Properties

Label 54.4.c.a.19.1
Level $54$
Weight $4$
Character 54.19
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 19.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 54.19
Dual form 54.4.c.a.37.1

$q$-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 \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).

\(n\) \(29\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 0.591534 0.806280i \(-0.298523\pi\)
−0.994026 + 0.109143i \(0.965189\pi\)
\(6\) 0 0
\(7\) 15.5000 26.8468i 0.836921 1.44959i −0.0555351 0.998457i \(-0.517686\pi\)
0.892456 0.451134i \(-0.148980\pi\)
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −18.0000 −0.569210
\(11\) −7.50000 + 12.9904i −0.205576 + 0.356068i −0.950316 0.311287i \(-0.899240\pi\)
0.744740 + 0.667355i \(0.232573\pi\)
\(12\) 0 0
\(13\) 18.5000 + 32.0429i 0.394691 + 0.683624i 0.993062 0.117595i \(-0.0375185\pi\)
−0.598371 + 0.801219i \(0.704185\pi\)
\(14\) −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 0.846947 + 0.531678i \(0.178438\pi\)
0.0369731 + 0.999316i \(0.488228\pi\)
\(24\) 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 −0.631801 0.775131i \(-0.717684\pi\)
0.987183 + 0.159590i \(0.0510173\pi\)
\(30\) 0 0
\(31\) 102.500 + 177.535i 0.593856 + 1.02859i 0.993707 + 0.112009i \(0.0357285\pi\)
−0.399851 + 0.916580i \(0.630938\pi\)
\(32\) 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 0.502905 0.864342i \(-0.332265\pi\)
−0.999994 + 0.00335732i \(0.998931\pi\)
\(42\) 0 0
\(43\) 21.5000 37.2391i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 60.0000 0.205576
\(45\) 0 0
\(46\) 390.000 1.25005
\(47\) 88.5000 153.286i 0.274661 0.475726i −0.695389 0.718634i \(-0.744768\pi\)
0.970049 + 0.242907i \(0.0781011\pi\)
\(48\) 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 0.940308 0.340325i \(-0.110537\pi\)
−0.764884 + 0.644168i \(0.777204\pi\)
\(60\) 0 0
\(61\) −95.5000 + 165.411i −0.200451 + 0.347192i −0.948674 0.316256i \(-0.897574\pi\)
0.748223 + 0.663448i \(0.230907\pi\)
\(62\) 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 0.991606 0.129294i \(-0.0412712\pi\)
−0.607775 + 0.794109i \(0.707938\pi\)
\(68\) −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 0.108290 + 0.994119i \(0.465463\pi\)
−0.915078 + 0.403278i \(0.867871\pi\)
\(80\) 144.000 0.201246
\(81\) 0 0
\(82\) −522.000 −0.702991
\(83\) −541.500 + 937.906i −0.716113 + 1.24034i 0.246416 + 0.969164i \(0.420747\pi\)
−0.962529 + 0.271179i \(0.912586\pi\)
\(84\) 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 −0.527910 0.849300i \(-0.677024\pi\)
0.999471 + 0.0325338i \(0.0103576\pi\)
\(98\) −1236.00 −1.27403
\(99\) 0 0
\(100\) −176.000 −0.176000
\(101\) 193.500 335.152i 0.190633 0.330187i −0.754827 0.655924i \(-0.772279\pi\)
0.945460 + 0.325737i \(0.105613\pi\)
\(102\) 0 0
\(103\) −275.500 477.180i −0.263552 0.456485i 0.703631 0.710565i \(-0.251561\pi\)
−0.967183 + 0.254080i \(0.918227\pi\)
\(104\) −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 −0.995102 0.0988572i \(-0.968481\pi\)
0.411938 0.911212i \(-0.364852\pi\)
\(114\) 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 0.999999 + 0.00140084i \(0.000445901\pi\)
−0.498786 + 0.866725i \(0.666221\pi\)
\(132\) 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 0.0685295 + 0.997649i \(0.478169\pi\)
−0.898254 + 0.439476i \(0.855164\pi\)
