Properties

Label 729.2.g.b.28.8
Level $729$
Weight $2$
Character 729.28
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 28.8
Character \(\chi\) \(=\) 729.28
Dual form 729.2.g.b.703.8

$q$-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 0.291612 0.956537i \(-0.405808\pi\)
0.993809 + 0.111102i \(0.0354381\pi\)
\(3\) 0 0
\(4\) 1.08293 2.51052i 0.541467 1.25526i
\(5\) 0.443651 0.470242i 0.198407 0.210299i −0.620530 0.784183i \(-0.713082\pi\)
0.818937 + 0.573884i \(0.194564\pi\)
\(6\) 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 −0.994231 0.107264i \(-0.965791\pi\)
0.889610 + 0.456720i \(0.150976\pi\)
\(12\) 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 0.589693 0.807628i \(-0.299249\pi\)
0.970864 + 0.239631i \(0.0770266\pi\)
\(18\) 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 −0.432530 0.901619i \(-0.642379\pi\)
−0.212944 + 0.977064i \(0.568305\pi\)
\(24\) 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 0.864241 0.503077i \(-0.167799\pi\)
0.112559 + 0.993645i \(0.464095\pi\)
\(30\) 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 0.620190 0.784452i \(-0.287055\pi\)
−0.474651 + 0.880174i \(0.657426\pi\)
\(42\) 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 −0.984073 0.177764i \(-0.943114\pi\)
0.452532 + 0.891748i \(0.350521\pi\)
\(48\) 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 \(0.365706\pi\)
−0.994833 + 0.101528i \(0.967627\pi\)
\(54\) 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 0.988082 0.153927i \(-0.0491921\pi\)
−0.910115 + 0.414356i \(0.864007\pi\)
\(60\) 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 \(0.216237\pi\)
−0.945957 + 0.324293i \(0.894874\pi\)
\(72\) 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 −0.202669 0.979247i \(-0.564961\pi\)
0.818888 + 0.573954i \(0.194591\pi\)
\(84\) 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 \(0.253709\pi\)
−0.412030 + 0.911170i \(0.635180\pi\)
\(90\) 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 0.984943 0.172880i \(-0.0553072\pi\)
−0.801657 + 0.597784i \(0.796048\pi\)
\(102\) 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 \(-0.950572\pi\)
0.360046 0.932935i \(-0.382761\pi\)
\(108\) 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 −0.461023 0.887388i \(-0.652517\pi\)
−0.810244 + 0.586092i \(0.800666\pi\)
\(114\) 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 \(0.0161058\pi\)
−0.237985 + 0.971269i \(0.576487\pi\)
\(132\) 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 0.997262 0.0739509i \(-0.0235608\pi\)
−0.999104 + 0.0423242i \(0.986524\pi\)
\(138\) 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 −0.999852 0.0171933i \(-0.994527\pi\)
0.995088 + 0.0989987i \(0.0315640\pi\)
\(150\) 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 −0.623024 0.782203i \(-0.714096\pi\)
0.817105 + 0.576489i \(0.195577\pi\)
\(168\) 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 \(-0.738926\pi\)
0.971715 0.236158i \(-0.0758884\pi\)
\(174\) 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 −0.327301 0.944920i \(-0.606139\pi\)
0.356656 + 0.934236i \(0.383917\pi\)
\(180\) 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 0.211903 0.977291i \(-0.432034\pi\)
−0.657368 + 0.753570i \(0.728330\pi\)
\(192\) 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 −0.382476 0.923965i \(-0.624929\pi\)
0.843512 + 0.537111i \(0.180484\pi\)
\(198\) 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 0.337843 0.941202i \(-0.390303\pi\)
−0.959254 + 0.282546i \(0.908821\pi\)
\(228\) 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 \(-0.888276\pi\)
0.999998 0.00192589i \(-0.000613031\pi\)
\(234\) 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 \(-0.695511\pi\)
0.989922 0.141615i \(-0.0452294\pi\)
\(240\) 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 \(-0.777552\pi\)
0.499385 0.866380i \(-0.333559\pi\)
\(252\) 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 −0.696573 0.717485i \(-0.745293\pi\)
0.159547 + 0.987190i \(0.448997\pi\)
\(258\) 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 0.817651 0.575715i \(-0.195276\pi\)
−0.979866 + 0.199658i \(0.936017\pi\)
\(264\) 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 \(0.186337\pi\)
0.0617568 + 0.998091i \(0.480330\pi\)
\(270\) 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 0.467316 0.884091i \(-0.345221\pi\)
0.814388 + 0.580321i \(0.197073\pi\)
\(282\) 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 0.640894 0.767630i \(-0.278564\pi\)
−0.919192 + 0.393811i \(0.871157\pi\)
\(294\) 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 \(0.158489\pi\)
−0.928088 + 0.372361i \(0.878548\pi\)
\(312\) 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 −0.699940 0.714202i \(-0.746790\pi\)
−0.845779 + 0.533533i \(0.820864\pi\)
