Properties

Label 729.2.g.c.28.1
Level $729$
Weight $2$
Character 729.28
Analytic conductor $5.821$
Analytic rank $0$
Dimension $144$
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 28.1
Character \(\chi\) \(=\) 729.28
Dual form 729.2.g.c.703.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.81786 + 1.19562i) q^{2} +(1.08293 - 2.51052i) q^{4} +(-0.443651 + 0.470242i) q^{5} +(1.81697 + 0.212373i) q^{7} +(0.277373 + 1.57306i) q^{8} +O(q^{10})\) \(q+(-1.81786 + 1.19562i) q^{2} +(1.08293 - 2.51052i) q^{4} +(-0.443651 + 0.470242i) q^{5} +(1.81697 + 0.212373i) q^{7} +(0.277373 + 1.57306i) q^{8} +(0.244261 - 1.38527i) q^{10} +(0.346986 - 1.15901i) q^{11} +(0.310113 - 5.32444i) q^{13} +(-3.55691 + 1.78635i) q^{14} +(1.36753 + 1.44950i) q^{16} +(-6.43434 + 2.34191i) q^{17} +(-5.97823 - 2.17590i) q^{19} +(0.700110 + 1.62304i) q^{20} +(0.754974 + 2.52179i) q^{22} +(3.09558 - 0.361822i) q^{23} +(0.266422 + 4.57429i) q^{25} +(5.80229 + 10.0499i) q^{26} +(2.50083 - 4.33156i) q^{28} +(-5.26023 - 2.64179i) q^{29} +(-1.65611 - 2.22454i) q^{31} +(-7.32759 - 1.73667i) q^{32} +(8.89668 - 11.9503i) q^{34} +(-0.905967 + 0.760197i) q^{35} +(-1.09453 - 0.918418i) q^{37} +(13.4691 - 3.19224i) q^{38} +(-0.862777 - 0.567457i) q^{40} +(-0.931903 - 0.612922i) q^{41} +(-9.37473 + 2.22185i) q^{43} +(-2.53397 - 2.12625i) q^{44} +(-5.19473 + 4.35890i) q^{46} +(3.64407 - 4.89483i) q^{47} +(-3.55504 - 0.842559i) q^{49} +(-5.95346 - 7.99688i) q^{50} +(-13.0313 - 6.54456i) q^{52} +(4.26135 - 7.38088i) q^{53} +(0.391077 + 0.677365i) q^{55} +(0.169902 + 2.91711i) q^{56} +(12.7209 - 1.48687i) q^{58} +(-0.598878 - 2.00039i) q^{59} +(-1.42194 - 3.29643i) q^{61} +(5.67029 + 2.06382i) q^{62} +(11.6517 - 4.24088i) q^{64} +(2.36619 + 2.50802i) q^{65} +(1.09003 - 0.547434i) q^{67} +(-1.08855 + 18.6897i) q^{68} +(0.738011 - 2.46513i) q^{70} +(1.41528 - 8.02646i) q^{71} +(1.11524 + 6.32482i) q^{73} +(3.08778 + 0.360910i) q^{74} +(-11.9367 + 12.6521i) q^{76} +(0.876607 - 2.03220i) q^{77} +(11.9127 - 7.83511i) q^{79} -1.28832 q^{80} +2.42689 q^{82} +(-5.61402 + 3.69240i) q^{83} +(1.75334 - 4.06469i) q^{85} +(14.3854 - 15.2477i) q^{86} +(1.91944 + 0.224351i) q^{88} +(-2.70557 - 15.3441i) q^{89} +(1.69423 - 9.60848i) q^{91} +(2.44395 - 8.16337i) q^{92} +(-0.772019 + 13.2550i) q^{94} +(3.67544 - 1.84588i) q^{95} +(2.55920 + 2.71259i) q^{97} +(7.46994 - 2.71884i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 144 q + 9 q^{2} + 9 q^{4} + 9 q^{5} + 9 q^{7} - 18 q^{8}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/729\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{22}{27}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.81786 + 1.19562i −1.28542 + 0.845434i −0.993809 0.111102i \(-0.964562\pi\)
−0.291612 + 0.956537i \(0.594192\pi\)
\(3\) 0 0
\(4\) 1.08293 2.51052i 0.541467 1.25526i
\(5\) −0.443651 + 0.470242i −0.198407 + 0.210299i −0.818937 0.573884i \(-0.805436\pi\)
0.620530 + 0.784183i \(0.286918\pi\)
\(6\) 0 0
\(7\) 1.81697 + 0.212373i 0.686750 + 0.0802696i 0.452310 0.891861i \(-0.350600\pi\)
0.234440 + 0.972131i \(0.424674\pi\)
\(8\) 0.277373 + 1.57306i 0.0980662 + 0.556161i
\(9\) 0 0
\(10\) 0.244261 1.38527i 0.0772422 0.438062i
\(11\) 0.346986 1.15901i 0.104620 0.349456i −0.889610 0.456720i \(-0.849024\pi\)
0.994231 + 0.107264i \(0.0342092\pi\)
\(12\) 0 0
\(13\) 0.310113 5.32444i 0.0860099 1.47673i −0.628883 0.777500i \(-0.716488\pi\)
0.714893 0.699233i \(-0.246475\pi\)
\(14\) −3.55691 + 1.78635i −0.950625 + 0.477422i
\(15\) 0 0
\(16\) 1.36753 + 1.44950i 0.341884 + 0.362375i
\(17\) −6.43434 + 2.34191i −1.56056 + 0.567996i −0.970864 0.239631i \(-0.922973\pi\)
−0.589693 + 0.807628i \(0.700751\pi\)
\(18\) 0 0
\(19\) −5.97823 2.17590i −1.37150 0.499185i −0.451909 0.892064i \(-0.649257\pi\)
−0.919590 + 0.392879i \(0.871479\pi\)
\(20\) 0.700110 + 1.62304i 0.156549 + 0.362922i
\(21\) 0 0
\(22\) 0.754974 + 2.52179i 0.160961 + 0.537648i
\(23\) 3.09558 0.361822i 0.645474 0.0754451i 0.212944 0.977064i \(-0.431695\pi\)
0.432530 + 0.901619i \(0.357621\pi\)
\(24\) 0 0
\(25\) 0.266422 + 4.57429i 0.0532845 + 0.914859i
\(26\) 5.80229 + 10.0499i 1.13792 + 1.97094i
\(27\) 0 0
\(28\) 2.50083 4.33156i 0.472612 0.818588i
\(29\) −5.26023 2.64179i −0.976800 0.490568i −0.112559 0.993645i \(-0.535905\pi\)
−0.864241 + 0.503077i \(0.832201\pi\)
\(30\) 0 0
\(31\) −1.65611 2.22454i −0.297446 0.399540i 0.628125 0.778112i \(-0.283822\pi\)
−0.925572 + 0.378572i \(0.876415\pi\)
\(32\) −7.32759 1.73667i −1.29535 0.307003i
\(33\) 0 0
\(34\) 8.89668 11.9503i 1.52577 2.04946i
\(35\) −0.905967 + 0.760197i −0.153136 + 0.128497i
\(36\) 0 0
\(37\) −1.09453 0.918418i −0.179939 0.150987i 0.548369 0.836236i \(-0.315249\pi\)
−0.728309 + 0.685249i \(0.759693\pi\)
\(38\) 13.4691 3.19224i 2.18498 0.517850i
\(39\) 0 0
\(40\) −0.862777 0.567457i −0.136417 0.0897229i
\(41\) −0.931903 0.612922i −0.145539 0.0957224i 0.474651 0.880174i \(-0.342574\pi\)
−0.620190 + 0.784452i \(0.712945\pi\)
\(42\) 0 0
\(43\) −9.37473 + 2.22185i −1.42963 + 0.338829i −0.871285 0.490777i \(-0.836713\pi\)
