Properties

Label 666.2.bs.b.17.6
Level $666$
Weight $2$
Character 666.17
Analytic conductor $5.318$
Analytic rank $0$
Dimension $96$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [666,2,Mod(17,666)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(666, base_ring=CyclotomicField(36))
 
chi = DirichletCharacter(H, H._module([18, 7]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("666.17");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 666.bs (of order \(36\), degree \(12\), 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: \(5.31803677462\)
Analytic rank: \(0\)
Dimension: \(96\)
Relative dimension: \(8\) over \(\Q(\zeta_{36})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label 17.6
Character \(\chi\) \(=\) 666.17
Dual form 666.2.bs.b.431.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.573576 - 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-1.31281 + 0.114856i) q^{5} +(-1.79970 - 1.51012i) q^{7} +(-0.965926 - 0.258819i) q^{8} +O(q^{10})\) \(q+(0.573576 - 0.819152i) q^{2} +(-0.342020 - 0.939693i) q^{4} +(-1.31281 + 0.114856i) q^{5} +(-1.79970 - 1.51012i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(-0.658910 + 1.14127i) q^{10} +(1.26790 + 2.19607i) q^{11} +(-5.68512 - 2.65102i) q^{13} +(-2.26929 + 0.608053i) q^{14} +(-0.766044 + 0.642788i) q^{16} +(2.17248 - 1.01304i) q^{17} +(-5.10508 + 3.57462i) q^{19} +(0.556935 + 1.19435i) q^{20} +(2.52616 + 0.221010i) q^{22} +(-1.95836 - 7.30871i) q^{23} +(-3.21377 + 0.566675i) q^{25} +(-5.43244 + 3.13642i) q^{26} +(-0.803520 + 2.20765i) q^{28} +(-2.27295 + 8.48275i) q^{29} +(1.77815 - 1.77815i) q^{31} +(0.0871557 + 0.996195i) q^{32} +(0.416246 - 2.36065i) q^{34} +(2.53610 + 1.77580i) q^{35} +(-6.02076 + 0.866319i) q^{37} +6.23215i q^{38} +(1.29780 + 0.228837i) q^{40} +(10.3026 - 3.74984i) q^{41} +(-0.789016 - 0.789016i) q^{43} +(1.62998 - 1.94254i) q^{44} +(-7.11021 - 2.58791i) q^{46} +(-9.67161 - 5.58391i) q^{47} +(-0.257106 - 1.45812i) q^{49} +(-1.37915 + 2.95760i) q^{50} +(-0.546714 + 6.24897i) q^{52} +(1.18964 + 1.41776i) q^{53} +(-1.91674 - 2.73739i) q^{55} +(1.34752 + 1.92446i) q^{56} +(5.64495 + 6.72739i) q^{58} +(-0.761646 + 8.70565i) q^{59} +(4.69196 - 10.0620i) q^{61} +(-0.436671 - 2.47649i) q^{62} +(0.866025 + 0.500000i) q^{64} +(7.76795 + 2.82730i) q^{65} +(5.02896 - 5.99328i) q^{67} +(-1.69498 - 1.69498i) q^{68} +(2.90929 - 1.05890i) q^{70} +(4.03601 + 0.711657i) q^{71} -10.8547i q^{73} +(-2.74372 + 5.42881i) q^{74} +(5.10508 + 3.57462i) q^{76} +(1.03450 - 5.86695i) q^{77} +(0.818534 + 9.35588i) q^{79} +(0.931840 - 0.931840i) q^{80} +(2.83764 - 10.5902i) q^{82} +(-0.388056 + 1.06617i) q^{83} +(-2.73569 + 1.57945i) q^{85} +(-1.09888 + 0.193763i) q^{86} +(-0.656315 - 2.44940i) q^{88} +(-0.317556 - 0.0277825i) q^{89} +(6.22813 + 13.3563i) q^{91} +(-6.19814 + 4.33998i) q^{92} +(-10.1215 + 4.71972i) q^{94} +(6.29142 - 5.27913i) q^{95} +(12.8298 - 3.43773i) q^{97} +(-1.34189 - 0.625736i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q+O(q^{10}) \) Copy content Toggle raw display \( 96 q - 12 q^{13} + 24 q^{19} + 12 q^{22} + 48 q^{31} + 72 q^{34} + 24 q^{37} + 72 q^{43} + 60 q^{46} + 12 q^{52} - 60 q^{55} + 12 q^{58} - 120 q^{61} + 36 q^{67} + 12 q^{70} - 24 q^{76} + 60 q^{79} + 96 q^{82} - 108 q^{85} - 24 q^{88} + 216 q^{91} - 60 q^{94} + 24 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\)
\(\chi(n)\) \(-1\) \(e\left(\frac{7}{36}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.573576 0.819152i 0.405580 0.579228i
\(3\) 0 0
\(4\) −0.342020 0.939693i −0.171010 0.469846i
\(5\) −1.31281 + 0.114856i −0.587105 + 0.0513650i −0.376838 0.926279i \(-0.622989\pi\)
−0.210267 + 0.977644i \(0.567433\pi\)
\(6\) 0 0
\(7\) −1.79970 1.51012i −0.680221 0.570773i 0.235850 0.971790i \(-0.424213\pi\)
−0.916071 + 0.401016i \(0.868657\pi\)
\(8\) −0.965926 0.258819i −0.341506 0.0915064i
\(9\) 0 0
\(10\) −0.658910 + 1.14127i −0.208366 + 0.360900i
\(11\) 1.26790 + 2.19607i 0.382287 + 0.662141i 0.991389 0.130951i \(-0.0418032\pi\)
−0.609102 + 0.793092i \(0.708470\pi\)
\(12\) 0 0
\(13\) −5.68512 2.65102i −1.57677 0.735260i −0.579928 0.814668i \(-0.696919\pi\)
−0.996842 + 0.0794083i \(0.974697\pi\)
\(14\) −2.26929 + 0.608053i −0.606492 + 0.162509i
\(15\) 0 0
\(16\) −0.766044 + 0.642788i −0.191511 + 0.160697i
\(17\) 2.17248 1.01304i 0.526903 0.245699i −0.140917 0.990021i \(-0.545005\pi\)
0.667820 + 0.744322i \(0.267227\pi\)
\(18\) 0 0
\(19\) −5.10508 + 3.57462i −1.17119 + 0.820073i −0.986666 0.162755i \(-0.947962\pi\)
−0.184520 + 0.982829i \(0.559073\pi\)
\(20\) 0.556935 + 1.19435i 0.124534 + 0.267065i
\(21\) 0 0
\(22\) 2.52616 + 0.221010i 0.538578 + 0.0471195i
\(23\) −1.95836 7.30871i −0.408347 1.52397i −0.797799 0.602924i \(-0.794002\pi\)
0.389452 0.921047i \(-0.372665\pi\)
\(24\) 0 0
\(25\) −3.21377 + 0.566675i −0.642754 + 0.113335i
\(26\) −5.43244 + 3.13642i −1.06539 + 0.615103i
\(27\) 0 0
\(28\) −0.803520 + 2.20765i −0.151851 + 0.417207i
\(29\) −2.27295 + 8.48275i −0.422075 + 1.57521i 0.348152 + 0.937438i \(0.386809\pi\)
−0.770228 + 0.637769i \(0.779857\pi\)
\(30\) 0 0
\(31\) 1.77815 1.77815i 0.319366 0.319366i −0.529158 0.848524i \(-0.677492\pi\)
