Properties

Label 729.2.e.l.163.1
Level $729$
Weight $2$
Character 729.163
Analytic conductor $5.821$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [729,2,Mod(82,729)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(729, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("729.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 729 = 3^{6} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 729.e (of order \(9\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(5.82109430735\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{9})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} + 18x^{10} + 105x^{8} + 266x^{6} + 306x^{4} + 132x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 163.1
Root \(3.10658i\) of defining polynomial
Character \(\chi\) \(=\) 729.163
Dual form 729.2.e.l.568.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.99687 + 0.726803i) q^{2} +(1.92717 - 1.61709i) q^{4} +(0.359615 + 2.03948i) q^{5} +(3.71430 + 3.11667i) q^{7} +(-0.547989 + 0.949144i) q^{8} +O(q^{10})\) \(q+(-1.99687 + 0.726803i) q^{2} +(1.92717 - 1.61709i) q^{4} +(0.359615 + 2.03948i) q^{5} +(3.71430 + 3.11667i) q^{7} +(-0.547989 + 0.949144i) q^{8} +(-2.20040 - 3.81121i) q^{10} +(-0.720551 + 4.08645i) q^{11} +(1.14268 + 0.415902i) q^{13} +(-9.68219 - 3.52403i) q^{14} +(-0.469286 + 2.66145i) q^{16} +(1.18182 + 2.04697i) q^{17} +(0.919003 - 1.59176i) q^{19} +(3.99106 + 3.34890i) q^{20} +(-1.53119 - 8.68382i) q^{22} +(3.29673 - 2.76628i) q^{23} +(0.668315 - 0.243247i) q^{25} -2.58407 q^{26} +12.1980 q^{28} +(2.80199 - 1.01984i) q^{29} +(1.12883 - 0.947203i) q^{31} +(-1.37788 - 7.81432i) q^{32} +(-3.84769 - 3.22859i) q^{34} +(-5.02066 + 8.69603i) q^{35} +(-4.48554 - 7.76918i) q^{37} +(-0.678238 + 3.84648i) q^{38} +(-2.13282 - 0.776284i) q^{40} +(2.12420 + 0.773145i) q^{41} +(-0.952435 + 5.40153i) q^{43} +(5.21953 + 9.04050i) q^{44} +(-4.57260 + 7.91998i) q^{46} +(-5.50260 - 4.61723i) q^{47} +(2.86687 + 16.2588i) q^{49} +(-1.15775 + 0.971466i) q^{50} +(2.87470 - 1.04630i) q^{52} +6.32803 q^{53} -8.59334 q^{55} +(-4.99356 + 1.81751i) q^{56} +(-4.85400 + 4.07299i) q^{58} +(-0.0455404 - 0.258272i) q^{59} +(-3.41319 - 2.86401i) q^{61} +(-1.56571 + 2.71188i) q^{62} +(5.72840 + 9.92188i) q^{64} +(-0.437297 + 2.48004i) q^{65} +(-3.88197 - 1.41292i) q^{67} +(5.58771 + 2.03376i) q^{68} +(3.70532 - 21.0139i) q^{70} +(1.54276 + 2.67213i) q^{71} +(-6.38003 + 11.0505i) q^{73} +(14.6037 + 12.2540i) q^{74} +(-0.802942 - 4.55371i) q^{76} +(-15.4124 + 12.9326i) q^{77} +(-4.27786 + 1.55701i) q^{79} -5.59674 q^{80} -4.80368 q^{82} +(-7.94328 + 2.89112i) q^{83} +(-3.74975 + 3.14642i) q^{85} +(-2.02395 - 11.4784i) q^{86} +(-3.48378 - 2.92323i) q^{88} +(8.48158 - 14.6905i) q^{89} +(2.94803 + 5.10614i) q^{91} +(1.88004 - 10.6622i) q^{92} +(14.3438 + 5.22072i) q^{94} +(3.57685 + 1.30187i) q^{95} +(-0.887302 + 5.03214i) q^{97} +(-17.5417 - 30.3831i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 3 q^{2} - 3 q^{4} + 12 q^{5} - 3 q^{7} - 6 q^{8} - 6 q^{10} - 3 q^{11} + 6 q^{13} - 6 q^{14} + 27 q^{16} + 9 q^{17} - 12 q^{19} + 39 q^{20} - 39 q^{22} + 21 q^{23} + 6 q^{25} + 48 q^{26} + 6 q^{28} + 6 q^{29} + 6 q^{31} + 27 q^{32} - 18 q^{34} - 30 q^{35} - 3 q^{37} + 3 q^{38} + 33 q^{40} - 15 q^{41} - 30 q^{43} + 33 q^{44} + 3 q^{46} - 21 q^{47} - 3 q^{49} + 6 q^{50} - 18 q^{53} + 30 q^{55} + 15 q^{56} - 3 q^{58} + 30 q^{59} - 30 q^{61} + 30 q^{62} - 6 q^{64} - 12 q^{65} - 39 q^{67} + 18 q^{68} + 51 q^{70} - 12 q^{73} + 57 q^{74} + 57 q^{76} - 24 q^{77} + 15 q^{79} - 42 q^{80} - 42 q^{82} - 21 q^{83} + 54 q^{85} - 60 q^{86} + 12 q^{88} + 9 q^{89} - 18 q^{91} - 15 q^{92} + 33 q^{94} + 42 q^{95} - 12 q^{97} - 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.99687 + 0.726803i −1.41200 + 0.513927i −0.931717 0.363185i \(-0.881689\pi\)
−0.480286 + 0.877112i \(0.659467\pi\)
\(3\) 0 0
\(4\) 1.92717 1.61709i 0.963587 0.808546i
\(5\) 0.359615 + 2.03948i 0.160825 + 0.912082i 0.953266 + 0.302134i \(0.0976989\pi\)
−0.792441 + 0.609949i \(0.791190\pi\)
\(6\) 0 0
\(7\) 3.71430 + 3.11667i 1.40387 + 1.17799i 0.959349 + 0.282222i \(0.0910716\pi\)
0.444524 + 0.895767i \(0.353373\pi\)
\(8\) −0.547989 + 0.949144i −0.193743 + 0.335573i
\(9\) 0 0
\(10\) −2.20040 3.81121i −0.695829 1.20521i
\(11\) −0.720551 + 4.08645i −0.217254 + 1.23211i 0.659697 + 0.751532i \(0.270685\pi\)
−0.876951 + 0.480579i \(0.840427\pi\)
\(12\) 0 0
\(13\) 1.14268 + 0.415902i 0.316923 + 0.115350i 0.495583 0.868560i \(-0.334954\pi\)
−0.178661 + 0.983911i \(0.557176\pi\)
\(14\) −9.68219 3.52403i −2.58767 0.941836i
\(15\) 0 0
\(16\) −0.469286 + 2.66145i −0.117322 + 0.665363i
\(17\) 1.18182 + 2.04697i 0.286633 + 0.496463i 0.973004 0.230789i \(-0.0741306\pi\)
−0.686371 + 0.727252i \(0.740797\pi\)
\(18\) 0 0
\(19\) 0.919003 1.59176i 0.210834 0.365175i −0.741142 0.671348i \(-0.765715\pi\)
0.951976 + 0.306174i \(0.0990488\pi\)
\(20\) 3.99106 + 3.34890i 0.892429 + 0.748837i
\(21\) 0 0
\(22\) −1.53119 8.68382i −0.326451 1.85140i
\(23\) 3.29673 2.76628i 0.687415 0.576809i −0.230748 0.973014i \(-0.574117\pi\)