−0.558348 + 0.829607i \(0.688565\pi\)
\(44\) −2.53397 2.12625i −0.382010 0.320545i
\(45\) 0 0
\(46\) −5.19473 + 4.35890i −0.765922 + 0.642685i
\(47\) 3.64407 4.89483i 0.531542 0.713984i −0.452532 0.891748i \(-0.649479\pi\)
0.984073 + 0.177764i \(0.0568864\pi\)
\(48\) 0 0
\(49\) −3.55504 0.842559i −0.507862 0.120366i
\(50\) −5.95346 7.99688i −0.841946 1.13093i
\(51\) 0 0
\(52\) −13.0313 6.54456i −1.80711 0.907567i
\(53\) 4.26135 7.38088i 0.585342 1.01384i −0.409491 0.912314i \(-0.634294\pi\)
0.994833 0.101528i \(-0.0323731\pi\)
\(54\) 0 0
\(55\) 0.391077 + 0.677365i 0.0527328 + 0.0913359i
\(56\) 0.169902 + 2.91711i 0.0227042 + 0.389815i
\(57\) 0 0
\(58\) 12.7209 1.48687i 1.67034 0.195235i
\(59\) −0.598878 2.00039i −0.0779672 0.260429i 0.910115 0.414356i \(-0.135993\pi\)
−0.988082 + 0.153927i \(0.950808\pi\)
\(60\) 0 0
\(61\) −1.42194 3.29643i −0.182061 0.422065i 0.802606 0.596510i \(-0.203446\pi\)
−0.984667 + 0.174445i \(0.944187\pi\)
\(62\) 5.67029 + 2.06382i 0.720128 + 0.262105i
\(63\) 0 0
\(64\) 11.6517 4.24088i 1.45646 0.530110i
\(65\) 2.36619 + 2.50802i 0.293490 + 0.311082i
\(66\) 0 0
\(67\) 1.09003 0.547434i 0.133168 0.0668796i −0.380967 0.924588i \(-0.624409\pi\)
0.514136 + 0.857709i \(0.328113\pi\)
\(68\) −1.08855 + 18.6897i −0.132006 + 2.26646i
\(69\) 0 0
\(70\) 0.738011 2.46513i 0.0882092 0.294639i
\(71\) 1.41528 8.02646i 0.167963 0.952565i −0.777994 0.628272i \(-0.783763\pi\)
0.945957 0.324293i \(-0.105126\pi\)
\(72\) 0 0
\(73\) 1.11524 + 6.32482i 0.130529 + 0.740264i 0.977870 + 0.209215i \(0.0670909\pi\)
−0.847341 + 0.531049i \(0.821798\pi\)
\(74\) 3.08778 + 0.360910i 0.358947 + 0.0419549i
\(75\) 0 0
\(76\) −11.9367 + 12.6521i −1.36923 + 1.45130i
\(77\) 0.876607 2.03220i 0.0998986 0.231591i
\(78\) 0 0
\(79\) 11.9127 7.83511i 1.34028 0.881518i 0.341978 0.939708i \(-0.388903\pi\)
0.998306 + 0.0581898i \(0.0185329\pi\)
\(80\) −1.28832 −0.144039
\(81\) 0 0
\(82\) 2.42689 0.268006
\(83\) −5.61402 + 3.69240i −0.616219 + 0.405294i −0.818888 0.573954i \(-0.805409\pi\)
0.202669 + 0.979247i \(0.435039\pi\)
\(84\) 0 0
\(85\) 1.75334 4.06469i 0.190176 0.440878i
\(86\) 14.3854 15.2477i 1.55122 1.64420i
\(87\) 0 0
\(88\) 1.91944 + 0.224351i 0.204613 + 0.0239159i
\(89\) −2.70557 15.3441i −0.286790 1.62647i −0.698820 0.715297i \(-0.746291\pi\)
0.412030 0.911170i \(-0.364820\pi\)
\(90\) 0 0
\(91\) 1.69423 9.60848i 0.177604 1.00724i
\(92\) 2.44395 8.16337i 0.254800 0.851090i
\(93\) 0 0
\(94\) −0.772019 + 13.2550i −0.0796276 + 1.36715i
\(95\) 3.67544 1.84588i 0.377093 0.189383i
\(96\) 0 0
\(97\) 2.55920 + 2.71259i 0.259847 + 0.275422i 0.844142 0.536120i \(-0.180110\pi\)
−0.584295 + 0.811541i \(0.698629\pi\)
\(98\) 7.46994 2.71884i 0.754578 0.274644i
\(99\) 0 0
\(100\) 11.7724 + 4.28480i 1.17724 + 0.428480i
\(101\) −1.84200 4.27024i −0.183286 0.424904i 0.801657 0.597784i \(-0.203952\pi\)
−0.984943 + 0.172880i \(0.944693\pi\)
\(102\) 0 0
\(103\) −1.48234 4.95138i −0.146060 0.487874i 0.853382 0.521286i \(-0.174548\pi\)
−0.999442 + 0.0334127i \(0.989362\pi\)
\(104\) 8.46168 0.989028i 0.829736 0.0969822i
\(105\) 0 0
\(106\) 1.07822 + 18.5124i 0.104726 + 1.79808i
\(107\) 6.49528 + 11.2502i 0.627922 + 1.08759i 0.987968 + 0.154659i \(0.0494278\pi\)
−0.360046 + 0.932935i \(0.617239\pi\)
\(108\) 0 0
\(109\) −0.888686 + 1.53925i −0.0851207 + 0.147433i −0.905443 0.424469i \(-0.860461\pi\)
0.820322 + 0.571902i \(0.193794\pi\)
\(110\) −1.52080 0.763773i −0.145002 0.0728229i
\(111\) 0 0
\(112\) 2.17693 + 2.92413i 0.205701 + 0.276304i
\(113\) 13.5138 + 3.20282i 1.27127 + 0.301296i 0.810244 0.586092i \(-0.199334\pi\)
0.461023 + 0.887388i \(0.347483\pi\)
\(114\) 0 0
\(115\) −1.20321 + 1.61620i −0.112200 + 0.150711i
\(116\) −12.3288 + 10.3451i −1.14470 + 0.960514i
\(117\) 0 0
\(118\) 3.48039 + 2.92040i 0.320396 + 0.268844i
\(119\) −12.1884 + 2.88869i −1.11731 + 0.264806i
\(120\) 0 0
\(121\) 7.96745 + 5.24027i 0.724314 + 0.476389i
\(122\) 6.52619 + 4.29234i 0.590853 + 0.388610i
\(123\) 0 0
\(124\) −7.37823 + 1.74867i −0.662584 + 0.157035i
\(125\) −4.74544 3.98190i −0.424445 0.356152i
\(126\) 0 0
\(127\) −8.72949 + 7.32491i −0.774617 + 0.649981i −0.941887 0.335930i \(-0.890949\pi\)
0.167270 + 0.985911i \(0.446505\pi\)
\(128\) −7.11678 + 9.55950i −0.629041 + 0.844948i
\(129\) 0 0
\(130\) −7.30006 1.73015i −0.640258 0.151744i
\(131\) −8.70702 11.6956i −0.760736 1.02185i −0.998720 0.0505763i \(-0.983894\pi\)
0.237985 0.971269i \(-0.423513\pi\)
\(132\) 0 0
\(133\) −10.4002 5.22315i −0.901808 0.452905i
\(134\) −1.32700 + 2.29842i −0.114635 + 0.198554i
\(135\) 0 0
\(136\) −5.46868 9.47202i −0.468935 0.812219i
\(137\) 0.0215606 + 0.370181i 0.00184204 + 0.0316267i 0.999104 0.0423242i \(-0.0134762\pi\)
−0.997262 + 0.0739509i \(0.976439\pi\)
\(138\) 0 0
\(139\) −14.8762 + 1.73878i −1.26179 + 0.147482i −0.720559 0.693394i \(-0.756115\pi\)
−0.541228 + 0.840876i \(0.682040\pi\)
\(140\) 0.927389 + 3.09770i 0.0783787 + 0.261803i
\(141\) 0 0
\(142\) 7.02385 + 16.2831i 0.589428 + 1.36645i
\(143\) −6.06349 2.20693i −0.507055 0.184553i
\(144\) 0 0
