\) −1.81423 10.2890i −0.0663347 0.376203i
\(749\) −0.466556 8.01045i −0.0170476 0.292696i
\(750\) 0 0
\(751\) 8.78368 20.3629i 0.320521 0.743051i −0.679436 0.733735i \(-0.737775\pi\)
0.999957 0.00931599i \(-0.00296541\pi\)
\(752\) 87.1395 43.7631i 3.17765 1.59588i
\(753\) 0 0
\(754\) 0.152839 0.0362235i 0.00556607 0.00131918i
\(755\) 17.4677 + 30.2549i 0.635713 + 1.10109i
\(756\) 0 0
\(757\) −1.95553 + 3.38708i −0.0710750 + 0.123106i −0.899373 0.437183i \(-0.855976\pi\)
0.828298 + 0.560288i \(0.189310\pi\)
\(758\) −9.76627 + 32.6216i −0.354727 + 1.18487i
\(759\) 0 0
\(760\) 117.140 + 77.0443i 4.24912 + 2.79469i
\(761\) −1.87452 2.51792i −0.0679514 0.0912745i 0.766848 0.641829i \(-0.221824\pi\)
−0.834800 + 0.550554i \(0.814417\pi\)
\(762\) 0 0
\(763\) −18.1978 + 11.9689i −0.658805 + 0.433303i
\(764\) 22.3071 + 8.11911i 0.807042 + 0.293739i
\(765\) 0 0
\(766\) −34.6905 + 12.6263i −1.25342 + 0.456207i
\(767\) 1.13544 1.52516i 0.0409985 0.0550705i
\(768\) 0 0
\(769\) 14.2206 15.0729i 0.512808 0.543544i −0.418290 0.908313i \(-0.637371\pi\)
0.931098 + 0.364769i \(0.118852\pi\)
\(770\) −18.3945 + 19.4970i −0.662892 + 0.702624i
\(771\) 0 0
\(772\) −19.0399 + 25.5751i −0.685262 + 0.920467i
\(773\) −18.6463 + 6.78668i −0.670659 + 0.244100i −0.654832 0.755775i \(-0.727260\pi\)
−0.0158274 + 0.999875i \(0.505038\pi\)
\(774\) 0 0
\(775\) −8.27738 3.01272i −0.297332 0.108220i
\(776\) −15.5946 + 10.2567i −0.559814 + 0.368195i
\(777\) 0 0
\(778\) −55.1568 74.0884i −1.97747 2.65620i
\(779\) −28.2221 18.5620i −1.01116 0.665051i
\(780\) 0 0
\(781\) 0.418959 1.39942i 0.0149915 0.0500752i
\(782\) −0.691441 + 1.19761i −0.0247259 + 0.0428264i
\(783\) 0