0.918162 + 0.396204i \(0.129673\pi\)
\(24\) 0 0
\(25\) 0.668315 0.243247i 0.133663 0.0486494i
\(26\) −2.58407 −0.506777
\(27\) 0 0
\(28\) 12.1980 2.30521
\(29\) 2.80199 1.01984i 0.520317 0.189380i −0.0684925 0.997652i \(-0.521819\pi\)
0.588810 + 0.808272i \(0.299597\pi\)
\(30\) 0 0
\(31\) 1.12883 0.947203i 0.202744 0.170123i −0.535762 0.844369i \(-0.679976\pi\)
0.738507 + 0.674246i \(0.235531\pi\)
\(32\) −1.37788 7.81432i −0.243576 1.38139i
\(33\) 0 0
\(34\) −3.84769 3.22859i −0.659873 0.553699i
\(35\) −5.02066 + 8.69603i −0.848646 + 1.46990i
\(36\) 0 0
\(37\) −4.48554 7.76918i −0.737418 1.27725i −0.953654 0.300905i \(-0.902711\pi\)
0.216236 0.976341i \(-0.430622\pi\)
\(38\) −0.678238 + 3.84648i −0.110025 + 0.623981i
\(39\) 0 0
\(40\) −2.13282 0.776284i −0.337229 0.122741i
\(41\) 2.12420 + 0.773145i 0.331744 + 0.120745i 0.502522 0.864565i \(-0.332406\pi\)
−0.170778 + 0.985310i \(0.554628\pi\)
\(42\) 0 0
\(43\) −0.952435 + 5.40153i −0.145245 + 0.823726i 0.821925 + 0.569596i \(0.192900\pi\)
−0.967170 + 0.254130i \(0.918211\pi\)
\(44\) 5.21953 + 9.04050i 0.786874 + 1.36291i
\(45\) 0 0
\(46\) −4.57260 + 7.91998i −0.674194 + 1.16774i
\(47\) −5.50260 4.61723i −0.802636 0.673492i 0.146202 0.989255i \(-0.453295\pi\)
−0.948838 + 0.315763i \(0.897740\pi\)
\(48\) 0 0
\(49\) 2.86687 + 16.2588i 0.409552 + 2.32269i
\(50\) −1.15775 + 0.971466i −0.163730 + 0.137386i
\(51\) 0 0
\(52\) 2.87470 1.04630i 0.398649 0.145096i
\(53\) 6.32803 0.869222 0.434611 0.900618i \(-0.356886\pi\)
0.434611 + 0.900618i \(0.356886\pi\)
\(54\) 0 0
\(55\) −8.59334 −1.15873
\(56\) −4.99356 + 1.81751i −0.667293 + 0.242875i
\(57\) 0 0
\(58\) −4.85400 + 4.07299i −0.637362 + 0.534810i
\(59\) −0.0455404 0.258272i −0.00592886 0.0336242i 0.981700 0.190435i \(-0.0609898\pi\)
−0.987629 + 0.156811i \(0.949879\pi\)
\(60\) 0 0
\(61\) −3.41319 2.86401i −0.437014 0.366699i 0.397576 0.917569i \(-0.369851\pi\)
−0.834591 + 0.550870i \(0.814296\pi\)
\(62\) −1.56571 + 2.71188i −0.198845 + 0.344410i
\(63\) 0 0
\(64\) 5.72840 + 9.92188i 0.716050 + 1.24024i
\(65\) −0.437297 + 2.48004i −0.0542401 + 0.307611i
\(66\) 0 0
\(67\) −3.88197 1.41292i −0.474258 0.172616i 0.0938223 0.995589i \(-0.470091\pi\)
−0.568080 + 0.822973i \(0.692314\pi\)
\(68\) 5.58771 + 2.03376i 0.677609 + 0.246630i
\(69\) 0 0
\(70\) 3.70532 21.0139i 0.442870 2.51164i
\(71\) 1.54276 + 2.67213i 0.183091 + 0.317124i 0.942932 0.332986i \(-0.108056\pi\)
−0.759840 + 0.650110i \(0.774723\pi\)
\(72\) 0 0
\(73\) −6.38003 + 11.0505i −0.746726 + 1.29337i 0.202658 + 0.979250i \(0.435042\pi\)
−0.949384 + 0.314118i \(0.898291\pi\)
\(74\) 14.6037 + 12.2540i 1.69765 + 1.42450i
\(75\) 0 0
\(76\) −0.802942 4.55371i −0.0921038 0.522346i
\(77\) −15.4124 + 12.9326i −1.75641 + 1.47380i
\(78\) 0 0
\(79\) −4.27786 + 1.55701i −0.481297 + 0.175178i −0.571263 0.820767i \(-0.693546\pi\)
0.0899659 + 0.995945i \(0.471324\pi\)
\(80\) −5.59674 −0.625734
\(81\) 0 0
\(82\) −4.80368 −0.530478
\(83\) −7.94328 + 2.89112i −0.871888 + 0.317341i −0.738931 0.673781i \(-0.764669\pi\)
−0.132956 + 0.991122i \(0.542447\pi\)
\(84\) 0 0
\(85\) −3.74975 + 3.14642i −0.406718 + 0.341277i
\(86\) −2.02395 11.4784i −0.218248 1.23775i
\(87\) 0 0
\(88\) −3.48378 2.92323i −0.371372 0.311618i
\(89\) 8.48158 14.6905i 0.899046 1.55719i 0.0703304 0.997524i \(-0.477595\pi\)
0.828716 0.559670i \(-0.189072\pi\)
\(90\) 0 0
\(91\) 2.94803 + 5.10614i 0.309038 + 0.535269i
\(92\) 1.88004 10.6622i 0.196007 1.11161i
\(93\) 0 0
\(94\) 14.3438 + 5.22072i 1.47945 + 0.538476i
\(95\) 3.57685 + 1.30187i 0.366977 + 0.133569i
\(96\) 0 0
\(97\) −0.887302 + 5.03214i −0.0900919 + 0.510937i 0.906049 + 0.423172i \(0.139083\pi\)
−0.996141 + 0.0877646i \(0.972028\pi\)
\(98\) −17.5417 30.3831i −1.77198 3.06916i
\(99\) 0 0
\(100\) 0.894607 1.54951i 0.0894607 0.154951i
\(101\) −14.2330 11.9429i −1.41624 1.18836i −0.953319 0.301964i \(-0.902358\pi\)
−0.462918 0.886401i \(-0.653198\pi\)
\(102\) 0 0
\(103\) 1.56384 + 8.86895i 0.154089 + 0.873884i 0.959614 + 0.281321i \(0.0907726\pi\)
−0.805524 + 0.592563i \(0.798116\pi\)
\(104\) −1.02093 + 0.856659i −0.100110 + 0.0840024i
\(105\) 0 0
\(106\) −12.6363 + 4.59923i −1.22734 + 0.446717i
\(107\) −7.42680 −0.717976 −0.358988 0.933342i \(-0.616878\pi\)
−0.358988 + 0.933342i \(0.616878\pi\)
\(108\) 0 0
\(109\) −5.62396 −0.538678 −0.269339 0.963045i \(-0.586805\pi\)
−0.269339 + 0.963045i \(0.586805\pi\)
\(110\) 17.1598 6.24567i 1.63612 0.595501i
\(111\) 0 0
\(112\) −10.0379 + 8.42283i −0.948495 + 0.795882i
\(113\) 0.417219 + 2.36617i 0.0392487 + 0.222590i 0.998123 0.0612406i \(-0.0195057\pi\)
−0.958874 + 0.283831i \(0.908395\pi\)
\(114\) 0 0
\(115\) 6.82732 + 5.72880i 0.636651 + 0.534214i
\(116\) 3.75075 6.49649i 0.348249 0.603184i
\(117\) 0 0
\(118\) 0.278652 + 0.482639i 0.0256520 + 0.0444305i
\(119\) −1.99010 + 11.2864i −0.182432 + 1.03462i
\(120\) 0 0
\(121\) −5.84325 2.12677i −0.531205 0.193343i
\(122\) 8.89728 + 3.23835i 0.805522 + 0.293186i
\(123\) 0 0
\(124\) 0.643744 3.65085i 0.0578099 0.327856i
\(125\) 5.91378 + 10.2430i 0.528945 + 0.916159i
