Properties

Label 54.4.c.a.37.1
Level $54$
Weight $4$
Character 54.37
Analytic conductor $3.186$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [54,4,Mod(19,54)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(54, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("54.19");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 54 = 2 \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 54.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.18610314031\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 18)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 37.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 54.37
Dual form 54.4.c.a.19.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.50000 + 7.79423i) q^{5} +(15.5000 + 26.8468i) q^{7} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.50000 + 7.79423i) q^{5} +(15.5000 + 26.8468i) q^{7} -8.00000 q^{8} -18.0000 q^{10} +(-7.50000 - 12.9904i) q^{11} +(18.5000 - 32.0429i) q^{13} +(-31.0000 + 53.6936i) q^{14} +(-8.00000 - 13.8564i) q^{16} +42.0000 q^{17} -28.0000 q^{19} +(-18.0000 - 31.1769i) q^{20} +(15.0000 - 25.9808i) q^{22} +(97.5000 - 168.875i) q^{23} +(22.0000 + 38.1051i) q^{25} +74.0000 q^{26} -124.000 q^{28} +(55.5000 + 96.1288i) q^{29} +(102.500 - 177.535i) q^{31} +(16.0000 - 27.7128i) q^{32} +(42.0000 + 72.7461i) q^{34} -279.000 q^{35} -166.000 q^{37} +(-28.0000 - 48.4974i) q^{38} +(36.0000 - 62.3538i) q^{40} +(-130.500 + 226.033i) q^{41} +(21.5000 + 37.2391i) q^{43} +60.0000 q^{44} +390.000 q^{46} +(88.5000 + 153.286i) q^{47} +(-309.000 + 535.204i) q^{49} +(-44.0000 + 76.2102i) q^{50} +(74.0000 + 128.172i) q^{52} -114.000 q^{53} +135.000 q^{55} +(-124.000 - 214.774i) q^{56} +(-111.000 + 192.258i) q^{58} +(79.5000 - 137.698i) q^{59} +(-95.5000 - 165.411i) q^{61} +410.000 q^{62} +64.0000 q^{64} +(166.500 + 288.386i) q^{65} +(210.500 - 364.597i) q^{67} +(-84.0000 + 145.492i) q^{68} +(-279.000 - 483.242i) q^{70} -156.000 q^{71} +182.000 q^{73} +(-166.000 - 287.520i) q^{74} +(56.0000 - 96.9948i) q^{76} +(232.500 - 402.702i) q^{77} +(-566.500 - 981.207i) q^{79} +144.000 q^{80} -522.000 q^{82} +(-541.500 - 937.906i) q^{83} +(-189.000 + 327.358i) q^{85} +(-43.0000 + 74.4782i) q^{86} +(60.0000 + 103.923i) q^{88} +1050.00 q^{89} +1147.00 q^{91} +(390.000 + 675.500i) q^{92} +(-177.000 + 306.573i) q^{94} +(126.000 - 218.238i) q^{95} +(450.500 + 780.289i) q^{97} -1236.00 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 4 q^{4} - 9 q^{5} + 31 q^{7} - 16 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 4 q^{4} - 9 q^{5} + 31 q^{7} - 16 q^{8} - 36 q^{10} - 15 q^{11} + 37 q^{13} - 62 q^{14} - 16 q^{16} + 84 q^{17} - 56 q^{19} - 36 q^{20} + 30 q^{22} + 195 q^{23} + 44 q^{25} + 148 q^{26} - 248 q^{28} + 111 q^{29} + 205 q^{31} + 32 q^{32} + 84 q^{34} - 558 q^{35} - 332 q^{37} - 56 q^{38} + 72 q^{40} - 261 q^{41} + 43 q^{43} + 120 q^{44} + 780 q^{46} + 177 q^{47} - 618 q^{49} - 88 q^{50} + 148 q^{52} - 228 q^{53} + 270 q^{55} - 248 q^{56} - 222 q^{58} + 159 q^{59} - 191 q^{61} + 820 q^{62} + 128 q^{64} + 333 q^{65} + 421 q^{67} - 168 q^{68} - 558 q^{70} - 312 q^{71} + 364 q^{73} - 332 q^{74} + 112 q^{76} + 465 q^{77} - 1133 q^{79} + 288 q^{80} - 1044 q^{82} - 1083 q^{83} - 378 q^{85} - 86 q^{86} + 120 q^{88} + 2100 q^{89} + 2294 q^{91} + 780 q^{92} - 354 q^{94} + 252 q^{95} + 901 q^{97} - 2472 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).

\(n\) \(29\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) −4.50000 + 7.79423i −0.402492 + 0.697137i −0.994026 0.109143i \(-0.965189\pi\)
0.591534 + 0.806280i \(0.298523\pi\)
\(6\) 0 0
\(7\) 15.5000 + 26.8468i 0.836921 + 1.44959i 0.892456 + 0.451134i \(0.148980\pi\)
−0.0555351 + 0.998457i \(0.517686\pi\)
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −18.0000 −0.569210
\(11\) −7.50000 12.9904i −0.205576 0.356068i 0.744740 0.667355i \(-0.232573\pi\)
−0.950316 + 0.311287i \(0.899240\pi\)
\(12\) 0 0
\(13\) 18.5000 32.0429i 0.394691 0.683624i −0.598371 0.801219i \(-0.704185\pi\)
0.993062 + 0.117595i \(0.0375185\pi\)
\(14\) −31.0000 + 53.6936i −0.591793 + 1.02502i
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 42.0000 0.599206 0.299603 0.954064i \(-0.403146\pi\)
0.299603 + 0.954064i \(0.403146\pi\)
\(18\) 0 0
\(19\) −28.0000 −0.338086 −0.169043 0.985609i \(-0.554068\pi\)
−0.169043 + 0.985609i \(0.554068\pi\)
\(20\) −18.0000 31.1769i −0.201246 0.348569i
\(21\) 0 0
\(22\) 15.0000 25.9808i 0.145364 0.251778i
\(23\) 97.5000 168.875i 0.883920 1.53099i 0.0369731 0.999316i \(-0.488228\pi\)
0.846947 0.531678i \(-0.178438\pi\)
\(24\) 0 0
\(25\) 22.0000 + 38.1051i 0.176000 + 0.304841i
\(26\) 74.0000 0.558177
\(27\) 0 0
\(28\) −124.000 −0.836921
