Properties

Label 405.2.j.d.109.2
Level $405$
Weight $2$
Character 405.109
Analytic conductor $3.234$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [405,2,Mod(109,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.j (of order \(6\), degree \(2\), 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: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 109.2
Root \(-1.18614 + 1.26217i\) of defining polynomial
Character \(\chi\) \(=\) 405.109
Dual form 405.2.j.d.379.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.18614 - 1.26217i) q^{2} +(2.18614 - 3.78651i) q^{4} +(-0.686141 + 2.12819i) q^{5} +(3.00000 - 1.73205i) q^{7} -5.98844i q^{8} +O(q^{10})\) \(q+(2.18614 - 1.26217i) q^{2} +(2.18614 - 3.78651i) q^{4} +(-0.686141 + 2.12819i) q^{5} +(3.00000 - 1.73205i) q^{7} -5.98844i q^{8} +(1.18614 + 5.51856i) q^{10} +(0.686141 + 1.18843i) q^{11} +(-3.55842 - 2.05446i) q^{13} +(4.37228 - 7.57301i) q^{14} +(-3.18614 - 5.51856i) q^{16} +2.52434i q^{17} -5.37228 q^{19} +(6.55842 + 7.25061i) q^{20} +(3.00000 + 1.73205i) q^{22} +(4.37228 + 2.52434i) q^{23} +(-4.05842 - 2.92048i) q^{25} -10.3723 q^{26} -15.1460i q^{28} +(-2.87228 - 4.97494i) q^{29} +(-0.313859 + 0.543620i) q^{31} +(-3.55842 - 2.05446i) q^{32} +(3.18614 + 5.51856i) q^{34} +(1.62772 + 7.57301i) q^{35} +7.57301i q^{37} +(-11.7446 + 6.78073i) q^{38} +(12.7446 + 4.10891i) q^{40} +(-0.686141 + 1.18843i) q^{41} +(3.00000 - 1.73205i) q^{43} +6.00000 q^{44} +12.7446 q^{46} +(-7.37228 + 4.25639i) q^{47} +(2.50000 - 4.33013i) q^{49} +(-12.5584 - 1.26217i) q^{50} +(-15.5584 + 8.98266i) q^{52} +5.34363i q^{53} +(-3.00000 + 0.644810i) q^{55} +(-10.3723 - 17.9653i) q^{56} +(-12.5584 - 7.25061i) q^{58} +(-3.68614 + 6.38458i) q^{59} +(-1.81386 - 3.14170i) q^{61} +1.58457i q^{62} +2.37228 q^{64} +(6.81386 - 6.16337i) q^{65} +(7.11684 + 4.10891i) q^{67} +(9.55842 + 5.51856i) q^{68} +(13.1168 + 14.5012i) q^{70} +4.11684 q^{71} -7.57301i q^{73} +(9.55842 + 16.5557i) q^{74} +(-11.7446 + 20.3422i) q^{76} +(4.11684 + 2.37686i) q^{77} +(-2.37228 - 4.10891i) q^{79} +(13.9307 - 2.99422i) q^{80} +3.46410i q^{82} +(4.62772 - 2.67181i) q^{83} +(-5.37228 - 1.73205i) q^{85} +(4.37228 - 7.57301i) q^{86} +(7.11684 - 4.10891i) q^{88} -3.00000 q^{89} -14.2337 q^{91} +(19.1168 - 11.0371i) q^{92} +(-10.7446 + 18.6101i) q^{94} +(3.68614 - 11.4333i) q^{95} +(16.1168 - 9.30506i) q^{97} -12.6217i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} + 3 q^{4} + 3 q^{5} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} + 3 q^{4} + 3 q^{5} + 12 q^{7} - q^{10} - 3 q^{11} + 3 q^{13} + 6 q^{14} - 7 q^{16} - 10 q^{19} + 9 q^{20} + 12 q^{22} + 6 q^{23} + q^{25} - 30 q^{26} - 7 q^{31} + 3 q^{32} + 7 q^{34} + 18 q^{35} - 24 q^{38} + 28 q^{40} + 3 q^{41} + 12 q^{43} + 24 q^{44} + 28 q^{46} - 18 q^{47} + 10 q^{49} - 33 q^{50} - 45 q^{52} - 12 q^{55} - 30 q^{56} - 33 q^{58} - 9 q^{59} - 13 q^{61} - 2 q^{64} + 33 q^{65} - 6 q^{67} + 21 q^{68} + 18 q^{70} - 18 q^{71} + 21 q^{74} - 24 q^{76} - 18 q^{77} + 2 q^{79} + 27 q^{80} + 30 q^{83} - 10 q^{85} + 6 q^{86} - 6 q^{88} - 12 q^{89} + 12 q^{91} + 42 q^{92} - 20 q^{94} + 9 q^{95} + 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.18614 1.26217i 1.54583 0.892488i 0.547382 0.836883i \(-0.315624\pi\)
0.998453 0.0556054i \(-0.0177089\pi\)
\(3\) 0 0
\(4\) 2.18614 3.78651i 1.09307 1.89325i
\(5\) −0.686141 + 2.12819i −0.306851 + 0.951757i
\(6\) 0 0
\(7\) 3.00000 1.73205i 1.13389 0.654654i 0.188982 0.981981i \(-0.439481\pi\)
0.944911 + 0.327327i \(0.106148\pi\)
\(8\) 5.98844i 2.11723i
\(9\) 0 0
\(10\) 1.18614 + 5.51856i 0.375091 + 1.74512i
\(11\) 0.686141 + 1.18843i 0.206879 + 0.358325i 0.950730 0.310021i \(-0.100336\pi\)
−0.743851 + 0.668346i \(0.767003\pi\)
\(12\) 0 0
\(13\) −3.55842 2.05446i −0.986929 0.569804i −0.0825739 0.996585i \(-0.526314\pi\)
−0.904355 + 0.426781i \(0.859647\pi\)
\(14\) 4.37228 7.57301i 1.16854 2.02397i
\(15\) 0 0
\(16\) −3.18614 5.51856i −0.796535 1.37964i
\(17\) 2.52434i 0.612242i 0.951993 + 0.306121i \(0.0990312\pi\)
−0.951993 + 0.306121i \(0.900969\pi\)
\(18\) 0 0
\(19\) −5.37228 −1.23249 −0.616243 0.787556i \(-0.711346\pi\)
−0.616243 + 0.787556i \(0.711346\pi\)
\(20\) 6.55842 + 7.25061i 1.46651 + 1.62129i
\(21\) 0 0
\(22\) 3.00000 + 1.73205i 0.639602 + 0.369274i
\(23\) 4.37228 + 2.52434i 0.911684 + 0.526361i 0.880972 0.473167i \(-0.156889\pi\)
0.0307112 + 0.999528i \(0.490223\pi\)
\(24\) 0 0
\(25\) −4.05842 2.92048i −0.811684 0.584096i
\(26\) −10.3723 −2.03417
\(27\) 0 0
\(28\) 15.1460i 2.86233i
\(29\) −2.87228 4.97494i −0.533369 0.923823i −0.999240 0.0389701i \(-0.987592\pi\)
0.465871 0.884853i \(-0.345741\pi\)
\(30\) 0 0
\(31\) −0.313859 + 0.543620i −0.0563708 + 0.0976371i −0.892834 0.450386i \(-0.851286\pi\)
