Properties

Label 855.2.k.h.676.2
Level $855$
Weight $2$
Character 855.676
Analytic conductor $6.827$
Analytic rank $0$
Dimension $8$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), degree \(2\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{3})\)
Coefficient field: 8.0.4601315889.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{7} + 6x^{6} - 3x^{5} + 26x^{4} - 14x^{3} + 31x^{2} + 12x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 95)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 676.2
Root \(-1.02359 + 1.77290i\) of defining polynomial
Character \(\chi\) \(=\) 855.676
Dual form 855.2.k.h.406.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.595455 + 1.03136i) q^{2} +(0.290867 + 0.503797i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.609175 q^{7} -3.07461 q^{8} +O(q^{10})\) \(q+(-0.595455 + 1.03136i) q^{2} +(0.290867 + 0.503797i) q^{4} +(0.500000 - 0.866025i) q^{5} -0.609175 q^{7} -3.07461 q^{8} +(0.595455 + 1.03136i) q^{10} -4.48517 q^{11} +(-2.21900 - 3.84342i) q^{13} +(0.362736 - 0.628278i) q^{14} +(1.24906 - 2.16343i) q^{16} +(1.45172 - 2.51445i) q^{17} +(3.60532 - 2.44983i) q^{19} +0.581734 q^{20} +(2.67071 - 4.62581i) q^{22} +(-1.42363 - 2.46580i) q^{23} +(-0.500000 - 0.866025i) q^{25} +5.28525 q^{26} +(-0.177189 - 0.306901i) q^{28} +(0.558149 + 0.966742i) q^{29} -6.22908 q^{31} +(-1.58710 - 2.74893i) q^{32} +(1.72886 + 2.99448i) q^{34} +(-0.304588 + 0.527561i) q^{35} -3.77264 q^{37} +(0.379847 + 5.17714i) q^{38} +(-1.53731 + 2.66269i) q^{40} +(-4.15184 + 7.19120i) q^{41} +(4.99438 - 8.65053i) q^{43} +(-1.30459 - 2.25961i) q^{44} +3.39082 q^{46} +(-2.94250 - 5.09656i) q^{47} -6.62891 q^{49} +1.19091 q^{50} +(1.29087 - 2.23585i) q^{52} +(4.22436 + 7.31681i) q^{53} +(-2.24258 + 3.88427i) q^{55} +1.87298 q^{56} -1.32941 q^{58} +(5.11793 - 8.86451i) q^{59} +(2.49099 + 4.31453i) q^{61} +(3.70913 - 6.42441i) q^{62} +8.77641 q^{64} -4.43800 q^{65} +(-4.23808 - 7.34057i) q^{67} +1.68903 q^{68} +(-0.362736 - 0.628278i) q^{70} +(5.80995 - 10.0631i) q^{71} +(-1.86162 + 3.22443i) q^{73} +(2.24644 - 3.89095i) q^{74} +(2.28289 + 1.10377i) q^{76} +2.73225 q^{77} +(-4.51908 + 7.82728i) q^{79} +(-1.24906 - 2.16343i) q^{80} +(-4.94447 - 8.56407i) q^{82} +2.12178 q^{83} +(-1.45172 - 2.51445i) q^{85} +(5.94786 + 10.3020i) q^{86} +13.7901 q^{88} +(3.96608 + 6.86946i) q^{89} +(1.35176 + 2.34131i) q^{91} +(0.828173 - 1.43444i) q^{92} +7.00850 q^{94} +(-0.318955 - 4.34721i) q^{95} +(4.83628 - 8.37668i) q^{97} +(3.94721 - 6.83677i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + q^{2} - 5 q^{4} + 4 q^{5} - 8 q^{7} - 24 q^{8} - q^{10} + 4 q^{11} - 7 q^{13} - q^{14} - 7 q^{16} - q^{17} + 5 q^{19} - 10 q^{20} - 2 q^{22} + 2 q^{23} - 4 q^{25} - 6 q^{26} + 19 q^{28} - q^{29} + 30 q^{32} - 15 q^{34} - 4 q^{35} - 4 q^{37} - 13 q^{38} - 12 q^{40} - 8 q^{41} - q^{43} - 12 q^{44} + 24 q^{46} - 12 q^{47} - 20 q^{49} - 2 q^{50} + 3 q^{52} - 5 q^{53} + 2 q^{55} + 82 q^{56} - 54 q^{58} - 5 q^{59} + 37 q^{62} + 112 q^{64} - 14 q^{65} - 4 q^{67} - 32 q^{68} + q^{70} + 20 q^{71} + 20 q^{73} + 25 q^{74} + 63 q^{76} - 28 q^{77} - 17 q^{79} + 7 q^{80} - 21 q^{82} - 2 q^{83} + q^{85} + 8 q^{86} - 14 q^{88} + 11 q^{89} - 6 q^{91} - q^{92} - 62 q^{94} + 4 q^{95} - q^{97} + 9 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.595455 + 1.03136i −0.421050 + 0.729280i −0.996042 0.0888786i \(-0.971672\pi\)
0.574992 + 0.818159i \(0.305005\pi\)
\(3\) 0 0
\(4\) 0.290867 + 0.503797i 0.145434 + 0.251898i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) −0.609175 −0.230247 −0.115123 0.993351i \(-0.536726\pi\)
−0.115123 + 0.993351i \(0.536726\pi\)
\(8\) −3.07461 −1.08704
\(9\) 0 0
\(10\) 0.595455 + 1.03136i 0.188299 + 0.326144i
\(11\) −4.48517 −1.35233 −0.676164 0.736751i \(-0.736359\pi\)
−0.676164 + 0.736751i \(0.736359\pi\)
\(12\) 0 0
\(13\) −2.21900 3.84342i −0.615439 1.06597i −0.990307 0.138894i \(-0.955645\pi\)
0.374868 0.927078i \(-0.377688\pi\)
\(14\) 0.362736 0.628278i 0.0969454 0.167914i
\(15\) 0 0
\(16\) 1.24906 2.16343i 0.312265 0.540858i
\(17\) 1.45172 2.51445i 0.352093 0.609843i −0.634523 0.772904i \(-0.718803\pi\)
0.986616 + 0.163061i \(0.0521368\pi\)
\(18\) 0 0
\(19\) 3.60532 2.44983i 0.827117 0.562030i
\(20\) 0.581734 0.130080
\(21\) 0 0
\(22\) 2.67071 4.62581i 0.569398 0.986227i
\(23\) −1.42363 2.46580i −0.296847 0.514154i 0.678566 0.734540i \(-0.262602\pi\)
−0.975413 + 0.220386i \(0.929268\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 5.28525 1.03652
\(27\) 0 0
\(28\) −0.177189 0.306901i −0.0334856 0.0579987i
\(29\) 0.558149 + 0.966742i 0.103646 + 0.179519i 0.913184 0.407547i \(-0.133616\pi\)
−0.809538 + 0.587067i \(0.800283\pi\)
\(30\) 0 0
\(31\) −6.22908 −1.11877 −0.559387 0.828906i \(-0.688964\pi\)