\(29\) 55.5000 + 96.1288i 0.355382 + 0.615540i 0.987183 0.159590i \(-0.0510173\pi\)
−0.631801 + 0.775131i \(0.717684\pi\)
\(30\) 0 0
\(31\) 102.500 177.535i 0.593856 1.02859i −0.399851 0.916580i \(-0.630938\pi\)
0.993707 0.112009i \(-0.0357285\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 42.0000 + 72.7461i 0.211851 + 0.366937i
\(35\) −279.000 −1.34742
\(36\) 0 0
\(37\) −166.000 −0.737574 −0.368787 0.929514i \(-0.620227\pi\)
−0.368787 + 0.929514i \(0.620227\pi\)
\(38\) −28.0000 48.4974i −0.119532 0.207035i
\(39\) 0 0
\(40\) 36.0000 62.3538i 0.142302 0.246475i
\(41\) −130.500 + 226.033i −0.497090 + 0.860985i −0.999994 0.00335732i \(-0.998931\pi\)
0.502905 + 0.864342i \(0.332265\pi\)
\(42\) 0 0
\(43\) 21.5000 + 37.2391i 0.0762493 + 0.132068i 0.901629 0.432511i \(-0.142372\pi\)
−0.825380 + 0.564578i \(0.809039\pi\)
\(44\) 60.0000 0.205576
\(45\) 0 0
\(46\) 390.000 1.25005
\(47\) 88.5000 + 153.286i 0.274661 + 0.475726i 0.970049 0.242907i \(-0.0781011\pi\)
−0.695389 + 0.718634i \(0.744768\pi\)
\(48\) 0 0
\(49\) −309.000 + 535.204i −0.900875 + 1.56036i
\(50\) −44.0000 + 76.2102i −0.124451 + 0.215555i
\(51\) 0 0
\(52\) 74.0000 + 128.172i 0.197345 + 0.341812i
\(53\) −114.000 −0.295455 −0.147727 0.989028i \(-0.547196\pi\)
−0.147727 + 0.989028i \(0.547196\pi\)
\(54\) 0 0
\(55\) 135.000 0.330971
\(56\) −124.000 214.774i −0.295896 0.512508i
\(57\) 0 0
\(58\) −111.000 + 192.258i −0.251293 + 0.435253i
\(59\) 79.5000 137.698i 0.175424 0.303843i −0.764884 0.644168i \(-0.777204\pi\)
0.940308 + 0.340325i \(0.110537\pi\)
\(60\) 0 0
\(61\) −95.5000 165.411i −0.200451 0.347192i 0.748223 0.663448i \(-0.230907\pi\)
−0.948674 + 0.316256i \(0.897574\pi\)
\(62\) 410.000 0.839840
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 166.500 + 288.386i 0.317720 + 0.550307i
\(66\) 0 0
\(67\) 210.500 364.597i 0.383831 0.664815i −0.607775 0.794109i \(-0.707938\pi\)
0.991606 + 0.129294i \(0.0412712\pi\)
\(68\) −84.0000 + 145.492i −0.149801 + 0.259464i
\(69\) 0 0
\(70\) −279.000 483.242i −0.476384 0.825121i
\(71\) −156.000 −0.260758 −0.130379 0.991464i \(-0.541619\pi\)
−0.130379 + 0.991464i \(0.541619\pi\)
\(72\) 0 0
\(73\) 182.000 0.291801 0.145901 0.989299i \(-0.453392\pi\)
0.145901 + 0.989299i \(0.453392\pi\)
\(74\) −166.000 287.520i −0.260772 0.451670i
\(75\) 0 0
\(76\) 56.0000 96.9948i 0.0845216 0.146396i
\(77\) 232.500 402.702i 0.344102 0.596002i
\(78\) 0 0
\(79\) −566.500 981.207i −0.806788 1.39740i −0.915078 0.403278i \(-0.867871\pi\)
0.108290 0.994119i \(-0.465463\pi\)
\(80\) 144.000 0.201246
\(81\) 0 0
\(82\) −522.000 −0.702991
\(83\) −541.500 937.906i −0.716113 1.24034i −0.962529 0.271179i \(-0.912586\pi\)
0.246416 0.969164i \(-0.420747\pi\)
\(84\) 0 0
\(85\) −189.000 + 327.358i −0.241176 + 0.417728i
\(86\) −43.0000 + 74.4782i −0.0539164 + 0.0933859i
\(87\) 0 0
\(88\) 60.0000 + 103.923i 0.0726821 + 0.125889i
\(89\) 1050.00 1.25056 0.625280 0.780401i \(-0.284985\pi\)
0.625280 + 0.780401i \(0.284985\pi\)
\(90\) 0 0
\(91\) 1147.00 1.32130
\(92\) 390.000 + 675.500i 0.441960 + 0.765497i
\(93\) 0 0
\(94\) −177.000 + 306.573i −0.194214 + 0.336389i
\(95\) 126.000 218.238i 0.136077 0.235693i
\(96\) 0 0
\(97\) 450.500 + 780.289i 0.471560 + 0.816766i 0.999471 0.0325338i \(-0.0103576\pi\)
−0.527910 + 0.849300i \(0.677024\pi\)
\(98\) −1236.00 −1.27403
\(99\) 0 0
\(100\) −176.000 −0.176000
\(101\) 193.500 + 335.152i 0.190633 + 0.330187i 0.945460 0.325737i \(-0.105613\pi\)
−0.754827 + 0.655924i \(0.772279\pi\)
\(102\) 0 0
\(103\) −275.500 + 477.180i −0.263552 + 0.456485i −0.967183 0.254080i \(-0.918227\pi\)
0.703631 + 0.710565i \(0.251561\pi\)
\(104\) −148.000 + 256.344i −0.139544 + 0.241698i
\(105\) 0 0
\(106\) −114.000 197.454i −0.104459 0.180928i
\(107\) 12.0000 0.0108419 0.00542095 0.999985i \(-0.498274\pi\)
0.00542095 + 0.999985i \(0.498274\pi\)
\(108\) 0 0
\(109\) −502.000 −0.441127 −0.220564 0.975373i \(-0.570790\pi\)
−0.220564 + 0.975373i \(0.570790\pi\)
\(110\) 135.000 + 233.827i 0.117016 + 0.202677i
\(111\) 0 0
\(112\) 248.000 429.549i 0.209230 0.362398i
\(113\) −700.500 + 1213.30i −0.583164 + 1.01007i 0.411938 + 0.911212i \(0.364852\pi\)
−0.995102 + 0.0988572i \(0.968481\pi\)
\(114\) 0 0
\(115\) 877.500 + 1519.87i 0.711542 + 1.23243i
\(116\) −444.000 −0.355382
\(117\) 0 0
\(118\) 318.000 0.248087
\(119\) 651.000 + 1127.57i 0.501488 + 0.868603i
\(120\) 0 0
\(121\) 553.000 957.824i 0.415477 0.719627i
\(122\) 191.000 330.822i 0.141740 0.245502i
\(123\) 0 0
\(124\) 410.000 + 710.141i 0.296928 + 0.514295i
\(125\) −1521.00 −1.08834
\(126\) 0 0
\(127\) −880.000 −0.614861 −0.307431 0.951571i \(-0.599469\pi\)
−0.307431 + 0.951571i \(0.599469\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −333.000 + 576.773i −0.224662 + 0.389126i