\(126\) 0 0
\(127\) 4.61735 7.99748i 0.409723 0.709662i −0.585135 0.810936i \(-0.698959\pi\)
0.994859 + 0.101274i \(0.0322919\pi\)
\(128\) −6.49322 5.44846i −0.573925 0.481580i
\(129\) 0 0
\(130\) −0.929269 5.27015i −0.0815023 0.462223i
\(131\) 11.7504 9.85972i 1.02663 0.861448i 0.0361871 0.999345i \(-0.488479\pi\)
0.990447 + 0.137897i \(0.0440343\pi\)
\(132\) 0 0
\(133\) 8.37444 3.04805i 0.726156 0.264299i
\(134\) 8.77871 0.758365
\(135\) 0 0
\(136\) −2.59049 −0.222133
\(137\) −3.42421 + 1.24631i −0.292550 + 0.106480i −0.484126 0.874998i \(-0.660862\pi\)
0.191576 + 0.981478i \(0.438640\pi\)
\(138\) 0 0
\(139\) 10.1697 8.53335i 0.862579 0.723789i −0.0999433 0.994993i \(-0.531866\pi\)
0.962522 + 0.271204i \(0.0874217\pi\)
\(140\) 4.38660 + 24.8776i 0.370735 + 2.10254i
\(141\) 0 0
\(142\) −5.02280 4.21463i −0.421504 0.353684i
\(143\) −2.52292 + 4.36983i −0.210977 + 0.365423i
\(144\) 0 0
\(145\) 3.08759 + 5.34786i 0.256410 + 0.444115i
\(146\) 4.70856 26.7036i 0.389683 2.21000i
\(147\) 0 0
\(148\) −21.2079 7.71904i −1.74328 0.634501i
\(149\) 8.37359 + 3.04774i 0.685991 + 0.249680i 0.661418 0.750018i \(-0.269955\pi\)
0.0245732 + 0.999698i \(0.492177\pi\)
\(150\) 0 0
\(151\) −0.123708 + 0.701581i −0.0100672 + 0.0570938i −0.989428 0.145028i \(-0.953673\pi\)
0.979360 + 0.202122i \(0.0647838\pi\)
\(152\) 1.00721 + 1.74453i 0.0816953 + 0.141500i
\(153\) 0 0
\(154\) 21.3773 37.0265i 1.72263 2.98368i
\(155\) 2.33775 + 1.96160i 0.187772 + 0.157560i
\(156\) 0 0
\(157\) −2.39948 13.6081i −0.191499 1.08605i −0.917316 0.398159i \(-0.869649\pi\)
0.725817 0.687888i \(-0.241462\pi\)
\(158\) 7.41071 6.21832i 0.589564 0.494703i
\(159\) 0 0
\(160\) 15.4416 5.62029i 1.22077 0.444323i
\(161\) 20.8666 1.64452
\(162\) 0 0
\(163\) −1.19321 −0.0934597 −0.0467298 0.998908i \(-0.514880\pi\)
−0.0467298 + 0.998908i \(0.514880\pi\)
\(164\) 5.34395 1.94504i 0.417292 0.151882i
\(165\) 0 0
\(166\) 13.7604 11.5464i 1.06802 0.896173i
\(167\) 4.15650 + 23.5727i 0.321640 + 1.82411i 0.532308 + 0.846551i \(0.321325\pi\)
−0.210669 + 0.977558i \(0.567564\pi\)
\(168\) 0 0
\(169\) −8.82583 7.40575i −0.678910 0.569673i
\(170\) 5.20096 9.00832i 0.398895 0.690907i
\(171\) 0 0
\(172\) 6.89926 + 11.9499i 0.526063 + 0.911169i
\(173\) 1.58714 9.00115i 0.120668 0.684344i −0.863118 0.505002i \(-0.831492\pi\)
0.983787 0.179343i \(-0.0573971\pi\)
\(174\) 0 0
\(175\) 3.24044 + 1.17942i 0.244954 + 0.0891561i
\(176\) −10.5377 3.83543i −0.794313 0.289106i
\(177\) 0 0
\(178\) −6.25953 + 35.4996i −0.469172 + 2.66081i
\(179\) 5.30038 + 9.18052i 0.396169 + 0.686184i 0.993250 0.115997i \(-0.0370062\pi\)
−0.597081 + 0.802181i \(0.703673\pi\)
\(180\) 0 0
\(181\) 0.731460 1.26693i 0.0543690 0.0941699i −0.837560 0.546345i \(-0.816019\pi\)
0.891929 + 0.452176i \(0.149352\pi\)
\(182\) −9.59800 8.05368i −0.711451 0.596978i
\(183\) 0 0
\(184\) 0.819031 + 4.64496i 0.0603798 + 0.342431i
\(185\) 14.2320 11.9421i 1.04636 0.877999i
\(186\) 0 0
\(187\) −9.21640 + 3.35450i −0.673970 + 0.245305i
\(188\) −18.0709 −1.31796
\(189\) 0 0
\(190\) −8.08871 −0.586817
\(191\) 11.6731 4.24867i 0.844637 0.307423i 0.116785 0.993157i \(-0.462741\pi\)
0.727852 + 0.685734i \(0.240519\pi\)
\(192\) 0 0
\(193\) 15.9133 13.3528i 1.14546 0.961157i 0.145859 0.989305i \(-0.453406\pi\)
0.999604 + 0.0281484i \(0.00896109\pi\)
\(194\) −1.88554 10.6934i −0.135374 0.767745i
\(195\) 0 0
\(196\) 31.8169 + 26.6976i 2.27264 + 1.90697i
\(197\) −7.09433 + 12.2877i −0.505450 + 0.875465i 0.494530 + 0.869161i \(0.335340\pi\)
−0.999980 + 0.00630469i \(0.997993\pi\)
\(198\) 0 0
\(199\) −10.1643 17.6051i −0.720529 1.24799i −0.960788 0.277284i \(-0.910566\pi\)
0.240259 0.970709i \(-0.422768\pi\)
\(200\) −0.135353 + 0.767624i −0.00957089 + 0.0542792i
\(201\) 0 0
\(202\) 37.1017 + 13.5039i 2.61046 + 0.950132i
\(203\) 13.5860 + 4.94488i 0.953547 + 0.347063i
\(204\) 0 0
\(205\) −0.812919 + 4.61029i −0.0567767 + 0.321997i
\(206\) −9.56876 16.5736i −0.666687 1.15474i
\(207\) 0 0
\(208\) −1.64315 + 2.84601i −0.113932 + 0.197336i
\(209\) 5.84246 + 4.90240i 0.404131 + 0.339106i
\(210\) 0 0
\(211\) −1.71275 9.71347i −0.117910 0.668703i −0.985268 0.171018i \(-0.945294\pi\)
0.867358 0.497685i \(-0.165817\pi\)
\(212\) 12.1952 10.2330i 0.837571 0.702805i
\(213\) 0 0
\(214\) 14.8304 5.39782i 1.01378 0.368987i
\(215\) −11.3588 −0.774665
\(216\) 0 0
\(217\) 7.14494 0.485030
\(218\) 11.2303 4.08751i 0.760615 0.276841i
\(219\) 0 0
\(220\) −16.5609 + 13.8962i −1.11653 + 0.936883i
\(221\) 0.499103 + 2.83055i 0.0335733 + 0.190404i
\(222\) 0 0
\(223\) 11.5453 + 9.68770i 0.773134 + 0.648736i 0.941509 0.336987i \(-0.109408\pi\)
−0.168376 + 0.985723i \(0.553852\pi\)
\(224\) 19.2368 33.3191i 1.28531 2.22623i
\(225\) 0 0
\(226\) −2.55287 4.42170i −0.169814 0.294127i
\(227\) 3.94052 22.3478i 0.261542 1.48328i −0.517164 0.855886i \(-0.673012\pi\)
0.778705 0.627390i \(-0.215877\pi\)
\(228\) 0 0
\(229\) −8.19102 2.98129i −0.541278 0.197009i 0.0568892 0.998381i \(-0.481882\pi\)
−0.598167 + 0.801371i \(0.704104\pi\)
\(230\) −17.7970 6.47758i −1.17350 0.427119i