0.848524 + 0.529158i \(0.177492\pi\)
\(32\) 0.0871557 + 0.996195i 0.0154071 + 0.176104i
\(33\) 0 0
\(34\) 0.416246 2.36065i 0.0713856 0.404848i
\(35\) 2.53610 + 1.77580i 0.428679 + 0.300164i
\(36\) 0 0
\(37\) −6.02076 + 0.866319i −0.989806 + 0.142422i
\(38\) 6.23215i 1.01099i
\(39\) 0 0
\(40\) 1.29780 + 0.228837i 0.205200 + 0.0361823i
\(41\) 10.3026 3.74984i 1.60899 0.585626i 0.627753 0.778412i \(-0.283975\pi\)
0.981241 + 0.192787i \(0.0617525\pi\)
\(42\) 0 0
\(43\) −0.789016 0.789016i −0.120324 0.120324i 0.644381 0.764705i \(-0.277115\pi\)
−0.764705 + 0.644381i \(0.777115\pi\)
\(44\) 1.62998 1.94254i 0.245729 0.292849i
\(45\) 0 0
\(46\) −7.11021 2.58791i −1.04834 0.381566i
\(47\) −9.67161 5.58391i −1.41075 0.814496i −0.415290 0.909689i \(-0.636320\pi\)
−0.995459 + 0.0951926i \(0.969653\pi\)
\(48\) 0 0
\(49\) −0.257106 1.45812i −0.0367295 0.208303i
\(50\) −1.37915 + 2.95760i −0.195041 + 0.418268i
\(51\) 0 0
\(52\) −0.546714 + 6.24897i −0.0758156 + 0.866576i
\(53\) 1.18964 + 1.41776i 0.163409 + 0.194744i 0.841536 0.540202i \(-0.181652\pi\)
−0.678126 + 0.734946i \(0.737208\pi\)
\(54\) 0 0
\(55\) −1.91674 2.73739i −0.258453 0.369110i
\(56\) 1.34752 + 1.92446i 0.180070 + 0.257167i
\(57\) 0 0
\(58\) 5.64495 + 6.72739i 0.741219 + 0.883350i
\(59\) −0.761646 + 8.70565i −0.0991579 + 1.13338i 0.769730 + 0.638370i \(0.220391\pi\)
−0.868887 + 0.495010i \(0.835165\pi\)
\(60\) 0 0
\(61\) 4.69196 10.0620i 0.600745 1.28830i −0.337173 0.941443i \(-0.609471\pi\)
0.937918 0.346858i \(-0.112751\pi\)
\(62\) −0.436671 2.47649i −0.0554573 0.314514i
\(63\) 0 0
\(64\) 0.866025 + 0.500000i 0.108253 + 0.0625000i
\(65\) 7.76795 + 2.82730i 0.963496 + 0.350684i
\(66\) 0 0
\(67\) 5.02896 5.99328i 0.614385 0.732196i −0.365709 0.930729i \(-0.619173\pi\)
0.980094 + 0.198534i \(0.0636179\pi\)
\(68\) −1.69498 1.69498i −0.205547 0.205547i
\(69\) 0 0
\(70\) 2.90929 1.05890i 0.347727 0.126562i
\(71\) 4.03601 + 0.711657i 0.478986 + 0.0844582i 0.407928 0.913014i \(-0.366251\pi\)
0.0710580 + 0.997472i \(0.477362\pi\)
\(72\) 0 0
\(73\) 10.8547i 1.27044i −0.772330 0.635222i \(-0.780909\pi\)
0.772330 0.635222i \(-0.219091\pi\)
\(74\) −2.74372 + 5.42881i −0.318951 + 0.631087i
\(75\) 0 0
\(76\) 5.10508 + 3.57462i 0.585593 + 0.410037i
\(77\) 1.03450 5.86695i 0.117892 0.668601i
\(78\) 0 0
\(79\) 0.818534 + 9.35588i 0.0920922 + 1.05262i 0.891861 + 0.452310i \(0.149400\pi\)
−0.799768 + 0.600309i \(0.795044\pi\)
\(80\) 0.931840 0.931840i 0.104183 0.104183i
\(81\) 0 0
\(82\) 2.83764 10.5902i 0.313365 1.16949i
\(83\) −0.388056 + 1.06617i −0.0425947 + 0.117028i −0.959166 0.282842i \(-0.908723\pi\)
0.916572 + 0.399870i \(0.130945\pi\)
\(84\) 0 0
\(85\) −2.73569 + 1.57945i −0.296727 + 0.171315i
\(86\) −1.09888 + 0.193763i −0.118496 + 0.0208940i
\(87\) 0 0
\(88\) −0.656315 2.44940i −0.0699634 0.261107i
\(89\) −0.317556 0.0277825i −0.0336609 0.00294494i 0.0703129 0.997525i \(-0.477600\pi\)
−0.103974 + 0.994580i \(0.533156\pi\)
\(90\) 0 0
\(91\) 6.22813 + 13.3563i 0.652886 + 1.40012i
\(92\) −6.19814 + 4.33998i −0.646201 + 0.452475i
\(93\) 0 0
\(94\) −10.1215 + 4.71972i −1.04395 + 0.486802i
\(95\) 6.29142 5.27913i 0.645486 0.541627i
\(96\) 0 0
\(97\) 12.8298 3.43773i 1.30267 0.349049i 0.460209 0.887811i \(-0.347774\pi\)
0.842458 + 0.538762i \(0.181108\pi\)
\(98\) −1.34189 0.625736i −0.135552 0.0632088i
\(99\) 0 0
\(100\) 1.63167 + 2.82614i 0.163167 + 0.282614i
\(101\) −0.0476198 + 0.0824799i −0.00473834 + 0.00820705i −0.868385 0.495891i \(-0.834842\pi\)
0.863647 + 0.504098i \(0.168175\pi\)
\(102\) 0 0
\(103\) −6.75270 1.80938i −0.665364 0.178284i −0.0896982 0.995969i \(-0.528590\pi\)
−0.575665 + 0.817685i \(0.695257\pi\)
\(104\) 4.80527 + 4.03210i 0.471196 + 0.395380i
\(105\) 0 0
\(106\) 1.84371 0.161303i 0.179077 0.0156672i
\(107\) −3.41452 9.38130i −0.330094 0.906925i −0.988086 0.153901i \(-0.950816\pi\)
0.657993 0.753024i \(-0.271406\pi\)
\(108\) 0 0
\(109\) −1.53963 + 2.19883i −0.147470 + 0.210609i −0.886090 0.463513i \(-0.846589\pi\)
0.738620 + 0.674122i \(0.235478\pi\)
\(110\) −3.34174 −0.318622
\(111\) 0 0
\(112\) 2.34934 0.221991
\(113\) −4.72723 + 6.75118i −0.444700 + 0.635098i −0.977448 0.211176i \(-0.932271\pi\)
0.532748 + 0.846274i \(0.321159\pi\)
\(114\) 0 0
\(115\) 3.41040 + 9.36999i 0.318021 + 0.873756i
\(116\) 8.74857 0.765401i 0.812284 0.0710657i
\(117\) 0 0
\(118\) 6.69439 + 5.61726i 0.616269 + 0.517111i
\(119\) −5.43962 1.45754i −0.498649 0.133613i
\(120\) 0 0
\(121\) 2.28485 3.95747i 0.207713 0.359770i
\(122\) −5.55107 9.61473i −0.502570 0.870477i
\(123\) 0 0
\(124\) −2.27908 1.06275i −0.204668 0.0954381i
\(125\) 10.5186 2.81844i 0.940808 0.252089i
\(126\) 0 0
\(127\) −10.4018 + 8.72817i −0.923013 + 0.774500i −0.974550 0.224171i \(-0.928033\pi\)
0.0515366 + 0.998671i \(0.483588\pi\)
\(128\) 0.906308 0.422618i 0.0801070 0.0373545i
\(129\) 0 0
\(130\) 6.77150 4.74146i 0.593900 0.415853i
\(131\) 0.343220 + 0.736037i 0.0299873 + 0.0643079i 0.920731 0.390198i \(-0.127594\pi\)
−0.890744 + 0.454506i \(0.849816\pi\)
\(132\) 0 0
\(133\) 14.5857 + 1.27608i 1.26474 + 0.110651i
\(134\) −2.02492 7.55709i −0.174926 0.652833i
