Properties

Label 666.2.bs.b.557.7
Level $666$
Weight $2$
Character 666.557
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 557.7
Character \(\chi\) \(=\) 666.557
Dual form 666.2.bs.b.611.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(0.0741011 + 0.0345539i) q^{5} +(-1.92570 + 0.700897i) q^{7} +(-0.258819 + 0.965926i) q^{8} +O(q^{10})\) \(q+(0.0871557 - 0.996195i) q^{2} +(-0.984808 - 0.173648i) q^{4} +(0.0741011 + 0.0345539i) q^{5} +(-1.92570 + 0.700897i) q^{7} +(-0.258819 + 0.965926i) q^{8} +(0.0408808 - 0.0708076i) q^{10} +(-0.0467419 - 0.0809593i) q^{11} +(-3.00542 - 4.29219i) q^{13} +(0.530394 + 1.97946i) q^{14} +(0.939693 + 0.342020i) q^{16} +(2.94921 - 4.21190i) q^{17} +(-7.61336 + 0.666082i) q^{19} +(-0.0669751 - 0.0468965i) q^{20} +(-0.0847251 + 0.0395080i) q^{22} +(-6.72256 + 1.80130i) q^{23} +(-3.20964 - 3.82510i) q^{25} +(-4.53780 + 2.61990i) q^{26} +(2.01815 - 0.355855i) q^{28} +(3.03735 + 0.813856i) q^{29} +(-0.356247 - 0.356247i) q^{31} +(0.422618 - 0.906308i) q^{32} +(-3.93883 - 3.30507i) q^{34} +(-0.166915 - 0.0146032i) q^{35} +(-6.08100 - 0.146577i) q^{37} +7.64244i q^{38} +(-0.0525553 + 0.0626330i) q^{40} +(-0.847815 + 4.80820i) q^{41} +(5.17585 - 5.17585i) q^{43} +(0.0319733 + 0.0878460i) q^{44} +(1.20854 + 6.85397i) q^{46} +(7.78930 + 4.49715i) q^{47} +(-2.14525 + 1.80008i) q^{49} +(-4.09028 + 2.86405i) q^{50} +(2.21443 + 4.74887i) q^{52} +(2.03092 - 5.57992i) q^{53} +(-0.000666164 - 0.00761429i) q^{55} +(-0.178607 - 2.04149i) q^{56} +(1.07548 - 2.95486i) q^{58} +(-3.74133 - 8.02332i) q^{59} +(-4.71665 + 3.30264i) q^{61} +(-0.385940 + 0.323842i) q^{62} +(-0.866025 - 0.500000i) q^{64} +(-0.0743933 - 0.421905i) q^{65} +(1.89197 + 5.19815i) q^{67} +(-3.63579 + 3.63579i) q^{68} +(-0.0290952 + 0.165007i) q^{70} +(-6.74204 + 8.03485i) q^{71} -4.72714i q^{73} +(-0.676013 + 6.04508i) q^{74} +(7.61336 + 0.666082i) q^{76} +(0.146755 + 0.123142i) q^{77} +(5.96506 - 12.7921i) q^{79} +(0.0578141 + 0.0578141i) q^{80} +(4.71601 + 1.26365i) q^{82} +(11.2270 - 1.97962i) q^{83} +(0.364077 - 0.210200i) q^{85} +(-4.70505 - 5.60726i) q^{86} +(0.0902984 - 0.0241954i) q^{88} +(-5.09003 + 2.37352i) q^{89} +(8.79593 + 6.15898i) q^{91} +(6.93322 - 0.606578i) q^{92} +(5.15892 - 7.36770i) q^{94} +(-0.587174 - 0.213714i) q^{95} +(0.309796 + 1.15618i) q^{97} +(1.60626 + 2.29398i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 96 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/666\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0871557 0.996195i 0.0616284 0.704416i
\(3\) 0 0
\(4\) −0.984808 0.173648i −0.492404 0.0868241i
\(5\) 0.0741011 + 0.0345539i 0.0331390 + 0.0154530i 0.439117 0.898430i \(-0.355291\pi\)
−0.405978 + 0.913883i \(0.633069\pi\)
\(6\) 0 0
\(7\) −1.92570 + 0.700897i −0.727846 + 0.264914i −0.679253 0.733904i \(-0.737696\pi\)
−0.0485931 + 0.998819i \(0.515474\pi\)
\(8\) −0.258819 + 0.965926i −0.0915064 + 0.341506i
\(9\) 0 0
\(10\) 0.0408808 0.0708076i 0.0129276 0.0223913i
\(11\) −0.0467419 0.0809593i −0.0140932 0.0244102i 0.858893 0.512155i \(-0.171153\pi\)
−0.872986 + 0.487745i \(0.837819\pi\)
\(12\) 0 0
\(13\) −3.00542 4.29219i −0.833555 1.19044i −0.979559 0.201156i \(-0.935530\pi\)
0.146004 0.989284i \(-0.453359\pi\)
\(14\) 0.530394 + 1.97946i 0.141754 + 0.529033i
\(15\) 0 0
\(16\) 0.939693 + 0.342020i 0.234923 + 0.0855050i
\(17\) 2.94921 4.21190i 0.715287 1.02154i −0.282767 0.959189i \(-0.591252\pi\)
0.998054 0.0623477i \(-0.0198588\pi\)
\(18\) 0 0
\(19\) −7.61336 + 0.666082i −1.74662 + 0.152810i −0.915245 0.402897i \(-0.868003\pi\)
−0.831379 + 0.555707i \(0.812448\pi\)
\(20\) −0.0669751 0.0468965i −0.0149761 0.0104864i
\(21\) 0 0
\(22\) −0.0847251 + 0.0395080i −0.0180634 + 0.00842312i
\(23\) −6.72256 + 1.80130i −1.40175 + 0.375598i −0.878973 0.476871i \(-0.841771\pi\)
−0.522777 + 0.852469i \(0.675104\pi\)
\(24\) 0 0
\(25\) −3.20964 3.82510i −0.641928 0.765020i
\(26\) −4.53780 + 2.61990i −0.889935 + 0.513805i
\(27\) 0 0
\(28\) 2.01815 0.355855i 0.381395 0.0672502i
\(29\) 3.03735 + 0.813856i 0.564022 + 0.151129i 0.529554 0.848277i \(-0.322359\pi\)
0.0344685 + 0.999406i \(0.489026\pi\)
\(30\) 0 0
\(31\) −0.356247 0.356247i −0.0639838 0.0639838i 0.674391 0.738375i \(-0.264406\pi\)
−0.738375 + 0.674391i \(0.764406\pi\)
\(32\) 0.422618 0.906308i 0.0747091 0.160214i
\(33\) 0 0
\(34\) −3.93883 3.30507i −0.675504 0.566816i
\(35\) −0.166915 0.0146032i −0.0282138 0.00246839i
\(36\) 0 0
\(37\) −6.08100 0.146577i −0.999710 0.0240971i
\(38\) 7.64244i 1.23977i
\(39\) 0 0
\(40\) −0.0525553 + 0.0626330i −0.00830972 + 0.00990314i
\(41\) −0.847815 + 4.80820i −0.132406 + 0.750915i 0.844224 + 0.535990i \(0.180062\pi\)
−0.976631 + 0.214924i \(0.931050\pi\)
\(42\) 0 0
\(43\) 5.17585 5.17585i 0.789310 0.789310i −0.192071 0.981381i \(-0.561520\pi\)
0.981381 + 0.192071i \(0.0615205\pi\)
\(44\) 0.0319733 + 0.0878460i 0.00482016 + 0.0132433i
\(45\) 0 0
\(46\) 1.20854 + 6.85397i 0.178190 + 1.01056i
\(47\) 7.78930 + 4.49715i 1.13619 + 0.655977i 0.945483 0.325671i \(-0.105590\pi\)
0.190702 + 0.981648i \(0.438923\pi\)
\(48\) 0 0