\(231\) 0 0
\(232\) −0.567483 + 3.21836i −0.0372571 + 0.211296i
\(233\) −11.7945 20.4286i −0.772682 1.33832i −0.936088 0.351766i \(-0.885581\pi\)
0.163406 0.986559i \(-0.447752\pi\)
\(234\) 0 0
\(235\) 7.43792 12.8829i 0.485196 0.840385i
\(236\) −0.505414 0.424093i −0.0328997 0.0276061i
\(237\) 0 0
\(238\) −4.22901 23.9839i −0.274126 1.55465i
\(239\) −7.62560 + 6.39864i −0.493259 + 0.413894i −0.855193 0.518310i \(-0.826561\pi\)
0.361933 + 0.932204i \(0.382117\pi\)
\(240\) 0 0
\(241\) −5.36889 + 1.95411i −0.345840 + 0.125876i −0.509100 0.860708i \(-0.670022\pi\)
0.163259 + 0.986583i \(0.447799\pi\)
\(242\) 13.2140 0.849427
\(243\) 0 0
\(244\) −11.2092 −0.717594
\(245\) −32.1285 + 11.6938i −2.05262 + 0.747091i
\(246\) 0 0
\(247\) 1.71214 1.43666i 0.108941 0.0914124i
\(248\) 0.280445 + 1.59048i 0.0178083 + 0.100996i
\(249\) 0 0
\(250\) −19.2537 16.1558i −1.21771 1.02178i
\(251\) −3.64483 + 6.31303i −0.230060 + 0.398475i −0.957825 0.287351i \(-0.907226\pi\)
0.727766 + 0.685826i \(0.240559\pi\)
\(252\) 0 0
\(253\) 8.92881 + 15.4651i 0.561349 + 0.972285i
\(254\) −3.40767 + 19.3259i −0.213816 + 1.21261i
\(255\) 0 0
\(256\) −4.60565 1.67632i −0.287853 0.104770i
\(257\) −21.8413 7.94960i −1.36243 0.495882i −0.445622 0.895221i \(-0.647018\pi\)
−0.916803 + 0.399339i \(0.869240\pi\)
\(258\) 0 0
\(259\) 7.55332 42.8370i 0.469340 2.66176i
\(260\) 3.16770 + 5.48661i 0.196452 + 0.340265i
\(261\) 0 0
\(262\) −16.2979 + 28.2288i −1.00689 + 1.74398i
\(263\) 20.9893 + 17.6121i 1.29426 + 1.08601i 0.991107 + 0.133067i \(0.0424827\pi\)
0.303150 + 0.952943i \(0.401962\pi\)
\(264\) 0 0
\(265\) 2.27565 + 12.9059i 0.139792 + 0.792802i
\(266\) −14.5074 + 12.1731i −0.889504 + 0.746382i
\(267\) 0 0
\(268\) −9.76605 + 3.55455i −0.596556 + 0.217129i
\(269\) −9.41973 −0.574331 −0.287166 0.957881i \(-0.592713\pi\)
−0.287166 + 0.957881i \(0.592713\pi\)
\(270\) 0 0
\(271\) 26.2797 1.59638 0.798189 0.602408i \(-0.205792\pi\)
0.798189 + 0.602408i \(0.205792\pi\)
\(272\) −6.00253 + 2.18474i −0.363957 + 0.132469i
\(273\) 0 0
\(274\) 5.93190 4.97745i 0.358359 0.300699i
\(275\) 0.512460 + 2.90631i 0.0309025 + 0.175257i
\(276\) 0 0
\(277\) 0.287123 + 0.240924i 0.0172515 + 0.0144757i 0.651373 0.758758i \(-0.274193\pi\)
−0.634121 + 0.773234i \(0.718638\pi\)
\(278\) −14.1054 + 24.4314i −0.845989 + 1.46530i
\(279\) 0 0
\(280\) −5.50253 9.53065i −0.328839 0.569566i
\(281\) −2.42788 + 13.7692i −0.144835 + 0.821400i 0.822665 + 0.568527i \(0.192487\pi\)
−0.967500 + 0.252873i \(0.918625\pi\)
\(282\) 0 0
\(283\) −14.6234 5.32248i −0.869270 0.316389i −0.131399 0.991330i \(-0.541947\pi\)
−0.737872 + 0.674941i \(0.764169\pi\)
\(284\) 7.29424 + 2.65488i 0.432833 + 0.157538i
\(285\) 0 0
\(286\) 1.86195 10.5597i 0.110100 0.624406i
\(287\) 5.48027 + 9.49211i 0.323490 + 0.560301i
\(288\) 0 0
\(289\) 5.70661 9.88413i 0.335683 0.581420i
\(290\) −10.0524 8.43493i −0.590295 0.495316i
\(291\) 0 0
\(292\) 5.57430 + 31.6134i 0.326211 + 1.85003i
\(293\) −18.8633 + 15.8281i −1.10200 + 0.924690i −0.997558 0.0698405i \(-0.977751\pi\)
−0.104445 + 0.994531i \(0.533307\pi\)
\(294\) 0 0
\(295\) 0.510364 0.185757i 0.0297145 0.0108152i
\(296\) 9.83210 0.571479
\(297\) 0 0
\(298\) −18.9361 −1.09694
\(299\) 4.91760 1.78986i 0.284392 0.103510i
\(300\) 0 0
\(301\) −20.3724 + 17.0945i −1.17425 + 0.985309i
\(302\) −0.262882 1.49088i −0.0151272 0.0857904i
\(303\) 0 0
\(304\) 3.80512 + 3.19288i 0.218239 + 0.183124i
\(305\) 4.61365 7.99107i 0.264177 0.457567i
\(306\) 0 0
\(307\) 10.1956 + 17.6593i 0.581893 + 1.00787i 0.995255 + 0.0973012i \(0.0310210\pi\)
−0.413362 + 0.910567i \(0.635646\pi\)
\(308\) −8.78931 + 49.8466i −0.500817 + 2.84028i
\(309\) 0 0
\(310\) −6.09388 2.21799i −0.346109 0.125973i
\(311\) 20.8415 + 7.58567i 1.18181 + 0.430144i 0.856841 0.515580i \(-0.172424\pi\)
0.324970 + 0.945724i \(0.394646\pi\)
\(312\) 0 0
\(313\) −1.94000 + 11.0023i −0.109656 + 0.621887i 0.879603 + 0.475709i \(0.157808\pi\)
−0.989258 + 0.146178i \(0.953303\pi\)
\(314\) 14.6819 + 25.4298i 0.828547 + 1.43508i
\(315\) 0 0
\(316\) −5.72635 + 9.91833i −0.322132 + 0.557950i
\(317\) −19.3171 16.2090i −1.08496 0.910386i −0.0886327 0.996064i \(-0.528250\pi\)
−0.996323 + 0.0856786i \(0.972694\pi\)
\(318\) 0 0
\(319\) 2.14855 + 12.1851i 0.120296 + 0.682232i
\(320\) −18.1754 + 15.2510i −1.01604 + 0.852557i
\(321\) 0 0
\(322\) −41.6680 + 15.1659i −2.32206 + 0.845162i
\(323\) 4.34438 0.241728
\(324\) 0 0
\(325\) 0.864837 0.0479725
\(326\) 2.38270 0.867231i 0.131965 0.0480315i
\(327\) 0 0
\(328\) −1.89786 + 1.59250i −0.104792 + 0.0879309i
\(329\) −6.04793 34.2995i −0.333433 1.89099i
\(330\) 0 0
\(331\) −20.0441 16.8190i −1.10172 0.924455i −0.104183 0.994558i \(-0.533223\pi\)
−0.997540 + 0.0701033i \(0.977667\pi\)
\(332\) −10.6329 + 18.4167i −0.583555 + 1.01075i
\(333\) 0 0
\(334\) −25.4327 44.0507i −1.39161 2.41035i
\(335\) 1.48561 8.42530i 0.0811674 0.460323i
\(336\) 0 0
\(337\) −10.2859 3.74377i −0.560310 0.203936i 0.0463114 0.998927i \(-0.485253\pi\)
−0.606621 + 0.794991i \(0.707476\pi\)
\(338\) 23.0066 + 8.37372i 1.25139 + 0.455470i