0.836463 + 0.548023i \(0.184620\pi\)
\(32\) −3.55842 2.05446i −0.629046 0.363180i
\(33\) 0 0
\(34\) 3.18614 + 5.51856i 0.546419 + 0.946425i
\(35\) 1.62772 + 7.57301i 0.275135 + 1.28007i
\(36\) 0 0
\(37\) 7.57301i 1.24500i 0.782621 + 0.622498i \(0.213882\pi\)
−0.782621 + 0.622498i \(0.786118\pi\)
\(38\) −11.7446 + 6.78073i −1.90522 + 1.09998i
\(39\) 0 0
\(40\) 12.7446 + 4.10891i 2.01509 + 0.649676i
\(41\) −0.686141 + 1.18843i −0.107157 + 0.185602i −0.914617 0.404320i \(-0.867508\pi\)
0.807460 + 0.589922i \(0.200841\pi\)
\(42\) 0 0
\(43\) 3.00000 1.73205i 0.457496 0.264135i −0.253495 0.967337i \(-0.581580\pi\)
0.710991 + 0.703201i \(0.248247\pi\)
\(44\) 6.00000 0.904534
\(45\) 0 0
\(46\) 12.7446 1.87908
\(47\) −7.37228 + 4.25639i −1.07536 + 0.620858i −0.929640 0.368468i \(-0.879882\pi\)
−0.145717 + 0.989326i \(0.546549\pi\)
\(48\) 0 0
\(49\) 2.50000 4.33013i 0.357143 0.618590i
\(50\) −12.5584 1.26217i −1.77603 0.178498i
\(51\) 0 0
\(52\) −15.5584 + 8.98266i −2.15756 + 1.24567i
\(53\) 5.34363i 0.734004i 0.930220 + 0.367002i \(0.119616\pi\)
−0.930220 + 0.367002i \(0.880384\pi\)
\(54\) 0 0
\(55\) −3.00000 + 0.644810i −0.404520 + 0.0869462i
\(56\) −10.3723 17.9653i −1.38605 2.40072i
\(57\) 0 0
\(58\) −12.5584 7.25061i −1.64900 0.952052i
\(59\) −3.68614 + 6.38458i −0.479895 + 0.831202i −0.999734 0.0230621i \(-0.992658\pi\)
0.519839 + 0.854264i \(0.325992\pi\)
\(60\) 0 0
\(61\) −1.81386 3.14170i −0.232241 0.402253i 0.726226 0.687456i \(-0.241272\pi\)
−0.958467 + 0.285203i \(0.907939\pi\)
\(62\) 1.58457i 0.201241i
\(63\) 0 0
\(64\) 2.37228 0.296535
\(65\) 6.81386 6.16337i 0.845155 0.764472i
\(66\) 0 0
\(67\) 7.11684 + 4.10891i 0.869461 + 0.501983i 0.867169 0.498014i \(-0.165937\pi\)
0.00229183 + 0.999997i \(0.499270\pi\)
\(68\) 9.55842 + 5.51856i 1.15913 + 0.669223i
\(69\) 0 0
\(70\) 13.1168 + 14.5012i 1.56776 + 1.73323i
\(71\) 4.11684 0.488579 0.244290 0.969702i \(-0.421445\pi\)
0.244290 + 0.969702i \(0.421445\pi\)
\(72\) 0 0
\(73\) 7.57301i 0.886354i −0.896434 0.443177i \(-0.853851\pi\)
0.896434 0.443177i \(-0.146149\pi\)
\(74\) 9.55842 + 16.5557i 1.11114 + 1.92456i
\(75\) 0 0
\(76\) −11.7446 + 20.3422i −1.34719 + 2.33341i
\(77\) 4.11684 + 2.37686i 0.469158 + 0.270868i
\(78\) 0 0
\(79\) −2.37228 4.10891i −0.266903 0.462289i 0.701158 0.713006i \(-0.252667\pi\)
−0.968060 + 0.250717i \(0.919334\pi\)
\(80\) 13.9307 2.99422i 1.55750 0.334764i
\(81\) 0 0
\(82\) 3.46410i 0.382546i
\(83\) 4.62772 2.67181i 0.507958 0.293270i −0.224036 0.974581i \(-0.571923\pi\)
0.731994 + 0.681311i \(0.238590\pi\)
\(84\) 0 0
\(85\) −5.37228 1.73205i −0.582706 0.187867i
\(86\) 4.37228 7.57301i 0.471475 0.816619i
\(87\) 0 0
\(88\) 7.11684 4.10891i 0.758658 0.438011i
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) −14.2337 −1.49210
\(92\) 19.1168 11.0371i 1.99307 1.15070i
\(93\) 0 0
\(94\) −10.7446 + 18.6101i −1.10822 + 1.91949i
\(95\) 3.68614 11.4333i 0.378190 1.17303i
\(96\) 0 0
\(97\) 16.1168 9.30506i 1.63642 0.944786i 0.654365 0.756179i \(-0.272936\pi\)
0.982053 0.188607i \(-0.0603973\pi\)
\(98\) 12.6217i 1.27498i
\(99\) 0 0
\(100\) −19.9307 + 8.98266i −1.99307 + 0.898266i
\(101\) −5.31386 9.20387i −0.528749 0.915820i −0.999438 0.0335207i \(-0.989328\pi\)
0.470689 0.882299i \(-0.344005\pi\)
\(102\) 0 0
\(103\) −6.00000 3.46410i −0.591198 0.341328i 0.174373 0.984680i \(-0.444210\pi\)
−0.765571 + 0.643352i \(0.777543\pi\)
\(104\) −12.3030 + 21.3094i −1.20641 + 2.08956i
\(105\) 0 0
\(106\) 6.74456 + 11.6819i 0.655090 + 1.13465i
\(107\) 13.2665i 1.28252i −0.767323 0.641260i \(-0.778412\pi\)
0.767323 0.641260i \(-0.221588\pi\)
\(108\) 0 0
\(109\) 1.74456 0.167099 0.0835494 0.996504i \(-0.473374\pi\)
0.0835494 + 0.996504i \(0.473374\pi\)
\(110\) −5.74456 + 5.19615i −0.547723 + 0.495434i
\(111\) 0 0
\(112\) −19.1168 11.0371i −1.80637 1.04291i
\(113\) −8.18614 4.72627i −0.770087 0.444610i 0.0628184 0.998025i \(-0.479991\pi\)
−0.832906 + 0.553415i \(0.813324\pi\)
\(114\) 0 0
\(115\) −8.37228 + 7.57301i −0.780719 + 0.706187i
\(116\) −25.1168 −2.33204
\(117\) 0 0
\(118\) 18.6101i 1.71320i
\(119\) 4.37228 + 7.57301i 0.400806 + 0.694217i
\(120\) 0 0
\(121\) 4.55842 7.89542i 0.414402 0.717765i
\(122\) −7.93070 4.57879i −0.718012 0.414545i
\(123\) 0 0
\(124\) 1.37228 + 2.37686i 0.123235 + 0.213448i
\(125\) 9.00000 6.63325i 0.804984 0.593296i
\(126\) 0 0
\(127\) 10.3923i 0.922168i −0.887357 0.461084i \(-0.847461\pi\)
0.887357 0.461084i \(-0.152539\pi\)
\(128\) 12.3030 7.10313i 1.08744 0.627834i
\(129\) 0 0
\(130\) 7.11684 22.0742i 0.624189 1.93604i
\(131\) −0.686141 + 1.18843i −0.0599484 + 0.103834i −0.894442 0.447184i \(-0.852427\pi\)
0.834494 + 0.551018i \(0.185760\pi\)
\(132\) 0 0
\(133\) −16.1168 + 9.30506i −1.39751 + 0.806851i