\(131\) 751.500 1301.64i 0.501213 0.868126i −0.498786 0.866725i \(-0.666221\pi\)
0.999999 0.00140084i \(-0.000445901\pi\)
\(132\) 0 0
\(133\) −434.000 751.710i −0.282952 0.490087i
\(134\) 842.000 0.542819
\(135\) 0 0
\(136\) −336.000 −0.211851
\(137\) −1330.50 2304.49i −0.829725 1.43713i −0.898254 0.439476i \(-0.855164\pi\)
0.0685295 0.997649i \(-0.478169\pi\)
\(138\) 0 0
\(139\) 60.5000 104.789i 0.0369176 0.0639431i −0.846976 0.531631i \(-0.821579\pi\)
0.883894 + 0.467688i \(0.154913\pi\)
\(140\) 558.000 966.484i 0.336854 0.583449i
\(141\) 0 0
\(142\) −156.000 270.200i −0.0921918 0.159681i
\(143\) −555.000 −0.324555
\(144\) 0 0
\(145\) −999.000 −0.572155
\(146\) 182.000 + 315.233i 0.103167 + 0.178691i
\(147\) 0 0
\(148\) 332.000 575.041i 0.184393 0.319379i
\(149\) −1414.50 + 2449.99i −0.777721 + 1.34705i 0.155532 + 0.987831i \(0.450291\pi\)
−0.933253 + 0.359221i \(0.883043\pi\)
\(150\) 0 0
\(151\) −230.500 399.238i −0.124224 0.215162i 0.797205 0.603708i \(-0.206311\pi\)
−0.921429 + 0.388546i \(0.872977\pi\)
\(152\) 224.000 0.119532
\(153\) 0 0
\(154\) 930.000 0.486633
\(155\) 922.500 + 1597.82i 0.478045 + 0.827998i
\(156\) 0 0
\(157\) 1488.50 2578.16i 0.756658 1.31057i −0.187889 0.982190i \(-0.560164\pi\)
0.944546 0.328379i \(-0.106502\pi\)
\(158\) 1133.00 1962.41i 0.570485 0.988109i
\(159\) 0 0
\(160\) 144.000 + 249.415i 0.0711512 + 0.123238i
\(161\) 6045.00 2.95909
\(162\) 0 0
\(163\) −3316.00 −1.59343 −0.796715 0.604355i \(-0.793431\pi\)
−0.796715 + 0.604355i \(0.793431\pi\)
\(164\) −522.000 904.131i −0.248545 0.430492i
\(165\) 0 0
\(166\) 1083.00 1875.81i 0.506368 0.877055i
\(167\) −340.500 + 589.763i −0.157777 + 0.273277i −0.934067 0.357099i \(-0.883766\pi\)
0.776290 + 0.630376i \(0.217099\pi\)
\(168\) 0 0
\(169\) 414.000 + 717.069i 0.188439 + 0.326386i
\(170\) −756.000 −0.341074
\(171\) 0 0
\(172\) −172.000 −0.0762493
\(173\) −1990.50 3447.65i −0.874768 1.51514i −0.857009 0.515301i \(-0.827680\pi\)
−0.0177589 0.999842i \(-0.505653\pi\)
\(174\) 0 0
\(175\) −682.000 + 1181.26i −0.294596 + 0.510256i
\(176\) −120.000 + 207.846i −0.0513940 + 0.0890170i
\(177\) 0 0
\(178\) 1050.00 + 1818.65i 0.442139 + 0.765808i
\(179\) −2004.00 −0.836793 −0.418397 0.908264i \(-0.637408\pi\)
−0.418397 + 0.908264i \(0.637408\pi\)
\(180\) 0 0
\(181\) 1274.00 0.523181 0.261590 0.965179i \(-0.415753\pi\)
0.261590 + 0.965179i \(0.415753\pi\)
\(182\) 1147.00 + 1986.66i 0.467150 + 0.809128i
\(183\) 0 0
\(184\) −780.000 + 1351.00i −0.312513 + 0.541288i
\(185\) 747.000 1293.84i 0.296868 0.514190i
\(186\) 0 0
\(187\) −315.000 545.596i −0.123182 0.213358i
\(188\) −708.000 −0.274661
\(189\) 0 0
\(190\) 504.000 0.192442
\(191\) 580.500 + 1005.46i 0.219914 + 0.380902i 0.954781 0.297309i \(-0.0960891\pi\)
−0.734868 + 0.678210i \(0.762756\pi\)
\(192\) 0 0
\(193\) −1805.50 + 3127.22i −0.673382 + 1.16633i 0.303557 + 0.952813i \(0.401826\pi\)
−0.976939 + 0.213519i \(0.931508\pi\)
\(194\) −901.000 + 1560.58i −0.333443 + 0.577541i
\(195\) 0 0
\(196\) −1236.00 2140.81i −0.450437 0.780180i
\(197\) −2046.00 −0.739957 −0.369978 0.929040i \(-0.620635\pi\)
−0.369978 + 0.929040i \(0.620635\pi\)
\(198\) 0 0
\(199\) 2996.00 1.06724 0.533620 0.845724i \(-0.320831\pi\)
0.533620 + 0.845724i \(0.320831\pi\)
\(200\) −176.000 304.841i −0.0622254 0.107778i
\(201\) 0 0
\(202\) −387.000 + 670.304i −0.134798 + 0.233477i
\(203\) −1720.50 + 2979.99i −0.594854 + 1.03032i
\(204\) 0 0
\(205\) −1174.50 2034.29i −0.400149 0.693079i
\(206\) −1102.00 −0.372718
\(207\) 0 0
\(208\) −592.000 −0.197345
\(209\) 210.000 + 363.731i 0.0695024 + 0.120382i
\(210\) 0 0
\(211\) −377.500 + 653.849i −0.123167 + 0.213331i −0.921015 0.389528i \(-0.872638\pi\)
0.797848 + 0.602858i \(0.205972\pi\)
\(212\) 228.000 394.908i 0.0738637 0.127936i
\(213\) 0 0
\(214\) 12.0000 + 20.7846i 0.00383319 + 0.00663928i
\(215\) −387.000 −0.122759
\(216\) 0 0
\(217\) 6355.00 1.98804
\(218\) −502.000 869.490i −0.155962 0.270134i
\(219\) 0 0
\(220\) −270.000 + 467.654i −0.0827427 + 0.143315i
\(221\) 777.000 1345.80i 0.236501 0.409631i
\(222\) 0 0
\(223\) 1731.50 + 2999.05i 0.519954 + 0.900587i 0.999731 + 0.0231966i \(0.00738438\pi\)
−0.479777 + 0.877391i \(0.659282\pi\)
\(224\) 992.000 0.295896
\(225\) 0 0
\(226\) −2802.00 −0.824718
\(227\) 3112.50 + 5391.01i 0.910061 + 1.57627i 0.813976 + 0.580899i \(0.197299\pi\)
0.0960856 + 0.995373i \(0.469368\pi\)
\(228\) 0 0
\(229\) 732.500 1268.73i 0.211375 0.366113i −0.740770 0.671759i \(-0.765539\pi\)
0.952145 + 0.305646i \(0.0988724\pi\)
\(230\) −1755.00 + 3039.75i −0.503136 + 0.871457i
\(231\) 0 0
\(232\) −444.000 769.031i −0.125647 0.217626i