−0.559387 + 0.828906i \(0.688964\pi\)
\(32\) −1.58710 2.74893i −0.280562 0.485947i
\(33\) 0 0
\(34\) 1.72886 + 2.99448i 0.296498 + 0.513549i
\(35\) −0.304588 + 0.527561i −0.0514847 + 0.0891741i
\(36\) 0 0
\(37\) −3.77264 −0.620219 −0.310109 0.950701i \(-0.600366\pi\)
−0.310109 + 0.950701i \(0.600366\pi\)
\(38\) 0.379847 + 5.17714i 0.0616193 + 0.839843i
\(39\) 0 0
\(40\) −1.53731 + 2.66269i −0.243069 + 0.421009i
\(41\) −4.15184 + 7.19120i −0.648409 + 1.12308i 0.335094 + 0.942185i \(0.391232\pi\)
−0.983503 + 0.180893i \(0.942101\pi\)
\(42\) 0 0
\(43\) 4.99438 8.65053i 0.761637 1.31919i −0.180370 0.983599i \(-0.557730\pi\)
0.942007 0.335594i \(-0.108937\pi\)
\(44\) −1.30459 2.25961i −0.196674 0.340649i
\(45\) 0 0
\(46\) 3.39082 0.499950
\(47\) −2.94250 5.09656i −0.429208 0.743409i 0.567595 0.823308i \(-0.307874\pi\)
−0.996803 + 0.0798983i \(0.974540\pi\)
\(48\) 0 0
\(49\) −6.62891 −0.946986
\(50\) 1.19091 0.168420
\(51\) 0 0
\(52\) 1.29087 2.23585i 0.179011 0.310056i
\(53\) 4.22436 + 7.31681i 0.580261 + 1.00504i 0.995448 + 0.0953049i \(0.0303826\pi\)
−0.415188 + 0.909736i \(0.636284\pi\)
\(54\) 0 0
\(55\) −2.24258 + 3.88427i −0.302390 + 0.523755i
\(56\) 1.87298 0.250287
\(57\) 0 0
\(58\) −1.32941 −0.174560
\(59\) 5.11793 8.86451i 0.666297 1.15406i −0.312634 0.949874i \(-0.601211\pi\)
0.978932 0.204187i \(-0.0654552\pi\)
\(60\) 0 0
\(61\) 2.49099 + 4.31453i 0.318939 + 0.552419i 0.980267 0.197678i \(-0.0633401\pi\)
−0.661328 + 0.750097i \(0.730007\pi\)
\(62\) 3.70913 6.42441i 0.471060 0.815900i
\(63\) 0 0
\(64\) 8.77641 1.09705
\(65\) −4.43800 −0.550466
\(66\) 0 0
\(67\) −4.23808 7.34057i −0.517764 0.896794i −0.999787 0.0206350i \(-0.993431\pi\)
0.482023 0.876159i \(-0.339902\pi\)
\(68\) 1.68903 0.204825
\(69\) 0 0
\(70\) −0.362736 0.628278i −0.0433553 0.0750936i
\(71\) 5.80995 10.0631i 0.689514 1.19427i −0.282481 0.959273i \(-0.591157\pi\)
0.971995 0.235001i \(-0.0755093\pi\)
\(72\) 0 0
\(73\) −1.86162 + 3.22443i −0.217887 + 0.377391i −0.954162 0.299292i \(-0.903250\pi\)
0.736275 + 0.676682i \(0.236583\pi\)
\(74\) 2.24644 3.89095i 0.261143 0.452313i
\(75\) 0 0
\(76\) 2.28289 + 1.10377i 0.261865 + 0.126611i
\(77\) 2.73225 0.311369
\(78\) 0 0
\(79\) −4.51908 + 7.82728i −0.508437 + 0.880638i 0.491516 + 0.870869i \(0.336443\pi\)
−0.999952 + 0.00976923i \(0.996890\pi\)
\(80\) −1.24906 2.16343i −0.139649 0.241879i
\(81\) 0 0
\(82\) −4.94447 8.56407i −0.546025 0.945744i
\(83\) 2.12178 0.232896 0.116448 0.993197i \(-0.462849\pi\)
0.116448 + 0.993197i \(0.462849\pi\)
\(84\) 0 0
\(85\) −1.45172 2.51445i −0.157461 0.272730i
\(86\) 5.94786 + 10.3020i 0.641374 + 1.11089i
\(87\) 0 0
\(88\) 13.7901 1.47003
\(89\) 3.96608 + 6.86946i 0.420404 + 0.728161i 0.995979 0.0895879i \(-0.0285550\pi\)
−0.575575 + 0.817749i \(0.695222\pi\)
\(90\) 0 0
\(91\) 1.35176 + 2.34131i 0.141703 + 0.245436i
\(92\) 0.828173 1.43444i 0.0863430 0.149551i
\(93\) 0 0
\(94\) 7.00850 0.722872
\(95\) −0.318955 4.34721i −0.0327241 0.446015i
\(96\) 0 0
\(97\) 4.83628 8.37668i 0.491050 0.850523i −0.508897 0.860827i \(-0.669947\pi\)
0.999947 + 0.0103043i \(0.00328001\pi\)
\(98\) 3.94721 6.83677i 0.398729 0.690619i
\(99\) 0 0
\(100\) 0.290867 0.503797i 0.0290867 0.0503797i
\(101\) −0.485632 0.841140i −0.0483222 0.0836965i 0.840853 0.541264i \(-0.182054\pi\)
−0.889175 + 0.457568i \(0.848721\pi\)
\(102\) 0 0
\(103\) −3.34143 −0.329241 −0.164620 0.986357i \(-0.552640\pi\)
−0.164620 + 0.986357i \(0.552640\pi\)
\(104\) 6.82256 + 11.8170i 0.669007 + 1.15875i
\(105\) 0 0
\(106\) −10.0617 −0.977275
\(107\) −9.51655 −0.920000 −0.460000 0.887919i \(-0.652151\pi\)
−0.460000 + 0.887919i \(0.652151\pi\)
\(108\) 0 0
\(109\) −2.77178 + 4.80087i −0.265489 + 0.459840i −0.967692 0.252137i \(-0.918867\pi\)
0.702203 + 0.711977i \(0.252200\pi\)
\(110\) −2.67071 4.62581i −0.254643 0.441054i
\(111\) 0 0
\(112\) −0.760896 + 1.31791i −0.0718979 + 0.124531i
\(113\) −1.54134 −0.144997 −0.0724987 0.997369i \(-0.523097\pi\)
−0.0724987 + 0.997369i \(0.523097\pi\)
\(114\) 0 0
\(115\) −2.84726 −0.265508
\(116\) −0.324694 + 0.562387i −0.0301471 + 0.0522163i
\(117\) 0 0
\(118\) 6.09499 + 10.5568i 0.561089 + 0.971835i
\(119\) −0.884350 + 1.53174i −0.0810682 + 0.140414i
\(120\) 0 0
\(121\) 9.11672 0.828793
\(122\) −5.93310 −0.537158
\(123\) 0 0
\(124\) −1.81183 3.13819i −0.162707 0.281818i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −1.15274 1.99661i −0.102289 0.177171i 0.810338 0.585963i \(-0.199283\pi\)
−0.912628 + 0.408792i \(0.865950\pi\)
\(128\) −2.05176 + 3.55376i −0.181352 + 0.314111i
\(129\) 0 0
\(130\) 2.64263 4.57716i 0.231774 0.401444i
\(131\) −6.45905 + 11.1874i −0.564330 + 0.977448i 0.432782 + 0.901499i \(0.357532\pi\)
−0.997112 + 0.0759493i \(0.975801\pi\)