\(134\) 20.7446 1.79206
\(135\) 0 0
\(136\) 15.1168 1.29626
\(137\) −1.93070 + 1.11469i −0.164951 + 0.0952346i −0.580203 0.814472i \(-0.697027\pi\)
0.415252 + 0.909706i \(0.363693\pi\)
\(138\) 0 0
\(139\) −3.05842 + 5.29734i −0.259412 + 0.449315i −0.966085 0.258226i \(-0.916862\pi\)
0.706673 + 0.707541i \(0.250195\pi\)
\(140\) 32.2337 + 10.3923i 2.72424 + 0.878310i
\(141\) 0 0
\(142\) 9.00000 5.19615i 0.755263 0.436051i
\(143\) 5.63858i 0.471522i
\(144\) 0 0
\(145\) 12.5584 2.69927i 1.04292 0.224162i
\(146\) −9.55842 16.5557i −0.791061 1.37016i
\(147\) 0 0
\(148\) 28.6753 + 16.5557i 2.35709 + 1.36087i
\(149\) −8.18614 + 14.1788i −0.670635 + 1.16157i 0.307090 + 0.951681i \(0.400645\pi\)
−0.977724 + 0.209893i \(0.932688\pi\)
\(150\) 0 0
\(151\) −9.05842 15.6896i −0.737164 1.27681i −0.953767 0.300546i \(-0.902831\pi\)
0.216603 0.976260i \(-0.430502\pi\)
\(152\) 32.1716i 2.60946i
\(153\) 0 0
\(154\) 12.0000 0.966988
\(155\) −0.941578 1.04095i −0.0756294 0.0836114i
\(156\) 0 0
\(157\) 18.5584 + 10.7147i 1.48112 + 0.855127i 0.999771 0.0214003i \(-0.00681243\pi\)
0.481352 + 0.876527i \(0.340146\pi\)
\(158\) −10.3723 5.98844i −0.825174 0.476415i
\(159\) 0 0
\(160\) 6.81386 6.16337i 0.538683 0.487257i
\(161\) 17.4891 1.37834
\(162\) 0 0
\(163\) 4.75372i 0.372340i 0.982518 + 0.186170i \(0.0596076\pi\)
−0.982518 + 0.186170i \(0.940392\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) 0 0
\(166\) 6.74456 11.6819i 0.523480 0.906693i
\(167\) 0.255437 + 0.147477i 0.0197663 + 0.0114121i 0.509851 0.860263i \(-0.329701\pi\)
−0.490084 + 0.871675i \(0.663034\pi\)
\(168\) 0 0
\(169\) 1.94158 + 3.36291i 0.149352 + 0.258686i
\(170\) −13.9307 + 2.99422i −1.06844 + 0.229646i
\(171\) 0 0
\(172\) 15.1460i 1.15487i
\(173\) −6.81386 + 3.93398i −0.518048 + 0.299095i −0.736136 0.676834i \(-0.763351\pi\)
0.218088 + 0.975929i \(0.430018\pi\)
\(174\) 0 0
\(175\) −17.2337 1.73205i −1.30274 0.130931i
\(176\) 4.37228 7.57301i 0.329573 0.570837i
\(177\) 0 0
\(178\) −6.55842 + 3.78651i −0.491575 + 0.283811i
\(179\) −22.1168 −1.65309 −0.826545 0.562870i \(-0.809697\pi\)
−0.826545 + 0.562870i \(0.809697\pi\)
\(180\) 0 0
\(181\) 14.8614 1.10464 0.552320 0.833632i \(-0.313743\pi\)
0.552320 + 0.833632i \(0.313743\pi\)
\(182\) −31.1168 + 17.9653i −2.30653 + 1.33168i
\(183\) 0 0
\(184\) 15.1168 26.1831i 1.11443 1.93025i
\(185\) −16.1168 5.19615i −1.18493 0.382029i
\(186\) 0 0
\(187\) −3.00000 + 1.73205i −0.219382 + 0.126660i
\(188\) 37.2203i 2.71457i
\(189\) 0 0
\(190\) −6.37228 29.6472i −0.462294 2.15084i
\(191\) 6.68614 + 11.5807i 0.483792 + 0.837953i 0.999827 0.0186152i \(-0.00592573\pi\)
−0.516035 + 0.856568i \(0.672592\pi\)
\(192\) 0 0
\(193\) 18.5584 + 10.7147i 1.33586 + 0.771262i 0.986191 0.165610i \(-0.0529593\pi\)
0.349673 + 0.936872i \(0.386293\pi\)
\(194\) 23.4891 40.6844i 1.68642 2.92097i
\(195\) 0 0
\(196\) −10.9307 18.9325i −0.780765 1.35232i
\(197\) 23.0140i 1.63968i −0.572593 0.819840i \(-0.694063\pi\)
0.572593 0.819840i \(-0.305937\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) −17.4891 + 24.3036i −1.23667 + 1.71853i
\(201\) 0 0
\(202\) −23.2337 13.4140i −1.63472 0.943804i
\(203\) −17.2337 9.94987i −1.20957 0.698344i
\(204\) 0 0
\(205\) −2.05842 2.27567i −0.143766 0.158940i
\(206\) −17.4891 −1.21853
\(207\) 0 0
\(208\) 26.1831i 1.81547i
\(209\) −3.68614 6.38458i −0.254976 0.441631i
\(210\) 0 0
\(211\) −13.4307 + 23.2627i −0.924608 + 1.60147i −0.132417 + 0.991194i \(0.542274\pi\)
−0.792191 + 0.610273i \(0.791060\pi\)
\(212\) 20.2337 + 11.6819i 1.38966 + 0.802318i
\(213\) 0 0
\(214\) −16.7446 29.0024i −1.14463 1.98257i
\(215\) 1.62772 + 7.57301i 0.111009 + 0.516475i
\(216\) 0 0
\(217\) 2.17448i 0.147613i
\(218\) 3.81386 2.20193i 0.258307 0.149134i
\(219\) 0 0
\(220\) −4.11684 + 12.7692i −0.277558 + 0.860897i
\(221\) 5.18614 8.98266i 0.348858 0.604239i
\(222\) 0 0
\(223\) −1.11684 + 0.644810i −0.0747894 + 0.0431797i −0.536928 0.843628i \(-0.680415\pi\)
0.462139 + 0.886808i \(0.347082\pi\)
\(224\) −14.2337 −0.951028
\(225\) 0 0
\(226\) −23.8614 −1.58724
\(227\) −0.255437 + 0.147477i −0.0169540 + 0.00978838i −0.508453 0.861090i \(-0.669782\pi\)
0.491499 + 0.870878i \(0.336449\pi\)
\(228\) 0 0
\(229\) 11.3030 19.5773i 0.746922 1.29371i −0.202369 0.979309i \(-0.564864\pi\)
0.949291 0.314398i \(-0.101803\pi\)
\(230\) −8.74456 + 27.1229i −0.576599 + 1.78843i
\(231\) 0 0
\(232\) −29.7921 + 17.2005i −1.95595 + 1.12927i
\(233\) 9.45254i 0.619257i 0.950858 + 0.309628i \(0.100205\pi\)
−0.950858 + 0.309628i \(0.899795\pi\)
\(234\) 0 0
\(235\) −4.00000 18.6101i −0.260931 1.21399i
\(236\) 16.1168 + 27.9152i 1.04912 + 1.81712i
\(237\) 0 0
\(238\) 19.1168 + 11.0371i 1.23916 + 0.715430i