\(233\) −2634.00 −0.740597 −0.370298 0.928913i \(-0.620745\pi\)
−0.370298 + 0.928913i \(0.620745\pi\)
\(234\) 0 0
\(235\) −1593.00 −0.442195
\(236\) 318.000 + 550.792i 0.0877120 + 0.151922i
\(237\) 0 0
\(238\) −1302.00 + 2255.13i −0.354606 + 0.614195i
\(239\) 3457.50 5988.57i 0.935762 1.62079i 0.162492 0.986710i \(-0.448047\pi\)
0.773270 0.634077i \(-0.218620\pi\)
\(240\) 0 0
\(241\) 744.500 + 1289.51i 0.198994 + 0.344667i 0.948202 0.317667i \(-0.102899\pi\)
−0.749209 + 0.662334i \(0.769566\pi\)
\(242\) 2212.00 0.587573
\(243\) 0 0
\(244\) 764.000 0.200451
\(245\) −2781.00 4816.83i −0.725190 1.25607i
\(246\) 0 0
\(247\) −518.000 + 897.202i −0.133439 + 0.231124i
\(248\) −820.000 + 1420.28i −0.209960 + 0.363661i
\(249\) 0 0
\(250\) −1521.00 2634.45i −0.384786 0.666469i
\(251\) 4620.00 1.16180 0.580900 0.813975i \(-0.302701\pi\)
0.580900 + 0.813975i \(0.302701\pi\)
\(252\) 0 0
\(253\) −2925.00 −0.726850
\(254\) −880.000 1524.20i −0.217386 0.376524i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) 1675.50 2902.05i 0.406672 0.704377i −0.587842 0.808976i \(-0.700022\pi\)
0.994515 + 0.104598i \(0.0333557\pi\)
\(258\) 0 0
\(259\) −2573.00 4456.57i −0.617291 1.06918i
\(260\) −1332.00 −0.317720
\(261\) 0 0
\(262\) 3006.00 0.708822
\(263\) −301.500 522.213i −0.0706893 0.122437i 0.828514 0.559968i \(-0.189187\pi\)
−0.899204 + 0.437530i \(0.855853\pi\)
\(264\) 0 0
\(265\) 513.000 888.542i 0.118918 0.205972i
\(266\) 868.000 1503.42i 0.200077 0.346544i
\(267\) 0 0
\(268\) 842.000 + 1458.39i 0.191915 + 0.332407i
\(269\) 1470.00 0.333188 0.166594 0.986026i \(-0.446723\pi\)
0.166594 + 0.986026i \(0.446723\pi\)
\(270\) 0 0
\(271\) 2072.00 0.464447 0.232223 0.972662i \(-0.425400\pi\)
0.232223 + 0.972662i \(0.425400\pi\)
\(272\) −336.000 581.969i −0.0749007 0.129732i
\(273\) 0 0
\(274\) 2661.00 4608.99i 0.586704 1.01620i
\(275\) 330.000 571.577i 0.0723627 0.125336i
\(276\) 0 0
\(277\) −3569.50 6182.56i −0.774262 1.34106i −0.935209 0.354097i \(-0.884788\pi\)
0.160947 0.986963i \(-0.448545\pi\)
\(278\) 242.000 0.0522093
\(279\) 0 0
\(280\) 2232.00 0.476384
\(281\) 4213.50 + 7298.00i 0.894507 + 1.54933i 0.834414 + 0.551138i \(0.185806\pi\)
0.0600924 + 0.998193i \(0.480860\pi\)
\(282\) 0 0
\(283\) 228.500 395.774i 0.0479962 0.0831318i −0.841029 0.540990i \(-0.818050\pi\)
0.889025 + 0.457858i \(0.151383\pi\)
\(284\) 312.000 540.400i 0.0651894 0.112911i
\(285\) 0 0
\(286\) −555.000 961.288i −0.114748 0.198749i
\(287\) −8091.00 −1.66410
\(288\) 0 0
\(289\) −3149.00 −0.640953
\(290\) −999.000 1730.32i −0.202287 0.350372i
\(291\) 0 0
\(292\) −364.000 + 630.466i −0.0729503 + 0.126354i
\(293\) −2944.50 + 5100.02i −0.587097 + 1.01688i 0.407513 + 0.913199i \(0.366396\pi\)
−0.994610 + 0.103683i \(0.966937\pi\)
\(294\) 0 0
\(295\) 715.500 + 1239.28i 0.141214 + 0.244589i
\(296\) 1328.00 0.260772
\(297\) 0 0
\(298\) −5658.00 −1.09986
\(299\) −3607.50 6248.37i −0.697750 1.20854i
\(300\) 0 0
\(301\) −666.500 + 1154.41i −0.127629 + 0.221060i
\(302\) 461.000 798.475i 0.0878396 0.152143i
\(303\) 0 0
\(304\) 224.000 + 387.979i 0.0422608 + 0.0731978i
\(305\) 1719.00 0.322720
\(306\) 0 0
\(307\) −1204.00 −0.223830 −0.111915 0.993718i \(-0.535698\pi\)
−0.111915 + 0.993718i \(0.535698\pi\)
\(308\) 930.000 + 1610.81i 0.172051 + 0.298001i
\(309\) 0 0
\(310\) −1845.00 + 3195.63i −0.338029 + 0.585483i
\(311\) −1642.50 + 2844.89i −0.299478 + 0.518711i −0.976017 0.217696i \(-0.930146\pi\)
0.676539 + 0.736407i \(0.263479\pi\)
\(312\) 0 0
\(313\) 5028.50 + 8709.62i 0.908075 + 1.57283i 0.816735 + 0.577013i \(0.195782\pi\)
0.0913406 + 0.995820i \(0.470885\pi\)
\(314\) 5954.00 1.07008
\(315\) 0 0
\(316\) 4532.00 0.806788
\(317\) 1147.50 + 1987.53i 0.203312 + 0.352147i 0.949594 0.313483i \(-0.101496\pi\)
−0.746281 + 0.665631i \(0.768163\pi\)
\(318\) 0 0
\(319\) 832.500 1441.93i 0.146116 0.253081i
\(320\) −288.000 + 498.831i −0.0503115 + 0.0871421i
\(321\) 0 0
\(322\) 6045.00 + 10470.2i 1.04619 + 1.81206i
\(323\) −1176.00 −0.202583
\(324\) 0 0
\(325\) 1628.00 0.277862
\(326\) −3316.00 5743.48i −0.563363 0.975773i
\(327\) 0 0
\(328\) 1044.00 1808.26i 0.175748 0.304404i
\(329\) −2743.50 + 4751.88i −0.459739 + 0.796291i
\(330\) 0 0
\(331\) 3339.50 + 5784.18i 0.554548 + 0.960506i 0.997939 + 0.0641773i \(0.0204423\pi\)
−0.443390 + 0.896329i \(0.646224\pi\)
\(332\) 4332.00 0.716113
\(333\) 0 0
\(334\) −1362.00 −0.223130
\(335\) 1894.50 + 3281.37i 0.308978 + 0.535165i
\(336\) 0 0
\(337\) −1091.50 + 1890.53i −0.176433 + 0.305590i −0.940656 0.339361i \(-0.889789\pi\)
0.764224 + 0.644951i \(0.223122\pi\)
\(338\) −828.000 + 1434.14i −0.133246 + 0.230789i
\(339\) 0 0
\(340\) −756.000 1309.43i −0.120588 0.208864i
\(341\) −3075.00 −0.488330
\(342\) 0 0