\(145\) 3.57599 1.30155i 0.296970 0.108088i
\(146\) −9.58945 10.1642i −0.793629 0.841197i
\(147\) 0 0
\(148\) −3.49101 + 1.75325i −0.286960 + 0.144116i
\(149\) 0.0581597 0.998563i 0.00476463 0.0818055i −0.995088 0.0989987i \(-0.968436\pi\)
0.999852 + 0.0171933i \(0.00547306\pi\)
\(150\) 0 0
\(151\) −0.00563064 + 0.0188076i −0.000458215 + 0.00153054i −0.958218 0.286038i \(-0.907662\pi\)
0.957760 + 0.287568i \(0.0928469\pi\)
\(152\) 1.76462 10.0076i 0.143129 0.811727i
\(153\) 0 0
\(154\) 0.836205 + 4.74235i 0.0673833 + 0.382150i
\(155\) 1.78081 + 0.208147i 0.143038 + 0.0167188i
\(156\) 0 0
\(157\) 5.35582 5.67684i 0.427441 0.453061i −0.477479 0.878643i \(-0.658449\pi\)
0.904920 + 0.425582i \(0.139931\pi\)
\(158\) −12.2878 + 28.4862i −0.977562 + 2.26624i
\(159\) 0 0
\(160\) 4.06755 2.67527i 0.321568 0.211498i
\(161\) 5.70142 0.449335
\(162\) 0 0
\(163\) −15.3947 −1.20581 −0.602905 0.797813i \(-0.705990\pi\)
−0.602905 + 0.797813i \(0.705990\pi\)
\(164\) −2.54795 + 1.67581i −0.198961 + 0.130859i
\(165\) 0 0
\(166\) 5.79078 13.4245i 0.449452 1.04195i
\(167\) −2.50809 + 2.65842i −0.194082 + 0.205714i −0.817105 0.576489i \(-0.804423\pi\)
0.623024 + 0.782203i \(0.285904\pi\)
\(168\) 0 0
\(169\) −15.3414 1.79315i −1.18010 0.137934i
\(170\) 1.67253 + 9.48537i 0.128277 + 0.727494i
\(171\) 0 0
\(172\) −4.57421 + 25.9416i −0.348780 + 1.97803i
\(173\) −3.80949 + 12.7246i −0.289630 + 0.967432i 0.682085 + 0.731273i \(0.261074\pi\)
−0.971715 + 0.236158i \(0.924112\pi\)
\(174\) 0 0
\(175\) −0.487377 + 8.36794i −0.0368422 + 0.632556i
\(176\) 2.15451 1.08203i 0.162402 0.0815614i
\(177\) 0 0
\(178\) 23.2641 + 24.6585i 1.74372 + 1.84823i
\(179\) −0.392738 + 0.142945i −0.0293546 + 0.0106842i −0.356656 0.934236i \(-0.616083\pi\)
0.327301 + 0.944920i \(0.393861\pi\)
\(180\) 0 0
\(181\) −19.5881 7.12947i −1.45597 0.529929i −0.511717 0.859154i \(-0.670990\pi\)
−0.944252 + 0.329225i \(0.893213\pi\)
\(182\) 8.40826 + 19.4925i 0.623262 + 1.44488i
\(183\) 0 0
\(184\) 1.42780 + 4.76918i 0.105259 + 0.351589i
\(185\) 0.917468 0.107237i 0.0674536 0.00788419i
\(186\) 0 0
\(187\) 0.481679 + 8.27010i 0.0352238 + 0.604770i
\(188\) −8.34230 14.4493i −0.608425 1.05382i
\(189\) 0 0
\(190\) −4.47446 + 7.75000i −0.324612 + 0.562244i
\(191\) 6.15645 + 3.09189i 0.445465 + 0.223721i 0.657368 0.753570i \(-0.271670\pi\)
−0.211903 + 0.977291i \(0.567966\pi\)
\(192\) 0 0
\(193\) −5.22298 7.01568i −0.375958 0.505000i 0.573365 0.819300i \(-0.305638\pi\)
−0.949324 + 0.314300i \(0.898230\pi\)
\(194\) −7.89550 1.87127i −0.566864 0.134349i
\(195\) 0 0
\(196\) −5.96514 + 8.01257i −0.426081 + 0.572326i
\(197\) −6.47094 + 5.42976i −0.461035 + 0.386855i −0.843512 0.537111i \(-0.819516\pi\)
0.382476 + 0.923965i \(0.375071\pi\)
\(198\) 0 0
\(199\) 9.66790 + 8.11233i 0.685339 + 0.575068i 0.917561 0.397595i \(-0.130155\pi\)
−0.232222 + 0.972663i \(0.574599\pi\)
\(200\) −7.12174 + 1.68788i −0.503583 + 0.119351i
\(201\) 0 0
\(202\) 8.45410 + 5.56035i 0.594828 + 0.391225i
\(203\) −8.99664 5.91718i −0.631440 0.415305i
\(204\) 0 0
\(205\) 0.701662 0.166297i 0.0490062 0.0116147i
\(206\) 8.61468 + 7.22858i 0.600213 + 0.503639i
\(207\) 0 0
\(208\) 8.14187 6.83184i 0.564537 0.473703i
\(209\) −4.59626 + 6.17384i −0.317930 + 0.427054i
\(210\) 0 0
\(211\) −5.52292 1.30896i −0.380213 0.0901122i 0.0360651 0.999349i \(-0.488518\pi\)
−0.416278 + 0.909237i \(0.636666\pi\)
\(212\) −13.9151 18.6912i −0.955694 1.28372i
\(213\) 0 0
\(214\) −25.2585 12.6853i −1.72663 0.867148i
\(215\) 3.11430 5.39413i 0.212393 0.367876i
\(216\) 0 0
\(217\) −2.53667 4.39364i −0.172200 0.298260i
\(218\) −0.224859 3.86067i −0.0152294 0.261478i
\(219\) 0 0
\(220\) 2.12405 0.248266i 0.143204 0.0167381i
\(221\) 10.4740 + 34.9855i 0.704555 + 2.35338i
\(222\) 0 0
\(223\) 2.98361 + 6.91679i 0.199797 + 0.463183i 0.988429 0.151683i \(-0.0484694\pi\)
−0.788632 + 0.614866i \(0.789210\pi\)
\(224\) −12.9452 4.71166i −0.864936 0.314811i
\(225\) 0 0
\(226\) −28.3955 + 10.3351i −1.88884 + 0.687481i
\(227\) 9.36249 + 9.92366i 0.621410 + 0.658656i 0.959254 0.282546i \(-0.0911789\pi\)
−0.337843 + 0.941202i \(0.609697\pi\)
\(228\) 0 0
\(229\) 14.2932 7.17833i 0.944523 0.474357i 0.0912534 0.995828i \(-0.470913\pi\)
0.853269 + 0.521471i \(0.174616\pi\)
\(230\) 0.254909 4.37661i 0.0168082 0.288585i
\(231\) 0 0
\(232\) 2.69665 9.00742i 0.177043 0.591366i
\(233\) −0.930605 + 5.27772i −0.0609660 + 0.345755i 0.939032 + 0.343829i \(0.111724\pi\)
−0.999998 + 0.00192589i \(0.999387\pi\)
\(234\) 0 0
\(235\) 0.685064 + 3.88519i 0.0446886 + 0.253442i
\(236\) −5.67057 0.662795i −0.369123 0.0431443i
\(237\) 0 0
\(238\) 18.7029 19.8239i 1.21233 1.28500i
\(239\) −6.39415 + 14.8233i −0.413603 + 0.958840i 0.576319 + 0.817225i \(0.304489\pi\)
−0.989922 + 0.141615i \(0.954771\pi\)
\(240\) 0 0
\(241\) 19.5404 12.8519i 1.25871 0.827864i 0.267938 0.963436i \(-0.413658\pi\)
0.990767 + 0.135572i \(0.0432873\pi\)
\(242\) −20.7491 −1.33380
\(243\) 0 0
\(244\) −9.81564 −0.628382
\(245\) 1.97340 1.29793i 0.126076 0.0829215i
\(246\) 0 0
\(247\) −13.4394 + 31.1559i −0.855125 + 1.98240i