\(339\) 0 0
\(340\) −2.13838 + 12.1274i −0.115970 + 0.657700i
\(341\) 3.05732 + 5.29543i 0.165563 + 0.286763i
\(342\) 0 0
\(343\) −23.0545 + 39.9316i −1.24483 + 2.15611i
\(344\) −4.60491 3.86398i −0.248280 0.208332i
\(345\) 0 0
\(346\) 3.37273 + 19.1277i 0.181319 + 1.02831i
\(347\) −2.69140 + 2.25836i −0.144482 + 0.121235i −0.712164 0.702013i \(-0.752285\pi\)
0.567682 + 0.823248i \(0.307840\pi\)
\(348\) 0 0
\(349\) 27.4361 9.98591i 1.46862 0.534534i 0.520894 0.853622i \(-0.325599\pi\)
0.947725 + 0.319088i \(0.103377\pi\)
\(350\) −7.32796 −0.391696
\(351\) 0 0
\(352\) 32.9256 1.75494
\(353\) −23.5645 + 8.57677i −1.25421 + 0.456496i −0.881823 0.471581i \(-0.843683\pi\)
−0.372389 + 0.928077i \(0.621461\pi\)
\(354\) 0 0
\(355\) −4.89495 + 4.10735i −0.259797 + 0.217996i
\(356\) −7.41044 42.0267i −0.392753 2.22741i
\(357\) 0 0
\(358\) −17.2566 14.4800i −0.912040 0.765293i
\(359\) 2.10362 3.64358i 0.111025 0.192301i −0.805159 0.593059i \(-0.797920\pi\)
0.916184 + 0.400758i \(0.131253\pi\)
\(360\) 0 0
\(361\) 7.81087 + 13.5288i 0.411098 + 0.712043i
\(362\) −0.539828 + 3.06152i −0.0283727 + 0.160910i
\(363\) 0 0
\(364\) 13.9385 + 5.07318i 0.730574 + 0.265907i
\(365\) −24.8317 9.03799i −1.29975 0.473070i
\(366\) 0 0
\(367\) 3.03826 17.2308i 0.158596 0.899441i −0.796829 0.604205i \(-0.793491\pi\)
0.955424 0.295236i \(-0.0953983\pi\)
\(368\) 5.81522 + 10.0723i 0.303139 + 0.525053i
\(369\) 0 0
\(370\) −19.7400 + 34.1907i −1.02623 + 1.77749i
\(371\) 23.5042 + 19.7224i 1.22028 + 1.02393i
\(372\) 0 0
\(373\) −5.14946 29.2040i −0.266629 1.51213i −0.764356 0.644794i \(-0.776943\pi\)
0.497727 0.867334i \(-0.334168\pi\)
\(374\) 15.9659 13.3970i 0.825579 0.692743i
\(375\) 0 0
\(376\) 7.39778 2.69257i 0.381511 0.138859i
\(377\) 3.62594 0.186745
\(378\) 0 0
\(379\) 20.9523 1.07625 0.538124 0.842865i \(-0.319133\pi\)
0.538124 + 0.842865i \(0.319133\pi\)
\(380\) 8.99844 3.27517i 0.461610 0.168012i
\(381\) 0 0
\(382\) −20.2218 + 16.9681i −1.03464 + 0.868164i
\(383\) −1.71856 9.74642i −0.0878142 0.498019i −0.996714 0.0810039i \(-0.974187\pi\)
0.908900 0.417015i \(-0.136924\pi\)
\(384\) 0 0
\(385\) −31.9182 26.7826i −1.62670 1.36497i
\(386\) −22.0719 + 38.2297i −1.12343 + 1.94584i
\(387\) 0 0
\(388\) 6.42745 + 11.1327i 0.326304 + 0.565175i
\(389\) 3.66654 20.7940i 0.185901 1.05430i −0.738891 0.673825i \(-0.764650\pi\)
0.924792 0.380472i \(-0.124239\pi\)
\(390\) 0 0
\(391\) 9.55863 + 3.47906i 0.483401 + 0.175943i
\(392\) −17.0030 6.18857i −0.858779 0.312570i
\(393\) 0 0
\(394\) 5.23572 29.6932i 0.263772 1.49592i
\(395\) −4.71388 8.16468i −0.237181 0.410810i
\(396\) 0 0
\(397\) 4.88955 8.46894i 0.245399 0.425044i −0.716845 0.697233i \(-0.754414\pi\)
0.962244 + 0.272189i \(0.0877476\pi\)
\(398\) 33.0923 + 27.7677i 1.65877 + 1.39187i
\(399\) 0 0
\(400\) 0.333759 + 1.89284i 0.0166880 + 0.0946421i
\(401\) 14.6616 12.3025i 0.732164 0.614359i −0.198556 0.980089i \(-0.563625\pi\)
0.930721 + 0.365731i \(0.119181\pi\)
\(402\) 0 0
\(403\) 1.68384 0.612867i 0.0838780 0.0305291i
\(404\) −46.7423 −2.32552
\(405\) 0 0
\(406\) −30.7234 −1.52478
\(407\) 34.9804 12.7318i 1.73392 0.631094i
\(408\) 0 0
\(409\) 11.4873 9.63896i 0.568009 0.476616i −0.312976 0.949761i \(-0.601326\pi\)
0.880984 + 0.473145i \(0.156881\pi\)
\(410\) −1.72748 9.79700i −0.0853139 0.483839i
\(411\) 0 0
\(412\) 17.3557 + 14.5631i 0.855053 + 0.717475i
\(413\) 0.635799 1.10124i 0.0312856 0.0541883i
\(414\) 0 0
\(415\) −8.75289 15.1604i −0.429662 0.744197i
\(416\) 1.67552 9.50233i 0.0821490 0.465890i
\(417\) 0 0
\(418\) −15.2297 5.54317i −0.744911 0.271125i
\(419\) 5.46131 + 1.98775i 0.266802 + 0.0971081i 0.471957 0.881621i \(-0.343548\pi\)
−0.205155 + 0.978729i \(0.565770\pi\)
\(420\) 0 0
\(421\) −2.31187 + 13.1113i −0.112674 + 0.639003i 0.875202 + 0.483757i \(0.160728\pi\)
−0.987876 + 0.155246i \(0.950383\pi\)
\(422\) 10.4799 + 18.1518i 0.510154 + 0.883613i
\(423\) 0 0
\(424\) −3.46769 + 6.00621i −0.168406 + 0.291687i
\(425\) 1.28775 + 1.08055i 0.0624649 + 0.0524143i
\(426\) 0 0
\(427\) −3.75146 21.2756i −0.181546 1.02960i
\(428\) −14.3127 + 12.0098i −0.691833 + 0.580516i
\(429\) 0 0
\(430\) 22.6821 8.25561i 1.09383 0.398121i
\(431\) 36.4166 1.75413 0.877064 0.480374i \(-0.159499\pi\)
0.877064 + 0.480374i \(0.159499\pi\)
\(432\) 0 0
\(433\) −10.8761 −0.522674 −0.261337 0.965248i \(-0.584163\pi\)
−0.261337 + 0.965248i \(0.584163\pi\)
\(434\) −14.2675 + 5.19296i −0.684864 + 0.249270i
\(435\) 0 0
\(436\) −10.8384 + 9.09446i −0.519063 + 0.435546i
\(437\) −1.37355 7.78982i −0.0657060 0.372637i
\(438\) 0 0
\(439\) 7.24162 + 6.07644i 0.345624 + 0.290013i 0.799030 0.601291i \(-0.205347\pi\)
−0.453406 + 0.891304i \(0.649791\pi\)
\(440\) 4.70906 8.15632i 0.224495 0.388837i
\(441\) 0 0
\(442\) −3.05390 5.28951i −0.145259 0.251596i
\(443\) −2.86935 + 16.2729i −0.136327 + 0.773148i 0.837600 + 0.546284i \(0.183958\pi\)
−0.973927 + 0.226863i \(0.927153\pi\)
\(444\) 0 0
\(445\) 33.0111 + 12.0151i 1.56488 + 0.569569i
\(446\) −30.0957 10.9539i −1.42507 0.518683i
\(447\) 0 0