\(135\) 0 0
\(136\) −2.36065 + 0.416246i −0.202424 + 0.0356928i
\(137\) 8.62186 4.97783i 0.736615 0.425285i −0.0842223 0.996447i \(-0.526841\pi\)
0.820837 + 0.571162i \(0.193507\pi\)
\(138\) 0 0
\(139\) 4.48900 12.3334i 0.380752 1.04611i −0.590289 0.807192i \(-0.700986\pi\)
0.971041 0.238915i \(-0.0767916\pi\)
\(140\) 0.801305 2.99051i 0.0677226 0.252744i
\(141\) 0 0
\(142\) 2.89792 2.89792i 0.243188 0.243188i
\(143\) −1.38636 15.8462i −0.115933 1.32512i
\(144\) 0 0
\(145\) 2.00965 11.3973i 0.166892 0.946491i
\(146\) −8.89163 6.22599i −0.735877 0.515266i
\(147\) 0 0
\(148\) 2.87329 + 5.36136i 0.236183 + 0.440701i
\(149\) 16.9610i 1.38950i −0.719252 0.694749i \(-0.755516\pi\)
0.719252 0.694749i \(-0.244484\pi\)
\(150\) 0 0
\(151\) −11.5457 2.03582i −0.939579 0.165673i −0.317173 0.948368i \(-0.602734\pi\)
−0.622406 + 0.782695i \(0.713845\pi\)
\(152\) 5.85631 2.13152i 0.475009 0.172889i
\(153\) 0 0
\(154\) −4.21256 4.21256i −0.339458 0.339458i
\(155\) −2.13014 + 2.53860i −0.171097 + 0.203905i
\(156\) 0 0
\(157\) 12.3075 + 4.47958i 0.982248 + 0.357509i 0.782714 0.622382i \(-0.213835\pi\)
0.199534 + 0.979891i \(0.436057\pi\)
\(158\) 8.13338 + 4.69581i 0.647057 + 0.373579i
\(159\) 0 0
\(160\) −0.228837 1.29780i −0.0180912 0.102600i
\(161\) −7.51260 + 16.1108i −0.592076 + 1.26971i
\(162\) 0 0
\(163\) −1.11467 + 12.7407i −0.0873078 + 0.997932i 0.818574 + 0.574401i \(0.194765\pi\)
−0.905882 + 0.423531i \(0.860790\pi\)
\(164\) −7.04739 8.39875i −0.550308 0.655832i
\(165\) 0 0
\(166\) 0.650780 + 0.929409i 0.0505103 + 0.0721362i
\(167\) −7.01571 10.0195i −0.542892 0.775330i 0.450167 0.892944i \(-0.351364\pi\)
−0.993059 + 0.117614i \(0.962475\pi\)
\(168\) 0 0
\(169\) 16.9365 + 20.1841i 1.30281 + 1.55263i
\(170\) −0.275316 + 3.14688i −0.0211158 + 0.241355i
\(171\) 0 0
\(172\) −0.471573 + 1.01129i −0.0359571 + 0.0771102i
\(173\) 0.949307 + 5.38379i 0.0721745 + 0.409322i 0.999394 + 0.0348039i \(0.0110807\pi\)
−0.927220 + 0.374518i \(0.877808\pi\)
\(174\) 0 0
\(175\) 6.63956 + 3.83335i 0.501904 + 0.289774i
\(176\) −2.38288 0.867297i −0.179616 0.0653749i
\(177\) 0 0
\(178\) −0.204901 + 0.244191i −0.0153580 + 0.0183029i
\(179\) −6.08023 6.08023i −0.454458 0.454458i 0.442373 0.896831i \(-0.354137\pi\)
−0.896831 + 0.442373i \(0.854137\pi\)
\(180\) 0 0
\(181\) −6.05881 + 2.20523i −0.450348 + 0.163913i −0.557230 0.830358i \(-0.688136\pi\)
0.106881 + 0.994272i \(0.465913\pi\)
\(182\) 14.5131 + 2.55906i 1.07578 + 0.189690i
\(183\) 0 0
\(184\) 7.56653i 0.557812i
\(185\) 7.80458 1.82883i 0.573804 0.134458i
\(186\) 0 0
\(187\) 4.97921 + 3.48648i 0.364116 + 0.254956i
\(188\) −1.93927 + 10.9981i −0.141436 + 0.802122i
\(189\) 0 0
\(190\) −0.715798 8.18161i −0.0519295 0.593556i
\(191\) −12.4651 + 12.4651i −0.901944 + 0.901944i −0.995604 0.0936599i \(-0.970143\pi\)
0.0936599 + 0.995604i \(0.470143\pi\)
\(192\) 0 0
\(193\) −5.29840 + 19.7739i −0.381387 + 1.42336i 0.462396 + 0.886673i \(0.346990\pi\)
−0.843783 + 0.536684i \(0.819677\pi\)
\(194\) 4.54284 12.4813i 0.326157 0.896108i
\(195\) 0 0
\(196\) −1.28225 + 0.740308i −0.0915894 + 0.0528792i
\(197\) 14.9921 2.64352i 1.06815 0.188343i 0.388177 0.921585i \(-0.373105\pi\)
0.679968 + 0.733242i \(0.261994\pi\)
\(198\) 0 0
\(199\) −6.16077 22.9923i −0.436726 1.62988i −0.736903 0.675999i \(-0.763712\pi\)
0.300177 0.953883i \(-0.402954\pi\)
\(200\) 3.25093 + 0.284420i 0.229875 + 0.0201115i
\(201\) 0 0
\(202\) 0.0402500 + 0.0863163i 0.00283198 + 0.00607320i
\(203\) 16.9006 11.8339i 1.18619 0.830580i
\(204\) 0 0
\(205\) −13.0946 + 6.10612i −0.914567 + 0.426470i
\(206\) −5.35535 + 4.49367i −0.373125 + 0.313089i
\(207\) 0 0
\(208\) 6.05910 1.62353i 0.420123 0.112572i
\(209\) −14.3229 6.67886i −0.990733 0.461987i
\(210\) 0 0
\(211\) −10.9534 18.9719i −0.754065 1.30608i −0.945838 0.324639i \(-0.894757\pi\)
0.191773 0.981439i \(-0.438576\pi\)
\(212\) 0.925375 1.60280i 0.0635550 0.110080i
\(213\) 0 0
\(214\) −9.64320 2.58389i −0.659196 0.176631i
\(215\) 1.12645 + 0.945201i 0.0768231 + 0.0644622i
\(216\) 0 0
\(217\) −5.88537 + 0.514903i −0.399525 + 0.0349539i
\(218\) 0.918075 + 2.52239i 0.0621799 + 0.170838i
\(219\) 0 0
\(220\) −1.91674 + 2.73739i −0.129227 + 0.184555i
\(221\) −15.0364 −1.01146
\(222\) 0 0
\(223\) −16.7142 −1.11926 −0.559632 0.828741i \(-0.689057\pi\)
−0.559632 + 0.828741i \(0.689057\pi\)
\(224\) 1.34752 1.92446i 0.0900352 0.128584i
\(225\) 0 0
\(226\) 2.81882 + 7.74464i 0.187505 + 0.515165i
\(227\) −15.3613 + 1.34394i −1.01956 + 0.0892003i −0.584662 0.811277i \(-0.698773\pi\)
−0.434902 + 0.900478i \(0.643217\pi\)
\(228\) 0 0
\(229\) −8.27385 6.94259i −0.546751 0.458779i 0.327088 0.944994i \(-0.393933\pi\)
−0.873839 + 0.486215i \(0.838377\pi\)
\(230\) 9.63157 + 2.58077i 0.635087 + 0.170171i
\(231\) 0 0
\(232\) 4.39099 7.60542i 0.288283 0.499321i
\(233\) 11.0002 + 19.0529i 0.720647 + 1.24820i 0.960741 + 0.277448i \(0.0894887\pi\)
−0.240093 + 0.970750i \(0.577178\pi\)
\(234\) 0 0
\(235\) 13.3383 + 6.21975i 0.870094 + 0.405732i
\(236\) 8.44114 2.26180i 0.549471 0.147230i
\(237\) 0 0
\(238\) −4.31399 + 3.61987i −0.279634 + 0.234641i
\(239\) 10.9181 5.09118i 0.706232 0.329321i −0.0361053 0.999348i \(-0.511495\pi\)