\(248\) 3.03998 3.22219i 0.193039 0.204609i
\(249\) 0 0
\(250\) 13.3874 + 1.56476i 0.846693 + 0.0989643i
\(251\) 4.21745 + 23.9183i 0.266203 + 1.50971i 0.765588 + 0.643331i \(0.222448\pi\)
−0.499385 + 0.866380i \(0.666441\pi\)
\(252\) 0 0
\(253\) 0.654768 3.71337i 0.0411649 0.233458i
\(254\) 7.11114 23.7529i 0.446193 1.49039i
\(255\) 0 0
\(256\) 0.0658029 1.12979i 0.00411268 0.0706120i
\(257\) 8.60919 4.32370i 0.537027 0.269705i −0.159547 0.987190i \(-0.551003\pi\)
0.696573 + 0.717485i \(0.254707\pi\)
\(258\) 0 0
\(259\) −1.79368 1.90119i −0.111454 0.118134i
\(260\) 8.85887 3.22437i 0.549404 0.199967i
\(261\) 0 0
\(262\) 29.8116 + 10.8505i 1.84177 + 0.670349i
\(263\) 2.63068 + 6.09861i 0.162215 + 0.376056i 0.979866 0.199658i \(-0.0639832\pi\)
−0.817651 + 0.575715i \(0.804724\pi\)
\(264\) 0 0
\(265\) 1.58025 + 5.27841i 0.0970740 + 0.324250i
\(266\) 25.1510 2.93972i 1.54210 0.180246i
\(267\) 0 0
\(268\) −0.193914 3.32938i −0.0118452 0.203374i
\(269\) −14.6832 25.4321i −0.895251 1.55062i −0.833494 0.552529i \(-0.813663\pi\)
−0.0617568 0.998091i \(-0.519670\pi\)
\(270\) 0 0
\(271\) 9.43957 16.3498i 0.573413 0.993180i −0.422799 0.906223i \(-0.638952\pi\)
0.996212 0.0869568i \(-0.0277142\pi\)
\(272\) −12.1938 6.12395i −0.739356 0.371319i
\(273\) 0 0
\(274\) −0.481791 0.647158i −0.0291061 0.0390963i
\(275\) 5.39412 + 1.27843i 0.325277 + 0.0770922i
\(276\) 0 0
\(277\) 8.38334 11.2608i 0.503706 0.676594i −0.475441 0.879748i \(-0.657712\pi\)
0.979147 + 0.203153i \(0.0651189\pi\)
\(278\) 24.9640 20.9473i 1.49724 1.25633i
\(279\) 0 0
\(280\) −1.44713 1.21428i −0.0864824 0.0725673i
\(281\) −21.4853 + 5.09210i −1.28170 + 0.303769i −0.814388 0.580321i \(-0.802927\pi\)
−0.467316 + 0.884091i \(0.654779\pi\)
\(282\) 0 0
\(283\) −3.30559 2.17412i −0.196497 0.129238i 0.447448 0.894310i \(-0.352333\pi\)
−0.643945 + 0.765072i \(0.722703\pi\)
\(284\) −18.6180 12.2452i −1.10477 0.726620i
\(285\) 0 0
\(286\) 13.6612 3.23777i 0.807806 0.191454i
\(287\) −1.56307 1.31157i −0.0922652 0.0774197i
\(288\) 0 0
\(289\) 22.8934 19.2099i 1.34667 1.12999i
\(290\) −4.94447 + 6.64158i −0.290349 + 0.390007i
\(291\) 0 0
\(292\) 17.0863 + 4.04954i 0.999902 + 0.236981i
\(293\) 4.76369 + 6.39875i 0.278298 + 0.373819i 0.919192 0.393811i \(-0.128843\pi\)
−0.640894 + 0.767630i \(0.721436\pi\)
\(294\) 0 0
\(295\) 1.20636 + 0.605857i 0.0702371 + 0.0352744i
\(296\) 1.14114 1.97650i 0.0663271 0.114882i
\(297\) 0 0
\(298\) 1.08818 + 1.88478i 0.0630366 + 0.109183i
\(299\) −0.966516 16.5944i −0.0558951 0.959682i
\(300\) 0 0
\(301\) −17.5055 + 2.04610i −1.00900 + 0.117935i
\(302\) −0.0122512 0.0409218i −0.000704976 0.00235478i
\(303\) 0 0
\(304\) −5.02146 11.6411i −0.288001 0.667661i
\(305\) 2.18097 + 0.793808i 0.124882 + 0.0454533i
\(306\) 0 0
\(307\) 1.95823 0.712736i 0.111762 0.0406780i −0.285534 0.958369i \(-0.592171\pi\)
0.397296 + 0.917691i \(0.369949\pi\)
\(308\) −4.15259 4.40149i −0.236616 0.250798i
\(309\) 0 0
\(310\) −3.48613 + 1.75080i −0.197999 + 0.0994387i
\(311\) 0.873011 14.9890i 0.0495039 0.849949i −0.878584 0.477588i \(-0.841511\pi\)
0.928088 0.372361i \(-0.121452\pi\)
\(312\) 0 0
\(313\) −1.46009 + 4.87703i −0.0825290 + 0.275666i −0.989287 0.145986i \(-0.953364\pi\)
0.906758 + 0.421652i \(0.138550\pi\)
\(314\) −2.94876 + 16.7232i −0.166408 + 0.943747i
\(315\) 0 0
\(316\) −6.76955 38.3920i −0.380817 2.15972i
\(317\) 27.5207 + 3.21671i 1.54572 + 0.180669i 0.845779 0.533533i \(-0.179136\pi\)
0.699940 + 0.714202i \(0.253210\pi\)
\(318\) 0 0
\(319\) −4.88710 + 5.18002i −0.273625 + 0.290025i
\(320\) −3.17505 + 7.36060i −0.177491 + 0.411470i
\(321\) 0 0
\(322\) −10.3644 + 6.81676i −0.577585 + 0.379883i
\(323\) 43.5617 2.42384
\(324\) 0 0
\(325\) 24.4382 1.35559
\(326\) 27.9855 18.4063i 1.54997 1.01943i
\(327\) 0 0
\(328\) 0.705679 1.63595i 0.0389646 0.0903301i
\(329\) 7.66069 8.11986i 0.422347 0.447662i
\(330\) 0 0
\(331\) −27.0847 3.16575i −1.48871 0.174005i −0.667492 0.744617i \(-0.732632\pi\)
−0.821220 + 0.570612i \(0.806706\pi\)
\(332\) 3.19024 + 18.0928i 0.175087 + 0.992969i
\(333\) 0 0
\(334\) 1.38088 7.83136i 0.0755584 0.428513i
\(335\) −0.226166 + 0.755448i −0.0123568 + 0.0412745i
\(336\) 0 0
\(337\) 0.739519 12.6970i 0.0402842 0.691652i −0.916353 0.400371i \(-0.868881\pi\)
0.956637 0.291281i \(-0.0940816\pi\)
\(338\) 30.0324 15.0828i 1.63355 0.820397i
\(339\) 0 0
\(340\) −8.30575 8.80358i −0.450443 0.477441i
\(341\) −3.15292 + 1.14757i −0.170740 + 0.0621444i
\(342\) 0 0
\(343\) −18.3136 6.66560i −0.988840 0.359908i
\(344\) −6.09541 14.1307i −0.328642 0.761879i
\(345\) 0 0
\(346\) −8.28871 27.6862i −0.445604 1.48842i
\(347\) −8.35624 + 0.976704i −0.448586 + 0.0524322i −0.337387 0.941366i \(-0.609543\pi\)
−0.111199 + 0.993798i \(0.535469\pi\)
\(348\) 0 0
\(349\) −1.75267 30.0922i −0.0938184 1.61080i −0.636783 0.771043i \(-0.719735\pi\)
0.542964 0.839756i \(-0.317302\pi\)
\(350\) −9.11893 15.7944i −0.487427 0.844249i
\(351\) 0 0
\(352\) −4.55540 + 7.89018i −0.242803 + 0.420548i
\(353\) 20.7603 + 10.4262i 1.10496 + 0.554932i 0.905231 0.424919i \(-0.139698\pi\)