\(49\) −2.14525 + 1.80008i −0.306464 + 0.257154i
\(50\) −4.09028 + 2.86405i −0.578454 + 0.405038i
\(51\) 0 0
\(52\) 2.21443 + 4.74887i 0.307087 + 0.658550i
\(53\) 2.03092 5.57992i 0.278969 0.766461i −0.718511 0.695515i \(-0.755176\pi\)
0.997480 0.0709454i \(-0.0226016\pi\)
\(54\) 0 0
\(55\) −0.000666164 0.00761429i −8.98255e−5 0.00102671i
\(56\) −0.178607 2.04149i −0.0238674 0.272805i
\(57\) 0 0
\(58\) 1.07548 2.95486i 0.141218 0.387992i
\(59\) −3.74133 8.02332i −0.487080 1.04455i −0.984232 0.176883i \(-0.943399\pi\)
0.497152 0.867664i \(-0.334379\pi\)
\(60\) 0 0
\(61\) −4.71665 + 3.30264i −0.603906 + 0.422859i −0.835139 0.550039i \(-0.814613\pi\)
0.231233 + 0.972898i \(0.425724\pi\)
\(62\) −0.385940 + 0.323842i −0.0490145 + 0.0411280i
\(63\) 0 0
\(64\) −0.866025 0.500000i −0.108253 0.0625000i
\(65\) −0.0743933 0.421905i −0.00922735 0.0523309i
\(66\) 0 0
\(67\) 1.89197 + 5.19815i 0.231141 + 0.635055i 0.999990 0.00437504i \(-0.00139262\pi\)
−0.768849 + 0.639430i \(0.779170\pi\)
\(68\) −3.63579 + 3.63579i −0.440904 + 0.440904i
\(69\) 0 0
\(70\) −0.0290952 + 0.165007i −0.00347755 + 0.0197221i
\(71\) −6.74204 + 8.03485i −0.800133 + 0.953561i −0.999653 0.0263324i \(-0.991617\pi\)
0.199520 + 0.979894i \(0.436062\pi\)
\(72\) 0 0
\(73\) 4.72714i 0.553270i −0.960975 0.276635i \(-0.910781\pi\)
0.960975 0.276635i \(-0.0892192\pi\)
\(74\) −0.676013 + 6.04508i −0.0785849 + 0.702726i
\(75\) 0 0
\(76\) 7.61336 + 0.666082i 0.873312 + 0.0764049i
\(77\) 0.146755 + 0.123142i 0.0167243 + 0.0140333i
\(78\) 0 0
\(79\) 5.96506 12.7921i 0.671122 1.43922i −0.215394 0.976527i \(-0.569104\pi\)
0.886516 0.462698i \(-0.153118\pi\)
\(80\) 0.0578141 + 0.0578141i 0.00646382 + 0.00646382i
\(81\) 0 0
\(82\) 4.71601 + 1.26365i 0.520796 + 0.139547i
\(83\) 11.2270 1.97962i 1.23232 0.217291i 0.480699 0.876886i \(-0.340383\pi\)
0.751622 + 0.659594i \(0.229272\pi\)
\(84\) 0 0
\(85\) 0.364077 0.210200i 0.0394897 0.0227994i
\(86\) −4.70505 5.60726i −0.507359 0.604646i
\(87\) 0 0
\(88\) 0.0902984 0.0241954i 0.00962584 0.00257924i
\(89\) −5.09003 + 2.37352i −0.539542 + 0.251593i −0.673233 0.739430i \(-0.735095\pi\)
0.133691 + 0.991023i \(0.457317\pi\)
\(90\) 0 0
\(91\) 8.79593 + 6.15898i 0.922064 + 0.645636i
\(92\) 6.93322 0.606578i 0.722838 0.0632402i
\(93\) 0 0
\(94\) 5.15892 7.36770i 0.532102 0.759921i
\(95\) −0.587174 0.213714i −0.0602428 0.0219266i
\(96\) 0 0
\(97\) 0.309796 + 1.15618i 0.0314551 + 0.117392i 0.979868 0.199645i \(-0.0639788\pi\)
−0.948413 + 0.317037i \(0.897312\pi\)
\(98\) 1.60626 + 2.29398i 0.162257 + 0.231726i
\(99\) 0 0
\(100\) 2.49666 + 4.32434i 0.249666 + 0.432434i
\(101\) 4.65686 8.06592i 0.463375 0.802589i −0.535752 0.844376i \(-0.679972\pi\)
0.999127 + 0.0417866i \(0.0133050\pi\)
\(102\) 0 0
\(103\) −5.00217 + 18.6684i −0.492879 + 1.83945i 0.0487214 + 0.998812i \(0.484485\pi\)
−0.541600 + 0.840636i \(0.682181\pi\)
\(104\) 4.92380 1.79212i 0.482818 0.175731i
\(105\) 0 0
\(106\) −5.38168 2.50952i −0.522715 0.243746i
\(107\) −6.82200 1.20290i −0.659508 0.116289i −0.166130 0.986104i \(-0.553127\pi\)
−0.493378 + 0.869815i \(0.664238\pi\)
\(108\) 0 0
\(109\) −0.415060 + 4.74416i −0.0397556 + 0.454408i 0.950061 + 0.312063i \(0.101020\pi\)
−0.989817 + 0.142346i \(0.954536\pi\)
\(110\) −0.00764338 −0.000728767
\(111\) 0 0
\(112\) −2.04929 −0.193639
\(113\) 1.75594 20.0705i 0.165185 1.88808i −0.235519 0.971870i \(-0.575679\pi\)
0.400704 0.916207i \(-0.368765\pi\)
\(114\) 0 0
\(115\) −0.560391 0.0988121i −0.0522568 0.00921427i
\(116\) −2.84988 1.32892i −0.264605 0.123387i
\(117\) 0 0
\(118\) −8.31886 + 3.02782i −0.765813 + 0.278733i
\(119\) −2.72717 + 10.1779i −0.249999 + 0.933011i
\(120\) 0 0
\(121\) 5.49563 9.51871i 0.499603 0.865337i
\(122\) 2.87899 + 4.98655i 0.260651 + 0.451461i
\(123\) 0 0
\(124\) 0.288973 + 0.412696i 0.0259505 + 0.0370612i
\(125\) −0.211473 0.789228i −0.0189147 0.0705907i
\(126\) 0 0
\(127\) 11.9540 + 4.35091i 1.06075 + 0.386081i 0.812710 0.582669i \(-0.197991\pi\)
0.248040 + 0.968750i \(0.420214\pi\)
\(128\) −0.573576 + 0.819152i −0.0506975 + 0.0724035i
\(129\) 0 0
\(130\) −0.426784 + 0.0373387i −0.0374314 + 0.00327482i
\(131\) 1.32503 + 0.927796i 0.115768 + 0.0810619i 0.630027 0.776573i \(-0.283044\pi\)
−0.514258 + 0.857635i \(0.671933\pi\)
\(132\) 0 0
\(133\) 14.1942 6.61885i 1.23079 0.573927i
\(134\) 5.34326 1.43172i 0.461588 0.123682i
\(135\) 0 0
\(136\) 3.30507 + 3.93883i 0.283408 + 0.337752i
\(137\) 13.7839 7.95811i 1.17763 0.679908i 0.222168 0.975008i \(-0.428687\pi\)
0.955466 + 0.295101i \(0.0953532\pi\)
\(138\) 0 0
\(139\) −5.21477 + 0.919504i −0.442311 + 0.0779913i −0.390368 0.920659i \(-0.627652\pi\)
−0.0519424 + 0.998650i \(0.516541\pi\)
\(140\) 0.161844 + 0.0433658i 0.0136783 + 0.00366508i
\(141\) 0 0
\(142\) 7.41667 + 7.41667i 0.622393 + 0.622393i
\(143\) −0.207014 + 0.443942i −0.0173114 + 0.0371243i
\(144\) 0 0
\(145\) 0.196949 + 0.165260i 0.0163557 + 0.0137241i
\(146\) −4.70915 0.411997i −0.389732 0.0340971i
\(147\) 0 0
\(148\) 5.96316 + 1.20030i 0.490169 + 0.0986644i
\(149\) 4.75836i 0.389820i −0.980821 0.194910i \(-0.937559\pi\)