0.742337 + 0.670027i \(0.233717\pi\)
\(240\) 0 0
\(241\) 12.3898 8.67541i 0.798095 0.558832i −0.101868 0.994798i \(-0.532482\pi\)
0.899963 + 0.435966i \(0.143593\pi\)
\(242\) −1.93123 4.14155i −0.124144 0.266229i
\(243\) 0 0
\(244\) −11.0599 0.967615i −0.708037 0.0619452i
\(245\) 0.505004 + 1.88470i 0.0322636 + 0.120409i
\(246\) 0 0
\(247\) 38.4994 6.78848i 2.44966 0.431941i
\(248\) −2.17778 + 1.25734i −0.138289 + 0.0798415i
\(249\) 0 0
\(250\) 3.72447 10.2329i 0.235556 0.647185i
\(251\) −3.19993 + 11.9423i −0.201977 + 0.753790i 0.788372 + 0.615199i \(0.210924\pi\)
−0.990350 + 0.138592i \(0.955742\pi\)
\(252\) 0 0
\(253\) 13.5674 13.5674i 0.852977 0.852977i
\(254\) 1.18346 + 13.5270i 0.0742566 + 0.848757i
\(255\) 0 0
\(256\) 0.173648 0.984808i 0.0108530 0.0615505i
\(257\) −6.29396 4.40708i −0.392606 0.274906i 0.360560 0.932736i \(-0.382586\pi\)
−0.753166 + 0.657830i \(0.771474\pi\)
\(258\) 0 0
\(259\) 12.1438 + 7.53298i 0.754578 + 0.468077i
\(260\) 8.26648i 0.512665i
\(261\) 0 0
\(262\) 0.799789 + 0.141024i 0.0494111 + 0.00871252i
\(263\) −4.23067 + 1.53984i −0.260874 + 0.0949504i −0.469146 0.883120i \(-0.655438\pi\)
0.208272 + 0.978071i \(0.433216\pi\)
\(264\) 0 0
\(265\) −1.72460 1.72460i −0.105941 0.105941i
\(266\) 9.41133 11.2160i 0.577046 0.687696i
\(267\) 0 0
\(268\) −7.35185 2.67585i −0.449086 0.163454i
\(269\) −3.71281 2.14359i −0.226374 0.130697i 0.382524 0.923946i \(-0.375055\pi\)
−0.608898 + 0.793248i \(0.708388\pi\)
\(270\) 0 0
\(271\) 3.01658 + 17.1079i 0.183244 + 1.03923i 0.928191 + 0.372105i \(0.121364\pi\)
−0.744947 + 0.667124i \(0.767525\pi\)
\(272\) −1.01304 + 2.17248i −0.0614248 + 0.131726i
\(273\) 0 0
\(274\) 0.867693 9.91778i 0.0524193 0.599155i
\(275\) −5.31921 6.33918i −0.320760 0.382267i
\(276\) 0 0
\(277\) −0.592556 0.846257i −0.0356032 0.0508467i 0.800956 0.598723i \(-0.204325\pi\)
−0.836559 + 0.547877i \(0.815436\pi\)
\(278\) −7.52816 10.7513i −0.451509 0.644822i
\(279\) 0 0
\(280\) −1.99007 2.37168i −0.118930 0.141735i
\(281\) −1.51781 + 17.3487i −0.0905451 + 1.03494i 0.805980 + 0.591943i \(0.201639\pi\)
−0.896525 + 0.442993i \(0.853917\pi\)
\(282\) 0 0
\(283\) −8.61652 + 18.4782i −0.512199 + 1.09841i 0.464848 + 0.885390i \(0.346109\pi\)
−0.977047 + 0.213024i \(0.931669\pi\)
\(284\) −0.711657 4.03601i −0.0422291 0.239493i
\(285\) 0 0
\(286\) −13.7756 7.95335i −0.814569 0.470292i
\(287\) −24.2042 8.80963i −1.42873 0.520016i
\(288\) 0 0
\(289\) −7.23399 + 8.62113i −0.425529 + 0.507125i
\(290\) −8.18341 8.18341i −0.480546 0.480546i
\(291\) 0 0
\(292\) −10.2001 + 3.71252i −0.596914 + 0.217259i
\(293\) 5.22200 + 0.920779i 0.305072 + 0.0537925i 0.324089 0.946027i \(-0.394942\pi\)
−0.0190163 + 0.999819i \(0.506053\pi\)
\(294\) 0 0
\(295\) 11.5163i 0.670506i
\(296\) 6.03982 + 0.721486i 0.351058 + 0.0419355i
\(297\) 0 0
\(298\) −13.8936 9.72842i −0.804836 0.563552i
\(299\) −8.24198 + 46.7426i −0.476646 + 2.70319i
\(300\) 0 0
\(301\) 0.228477 + 2.61150i 0.0131692 + 0.150524i
\(302\) −8.29001 + 8.29001i −0.477037 + 0.477037i
\(303\) 0 0
\(304\) 1.61300 6.01980i 0.0925119 0.345259i
\(305\) −5.00397 + 13.7483i −0.286526 + 0.787225i
\(306\) 0 0
\(307\) −14.5787 + 8.41700i −0.832049 + 0.480384i −0.854554 0.519363i \(-0.826169\pi\)
0.0225047 + 0.999747i \(0.492836\pi\)
\(308\) −5.86695 + 1.03450i −0.334301 + 0.0589462i
\(309\) 0 0
\(310\) 0.857703 + 3.20099i 0.0487143 + 0.181804i
\(311\) 18.3471 + 1.60516i 1.04037 + 0.0910202i 0.594513 0.804086i \(-0.297345\pi\)
0.445853 + 0.895106i \(0.352900\pi\)
\(312\) 0 0
\(313\) −10.8404 23.2473i −0.612734 1.31401i −0.930656 0.365896i \(-0.880763\pi\)
0.317921 0.948117i \(-0.397015\pi\)
\(314\) 10.7288 7.51236i 0.605459 0.423947i
\(315\) 0 0
\(316\) 8.51170 3.96907i 0.478820 0.223278i
\(317\) −7.32092 + 6.14298i −0.411184 + 0.345024i −0.824797 0.565428i \(-0.808711\pi\)
0.413614 + 0.910452i \(0.364266\pi\)
\(318\) 0 0
\(319\) −21.5106 + 5.76375i −1.20436 + 0.322708i
\(320\) −1.19435 0.556935i −0.0667663 0.0311336i
\(321\) 0 0
\(322\) 8.88817 + 15.3948i 0.495318 + 0.857916i
\(323\) −7.46944 + 12.9374i −0.415611 + 0.719859i
\(324\) 0 0
\(325\) 19.7729 + 5.29815i 1.09681 + 0.293888i
\(326\) 9.79726 + 8.22088i 0.542620 + 0.455312i
\(327\) 0 0
\(328\) −10.9221 + 0.955557i −0.603070 + 0.0527618i
\(329\) 8.97357 + 24.6547i 0.494729 + 1.35926i
\(330\) 0 0
\(331\) −4.54433 + 6.48997i −0.249779 + 0.356721i −0.924388 0.381454i \(-0.875423\pi\)
0.674609 + 0.738175i \(0.264312\pi\)
\(332\) 1.13460 0.0622692
\(333\) 0 0
\(334\) −12.2315 −0.669279
\(335\) −5.91369 + 8.44562i −0.323099 + 0.461433i
\(336\) 0 0
\(337\) −2.09974 5.76900i −0.114380 0.314257i 0.869272 0.494333i \(-0.164588\pi\)
−0.983653 + 0.180076i \(0.942366\pi\)
\(338\) 26.2483 2.29643i 1.42772 0.124909i
\(339\) 0 0
\(340\) 2.41986 + 2.03050i 0.131235 + 0.110119i
\(341\) 6.15948 + 1.65043i 0.333555 + 0.0893757i
\(342\) 0 0
\(343\) −9.96191 + 17.2545i −0.537893 + 0.931658i
\(344\) 0.557918 + 0.966343i 0.0300809 + 0.0521017i
\(345\) 0 0
\(346\) 4.95464 + 2.31039i 0.266363 + 0.124207i
\(347\) −25.1023 + 6.72615i −1.34756 + 0.361078i −0.859235 0.511582i \(-0.829060\pi\)