\(132\) 0 0
\(133\) −2.19627 + 1.49238i −0.190441 + 0.129405i
\(134\) 10.0943 0.872018
\(135\) 0 0
\(136\) −4.46346 + 7.73095i −0.382739 + 0.662923i
\(137\) −6.36677 11.0276i −0.543950 0.942149i −0.998672 0.0515159i \(-0.983595\pi\)
0.454722 0.890633i \(-0.349739\pi\)
\(138\) 0 0
\(139\) −5.30433 9.18738i −0.449908 0.779263i 0.548472 0.836169i \(-0.315210\pi\)
−0.998380 + 0.0569059i \(0.981876\pi\)
\(140\) −0.354378 −0.0299504
\(141\) 0 0
\(142\) 6.91913 + 11.9843i 0.580640 + 1.00570i
\(143\) 9.95258 + 17.2384i 0.832276 + 1.44154i
\(144\) 0 0
\(145\) 1.11630 0.0927035
\(146\) −2.21703 3.84000i −0.183482 0.317801i
\(147\) 0 0
\(148\) −1.09734 1.90065i −0.0902006 0.156232i
\(149\) 1.88653 3.26757i 0.154551 0.267690i −0.778344 0.627837i \(-0.783940\pi\)
0.932895 + 0.360147i \(0.117274\pi\)
\(150\) 0 0
\(151\) −9.51562 −0.774370 −0.387185 0.922002i \(-0.626553\pi\)
−0.387185 + 0.922002i \(0.626553\pi\)
\(152\) −11.0850 + 7.53228i −0.899109 + 0.610948i
\(153\) 0 0
\(154\) −1.62693 + 2.81793i −0.131102 + 0.227075i
\(155\) −3.11454 + 5.39454i −0.250166 + 0.433300i
\(156\) 0 0
\(157\) 1.72822 2.99336i 0.137927 0.238896i −0.788785 0.614669i \(-0.789290\pi\)
0.926712 + 0.375773i \(0.122623\pi\)
\(158\) −5.38182 9.32158i −0.428155 0.741585i
\(159\) 0 0
\(160\) −3.17419 −0.250942
\(161\) 0.867239 + 1.50210i 0.0683480 + 0.118382i
\(162\) 0 0
\(163\) 6.65283 0.521090 0.260545 0.965462i \(-0.416098\pi\)
0.260545 + 0.965462i \(0.416098\pi\)
\(164\) −4.83054 −0.377202
\(165\) 0 0
\(166\) −1.26343 + 2.18832i −0.0980609 + 0.169846i
\(167\) −8.22775 14.2509i −0.636682 1.10277i −0.986156 0.165820i \(-0.946973\pi\)
0.349474 0.936946i \(-0.386360\pi\)
\(168\) 0 0
\(169\) −3.34790 + 5.79874i −0.257531 + 0.446057i
\(170\) 3.45773 0.265195
\(171\) 0 0
\(172\) 5.81081 0.443070
\(173\) −11.3912 + 19.7302i −0.866058 + 1.50006i −6.58713e−5 1.00000i \(0.500021\pi\)
−0.865992 + 0.500057i \(0.833312\pi\)
\(174\) 0 0
\(175\) 0.304588 + 0.527561i 0.0230247 + 0.0398799i
\(176\) −5.60224 + 9.70336i −0.422284 + 0.731418i
\(177\) 0 0
\(178\) −9.44650 −0.708045
\(179\) 2.32916 0.174090 0.0870449 0.996204i \(-0.472258\pi\)
0.0870449 + 0.996204i \(0.472258\pi\)
\(180\) 0 0
\(181\) 11.1696 + 19.3463i 0.830230 + 1.43800i 0.897856 + 0.440290i \(0.145124\pi\)
−0.0676258 + 0.997711i \(0.521542\pi\)
\(182\) −3.21965 −0.238656
\(183\) 0 0
\(184\) 4.37710 + 7.58137i 0.322684 + 0.558906i
\(185\) −1.88632 + 3.26721i −0.138685 + 0.240210i
\(186\) 0 0
\(187\) −6.51119 + 11.2777i −0.476145 + 0.824708i
\(188\) 1.71175 2.96484i 0.124842 0.216233i
\(189\) 0 0
\(190\) 4.67346 + 2.25961i 0.339048 + 0.163929i
\(191\) −2.23766 −0.161911 −0.0809556 0.996718i \(-0.525797\pi\)
−0.0809556 + 0.996718i \(0.525797\pi\)
\(192\) 0 0
\(193\) 2.27153 3.93441i 0.163508 0.283205i −0.772616 0.634873i \(-0.781052\pi\)
0.936125 + 0.351669i \(0.114386\pi\)
\(194\) 5.75957 + 9.97587i 0.413513 + 0.716226i
\(195\) 0 0
\(196\) −1.92813 3.33962i −0.137724 0.238544i
\(197\) 19.2236 1.36962 0.684812 0.728720i \(-0.259884\pi\)
0.684812 + 0.728720i \(0.259884\pi\)
\(198\) 0 0
\(199\) 3.07547 + 5.32687i 0.218014 + 0.377612i 0.954201 0.299167i \(-0.0967087\pi\)
−0.736186 + 0.676779i \(0.763375\pi\)
\(200\) 1.53731 + 2.66269i 0.108704 + 0.188281i
\(201\) 0 0
\(202\) 1.15669 0.0813843
\(203\) −0.340010 0.588915i −0.0238641 0.0413338i
\(204\) 0 0
\(205\) 4.15184 + 7.19120i 0.289977 + 0.502255i
\(206\) 1.98967 3.44621i 0.138627 0.240109i
\(207\) 0 0
\(208\) −11.0866 −0.768720
\(209\) −16.1705 + 10.9879i −1.11853 + 0.760049i
\(210\) 0 0
\(211\) −6.34661 + 10.9926i −0.436919 + 0.756765i −0.997450 0.0713679i \(-0.977264\pi\)
0.560531 + 0.828133i \(0.310597\pi\)
\(212\) −2.45746 + 4.25644i −0.168779 + 0.292333i
\(213\) 0 0
\(214\) 5.66668 9.81497i 0.387366 0.670938i
\(215\) −4.99438 8.65053i −0.340614 0.589961i
\(216\) 0 0
\(217\) 3.79460 0.257594
\(218\) −3.30094 5.71740i −0.223568 0.387231i
\(219\) 0 0
\(220\) −2.60918 −0.175911
\(221\) −12.8854 −0.866767
\(222\) 0 0
\(223\) −11.2688 + 19.5181i −0.754614 + 1.30703i 0.190952 + 0.981599i \(0.438842\pi\)
−0.945566 + 0.325430i \(0.894491\pi\)
\(224\) 0.966820 + 1.67458i 0.0645984 + 0.111888i
\(225\) 0 0
\(226\) 0.917800 1.58968i 0.0610512 0.105744i
\(227\) −18.1124 −1.20216 −0.601080 0.799189i \(-0.705263\pi\)
−0.601080 + 0.799189i \(0.705263\pi\)
\(228\) 0 0
\(229\) −9.41604 −0.622229 −0.311115 0.950372i \(-0.600702\pi\)
−0.311115 + 0.950372i \(0.600702\pi\)
\(230\) 1.69541 2.93654i 0.111792 0.193630i
\(231\) 0 0
\(232\) −1.71609 2.97236i −0.112667 0.195145i
\(233\) 7.85000 13.5966i 0.514271 0.890743i −0.485592 0.874185i \(-0.661396\pi\)
0.999863 0.0165573i \(-0.00527061\pi\)
\(234\) 0 0
\(235\) −5.88500 −0.383895
\(236\) 5.95455 0.387608