0.980821 0.194910i \(-0.0624414\pi\)
\(150\) 0 0
\(151\) 2.62654 3.13019i 0.213745 0.254731i −0.648510 0.761206i \(-0.724607\pi\)
0.862254 + 0.506475i \(0.169052\pi\)
\(152\) 1.32710 7.52633i 0.107642 0.610466i
\(153\) 0 0
\(154\) 0.135464 0.135464i 0.0109160 0.0109160i
\(155\) −0.0140886 0.0387080i −0.00113162 0.00310910i
\(156\) 0 0
\(157\) −0.745032 4.22529i −0.0594600 0.337215i 0.940537 0.339692i \(-0.110323\pi\)
−0.999997 + 0.00247695i \(0.999212\pi\)
\(158\) −12.2235 7.05727i −0.972453 0.561446i
\(159\) 0 0
\(160\) 0.0626330 0.0525553i 0.00495157 0.00415486i
\(161\) 11.6831 8.18059i 0.920757 0.644721i
\(162\) 0 0
\(163\) −1.73199 3.71427i −0.135660 0.290924i 0.826728 0.562601i \(-0.190199\pi\)
−0.962388 + 0.271677i \(0.912422\pi\)
\(164\) 1.66987 4.58793i 0.130395 0.358257i
\(165\) 0 0
\(166\) −0.993590 11.3568i −0.0771176 0.881458i
\(167\) 0.228078 + 2.60695i 0.0176492 + 0.201732i 0.999900 + 0.0141579i \(0.00450676\pi\)
−0.982251 + 0.187574i \(0.939938\pi\)
\(168\) 0 0
\(169\) −4.94407 + 13.5837i −0.380313 + 1.04490i
\(170\) −0.177669 0.381012i −0.0136266 0.0292223i
\(171\) 0 0
\(172\) −5.99599 + 4.19844i −0.457190 + 0.320128i
\(173\) 0.932633 0.782572i 0.0709068 0.0594978i −0.606645 0.794973i \(-0.707485\pi\)
0.677552 + 0.735475i \(0.263041\pi\)
\(174\) 0 0
\(175\) 8.86181 + 5.11637i 0.669890 + 0.386761i
\(176\) −0.0162333 0.0920635i −0.00122363 0.00693955i
\(177\) 0 0
\(178\) 1.92086 + 5.27753i 0.143975 + 0.395567i
\(179\) 5.10868 5.10868i 0.381840 0.381840i −0.489924 0.871765i \(-0.662976\pi\)
0.871765 + 0.489924i \(0.162976\pi\)
\(180\) 0 0
\(181\) −1.95114 + 11.0655i −0.145027 + 0.822490i 0.822318 + 0.569028i \(0.192680\pi\)
−0.967345 + 0.253462i \(0.918431\pi\)
\(182\) 6.90215 8.22567i 0.511622 0.609727i
\(183\) 0 0
\(184\) 6.95971i 0.513076i
\(185\) −0.445544 0.220984i −0.0327570 0.0162470i
\(186\) 0 0
\(187\) −0.478844 0.0418934i −0.0350166 0.00306355i
\(188\) −6.89004 5.78143i −0.502508 0.421654i
\(189\) 0 0
\(190\) −0.264076 + 0.566313i −0.0191581 + 0.0410847i
\(191\) −7.95827 7.95827i −0.575840 0.575840i 0.357914 0.933754i \(-0.383488\pi\)
−0.933754 + 0.357914i \(0.883488\pi\)
\(192\) 0 0
\(193\) −18.8822 5.05946i −1.35917 0.364188i −0.495658 0.868518i \(-0.665073\pi\)
−0.863511 + 0.504330i \(0.831740\pi\)
\(194\) 1.17878 0.207850i 0.0846313 0.0149228i
\(195\) 0 0
\(196\) 2.42524 1.40021i 0.173231 0.100015i
\(197\) 5.28637 + 6.30005i 0.376638 + 0.448860i 0.920750 0.390153i \(-0.127578\pi\)
−0.544112 + 0.839013i \(0.683133\pi\)
\(198\) 0 0
\(199\) 6.27114 1.68035i 0.444549 0.119117i −0.0295987 0.999562i \(-0.509423\pi\)
0.474148 + 0.880445i \(0.342756\pi\)
\(200\) 4.52548 2.11027i 0.320000 0.149218i
\(201\) 0 0
\(202\) −7.62936 5.34213i −0.536800 0.375871i
\(203\) −6.41945 + 0.561630i −0.450557 + 0.0394187i
\(204\) 0 0
\(205\) −0.228966 + 0.326998i −0.0159917 + 0.0228385i
\(206\) 18.1614 + 6.61019i 1.26536 + 0.460554i
\(207\) 0 0
\(208\) −1.35616 5.06126i −0.0940327 0.350935i
\(209\) 0.409788 + 0.585238i 0.0283456 + 0.0404818i
\(210\) 0 0
\(211\) −6.66962 11.5521i −0.459156 0.795281i 0.539761 0.841818i \(-0.318515\pi\)
−0.998917 + 0.0465376i \(0.985181\pi\)
\(212\) −2.96901 + 5.14248i −0.203913 + 0.353187i
\(213\) 0 0
\(214\) −1.79290 + 6.69120i −0.122560 + 0.457401i
\(215\) 0.562382 0.204690i 0.0383541 0.0139598i
\(216\) 0 0
\(217\) 0.935717 + 0.436332i 0.0635206 + 0.0296201i
\(218\) 4.68994 + 0.826962i 0.317642 + 0.0560089i
\(219\) 0 0
\(220\) −0.000666164 0.00761429i −4.49128e−5 0.000513355i
\(221\) −26.9419 −1.81231
\(222\) 0 0
\(223\) −8.61963 −0.577213 −0.288606 0.957448i \(-0.593192\pi\)
−0.288606 + 0.957448i \(0.593192\pi\)
\(224\) −0.178607 + 2.04149i −0.0119337 + 0.136403i
\(225\) 0 0
\(226\) −19.8411 3.49852i −1.31981 0.232718i
\(227\) 1.54260 + 0.719325i 0.102386 + 0.0477433i 0.473136 0.880989i \(-0.343122\pi\)
−0.370751 + 0.928732i \(0.620900\pi\)
\(228\) 0 0
\(229\) 20.2839 7.38274i 1.34040 0.487865i 0.430461 0.902609i \(-0.358351\pi\)
0.909938 + 0.414744i \(0.136129\pi\)
\(230\) −0.147277 + 0.549647i −0.00971118 + 0.0362426i
\(231\) 0 0
\(232\) −1.57225 + 2.72322i −0.103223 + 0.178788i
\(233\) 7.87150 + 13.6338i 0.515679 + 0.893182i 0.999834 + 0.0182000i \(0.00579357\pi\)
−0.484155 + 0.874982i \(0.660873\pi\)
\(234\) 0 0
\(235\) 0.421801 + 0.602395i 0.0275153 + 0.0392959i
\(236\) 2.29126 + 8.55110i 0.149148 + 0.556629i
\(237\) 0 0
\(238\) 9.90153 + 3.60386i 0.641821 + 0.233604i
\(239\) −6.16633 + 8.80642i −0.398866 + 0.569640i −0.967475 0.252968i \(-0.918593\pi\)
0.568608 + 0.822609i \(0.307482\pi\)
\(240\) 0 0
\(241\) 7.12164 0.623063i 0.458745 0.0401350i 0.144558 0.989496i \(-0.453824\pi\)
0.314187 + 0.949361i \(0.398268\pi\)
\(242\) −9.00351 6.30433i −0.578768 0.405258i
\(243\) 0 0
\(244\) 5.21849 2.43342i 0.334080 0.155784i
\(245\) −0.221165 + 0.0592611i −0.0141297 + 0.00378605i
\(246\) 0 0
\(247\) 25.7403 + 30.6761i 1.63782 + 1.95188i
\(248\) 0.436312 0.251905i 0.0277058 0.0159960i
\(249\) 0 0
\(250\) −0.804656 + 0.141882i −0.0508909 + 0.00897344i
\(251\) −11.9186 3.19357i −0.752292 0.201576i −0.137758 0.990466i \(-0.543990\pi\)