−0.488328 + 0.872660i \(0.662393\pi\)
\(348\) 0 0
\(349\) 10.7419 9.01354i 0.575002 0.482484i −0.308300 0.951289i \(-0.599760\pi\)
0.883301 + 0.468806i \(0.155316\pi\)
\(350\) 6.94839 3.24009i 0.371407 0.173190i
\(351\) 0 0
\(352\) −2.07721 + 1.45448i −0.110716 + 0.0775240i
\(353\) 2.25571 + 4.83739i 0.120059 + 0.257468i 0.957148 0.289599i \(-0.0935219\pi\)
−0.837089 + 0.547067i \(0.815744\pi\)
\(354\) 0 0
\(355\) −5.38024 0.470710i −0.285553 0.0249827i
\(356\) 0.0825035 + 0.307907i 0.00437268 + 0.0163190i
\(357\) 0 0
\(358\) −8.46811 + 1.49316i −0.447553 + 0.0789157i
\(359\) −2.61646 + 1.51062i −0.138092 + 0.0797273i −0.567454 0.823405i \(-0.692072\pi\)
0.429363 + 0.903132i \(0.358738\pi\)
\(360\) 0 0
\(361\) 6.78560 18.6433i 0.357137 0.981225i
\(362\) −1.66878 + 6.22796i −0.0877089 + 0.327334i
\(363\) 0 0
\(364\) 10.4206 10.4206i 0.546190 0.546190i
\(365\) 1.24672 + 14.2501i 0.0652564 + 0.745884i
\(366\) 0 0
\(367\) −1.08395 + 6.14738i −0.0565817 + 0.320891i −0.999941 0.0108828i \(-0.996536\pi\)
0.943359 + 0.331773i \(0.107647\pi\)
\(368\) 6.19814 + 4.33998i 0.323100 + 0.226237i
\(369\) 0 0
\(370\) 2.97844 7.44211i 0.154842 0.386897i
\(371\) 4.34803i 0.225739i
\(372\) 0 0
\(373\) −36.7948 6.48792i −1.90516 0.335932i −0.908522 0.417836i \(-0.862789\pi\)
−0.996640 + 0.0819046i \(0.973900\pi\)
\(374\) 5.71191 2.07897i 0.295356 0.107501i
\(375\) 0 0
\(376\) 7.89684 + 7.89684i 0.407248 + 0.407248i
\(377\) 35.4099 42.1999i 1.82370 2.17340i
\(378\) 0 0
\(379\) −3.73631 1.35990i −0.191921 0.0698536i 0.244272 0.969707i \(-0.421451\pi\)
−0.436193 + 0.899853i \(0.643673\pi\)
\(380\) −7.11255 4.10643i −0.364866 0.210655i
\(381\) 0 0
\(382\) 3.06113 + 17.3605i 0.156621 + 0.888242i
\(383\) −2.84516 + 6.10146i −0.145381 + 0.311770i −0.965491 0.260435i \(-0.916134\pi\)
0.820111 + 0.572205i \(0.193912\pi\)
\(384\) 0 0
\(385\) −0.684248 + 7.82099i −0.0348725 + 0.398595i
\(386\) 13.1588 + 15.6820i 0.669765 + 0.798195i
\(387\) 0 0
\(388\) −7.61845 10.8803i −0.386768 0.552362i
\(389\) 12.2696 + 17.5228i 0.622095 + 0.888443i 0.999289 0.0376907i \(-0.0120002\pi\)
−0.377195 + 0.926134i \(0.623111\pi\)
\(390\) 0 0
\(391\) −11.6585 13.8941i −0.589597 0.702655i
\(392\) −0.129044 + 1.47498i −0.00651772 + 0.0744979i
\(393\) 0 0
\(394\) 6.43369 13.7971i 0.324125 0.695088i
\(395\) −2.14915 12.1884i −0.108136 0.613267i
\(396\) 0 0
\(397\) 20.4209 + 11.7900i 1.02490 + 0.591724i 0.915518 0.402276i \(-0.131781\pi\)
0.109378 + 0.994000i \(0.465114\pi\)
\(398\) −22.3679 8.14124i −1.12120 0.408084i
\(399\) 0 0
\(400\) 2.09764 2.49987i 0.104882 0.124993i
\(401\) 2.98281 + 2.98281i 0.148954 + 0.148954i 0.777651 0.628697i \(-0.216411\pi\)
−0.628697 + 0.777651i \(0.716411\pi\)
\(402\) 0 0
\(403\) −14.8229 + 5.39511i −0.738383 + 0.268750i
\(404\) 0.0937926 + 0.0165382i 0.00466636 + 0.000822805i
\(405\) 0 0
\(406\) 20.6318i 1.02394i
\(407\) −9.53623 12.1236i −0.472693 0.600945i
\(408\) 0 0
\(409\) −6.82901 4.78172i −0.337673 0.236441i 0.392425 0.919784i \(-0.371636\pi\)
−0.730097 + 0.683343i \(0.760525\pi\)
\(410\) −2.50892 + 14.2288i −0.123907 + 0.702710i
\(411\) 0 0
\(412\) 0.609298 + 6.96431i 0.0300180 + 0.343107i
\(413\) 14.5174 14.5174i 0.714352 0.714352i
\(414\) 0 0
\(415\) 0.386986 1.44425i 0.0189964 0.0708955i
\(416\) 2.14544 5.89454i 0.105189 0.289004i
\(417\) 0 0
\(418\) −13.6863 + 7.90177i −0.669417 + 0.386488i
\(419\) −15.3211 + 2.70153i −0.748487 + 0.131978i −0.534864 0.844938i \(-0.679637\pi\)
−0.213622 + 0.976916i \(0.568526\pi\)
\(420\) 0 0
\(421\) −4.33319 16.1717i −0.211187 0.788160i −0.987474 0.157781i \(-0.949566\pi\)
0.776287 0.630379i \(-0.217101\pi\)
\(422\) −21.8235 1.90931i −1.06235 0.0929436i
\(423\) 0 0
\(424\) −0.782161 1.67735i −0.0379851 0.0814593i
\(425\) −6.40778 + 4.48678i −0.310823 + 0.217641i
\(426\) 0 0
\(427\) −23.6389 + 11.0230i −1.14397 + 0.533441i
\(428\) −7.64771 + 6.41719i −0.369666 + 0.310187i
\(429\) 0 0
\(430\) 1.42037 0.380586i 0.0684962 0.0183535i
\(431\) −13.9763 6.51724i −0.673214 0.313925i 0.0557821 0.998443i \(-0.482235\pi\)
−0.728996 + 0.684518i \(0.760013\pi\)
\(432\) 0 0
\(433\) −1.08383 1.87724i −0.0520854 0.0902145i 0.838807 0.544429i \(-0.183253\pi\)
−0.890893 + 0.454214i \(0.849920\pi\)
\(434\) −2.95393 + 5.11635i −0.141793 + 0.245593i
\(435\) 0 0
\(436\) 2.59281 + 0.694740i 0.124173 + 0.0332720i
\(437\) 36.1234 + 30.3112i 1.72802 + 1.44998i
\(438\) 0 0
\(439\) −12.0667 + 1.05570i −0.575910 + 0.0503856i −0.371390 0.928477i \(-0.621119\pi\)
−0.204520 + 0.978862i \(0.565563\pi\)
\(440\) 1.14294 + 3.14021i 0.0544876 + 0.149703i
\(441\) 0 0
\(442\) −8.62452 + 12.3171i −0.410227 + 0.585865i
\(443\) 11.5779 0.550081 0.275040 0.961433i \(-0.411309\pi\)
0.275040 + 0.961433i \(0.411309\pi\)
\(444\) 0 0
\(445\) 0.420080 0.0199137
\(446\) −9.58686 + 13.6915i −0.453951 + 0.648309i
\(447\) 0 0
\(448\) −0.803520 2.20765i −0.0379628 0.104302i
\(449\) −32.9131 + 2.87952i −1.55327 + 0.135893i −0.831216 0.555949i \(-0.812355\pi\)
−0.722049 + 0.691842i \(0.756799\pi\)
\(450\) 0 0
\(451\) 21.2976 + 17.8708i 1.00286 + 0.841503i
\(452\) 7.96084 + 2.13310i 0.374446 + 0.100333i
\(453\) 0 0