\(239\) 11.4891 19.8997i 0.743170 1.28721i −0.207875 0.978155i \(-0.566655\pi\)
0.951045 0.309052i \(-0.100012\pi\)
\(240\) 0 0
\(241\) 12.2446 + 21.2082i 0.788742 + 1.36614i 0.926738 + 0.375708i \(0.122600\pi\)
−0.137997 + 0.990433i \(0.544066\pi\)
\(242\) 23.0140i 1.47940i
\(243\) 0 0
\(244\) −15.8614 −1.01542
\(245\) 7.50000 + 8.29156i 0.479157 + 0.529728i
\(246\) 0 0
\(247\) 19.1168 + 11.0371i 1.21638 + 0.702275i
\(248\) 3.25544 + 1.87953i 0.206720 + 0.119350i
\(249\) 0 0
\(250\) 11.3030 25.8607i 0.714864 1.63558i
\(251\) −14.2337 −0.898422 −0.449211 0.893426i \(-0.648295\pi\)
−0.449211 + 0.893426i \(0.648295\pi\)
\(252\) 0 0
\(253\) 6.92820i 0.435572i
\(254\) −13.1168 22.7190i −0.823024 1.42552i
\(255\) 0 0
\(256\) 15.5584 26.9480i 0.972401 1.68425i
\(257\) 19.9307 + 11.5070i 1.24324 + 0.717787i 0.969753 0.244088i \(-0.0784886\pi\)
0.273490 + 0.961875i \(0.411822\pi\)
\(258\) 0 0
\(259\) 13.1168 + 22.7190i 0.815041 + 1.41169i
\(260\) −8.44158 39.2747i −0.523524 2.43571i
\(261\) 0 0
\(262\) 3.46410i 0.214013i
\(263\) 22.9783 13.2665i 1.41690 0.818047i 0.420874 0.907119i \(-0.361723\pi\)
0.996025 + 0.0890715i \(0.0283900\pi\)
\(264\) 0 0
\(265\) −11.3723 3.66648i −0.698594 0.225230i
\(266\) −23.4891 + 40.6844i −1.44021 + 2.49452i
\(267\) 0 0
\(268\) 31.1168 17.9653i 1.90076 1.09741i
\(269\) 5.23369 0.319104 0.159552 0.987190i \(-0.448995\pi\)
0.159552 + 0.987190i \(0.448995\pi\)
\(270\) 0 0
\(271\) 16.7446 1.01716 0.508580 0.861015i \(-0.330171\pi\)
0.508580 + 0.861015i \(0.330171\pi\)
\(272\) 13.9307 8.04290i 0.844673 0.487672i
\(273\) 0 0
\(274\) −2.81386 + 4.87375i −0.169991 + 0.294434i
\(275\) 0.686141 6.82701i 0.0413758 0.411684i
\(276\) 0 0
\(277\) −1.88316 + 1.08724i −0.113148 + 0.0653260i −0.555506 0.831513i \(-0.687475\pi\)
0.442358 + 0.896839i \(0.354142\pi\)
\(278\) 15.4410i 0.926088i
\(279\) 0 0
\(280\) 45.3505 9.74749i 2.71021 0.582524i
\(281\) 2.18614 + 3.78651i 0.130414 + 0.225884i 0.923836 0.382788i \(-0.125036\pi\)
−0.793422 + 0.608672i \(0.791703\pi\)
\(282\) 0 0
\(283\) −24.0000 13.8564i −1.42665 0.823678i −0.429797 0.902926i \(-0.641415\pi\)
−0.996855 + 0.0792477i \(0.974748\pi\)
\(284\) 9.00000 15.5885i 0.534052 0.925005i
\(285\) 0 0
\(286\) −7.11684 12.3267i −0.420828 0.728895i
\(287\) 4.75372i 0.280603i
\(288\) 0 0
\(289\) 10.6277 0.625160
\(290\) 24.0475 21.7518i 1.41212 1.27731i
\(291\) 0 0
\(292\) −28.6753 16.5557i −1.67809 0.968847i
\(293\) −2.18614 1.26217i −0.127716 0.0737367i 0.434781 0.900536i \(-0.356826\pi\)
−0.562497 + 0.826800i \(0.690159\pi\)
\(294\) 0 0
\(295\) −11.0584 12.2255i −0.643846 0.711799i
\(296\) 45.3505 2.63595
\(297\) 0 0
\(298\) 41.3292i 2.39413i
\(299\) −10.3723 17.9653i −0.599845 1.03896i
\(300\) 0 0
\(301\) 6.00000 10.3923i 0.345834 0.599002i
\(302\) −39.6060 22.8665i −2.27907 1.31582i
\(303\) 0 0
\(304\) 17.1168 + 29.6472i 0.981718 + 1.70039i
\(305\) 7.93070 1.70460i 0.454111 0.0976051i
\(306\) 0 0
\(307\) 4.75372i 0.271309i 0.990756 + 0.135655i \(0.0433138\pi\)
−0.990756 + 0.135655i \(0.956686\pi\)
\(308\) 18.0000 10.3923i 1.02565 0.592157i
\(309\) 0 0
\(310\) −3.37228 1.08724i −0.191533 0.0617511i
\(311\) 6.43070 11.1383i 0.364652 0.631595i −0.624068 0.781370i \(-0.714521\pi\)
0.988720 + 0.149774i \(0.0478547\pi\)
\(312\) 0 0
\(313\) 4.67527 2.69927i 0.264262 0.152572i −0.362015 0.932172i \(-0.617911\pi\)
0.626277 + 0.779601i \(0.284578\pi\)
\(314\) 54.0951 3.05276
\(315\) 0 0
\(316\) −20.7446 −1.16697
\(317\) −6.04755 + 3.49155i −0.339664 + 0.196105i −0.660123 0.751157i \(-0.729496\pi\)
0.320459 + 0.947262i \(0.396163\pi\)
\(318\) 0 0
\(319\) 3.94158 6.82701i 0.220686 0.382239i
\(320\) −1.62772 + 5.04868i −0.0909922 + 0.282230i
\(321\) 0 0
\(322\) 38.2337 22.0742i 2.13068 1.23015i
\(323\) 13.5615i 0.754579i
\(324\) 0 0
\(325\) 8.44158 + 18.7302i 0.468254 + 1.03896i
\(326\) 6.00000 + 10.3923i 0.332309 + 0.575577i
\(327\) 0 0
\(328\) 7.11684 + 4.10891i 0.392962 + 0.226877i
\(329\) −14.7446 + 25.5383i −0.812894 + 1.40797i
\(330\) 0 0
\(331\) 4.05842 + 7.02939i 0.223071 + 0.386370i 0.955739 0.294216i \(-0.0950585\pi\)
−0.732668 + 0.680586i \(0.761725\pi\)
\(332\) 23.3639i 1.28226i
\(333\) 0 0
\(334\) 0.744563 0.0407407
\(335\) −13.6277 + 12.3267i −0.744562 + 0.673481i
\(336\) 0 0
\(337\) −6.00000 3.46410i −0.326841 0.188702i 0.327597 0.944818i \(-0.393761\pi\)
−0.654438 + 0.756116i \(0.727095\pi\)
\(338\) 8.48913 + 4.90120i 0.461748 + 0.266590i
\(339\) 0 0
\(340\) −18.3030 + 16.5557i −0.992619 + 0.897857i
\(341\) −0.861407 −0.0466478
\(342\) 0 0
\(343\) 6.92820i 0.374088i
\(344\) −10.3723 17.9653i −0.559236 0.968625i
\(345\) 0 0
\(346\) −9.93070 + 17.2005i −0.533878 + 0.924704i
\(347\) 20.4891 + 11.8294i 1.09991 + 0.635036i 0.936198 0.351472i \(-0.114319\pi\)