\(343\) −8525.00 −1.34200
\(344\) −172.000 297.913i −0.0269582 0.0466930i
\(345\) 0 0
\(346\) 3981.00 6895.29i 0.618555 1.07137i
\(347\) 1945.50 3369.70i 0.300980 0.521312i −0.675379 0.737471i \(-0.736020\pi\)
0.976358 + 0.216159i \(0.0693531\pi\)
\(348\) 0 0
\(349\) −1397.50 2420.54i −0.214345 0.371257i 0.738725 0.674007i \(-0.235428\pi\)
−0.953070 + 0.302751i \(0.902095\pi\)
\(350\) −2728.00 −0.416622
\(351\) 0 0
\(352\) −480.000 −0.0726821
\(353\) 2377.50 + 4117.95i 0.358475 + 0.620896i 0.987706 0.156322i \(-0.0499636\pi\)
−0.629232 + 0.777218i \(0.716630\pi\)
\(354\) 0 0
\(355\) 702.000 1215.90i 0.104953 0.181784i
\(356\) −2100.00 + 3637.31i −0.312640 + 0.541508i
\(357\) 0 0
\(358\) −2004.00 3471.03i −0.295851 0.512429i
\(359\) −4608.00 −0.677440 −0.338720 0.940887i \(-0.609994\pi\)
−0.338720 + 0.940887i \(0.609994\pi\)
\(360\) 0 0
\(361\) −6075.00 −0.885698
\(362\) 1274.00 + 2206.63i 0.184972 + 0.320381i
\(363\) 0 0
\(364\) −2294.00 + 3973.32i −0.330325 + 0.572140i
\(365\) −819.000 + 1418.55i −0.117448 + 0.203425i
\(366\) 0 0
\(367\) −1922.50 3329.87i −0.273443 0.473618i 0.696298 0.717753i \(-0.254829\pi\)
−0.969741 + 0.244135i \(0.921496\pi\)
\(368\) −3120.00 −0.441960
\(369\) 0 0
\(370\) 2988.00 0.419834
\(371\) −1767.00 3060.53i −0.247272 0.428288i
\(372\) 0 0
\(373\) 4158.50 7202.73i 0.577263 0.999848i −0.418529 0.908203i \(-0.637454\pi\)
0.995792 0.0916449i \(-0.0292125\pi\)
\(374\) 630.000 1091.19i 0.0871030 0.150867i
\(375\) 0 0
\(376\) −708.000 1226.29i −0.0971072 0.168195i
\(377\) 4107.00 0.561064
\(378\) 0 0
\(379\) 12560.0 1.70228 0.851140 0.524939i \(-0.175912\pi\)
0.851140 + 0.524939i \(0.175912\pi\)
\(380\) 504.000 + 872.954i 0.0680386 + 0.117846i
\(381\) 0 0
\(382\) −1161.00 + 2010.91i −0.155502 + 0.269338i
\(383\) 6043.50 10467.6i 0.806288 1.39653i −0.109130 0.994028i \(-0.534806\pi\)
0.915418 0.402505i \(-0.131860\pi\)
\(384\) 0 0
\(385\) 2092.50 + 3624.32i 0.276997 + 0.479772i
\(386\) −7222.00 −0.952306
\(387\) 0 0
\(388\) −3604.00 −0.471560
\(389\) −4270.50 7396.72i −0.556614 0.964084i −0.997776 0.0666565i \(-0.978767\pi\)
0.441162 0.897428i \(-0.354567\pi\)
\(390\) 0 0
\(391\) 4095.00 7092.75i 0.529650 0.917380i
\(392\) 2472.00 4281.63i 0.318507 0.551671i
\(393\) 0 0
\(394\) −2046.00 3543.78i −0.261614 0.453129i
\(395\) 10197.0 1.29890
\(396\) 0 0
\(397\) −13174.0 −1.66545 −0.832726 0.553686i \(-0.813221\pi\)
−0.832726 + 0.553686i \(0.813221\pi\)
\(398\) 2996.00 + 5189.22i 0.377326 + 0.653549i
\(399\) 0 0
\(400\) 352.000 609.682i 0.0440000 0.0762102i
\(401\) 4801.50 8316.44i 0.597944 1.03567i −0.395180 0.918604i \(-0.629318\pi\)
0.993124 0.117066i \(-0.0373488\pi\)
\(402\) 0 0
\(403\) −3792.50 6568.80i −0.468779 0.811949i
\(404\) −1548.00 −0.190633
\(405\) 0 0
\(406\) −6882.00 −0.841251
\(407\) 1245.00 + 2156.40i 0.151627 + 0.262626i
\(408\) 0 0
\(409\) −5735.50 + 9934.18i −0.693404 + 1.20101i 0.277312 + 0.960780i \(0.410557\pi\)
−0.970716 + 0.240231i \(0.922777\pi\)
\(410\) 2349.00 4068.59i 0.282948 0.490081i
\(411\) 0 0
\(412\) −1102.00 1908.72i −0.131776 0.228242i
\(413\) 4929.00 0.587264
\(414\) 0 0
\(415\) 9747.00 1.15292
\(416\) −592.000 1025.37i −0.0697721 0.120849i
\(417\) 0 0
\(418\) −420.000 + 727.461i −0.0491456 + 0.0851227i
\(419\) −2986.50 + 5172.77i −0.348210 + 0.603118i −0.985932 0.167149i \(-0.946544\pi\)
0.637721 + 0.770267i \(0.279877\pi\)
\(420\) 0 0
\(421\) 4452.50 + 7711.96i 0.515443 + 0.892774i 0.999839 + 0.0179250i \(0.00570601\pi\)
−0.484396 + 0.874849i \(0.660961\pi\)
\(422\) −1510.00 −0.174184
\(423\) 0 0
\(424\) 912.000 0.104459
\(425\) 924.000 + 1600.41i 0.105460 + 0.182662i
\(426\) 0 0
\(427\) 2960.50 5127.74i 0.335524 0.581144i
\(428\) −24.0000 + 41.5692i −0.00271048 + 0.00469468i
\(429\) 0 0
\(430\) −387.000 670.304i −0.0434019 0.0751742i
\(431\) −1416.00 −0.158251 −0.0791257 0.996865i \(-0.525213\pi\)
−0.0791257 + 0.996865i \(0.525213\pi\)
\(432\) 0 0
\(433\) 10766.0 1.19488 0.597438 0.801915i \(-0.296186\pi\)
0.597438 + 0.801915i \(0.296186\pi\)
\(434\) 6355.00 + 11007.2i 0.702880 + 1.21742i
\(435\) 0 0
\(436\) 1004.00 1738.98i 0.110282 0.191014i
\(437\) −2730.00 + 4728.50i −0.298841 + 0.517608i
\(438\) 0 0
\(439\) −2174.50 3766.34i −0.236408 0.409471i 0.723273 0.690562i \(-0.242637\pi\)
−0.959681 + 0.281091i \(0.909304\pi\)
\(440\) −1080.00 −0.117016
\(441\) 0 0
\(442\) 3108.00 0.334463
\(443\) −7273.50 12598.1i −0.780078 1.35113i −0.931896 0.362726i \(-0.881846\pi\)
0.151818 0.988408i \(-0.451487\pi\)
\(444\) 0 0
\(445\) −4725.00 + 8183.94i −0.503340 + 0.871811i
\(446\) −3463.00 + 5998.09i −0.367663 + 0.636811i
\(447\) 0 0
\(448\) 992.000 + 1718.19i 0.104615 + 0.181199i
\(449\) 3330.00 0.350005 0.175003 0.984568i \(-0.444007\pi\)