\(237\) 0 0
\(238\) −1.05318 1.82416i −0.0682676 0.118243i
\(239\) 23.4610 1.51757 0.758783 0.651344i \(-0.225795\pi\)
0.758783 + 0.651344i \(0.225795\pi\)
\(240\) 0 0
\(241\) −6.58469 11.4050i −0.424157 0.734662i 0.572184 0.820125i \(-0.306096\pi\)
−0.996341 + 0.0854634i \(0.972763\pi\)
\(242\) −5.42860 + 9.40260i −0.348963 + 0.604422i
\(243\) 0 0
\(244\) −1.44910 + 2.50991i −0.0927689 + 0.160680i
\(245\) −3.31445 + 5.74080i −0.211753 + 0.366766i
\(246\) 0 0
\(247\) −17.4159 8.42058i −1.10815 0.535789i
\(248\) 19.1520 1.21615
\(249\) 0 0
\(250\) 0.595455 1.03136i 0.0376599 0.0652288i
\(251\) −8.66257 15.0040i −0.546776 0.947045i −0.998493 0.0548830i \(-0.982521\pi\)
0.451716 0.892162i \(-0.350812\pi\)
\(252\) 0 0
\(253\) 6.38521 + 11.0595i 0.401435 + 0.695305i
\(254\) 2.74563 0.172276
\(255\) 0 0
\(256\) 6.33295 + 10.9690i 0.395809 + 0.685562i
\(257\) −2.83980 4.91867i −0.177142 0.306818i 0.763759 0.645502i \(-0.223352\pi\)
−0.940900 + 0.338683i \(0.890018\pi\)
\(258\) 0 0
\(259\) 2.29820 0.142803
\(260\) −1.29087 2.23585i −0.0800562 0.138661i
\(261\) 0 0
\(262\) −7.69215 13.3232i −0.475222 0.823109i
\(263\) 2.82882 4.89966i 0.174433 0.302126i −0.765532 0.643398i \(-0.777524\pi\)
0.939965 + 0.341272i \(0.110858\pi\)
\(264\) 0 0
\(265\) 8.44872 0.519001
\(266\) −0.231393 3.15379i −0.0141876 0.193371i
\(267\) 0 0
\(268\) 2.46544 4.27026i 0.150601 0.260848i
\(269\) −11.9959 + 20.7775i −0.731402 + 1.26683i 0.224881 + 0.974386i \(0.427801\pi\)
−0.956284 + 0.292440i \(0.905533\pi\)
\(270\) 0 0
\(271\) 10.6497 18.4459i 0.646926 1.12051i −0.336927 0.941531i \(-0.609388\pi\)
0.983853 0.178978i \(-0.0572791\pi\)
\(272\) −3.62656 6.28138i −0.219892 0.380865i
\(273\) 0 0
\(274\) 15.1645 0.916121
\(275\) 2.24258 + 3.88427i 0.135233 + 0.234230i
\(276\) 0 0
\(277\) −0.821109 −0.0493357 −0.0246678 0.999696i \(-0.507853\pi\)
−0.0246678 + 0.999696i \(0.507853\pi\)
\(278\) 12.6340 0.757735
\(279\) 0 0
\(280\) 0.936489 1.62205i 0.0559659 0.0969358i
\(281\) −0.293739 0.508772i −0.0175230 0.0303508i 0.857131 0.515099i \(-0.172245\pi\)
−0.874654 + 0.484748i \(0.838911\pi\)
\(282\) 0 0
\(283\) −15.4712 + 26.7969i −0.919667 + 1.59291i −0.119746 + 0.992805i \(0.538208\pi\)
−0.799921 + 0.600105i \(0.795125\pi\)
\(284\) 6.75969 0.401114
\(285\) 0 0
\(286\) −23.7052 −1.40172
\(287\) 2.52920 4.38070i 0.149294 0.258585i
\(288\) 0 0
\(289\) 4.28504 + 7.42191i 0.252061 + 0.436583i
\(290\) −0.664705 + 1.15130i −0.0390328 + 0.0676068i
\(291\) 0 0
\(292\) −2.16594 −0.126752
\(293\) −3.76271 −0.219820 −0.109910 0.993942i \(-0.535056\pi\)
−0.109910 + 0.993942i \(0.535056\pi\)
\(294\) 0 0
\(295\) −5.11793 8.86451i −0.297977 0.516112i
\(296\) 11.5994 0.674202
\(297\) 0 0
\(298\) 2.24669 + 3.89138i 0.130147 + 0.225422i
\(299\) −6.31806 + 10.9432i −0.365383 + 0.632861i
\(300\) 0 0
\(301\) −3.04246 + 5.26969i −0.175364 + 0.303740i
\(302\) 5.66612 9.81401i 0.326049 0.564733i
\(303\) 0 0
\(304\) −0.796788 10.8598i −0.0456989 0.622855i
\(305\) 4.98199 0.285268
\(306\) 0 0
\(307\) −10.1709 + 17.6166i −0.580485 + 1.00543i 0.414936 + 0.909850i \(0.363804\pi\)
−0.995422 + 0.0955798i \(0.969529\pi\)
\(308\) 0.794723 + 1.37650i 0.0452835 + 0.0784334i
\(309\) 0 0
\(310\) −3.70913 6.42441i −0.210665 0.364882i
\(311\) 7.67830 0.435397 0.217698 0.976016i \(-0.430145\pi\)
0.217698 + 0.976016i \(0.430145\pi\)
\(312\) 0 0
\(313\) −11.9964 20.7783i −0.678074 1.17446i −0.975560 0.219733i \(-0.929481\pi\)
0.297486 0.954726i \(-0.403852\pi\)
\(314\) 2.05815 + 3.56482i 0.116148 + 0.201174i
\(315\) 0 0
\(316\) −5.25781 −0.295775
\(317\) 0.519518 + 0.899831i 0.0291790 + 0.0505395i 0.880246 0.474517i \(-0.157377\pi\)
−0.851067 + 0.525057i \(0.824044\pi\)
\(318\) 0 0
\(319\) −2.50339 4.33600i −0.140163 0.242769i
\(320\) 4.38821 7.60059i 0.245308 0.424886i
\(321\) 0 0
\(322\) −2.06561 −0.115112
\(323\) −0.926066 12.6218i −0.0515277 0.702298i
\(324\) 0 0
\(325\) −2.21900 + 3.84342i −0.123088 + 0.213194i
\(326\) −3.96146 + 6.86145i −0.219405 + 0.380020i
\(327\) 0 0
\(328\) 12.7653 22.1102i 0.704846 1.22083i
\(329\) 1.79250 + 3.10470i 0.0988236 + 0.171167i
\(330\) 0 0
\(331\) 30.8316 1.69466 0.847328 0.531069i \(-0.178210\pi\)
0.847328 + 0.531069i \(0.178210\pi\)
\(332\) 0.617157 + 1.06895i 0.0338709 + 0.0586661i
\(333\) 0 0
\(334\) 19.5970 1.07230
\(335\) −8.47616 −0.463102
\(336\) 0 0
\(337\) −10.3576 + 17.9400i −0.564217 + 0.977252i 0.432906 + 0.901439i \(0.357488\pi\)
−0.997122 + 0.0758124i \(0.975845\pi\)
\(338\) −3.98705 6.90577i −0.216867 0.375625i
\(339\) 0 0
\(340\) 0.844513 1.46274i 0.0458002 0.0793282i
\(341\) 27.9384 1.51295
\(342\) 0 0
\(343\) 8.30239 0.448287
\(344\) −15.3558 + 26.5970i −0.827929 + 1.43402i
\(345\) 0 0
\(346\) −13.5659 23.4968i −0.729308 1.26320i