0.163715 + 0.986508i \(0.447652\pi\)
\(348\) 0 0
\(349\) 6.80298 + 11.7831i 0.364155 + 0.630736i 0.988640 0.150301i \(-0.0480244\pi\)
−0.624485 + 0.781037i \(0.714691\pi\)
\(350\) −39.8614 + 17.9653i −2.13068 + 0.960287i
\(351\) 0 0
\(352\) 5.63858i 0.300537i
\(353\) −7.37228 + 4.25639i −0.392387 + 0.226545i −0.683194 0.730237i \(-0.739410\pi\)
0.290807 + 0.956782i \(0.406076\pi\)
\(354\) 0 0
\(355\) −2.82473 + 8.76144i −0.149921 + 0.465009i
\(356\) −6.55842 + 11.3595i −0.347596 + 0.602053i
\(357\) 0 0
\(358\) −48.3505 + 27.9152i −2.55541 + 1.47536i
\(359\) −28.1168 −1.48395 −0.741975 0.670427i \(-0.766111\pi\)
−0.741975 + 0.670427i \(0.766111\pi\)
\(360\) 0 0
\(361\) 9.86141 0.519021
\(362\) 32.4891 18.7576i 1.70759 0.985878i
\(363\) 0 0
\(364\) −31.1168 + 53.8960i −1.63097 + 2.82492i
\(365\) 16.1168 + 5.19615i 0.843594 + 0.271979i
\(366\) 0 0
\(367\) 20.2337 11.6819i 1.05619 0.609792i 0.131814 0.991274i \(-0.457920\pi\)
0.924376 + 0.381483i \(0.124586\pi\)
\(368\) 32.1716i 1.67706i
\(369\) 0 0
\(370\) −41.7921 + 8.98266i −2.17267 + 0.466986i
\(371\) 9.25544 + 16.0309i 0.480518 + 0.832282i
\(372\) 0 0
\(373\) −10.1168 5.84096i −0.523830 0.302434i 0.214670 0.976687i \(-0.431132\pi\)
−0.738500 + 0.674253i \(0.764466\pi\)
\(374\) −4.37228 + 7.57301i −0.226085 + 0.391591i
\(375\) 0 0
\(376\) 25.4891 + 44.1485i 1.31450 + 2.27678i
\(377\) 23.6039i 1.21566i
\(378\) 0 0
\(379\) −21.4891 −1.10382 −0.551911 0.833903i \(-0.686101\pi\)
−0.551911 + 0.833903i \(0.686101\pi\)
\(380\) −35.2337 38.9523i −1.80745 1.99821i
\(381\) 0 0
\(382\) 29.2337 + 16.8781i 1.49573 + 0.863558i
\(383\) 30.6060 + 17.6704i 1.56389 + 0.902913i 0.996857 + 0.0792196i \(0.0252428\pi\)
0.567035 + 0.823694i \(0.308090\pi\)
\(384\) 0 0
\(385\) −7.88316 + 7.13058i −0.401763 + 0.363408i
\(386\) 54.0951 2.75337
\(387\) 0 0
\(388\) 81.3687i 4.13087i
\(389\) 11.7446 + 20.3422i 0.595473 + 1.03139i 0.993480 + 0.114007i \(0.0363686\pi\)
−0.398007 + 0.917382i \(0.630298\pi\)
\(390\) 0 0
\(391\) −6.37228 + 11.0371i −0.322260 + 0.558171i
\(392\) −25.9307 14.9711i −1.30970 0.756155i
\(393\) 0 0
\(394\) −29.0475 50.3118i −1.46339 2.53467i
\(395\) 10.3723 2.22938i 0.521886 0.112172i
\(396\) 0 0
\(397\) 12.3267i 0.618661i −0.950955 0.309331i \(-0.899895\pi\)
0.950955 0.309331i \(-0.100105\pi\)
\(398\) −34.9783 + 20.1947i −1.75330 + 1.01227i
\(399\) 0 0
\(400\) −3.18614 + 31.7017i −0.159307 + 1.58508i
\(401\) 9.81386 16.9981i 0.490081 0.848845i −0.509854 0.860261i \(-0.670301\pi\)
0.999935 + 0.0114161i \(0.00363395\pi\)
\(402\) 0 0
\(403\) 2.23369 1.28962i 0.111268 0.0642406i
\(404\) −46.4674 −2.31184
\(405\) 0 0
\(406\) −50.2337 −2.49306
\(407\) −9.00000 + 5.19615i −0.446113 + 0.257564i
\(408\) 0 0
\(409\) −2.93070 + 5.07613i −0.144914 + 0.250998i −0.929341 0.369223i \(-0.879624\pi\)
0.784427 + 0.620221i \(0.212957\pi\)
\(410\) −7.37228 2.37686i −0.364091 0.117385i
\(411\) 0 0
\(412\) −26.2337 + 15.1460i −1.29244 + 0.746191i
\(413\) 25.5383i 1.25666i
\(414\) 0 0
\(415\) 2.51087 + 11.6819i 0.123254 + 0.573443i
\(416\) 8.44158 + 14.6212i 0.413882 + 0.716865i
\(417\) 0 0
\(418\) −16.1168 9.30506i −0.788301 0.455126i
\(419\) −2.74456 + 4.75372i −0.134081 + 0.232235i −0.925246 0.379368i \(-0.876141\pi\)
0.791165 + 0.611602i \(0.209475\pi\)
\(420\) 0 0
\(421\) 5.12772 + 8.88147i 0.249910 + 0.432856i 0.963501 0.267706i \(-0.0862657\pi\)
−0.713591 + 0.700563i \(0.752932\pi\)
\(422\) 67.8073i 3.30081i
\(423\) 0 0
\(424\) 32.0000 1.55406
\(425\) 7.37228 10.2448i 0.357608 0.496947i
\(426\) 0 0
\(427\) −10.8832 6.28339i −0.526673 0.304075i
\(428\) −50.2337 29.0024i −2.42814 1.40189i
\(429\) 0 0
\(430\) 13.1168 + 14.5012i 0.632550 + 0.699311i
\(431\) −18.3505 −0.883914 −0.441957 0.897036i \(-0.645716\pi\)
−0.441957 + 0.897036i \(0.645716\pi\)
\(432\) 0 0
\(433\) 2.81929i 0.135487i 0.997703 + 0.0677433i \(0.0215799\pi\)
−0.997703 + 0.0677433i \(0.978420\pi\)
\(434\) 2.74456 + 4.75372i 0.131743 + 0.228186i
\(435\) 0 0
\(436\) 3.81386 6.60580i 0.182651 0.316360i
\(437\) −23.4891 13.5615i −1.12364 0.648732i
\(438\) 0 0
\(439\) 1.56930 + 2.71810i 0.0748984 + 0.129728i 0.901042 0.433732i \(-0.142803\pi\)
−0.826144 + 0.563460i \(0.809470\pi\)
\(440\) 3.86141 + 17.9653i 0.184085 + 0.856463i
\(441\) 0 0
\(442\) 26.1831i 1.24541i
\(443\) −21.6060 + 12.4742i −1.02653 + 0.592668i −0.915989 0.401204i \(-0.868592\pi\)
−0.110542 + 0.993871i \(0.535259\pi\)
\(444\) 0 0
\(445\) 2.05842 6.38458i 0.0975786 0.302658i
\(446\) −1.62772 + 2.81929i −0.0770747 + 0.133497i
\(447\) 0 0
\(448\) 7.11684 4.10891i 0.336239 0.194128i
\(449\) −28.1168 −1.32692 −0.663458 0.748214i \(-0.730912\pi\)
−0.663458 + 0.748214i \(0.730912\pi\)
\(450\) 0 0
\(451\) −1.88316 −0.0886744