\(454\) −7.70998 + 13.3541i −0.361847 + 0.626738i
\(455\) −9.71037 16.8189i −0.455229 0.788480i
\(456\) 0 0
\(457\) −22.9391 10.6967i −1.07304 0.500369i −0.195914 0.980621i \(-0.562767\pi\)
−0.877130 + 0.480252i \(0.840545\pi\)
\(458\) −10.4327 + 2.79544i −0.487489 + 0.130622i
\(459\) 0 0
\(460\) 7.63848 6.40945i 0.356146 0.298842i
\(461\) 18.7010 8.72044i 0.870995 0.406152i 0.0648676 0.997894i \(-0.479337\pi\)
0.806127 + 0.591742i \(0.201560\pi\)
\(462\) 0 0
\(463\) 24.4192 17.0985i 1.13486 0.794635i 0.153751 0.988110i \(-0.450865\pi\)
0.981105 + 0.193475i \(0.0619757\pi\)
\(464\) −3.71143 7.95918i −0.172299 0.369496i
\(465\) 0 0
\(466\) 21.9167 + 1.91746i 1.01527 + 0.0888247i
\(467\) −9.83159 36.6920i −0.454952 1.69790i −0.688229 0.725493i \(-0.741612\pi\)
0.233278 0.972410i \(-0.425055\pi\)
\(468\) 0 0
\(469\) −18.1012 + 3.19173i −0.835836 + 0.147380i
\(470\) 12.7454 7.35859i 0.587904 0.339426i
\(471\) 0 0
\(472\) 2.98888 8.21189i 0.137574 0.377983i
\(473\) 0.732340 2.73313i 0.0336730 0.125669i
\(474\) 0 0
\(475\) 14.3809 14.3809i 0.659842 0.659842i
\(476\) 0.490818 + 5.61008i 0.0224966 + 0.257138i
\(477\) 0 0
\(478\) 2.09190 11.8637i 0.0956812 0.542635i
\(479\) 29.9858 + 20.9963i 1.37009 + 0.959345i 0.999534 + 0.0305337i \(0.00972068\pi\)
0.370553 + 0.928811i \(0.379168\pi\)
\(480\) 0 0
\(481\) 36.5254 + 11.0360i 1.66541 + 0.503198i
\(482\) 15.1251i 0.688930i
\(483\) 0 0
\(484\) −4.50027 0.793518i −0.204558 0.0360690i
\(485\) −16.4482 + 5.98664i −0.746873 + 0.271840i
\(486\) 0 0
\(487\) 17.6239 + 17.6239i 0.798617 + 0.798617i 0.982877 0.184261i \(-0.0589890\pi\)
−0.184261 + 0.982877i \(0.558989\pi\)
\(488\) −7.13631 + 8.50473i −0.323046 + 0.384991i
\(489\) 0 0
\(490\) 1.83352 + 0.667345i 0.0828298 + 0.0301476i
\(491\) −21.0419 12.1486i −0.949609 0.548257i −0.0566498 0.998394i \(-0.518042\pi\)
−0.892960 + 0.450137i \(0.851375\pi\)
\(492\) 0 0
\(493\) 3.65547 + 20.7312i 0.164634 + 0.933685i
\(494\) 16.5215 35.4306i 0.743340 1.59410i
\(495\) 0 0
\(496\) −0.219170 + 2.50512i −0.00984101 + 0.112483i
\(497\) −6.18890 7.37564i −0.277610 0.330843i
\(498\) 0 0
\(499\) −1.85420 2.64808i −0.0830056 0.118544i 0.775502 0.631345i \(-0.217497\pi\)
−0.858508 + 0.512801i \(0.828608\pi\)
\(500\) −6.24602 8.92025i −0.279331 0.398926i
\(501\) 0 0
\(502\) 7.94714 + 9.47104i 0.354698 + 0.422713i
\(503\) −0.942043 + 10.7676i −0.0420036 + 0.480104i 0.945838 + 0.324639i \(0.105243\pi\)
−0.987842 + 0.155464i \(0.950313\pi\)
\(504\) 0 0
\(505\) 0.0530422 0.113749i 0.00236035 0.00506178i
\(506\) −3.33183 18.8958i −0.148118 0.840019i
\(507\) 0 0
\(508\) 11.7594 + 6.78931i 0.521741 + 0.301227i
\(509\) −0.0209050 0.00760879i −0.000926597 0.000337254i 0.341557 0.939861i \(-0.389046\pi\)
−0.342483 + 0.939524i \(0.611268\pi\)
\(510\) 0 0
\(511\) −16.3919 + 19.5351i −0.725136 + 0.864183i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 0 0
\(514\) −7.22013 + 2.62791i −0.318466 + 0.115912i
\(515\) 9.07281 + 1.59978i 0.399796 + 0.0704948i
\(516\) 0 0
\(517\) 28.3194i 1.24549i
\(518\) 13.1360 5.62686i 0.577165 0.247230i
\(519\) 0 0
\(520\) −6.77150 4.74146i −0.296950 0.207927i
\(521\) 6.13550 34.7961i 0.268801 1.52445i −0.489188 0.872179i \(-0.662707\pi\)
0.757989 0.652268i \(-0.226182\pi\)
\(522\) 0 0
\(523\) −1.20573 13.7815i −0.0527227 0.602623i −0.975896 0.218238i \(-0.929969\pi\)
0.923173 0.384385i \(-0.125586\pi\)
\(524\) 0.574261 0.574261i 0.0250867 0.0250867i
\(525\) 0 0
\(526\) −1.16525 + 4.34878i −0.0508074 + 0.189616i
\(527\) 2.06165 5.66435i 0.0898070 0.246743i
\(528\) 0 0
\(529\) −29.6634 + 17.1262i −1.28972 + 0.744617i
\(530\) −2.40190 + 0.423520i −0.104332 + 0.0183965i
\(531\) 0 0
\(532\) −3.78948 14.1425i −0.164295 0.613157i
\(533\) −68.5124 5.99406i −2.96760 0.259631i
\(534\) 0 0
\(535\) 5.56009 + 11.9237i 0.240384 + 0.515505i
\(536\) −6.40878 + 4.48747i −0.276817 + 0.193829i
\(537\) 0 0
\(538\) −3.88551 + 1.81184i −0.167516 + 0.0781141i
\(539\) 2.87616 2.41338i 0.123885 0.103952i
\(540\) 0 0
\(541\) 23.2053 6.21785i 0.997675 0.267326i 0.277204 0.960811i \(-0.410592\pi\)
0.720471 + 0.693485i \(0.243926\pi\)
\(542\) 15.7442 + 7.34163i 0.676271 + 0.315350i
\(543\) 0 0
\(544\) 1.19853 + 2.07592i 0.0513866 + 0.0890043i
\(545\) 1.76869 3.06347i 0.0757625 0.131225i
\(546\) 0 0
\(547\) 12.1411 + 3.25320i 0.519116 + 0.139097i 0.508858 0.860851i \(-0.330068\pi\)
0.0102585 + 0.999947i \(0.496735\pi\)
\(548\) −7.62648 6.39938i −0.325787 0.273368i
\(549\) 0 0
\(550\) −8.24373 + 0.721233i −0.351514 + 0.0307535i
\(551\) −18.7190 51.4300i −0.797456 2.19099i
\(552\) 0 0
\(553\) 12.6554 18.0738i 0.538164 0.768578i
\(554\) −1.03309 −0.0438917
\(555\) 0 0
\(556\) −13.1249 −0.556622
\(557\) 13.3197 19.0225i 0.564372 0.806007i −0.430975 0.902364i \(-0.641830\pi\)
0.995347 + 0.0963569i \(0.0307190\pi\)
\(558\) 0 0
\(559\) 2.39396 + 6.57734i 0.101254 + 0.278192i
\(560\) −3.08422 + 0.269835i −0.130332 + 0.0114026i
\(561\) 0 0
\(562\) 13.3406 + 11.1941i 0.562740 + 0.472195i
\(563\) 33.9900 + 9.10760i 1.43251 + 0.383840i 0.889904 0.456148i \(-0.150771\pi\)
0.542605 + 0.839988i \(0.317438\pi\)
\(564\) 0 0
\(565\) 5.43052 9.40594i 0.228464 0.395711i