\(448\) −9.64620 + 54.7063i −0.455740 + 2.58463i
\(449\) −2.37181 4.10809i −0.111933 0.193873i 0.804617 0.593794i \(-0.202371\pi\)
−0.916549 + 0.399921i \(0.869037\pi\)
\(450\) 0 0
\(451\) −4.69001 + 8.12334i −0.220844 + 0.382513i
\(452\) 4.63036 + 3.88533i 0.217794 + 0.182751i
\(453\) 0 0
\(454\) 8.37372 + 47.4897i 0.392998 + 2.22880i
\(455\) −9.35370 + 7.84869i −0.438508 + 0.367952i
\(456\) 0 0
\(457\) 21.0571 7.66417i 0.985012 0.358515i 0.201225 0.979545i \(-0.435508\pi\)
0.783787 + 0.621030i \(0.213286\pi\)
\(458\) 18.5232 0.865534
\(459\) 0 0
\(460\) 22.4214 1.04540
\(461\) −14.0223 + 5.10371i −0.653085 + 0.237704i −0.647248 0.762279i \(-0.724080\pi\)
−0.00583713 + 0.999983i \(0.501858\pi\)
\(462\) 0 0
\(463\) −11.3736 + 9.54358i −0.528576 + 0.443528i −0.867609 0.497247i \(-0.834344\pi\)
0.339033 + 0.940774i \(0.389900\pi\)
\(464\) 1.39933 + 7.93597i 0.0649621 + 0.368418i
\(465\) 0 0
\(466\) 38.3997 + 32.2212i 1.77883 + 1.49262i
\(467\) −7.67571 + 13.2947i −0.355190 + 0.615206i −0.987150 0.159794i \(-0.948917\pi\)
0.631961 + 0.775000i \(0.282250\pi\)
\(468\) 0 0
\(469\) −10.0152 17.3468i −0.462458 0.801001i
\(470\) −5.48929 + 31.1313i −0.253202 + 1.43598i
\(471\) 0 0
\(472\) 0.270093 + 0.0983060i 0.0124321 + 0.00452490i
\(473\) −21.3868 7.78416i −0.983366 0.357916i
\(474\) 0 0
\(475\) 0.226993 1.28734i 0.0104152 0.0590673i
\(476\) 14.4159 + 24.9690i 0.660750 + 1.14445i
\(477\) 0 0
\(478\) 10.5768 18.3196i 0.483772 0.837918i
\(479\) −8.00410 6.71624i −0.365717 0.306873i 0.441348 0.897336i \(-0.354501\pi\)
−0.807064 + 0.590464i \(0.798945\pi\)
\(480\) 0 0
\(481\) −1.89432 10.7432i −0.0863737 0.489850i
\(482\) 9.30073 7.80424i 0.423637 0.355473i
\(483\) 0 0
\(484\) −14.7001 + 5.35041i −0.668188 + 0.243201i
\(485\) −10.5820 −0.480505
\(486\) 0 0
\(487\) −16.1649 −0.732500 −0.366250 0.930516i \(-0.619359\pi\)
−0.366250 + 0.930516i \(0.619359\pi\)
\(488\) 4.58875 1.67017i 0.207723 0.0756049i
\(489\) 0 0
\(490\) 55.6575 46.7022i 2.51435 2.10979i
\(491\) 1.87147 + 10.6136i 0.0844581 + 0.478985i 0.997472 + 0.0710576i \(0.0226374\pi\)
−0.913014 + 0.407928i \(0.866251\pi\)
\(492\) 0 0
\(493\) 5.39904 + 4.53033i 0.243160 + 0.204036i
\(494\) −2.37477 + 4.11322i −0.106846 + 0.185062i
\(495\) 0 0
\(496\) 1.99119 + 3.44885i 0.0894071 + 0.154858i
\(497\) −2.59789 + 14.7333i −0.116531 + 0.660881i
\(498\) 0 0
\(499\) 18.0301 + 6.56240i 0.807136 + 0.293774i 0.712440 0.701733i \(-0.247590\pi\)
0.0946959 + 0.995506i \(0.469812\pi\)
\(500\) 27.9607 + 10.1769i 1.25044 + 0.455123i
\(501\) 0 0
\(502\) 2.68994 15.2554i 0.120058 0.680882i
\(503\) −6.01253 10.4140i −0.268086 0.464338i 0.700282 0.713866i \(-0.253058\pi\)
−0.968367 + 0.249529i \(0.919724\pi\)
\(504\) 0 0
\(505\) 19.2389 33.3228i 0.856120 1.48284i
\(506\) −29.0698 24.3925i −1.29231 1.08438i
\(507\) 0 0
\(508\) −4.03422 22.8792i −0.178990 1.01510i
\(509\) 11.4547 9.61162i 0.507720 0.426027i −0.352606 0.935772i \(-0.614704\pi\)
0.860326 + 0.509744i \(0.170260\pi\)
\(510\) 0 0
\(511\) −58.1382 + 21.1606i −2.57188 + 0.936088i
\(512\) 27.3678 1.20950
\(513\) 0 0
\(514\) 49.3922 2.17860
\(515\) −17.5257 + 6.37882i −0.772273 + 0.281084i
\(516\) 0 0
\(517\) 22.8330 19.1591i 1.00419 0.842618i
\(518\) 16.0510 + 91.0299i 0.705241 + 3.99962i
\(519\) 0 0
\(520\) −2.11428 1.77409i −0.0927172 0.0777990i
\(521\) 18.7094 32.4056i 0.819673 1.41972i −0.0862502 0.996274i \(-0.527488\pi\)
0.905923 0.423442i \(-0.139178\pi\)
\(522\) 0 0
\(523\) 4.22489 + 7.31773i 0.184742 + 0.319982i 0.943489 0.331403i \(-0.107522\pi\)
−0.758748 + 0.651385i \(0.774188\pi\)
\(524\) 6.70092 38.0028i 0.292731 1.66016i
\(525\) 0 0
\(526\) −54.7136 19.9141i −2.38562 0.868296i
\(527\) 3.27297 + 1.19126i 0.142573 + 0.0518923i
\(528\) 0 0
\(529\) −0.777821 + 4.41124i −0.0338183 + 0.191793i
\(530\) −13.9242 24.1175i −0.604829 1.04760i
\(531\) 0 0
\(532\) 11.2100 19.4163i 0.486017 0.841805i
\(533\) 2.10573 + 1.76692i 0.0912092 + 0.0765336i
\(534\) 0 0
\(535\) −2.67079 15.1468i −0.115468 0.654853i
\(536\) 3.46834 2.91028i 0.149809 0.125705i
\(537\) 0 0
\(538\) 18.8100 6.84628i 0.810957 0.295164i
\(539\) −68.5065 −2.95078
\(540\) 0 0
\(541\) 12.6259 0.542828 0.271414 0.962463i \(-0.412509\pi\)
0.271414 + 0.962463i \(0.412509\pi\)
\(542\) −52.4772 + 19.1001i −2.25409 + 0.820422i
\(543\) 0 0
\(544\) 14.3673 12.0556i 0.615992 0.516879i
\(545\) −2.02246 11.4699i −0.0866327 0.491319i
\(546\) 0 0
\(547\) 24.0500 + 20.1804i 1.02830 + 0.862850i 0.990648 0.136441i \(-0.0435665\pi\)
0.0376558 + 0.999291i \(0.488011\pi\)
\(548\) −4.58365 + 7.93912i −0.195804 + 0.339142i
\(549\) 0 0
\(550\) −3.13563 5.43107i −0.133704 0.231582i
\(551\) 0.951697 5.39734i 0.0405437 0.229934i
\(552\) 0 0
\(553\) −20.7420 7.54945i −0.882038 0.321035i
\(554\) −0.748452 0.272414i −0.0317987 0.0115738i
\(555\) 0 0
\(556\) 5.79948 32.8905i 0.245953 1.39487i
\(557\) −7.96515 13.7960i −0.337494 0.584557i 0.646467 0.762942i \(-0.276246\pi\)
−0.983961 + 0.178385i \(0.942913\pi\)
\(558\) 0 0
\(559\) −3.33484 + 5.77610i −0.141048 + 0.244303i
\(560\) −20.7880 17.4432i −0.878452 0.737108i