0.199729 + 0.979851i \(0.435994\pi\)
\(354\) 0 0
\(355\) 3.14649 + 4.22647i 0.166998 + 0.224318i
\(356\) −41.4516 9.82421i −2.19693 0.520682i
\(357\) 0 0
\(358\) 0.543034 0.729421i 0.0287002 0.0385511i
\(359\) 3.19290 2.67916i 0.168515 0.141401i −0.554630 0.832097i \(-0.687140\pi\)
0.723145 + 0.690696i \(0.242696\pi\)
\(360\) 0 0
\(361\) 16.4498 + 13.8030i 0.865780 + 0.726476i
\(362\) 44.1325 10.4596i 2.31955 0.549744i
\(363\) 0 0
\(364\) −22.2876 14.6588i −1.16819 0.768328i
\(365\) −3.46897 2.28158i −0.181574 0.119423i
\(366\) 0 0
\(367\) −11.4051 + 2.70306i −0.595341 + 0.141098i −0.517230 0.855846i \(-0.673037\pi\)
−0.0781107 + 0.996945i \(0.524889\pi\)
\(368\) 4.75778 + 3.99225i 0.248016 + 0.208110i
\(369\) 0 0
\(370\) −1.53961 + 1.29189i −0.0800407 + 0.0671621i
\(371\) 9.31026 12.5058i 0.483364 0.649271i
\(372\) 0 0
\(373\) 35.3913 + 8.38790i 1.83249 + 0.434309i 0.993885 0.110423i \(-0.0352207\pi\)
0.838610 + 0.544733i \(0.183369\pi\)
\(374\) −10.7636 14.4580i −0.556571 0.747604i
\(375\) 0 0
\(376\) 8.71063 + 4.37464i 0.449216 + 0.225605i
\(377\) −15.6973 + 27.1885i −0.808452 + 1.40028i
\(378\) 0 0
\(379\) 5.02516 + 8.70383i 0.258125 + 0.447086i 0.965740 0.259513i \(-0.0835620\pi\)
−0.707615 + 0.706599i \(0.750229\pi\)
\(380\) −0.653855 11.2263i −0.0335420 0.575895i
\(381\) 0 0
\(382\) −14.8883 + 1.74019i −0.761751 + 0.0890360i
\(383\) 0.0867894 + 0.289897i 0.00443473 + 0.0148130i 0.960178 0.279388i \(-0.0901316\pi\)
−0.955744 + 0.294201i \(0.904946\pi\)
\(384\) 0 0
\(385\) 0.566721 + 1.31381i 0.0288828 + 0.0669578i
\(386\) 17.8828 + 6.50880i 0.910209 + 0.331289i
\(387\) 0 0
\(388\) 9.58146 3.48737i 0.486425 0.177044i
\(389\) −5.16022 5.46952i −0.261634 0.277315i 0.583218 0.812315i \(-0.301793\pi\)
−0.844852 + 0.535000i \(0.820312\pi\)
\(390\) 0 0
\(391\) −19.0707 + 9.57766i −0.964446 + 0.484363i
\(392\) 0.339325 5.82599i 0.0171385 0.294257i
\(393\) 0 0
\(394\) 5.27130 17.6074i 0.265564 0.887046i
\(395\) −1.60068 + 9.07791i −0.0805390 + 0.456759i
\(396\) 0 0
\(397\) 2.95983 + 16.7860i 0.148549 + 0.842466i 0.964448 + 0.264271i \(0.0851314\pi\)
−0.815899 + 0.578195i \(0.803757\pi\)
\(398\) −27.2742 3.18790i −1.36713 0.159795i
\(399\) 0 0
\(400\) −6.26610 + 6.64168i −0.313305 + 0.332084i
\(401\) 5.37775 12.4670i 0.268552 0.622574i −0.729565 0.683911i \(-0.760277\pi\)
0.998117 + 0.0613379i \(0.0195367\pi\)
\(402\) 0 0
\(403\) −12.3580 + 8.12800i −0.615597 + 0.404884i
\(404\) −12.7153 −0.632609
\(405\) 0 0
\(406\) 23.4293 1.16278
\(407\) −1.44425 + 0.949896i −0.0715886 + 0.0470846i
\(408\) 0 0
\(409\) −0.266304 + 0.617363i −0.0131679 + 0.0305266i −0.924673 0.380762i \(-0.875662\pi\)
0.911505 + 0.411288i \(0.134921\pi\)
\(410\) −1.07669 + 1.14123i −0.0531741 + 0.0563613i
\(411\) 0 0
\(412\) −14.0358 1.64055i −0.691496 0.0808242i
\(413\) −0.663313 3.76184i −0.0326395 0.185108i
\(414\) 0 0
\(415\) 0.754343 4.27809i 0.0370292 0.210003i
\(416\) −11.5192 + 38.4767i −0.564774 + 1.88648i
\(417\) 0 0
\(418\) 0.973746 16.7186i 0.0476275 0.817733i
\(419\) −17.7708 + 8.92485i −0.868163 + 0.436008i −0.826376 0.563119i \(-0.809601\pi\)
−0.0417867 + 0.999127i \(0.513305\pi\)
\(420\) 0 0
\(421\) −8.61615 9.13258i −0.419925 0.445095i 0.482529 0.875880i \(-0.339718\pi\)
−0.902455 + 0.430785i \(0.858237\pi\)
\(422\) 11.6049 4.22384i 0.564918 0.205613i
\(423\) 0 0
\(424\) 12.7926 + 4.65611i 0.621262 + 0.226121i
\(425\) −12.4268 28.8086i −0.602790 1.39742i
\(426\) 0 0
\(427\) −1.88355 6.29150i −0.0911515 0.304467i
\(428\) 35.2777 4.12338i 1.70521 0.199311i
\(429\) 0 0
\(430\) 0.787992 + 13.5293i 0.0380003 + 0.652441i
\(431\) 10.8013 + 18.7084i 0.520281 + 0.901153i 0.999722 + 0.0235787i \(0.00750603\pi\)
−0.479441 + 0.877574i \(0.659161\pi\)
\(432\) 0 0
\(433\) −1.99970 + 3.46358i −0.0960993 + 0.166449i −0.910067 0.414461i \(-0.863970\pi\)
0.813968 + 0.580910i \(0.197303\pi\)
\(434\) 9.86445 + 4.95412i 0.473509 + 0.237805i
\(435\) 0 0
\(436\) 2.90193 + 3.89797i 0.138977 + 0.186679i
\(437\) −19.2934 4.57262i −0.922928 0.218738i
\(438\) 0 0
\(439\) −18.6380 + 25.0352i −0.889544 + 1.19486i 0.0904630 + 0.995900i \(0.471165\pi\)
−0.980007 + 0.198965i \(0.936242\pi\)
\(440\) −0.957063 + 0.803071i −0.0456262 + 0.0382849i
\(441\) 0 0
\(442\) −60.8697 51.0758i −2.89528 2.42943i
\(443\) 1.55899 0.369487i 0.0740699 0.0175549i −0.193414 0.981117i \(-0.561956\pi\)
0.267484 + 0.963562i \(0.413808\pi\)
\(444\) 0 0
\(445\) 8.41576 + 5.53513i 0.398945 + 0.262390i
\(446\) −13.6937 9.00647i −0.648414 0.426469i
\(447\) 0 0
\(448\) 22.0715 5.23103i 1.04278 0.247143i
\(449\) 8.04720 + 6.75241i 0.379771 + 0.318666i 0.812613 0.582804i \(-0.198045\pi\)
−0.432841 + 0.901470i \(0.642489\pi\)
\(450\) 0 0
\(451\) −1.03374 + 0.867414i −0.0486771 + 0.0408449i
\(452\) 22.6753 30.4582i 1.06655 1.43263i
\(453\) 0 0
\(454\) −28.8847 6.84579i −1.35562 0.321289i
\(455\) 3.76667 + 5.05951i 0.176584 + 0.237194i
\(456\) 0 0
\(457\) 36.7648 + 18.4640i 1.71979 + 0.863709i 0.982050 + 0.188620i \(0.0604014\pi\)
0.737736 + 0.675089i \(0.235895\pi\)