\(138\) 0 0
\(139\) 60.5000 + 104.789i 0.0369176 + 0.0639431i 0.883894 0.467688i \(-0.154913\pi\)
−0.846976 + 0.531631i \(0.821579\pi\)
\(140\) 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 −0.933253 0.359221i \(-0.883043\pi\)
0.155532 0.987831i \(-0.450291\pi\)
\(150\) 0 0
\(151\) −230.500 + 399.238i −0.124224 + 0.215162i −0.921429 0.388546i \(-0.872977\pi\)
0.797205 + 0.603708i \(0.206311\pi\)
\(152\) 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 0.944546 + 0.328379i \(0.106502\pi\)
−0.187889 + 0.982190i \(0.560164\pi\)
\(158\) 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 0.776290 0.630376i \(-0.217099\pi\)
−0.934067 + 0.357099i \(0.883766\pi\)
\(168\) 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 −0.0177589 + 0.999842i \(0.505653\pi\)
−0.857009 + 0.515301i \(0.827680\pi\)
\(174\) 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 −0.734868 0.678210i \(-0.762756\pi\)
0.954781 + 0.297309i \(0.0960891\pi\)
\(192\) 0 0
\(193\) −1805.50 3127.22i −0.673382 1.16633i −0.976939 0.213519i \(-0.931508\pi\)
0.303557 0.952813i \(-0.401826\pi\)
\(194\) −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 0.797848 0.602858i \(-0.205972\pi\)
−0.921015 + 0.389528i \(0.872638\pi\)
\(212\) 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 −0.479777 0.877391i \(-0.659282\pi\)
0.999731 0.0231966i \(-0.00738438\pi\)
\(224\) 992.000 0.295896
\(225\) 0 0
\(226\) −2802.00 −0.824718
\(227\) 3112.50 5391.01i 0.910061 1.57627i 0.0960856 0.995373i \(-0.469368\pi\)
0.813976 0.580899i \(-0.197299\pi\)
\(228\) 0 0
\(229\) 732.500 + 1268.73i 0.211375 + 0.366113i 0.952145 0.305646i \(-0.0988724\pi\)
−0.740770 + 0.671759i \(0.765539\pi\)
\(230\) −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 0.773270 + 0.634077i \(0.218620\pi\)
0.162492 + 0.986710i \(0.448047\pi\)
\(240\) 0 0
\(241\) 744.500 1289.51i 0.198994 0.344667i −0.749209 0.662334i \(-0.769566\pi\)
0.948202 + 0.317667i \(0.102899\pi\)
\(242\) 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 0.994515 0.104598i \(-0.0333557\pi\)
−0.587842 + 0.808976i \(0.700022\pi\)
\(258\) 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 −0.899204 0.437530i \(-0.855853\pi\)
0.828514 + 0.559968i \(0.189187\pi\)
\(264\) 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 0.160947 + 0.986963i \(0.448545\pi\)
−0.935209 + 0.354097i \(0.884788\pi\)
\(278\) 242.000 0.0522093
\(279\) 0 0
\(280\) 2232.00 0.476384
\(281\) 4213.50 7298.00i 0.894507 1.54933i 0.0600924 0.998193i \(-0.480860\pi\)
0.834414 0.551138i \(-0.185806\pi\)
\(282\) 0 0
\(283\) 228.500 + 395.774i 0.0479962 + 0.0831318i 0.889025 0.457858i \(-0.151383\pi\)
−0.841029 + 0.540990i \(0.818050\pi\)
\(284\) 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 −0.994610 0.103683i \(-0.966937\pi\)
0.407513 0.913199i \(-0.366396\pi\)
\(294\) 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 0.676539 0.736407i \(-0.263479\pi\)
−0.976017 + 0.217696i \(0.930146\pi\)
\(312\) 0 0
\(313\) 5028.50 8709.62i 0.908075 1.57283i 0.0913406 0.995820i \(-0.470885\pi\)
0.816735 0.577013i \(-0.195782\pi\)
\(314\) 5954.00 1.07008
\(315\) 0 0
\(316\) 4532.00 0.806788
\(317\) 1147.50 1987.53i 0.203312 0.352147i −0.746281 0.665631i \(-0.768163\pi\)
0.949594 + 0.313483i \(0.101496\pi\)