\(452\) −35.7921 + 20.6646i −1.68352 + 0.971980i
\(453\) 0 0
\(454\) −0.372281 + 0.644810i −0.0174720 + 0.0302624i
\(455\) 9.76631 30.2921i 0.457852 1.42011i
\(456\) 0 0
\(457\) −7.67527 + 4.43132i −0.359034 + 0.207288i −0.668657 0.743571i \(-0.733130\pi\)
0.309623 + 0.950859i \(0.399797\pi\)
\(458\) 57.0651i 2.66648i
\(459\) 0 0
\(460\) 10.3723 + 48.2574i 0.483610 + 2.25001i
\(461\) −19.5475 33.8573i −0.910420 1.57689i −0.813472 0.581604i \(-0.802425\pi\)
−0.0969482 0.995289i \(-0.530908\pi\)
\(462\) 0 0
\(463\) 12.0000 + 6.92820i 0.557687 + 0.321981i 0.752217 0.658916i \(-0.228985\pi\)
−0.194529 + 0.980897i \(0.562318\pi\)
\(464\) −18.3030 + 31.7017i −0.849695 + 1.47171i
\(465\) 0 0
\(466\) 11.9307 + 20.6646i 0.552679 + 0.957268i
\(467\) 14.8511i 0.687226i 0.939111 + 0.343613i \(0.111651\pi\)
−0.939111 + 0.343613i \(0.888349\pi\)
\(468\) 0 0
\(469\) 28.4674 1.31450
\(470\) −32.2337 35.6357i −1.48683 1.64375i
\(471\) 0 0
\(472\) 38.2337 + 22.0742i 1.75985 + 1.01605i
\(473\) 4.11684 + 2.37686i 0.189293 + 0.109288i
\(474\) 0 0
\(475\) 21.8030 + 15.6896i 1.00039 + 0.719890i
\(476\) 38.2337 1.75244
\(477\) 0 0
\(478\) 58.0049i 2.65308i
\(479\) 10.8030 + 18.7113i 0.493601 + 0.854942i 0.999973 0.00737327i \(-0.00234701\pi\)
−0.506372 + 0.862315i \(0.669014\pi\)
\(480\) 0 0
\(481\) 15.5584 26.9480i 0.709403 1.22872i
\(482\) 53.5367 + 30.9094i 2.43853 + 1.40789i
\(483\) 0 0
\(484\) −19.9307 34.5210i −0.905941 1.56914i
\(485\) 8.74456 + 40.6844i 0.397070 + 1.84738i
\(486\) 0 0
\(487\) 30.2921i 1.37266i 0.727288 + 0.686332i \(0.240780\pi\)
−0.727288 + 0.686332i \(0.759220\pi\)
\(488\) −18.8139 + 10.8622i −0.851663 + 0.491708i
\(489\) 0 0
\(490\) 26.8614 + 8.66025i 1.21347 + 0.391230i
\(491\) −18.6861 + 32.3653i −0.843294 + 1.46063i 0.0438011 + 0.999040i \(0.486053\pi\)
−0.887095 + 0.461587i \(0.847280\pi\)
\(492\) 0 0
\(493\) 12.5584 7.25061i 0.565603 0.326551i
\(494\) 55.7228 2.50709
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) 12.3505 7.13058i 0.553997 0.319850i
\(498\) 0 0
\(499\) −9.31386 + 16.1321i −0.416946 + 0.722171i −0.995631 0.0933802i \(-0.970233\pi\)
0.578685 + 0.815551i \(0.303566\pi\)
\(500\) −5.44158 48.5798i −0.243355 2.17255i
\(501\) 0 0
\(502\) −31.1168 + 17.9653i −1.38881 + 0.801831i
\(503\) 10.0974i 0.450219i 0.974334 + 0.225109i \(0.0722739\pi\)
−0.974334 + 0.225109i \(0.927726\pi\)
\(504\) 0 0
\(505\) 23.2337 4.99377i 1.03389 0.222220i
\(506\) 8.74456 + 15.1460i 0.388743 + 0.673323i
\(507\) 0 0
\(508\) −39.3505 22.7190i −1.74590 1.00799i
\(509\) −11.7446 + 20.3422i −0.520569 + 0.901651i 0.479145 + 0.877736i \(0.340947\pi\)
−0.999714 + 0.0239157i \(0.992387\pi\)
\(510\) 0 0
\(511\) −13.1168 22.7190i −0.580255 1.00503i
\(512\) 50.1369i 2.21576i
\(513\) 0 0
\(514\) 58.0951 2.56246
\(515\) 11.4891 10.3923i 0.506271 0.457940i
\(516\) 0 0
\(517\) −10.1168 5.84096i −0.444938 0.256885i
\(518\) 57.3505 + 33.1113i 2.51984 + 1.45483i
\(519\) 0 0
\(520\) −36.9090 40.8044i −1.61856 1.78939i
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 15.1460i 0.662290i −0.943580 0.331145i \(-0.892565\pi\)
0.943580 0.331145i \(-0.107435\pi\)
\(524\) 3.00000 + 5.19615i 0.131056 + 0.226995i
\(525\) 0 0
\(526\) 33.4891 58.0049i 1.46020 2.52913i
\(527\) −1.37228 0.792287i −0.0597775 0.0345126i
\(528\) 0 0
\(529\) 1.24456 + 2.15565i 0.0541114 + 0.0937237i
\(530\) −29.4891 + 6.33830i −1.28093 + 0.275318i
\(531\) 0 0
\(532\) 81.3687i 3.52778i
\(533\) 4.88316 2.81929i 0.211513 0.122117i
\(534\) 0 0
\(535\) 28.2337 + 9.10268i 1.22065 + 0.393543i
\(536\) 24.6060 42.6188i 1.06282 1.84085i
\(537\) 0 0
\(538\) 11.4416 6.60580i 0.493281 0.284796i
\(539\) 6.86141 0.295542
\(540\) 0 0
\(541\) −15.2337 −0.654947 −0.327474 0.944860i \(-0.606197\pi\)
−0.327474 + 0.944860i \(0.606197\pi\)
\(542\) 36.6060 21.1345i 1.57236 0.907803i
\(543\) 0 0
\(544\) 5.18614 8.98266i 0.222354 0.385128i
\(545\) −1.19702 + 3.71277i −0.0512745 + 0.159038i
\(546\) 0 0
\(547\) −6.00000 + 3.46410i −0.256541 + 0.148114i −0.622756 0.782416i \(-0.713987\pi\)
0.366214 + 0.930531i \(0.380654\pi\)
\(548\) 9.74749i 0.416392i
\(549\) 0 0
\(550\) −7.11684 15.7908i −0.303463 0.673324i
\(551\) 15.4307 + 26.7268i 0.657370 + 1.13860i
\(552\) 0 0
\(553\) −14.2337 8.21782i −0.605278 0.349457i
\(554\) −2.74456 + 4.75372i −0.116605 + 0.201966i
\(555\) 0 0
\(556\) 13.3723 + 23.1615i 0.567111 + 0.982265i
\(557\) 21.7244i 0.920491i −0.887792 0.460246i \(-0.847761\pi\)
0.887792 0.460246i \(-0.152239\pi\)
\(558\) 0 0
\(559\) −14.2337 −0.602021
\(560\) 36.6060 33.1113i 1.54688 1.39921i
\(561\) 0 0
\(562\) 9.55842 + 5.51856i 0.403198 + 0.232786i
\(563\) −0.861407 0.497333i −0.0363040 0.0209601i 0.481738 0.876315i \(-0.340006\pi\)
−0.518042 + 0.855355i \(0.673339\pi\)