\(458\) −17.4005 + 30.1385i −0.813071 + 1.40828i
\(459\) 0 0
\(460\) 2.75450 + 4.77093i 0.128429 + 0.222446i
\(461\) 1.99431 + 34.2409i 0.0928841 + 1.59476i 0.647113 + 0.762394i \(0.275976\pi\)
−0.554229 + 0.832364i \(0.686987\pi\)
\(462\) 0 0
\(463\) 33.1075 3.86972i 1.53864 0.179841i 0.695890 0.718149i \(-0.255010\pi\)
0.842748 + 0.538308i \(0.180936\pi\)
\(464\) −3.36427 11.2374i −0.156182 0.521685i
\(465\) 0 0
\(466\) −4.61847 10.7068i −0.213946 0.495984i
\(467\) −9.76380 3.55373i −0.451815 0.164447i 0.106082 0.994357i \(-0.466169\pi\)
−0.557897 + 0.829910i \(0.688392\pi\)
\(468\) 0 0
\(469\) 2.09681 0.763177i 0.0968218 0.0352402i
\(470\) −5.89058 6.24365i −0.271712 0.287998i
\(471\) 0 0
\(472\) 2.98062 1.49693i 0.137194 0.0689016i
\(473\) −0.677743 + 11.6364i −0.0311627 + 0.535042i
\(474\) 0 0
\(475\) 8.36046 27.9259i 0.383604 1.28133i
\(476\) −5.94706 + 33.7274i −0.272583 + 1.54589i
\(477\) 0 0
\(478\) −6.09945 34.5917i −0.278982 1.58219i
\(479\) −20.1592 2.35628i −0.921100 0.107661i −0.357691 0.933840i \(-0.616436\pi\)
−0.563408 + 0.826179i \(0.690510\pi\)
\(480\) 0 0
\(481\) −5.22949 + 5.54293i −0.238444 + 0.252736i
\(482\) −20.1556 + 46.7259i −0.918062 + 2.12831i
\(483\) 0 0
\(484\) 21.7841 14.3276i 0.990184 0.651255i
\(485\) −2.41096 −0.109476
\(486\) 0 0
\(487\) −27.5716 −1.24939 −0.624694 0.780870i \(-0.714776\pi\)
−0.624694 + 0.780870i \(0.714776\pi\)
\(488\) 4.79108 3.15114i 0.216882 0.142646i
\(489\) 0 0
\(490\) −2.03553 + 4.71890i −0.0919561 + 0.213178i
\(491\) −7.01152 + 7.43178i −0.316426 + 0.335391i −0.865991 0.500059i \(-0.833312\pi\)
0.549566 + 0.835450i \(0.314793\pi\)
\(492\) 0 0
\(493\) 40.0329 + 4.67918i 1.80299 + 0.210740i
\(494\) −12.8199 72.7055i −0.576796 3.27117i
\(495\) 0 0
\(496\) 0.959690 5.44267i 0.0430914 0.244383i
\(497\) 4.27613 14.2833i 0.191811 0.640692i
\(498\) 0 0
\(499\) 0.508397 8.72884i 0.0227590 0.390756i −0.967623 0.252399i \(-0.918781\pi\)
0.990382 0.138358i \(-0.0441824\pi\)
\(500\) −15.1356 + 7.60141i −0.676887 + 0.339945i
\(501\) 0 0
\(502\) −36.2641 38.4377i −1.61854 1.71556i
\(503\) −12.2947 + 4.47489i −0.548192 + 0.199526i −0.601243 0.799066i \(-0.705328\pi\)
0.0530509 + 0.998592i \(0.483105\pi\)
\(504\) 0 0
\(505\) 2.82525 + 1.02831i 0.125722 + 0.0457591i
\(506\) 3.24953 + 7.53325i 0.144459 + 0.334894i
\(507\) 0 0
\(508\) 8.93590 + 29.8480i 0.396467 + 1.32429i
\(509\) 30.2154 3.53167i 1.33927 0.156538i 0.583895 0.811829i \(-0.301528\pi\)
0.755377 + 0.655291i \(0.227454\pi\)
\(510\) 0 0
\(511\) 0.683128 + 11.7289i 0.0302198 + 0.518854i
\(512\) −10.6866 18.5097i −0.472284 0.818019i
\(513\) 0 0
\(514\) −10.4808 + 18.1532i −0.462287 + 0.800705i
\(515\) 2.98599 + 1.49962i 0.131578 + 0.0660812i
\(516\) 0 0
\(517\) −4.40874 5.92196i −0.193896 0.260448i
\(518\) 5.53376 + 1.31153i 0.243139 + 0.0576251i
\(519\) 0 0
\(520\) −3.28895 + 4.41782i −0.144230 + 0.193734i
\(521\) 8.25925 6.93034i 0.361845 0.303624i −0.443681 0.896185i \(-0.646328\pi\)
0.805525 + 0.592561i \(0.201883\pi\)
\(522\) 0 0
\(523\) 9.44644 + 7.92650i 0.413064 + 0.346602i 0.825517 0.564377i \(-0.190884\pi\)
−0.412453 + 0.910979i \(0.635328\pi\)
\(524\) −38.7911 + 9.19366i −1.69460 + 0.401627i
\(525\) 0 0
\(526\) −12.0739 7.94111i −0.526446 0.346249i
\(527\) 15.8657 + 10.4350i 0.691119 + 0.454556i
\(528\) 0 0
\(529\) −12.9283 + 3.06406i −0.562100 + 0.133220i
\(530\) −9.18367 7.70601i −0.398913 0.334728i
\(531\) 0 0
\(532\) −24.3755 + 20.4535i −1.05681 + 0.886772i
\(533\) −3.55246 + 4.77178i −0.153874 + 0.206689i
\(534\) 0 0
\(535\) −8.17194 1.93678i −0.353304 0.0837345i
\(536\) 1.16349 + 1.56284i 0.0502552 + 0.0675044i
\(537\) 0 0
\(538\) 57.0992 + 28.6763i 2.46172 + 1.23632i
\(539\) −2.21009 + 3.82798i −0.0951952 + 0.164883i
\(540\) 0 0
\(541\) 7.99279 + 13.8439i 0.343637 + 0.595196i 0.985105 0.171953i \(-0.0550078\pi\)
−0.641468 + 0.767149i \(0.721674\pi\)
\(542\) 2.38843 + 41.0078i 0.102592 + 1.76144i
\(543\) 0 0
\(544\) 51.2153 5.98621i 2.19584 0.256657i
\(545\) −0.329554 1.10079i −0.0141165 0.0471525i
\(546\) 0 0
\(547\) 0.489796 + 1.13547i 0.0209422 + 0.0485494i 0.928366 0.371667i \(-0.121214\pi\)
−0.907424 + 0.420216i \(0.861954\pi\)
\(548\) 0.952696 + 0.346753i 0.0406972 + 0.0148126i
\(549\) 0 0
\(550\) −11.3343 + 4.12534i −0.483295 + 0.175905i
\(551\) 25.6986 + 27.2389i 1.09480 + 1.16042i
\(552\) 0 0
\(553\) 23.3090 11.7062i 0.991199 0.497799i
\(554\) −1.77606 + 30.4938i −0.0754577 + 1.29556i
\(555\) 0 0
\(556\) −11.7447 + 39.2302i −0.498088 + 1.66373i
\(557\) 2.28246 12.9445i 0.0967109 0.548475i −0.897499 0.441017i \(-0.854618\pi\)
0.994210 0.107458i \(-0.0342710\pi\)
\(558\) 0 0
\(559\) 8.92289 + 50.6042i 0.377398 + 2.14033i
\(560\) −2.34085 0.273606i −0.0989189 0.0115620i
\(561\) 0 0
\(562\) 32.9689 34.9450i 1.39071 1.47407i
\(563\) 2.41169 5.59094i 0.101641 0.235630i −0.859806 0.510621i \(-0.829416\pi\)
0.961447 + 0.274991i \(0.0886749\pi\)
\(564\) 0 0
\(565\) −7.50149 + 4.93381i −0.315590 + 0.207567i
\(566\) 8.60852 0.361843
\(567\) 0 0
\(568\) 13.0187 0.546251