\(318\) 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 −0.443390 0.896329i \(-0.646224\pi\)
0.997939 0.0641773i \(-0.0204423\pi\)
\(332\) 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 0.764224 0.644951i \(-0.223122\pi\)
−0.940656 + 0.339361i \(0.889789\pi\)
\(338\) −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 0.976358 0.216159i \(-0.0693531\pi\)
−0.675379 + 0.737471i \(0.736020\pi\)
\(348\) 0 0
\(349\) −1397.50 + 2420.54i −0.214345 + 0.371257i −0.953070 0.302751i \(-0.902095\pi\)
0.738725 + 0.674007i \(0.235428\pi\)
\(350\) −2728.00 −0.416622
\(351\) 0 0
\(352\) −480.000 −0.0726821
\(353\) 2377.50 4117.95i 0.358475 0.620896i −0.629232 0.777218i \(-0.716630\pi\)
0.987706 + 0.156322i \(0.0499636\pi\)
\(354\) 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 −0.969741 0.244135i \(-0.921496\pi\)
0.696298 + 0.717753i \(0.254829\pi\)
\(368\) −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 0.995792 + 0.0916449i \(0.0292125\pi\)
−0.418529 + 0.908203i \(0.637454\pi\)
\(374\) 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 0.915418 + 0.402505i \(0.131860\pi\)
−0.109130 + 0.994028i \(0.534806\pi\)
\(384\) 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 0.441162 + 0.897428i \(0.354567\pi\)
−0.997776 + 0.0666565i \(0.978767\pi\)
\(390\) 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 0.993124 + 0.117066i \(0.0373488\pi\)
−0.395180 + 0.918604i \(0.629318\pi\)
\(402\) 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 −0.970716 0.240231i \(-0.922777\pi\)
0.277312 0.960780i \(-0.410557\pi\)
\(410\) 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 0.637721 0.770267i \(-0.279877\pi\)
−0.985932 + 0.167149i \(0.946544\pi\)
\(420\) 0 0
\(421\) 4452.50 7711.96i 0.515443 0.892774i −0.484396 0.874849i \(-0.660961\pi\)
0.999839 0.0179250i \(-0.00570601\pi\)
\(422\) −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 −0.959681 0.281091i \(-0.909304\pi\)
0.723273 + 0.690562i \(0.242637\pi\)
\(440\) −1080.00 −0.117016
\(441\) 0 0
\(442\) 3108.00 0.334463
\(443\) −7273.50 + 12598.1i −0.780078 + 1.35113i 0.151818 + 0.988408i \(0.451487\pi\)
−0.931896 + 0.362726i \(0.881846\pi\)
\(444\) 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 −0.995632 0.0933655i \(-0.970237\pi\)
0.578673 + 0.815560i \(0.303571\pi\)
\(458\) 2930.00 0.298930
\(459\) 0 0
\(460\) −7020.00 −0.711542
\(461\) 4015.50 6955.05i 0.405684 0.702666i −0.588717 0.808340i \(-0.700367\pi\)
0.994401 + 0.105674i \(0.0336999\pi\)
\(462\) 0 0
\(463\) −2141.50 3709.19i −0.214955 0.372312i 0.738304 0.674468i \(-0.235627\pi\)
−0.953259 + 0.302156i \(0.902294\pi\)
\(464\) 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 −0.855614 0.517615i \(-0.826820\pi\)
0.876075 + 0.482176i \(0.160153\pi\)
\(480\) 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 −0.976667 0.214760i \(-0.931103\pi\)
0.302346 0.953198i \(-0.402230\pi\)
\(492\) 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 −0.992392 0.123116i \(-0.960711\pi\)
0.389574 0.920995i \(-0.372622\pi\)
\(500\) 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 0.771671 0.636021i \(-0.219421\pi\)
−0.936646 + 0.350276i \(0.886088\pi\)
\(510\) 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 −0.588891 0.808213i \(-0.700435\pi\)
0.994378 + 0.105888i \(0.0337686\pi\)
\(548\) 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 −0.926281 0.376834i \(-0.877013\pi\)