\(318\) 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 0.111199 0.993798i \(-0.464531\pi\)
0.337387 + 0.941366i \(0.390457\pi\)
\(348\) 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 −0.199729 0.979851i \(-0.564006\pi\)
−0.905231 + 0.424919i \(0.860302\pi\)
\(354\) 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 −0.723145 0.690696i \(-0.757304\pi\)
0.554630 + 0.832097i \(0.312860\pi\)
\(360\) 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 0.955744 0.294201i \(-0.0950536\pi\)
−0.960178 + 0.279388i \(0.909868\pi\)
\(384\) 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 0.844852 0.535000i \(-0.179688\pi\)
−0.583218 + 0.812315i \(0.698207\pi\)
\(390\) 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 −0.998117 0.0613379i \(-0.980463\pi\)
0.729565 + 0.683911i \(0.239723\pi\)
\(402\) 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 0.0417867 0.999127i \(-0.486695\pi\)
0.826376 + 0.563119i \(0.190399\pi\)
\(420\) 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 \(-0.992494\pi\)
0.479441 0.877574i \(-0.340839\pi\)
\(432\) 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 −0.267484 0.963562i \(-0.586192\pi\)
0.193414 + 0.981117i \(0.438044\pi\)
\(444\) 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 0.432841 0.901470i \(-0.357511\pi\)
−0.812613 + 0.582804i \(0.801955\pi\)
\(450\) 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 \(-0.724024\pi\)
0.554229 0.832364i \(-0.313013\pi\)
\(462\) 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 0.557897 0.829910i \(-0.311608\pi\)
−0.106082 + 0.994357i \(0.533831\pi\)
\(468\) 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 0.563408 0.826179i \(-0.309490\pi\)
0.357691 + 0.933840i \(0.383564\pi\)
\(480\) 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 −0.549566 0.835450i \(-0.685207\pi\)
0.865991 + 0.500059i \(0.166688\pi\)
\(492\) 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 −0.0530509 0.998592i \(-0.516895\pi\)
0.601243 + 0.799066i \(0.294672\pi\)
\(504\) 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 −0.755377 0.655291i \(-0.772546\pi\)
−0.583895 + 0.811829i \(0.698472\pi\)
\(510\) 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 −0.805525 0.592561i \(-0.798117\pi\)
0.443681 + 0.896185i \(0.353672\pi\)
\(522\) 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 \(0.145382\pi\)
−0.994210 + 0.107458i \(0.965729\pi\)
\(558\) 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 −0.961447 0.274991i \(-0.911325\pi\)
0.859806 + 0.510621i \(0.170584\pi\)
\(564\) 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 −0.224945 0.974371i \(-0.572220\pi\)
0.805587 + 0.592477i \(0.201850\pi\)
\(570\) 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 \(0.241591\pi\)
0.00267106 + 0.999996i \(0.499150\pi\)
\(588\) 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 0.587756 0.809038i \(-0.300011\pi\)
−0.994526 + 0.104493i \(0.966678\pi\)
\(594\) 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 0.744575 0.667539i \(-0.232652\pi\)
0.365785 + 0.930699i \(0.380800\pi\)
\(600\) 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 0.993770 0.111450i \(-0.0355494\pi\)
−0.391784 + 0.920057i \(0.628142\pi\)
\(618\) 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 −0.0608823 0.998145i \(-0.519391\pi\)
−0.289429 + 0.957199i \(0.593466\pi\)
\(642\) 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 \(-0.0928736\pi\)
0.957736 + 0.287649i \(0.0928736\pi\)
\(648\) 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 −0.659634 0.751587i \(-0.729289\pi\)
0.788669 + 0.614818i \(0.210770\pi\)
\(654\) 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 \(0.256559\pi\)
−0.974966 + 0.222352i \(0.928626\pi\)
\(660\) 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 0.683872 0.729602i \(-0.260295\pi\)
−0.176851 + 0.984238i \(0.556591\pi\)
\(678\) 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 −0.281263 0.959631i \(-0.590753\pi\)
0.896211 + 0.443628i \(0.146309\pi\)
\(684\) 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 \(0.474691\pi\)
−0.903003 + 0.429634i \(0.858643\pi\)
\(702\) 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 \(-0.834607\pi\)
0.985494 0.169708i \(-0.0542824\pi\)
\(720\) 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 −0.0912051 0.995832i \(-0.529072\pi\)
0.744316 + 0.667827i \(0.232776\pi\)
\(744\) 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 −0.523397 0.852089i \(-0.675335\pi\)
−0.850141 + 0.526555i \(0.823484\pi\)
\(762\) 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 0.683546 0.729907i \(-0.260437\pi\)
−0.600122 + 0.799909i \(0.704881\pi\)
\(774\) 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
\(782\) −23.2165 + 40.2122i −0.830222 + 1.43799i
\(783\) 0 0