\(566\) 10.1942 + 17.6569i 0.428495 + 0.742175i
\(567\) 0 0
\(568\) −3.71430 1.73200i −0.155848 0.0726733i
\(569\) 1.45924 0.391001i 0.0611744 0.0163916i −0.228102 0.973637i \(-0.573252\pi\)
0.289276 + 0.957246i \(0.406585\pi\)
\(570\) 0 0
\(571\) 22.7016 19.0489i 0.950034 0.797173i −0.0292690 0.999572i \(-0.509318\pi\)
0.979303 + 0.202398i \(0.0648735\pi\)
\(572\) −14.4164 + 6.72246i −0.602779 + 0.281080i
\(573\) 0 0
\(574\) −21.0994 + 14.7740i −0.880672 + 0.616653i
\(575\) 10.4354 + 22.3788i 0.435186 + 0.933259i
\(576\) 0 0
\(577\) −2.35290 0.205852i −0.0979525 0.00856973i 0.0380741 0.999275i \(-0.487878\pi\)
−0.136027 + 0.990705i \(0.543433\pi\)
\(578\) 2.91277 + 10.8706i 0.121155 + 0.452158i
\(579\) 0 0
\(580\) −11.3973 + 2.00965i −0.473246 + 0.0834460i
\(581\) 2.30844 1.33278i 0.0957702 0.0552930i
\(582\) 0 0
\(583\) −1.60515 + 4.41011i −0.0664785 + 0.182648i
\(584\) −2.80940 + 10.4848i −0.116254 + 0.433865i
\(585\) 0 0
\(586\) 3.74947 3.74947i 0.154889 0.154889i
\(587\) 0.987670 + 11.2891i 0.0407655 + 0.465952i 0.988952 + 0.148237i \(0.0473598\pi\)
−0.948186 + 0.317715i \(0.897085\pi\)
\(588\) 0 0
\(589\) −2.72140 + 15.4338i −0.112133 + 0.635940i
\(590\) −9.43361 6.60549i −0.388376 0.271944i
\(591\) 0 0
\(592\) 4.05531 4.53371i 0.166672 0.186334i
\(593\) 2.74452i 0.112704i −0.998411 0.0563519i \(-0.982053\pi\)
0.998411 0.0563519i \(-0.0179469\pi\)
\(594\) 0 0
\(595\) 7.30857 + 1.28870i 0.299622 + 0.0528315i
\(596\) −15.9381 + 5.80100i −0.652850 + 0.237618i
\(597\) 0 0
\(598\) 33.5619 + 33.5619i 1.37245 + 1.37245i
\(599\) 27.4401 32.7018i 1.12117 1.33616i 0.185763 0.982595i \(-0.440524\pi\)
0.935409 0.353567i \(-0.115031\pi\)
\(600\) 0 0
\(601\) −5.25901 1.91412i −0.214519 0.0780787i 0.232525 0.972590i \(-0.425301\pi\)
−0.447044 + 0.894512i \(0.647523\pi\)
\(602\) 2.27026 + 1.31074i 0.0925291 + 0.0534217i
\(603\) 0 0
\(604\) 2.03582 + 11.5457i 0.0828365 + 0.469789i
\(605\) −2.54502 + 5.45782i −0.103470 + 0.221892i
\(606\) 0 0
\(607\) 1.05141 12.0177i 0.0426754 0.487782i −0.944541 0.328394i \(-0.893493\pi\)
0.987216 0.159388i \(-0.0509519\pi\)
\(608\) −4.00595 4.77411i −0.162463 0.193616i
\(609\) 0 0
\(610\) 8.39178 + 11.9847i 0.339773 + 0.485247i
\(611\) 40.1813 + 57.3848i 1.62556 + 2.32154i
\(612\) 0 0
\(613\) 27.0267 + 32.2092i 1.09160 + 1.30092i 0.950433 + 0.310930i \(0.100641\pi\)
0.141166 + 0.989986i \(0.454915\pi\)
\(614\) −1.46718 + 16.7699i −0.0592106 + 0.676780i
\(615\) 0 0
\(616\) −2.51773 + 5.39929i −0.101442 + 0.217544i
\(617\) −5.74253 32.5675i −0.231186 1.31112i −0.850500 0.525976i \(-0.823700\pi\)
0.619314 0.785143i \(-0.287411\pi\)
\(618\) 0 0
\(619\) 5.29830 + 3.05897i 0.212957 + 0.122951i 0.602685 0.797979i \(-0.294098\pi\)
−0.389728 + 0.920930i \(0.627431\pi\)
\(620\) 3.11406 + 1.13342i 0.125064 + 0.0455194i
\(621\) 0 0
\(622\) 11.8383 14.1083i 0.474673 0.565693i
\(623\) 0.529549 + 0.529549i 0.0212159 + 0.0212159i
\(624\) 0 0
\(625\) 1.84761 0.672475i 0.0739044 0.0268990i
\(626\) −25.2608 4.45417i −1.00963 0.178024i
\(627\) 0 0
\(628\) 13.0974i 0.522643i
\(629\) −12.2023 + 7.98134i −0.486539 + 0.318237i
\(630\) 0 0
\(631\) −35.6483 24.9612i −1.41914 0.993690i −0.996160 0.0875491i \(-0.972097\pi\)
−0.422976 0.906141i \(-0.639015\pi\)
\(632\) 1.63084 9.24894i 0.0648712 0.367903i
\(633\) 0 0
\(634\) 0.832928 + 9.52041i 0.0330798 + 0.378104i
\(635\) 12.6531 12.6531i 0.502123 0.502123i
\(636\) 0 0
\(637\) −2.40383 + 8.97120i −0.0952431 + 0.355452i
\(638\) −7.61659 + 20.9264i −0.301544 + 0.828484i
\(639\) 0 0
\(640\) −1.14127 + 0.658910i −0.0451125 + 0.0260457i
\(641\) 38.4935 6.78745i 1.52040 0.268088i 0.649812 0.760095i \(-0.274848\pi\)
0.870591 + 0.492007i \(0.163736\pi\)
\(642\) 0 0
\(643\) −10.4218 38.8946i −0.410995 1.53385i −0.792725 0.609579i \(-0.791338\pi\)
0.381731 0.924274i \(-0.375328\pi\)
\(644\) 17.7087 + 1.54931i 0.697820 + 0.0610513i
\(645\) 0 0
\(646\) 6.31344 + 13.5392i 0.248399 + 0.532693i
\(647\) 40.6484 28.4623i 1.59805 1.11897i 0.672666 0.739946i \(-0.265149\pi\)
0.925387 0.379022i \(-0.123740\pi\)
\(648\) 0 0
\(649\) −20.0839 + 9.36529i −0.788364 + 0.367620i
\(650\) 15.6813 13.1582i 0.615071 0.516106i
\(651\) 0 0
\(652\) 12.3536 3.31014i 0.483805 0.129635i
\(653\) −16.9635 7.91019i −0.663831 0.309550i 0.0613413 0.998117i \(-0.480462\pi\)
−0.725172 + 0.688567i \(0.758240\pi\)
\(654\) 0 0
\(655\) −0.535119 0.926853i −0.0209088 0.0362152i
\(656\) −5.48189 + 9.49492i −0.214032 + 0.370714i
\(657\) 0 0
\(658\) 25.3429 + 6.79062i 0.987971 + 0.264726i
\(659\) 0.893583 + 0.749805i 0.0348090 + 0.0292083i 0.660026 0.751243i \(-0.270545\pi\)
−0.625217 + 0.780451i \(0.714990\pi\)
\(660\) 0 0
\(661\) −22.2984 + 1.95086i −0.867309 + 0.0758797i −0.512119 0.858915i \(-0.671139\pi\)
−0.355190 + 0.934794i \(0.615584\pi\)
\(662\) 2.70976 + 7.44499i 0.105318 + 0.289358i
\(663\) 0 0
\(664\) 0.650780 0.929409i 0.0252551 0.0360681i
\(665\) −19.2948 −0.748220
\(666\) 0 0
\(667\) 66.4492 2.57292
\(668\) −7.01571 + 10.0195i −0.271446 + 0.387665i
\(669\) 0 0
\(670\) 3.52630 + 9.68842i 0.136233 + 0.374296i
\(671\) 28.0457 2.45368i 1.08269 0.0947234i
\(672\) 0 0