\(347\) 4.11068 7.11991i 0.220673 0.382217i −0.734340 0.678782i \(-0.762508\pi\)
0.955013 + 0.296566i \(0.0958413\pi\)
\(348\) 0 0
\(349\) 11.9216 0.638150 0.319075 0.947730i \(-0.396628\pi\)
0.319075 + 0.947730i \(0.396628\pi\)
\(350\) −0.725473 −0.0387782
\(351\) 0 0
\(352\) 7.11839 + 12.3294i 0.379412 + 0.657160i
\(353\) 11.7983 0.627959 0.313980 0.949430i \(-0.398338\pi\)
0.313980 + 0.949430i \(0.398338\pi\)
\(354\) 0 0
\(355\) −5.80995 10.0631i −0.308360 0.534095i
\(356\) −2.30721 + 3.99620i −0.122282 + 0.211798i
\(357\) 0 0
\(358\) −1.38691 + 2.40220i −0.0733005 + 0.126960i
\(359\) 0.0554058 0.0959656i 0.00292420 0.00506487i −0.864560 0.502530i \(-0.832403\pi\)
0.867484 + 0.497465i \(0.165736\pi\)
\(360\) 0 0
\(361\) 6.99666 17.6648i 0.368245 0.929729i
\(362\) −26.6040 −1.39827
\(363\) 0 0
\(364\) −0.786364 + 1.36202i −0.0412167 + 0.0713894i
\(365\) 1.86162 + 3.22443i 0.0974418 + 0.168774i
\(366\) 0 0
\(367\) −5.86986 10.1669i −0.306404 0.530708i 0.671169 0.741305i \(-0.265793\pi\)
−0.977573 + 0.210597i \(0.932459\pi\)
\(368\) −7.11278 −0.370779
\(369\) 0 0
\(370\) −2.24644 3.89095i −0.116787 0.202281i
\(371\) −2.57338 4.45722i −0.133603 0.231407i
\(372\) 0 0
\(373\) 14.5190 0.751763 0.375882 0.926668i \(-0.377340\pi\)
0.375882 + 0.926668i \(0.377340\pi\)
\(374\) −7.75424 13.4307i −0.400962 0.694487i
\(375\) 0 0
\(376\) 9.04704 + 15.6699i 0.466566 + 0.808115i
\(377\) 2.47706 4.29040i 0.127575 0.220967i
\(378\) 0 0
\(379\) −6.59023 −0.338518 −0.169259 0.985572i \(-0.554137\pi\)
−0.169259 + 0.985572i \(0.554137\pi\)
\(380\) 2.09734 1.42515i 0.107591 0.0731087i
\(381\) 0 0
\(382\) 1.33242 2.30782i 0.0681727 0.118079i
\(383\) −1.43461 + 2.48481i −0.0733049 + 0.126968i −0.900348 0.435171i \(-0.856688\pi\)
0.827043 + 0.562139i \(0.190021\pi\)
\(384\) 0 0
\(385\) 1.36613 2.36620i 0.0696243 0.120593i
\(386\) 2.70519 + 4.68552i 0.137690 + 0.238487i
\(387\) 0 0
\(388\) 5.62686 0.285660
\(389\) −3.16575 5.48323i −0.160510 0.278011i 0.774542 0.632523i \(-0.217980\pi\)
−0.935052 + 0.354512i \(0.884647\pi\)
\(390\) 0 0
\(391\) −8.26682 −0.418071
\(392\) 20.3813 1.02941
\(393\) 0 0
\(394\) −11.4468 + 19.8264i −0.576680 + 0.998840i
\(395\) 4.51908 + 7.82728i 0.227380 + 0.393833i
\(396\) 0 0
\(397\) 15.2749 26.4569i 0.766626 1.32784i −0.172756 0.984965i \(-0.555267\pi\)
0.939382 0.342871i \(-0.111399\pi\)
\(398\) −7.32522 −0.367180
\(399\) 0 0
\(400\) −2.49812 −0.124906
\(401\) 15.1711 26.2771i 0.757609 1.31222i −0.186458 0.982463i \(-0.559701\pi\)
0.944067 0.329754i \(-0.106966\pi\)
\(402\) 0 0
\(403\) 13.8223 + 23.9409i 0.688538 + 1.19258i
\(404\) 0.282509 0.489320i 0.0140553 0.0243446i
\(405\) 0 0
\(406\) 0.809843 0.0401919
\(407\) 16.9209 0.838740
\(408\) 0 0
\(409\) 7.48628 + 12.9666i 0.370173 + 0.641158i 0.989592 0.143903i \(-0.0459652\pi\)
−0.619419 + 0.785060i \(0.712632\pi\)
\(410\) −9.88894 −0.488380
\(411\) 0 0
\(412\) −0.971912 1.68340i −0.0478827 0.0829352i
\(413\) −3.11772 + 5.40004i −0.153413 + 0.265719i
\(414\) 0 0
\(415\) 1.06089 1.83752i 0.0520771 0.0902002i
\(416\) −7.04353 + 12.1997i −0.345337 + 0.598142i
\(417\) 0 0
\(418\) −1.70368 23.2203i −0.0833296 1.13574i
\(419\) 6.17419 0.301629 0.150815 0.988562i \(-0.451810\pi\)
0.150815 + 0.988562i \(0.451810\pi\)
\(420\) 0 0
\(421\) 13.7714 23.8528i 0.671177 1.16251i −0.306394 0.951905i \(-0.599122\pi\)
0.977571 0.210608i \(-0.0675443\pi\)
\(422\) −7.55824 13.0913i −0.367929 0.637272i
\(423\) 0 0
\(424\) −12.9883 22.4963i −0.630766 1.09252i
\(425\) −2.90343 −0.140837
\(426\) 0 0
\(427\) −1.51745 2.62830i −0.0734347 0.127193i
\(428\) −2.76805 4.79441i −0.133799 0.231746i
\(429\) 0 0
\(430\) 11.8957 0.573663
\(431\) −7.52941 13.0413i −0.362679 0.628179i 0.625722 0.780046i \(-0.284805\pi\)
−0.988401 + 0.151868i \(0.951471\pi\)
\(432\) 0 0
\(433\) 0.485420 + 0.840772i 0.0233278 + 0.0404049i 0.877454 0.479661i \(-0.159241\pi\)
−0.854126 + 0.520066i \(0.825907\pi\)
\(434\) −2.25951 + 3.91359i −0.108460 + 0.187858i
\(435\) 0 0
\(436\) −3.22488 −0.154444
\(437\) −11.1734 5.40234i −0.534497 0.258429i
\(438\) 0 0
\(439\) 13.7187 23.7616i 0.654760 1.13408i −0.327194 0.944957i \(-0.606103\pi\)
0.981954 0.189120i \(-0.0605636\pi\)
\(440\) 6.89507 11.9426i 0.328710 0.569342i
\(441\) 0 0
\(442\) 7.67269 13.2895i 0.364952 0.632116i
\(443\) −4.38272 7.59109i −0.208229 0.360664i 0.742928 0.669372i \(-0.233437\pi\)
−0.951157 + 0.308708i \(0.900103\pi\)
\(444\) 0 0
\(445\) 7.93217 0.376021
\(446\) −13.4201 23.2443i −0.635461 1.10065i
\(447\) 0 0
\(448\) −5.34637 −0.252592
\(449\) 9.63397 0.454655 0.227327 0.973818i \(-0.427001\pi\)
0.227327 + 0.973818i \(0.427001\pi\)
\(450\) 0 0
\(451\) 18.6217 32.2538i 0.876862 1.51877i
\(452\) −0.448326 0.776524i −0.0210875 0.0365246i