0.175003 + 0.984568i \(0.444007\pi\)
\(450\) 0 0
\(451\) 3915.00 0.408759
\(452\) −2802.00 4853.21i −0.291582 0.505035i
\(453\) 0 0
\(454\) −6225.00 + 10782.0i −0.643510 + 1.11459i
\(455\) −5161.50 + 8939.98i −0.531813 + 0.921127i
\(456\) 0 0
\(457\) −4073.50 7055.51i −0.416959 0.722194i 0.578673 0.815560i \(-0.303571\pi\)
−0.995632 + 0.0933655i \(0.970237\pi\)
\(458\) 2930.00 0.298930
\(459\) 0 0
\(460\) −7020.00 −0.711542
\(461\) 4015.50 + 6955.05i 0.405684 + 0.702666i 0.994401 0.105674i \(-0.0336999\pi\)
−0.588717 + 0.808340i \(0.700367\pi\)
\(462\) 0 0
\(463\) −2141.50 + 3709.19i −0.214955 + 0.372312i −0.953259 0.302156i \(-0.902294\pi\)
0.738304 + 0.674468i \(0.235627\pi\)
\(464\) 888.000 1538.06i 0.0888456 0.153885i
\(465\) 0 0
\(466\) −2634.00 4562.22i −0.261841 0.453521i
\(467\) −5460.00 −0.541025 −0.270512 0.962716i \(-0.587193\pi\)
−0.270512 + 0.962716i \(0.587193\pi\)
\(468\) 0 0
\(469\) 13051.0 1.28494
\(470\) −1593.00 2759.16i −0.156340 0.270788i
\(471\) 0 0
\(472\) −636.000 + 1101.58i −0.0620218 + 0.107425i
\(473\) 322.500 558.586i 0.0313500 0.0542999i
\(474\) 0 0
\(475\) −616.000 1066.94i −0.0595032 0.103063i
\(476\) −5208.00 −0.501488
\(477\) 0 0
\(478\) 13830.0 1.32337
\(479\) 214.500 + 371.525i 0.0204609 + 0.0354393i 0.876075 0.482176i \(-0.160153\pi\)
−0.855614 + 0.517615i \(0.826820\pi\)
\(480\) 0 0
\(481\) −3071.00 + 5319.13i −0.291113 + 0.504223i
\(482\) −1489.00 + 2579.02i −0.140710 + 0.243716i
\(483\) 0 0
\(484\) 2212.00 + 3831.30i 0.207739 + 0.359814i
\(485\) −8109.00 −0.759197
\(486\) 0 0
\(487\) −11296.0 −1.05107 −0.525535 0.850772i \(-0.676135\pi\)
−0.525535 + 0.850772i \(0.676135\pi\)
\(488\) 764.000 + 1323.29i 0.0708702 + 0.122751i
\(489\) 0 0
\(490\) 5562.00 9633.67i 0.512787 0.888173i
\(491\) −7336.50 + 12707.2i −0.674321 + 1.16796i 0.302346 + 0.953198i \(0.402230\pi\)
−0.976667 + 0.214760i \(0.931103\pi\)
\(492\) 0 0
\(493\) 2331.00 + 4037.41i 0.212947 + 0.368835i
\(494\) −2072.00 −0.188712
\(495\) 0 0
\(496\) −3280.00 −0.296928
\(497\) −2418.00 4188.10i −0.218234 0.377992i
\(498\) 0 0
\(499\) −6719.50 + 11638.5i −0.602818 + 1.04411i 0.389574 + 0.920995i \(0.372622\pi\)
−0.992392 + 0.123116i \(0.960711\pi\)
\(500\) 3042.00 5268.90i 0.272085 0.471265i
\(501\) 0 0
\(502\) 4620.00 + 8002.07i 0.410758 + 0.711454i
\(503\) 17388.0 1.54134 0.770669 0.637236i \(-0.219922\pi\)
0.770669 + 0.637236i \(0.219922\pi\)
\(504\) 0 0
\(505\) −3483.00 −0.306914
\(506\) −2925.00 5066.25i −0.256980 0.445103i
\(507\) 0 0
\(508\) 1760.00 3048.41i 0.153715 0.266243i
\(509\) −1894.50 + 3281.37i −0.164975 + 0.285745i −0.936646 0.350276i \(-0.886088\pi\)
0.771671 + 0.636021i \(0.219421\pi\)
\(510\) 0 0
\(511\) 2821.00 + 4886.12i 0.244215 + 0.422992i
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 6702.00 0.575122
\(515\) −2479.50 4294.62i −0.212155 0.367463i
\(516\) 0 0
\(517\) 1327.50 2299.30i 0.112927 0.195596i
\(518\) 5146.00 8913.13i 0.436491 0.756024i
\(519\) 0 0
\(520\) −1332.00 2307.09i −0.112331 0.194563i
\(521\) −9786.00 −0.822903 −0.411451 0.911432i \(-0.634978\pi\)
−0.411451 + 0.911432i \(0.634978\pi\)
\(522\) 0 0
\(523\) −8008.00 −0.669532 −0.334766 0.942301i \(-0.608657\pi\)
−0.334766 + 0.942301i \(0.608657\pi\)
\(524\) 3006.00 + 5206.54i 0.250606 + 0.434063i
\(525\) 0 0
\(526\) 603.000 1044.43i 0.0499849 0.0865764i
\(527\) 4305.00 7456.48i 0.355842 0.616336i
\(528\) 0 0
\(529\) −12929.0 22393.7i −1.06263 1.84053i
\(530\) 2052.00 0.168176
\(531\) 0 0
\(532\) 3472.00 0.282952
\(533\) 4828.50 + 8363.21i 0.392393 + 0.679645i
\(534\) 0 0
\(535\) −54.0000 + 93.5307i −0.00436378 + 0.00755829i
\(536\) −1684.00 + 2916.77i −0.135705 + 0.235047i
\(537\) 0 0
\(538\) 1470.00 + 2546.11i 0.117800 + 0.204035i
\(539\) 9270.00 0.740793
\(540\) 0 0
\(541\) −2938.00 −0.233483 −0.116742 0.993162i \(-0.537245\pi\)
−0.116742 + 0.993162i \(0.537245\pi\)
\(542\) 2072.00 + 3588.81i 0.164207 + 0.284414i
\(543\) 0 0
\(544\) 672.000 1163.94i 0.0529628 0.0917343i
\(545\) 2259.00 3912.70i 0.177550 0.307526i
\(546\) 0 0
\(547\) 5187.50 + 8985.01i 0.405487 + 0.702324i 0.994378 0.105888i \(-0.0337686\pi\)
−0.588891 + 0.808213i \(0.700435\pi\)
\(548\) 10644.0 0.829725
\(549\) 0 0
\(550\) 1320.00 0.102336
\(551\) −1554.00 2691.61i −0.120150 0.208106i
\(552\) 0 0
\(553\) 17561.5 30417.4i 1.35044 2.33902i
\(554\) 7139.00 12365.1i 0.547486 0.948273i
\(555\) 0 0
\(556\) 242.000 + 419.156i 0.0184588 + 0.0319716i
\(557\) −3306.00 −0.251490 −0.125745 0.992063i \(-0.540132\pi\)
−0.125745 + 0.992063i \(0.540132\pi\)
\(558\) 0 0
\(559\) 1591.00 0.120379
\(560\) 2232.00 + 3865.94i 0.168427 + 0.291724i
\(561\) 0 0
\(562\) −8427.00 + 14596.0i −0.632512 + 1.09554i