\(564\) 0 0
\(565\) 15.6753 14.1788i 0.659463 0.596507i
\(566\) −69.9565 −2.94049
\(567\) 0 0
\(568\) 24.6535i 1.03444i
\(569\) 1.24456 + 2.15565i 0.0521748 + 0.0903694i 0.890933 0.454134i \(-0.150051\pi\)
−0.838758 + 0.544504i \(0.816718\pi\)
\(570\) 0 0
\(571\) −16.4307 + 28.4588i −0.687604 + 1.19096i 0.285007 + 0.958525i \(0.408004\pi\)
−0.972611 + 0.232439i \(0.925329\pi\)
\(572\) −21.3505 12.3267i −0.892711 0.515407i
\(573\) 0 0
\(574\) 6.00000 + 10.3923i 0.250435 + 0.433766i
\(575\) −10.3723 23.0140i −0.432554 0.959750i
\(576\) 0 0
\(577\) 28.3576i 1.18054i 0.807205 + 0.590272i \(0.200979\pi\)
−0.807205 + 0.590272i \(0.799021\pi\)
\(578\) 23.2337 13.4140i 0.966394 0.557948i
\(579\) 0 0
\(580\) 17.2337 53.4535i 0.715590 2.21954i
\(581\) 9.25544 16.0309i 0.383980 0.665073i
\(582\) 0 0
\(583\) −6.35053 + 3.66648i −0.263012 + 0.151850i
\(584\) −45.3505 −1.87662
\(585\) 0 0
\(586\) −6.37228 −0.263237
\(587\) −8.48913 + 4.90120i −0.350384 + 0.202294i −0.664854 0.746973i \(-0.731506\pi\)
0.314471 + 0.949267i \(0.398173\pi\)
\(588\) 0 0
\(589\) 1.68614 2.92048i 0.0694762 0.120336i
\(590\) −39.6060 12.7692i −1.63055 0.525698i
\(591\) 0 0
\(592\) 41.7921 24.1287i 1.71765 0.991683i
\(593\) 38.1600i 1.56704i −0.621364 0.783522i \(-0.713421\pi\)
0.621364 0.783522i \(-0.286579\pi\)
\(594\) 0 0
\(595\) −19.1168 + 4.10891i −0.783714 + 0.168449i
\(596\) 35.7921 + 61.9938i 1.46610 + 2.53936i
\(597\) 0 0
\(598\) −45.3505 26.1831i −1.85452 1.07071i
\(599\) −3.68614 + 6.38458i −0.150612 + 0.260867i −0.931452 0.363863i \(-0.881458\pi\)
0.780841 + 0.624730i \(0.214791\pi\)
\(600\) 0 0
\(601\) −13.9891 24.2299i −0.570628 0.988357i −0.996502 0.0835744i \(-0.973366\pi\)
0.425873 0.904783i \(-0.359967\pi\)
\(602\) 30.2921i 1.23461i
\(603\) 0 0
\(604\) −79.2119 −3.22309
\(605\) 13.6753 + 15.1186i 0.555979 + 0.614657i
\(606\) 0 0
\(607\) −31.4674 18.1677i −1.27722 0.737404i −0.300885 0.953661i \(-0.597282\pi\)
−0.976337 + 0.216256i \(0.930615\pi\)
\(608\) 19.1168 + 11.0371i 0.775290 + 0.447614i
\(609\) 0 0
\(610\) 15.1861 13.7364i 0.614869 0.556170i
\(611\) 34.9783 1.41507
\(612\) 0 0
\(613\) 9.50744i 0.384002i −0.981395 0.192001i \(-0.938502\pi\)
0.981395 0.192001i \(-0.0614977\pi\)
\(614\) 6.00000 + 10.3923i 0.242140 + 0.419399i
\(615\) 0 0
\(616\) 14.2337 24.6535i 0.573492 0.993317i
\(617\) −19.4198 11.2120i −0.781813 0.451380i 0.0552595 0.998472i \(-0.482401\pi\)
−0.837072 + 0.547092i \(0.815735\pi\)
\(618\) 0 0
\(619\) 2.00000 + 3.46410i 0.0803868 + 0.139234i 0.903416 0.428765i \(-0.141051\pi\)
−0.823029 + 0.567999i \(0.807718\pi\)
\(620\) −6.00000 + 1.28962i −0.240966 + 0.0517924i
\(621\) 0 0
\(622\) 32.4665i 1.30179i
\(623\) −9.00000 + 5.19615i −0.360577 + 0.208179i
\(624\) 0 0
\(625\) 7.94158 + 23.7051i 0.317663 + 0.948204i
\(626\) 6.81386 11.8020i 0.272337 0.471701i
\(627\) 0 0
\(628\) 81.1426 46.8477i 3.23794 1.86943i
\(629\) −19.1168 −0.762238
\(630\) 0 0
\(631\) 0.627719 0.0249891 0.0124945 0.999922i \(-0.496023\pi\)
0.0124945 + 0.999922i \(0.496023\pi\)
\(632\) −24.6060 + 14.2063i −0.978773 + 0.565095i
\(633\) 0 0
\(634\) −8.81386 + 15.2661i −0.350043 + 0.606292i
\(635\) 22.1168 + 7.13058i 0.877680 + 0.282969i
\(636\) 0 0
\(637\) −17.7921 + 10.2723i −0.704949 + 0.407003i
\(638\) 19.8997i 0.787839i
\(639\) 0 0
\(640\) 6.67527 + 31.0569i 0.263863 + 1.22763i
\(641\) −18.9891 32.8901i −0.750025 1.29908i −0.947810 0.318836i \(-0.896708\pi\)
0.197784 0.980246i \(-0.436625\pi\)
\(642\) 0 0
\(643\) 16.1168 + 9.30506i 0.635586 + 0.366956i 0.782912 0.622132i \(-0.213733\pi\)
−0.147326 + 0.989088i \(0.547067\pi\)
\(644\) 38.2337 66.2227i 1.50662 2.60954i
\(645\) 0 0
\(646\) −17.1168 29.6472i −0.673453 1.16646i
\(647\) 4.45877i 0.175292i 0.996152 + 0.0876461i \(0.0279345\pi\)
−0.996152 + 0.0876461i \(0.972066\pi\)
\(648\) 0 0
\(649\) −10.1168 −0.397121
\(650\) 42.0951 + 30.2921i 1.65111 + 1.18815i
\(651\) 0 0
\(652\) 18.0000 + 10.3923i 0.704934 + 0.406994i
\(653\) 17.4891 + 10.0974i 0.684402 + 0.395140i 0.801512 0.597979i \(-0.204029\pi\)
−0.117109 + 0.993119i \(0.537363\pi\)
\(654\) 0 0
\(655\) −2.05842 2.27567i −0.0804292 0.0889178i
\(656\) 8.74456 0.341418
\(657\) 0 0
\(658\) 74.4405i 2.90199i
\(659\) −16.3723 28.3576i −0.637774 1.10466i −0.985920 0.167216i \(-0.946522\pi\)
0.348147 0.937440i \(-0.386811\pi\)
\(660\) 0 0
\(661\) −9.61684 + 16.6569i −0.374052 + 0.647877i −0.990185 0.139765i \(-0.955365\pi\)
0.616133 + 0.787642i \(0.288698\pi\)
\(662\) 17.7446 + 10.2448i 0.689662 + 0.398177i
\(663\) 0 0
\(664\) −16.0000 27.7128i −0.620920 1.07547i
\(665\) −8.74456 40.6844i −0.339100 1.57767i
\(666\) 0 0
\(667\) 29.0024i 1.12298i
\(668\) 1.11684 0.644810i 0.0432120 0.0249485i
\(669\) 0 0