−0.614535 + 0.788890i \(0.710656\pi\)
\(252\) 0 0
\(253\) 0.460058 + 0.460058i 0.0289236 + 0.0289236i
\(254\) 5.37622 11.5293i 0.337334 0.723415i
\(255\) 0 0
\(256\) 0.766044 + 0.642788i 0.0478778 + 0.0401742i
\(257\) 21.8099 + 1.90812i 1.36046 + 0.119025i 0.743906 0.668285i \(-0.232971\pi\)
0.616558 + 0.787310i \(0.288527\pi\)
\(258\) 0 0
\(259\) 11.8129 3.97989i 0.734018 0.247298i
\(260\) 0.428414i 0.0265691i
\(261\) 0 0
\(262\) 1.03975 1.23913i 0.0642360 0.0765534i
\(263\) −1.66000 + 9.41434i −0.102360 + 0.580513i 0.889882 + 0.456191i \(0.150787\pi\)
−0.992242 + 0.124322i \(0.960324\pi\)
\(264\) 0 0
\(265\) 0.343302 0.343302i 0.0210889 0.0210889i
\(266\) −5.35656 14.7170i −0.328432 0.902359i
\(267\) 0 0
\(268\) −0.960579 5.44771i −0.0586767 0.332772i
\(269\) −24.6295 14.2199i −1.50169 0.867001i −0.999998 0.00195476i \(-0.999378\pi\)
−0.501692 0.865046i \(-0.667289\pi\)
\(270\) 0 0
\(271\) 0.258733 0.217103i 0.0157169 0.0131881i −0.634895 0.772598i \(-0.718957\pi\)
0.650612 + 0.759410i \(0.274512\pi\)
\(272\) 4.21190 2.94921i 0.255384 0.178822i
\(273\) 0 0
\(274\) −6.72649 14.4250i −0.406362 0.871446i
\(275\) −0.159653 + 0.438643i −0.00962743 + 0.0264512i
\(276\) 0 0
\(277\) −0.787339 8.99932i −0.0473066 0.540717i −0.982460 0.186474i \(-0.940294\pi\)
0.935153 0.354243i \(-0.115261\pi\)
\(278\) 0.461508 + 5.27506i 0.0276794 + 0.316377i
\(279\) 0 0
\(280\) 0.0573064 0.157448i 0.00342471 0.00940932i
\(281\) 11.8672 + 25.4492i 0.707936 + 1.51817i 0.849125 + 0.528191i \(0.177130\pi\)
−0.141189 + 0.989983i \(0.545093\pi\)
\(282\) 0 0
\(283\) −11.1429 + 7.80236i −0.662378 + 0.463802i −0.855796 0.517314i \(-0.826932\pi\)
0.193417 + 0.981117i \(0.438043\pi\)
\(284\) 8.03485 6.74204i 0.476781 0.400066i
\(285\) 0 0
\(286\) 0.424211 + 0.244918i 0.0250841 + 0.0144823i
\(287\) −1.73742 9.85338i −0.102556 0.581626i
\(288\) 0 0
\(289\) −3.22796 8.86875i −0.189880 0.521691i
\(290\) 0.181796 0.181796i 0.0106755 0.0106755i
\(291\) 0 0
\(292\) −0.820859 + 4.65532i −0.0480371 + 0.272432i
\(293\) −16.0120 + 19.0823i −0.935430 + 1.11480i 0.0577640 + 0.998330i \(0.481603\pi\)
−0.993194 + 0.116472i \(0.962842\pi\)
\(294\) 0 0
\(295\) 0.723814i 0.0421421i
\(296\) 1.71546 5.83585i 0.0997091 0.339202i
\(297\) 0 0
\(298\) −4.74025 0.414718i −0.274595 0.0240240i
\(299\) 27.9357 + 23.4408i 1.61556 + 1.35562i
\(300\) 0 0
\(301\) −6.33939 + 13.5949i −0.365396 + 0.783595i
\(302\) −2.88936 2.88936i −0.166264 0.166264i
\(303\) 0 0
\(304\) −7.38203 1.97801i −0.423388 0.113447i
\(305\) −0.463628 + 0.0817502i −0.0265473 + 0.00468100i
\(306\) 0 0
\(307\) −5.88777 + 3.39930i −0.336033 + 0.194008i −0.658516 0.752567i \(-0.728816\pi\)
0.322484 + 0.946575i \(0.395482\pi\)
\(308\) −0.123142 0.146755i −0.00701667 0.00836214i
\(309\) 0 0
\(310\) −0.0397886 + 0.0106613i −0.00225984 + 0.000605523i
\(311\) −31.8564 + 14.8549i −1.80641 + 0.842344i −0.868272 + 0.496088i \(0.834769\pi\)
−0.938140 + 0.346256i \(0.887453\pi\)
\(312\) 0 0
\(313\) −24.1676 16.9223i −1.36603 0.956506i −0.999661 0.0260366i \(-0.991711\pi\)
−0.366371 0.930469i \(-0.619400\pi\)
\(314\) −4.27414 + 0.373939i −0.241204 + 0.0211026i
\(315\) 0 0
\(316\) −8.09576 + 11.5619i −0.455422 + 0.650410i
\(317\) 32.0131 + 11.6518i 1.79804 + 0.654432i 0.998555 + 0.0537429i \(0.0171151\pi\)
0.799483 + 0.600689i \(0.205107\pi\)
\(318\) 0 0
\(319\) −0.0760823 0.283943i −0.00425979 0.0158978i
\(320\) −0.0468965 0.0669751i −0.00262159 0.00374402i
\(321\) 0 0
\(322\) −7.13121 12.3516i −0.397407 0.688329i
\(323\) −19.6479 + 34.0311i −1.09324 + 1.89354i
\(324\) 0 0
\(325\) −6.77173 + 25.2724i −0.375628 + 1.40186i
\(326\) −3.85109 + 1.40168i −0.213292 + 0.0776320i
\(327\) 0 0
\(328\) −4.42493 2.06338i −0.244326 0.113931i
\(329\) −18.1519 3.20067i −1.00075 0.176458i
\(330\) 0 0
\(331\) 0.437724 5.00321i 0.0240595 0.275001i −0.974630 0.223822i \(-0.928147\pi\)
0.998689 0.0511790i \(-0.0162979\pi\)
\(332\) −11.4002 −0.625666
\(333\) 0 0
\(334\) 2.61690 0.143191
\(335\) −0.0394192 + 0.450564i −0.00215370 + 0.0246169i
\(336\) 0 0
\(337\) −22.3573 3.94219i −1.21788 0.214745i −0.472466 0.881349i \(-0.656636\pi\)
−0.745412 + 0.666604i \(0.767747\pi\)
\(338\) 13.1011 + 6.10915i 0.712607 + 0.332294i
\(339\) 0 0
\(340\) −0.395047 + 0.143785i −0.0214244 + 0.00779785i
\(341\) −0.0121899 + 0.0454932i −0.000660118 + 0.00246359i
\(342\) 0 0
\(343\) 10.0419 17.3931i 0.542214 0.939142i
\(344\) 3.65988 + 6.33910i 0.197327 + 0.341781i
\(345\) 0 0
\(346\) −0.698310 0.997290i −0.0375414 0.0536146i
\(347\) 3.97719 + 14.8431i 0.213507 + 0.796817i 0.986687 + 0.162631i \(0.0519981\pi\)
−0.773180 + 0.634186i \(0.781335\pi\)
\(348\) 0 0
\(349\) −6.38284 2.32316i −0.341666 0.124356i 0.165488 0.986212i \(-0.447080\pi\)
−0.507154 + 0.861856i \(0.669302\pi\)
\(350\) 5.86925 8.38216i 0.313725 0.448045i
\(351\) 0 0
\(352\) −0.0931280 + 0.00814765i −0.00496374 + 0.000434271i
\(353\) −13.7006 9.59325i −0.729209 0.510597i 0.149023 0.988834i \(-0.452387\pi\)
−0.878231 + 0.478236i \(0.841276\pi\)
\(354\) 0 0
\(355\) −0.777228 + 0.362427i −0.0412510 + 0.0192356i