\(453\) 0 0
\(454\) 10.7851 18.6803i 0.506169 0.876711i
\(455\) 2.70352 0.126743
\(456\) 0 0
\(457\) −10.6708 −0.499161 −0.249580 0.968354i \(-0.580293\pi\)
−0.249580 + 0.968354i \(0.580293\pi\)
\(458\) 5.60683 9.71131i 0.261990 0.453780i
\(459\) 0 0
\(460\) −0.828173 1.43444i −0.0386138 0.0668810i
\(461\) 2.84340 4.92491i 0.132430 0.229376i −0.792183 0.610284i \(-0.791055\pi\)
0.924613 + 0.380908i \(0.124389\pi\)
\(462\) 0 0
\(463\) 35.3550 1.64309 0.821543 0.570147i \(-0.193114\pi\)
0.821543 + 0.570147i \(0.193114\pi\)
\(464\) 2.78864 0.129459
\(465\) 0 0
\(466\) 9.34864 + 16.1923i 0.433067 + 0.750095i
\(467\) 32.9071 1.52276 0.761380 0.648306i \(-0.224522\pi\)
0.761380 + 0.648306i \(0.224522\pi\)
\(468\) 0 0
\(469\) 2.58173 + 4.47169i 0.119213 + 0.206484i
\(470\) 3.50425 6.06954i 0.161639 0.279967i
\(471\) 0 0
\(472\) −15.7356 + 27.2549i −0.724292 + 1.25451i
\(473\) −22.4006 + 38.7991i −1.02998 + 1.78398i
\(474\) 0 0
\(475\) −3.92428 1.89738i −0.180058 0.0870579i
\(476\) −1.02891 −0.0471602
\(477\) 0 0
\(478\) −13.9700 + 24.1967i −0.638971 + 1.10673i
\(479\) −4.52861 7.84378i −0.206917 0.358391i 0.743825 0.668375i \(-0.233010\pi\)
−0.950742 + 0.309984i \(0.899676\pi\)
\(480\) 0 0
\(481\) 8.37149 + 14.4998i 0.381707 + 0.661136i
\(482\) 15.6835 0.714366
\(483\) 0 0
\(484\) 2.65175 + 4.59297i 0.120534 + 0.208772i
\(485\) −4.83628 8.37668i −0.219604 0.380365i
\(486\) 0 0
\(487\) −16.5206 −0.748620 −0.374310 0.927304i \(-0.622120\pi\)
−0.374310 + 0.927304i \(0.622120\pi\)
\(488\) −7.65884 13.2655i −0.346700 0.600501i
\(489\) 0 0
\(490\) −3.94721 6.83677i −0.178317 0.308854i
\(491\) −0.695625 + 1.20486i −0.0313931 + 0.0543745i −0.881295 0.472566i \(-0.843328\pi\)
0.849902 + 0.526941i \(0.176661\pi\)
\(492\) 0 0
\(493\) 3.24109 0.145972
\(494\) 19.0550 12.9480i 0.857326 0.582557i
\(495\) 0 0
\(496\) −7.78048 + 13.4762i −0.349354 + 0.605099i
\(497\) −3.53928 + 6.13021i −0.158758 + 0.274977i
\(498\) 0 0
\(499\) 8.33255 14.4324i 0.373016 0.646083i −0.617012 0.786954i \(-0.711657\pi\)
0.990028 + 0.140871i \(0.0449902\pi\)
\(500\) −0.290867 0.503797i −0.0130080 0.0225305i
\(501\) 0 0
\(502\) 20.6327 0.920881
\(503\) 7.81956 + 13.5439i 0.348657 + 0.603892i 0.986011 0.166679i \(-0.0533045\pi\)
−0.637354 + 0.770571i \(0.719971\pi\)
\(504\) 0 0
\(505\) −0.971265 −0.0432207
\(506\) −15.2084 −0.676096
\(507\) 0 0
\(508\) 0.670591 1.16150i 0.0297526 0.0515331i
\(509\) −9.57702 16.5879i −0.424494 0.735245i 0.571879 0.820338i \(-0.306215\pi\)
−0.996373 + 0.0850929i \(0.972881\pi\)
\(510\) 0 0
\(511\) 1.13406 1.96424i 0.0501677 0.0868929i
\(512\) −23.2910 −1.02933
\(513\) 0 0
\(514\) 6.76389 0.298342
\(515\) −1.67071 + 2.89376i −0.0736205 + 0.127514i
\(516\) 0 0
\(517\) 13.1976 + 22.8589i 0.580430 + 1.00533i
\(518\) −1.36848 + 2.37027i −0.0601273 + 0.104144i
\(519\) 0 0
\(520\) 13.6451 0.598378
\(521\) 19.2394 0.842892 0.421446 0.906853i \(-0.361523\pi\)
0.421446 + 0.906853i \(0.361523\pi\)
\(522\) 0 0
\(523\) −3.31973 5.74993i −0.145161 0.251427i 0.784272 0.620418i \(-0.213037\pi\)
−0.929433 + 0.368990i \(0.879704\pi\)
\(524\) −7.51490 −0.328290
\(525\) 0 0
\(526\) 3.36887 + 5.83505i 0.146890 + 0.254420i
\(527\) −9.04285 + 15.6627i −0.393913 + 0.682277i
\(528\) 0 0
\(529\) 7.44657 12.8978i 0.323764 0.560775i
\(530\) −5.03083 + 8.71366i −0.218525 + 0.378497i
\(531\) 0 0
\(532\) −1.39068 0.672391i −0.0602935 0.0291519i
\(533\) 36.8517 1.59623
\(534\) 0 0
\(535\) −4.75828 + 8.24158i −0.205718 + 0.356314i
\(536\) 13.0305 + 22.5694i 0.562830 + 0.974850i
\(537\) 0 0
\(538\) −14.2860 24.7441i −0.615914 1.06679i
\(539\) 29.7317 1.28064
\(540\) 0 0
\(541\) −20.8756 36.1575i −0.897510 1.55453i −0.830667 0.556770i \(-0.812040\pi\)
−0.0668435 0.997763i \(-0.521293\pi\)
\(542\) 12.6829 + 21.9674i 0.544777 + 0.943581i
\(543\) 0 0
\(544\) −9.21606 −0.395135
\(545\) 2.77178 + 4.80087i 0.118730 + 0.205647i
\(546\) 0 0
\(547\) −6.10258 10.5700i −0.260927 0.451939i 0.705561 0.708649i \(-0.250695\pi\)
−0.966489 + 0.256710i \(0.917362\pi\)
\(548\) 3.70377 6.41512i 0.158217 0.274040i
\(549\) 0 0
\(550\) −5.34143 −0.227759
\(551\) 4.38066 + 2.11804i 0.186622 + 0.0902317i
\(552\) 0 0
\(553\) 2.75291 4.76819i 0.117066 0.202764i
\(554\) 0.488934 0.846858i 0.0207728 0.0359795i
\(555\) 0 0
\(556\) 3.08571 5.34461i 0.130863 0.226662i
\(557\) 17.5774 + 30.4450i 0.744779 + 1.28999i 0.950298 + 0.311342i \(0.100778\pi\)
−0.205519 + 0.978653i \(0.565888\pi\)
\(558\) 0 0
\(559\) −44.3301 −1.87496
\(560\) 0.760896 + 1.31791i 0.0321537 + 0.0556919i
\(561\) 0 0
\(562\) 0.699634 0.0295123
\(563\) −17.8406 −0.751891 −0.375945 0.926642i \(-0.622682\pi\)
−0.375945 + 0.926642i \(0.622682\pi\)
\(564\) 0 0
\(565\) −0.770672 + 1.33484i −0.0324224 + 0.0561572i