\(563\) −10546.5 + 18267.1i −0.789488 + 1.36743i 0.136792 + 0.990600i \(0.456321\pi\)
−0.926281 + 0.376834i \(0.877013\pi\)
\(564\) 0 0
\(565\) −6304.50 10919.7i −0.469438 0.813090i
\(566\) 914.000 0.0678768
\(567\) 0 0
\(568\) 1248.00 0.0921918
\(569\) 643.500 + 1114.57i 0.0474111 + 0.0821185i 0.888757 0.458379i \(-0.151570\pi\)
−0.841346 + 0.540497i \(0.818236\pi\)
\(570\) 0 0
\(571\) −7517.50 + 13020.7i −0.550959 + 0.954289i 0.447247 + 0.894411i \(0.352405\pi\)
−0.998206 + 0.0598783i \(0.980929\pi\)
\(572\) 1110.00 1922.58i 0.0811389 0.140537i
\(573\) 0 0
\(574\) −8091.00 14014.0i −0.588348 1.01905i
\(575\) 8580.00 0.622280
\(576\) 0 0
\(577\) 1190.00 0.0858585 0.0429292 0.999078i \(-0.486331\pi\)
0.0429292 + 0.999078i \(0.486331\pi\)
\(578\) −3149.00 5454.23i −0.226611 0.392502i
\(579\) 0 0
\(580\) 1998.00 3460.64i 0.143039 0.247750i
\(581\) 16786.5 29075.1i 1.19866 2.07614i
\(582\) 0 0
\(583\) 855.000 + 1480.90i 0.0607384 + 0.105202i
\(584\) −1456.00 −0.103167
\(585\) 0 0
\(586\) −11778.0 −0.830281
\(587\) −8941.50 15487.1i −0.628714 1.08896i −0.987810 0.155664i \(-0.950248\pi\)
0.359096 0.933301i \(-0.383085\pi\)
\(588\) 0 0
\(589\) −2870.00 + 4970.99i −0.200775 + 0.347752i
\(590\) −1431.00 + 2478.56i −0.0998531 + 0.172951i
\(591\) 0 0
\(592\) 1328.00 + 2300.16i 0.0921967 + 0.159689i
\(593\) −20118.0 −1.39317 −0.696583 0.717476i \(-0.745297\pi\)
−0.696583 + 0.717476i \(0.745297\pi\)
\(594\) 0 0
\(595\) −11718.0 −0.807380
\(596\) −5658.00 9799.94i −0.388860 0.673526i
\(597\) 0 0
\(598\) 7215.00 12496.7i 0.493383 0.854565i
\(599\) −532.500 + 922.317i −0.0363228 + 0.0629129i −0.883615 0.468214i \(-0.844898\pi\)
0.847293 + 0.531127i \(0.178231\pi\)
\(600\) 0 0
\(601\) 10362.5 + 17948.4i 0.703320 + 1.21819i 0.967294 + 0.253656i \(0.0816331\pi\)
−0.263975 + 0.964530i \(0.585034\pi\)
\(602\) −2666.00 −0.180495
\(603\) 0 0
\(604\) 1844.00 0.124224
\(605\) 4977.00 + 8620.42i 0.334453 + 0.579289i
\(606\) 0 0
\(607\) 7872.50 13635.6i 0.526417 0.911780i −0.473110 0.881004i \(-0.656869\pi\)
0.999526 0.0307768i \(-0.00979812\pi\)
\(608\) −448.000 + 775.959i −0.0298829 + 0.0517587i
\(609\) 0 0
\(610\) 1719.00 + 2977.40i 0.114099 + 0.197625i
\(611\) 6549.00 0.433624
\(612\) 0 0
\(613\) 5042.00 0.332210 0.166105 0.986108i \(-0.446881\pi\)
0.166105 + 0.986108i \(0.446881\pi\)
\(614\) −1204.00 2085.39i −0.0791360 0.137068i
\(615\) 0 0
\(616\) −1860.00 + 3221.61i −0.121658 + 0.210718i
\(617\) −5026.50 + 8706.15i −0.327973 + 0.568066i −0.982110 0.188311i \(-0.939699\pi\)
0.654137 + 0.756376i \(0.273032\pi\)
\(618\) 0 0
\(619\) 2991.50 + 5181.43i 0.194246 + 0.336445i 0.946653 0.322254i \(-0.104441\pi\)
−0.752407 + 0.658699i \(0.771107\pi\)
\(620\) −7380.00 −0.478045
\(621\) 0 0
\(622\) −6570.00 −0.423526
\(623\) 16275.0 + 28189.1i 1.04662 + 1.81280i
\(624\) 0 0
\(625\) 4094.50 7091.88i 0.262048 0.453880i
\(626\) −10057.0 + 17419.2i −0.642106 + 1.11216i
\(627\) 0 0
\(628\) 5954.00 + 10312.6i 0.378329 + 0.655285i
\(629\) −6972.00 −0.441958
\(630\) 0 0
\(631\) −19696.0 −1.24261 −0.621304 0.783570i \(-0.713397\pi\)
−0.621304 + 0.783570i \(0.713397\pi\)
\(632\) 4532.00 + 7849.65i 0.285243 + 0.494055i
\(633\) 0 0
\(634\) −2295.00 + 3975.06i −0.143764 + 0.249006i
\(635\) 3960.00 6858.92i 0.247477 0.428642i
\(636\) 0 0
\(637\) 11433.0 + 19802.5i 0.711133 + 1.23172i
\(638\) 3330.00 0.206639
\(639\) 0 0
\(640\) −1152.00 −0.0711512
\(641\) −5488.50 9506.36i −0.338195 0.585770i 0.645899 0.763423i \(-0.276483\pi\)
−0.984093 + 0.177653i \(0.943150\pi\)
\(642\) 0 0
\(643\) 7914.50 13708.3i 0.485408 0.840752i −0.514451 0.857520i \(-0.672004\pi\)
0.999859 + 0.0167681i \(0.00533770\pi\)
\(644\) −12090.0 + 20940.5i −0.739771 + 1.28132i
\(645\) 0 0
\(646\) −1176.00 2036.89i −0.0716240 0.124056i
\(647\) −28224.0 −1.71499 −0.857496 0.514490i \(-0.827981\pi\)
−0.857496 + 0.514490i \(0.827981\pi\)
\(648\) 0 0
\(649\) −2385.00 −0.144252
\(650\) 1628.00 + 2819.78i 0.0982391 + 0.170155i
\(651\) 0 0
\(652\) 6632.00 11487.0i 0.398358 0.689976i
\(653\) 14083.5 24393.3i 0.843997 1.46185i −0.0424927 0.999097i \(-0.513530\pi\)
0.886490 0.462749i \(-0.153137\pi\)
\(654\) 0 0
\(655\) 6763.50 + 11714.7i 0.403468 + 0.698828i
\(656\) 4176.00 0.248545
\(657\) 0 0
\(658\) −10974.0 −0.650169
\(659\) 5368.50 + 9298.51i 0.317340 + 0.549649i 0.979932 0.199331i \(-0.0638770\pi\)
−0.662592 + 0.748980i \(0.730544\pi\)
\(660\) 0 0
\(661\) −5063.50 + 8770.24i −0.297954 + 0.516071i −0.975668 0.219255i \(-0.929637\pi\)
0.677714 + 0.735326i \(0.262971\pi\)
\(662\) −6679.00 + 11568.4i −0.392125 + 0.679180i
\(663\) 0 0
\(664\) 4332.00 + 7503.24i 0.253184 + 0.438528i
\(665\) 7812.00 0.455543
\(666\) 0 0
\(667\) 21645.0 1.25652