\(356\) 5.42486 1.45359i 0.287517 0.0770399i
\(357\) 0 0
\(358\) −4.64399 5.53449i −0.245442 0.292507i
\(359\) −21.3335 + 12.3169i −1.12594 + 0.650062i −0.942911 0.333045i \(-0.891924\pi\)
−0.183030 + 0.983107i \(0.558591\pi\)
\(360\) 0 0
\(361\) 38.8082 6.84293i 2.04254 0.360154i
\(362\) 10.8533 + 2.90813i 0.570437 + 0.152848i
\(363\) 0 0
\(364\) −7.59280 7.59280i −0.397971 0.397971i
\(365\) 0.163341 0.350286i 0.00854966 0.0183348i
\(366\) 0 0
\(367\) 6.82666 + 5.72824i 0.356349 + 0.299012i 0.803333 0.595530i \(-0.203058\pi\)
−0.446985 + 0.894542i \(0.647502\pi\)
\(368\) −6.93322 0.606578i −0.361419 0.0316201i
\(369\) 0 0
\(370\) −0.258974 + 0.424588i −0.0134634 + 0.0220733i
\(371\) 12.1687i 0.631768i
\(372\) 0 0
\(373\) 17.9693 21.4149i 0.930413 1.10882i −0.0634257 0.997987i \(-0.520203\pi\)
0.993839 0.110836i \(-0.0353530\pi\)
\(374\) −0.0834680 + 0.473371i −0.00431603 + 0.0244774i
\(375\) 0 0
\(376\) −6.35993 + 6.35993i −0.327989 + 0.327989i
\(377\) −5.63531 15.4829i −0.290233 0.797409i
\(378\) 0 0
\(379\) −1.67165 9.48042i −0.0858671 0.486977i −0.997166 0.0752313i \(-0.976030\pi\)
0.911299 0.411745i \(-0.135081\pi\)
\(380\) 0.541142 + 0.312429i 0.0277600 + 0.0160273i
\(381\) 0 0
\(382\) −8.62159 + 7.23437i −0.441119 + 0.370143i
\(383\) −7.69620 + 5.38893i −0.393257 + 0.275362i −0.753436 0.657522i \(-0.771605\pi\)
0.360178 + 0.932884i \(0.382716\pi\)
\(384\) 0 0
\(385\) 0.00661967 + 0.0141959i 0.000337369 + 0.000723491i
\(386\) −6.68590 + 18.3694i −0.340303 + 0.934976i
\(387\) 0 0
\(388\) −0.104322 1.19241i −0.00529615 0.0605353i
\(389\) −0.198208 2.26553i −0.0100496 0.114867i 0.989513 0.144444i \(-0.0461395\pi\)
−0.999562 + 0.0295773i \(0.990584\pi\)
\(390\) 0 0
\(391\) −12.2393 + 33.6272i −0.618968 + 1.70060i
\(392\) −1.18351 2.53805i −0.0597763 0.128191i
\(393\) 0 0
\(394\) 6.73682 4.71717i 0.339396 0.237648i
\(395\) 0.884035 0.741793i 0.0444806 0.0373237i
\(396\) 0 0
\(397\) −33.3296 19.2428i −1.67276 0.965770i −0.966081 0.258238i \(-0.916858\pi\)
−0.706681 0.707532i \(-0.749809\pi\)
\(398\) −1.12739 6.39372i −0.0565108 0.320488i
\(399\) 0 0
\(400\) −1.70781 4.69218i −0.0853907 0.234609i
\(401\) 19.6027 19.6027i 0.978914 0.978914i −0.0208684 0.999782i \(-0.506643\pi\)
0.999782 + 0.0208684i \(0.00664310\pi\)
\(402\) 0 0
\(403\) −0.458407 + 2.59975i −0.0228349 + 0.129503i
\(404\) −5.98675 + 7.13473i −0.297852 + 0.354966i
\(405\) 0 0
\(406\) 6.44398i 0.319809i
\(407\) 0.272370 + 0.499165i 0.0135009 + 0.0247427i
\(408\) 0 0
\(409\) −20.3493 1.78033i −1.00621 0.0880319i −0.427880 0.903835i \(-0.640739\pi\)
−0.578329 + 0.815804i \(0.696295\pi\)
\(410\) 0.305797 + 0.256595i 0.0151023 + 0.0126723i
\(411\) 0 0
\(412\) 8.16791 17.5161i 0.402404 0.862958i
\(413\) 12.8282 + 12.8282i 0.631235 + 0.631235i
\(414\) 0 0
\(415\) 0.900335 + 0.241244i 0.0441957 + 0.0118422i
\(416\) −5.16019 + 0.909881i −0.252999 + 0.0446106i
\(417\) 0 0
\(418\) 0.618727 0.357222i 0.0302629 0.0174723i
\(419\) −15.8623 18.9040i −0.774925 0.923520i 0.223767 0.974643i \(-0.428164\pi\)
−0.998692 + 0.0511230i \(0.983720\pi\)
\(420\) 0 0
\(421\) −34.0718 + 9.12952i −1.66056 + 0.444945i −0.962541 0.271135i \(-0.912601\pi\)
−0.698018 + 0.716080i \(0.745934\pi\)
\(422\) −12.0895 + 5.63741i −0.588505 + 0.274425i
\(423\) 0 0
\(424\) 4.86414 + 3.40591i 0.236224 + 0.165406i
\(425\) −25.5768 + 2.23768i −1.24066 + 0.108544i
\(426\) 0 0
\(427\) 6.76805 9.66577i 0.327529 0.467760i
\(428\) 6.50948 + 2.36926i 0.314648 + 0.114522i
\(429\) 0 0
\(430\) −0.154897 0.578082i −0.00746978 0.0278776i
\(431\) 13.0562 + 18.6462i 0.628897 + 0.898158i 0.999531 0.0306209i \(-0.00974847\pi\)
−0.370634 + 0.928779i \(0.620860\pi\)
\(432\) 0 0
\(433\) −13.3867 23.1864i −0.643322 1.11427i −0.984686 0.174336i \(-0.944222\pi\)
0.341364 0.939931i \(-0.389111\pi\)
\(434\) 0.516225 0.894127i 0.0247796 0.0429195i
\(435\) 0 0
\(436\) 1.23257 4.60001i 0.0590294 0.220301i
\(437\) 49.9814 18.1918i 2.39094 0.870230i
\(438\) 0 0
\(439\) −13.6646 6.37192i −0.652177 0.304115i 0.0682269 0.997670i \(-0.478266\pi\)
−0.720404 + 0.693555i \(0.756044\pi\)
\(440\) 0.00752726 + 0.00132726i 0.000358848 + 6.32746e-5i
\(441\) 0 0
\(442\) −2.34814 + 26.8394i −0.111690 + 1.27662i
\(443\) 16.9338 0.804548 0.402274 0.915519i \(-0.368220\pi\)
0.402274 + 0.915519i \(0.368220\pi\)
\(444\) 0 0
\(445\) −0.459191 −0.0217678
\(446\) −0.751250 + 8.58683i −0.0355727 + 0.406598i
\(447\) 0 0
\(448\) 2.01815 + 0.355855i 0.0953488 + 0.0168126i
\(449\) −21.3254 9.94421i −1.00641 0.469296i −0.151713 0.988425i \(-0.548479\pi\)
−0.854696 + 0.519129i \(0.826257\pi\)
\(450\) 0 0
\(451\) 0.428897 0.156106i 0.0201960 0.00735073i
\(452\) −5.21448 + 19.4607i −0.245268 + 0.915354i
\(453\) 0 0
\(454\) 0.851034 1.47403i 0.0399410 0.0691798i
\(455\) 0.438971 + 0.760321i 0.0205793 + 0.0356444i
\(456\) 0 0
\(457\) 20.3937 + 29.1252i 0.953978 + 1.36242i 0.931920 + 0.362665i \(0.118133\pi\)
0.0220584 + 0.999757i \(0.492978\pi\)
\(458\) −5.58679 20.8502i −0.261053 0.974265i
\(459\) 0 0
\(460\) 0.534719 + 0.194622i 0.0249314 + 0.00907429i