\(673\) 14.2359 + 11.9454i 0.548755 + 0.460460i 0.874519 0.484991i \(-0.161177\pi\)
−0.325764 + 0.945451i \(0.605621\pi\)
\(674\) −5.93005 1.58895i −0.228417 0.0612042i
\(675\) 0 0
\(676\) 13.1743 22.8185i 0.506702 0.877634i
\(677\) 9.05630 + 15.6860i 0.348062 + 0.602861i 0.985905 0.167305i \(-0.0535066\pi\)
−0.637843 + 0.770166i \(0.720173\pi\)
\(678\) 0 0
\(679\) −28.2811 13.1877i −1.08533 0.506097i
\(680\) 3.05126 0.817584i 0.117011 0.0313529i
\(681\) 0 0
\(682\) 4.88488 4.09890i 0.187052 0.156955i
\(683\) −2.02560 + 0.944551i −0.0775073 + 0.0361422i −0.460985 0.887408i \(-0.652504\pi\)
0.383478 + 0.923550i \(0.374726\pi\)
\(684\) 0 0
\(685\) −10.7471 + 7.52520i −0.410625 + 0.287523i
\(686\) 8.42017 + 18.0571i 0.321484 + 0.689424i
\(687\) 0 0
\(688\) 1.11159 + 0.0972516i 0.0423790 + 0.00370768i
\(689\) −3.00475 11.2139i −0.114472 0.427215i
\(690\) 0 0
\(691\) 43.5634 7.68141i 1.65723 0.292215i 0.734774 0.678312i \(-0.237288\pi\)
0.922458 + 0.386098i \(0.126177\pi\)
\(692\) 4.73442 2.73342i 0.179976 0.103909i
\(693\) 0 0
\(694\) −8.88836 + 24.4206i −0.337398 + 0.926992i
\(695\) −4.47662 + 16.7070i −0.169808 + 0.633732i
\(696\) 0 0
\(697\) 18.5834 18.5834i 0.703896 0.703896i
\(698\) −1.22215 13.9692i −0.0462590 0.528743i
\(699\) 0 0
\(700\) 1.33131 7.55023i 0.0503188 0.285372i
\(701\) 5.74480 + 4.02255i 0.216978 + 0.151930i 0.677013 0.735971i \(-0.263274\pi\)
−0.460035 + 0.887901i \(0.652163\pi\)
\(702\) 0 0
\(703\) 27.6397 25.9445i 1.04245 0.978516i
\(704\) 2.53581i 0.0955718i
\(705\) 0 0
\(706\) 5.25638 + 0.926842i 0.197827 + 0.0348822i
\(707\) 0.210256 0.0765269i 0.00790749 0.00287809i
\(708\) 0 0
\(709\) −12.1883 12.1883i −0.457742 0.457742i 0.440172 0.897914i \(-0.354918\pi\)
−0.897914 + 0.440172i \(0.854918\pi\)
\(710\) −3.47156 + 4.13724i −0.130285 + 0.155268i
\(711\) 0 0
\(712\) 0.299545 + 0.109025i 0.0112259 + 0.00408590i
\(713\) −16.4783 9.51374i −0.617116 0.356292i
\(714\) 0 0
\(715\) 3.64005 + 20.6437i 0.136130 + 0.772031i
\(716\) −3.63398 + 7.79310i −0.135808 + 0.291242i
\(717\) 0 0
\(718\) −0.263318 + 3.00974i −0.00982693 + 0.112322i
\(719\) −23.0445 27.4634i −0.859416 1.02421i −0.999420 0.0340616i \(-0.989156\pi\)
0.140003 0.990151i \(-0.455289\pi\)
\(720\) 0 0
\(721\) 9.42043 + 13.4538i 0.350835 + 0.501044i
\(722\) −11.3796 16.2518i −0.423505 0.604828i
\(723\) 0 0
\(724\) 4.14447 + 4.93919i 0.154028 + 0.183564i
\(725\) 2.49777 28.5496i 0.0927648 1.06031i
\(726\) 0 0
\(727\) 0.923111 1.97962i 0.0342363 0.0734200i −0.888446 0.458981i \(-0.848214\pi\)
0.922682 + 0.385561i \(0.125992\pi\)
\(728\) −2.55906 14.5131i −0.0948449 0.537892i
\(729\) 0 0
\(730\) 12.3881 + 7.15226i 0.458503 + 0.264717i
\(731\) −2.51343 0.914812i −0.0929624 0.0338355i
\(732\) 0 0
\(733\) 23.1990 27.6475i 0.856873 1.02118i −0.142633 0.989776i \(-0.545557\pi\)
0.999507 0.0314064i \(-0.00999862\pi\)
\(734\) 4.41391 + 4.41391i 0.162920 + 0.162920i
\(735\) 0 0
\(736\) 7.11021 2.58791i 0.262086 0.0953915i
\(737\) 19.5379 + 3.44506i 0.719688 + 0.126900i
\(738\) 0 0
\(739\) 20.3972i 0.750324i 0.926959 + 0.375162i \(0.122413\pi\)
−0.926959 + 0.375162i \(0.877587\pi\)
\(740\) −4.38786 6.70841i −0.161301 0.246606i
\(741\) 0 0
\(742\) −3.56170 2.49393i −0.130754 0.0915550i
\(743\) 3.57765 20.2899i 0.131251 0.744363i −0.846146 0.532951i \(-0.821083\pi\)
0.977397 0.211412i \(-0.0678061\pi\)
\(744\) 0 0
\(745\) 1.94806 + 22.2665i 0.0713716 + 0.815781i
\(746\) −26.4192 + 26.4192i −0.967276 + 0.967276i
\(747\) 0 0
\(748\) 1.57323 5.87137i 0.0575229 0.214678i
\(749\) −8.02185 + 22.0398i −0.293112 + 0.805318i
\(750\) 0 0
\(751\) 1.33664 0.771711i 0.0487748 0.0281601i −0.475414 0.879762i \(-0.657702\pi\)
0.524189 + 0.851602i \(0.324369\pi\)
\(752\) 10.9981 1.93927i 0.401061 0.0707179i
\(753\) 0 0
\(754\) −14.2578 53.2109i −0.519239 1.93783i
\(755\) 15.3911 + 1.34655i 0.560141 + 0.0490060i
\(756\) 0 0
\(757\) 11.1804 + 23.9764i 0.406358 + 0.871438i 0.997876 + 0.0651456i \(0.0207512\pi\)
−0.591518 + 0.806292i \(0.701471\pi\)
\(758\) −3.25703 + 2.28059i −0.118300 + 0.0828349i
\(759\) 0 0
\(760\) −7.44338 + 3.47091i −0.270000 + 0.125903i
\(761\) −11.0793 + 9.29662i −0.401624 + 0.337002i −0.821121 0.570754i \(-0.806651\pi\)
0.419497 + 0.907757i \(0.362206\pi\)
\(762\) 0 0
\(763\) 6.09137 1.63218i 0.220523 0.0590888i
\(764\) 15.9767 + 7.45006i 0.578017 + 0.269534i
\(765\) 0 0
\(766\) 3.36611 + 5.83027i 0.121622 + 0.210656i
\(767\) 27.4089 47.4736i 0.989678 1.71417i
\(768\) 0 0
\(769\) −17.0925 4.57993i −0.616373 0.165157i −0.0628946 0.998020i \(-0.520033\pi\)
−0.553478 + 0.832864i \(0.686700\pi\)
\(770\) 6.01411 + 5.04644i 0.216734 + 0.181861i
\(771\) 0 0
\(772\) 20.3936 1.78421i 0.733980 0.0642149i
\(773\) 11.1070 + 30.5161i 0.399489 + 1.09759i 0.962534 + 0.271161i \(0.0874077\pi\)
−0.563045 + 0.826427i \(0.690370\pi\)
\(774\) 0 0
\(775\) −4.70694 + 6.72221i −0.169078 + 0.241469i
\(776\) −13.2824 −0.476809
\(777\) 0 0
\(778\) 21.3914 0.766920
\(779\) −39.1913 + 55.9710i −1.40418 + 2.00537i
\(780\) 0 0
\(781\) 3.55442 + 9.76568i 0.127187 + 0.349444i
\(782\) −18.0684 + 1.58078i −0.646126 + 0.0565287i
\(783\) 0 0
\(784\) 1.13422 + 0.951722i 0.0405078 + 0.0339901i