\(668\) −1362.00 2359.05i −0.0788883 0.136638i
\(669\) 0 0
\(670\) −3789.00 + 6562.74i −0.218480 + 0.378419i
\(671\) −1432.50 + 2481.16i −0.0824159 + 0.142748i
\(672\) 0 0
\(673\) −125.500 217.372i −0.00718822 0.0124504i 0.862409 0.506212i \(-0.168955\pi\)
−0.869597 + 0.493762i \(0.835621\pi\)
\(674\) −4366.00 −0.249513
\(675\) 0 0
\(676\) −3312.00 −0.188439
\(677\) 4225.50 + 7318.78i 0.239881 + 0.415485i 0.960680 0.277659i \(-0.0895584\pi\)
−0.720799 + 0.693144i \(0.756225\pi\)
\(678\) 0 0
\(679\) −13965.5 + 24189.0i −0.789318 + 1.36714i
\(680\) 1512.00 2618.86i 0.0852685 0.147689i
\(681\) 0 0
\(682\) −3075.00 5326.06i −0.172651 0.299040i
\(683\) 25884.0 1.45011 0.725054 0.688692i \(-0.241815\pi\)
0.725054 + 0.688692i \(0.241815\pi\)
\(684\) 0 0
\(685\) 23949.0 1.33583
\(686\) −8525.00 14765.7i −0.474469 0.821805i
\(687\) 0 0
\(688\) 344.000 595.825i 0.0190623 0.0330169i
\(689\) −2109.00 + 3652.90i −0.116613 + 0.201980i
\(690\) 0 0
\(691\) −3182.50 5512.25i −0.175207 0.303467i 0.765026 0.643999i \(-0.222726\pi\)
−0.940233 + 0.340532i \(0.889393\pi\)
\(692\) 15924.0 0.874768
\(693\) 0 0
\(694\) 7782.00 0.425649
\(695\) 544.500 + 943.102i 0.0297181 + 0.0514732i
\(696\) 0 0
\(697\) −5481.00 + 9493.37i −0.297859 + 0.515907i
\(698\) 2795.00 4841.08i 0.151565 0.262518i
\(699\) 0 0
\(700\) −2728.00 4725.03i −0.147298 0.255128i
\(701\) −1122.00 −0.0604527 −0.0302264 0.999543i \(-0.509623\pi\)
−0.0302264 + 0.999543i \(0.509623\pi\)
\(702\) 0 0
\(703\) 4648.00 0.249364
\(704\) −480.000 831.384i −0.0256970 0.0445085i
\(705\) 0 0
\(706\) −4755.00 + 8235.90i −0.253480 + 0.439040i
\(707\) −5998.50 + 10389.7i −0.319090 + 0.552681i
\(708\) 0 0
\(709\) −2141.50 3709.19i −0.113435 0.196476i 0.803718 0.595011i \(-0.202852\pi\)
−0.917153 + 0.398535i \(0.869519\pi\)
\(710\) 2808.00 0.148426
\(711\) 0 0
\(712\) −8400.00 −0.442139
\(713\) −19987.5 34619.4i −1.04984 1.81838i
\(714\) 0 0
\(715\) 2497.50 4325.80i 0.130631 0.226260i
\(716\) 4008.00 6942.06i 0.209198 0.362342i
\(717\) 0 0
\(718\) −4608.00 7981.29i −0.239511 0.414846i
\(719\) −4032.00 −0.209135 −0.104568 0.994518i \(-0.533346\pi\)
−0.104568 + 0.994518i \(0.533346\pi\)
\(720\) 0 0
\(721\) −17081.0 −0.882288
\(722\) −6075.00 10522.2i −0.313141 0.542377i
\(723\) 0 0
\(724\) −2548.00 + 4413.27i −0.130795 + 0.226544i
\(725\) −2442.00 + 4229.67i −0.125095 + 0.216670i
\(726\) 0 0
\(727\) −12002.5 20788.9i −0.612308 1.06055i −0.990850 0.134965i \(-0.956908\pi\)
0.378542 0.925584i \(-0.376426\pi\)
\(728\) −9176.00 −0.467150
\(729\) 0 0
\(730\) −3276.00 −0.166096
\(731\) 903.000 + 1564.04i 0.0456890 + 0.0791357i
\(732\) 0 0
\(733\) 18750.5 32476.8i 0.944837 1.63651i 0.188760 0.982023i \(-0.439553\pi\)
0.756077 0.654482i \(-0.227113\pi\)
\(734\) 3845.00 6659.74i 0.193354 0.334898i
\(735\) 0 0
\(736\) −3120.00 5404.00i −0.156256 0.270644i
\(737\) −6315.00 −0.315626
\(738\) 0 0
\(739\) −880.000 −0.0438042 −0.0219021 0.999760i \(-0.506972\pi\)
−0.0219021 + 0.999760i \(0.506972\pi\)
\(740\) 2988.00 + 5175.37i 0.148434 + 0.257095i
\(741\) 0 0
\(742\) 3534.00 6121.07i 0.174848 0.302846i
\(743\) 811.500 1405.56i 0.0400687 0.0694010i −0.845296 0.534299i \(-0.820576\pi\)
0.885364 + 0.464898i \(0.153909\pi\)
\(744\) 0 0
\(745\) −12730.5 22049.9i −0.626053 1.08436i
\(746\) 16634.0 0.816373
\(747\) 0 0
\(748\) 2520.00 0.123182
\(749\) 186.000 + 322.161i 0.00907382 + 0.0157163i
\(750\) 0 0
\(751\) 3444.50 5966.05i 0.167366 0.289886i −0.770127 0.637890i \(-0.779807\pi\)
0.937493 + 0.348005i \(0.113141\pi\)
\(752\) 1416.00 2452.58i 0.0686652 0.118932i
\(753\) 0 0
\(754\) 4107.00 + 7113.53i 0.198366 + 0.343580i
\(755\) 4149.00 0.199997
\(756\) 0 0
\(757\) −12850.0 −0.616963 −0.308482 0.951230i \(-0.599821\pi\)
−0.308482 + 0.951230i \(0.599821\pi\)
\(758\) 12560.0 + 21754.6i 0.601847 + 1.04243i
\(759\) 0 0
\(760\) −1008.00 + 1745.91i −0.0481105 + 0.0833299i
\(761\) 2305.50 3993.24i 0.109822 0.190217i −0.805876 0.592084i \(-0.798305\pi\)
0.915698 + 0.401867i \(0.131639\pi\)
\(762\) 0 0
\(763\) −7781.00 13477.1i −0.369189 0.639454i
\(764\) −4644.00 −0.219914
\(765\) 0 0
\(766\) 24174.0 1.14026
\(767\) −2941.50 5094.83i −0.138476 0.239848i
\(768\) 0 0
\(769\) 1152.50 1996.19i 0.0540445 0.0936078i −0.837737 0.546073i \(-0.816122\pi\)
0.891782 + 0.452465i \(0.149455\pi\)
\(770\) −4185.00 + 7248.63i −0.195866 + 0.339250i
\(771\) 0 0
\(772\) −7222.00 12508.9i −0.336691 0.583166i
\(773\) 34902.0 1.62398 0.811991 0.583670i \(-0.198384\pi\)
0.811991 + 0.583670i \(0.198384\pi\)
\(774\) 0 0
\(775\) 9020.00 0.418075
\(776\) −3604.00 6242.31i −0.166722 0.288771i
\(777\) 0 0
\(778\) 8541.00 14793.4i 0.393586 0.681710i
\(779\) 3654.00 6328.91i 0.168059 0.291087i