\(561\) 0 0
\(562\) −5.15931 29.2599i −0.217632 1.23425i
\(563\) 19.0445 15.9802i 0.802631 0.673487i −0.146206 0.989254i \(-0.546706\pi\)
0.948837 + 0.315767i \(0.102262\pi\)
\(564\) 0 0
\(565\) −4.67571 + 1.70182i −0.196708 + 0.0715960i
\(566\) 33.0695 1.39001
\(567\) 0 0
\(568\) −3.38165 −0.141891
\(569\) 18.0327 6.56337i 0.755970 0.275151i 0.0648545 0.997895i \(-0.479342\pi\)
0.691116 + 0.722744i \(0.257119\pi\)
\(570\) 0 0
\(571\) −15.6114 + 13.0995i −0.653317 + 0.548198i −0.908075 0.418807i \(-0.862448\pi\)
0.254759 + 0.967005i \(0.418004\pi\)
\(572\) 2.20430 + 12.5012i 0.0921664 + 0.522702i
\(573\) 0 0
\(574\) −17.8423 14.9715i −0.744723 0.624897i
\(575\) 1.53036 2.65066i 0.0638205 0.110540i
\(576\) 0 0
\(577\) −11.6495 20.1776i −0.484976 0.840004i 0.514875 0.857265i \(-0.327838\pi\)
−0.999851 + 0.0172619i \(0.994505\pi\)
\(578\) −4.21156 + 23.8849i −0.175178 + 0.993483i
\(579\) 0 0
\(580\) 14.5983 + 5.31334i 0.606161 + 0.220624i
\(581\) −38.5143 14.0181i −1.59784 0.581568i
\(582\) 0 0
\(583\) −4.55967 + 25.8592i −0.188842 + 1.07098i
\(584\) −6.99237 12.1111i −0.289346 0.501163i
\(585\) 0 0
\(586\) 26.1636 45.3167i 1.08081 1.87201i
\(587\) 28.2741 + 23.7248i 1.16700 + 0.979228i 0.999977 0.00672500i \(-0.00214065\pi\)
0.167021 + 0.985953i \(0.446585\pi\)
\(588\) 0 0
\(589\) −0.470319 2.66731i −0.0193792 0.109905i
\(590\) −0.884124 + 0.741868i −0.0363988 + 0.0305422i
\(591\) 0 0
\(592\) 22.7823 8.29209i 0.936348 0.340803i
\(593\) −4.36830 −0.179385 −0.0896923 0.995970i \(-0.528588\pi\)
−0.0896923 + 0.995970i \(0.528588\pi\)
\(594\) 0 0
\(595\) −23.7340 −0.973000
\(596\) 21.0658 7.66733i 0.862890 0.314066i
\(597\) 0 0
\(598\) −8.51896 + 7.14826i −0.348366 + 0.292314i
\(599\) 5.41880 + 30.7315i 0.221406 + 1.25566i 0.869438 + 0.494043i \(0.164481\pi\)
−0.648032 + 0.761613i \(0.724408\pi\)
\(600\) 0 0
\(601\) 33.6578 + 28.2422i 1.37293 + 1.15202i 0.971747 + 0.236027i \(0.0758452\pi\)
0.401183 + 0.915998i \(0.368599\pi\)
\(602\) 28.2568 48.9422i 1.15166 1.99474i
\(603\) 0 0
\(604\) 0.896114 + 1.55211i 0.0364623 + 0.0631546i
\(605\) 2.23618 12.6820i 0.0909136 0.515597i
\(606\) 0 0
\(607\) −16.3118 5.93701i −0.662075 0.240976i −0.0109432 0.999940i \(-0.503483\pi\)
−0.651132 + 0.758964i \(0.725706\pi\)
\(608\) −13.7048 4.98814i −0.555803 0.202296i
\(609\) 0 0
\(610\) −3.40494 + 19.3104i −0.137862 + 0.781854i
\(611\) −4.36740 7.56456i −0.176686 0.306029i
\(612\) 0 0
\(613\) 0.599024 1.03754i 0.0241944 0.0419059i −0.853675 0.520807i \(-0.825631\pi\)
0.877869 + 0.478901i \(0.158965\pi\)
\(614\) −33.1941 27.8532i −1.33961 1.12406i
\(615\) 0 0
\(616\) −3.82903 21.7155i −0.154276 0.874944i
\(617\) −19.9277 + 16.7213i −0.802257 + 0.673174i −0.948746 0.316038i \(-0.897647\pi\)
0.146489 + 0.989212i \(0.453203\pi\)
\(618\) 0 0
\(619\) −9.05051 + 3.29412i −0.363771 + 0.132402i −0.517437 0.855721i \(-0.673114\pi\)
0.153667 + 0.988123i \(0.450892\pi\)
\(620\) 7.67733 0.308329
\(621\) 0 0
\(622\) −47.1311 −1.88978
\(623\) 77.2886 28.1308i 3.09650 1.12704i
\(624\) 0 0
\(625\) −16.0396 + 13.4588i −0.641582 + 0.538351i
\(626\) −4.12256 23.3802i −0.164771 0.934462i
\(627\) 0 0
\(628\) −26.6298 22.3451i −1.06264 0.891665i
\(629\) 10.6022 18.3635i 0.422737 0.732202i
\(630\) 0 0
\(631\) 7.08366 + 12.2693i 0.281996 + 0.488431i 0.971876 0.235492i \(-0.0756702\pi\)
−0.689880 + 0.723924i \(0.742337\pi\)
\(632\) 0.866389 4.91354i 0.0344631 0.195450i
\(633\) 0 0
\(634\) 50.3545 + 18.3275i 1.99983 + 0.727879i
\(635\) 17.9712 + 6.54096i 0.713163 + 0.259570i
\(636\) 0 0
\(637\) −3.48615 + 19.7710i −0.138126 + 0.783354i
\(638\) −13.1465 22.7704i −0.520476 0.901490i
\(639\) 0 0
\(640\) 8.77695 15.2021i 0.346939 0.600917i
\(641\) −17.0069 14.2705i −0.671732 0.563650i 0.241846 0.970315i \(-0.422247\pi\)
−0.913577 + 0.406665i \(0.866692\pi\)
\(642\) 0 0
\(643\) 3.73982 + 21.2096i 0.147484 + 0.836425i 0.965339 + 0.261000i \(0.0840522\pi\)
−0.817855 + 0.575425i \(0.804837\pi\)
\(644\) 40.2136 33.7432i 1.58464 1.32967i
\(645\) 0 0
\(646\) −8.67518 + 3.15751i −0.341321 + 0.124231i
\(647\) −13.4037 −0.526952 −0.263476 0.964666i \(-0.584869\pi\)
−0.263476 + 0.964666i \(0.584869\pi\)
\(648\) 0 0
\(649\) 1.08823 0.0427168
\(650\) −1.72697 + 0.628566i −0.0677374 + 0.0246544i
\(651\) 0 0
\(652\) −2.29953 + 1.92953i −0.0900565 + 0.0755664i
\(653\) 3.28384 + 18.6236i 0.128506 + 0.728796i 0.979163 + 0.203075i \(0.0650935\pi\)
−0.850657 + 0.525722i \(0.823795\pi\)
\(654\) 0 0
\(655\) 24.3343 + 20.4189i 0.950820 + 0.797832i
\(656\) −3.05455 + 5.29063i −0.119260 + 0.206564i
\(657\) 0 0
\(658\) 37.0059 + 64.0962i 1.44264 + 2.49873i
\(659\) 0.00489366 0.0277533i 0.000190630 0.00108112i −0.984712 0.174189i \(-0.944270\pi\)
0.984903 + 0.173108i \(0.0553808\pi\)
\(660\) 0 0
\(661\) 42.3254 + 15.4052i 1.64627 + 0.599192i 0.988118 0.153696i \(-0.0491177\pi\)
0.658148 + 0.752888i \(0.271340\pi\)
\(662\) 52.2496 + 19.0173i 2.03074 + 0.739128i
\(663\) 0 0
\(664\) 1.60874 9.12361i 0.0624312 0.354065i
\(665\) 9.22800 + 15.9834i 0.357846 + 0.619808i
\(666\) 0 0