\(670\) −14.2337 + 44.1485i −0.549895 + 1.70560i
\(671\) 2.48913 4.31129i 0.0960916 0.166436i
\(672\) 0 0
\(673\) −16.6753 + 9.62747i −0.642784 + 0.371112i −0.785686 0.618625i \(-0.787690\pi\)
0.142902 + 0.989737i \(0.454357\pi\)
\(674\) −17.4891 −0.673656
\(675\) 0 0
\(676\) 16.9783 0.653010
\(677\) 22.9783 13.2665i 0.883126 0.509873i 0.0114381 0.999935i \(-0.496359\pi\)
0.871688 + 0.490062i \(0.163026\pi\)
\(678\) 0 0
\(679\) 32.2337 55.8304i 1.23702 2.14257i
\(680\) −10.3723 + 32.1716i −0.397759 + 1.23372i
\(681\) 0 0
\(682\) −1.88316 + 1.08724i −0.0721098 + 0.0416326i
\(683\) 0.589907i 0.0225722i 0.999936 + 0.0112861i \(0.00359255\pi\)
−0.999936 + 0.0112861i \(0.996407\pi\)
\(684\) 0 0
\(685\) −1.04755 4.87375i −0.0400247 0.186216i
\(686\) 8.74456 + 15.1460i 0.333869 + 0.578278i
\(687\) 0 0
\(688\) −19.1168 11.0371i −0.728823 0.420786i
\(689\) 10.9783 19.0149i 0.418238 0.724410i
\(690\) 0 0
\(691\) 5.86141 + 10.1523i 0.222978 + 0.386210i 0.955711 0.294307i \(-0.0950887\pi\)
−0.732733 + 0.680517i \(0.761755\pi\)
\(692\) 34.4010i 1.30773i
\(693\) 0 0
\(694\) 59.7228 2.26705
\(695\) −9.17527 10.1436i −0.348038 0.384770i
\(696\) 0 0
\(697\) −3.00000 1.73205i −0.113633 0.0656061i
\(698\) 29.7446 + 17.1730i 1.12585 + 0.650009i
\(699\) 0 0
\(700\) −44.2337 + 61.4690i −1.67188 + 2.32331i
\(701\) 17.2337 0.650907 0.325454 0.945558i \(-0.394483\pi\)
0.325454 + 0.945558i \(0.394483\pi\)
\(702\) 0 0
\(703\) 40.6844i 1.53444i
\(704\) 1.62772 + 2.81929i 0.0613470 + 0.106256i
\(705\) 0 0
\(706\) −10.7446 + 18.6101i −0.404377 + 0.700401i
\(707\) −31.8832 18.4077i −1.19909 0.692295i
\(708\) 0 0
\(709\) 0.324734 + 0.562456i 0.0121956 + 0.0211235i 0.872059 0.489401i \(-0.162785\pi\)
−0.859863 + 0.510525i \(0.829451\pi\)
\(710\) 4.88316 + 22.7190i 0.183262 + 0.852630i
\(711\) 0 0
\(712\) 17.9653i 0.673279i
\(713\) −2.74456 + 1.58457i −0.102785 + 0.0593428i
\(714\) 0 0
\(715\) 12.0000 + 3.86886i 0.448775 + 0.144687i
\(716\) −48.3505 + 83.7456i −1.80694 + 3.12972i
\(717\) 0 0
\(718\) −61.4674 + 35.4882i −2.29394 + 1.32441i
\(719\) 28.1168 1.04858 0.524291 0.851539i \(-0.324331\pi\)
0.524291 + 0.851539i \(0.324331\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 21.5584 12.4468i 0.802321 0.463220i
\(723\) 0 0
\(724\) 32.4891 56.2728i 1.20745 2.09136i
\(725\) −2.87228 + 28.5788i −0.106674 + 1.06139i
\(726\) 0 0
\(727\) −9.35053 + 5.39853i −0.346792 + 0.200220i −0.663271 0.748379i \(-0.730833\pi\)
0.316479 + 0.948599i \(0.397499\pi\)
\(728\) 85.2376i 3.15911i
\(729\) 0 0
\(730\) 41.7921 8.98266i 1.54680 0.332463i
\(731\) 4.37228 + 7.57301i 0.161715 + 0.280098i
\(732\) 0 0
\(733\) 20.2337 + 11.6819i 0.747348 + 0.431482i 0.824735 0.565519i \(-0.191324\pi\)
−0.0773867 + 0.997001i \(0.524658\pi\)
\(734\) 29.4891 51.0767i 1.08846 1.88527i
\(735\) 0 0
\(736\) −10.3723 17.9653i −0.382327 0.662210i
\(737\) 11.2772i 0.415400i
\(738\) 0 0
\(739\) −11.3723 −0.418336 −0.209168 0.977880i \(-0.567076\pi\)
−0.209168 + 0.977880i \(0.567076\pi\)
\(740\) −54.9090 + 49.6670i −2.01849 + 1.82580i
\(741\) 0 0
\(742\) 40.4674 + 23.3639i 1.48560 + 0.857714i
\(743\) −36.8614 21.2819i −1.35231 0.780759i −0.363741 0.931500i \(-0.618501\pi\)
−0.988573 + 0.150742i \(0.951834\pi\)
\(744\) 0 0
\(745\) −24.5584 27.1504i −0.899751 0.994712i
\(746\) −29.4891 −1.07967
\(747\) 0 0
\(748\) 15.1460i 0.553794i
\(749\) −22.9783 39.7995i −0.839607 1.45424i
\(750\) 0 0
\(751\) 17.8614 30.9369i 0.651772 1.12890i −0.330921 0.943659i \(-0.607359\pi\)
0.982693 0.185244i \(-0.0593074\pi\)
\(752\) 46.9783 + 27.1229i 1.71312 + 0.989071i
\(753\) 0 0
\(754\) 29.7921 + 51.6014i 1.08496 + 1.87921i
\(755\) 39.6060 8.51278i 1.44141 0.309812i
\(756\) 0 0
\(757\) 41.5692i 1.51086i −0.655230 0.755429i \(-0.727428\pi\)
0.655230 0.755429i \(-0.272572\pi\)
\(758\) −46.9783 + 27.1229i −1.70633 + 0.985148i
\(759\) 0 0
\(760\) −68.4674 22.0742i −2.48357 0.800716i
\(761\) 4.75544 8.23666i 0.172384 0.298579i −0.766869 0.641804i \(-0.778186\pi\)
0.939253 + 0.343226i \(0.111520\pi\)
\(762\) 0 0
\(763\) 5.23369 3.02167i 0.189472 0.109392i
\(764\) 58.4674 2.11528
\(765\) 0 0
\(766\) 89.2119 3.22336
\(767\) 26.2337 15.1460i 0.947244 0.546891i
\(768\) 0 0
\(769\) 3.24456 5.61975i 0.117002 0.202653i −0.801576 0.597892i \(-0.796005\pi\)
0.918578 + 0.395239i \(0.129338\pi\)
\(770\) −8.23369 + 25.5383i −0.296722 + 0.920338i
\(771\) 0 0
\(772\) 81.1426 46.8477i 2.92039 1.68609i
\(773\) 18.2603i 0.656776i −0.944543 0.328388i \(-0.893495\pi\)
0.944543 0.328388i \(-0.106505\pi\)
\(774\) 0 0
\(775\) 2.86141 1.28962i 0.102785 0.0463245i
\(776\) −55.7228 96.5147i −2.00033 3.46468i
\(777\) 0 0
\(778\) 51.3505 + 29.6472i 1.84101 + 1.06291i
\(779\) 3.68614 6.38458i 0.132070 0.228751i
\(780\) 0 0
\(781\) 2.82473