0.136792 0.990600i \(-0.456321\pi\)
\(564\) 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 −0.841346 0.540497i \(-0.818236\pi\)
0.888757 + 0.458379i \(0.151570\pi\)
\(570\) 0 0
\(571\) −7517.50 13020.7i −0.550959 0.954289i −0.998206 0.0598783i \(-0.980929\pi\)
0.447247 0.894411i \(-0.352405\pi\)
\(572\) 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 0.359096 + 0.933301i \(0.383085\pi\)
−0.987810 + 0.155664i \(0.950248\pi\)
\(588\) 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 0.847293 0.531127i \(-0.178231\pi\)
−0.883615 + 0.468214i \(0.844898\pi\)
\(600\) 0 0
\(601\) 10362.5 17948.4i 0.703320 1.21819i −0.263975 0.964530i \(-0.585034\pi\)
0.967294 0.253656i \(-0.0816331\pi\)
\(602\) −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 0.999526 + 0.0307768i \(0.00979812\pi\)
−0.473110 + 0.881004i \(0.656869\pi\)
\(608\) −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 0.654137 0.756376i \(-0.273032\pi\)
−0.982110 + 0.188311i \(0.939699\pi\)
\(618\) 0 0
\(619\) 2991.50 5181.43i 0.194246 0.336445i −0.752407 0.658699i \(-0.771107\pi\)
0.946653 + 0.322254i \(0.104441\pi\)
\(620\) −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 −0.984093 0.177653i \(-0.943150\pi\)
0.645899 + 0.763423i \(0.276483\pi\)
\(642\) 0 0
\(643\) 7914.50 + 13708.3i 0.485408 + 0.840752i 0.999859 0.0167681i \(-0.00533770\pi\)
−0.514451 + 0.857520i \(0.672004\pi\)
\(644\) −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 0.886490 + 0.462749i \(0.153137\pi\)
−0.0424927 + 0.999097i \(0.513530\pi\)
\(654\) 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 −0.662592 0.748980i \(-0.730544\pi\)
0.979932 + 0.199331i \(0.0638770\pi\)
\(660\) 0 0
\(661\) −5063.50 8770.24i −0.297954 0.516071i 0.677714 0.735326i \(-0.262971\pi\)
−0.975668 + 0.219255i \(0.929637\pi\)
\(662\) −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 −0.869597 0.493762i \(-0.835621\pi\)
0.862409 + 0.506212i \(0.168955\pi\)
\(674\) −4366.00 −0.249513
\(675\) 0 0
\(676\) −3312.00 −0.188439
\(677\) 4225.50 7318.78i 0.239881 0.415485i −0.720799 0.693144i \(-0.756225\pi\)
0.960680 + 0.277659i \(0.0895584\pi\)
\(678\) 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 −0.940233 0.340532i \(-0.889393\pi\)
0.765026 + 0.643999i \(0.222726\pi\)
\(692\) 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 −0.917153 0.398535i \(-0.869519\pi\)
0.803718 + 0.595011i \(0.202852\pi\)
\(710\) 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 0.378542 + 0.925584i \(0.376426\pi\)
−0.990850 + 0.134965i \(0.956908\pi\)
\(728\) −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 0.756077 + 0.654482i \(0.227113\pi\)
0.188760 + 0.982023i \(0.439553\pi\)
\(734\) 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 0.885364 0.464898i \(-0.153909\pi\)
−0.845296 + 0.534299i \(0.820576\pi\)
\(744\) 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 0.937493 0.348005i \(-0.113141\pi\)
−0.770127 + 0.637890i \(0.779807\pi\)
\(752\) 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 0.915698 0.401867i \(-0.131639\pi\)
−0.805876 + 0.592084i \(0.798305\pi\)
\(762\) 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 0.891782 0.452465i \(-0.149455\pi\)
−0.837737 + 0.546073i \(0.816122\pi\)
\(770\) −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