\(566\) −18.4248 31.9127i −0.774452 1.34139i
\(567\) 0 0
\(568\) −17.8633 + 30.9402i −0.749529 + 1.29822i
\(569\) −31.6042 −1.32492 −0.662459 0.749098i \(-0.730487\pi\)
−0.662459 + 0.749098i \(0.730487\pi\)
\(570\) 0 0
\(571\) −4.73053 −0.197967 −0.0989833 0.995089i \(-0.531559\pi\)
−0.0989833 + 0.995089i \(0.531559\pi\)
\(572\) −5.78975 + 10.0281i −0.242082 + 0.419298i
\(573\) 0 0
\(574\) 3.01205 + 5.21702i 0.125721 + 0.217754i
\(575\) −1.42363 + 2.46580i −0.0593694 + 0.102831i
\(576\) 0 0
\(577\) 24.4074 1.01609 0.508047 0.861330i \(-0.330368\pi\)
0.508047 + 0.861330i \(0.330368\pi\)
\(578\) −10.2062 −0.424522
\(579\) 0 0
\(580\) 0.324694 + 0.562387i 0.0134822 + 0.0233518i
\(581\) −1.29254 −0.0536235
\(582\) 0 0
\(583\) −18.9470 32.8171i −0.784703 1.35915i
\(584\) 5.72377 9.91386i 0.236851 0.410239i
\(585\) 0 0
\(586\) 2.24052 3.88070i 0.0925551 0.160310i
\(587\) −14.3077 + 24.7817i −0.590543 + 1.02285i 0.403616 + 0.914928i \(0.367753\pi\)
−0.994159 + 0.107922i \(0.965580\pi\)
\(588\) 0 0
\(589\) −22.4578 + 15.2602i −0.925358 + 0.628785i
\(590\) 12.1900 0.501853
\(591\) 0 0
\(592\) −4.71225 + 8.16186i −0.193672 + 0.335450i
\(593\) 1.85756 + 3.21738i 0.0762807 + 0.132122i 0.901642 0.432482i \(-0.142362\pi\)
−0.825362 + 0.564604i \(0.809029\pi\)
\(594\) 0 0
\(595\) 0.884350 + 1.53174i 0.0362548 + 0.0627952i
\(596\) 2.19492 0.0899076
\(597\) 0 0
\(598\) −7.52423 13.0324i −0.307689 0.532933i
\(599\) 3.54970 + 6.14826i 0.145037 + 0.251211i 0.929387 0.369108i \(-0.120337\pi\)
−0.784350 + 0.620319i \(0.787003\pi\)
\(600\) 0 0
\(601\) −11.0596 −0.451131 −0.225566 0.974228i \(-0.572423\pi\)
−0.225566 + 0.974228i \(0.572423\pi\)
\(602\) −3.62329 6.27572i −0.147674 0.255779i
\(603\) 0 0
\(604\) −2.76778 4.79394i −0.112619 0.195063i
\(605\) 4.55836 7.89531i 0.185324 0.320990i
\(606\) 0 0
\(607\) 27.1193 1.10074 0.550369 0.834921i \(-0.314487\pi\)
0.550369 + 0.834921i \(0.314487\pi\)
\(608\) −12.4564 6.02266i −0.505174 0.244251i
\(609\) 0 0
\(610\) −2.96655 + 5.13821i −0.120112 + 0.208040i
\(611\) −13.0588 + 22.6185i −0.528302 + 0.915046i
\(612\) 0 0
\(613\) −20.9156 + 36.2268i −0.844772 + 1.46319i 0.0410468 + 0.999157i \(0.486931\pi\)
−0.885819 + 0.464031i \(0.846403\pi\)
\(614\) −12.1127 20.9797i −0.488827 0.846673i
\(615\) 0 0
\(616\) −8.40062 −0.338471
\(617\) −8.85262 15.3332i −0.356393 0.617291i 0.630962 0.775813i \(-0.282660\pi\)
−0.987355 + 0.158523i \(0.949327\pi\)
\(618\) 0 0
\(619\) −39.8064 −1.59995 −0.799976 0.600032i \(-0.795155\pi\)
−0.799976 + 0.600032i \(0.795155\pi\)
\(620\) −3.62367 −0.145530
\(621\) 0 0
\(622\) −4.57208 + 7.91908i −0.183324 + 0.317526i
\(623\) −2.41604 4.18471i −0.0967966 0.167657i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 28.5732 1.14201
\(627\) 0 0
\(628\) 2.01072 0.0802366
\(629\) −5.47681 + 9.48611i −0.218375 + 0.378236i
\(630\) 0 0
\(631\) −23.0990 40.0087i −0.919557 1.59272i −0.800088 0.599882i \(-0.795214\pi\)
−0.119469 0.992838i \(-0.538119\pi\)
\(632\) 13.8944 24.0659i 0.552691 0.957288i
\(633\) 0 0
\(634\) −1.23740 −0.0491433
\(635\) −2.30549 −0.0914905
\(636\) 0 0
\(637\) 14.7095 + 25.4776i 0.582813 + 1.00946i
\(638\) 5.96262 0.236062
\(639\) 0 0
\(640\) 2.05176 + 3.55376i 0.0811030 + 0.140475i
\(641\) 3.30674 5.72744i 0.130608 0.226220i −0.793303 0.608827i \(-0.791640\pi\)
0.923911 + 0.382607i \(0.124974\pi\)
\(642\) 0 0
\(643\) 15.3076 26.5135i 0.603673 1.04559i −0.388587 0.921412i \(-0.627037\pi\)
0.992260 0.124180i \(-0.0396300\pi\)
\(644\) −0.504503 + 0.873824i −0.0198802 + 0.0344335i
\(645\) 0 0
\(646\) 13.5691 + 6.56063i 0.533868 + 0.258125i
\(647\) 11.8979 0.467753 0.233877 0.972266i \(-0.424859\pi\)
0.233877 + 0.972266i \(0.424859\pi\)
\(648\) 0 0
\(649\) −22.9548 + 39.7588i −0.901053 + 1.56067i
\(650\) −2.64263 4.57716i −0.103652 0.179531i
\(651\) 0 0
\(652\) 1.93509 + 3.35167i 0.0757839 + 0.131262i
\(653\) 1.42899 0.0559207 0.0279604 0.999609i \(-0.491099\pi\)
0.0279604 + 0.999609i \(0.491099\pi\)
\(654\) 0 0
\(655\) 6.45905 + 11.1874i 0.252376 + 0.437128i
\(656\) 10.3718 + 17.9645i 0.404950 + 0.701395i
\(657\) 0 0
\(658\) −4.26941 −0.166439
\(659\) −12.2485 21.2150i −0.477134 0.826420i 0.522523 0.852625i \(-0.324991\pi\)
−0.999657 + 0.0262051i \(0.991658\pi\)
\(660\) 0 0
\(661\) 1.61303 + 2.79385i 0.0627396 + 0.108668i 0.895689 0.444681i \(-0.146683\pi\)
−0.832949 + 0.553349i \(0.813350\pi\)
\(662\) −18.3588 + 31.7984i −0.713535 + 1.23588i
\(663\) 0 0
\(664\) −6.52366 −0.253167
\(665\) 0.194300 + 2.64822i 0.00753462 + 0.102693i
\(666\) 0 0
\(667\) 1.58919 2.75256i 0.0615338 0.106580i
\(668\) 4.78636 8.29023i 0.185190 0.320758i
\(669\) 0 0
\(670\) 5.04717 8.74196i 0.194989 0.337731i
\(671\) −11.1725 19.3514i −0.431311 0.747052i