\(461\) 10.6754 15.2460i 0.497202 0.710078i −0.489612 0.871941i \(-0.662861\pi\)
0.986813 + 0.161863i \(0.0517503\pi\)
\(462\) 0 0
\(463\) −9.07890 + 0.794301i −0.421932 + 0.0369143i −0.296145 0.955143i \(-0.595701\pi\)
−0.125787 + 0.992057i \(0.540146\pi\)
\(464\) 2.57582 + 1.80361i 0.119580 + 0.0837305i
\(465\) 0 0
\(466\) 14.2680 6.65328i 0.660952 0.308207i
\(467\) 6.23587 1.67090i 0.288562 0.0773199i −0.111635 0.993749i \(-0.535609\pi\)
0.400196 + 0.916429i \(0.368942\pi\)
\(468\) 0 0
\(469\) −7.28674 8.68399i −0.336470 0.400990i
\(470\) 0.636865 0.367694i 0.0293764 0.0169605i
\(471\) 0 0
\(472\) 8.71826 1.53726i 0.401290 0.0707583i
\(473\) −0.660962 0.177104i −0.0303911 0.00814327i
\(474\) 0 0
\(475\) 26.9840 + 26.9840i 1.23811 + 1.23811i
\(476\) 4.45312 9.54975i 0.204109 0.437712i
\(477\) 0 0
\(478\) 8.23548 + 6.91039i 0.376682 + 0.316074i
\(479\) −21.2061 1.85530i −0.968933 0.0847707i −0.408311 0.912843i \(-0.633882\pi\)
−0.560622 + 0.828072i \(0.689438\pi\)
\(480\) 0 0
\(481\) 17.6468 + 26.5413i 0.804627 + 1.21018i
\(482\) 7.14884i 0.325621i
\(483\) 0 0
\(484\) −7.06505 + 8.41979i −0.321138 + 0.382718i
\(485\) −0.0169941 + 0.0963786i −0.000771664 + 0.00437633i
\(486\) 0 0
\(487\) 9.59314 9.59314i 0.434707 0.434707i −0.455519 0.890226i \(-0.650546\pi\)
0.890226 + 0.455519i \(0.150546\pi\)
\(488\) −1.96934 5.41072i −0.0891479 0.244932i
\(489\) 0 0
\(490\) 0.0397597 + 0.225489i 0.00179616 + 0.0101865i
\(491\) 23.0346 + 13.2990i 1.03954 + 0.600177i 0.919702 0.392616i \(-0.128430\pi\)
0.119835 + 0.992794i \(0.461763\pi\)
\(492\) 0 0
\(493\) 12.3857 10.3928i 0.557822 0.468068i
\(494\) 32.8028 22.9688i 1.47587 1.03341i
\(495\) 0 0
\(496\) −0.212919 0.456606i −0.00956034 0.0205022i
\(497\) 7.35154 20.1982i 0.329761 0.906012i
\(498\) 0 0
\(499\) −0.583121 6.66511i −0.0261041 0.298371i −0.998013 0.0630127i \(-0.979929\pi\)
0.971909 0.235358i \(-0.0756264\pi\)
\(500\) 0.0712122 + 0.813959i 0.00318471 + 0.0364014i
\(501\) 0 0
\(502\) −4.22018 + 11.5949i −0.188356 + 0.517504i
\(503\) −13.8860 29.7785i −0.619144 1.32776i −0.926547 0.376179i \(-0.877238\pi\)
0.307403 0.951579i \(-0.400540\pi\)
\(504\) 0 0
\(505\) 0.623788 0.436781i 0.0277582 0.0194365i
\(506\) 0.498404 0.418210i 0.0221567 0.0185917i
\(507\) 0 0
\(508\) −11.0169 6.36061i −0.488796 0.282206i
\(509\) 0.923450 + 5.23715i 0.0409312 + 0.232132i 0.998410 0.0563717i \(-0.0179532\pi\)
−0.957479 + 0.288504i \(0.906842\pi\)
\(510\) 0 0
\(511\) 3.31324 + 9.10305i 0.146569 + 0.402695i
\(512\) 0.707107 0.707107i 0.0312500 0.0312500i
\(513\) 0 0
\(514\) 3.80171 21.5606i 0.167686 0.950997i
\(515\) −1.01573 + 1.21050i −0.0447585 + 0.0533411i
\(516\) 0 0
\(517\) 0.840822i 0.0369793i
\(518\) −2.93518 12.1148i −0.128965 0.532295i
\(519\) 0 0
\(520\) 0.426784 + 0.0373387i 0.0187157 + 0.00163741i
\(521\) −8.93876 7.50051i −0.391614 0.328603i 0.425627 0.904898i \(-0.360053\pi\)
−0.817242 + 0.576295i \(0.804498\pi\)
\(522\) 0 0
\(523\) 16.5894 35.5761i 0.725405 1.55564i −0.102478 0.994735i \(-0.532677\pi\)
0.827883 0.560901i \(-0.189545\pi\)
\(524\) −1.14379 1.14379i −0.0499667 0.0499667i
\(525\) 0 0
\(526\) 9.23383 + 2.47420i 0.402614 + 0.107880i
\(527\) −2.55112 + 0.449832i −0.111129 + 0.0195950i
\(528\) 0 0
\(529\) 22.0295 12.7188i 0.957806 0.552989i
\(530\) −0.312075 0.371916i −0.0135557 0.0161550i
\(531\) 0 0
\(532\) −15.1279 + 4.05351i −0.655877 + 0.175742i
\(533\) 23.1858 10.8117i 1.00429 0.468307i
\(534\) 0 0
\(535\) −0.463953 0.324863i −0.0200584 0.0140451i
\(536\) −5.51070 + 0.482124i −0.238026 + 0.0208246i
\(537\) 0 0
\(538\) −16.3124 + 23.2965i −0.703276 + 1.00438i
\(539\) 0.246006 + 0.0895390i 0.0105962 + 0.00385672i
\(540\) 0 0
\(541\) −1.59701 5.96011i −0.0686607 0.256245i 0.923061 0.384655i \(-0.125679\pi\)
−0.991721 + 0.128410i \(0.959013\pi\)
\(542\) −0.193727 0.276671i −0.00832128 0.0118840i
\(543\) 0 0
\(544\) −2.57089 4.45291i −0.110226 0.190917i
\(545\) −0.194686 + 0.337206i −0.00833942 + 0.0144443i
\(546\) 0 0
\(547\) −5.17369 + 19.3085i −0.221211 + 0.825571i 0.762676 + 0.646781i \(0.223885\pi\)
−0.983887 + 0.178791i \(0.942782\pi\)
\(548\) −14.9564 + 5.44367i −0.638904 + 0.232542i
\(549\) 0 0
\(550\) 0.423059 + 0.197276i 0.0180393 + 0.00841186i
\(551\) −23.6665 4.17305i −1.00823 0.177778i
\(552\) 0 0
\(553\) −2.52096 + 28.8146i −0.107202 + 1.22532i
\(554\) −9.03370 −0.383805
\(555\) 0 0
\(556\) 5.29521 0.224567
\(557\) 3.31456 37.8856i 0.140442 1.60526i −0.519852 0.854256i \(-0.674013\pi\)
0.660294 0.751007i \(-0.270432\pi\)
\(558\) 0 0
\(559\) −37.7714 6.66011i −1.59756 0.281693i
\(560\) −0.151854 0.0708109i −0.00641702 0.00299230i
\(561\) 0 0
\(562\) 26.3867 9.60397i 1.11306 0.405119i
\(563\) 10.5776 39.4761i 0.445792 1.66372i −0.268045 0.963407i \(-0.586377\pi\)
0.713837 0.700312i \(-0.246956\pi\)
\(564\) 0 0
\(565\) 0.823633 1.42657i 0.0346505 0.0600164i
\(566\) 6.80150 + 11.7805i 0.285888 + 0.495173i
\(567\) 0 0
\(568\) −6.01610 8.59188i −0.252430 0.360507i
\(569\) 9.76404 + 36.4399i 0.409330 + 1.52764i 0.795928 + 0.605392i \(0.206983\pi\)
−0.386598 + 0.922248i \(0.626350\pi\)
\(570\) 0 0