\(569\) −13.8505 + 9.10960i −0.580642 + 0.381894i −0.805587 0.592477i \(-0.798150\pi\)
0.224945 + 0.974371i \(0.427780\pi\)
\(570\) 0 0
\(571\) 13.8023 31.9973i 0.577608 1.33905i −0.339574 0.940579i \(-0.610283\pi\)
0.917182 0.398468i \(-0.130458\pi\)
\(572\) −12.1069 + 12.8326i −0.506216 + 0.536557i
\(573\) 0 0
\(574\) 4.40959 + 0.515408i 0.184053 + 0.0215127i
\(575\) 2.47981 + 14.0637i 0.103415 + 0.586497i
\(576\) 0 0
\(577\) 5.38675 30.5498i 0.224254 1.27180i −0.639854 0.768497i \(-0.721005\pi\)
0.864107 0.503308i \(-0.167884\pi\)
\(578\) −18.6492 + 62.2928i −0.775706 + 2.59104i
\(579\) 0 0
\(580\) 0.604979 10.3871i 0.0251204 0.431301i
\(581\) −10.9847 + 5.51671i −0.455721 + 0.228872i
\(582\) 0 0
\(583\) −7.07592 7.50004i −0.293055 0.310620i
\(584\) −9.63999 + 3.50867i −0.398906 + 0.145190i
\(585\) 0 0
\(586\) −16.3102 5.93644i −0.673769 0.245232i
\(587\) −17.6431 40.9013i −0.728209 1.68818i −0.725538 0.688182i \(-0.758409\pi\)
−0.00267106 0.999996i \(-0.500850\pi\)
\(588\) 0 0
\(589\) 5.06023 + 16.9023i 0.208503 + 0.696449i
\(590\) −2.91737 + 0.340992i −0.120106 + 0.0140384i
\(591\) 0 0
\(592\) −0.165556 2.84249i −0.00680432 0.116826i
\(593\) 9.90549 + 17.1568i 0.406770 + 0.704546i 0.994526 0.104493i \(-0.0333219\pi\)
−0.587756 + 0.809038i \(0.699989\pi\)
\(594\) 0 0
\(595\) 4.04899 7.01306i 0.165992 0.287507i
\(596\) −2.44393 1.22739i −0.100107 0.0502758i
\(597\) 0 0
\(598\) 21.5977 + 29.0108i 0.883197 + 1.18634i
\(599\) −27.1755 6.44071i −1.11036 0.263160i −0.365785 0.930699i \(-0.619200\pi\)
−0.744575 + 0.667539i \(0.767348\pi\)
\(600\) 0 0
\(601\) −6.05803 + 8.13735i −0.247112 + 0.331929i −0.908322 0.418272i \(-0.862636\pi\)
0.661210 + 0.750201i \(0.270043\pi\)
\(602\) 29.3761 24.6495i 1.19728 1.00464i
\(603\) 0 0
\(604\) 0.0411194 + 0.0345033i 0.00167313 + 0.00140392i
\(605\) −5.99897 + 1.42178i −0.243893 + 0.0578036i
\(606\) 0 0
\(607\) −9.03698 5.94371i −0.366800 0.241248i 0.352706 0.935734i \(-0.385261\pi\)
−0.719506 + 0.694486i \(0.755632\pi\)
\(608\) 40.0272 + 26.3263i 1.62332 + 1.06767i
\(609\) 0 0
\(610\) −4.91379 + 1.16459i −0.198954 + 0.0471529i
\(611\) −24.9321 20.9205i −1.00865 0.846355i
\(612\) 0 0
\(613\) 4.13859 3.47269i 0.167156 0.140261i −0.555372 0.831602i \(-0.687424\pi\)
0.722528 + 0.691341i \(0.242980\pi\)
\(614\) −2.70762 + 3.63696i −0.109270 + 0.146776i
\(615\) 0 0
\(616\) 3.43993 + 0.815278i 0.138599 + 0.0328485i
\(617\) −14.9530 20.0854i −0.601986 0.808608i 0.391784 0.920057i \(-0.371858\pi\)
−0.993770 + 0.111450i \(0.964451\pi\)
\(618\) 0 0
\(619\) 22.7743 + 11.4377i 0.915376 + 0.459719i 0.843156 0.537669i \(-0.180695\pi\)
0.0722206 + 0.997389i \(0.476991\pi\)
\(620\) 2.45106 4.24535i 0.0984368 0.170498i
\(621\) 0 0
\(622\) 16.3342 + 28.2917i 0.654943 + 1.13439i
\(623\) −1.65727 28.4543i −0.0663973 1.14000i
\(624\) 0 0
\(625\) −18.7775 + 2.19478i −0.751102 + 0.0877912i
\(626\) −3.17687 10.6115i −0.126973 0.424120i
\(627\) 0 0
\(628\) −8.45183 19.5936i −0.337265 0.781868i
\(629\) 9.19342 + 3.34613i 0.366566 + 0.133419i
\(630\) 0 0
\(631\) −18.7709 + 6.83203i −0.747256 + 0.271979i −0.687451 0.726231i \(-0.741270\pi\)
−0.0598054 + 0.998210i \(0.519048\pi\)
\(632\) 15.6294 + 16.5662i 0.621702 + 0.658966i
\(633\) 0 0
\(634\) −53.8748 + 27.0570i −2.13964 + 1.07457i
\(635\) 0.428361 7.35468i 0.0169990 0.291862i
\(636\) 0 0
\(637\) −5.58862 + 18.6673i −0.221429 + 0.739625i
\(638\) 2.69069 15.2597i 0.106526 0.604137i
\(639\) 0 0
\(640\) −1.33792 7.58769i −0.0528857 0.299930i
\(641\) 8.86918 + 1.03666i 0.350312 + 0.0409456i 0.289429 0.957199i \(-0.406534\pi\)
0.0608823 + 0.998145i \(0.480609\pi\)
\(642\) 0 0
\(643\) −9.19558 + 9.74674i −0.362638 + 0.384374i −0.882844 0.469667i \(-0.844374\pi\)
0.520205 + 0.854041i \(0.325855\pi\)
\(644\) 6.17427 14.3136i 0.243300 0.564033i
\(645\) 0 0
\(646\) −79.1890 + 52.0834i −3.11565 + 2.04920i
\(647\) −48.7223 −1.91547 −0.957736 0.287649i \(-0.907126\pi\)
−0.957736 + 0.287649i \(0.907126\pi\)
\(648\) 0 0
\(649\) −2.52628 −0.0991653
\(650\) −44.4251 + 29.2189i −1.74250 + 1.14606i
\(651\) 0 0
\(652\) −16.6715 + 38.6489i −0.652906 + 1.51361i
\(653\) −3.29734 + 3.49498i −0.129035 + 0.136769i −0.788669 0.614818i \(-0.789230\pi\)
0.659634 + 0.751587i \(0.270711\pi\)
\(654\) 0 0
\(655\) 9.36262 + 1.09433i 0.365828 + 0.0427592i
\(656\) −0.385978 2.18899i −0.0150699 0.0854656i
\(657\) 0 0
\(658\) −4.21775 + 23.9201i −0.164425 + 0.932501i
\(659\) 7.25407 24.2303i 0.282579 0.943878i −0.692388 0.721526i \(-0.743441\pi\)
0.974966 0.222352i \(-0.0713736\pi\)
\(660\) 0 0
\(661\) 0.821956 14.1124i 0.0319704 0.548910i −0.943855 0.330359i \(-0.892830\pi\)
0.975826 0.218551i \(-0.0701329\pi\)
\(662\) 53.0213 26.6283i 2.06073 1.03494i
\(663\) 0 0
\(664\) −7.36555 7.80703i −0.285839 0.302971i
\(665\) 7.07019 2.57334i 0.274170 0.0997898i
\(666\) 0 0
\(667\) −17.2393 6.27461i −0.667510 0.242954i
\(668\) 3.95792 + 9.17550i 0.153137 + 0.355011i
\(669\) 0 0
\(670\) −0.492094 1.64371i −0.0190112 0.0635020i
\(671\) −4.31401 + 0.504235i −0.166540 + 0.0194658i
\(672\) 0 0
\(673\) −0.155093 2.66284i −0.00597839 0.102645i 0.993999 0.109390i \(-0.0348899\pi\)