\(672\) 0 0
\(673\) 37.1424 1.43173 0.715866 0.698237i \(-0.246032\pi\)
0.715866 + 0.698237i \(0.246032\pi\)
\(674\) −12.3350 21.3649i −0.475127 0.822944i
\(675\) 0 0
\(676\) −3.89518 −0.149815
\(677\) 24.7550 0.951412 0.475706 0.879604i \(-0.342193\pi\)
0.475706 + 0.879604i \(0.342193\pi\)
\(678\) 0 0
\(679\) −2.94614 + 5.10287i −0.113063 + 0.195830i
\(680\) 4.46346 + 7.73095i 0.171166 + 0.296468i
\(681\) 0 0
\(682\) −16.6361 + 28.8145i −0.637028 + 1.10337i
\(683\) −40.1153 −1.53497 −0.767484 0.641068i \(-0.778492\pi\)
−0.767484 + 0.641068i \(0.778492\pi\)
\(684\) 0 0
\(685\) −12.7335 −0.486524
\(686\) −4.94370 + 8.56274i −0.188751 + 0.326927i
\(687\) 0 0
\(688\) −12.4766 21.6100i −0.475664 0.823875i
\(689\) 18.7477 32.4720i 0.714230 1.23708i
\(690\) 0 0
\(691\) 39.4963 1.50251 0.751254 0.660013i \(-0.229449\pi\)
0.751254 + 0.660013i \(0.229449\pi\)
\(692\) −13.2533 −0.503816
\(693\) 0 0
\(694\) 4.89545 + 8.47917i 0.185829 + 0.321865i
\(695\) −10.6087 −0.402410
\(696\) 0 0
\(697\) 12.0546 + 20.8792i 0.456600 + 0.790855i
\(698\) −7.09879 + 12.2955i −0.268693 + 0.465390i
\(699\) 0 0
\(700\) −0.177189 + 0.306901i −0.00669712 + 0.0115997i
\(701\) 0.0109776 0.0190137i 0.000414618 0.000718139i −0.865818 0.500359i \(-0.833201\pi\)
0.866233 + 0.499641i \(0.166535\pi\)
\(702\) 0 0
\(703\) −13.6016 + 9.24234i −0.512994 + 0.348581i
\(704\) −39.3637 −1.48357
\(705\) 0 0
\(706\) −7.02535 + 12.1683i −0.264402 + 0.457958i
\(707\) 0.295835 + 0.512402i 0.0111260 + 0.0192708i
\(708\) 0 0
\(709\) 8.90087 + 15.4168i 0.334279 + 0.578989i 0.983346 0.181743i \(-0.0581738\pi\)
−0.649067 + 0.760731i \(0.724840\pi\)
\(710\) 13.8383 0.519340
\(711\) 0 0
\(712\) −12.1942 21.1209i −0.456996 0.791540i
\(713\) 8.86789 + 15.3596i 0.332105 + 0.575223i
\(714\) 0 0
\(715\) 19.9052 0.744410
\(716\) 0.677477 + 1.17342i 0.0253185 + 0.0438529i
\(717\) 0 0
\(718\) 0.0659833 + 0.114286i 0.00246247 + 0.00426513i
\(719\) 9.40515 16.2902i 0.350753 0.607522i −0.635629 0.771995i \(-0.719259\pi\)
0.986382 + 0.164473i \(0.0525923\pi\)
\(720\) 0 0
\(721\) 2.03552 0.0758066
\(722\) 14.0526 + 17.7347i 0.522983 + 0.660016i
\(723\) 0 0
\(724\) −6.49774 + 11.2544i −0.241487 + 0.418267i
\(725\) 0.558149 0.966742i 0.0207291 0.0359039i
\(726\) 0 0
\(727\) −2.50151 + 4.33274i −0.0927758 + 0.160692i −0.908678 0.417497i \(-0.862907\pi\)
0.815902 + 0.578190i \(0.196241\pi\)
\(728\) −4.15613 7.19864i −0.154037 0.266799i
\(729\) 0 0
\(730\) −4.43405 −0.164112
\(731\) −14.5009 25.1162i −0.536334 0.928957i
\(732\) 0 0
\(733\) −23.5259 −0.868950 −0.434475 0.900684i \(-0.643066\pi\)
−0.434475 + 0.900684i \(0.643066\pi\)
\(734\) 13.9809 0.516046
\(735\) 0 0
\(736\) −4.51887 + 7.82691i −0.166568 + 0.288504i
\(737\) 19.0085 + 32.9237i 0.700187 + 1.21276i
\(738\) 0 0
\(739\) 18.6918 32.3752i 0.687590 1.19094i −0.285026 0.958520i \(-0.592002\pi\)
0.972615 0.232421i \(-0.0746646\pi\)
\(740\) −2.19468 −0.0806779
\(741\) 0 0
\(742\) 6.12932 0.225014
\(743\) 5.19430 8.99679i 0.190560 0.330060i −0.754876 0.655868i \(-0.772303\pi\)
0.945436 + 0.325808i \(0.105636\pi\)
\(744\) 0 0
\(745\) −1.88653 3.26757i −0.0691173 0.119715i
\(746\) −8.64539 + 14.9742i −0.316530 + 0.548246i
\(747\) 0 0
\(748\) −7.57556 −0.276990
\(749\) 5.79725 0.211827
\(750\) 0 0
\(751\) 15.6413 + 27.0915i 0.570758 + 0.988581i 0.996488 + 0.0837314i \(0.0266838\pi\)
−0.425731 + 0.904850i \(0.639983\pi\)
\(752\) −14.7014 −0.536105
\(753\) 0 0
\(754\) 2.94996 + 5.10947i 0.107431 + 0.186076i
\(755\) −4.75781 + 8.24077i −0.173154 + 0.299912i
\(756\) 0 0
\(757\) 6.31205 10.9328i 0.229415 0.397359i −0.728220 0.685344i \(-0.759652\pi\)
0.957635 + 0.287985i \(0.0929853\pi\)
\(758\) 3.92419 6.79689i 0.142533 0.246874i
\(759\) 0 0
\(760\) 0.980664 + 13.3660i 0.0355724 + 0.484836i
\(761\) −11.5495 −0.418668 −0.209334 0.977844i \(-0.567130\pi\)
−0.209334 + 0.977844i \(0.567130\pi\)
\(762\) 0 0
\(763\) 1.68850 2.92457i 0.0611279 0.105877i
\(764\) −0.650861 1.12732i −0.0235473 0.0407851i
\(765\) 0 0
\(766\) −1.70849 2.95918i −0.0617301 0.106920i
\(767\) −45.4267 −1.64026
\(768\) 0 0
\(769\) 13.4603 + 23.3140i 0.485392 + 0.840724i 0.999859 0.0167864i \(-0.00534353\pi\)
−0.514467 + 0.857510i \(0.672010\pi\)
\(770\) 1.62693 + 2.81793i 0.0586306 + 0.101551i
\(771\) 0 0
\(772\) 2.64286 0.0951184
\(773\) 10.6666 + 18.4750i 0.383649 + 0.664500i 0.991581 0.129489i \(-0.0413338\pi\)
−0.607932 + 0.793989i \(0.708001\pi\)
\(774\) 0 0
\(775\) 3.11454 + 5.39454i 0.111877 + 0.193778i
\(776\) −14.8697 + 25.7550i −0.533790 + 0.924552i
\(777\) 0 0
\(778\) 7.54024 0.270331
\(779\) 2.64851 + 36.0979i 0.0948926 + 1.29334i
\(780\) 0 0
\(781\) −26.0586 + 45.1348i −0.932450 + 1.61505i
\(782\) 4.92252 8.52605i 0.176029 0.304891i
\(783\)