\(571\) −13.6730 4.97657i −0.572198 0.208263i 0.0396837 0.999212i \(-0.487365\pi\)
−0.611882 + 0.790949i \(0.709587\pi\)
\(572\) 0.280958 0.401250i 0.0117475 0.0167771i
\(573\) 0 0
\(574\) −9.96731 + 0.872026i −0.416027 + 0.0363977i
\(575\) 28.4672 + 19.9329i 1.18716 + 0.831261i
\(576\) 0 0
\(577\) 28.4758 13.2785i 1.18546 0.552791i 0.273026 0.962007i \(-0.411976\pi\)
0.912438 + 0.409216i \(0.134198\pi\)
\(578\) −9.11634 + 2.44272i −0.379190 + 0.101604i
\(579\) 0 0
\(580\) −0.165260 0.196949i −0.00686205 0.00817787i
\(581\) −20.2323 + 11.6811i −0.839376 + 0.484614i
\(582\) 0 0
\(583\) −0.546676 + 0.0963936i −0.0226410 + 0.00399222i
\(584\) 4.56607 + 1.22347i 0.188945 + 0.0506277i
\(585\) 0 0
\(586\) 17.6142 + 17.6142i 0.727635 + 0.727635i
\(587\) 18.7182 40.1414i 0.772584 1.65681i 0.0186807 0.999826i \(-0.494053\pi\)
0.753903 0.656986i \(-0.228169\pi\)
\(588\) 0 0
\(589\) 2.94952 + 2.47494i 0.121533 + 0.101978i
\(590\) −0.721060 0.0630846i −0.0296856 0.00259715i
\(591\) 0 0
\(592\) −5.66414 2.21756i −0.232795 0.0911412i
\(593\) 28.5125i 1.17087i 0.810721 + 0.585433i \(0.199076\pi\)
−0.810721 + 0.585433i \(0.800924\pi\)
\(594\) 0 0
\(595\) −0.553774 + 0.659962i −0.0227025 + 0.0270558i
\(596\) −0.826280 + 4.68607i −0.0338457 + 0.191949i
\(597\) 0 0
\(598\) 25.7864 25.7864i 1.05448 1.05448i
\(599\) −4.98253 13.6894i −0.203581 0.559333i 0.795321 0.606188i \(-0.207302\pi\)
−0.998902 + 0.0468554i \(0.985080\pi\)
\(600\) 0 0
\(601\) 1.16812 + 6.62472i 0.0476485 + 0.270228i 0.999319 0.0368922i \(-0.0117458\pi\)
−0.951671 + 0.307120i \(0.900635\pi\)
\(602\) 12.9906 + 7.50014i 0.529458 + 0.305683i
\(603\) 0 0
\(604\) −3.13019 + 2.62654i −0.127366 + 0.106872i
\(605\) 0.736141 0.515451i 0.0299284 0.0209561i
\(606\) 0 0
\(607\) 10.2261 + 21.9300i 0.415066 + 0.890112i 0.997039 + 0.0769037i \(0.0245034\pi\)
−0.581972 + 0.813209i \(0.697719\pi\)
\(608\) −2.61387 + 7.18154i −0.106006 + 0.291250i
\(609\) 0 0
\(610\) 0.0410312 + 0.468989i 0.00166131 + 0.0189888i
\(611\) −4.10751 46.9490i −0.166172 1.89935i
\(612\) 0 0
\(613\) −0.234258 + 0.643620i −0.00946161 + 0.0259956i −0.944334 0.328990i \(-0.893292\pi\)
0.934872 + 0.354985i \(0.115514\pi\)
\(614\) 2.87322 + 6.16163i 0.115954 + 0.248663i
\(615\) 0 0
\(616\) −0.156929 + 0.109883i −0.00632285 + 0.00442731i
\(617\) −5.94794 + 4.99091i −0.239455 + 0.200927i −0.754616 0.656167i \(-0.772177\pi\)
0.515161 + 0.857094i \(0.327732\pi\)
\(618\) 0 0
\(619\) −24.3094 14.0350i −0.977076 0.564115i −0.0756901 0.997131i \(-0.524116\pi\)
−0.901386 + 0.433016i \(0.857449\pi\)
\(620\) 0.00715295 + 0.0405664i 0.000287269 + 0.00162919i
\(621\) 0 0
\(622\) 12.0219 + 33.0299i 0.482034 + 1.32438i
\(623\) 8.13827 8.13827i 0.326053 0.326053i
\(624\) 0 0
\(625\) −4.32380 + 24.5215i −0.172952 + 0.980859i
\(626\) −18.9643 + 22.6007i −0.757964 + 0.903307i
\(627\) 0 0
\(628\) 4.29047i 0.171208i
\(629\) −18.5515 + 25.1803i −0.739696 + 1.00400i
\(630\) 0 0
\(631\) 31.9009 + 2.79097i 1.26996 + 0.111107i 0.702134 0.712045i \(-0.252231\pi\)
0.567821 + 0.823152i \(0.307786\pi\)
\(632\) 10.8124 + 9.07265i 0.430093 + 0.360891i
\(633\) 0 0
\(634\) 14.3976 30.8758i 0.571803 1.22623i
\(635\) 0.735466 + 0.735466i 0.0291861 + 0.0291861i
\(636\) 0 0
\(637\) 14.1737 + 3.79783i 0.561582 + 0.150475i
\(638\) −0.289494 + 0.0510455i −0.0114612 + 0.00202091i
\(639\) 0 0
\(640\) −0.0708076 + 0.0408808i −0.00279891 + 0.00161595i
\(641\) 8.62878 + 10.2834i 0.340816 + 0.406169i 0.909043 0.416703i \(-0.136815\pi\)
−0.568226 + 0.822872i \(0.692370\pi\)
\(642\) 0 0
\(643\) 5.56362 1.49077i 0.219408 0.0587902i −0.147440 0.989071i \(-0.547103\pi\)
0.366848 + 0.930281i \(0.380437\pi\)
\(644\) −12.9262 + 6.02756i −0.509362 + 0.237519i
\(645\) 0 0
\(646\) 32.1892 + 22.5391i 1.26647 + 0.886790i
\(647\) 27.5548 2.41073i 1.08329 0.0947757i 0.468498 0.883464i \(-0.344795\pi\)
0.614793 + 0.788689i \(0.289240\pi\)
\(648\) 0 0
\(649\) −0.474685 + 0.677921i −0.0186330 + 0.0266107i
\(650\) 24.5861 + 8.94860i 0.964346 + 0.350993i
\(651\) 0 0
\(652\) 1.06070 + 3.95860i 0.0415404 + 0.155031i
\(653\) −13.5295 19.3221i −0.529451 0.756134i 0.461963 0.886899i \(-0.347145\pi\)
−0.991413 + 0.130765i \(0.958257\pi\)
\(654\) 0 0
\(655\) 0.0661272 + 0.114536i 0.00258380 + 0.00447528i
\(656\) −2.44119 + 4.22826i −0.0953123 + 0.165086i
\(657\) 0 0
\(658\) −4.77053 + 17.8039i −0.185975 + 0.694066i
\(659\) 15.3229 5.57707i 0.596895 0.217252i −0.0258646 0.999665i \(-0.508234\pi\)
0.622759 + 0.782414i \(0.286012\pi\)
\(660\) 0 0
\(661\) −2.49678 1.16427i −0.0971135 0.0452848i 0.373455 0.927648i \(-0.378173\pi\)
−0.470568 + 0.882364i \(0.655951\pi\)
\(662\) −4.94602 0.872116i −0.192232 0.0338958i
\(663\) 0 0
\(664\) −0.993590 + 11.3568i −0.0385588 + 0.440729i
\(665\) 1.28051 0.0496561
\(666\) 0 0
\(667\) −21.8848 −0.847382
\(668\) 0.228078 2.60695i 0.00882461 0.100866i
\(669\) 0 0
\(670\) 0.445413 + 0.0785384i 0.0172078 + 0.00303420i
\(671\) 0.487845 + 0.227486i 0.0188330 + 0.00878199i
\(672\) 0 0
\(673\) −14.8999 + 5.42313i −0.574350 + 0.209046i −0.612832 0.790213i \(-0.709970\pi\)
0.0384821 + 0.999259i \(0.487748\pi\)