\(667\) 6.41623 11.1132i 0.248438 0.430306i
\(668\) 46.1295 + 38.7072i 1.78480 + 1.49763i
\(669\) 0 0
\(670\) 3.15696 + 17.9040i 0.121964 + 0.691692i
\(671\) 14.1630 11.8842i 0.546757 0.458783i
\(672\) 0 0
\(673\) 9.17111 3.33801i 0.353520 0.128671i −0.159155 0.987254i \(-0.550877\pi\)
0.512675 + 0.858583i \(0.328655\pi\)
\(674\) 23.2607 0.895968
\(675\) 0 0
\(676\) −28.9847 −1.11480
\(677\) 38.4153 13.9820i 1.47642 0.537374i 0.526586 0.850122i \(-0.323472\pi\)
0.949836 + 0.312748i \(0.101250\pi\)
\(678\) 0 0
\(679\) −18.9792 + 15.9255i −0.728356 + 0.611163i
\(680\) −0.931581 5.28326i −0.0357245 0.202604i
\(681\) 0 0
\(682\) −9.95380 8.35223i −0.381151 0.319823i
\(683\) −22.0126 + 38.1269i −0.842287 + 1.45888i 0.0456696 + 0.998957i \(0.485458\pi\)
−0.887957 + 0.459927i \(0.847875\pi\)
\(684\) 0 0
\(685\) −3.77322 6.53541i −0.144167 0.249705i
\(686\) 17.0146 96.4945i 0.649620 3.68418i
\(687\) 0 0
\(688\) −13.9290 5.06973i −0.531036 0.193281i
\(689\) 7.23092 + 2.63184i 0.275476 + 0.100265i
\(690\) 0 0
\(691\) 3.74240 21.2242i 0.142368 0.807406i −0.827076 0.562090i \(-0.809997\pi\)
0.969443 0.245316i \(-0.0788916\pi\)
\(692\) −11.4970 19.9133i −0.437049 0.756991i
\(693\) 0 0
\(694\) 3.73302 6.46577i 0.141703 0.245437i
\(695\) 21.0607 + 17.6721i 0.798880 + 0.670340i
\(696\) 0 0
\(697\) 0.927813 + 5.26189i 0.0351434 + 0.199308i
\(698\) −47.5286 + 39.8812i −1.79898 + 1.50953i
\(699\) 0 0
\(700\) 8.15213 2.96713i 0.308122 0.112147i
\(701\) 12.8521 0.485419 0.242709 0.970099i \(-0.421964\pi\)
0.242709 + 0.970099i \(0.421964\pi\)
\(702\) 0 0
\(703\) −16.4889 −0.621891
\(704\) −44.6729 + 16.2596i −1.68367 + 0.612806i
\(705\) 0 0
\(706\) 40.8217 34.2535i 1.53634 1.28915i
\(707\) −15.6436 88.7191i −0.588337 3.33663i
\(708\) 0 0
\(709\) −38.0814 31.9541i −1.43018 1.20006i −0.945609 0.325306i \(-0.894533\pi\)
−0.484567 0.874754i \(-0.661023\pi\)
\(710\) 6.78937 11.7595i 0.254800 0.441327i
\(711\) 0 0
\(712\) 9.29562 + 16.1005i 0.348368 + 0.603392i
\(713\) 1.10122 6.24534i 0.0412411 0.233890i
\(714\) 0 0
\(715\) −9.81945 3.57399i −0.367227 0.133660i
\(716\) 25.0605 + 9.12127i 0.936554 + 0.340878i
\(717\) 0 0
\(718\) −1.55250 + 8.80469i −0.0579389 + 0.328588i
\(719\) −2.81873 4.88218i −0.105121 0.182075i 0.808667 0.588267i \(-0.200190\pi\)
−0.913788 + 0.406192i \(0.866856\pi\)
\(720\) 0 0
\(721\) −21.8330 + 37.8159i −0.813104 + 1.40834i
\(722\) −25.4301 21.3384i −0.946410 0.794132i
\(723\) 0 0
\(724\) −0.639084 3.62442i −0.0237514 0.134701i
\(725\) 1.62454 1.36315i 0.0603340 0.0506262i
\(726\) 0 0
\(727\) 42.6755 15.5326i 1.58275 0.576072i 0.606947 0.794743i \(-0.292394\pi\)
0.975799 + 0.218670i \(0.0701719\pi\)
\(728\) −6.46195 −0.239496
\(729\) 0 0
\(730\) 56.1546 2.07837
\(731\) −12.1824 + 4.43402i −0.450582 + 0.163998i
\(732\) 0 0
\(733\) −19.6620 + 16.4983i −0.726231 + 0.609380i −0.929101 0.369826i \(-0.879417\pi\)
0.202870 + 0.979206i \(0.434973\pi\)
\(734\) 6.45639 + 36.6160i 0.238310 + 1.35152i
\(735\) 0 0
\(736\) −26.1591 21.9501i −0.964236 0.809090i
\(737\) 8.57098 14.8454i 0.315716 0.546837i
\(738\) 0 0
\(739\) 7.22763 + 12.5186i 0.265873 + 0.460505i 0.967792 0.251752i \(-0.0810066\pi\)
−0.701919 + 0.712256i \(0.747673\pi\)
\(740\) 8.11614 46.0289i 0.298355 1.69206i
\(741\) 0 0
\(742\) −61.2692 22.3002i −2.24926 0.818664i
\(743\) 32.6954 + 11.9002i 1.19948 + 0.436574i 0.863042 0.505132i \(-0.168556\pi\)
0.336436 + 0.941706i \(0.390778\pi\)
\(744\) 0 0
\(745\) −3.20452 + 18.1738i −0.117405 + 0.665835i
\(746\) 31.5084 + 54.5742i 1.15360 + 1.99810i
\(747\) 0 0
\(748\) −12.3371 + 21.3685i −0.451089 + 0.781308i
\(749\) −27.5854 23.1469i −1.00795 0.845768i
\(750\) 0 0
\(751\) 3.14624 + 17.8432i 0.114808 + 0.651107i 0.986845 + 0.161668i \(0.0516874\pi\)
−0.872037 + 0.489439i \(0.837202\pi\)
\(752\) 14.8708 12.4781i 0.542283 0.455030i
\(753\) 0 0
\(754\) −7.24054 + 2.63534i −0.263685 + 0.0959735i
\(755\) −1.47535 −0.0536933
\(756\) 0 0
\(757\) −37.0045 −1.34495 −0.672475 0.740120i \(-0.734769\pi\)
−0.672475 + 0.740120i \(0.734769\pi\)
\(758\) −41.8391 + 15.2282i −1.51967 + 0.553113i
\(759\) 0 0
\(760\) −3.19573 + 2.68154i −0.115921 + 0.0972696i
\(761\) 2.16095 + 12.2554i 0.0783344 + 0.444256i 0.998597 + 0.0529549i \(0.0168640\pi\)
−0.920263 + 0.391302i \(0.872025\pi\)
\(762\) 0 0
\(763\) −20.8891 17.5280i −0.756235 0.634557i
\(764\) 15.6257 27.0644i 0.565316 0.979156i
\(765\) 0 0
\(766\) 10.5155 + 18.2133i 0.379939 + 0.658074i
\(767\) 0.0553778 0.314063i 0.00199958 0.0113402i
\(768\) 0 0
\(769\) 38.4199 + 13.9837i 1.38546 + 0.504265i 0.923828 0.382809i \(-0.125043\pi\)
0.461628 + 0.887074i \(0.347265\pi\)
\(770\) 83.2024 + 30.2832i 2.99841 + 1.09133i
\(771\) 0 0
\(772\) 9.07492 51.4664i 0.326613 1.85232i
\(773\) −18.2081 31.5374i −0.654900 1.13432i −0.981919 0.189302i \(-0.939377\pi\)
0.327019 0.945018i \(-0.393956\pi\)
\(774\) 0 0
\(775\) 0.524012 0.907615i 0.0188231 0.0326025i
\(776\) −4.29000 3.59974i −0.154002 0.129223i
\(777\) 0 0
\(778\) 7.79150 + 44.1878i 0.279339 + 1.58421i
\(779\) 3.18281 2.67069i 0.114036 0.0956875i
\(780\) 0 0