−0.999977 + 0.00674548i \(0.997853\pi\)
\(674\) 13.8366 + 23.9656i 0.532965 + 0.923122i
\(675\) 0 0
\(676\) −21.1154 + 36.5730i −0.812131 + 1.40665i
\(677\) −13.1923 6.62542i −0.507021 0.254636i 0.176851 0.984238i \(-0.443409\pi\)
−0.683872 + 0.729602i \(0.739705\pi\)
\(678\) 0 0
\(679\) 4.07390 + 5.47220i 0.156342 + 0.210004i
\(680\) 6.88033 + 1.63067i 0.263849 + 0.0625333i
\(681\) 0 0
\(682\) 4.35951 5.85584i 0.166934 0.224232i
\(683\) −16.0712 + 13.4854i −0.614948 + 0.516003i −0.896211 0.443628i \(-0.853691\pi\)
0.281263 + 0.959631i \(0.409247\pi\)
\(684\) 0 0
\(685\) −0.183640 0.154092i −0.00701653 0.00588756i
\(686\) 41.2611 9.77905i 1.57535 0.373366i
\(687\) 0 0
\(688\) −16.0408 10.5502i −0.611552 0.402224i
\(689\) −37.9775 24.9782i −1.44683 0.951594i
\(690\) 0 0
\(691\) 33.8949 8.03323i 1.28942 0.305598i 0.471979 0.881610i \(-0.343540\pi\)
0.817442 + 0.576011i \(0.195392\pi\)
\(692\) 27.8199 + 23.3437i 1.05755 + 0.887394i
\(693\) 0 0
\(694\) 14.0227 11.7664i 0.532294 0.446648i
\(695\) 5.78221 7.76686i 0.219332 0.294614i
\(696\) 0 0
\(697\) 7.43159 + 1.76132i 0.281492 + 0.0667147i
\(698\) 39.1651 + 52.6079i 1.48242 + 1.99124i
\(699\) 0 0
\(700\) 20.4801 + 10.2855i 0.774075 + 0.388755i
\(701\) 21.8053 37.7679i 0.823576 1.42647i −0.0794276 0.996841i \(-0.525309\pi\)
0.903003 0.429634i \(-0.141357\pi\)
\(702\) 0 0
\(703\) 4.54496 + 7.87209i 0.171416 + 0.296902i
\(704\) −0.872254 14.9760i −0.0328743 0.564430i
\(705\) 0 0
\(706\) −50.2052 + 5.86815i −1.88950 + 0.220851i
\(707\) −2.43997 8.15008i −0.0917647 0.306515i
\(708\) 0 0
\(709\) 7.23533 + 16.7734i 0.271728 + 0.629937i 0.998370 0.0570799i \(-0.0181790\pi\)
−0.726641 + 0.687017i \(0.758920\pi\)
\(710\) −10.7731 3.92111i −0.404309 0.147156i
\(711\) 0 0
\(712\) 23.3867 8.51206i 0.876453 0.319003i
\(713\) −5.93152 6.28704i −0.222137 0.235452i
\(714\) 0 0
\(715\) 3.72787 1.87221i 0.139414 0.0700165i
\(716\) −0.0664428 + 1.14078i −0.00248308 + 0.0426329i
\(717\) 0 0
\(718\) −2.60097 + 8.68786i −0.0970675 + 0.324228i
\(719\) −3.15002 + 17.8647i −0.117476 + 0.666240i 0.868018 + 0.496532i \(0.165393\pi\)
−0.985494 + 0.169708i \(0.945718\pi\)
\(720\) 0 0
\(721\) −1.64184 9.31131i −0.0611451 0.346771i
\(722\) −46.4067 5.42417i −1.72708 0.201867i
\(723\) 0 0
\(724\) −39.1113 + 41.4555i −1.45356 + 1.54068i
\(725\) 10.6829 24.7657i 0.396752 0.919774i
\(726\) 0 0
\(727\) −16.9219 + 11.1297i −0.627599 + 0.412778i −0.823077 0.567930i \(-0.807744\pi\)
0.195478 + 0.980708i \(0.437374\pi\)
\(728\) 15.5847 0.577606
\(729\) 0 0
\(730\) 9.03402 0.334364
\(731\) 55.1169 36.2509i 2.03857 1.34079i
\(732\) 0 0
\(733\) −0.700264 + 1.62339i −0.0258648 + 0.0599615i −0.930659 0.365888i \(-0.880765\pi\)
0.904794 + 0.425849i \(0.140025\pi\)
\(734\) 17.5010 18.5500i 0.645974 0.684693i
\(735\) 0 0
\(736\) −23.3115 2.72473i −0.859274 0.100435i
\(737\) −0.256258 1.45331i −0.00943939 0.0535334i
\(738\) 0 0
\(739\) −1.58340 + 8.97988i −0.0582461 + 0.330330i −0.999982 0.00602346i \(-0.998083\pi\)
0.941736 + 0.336354i \(0.109194\pi\)
\(740\) 0.724337 2.41946i 0.0266272 0.0889409i
\(741\) 0 0
\(742\) −1.97244 + 33.8654i −0.0724104 + 1.24324i
\(743\) −17.8025 + 8.94076i −0.653111 + 0.328005i −0.744316 0.667827i \(-0.767224\pi\)
0.0912051 + 0.995832i \(0.470928\pi\)
\(744\) 0 0
\(745\) 0.443764 + 0.470363i 0.0162583 + 0.0172327i
\(746\) −74.3653 + 27.0667i −2.72271 + 0.990984i
\(747\) 0 0
\(748\) 21.2839 + 7.74671i 0.778217 + 0.283248i
\(749\) 9.41249 + 21.8206i 0.343925 + 0.797308i
\(750\) 0 0
\(751\) 11.0579 + 36.9360i 0.403509 + 1.34781i 0.882631 + 0.470066i \(0.155770\pi\)
−0.479122 + 0.877748i \(0.659045\pi\)
\(752\) 12.0784 1.41177i 0.440456 0.0514819i
\(753\) 0 0
\(754\) −3.97179 68.1930i −0.144644 2.48344i
\(755\) −0.00634611 0.0109918i −0.000230959 0.000400032i
\(756\) 0 0
\(757\) 25.4729 44.1204i 0.925829 1.60358i 0.135606 0.990763i \(-0.456702\pi\)
0.790223 0.612820i \(-0.209965\pi\)
\(758\) −19.5415 9.81413i −0.709781 0.356465i
\(759\) 0 0
\(760\) 3.92315 + 5.26970i 0.142307 + 0.191152i
\(761\) 37.8907 + 8.98027i 1.37354 + 0.325534i 0.850141 0.526555i \(-0.176516\pi\)
0.523397 + 0.852089i \(0.324665\pi\)
\(762\) 0 0
\(763\) −1.94161 + 2.60804i −0.0702911 + 0.0944173i
\(764\) 14.4293 12.1076i 0.522033 0.438038i
\(765\) 0 0
\(766\) −0.504379 0.423224i −0.0182239 0.0152917i
\(767\) −10.8367 + 2.56834i −0.391290 + 0.0927373i
\(768\) 0 0
\(769\) −28.5331 18.7665i −1.02893 0.676739i −0.0814918 0.996674i \(-0.525968\pi\)
−0.947439 + 0.319935i \(0.896339\pi\)
\(770\) −2.60104 1.71073i −0.0937349 0.0616504i
\(771\) 0 0
\(772\) −23.2692 + 5.51490i −0.837476 + 0.198485i
\(773\) −2.31945 1.94625i −0.0834247 0.0700016i 0.600122 0.799909i \(-0.295119\pi\)
−0.683546 + 0.729907i \(0.739563\pi\)
\(774\) 0 0
\(775\) 9.73449 8.16820i 0.349673 0.293411i
\(776\) −3.55722 + 4.77817i −0.127697 + 0.171526i
\(777\) 0 0
\(778\) 15.9200 + 3.77312i 0.570761 + 0.135273i
\(779\) 4.23747 + 5.69191i 0.151823 + 0.203934i
\(780\) 0 0
\(781\) −8.81169 4.42540i −0.315307 0.158353i