\(674\) −5.87575 + 21.9286i −0.226325 + 0.844658i
\(675\) 0 0
\(676\) 7.22774 12.5188i 0.277990 0.481493i
\(677\) 2.29819 + 3.98058i 0.0883266 + 0.152986i 0.906804 0.421553i \(-0.138515\pi\)
−0.818477 + 0.574539i \(0.805181\pi\)
\(678\) 0 0
\(679\) −1.40694 2.00931i −0.0539932 0.0771103i
\(680\) 0.108808 + 0.406075i 0.00417258 + 0.0155723i
\(681\) 0 0
\(682\) 0.0442576 + 0.0161085i 0.00169471 + 0.000616825i
\(683\) 27.1672 38.7988i 1.03952 1.48459i 0.173346 0.984861i \(-0.444542\pi\)
0.866179 0.499734i \(-0.166569\pi\)
\(684\) 0 0
\(685\) 1.29638 0.113419i 0.0495322 0.00433351i
\(686\) −16.4517 11.5196i −0.628131 0.439822i
\(687\) 0 0
\(688\) 6.63395 3.09346i 0.252917 0.117937i
\(689\) −30.0539 + 8.05291i −1.14496 + 0.306791i
\(690\) 0 0
\(691\) −10.0433 11.9691i −0.382065 0.455327i 0.540400 0.841408i \(-0.318273\pi\)
−0.922465 + 0.386081i \(0.873828\pi\)
\(692\) −1.05436 + 0.608733i −0.0400806 + 0.0231406i
\(693\) 0 0
\(694\) 15.1332 2.66839i 0.574449 0.101291i
\(695\) −0.418192 0.112054i −0.0158629 0.00425046i
\(696\) 0 0
\(697\) 17.7513 + 17.7513i 0.672378 + 0.672378i
\(698\) −2.87062 + 6.15607i −0.108655 + 0.233011i
\(699\) 0 0
\(700\) −7.83873 6.57747i −0.296276 0.248605i
\(701\) −1.81313 0.158628i −0.0684810 0.00599131i 0.0528638 0.998602i \(-0.483165\pi\)
−0.121345 + 0.992610i \(0.538721\pi\)
\(702\) 0 0
\(703\) 46.3944 2.93450i 1.74980 0.110677i
\(704\) 0.0934838i 0.00352330i
\(705\) 0 0
\(706\) −10.7508 + 12.8123i −0.404613 + 0.482199i
\(707\) −3.31433 + 18.7965i −0.124648 + 0.706916i
\(708\) 0 0
\(709\) 30.3617 30.3617i 1.14026 1.14026i 0.151857 0.988402i \(-0.451475\pi\)
0.988402 0.151857i \(-0.0485253\pi\)
\(710\) 0.293308 + 0.805858i 0.0110077 + 0.0302433i
\(711\) 0 0
\(712\) −0.975248 5.53090i −0.0365490 0.207279i
\(713\) 3.03660 + 1.75318i 0.113722 + 0.0656572i
\(714\) 0 0
\(715\) −0.0306799 + 0.0257435i −0.00114736 + 0.000962752i
\(716\) −5.91818 + 4.14395i −0.221173 + 0.154867i
\(717\) 0 0
\(718\) 10.4107 + 22.3258i 0.388524 + 0.833193i
\(719\) 0.175409 0.481933i 0.00654166 0.0179731i −0.936379 0.350991i \(-0.885845\pi\)
0.942920 + 0.333018i \(0.108067\pi\)
\(720\) 0 0
\(721\) −3.45192 39.4557i −0.128556 1.46941i
\(722\) −3.43454 39.2569i −0.127820 1.46099i
\(723\) 0 0
\(724\) 3.84300 10.5585i 0.142824 0.392405i
\(725\) −6.63573 14.2304i −0.246445 0.528502i
\(726\) 0 0
\(727\) −7.88484 + 5.52102i −0.292432 + 0.204763i −0.710581 0.703615i \(-0.751568\pi\)
0.418149 + 0.908379i \(0.362679\pi\)
\(728\) −8.22567 + 6.90215i −0.304864 + 0.255811i
\(729\) 0 0
\(730\) −0.334717 0.193249i −0.0123884 0.00715247i
\(731\) −6.53553 37.0648i −0.241725 1.37089i
\(732\) 0 0
\(733\) 11.6456 + 31.9960i 0.430139 + 1.18180i 0.945727 + 0.324961i \(0.105351\pi\)
−0.515588 + 0.856836i \(0.672427\pi\)
\(734\) 6.30143 6.30143i 0.232590 0.232590i
\(735\) 0 0
\(736\) −1.20854 + 6.85397i −0.0445474 + 0.252641i
\(737\) 0.332404 0.396144i 0.0122443 0.0145922i
\(738\) 0 0
\(739\) 21.9621i 0.807888i 0.914784 + 0.403944i \(0.132361\pi\)
−0.914784 + 0.403944i \(0.867639\pi\)
\(740\) 0.400401 + 0.294994i 0.0147191 + 0.0108442i
\(741\) 0 0
\(742\) 12.1224 + 1.06057i 0.445027 + 0.0389349i
\(743\) 22.7466 + 19.0867i 0.834492 + 0.700222i 0.956318 0.292329i \(-0.0944303\pi\)
−0.121825 + 0.992552i \(0.538875\pi\)
\(744\) 0 0
\(745\) 0.164420 0.352599i 0.00602388 0.0129182i
\(746\) −19.7673 19.7673i −0.723733 0.723733i
\(747\) 0 0
\(748\) 0.464295 + 0.124407i 0.0169763 + 0.00454878i
\(749\) 13.9802 2.46509i 0.510827 0.0900726i
\(750\) 0 0
\(751\) −37.0006 + 21.3623i −1.35017 + 0.779521i −0.988273 0.152697i \(-0.951204\pi\)
−0.361897 + 0.932218i \(0.617871\pi\)
\(752\) 5.78143 + 6.89004i 0.210827 + 0.251254i
\(753\) 0 0
\(754\) −15.9151 + 4.26444i −0.579594 + 0.155302i
\(755\) 0.302790 0.141193i 0.0110196 0.00513854i
\(756\) 0 0
\(757\) 5.26333 + 3.68542i 0.191299 + 0.133949i 0.665302 0.746574i \(-0.268303\pi\)
−0.474003 + 0.880523i \(0.657192\pi\)
\(758\) −9.59004 + 0.839020i −0.348326 + 0.0304746i
\(759\) 0 0
\(760\) 0.358404 0.511853i 0.0130007 0.0185669i
\(761\) −14.9673 5.44766i −0.542565 0.197477i 0.0561751 0.998421i \(-0.482109\pi\)
−0.598740 + 0.800943i \(0.704332\pi\)
\(762\) 0 0
\(763\) −2.52589 9.42674i −0.0914433 0.341271i
\(764\) 6.45542 + 9.21930i 0.233549 + 0.333543i
\(765\) 0 0
\(766\) 4.69766 + 8.13659i 0.169733 + 0.293987i
\(767\) −23.1933 + 40.1720i −0.837462 + 1.45053i
\(768\) 0 0
\(769\) 1.24915 4.66189i 0.0450455 0.168112i −0.939739 0.341893i \(-0.888932\pi\)
0.984784 + 0.173781i \(0.0555986\pi\)
\(770\) 0.0147188 0.00535722i 0.000530430 0.000193061i
\(771\) 0 0
\(772\) 17.7167 + 8.26146i 0.637640 + 0.297336i
\(773\) 35.3635 + 6.23554i 1.27194 + 0.224277i 0.768553 0.639786i \(-0.220977\pi\)
0.503384 + 0.864063i \(0.332088\pi\)
\(774\) 0 0
\(775\) −0.219256 + 2.50610i −0.00787590 + 0.0900219i
\(776\) −1.19696 −0.0429684
\(777\) 0 0
\(778\) −2.27419 −0.0815335
\(779\) 3.25206 37.1713i 0.116517 1.33180i
\(780\) 0 0
\(781\) 0.965632 + 0.170267i 0.0345530 + 0.00609263i
\(782\) 32.4325 + 15.1235i 1.15978 + 0.540816i
\(783\) 0 0
\(784\)