Properties

Label 13.4.c.a.9.1
Level $13$
Weight $4$
Character 13.9
Analytic conductor $0.767$
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] = [13,4,Mod(3,13)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(13, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("13.3");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 13 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 13.c (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: \(0.767024830075\)
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: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 9.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 13.9
Dual form 13.4.c.a.3.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.00000 + 3.46410i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-4.00000 - 6.92820i) q^{4} +17.0000 q^{5} +(-4.00000 - 6.92820i) q^{6} +(-10.0000 - 17.3205i) q^{7} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\) \(q+(-2.00000 + 3.46410i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-4.00000 - 6.92820i) q^{4} +17.0000 q^{5} +(-4.00000 - 6.92820i) q^{6} +(-10.0000 - 17.3205i) q^{7} +(11.5000 + 19.9186i) q^{9} +(-34.0000 + 58.8897i) q^{10} +(16.0000 - 27.7128i) q^{11} +16.0000 q^{12} +(-45.5000 - 11.2583i) q^{13} +80.0000 q^{14} +(-17.0000 + 29.4449i) q^{15} +(32.0000 - 55.4256i) q^{16} +(6.50000 + 11.2583i) q^{17} -92.0000 q^{18} +(-15.0000 - 25.9808i) q^{19} +(-68.0000 - 117.779i) q^{20} +40.0000 q^{21} +(64.0000 + 110.851i) q^{22} +(-39.0000 + 67.5500i) q^{23} +164.000 q^{25} +(130.000 - 135.100i) q^{26} -100.000 q^{27} +(-80.0000 + 138.564i) q^{28} +(-98.5000 + 170.607i) q^{29} +(-68.0000 - 117.779i) q^{30} -74.0000 q^{31} +(128.000 + 221.703i) q^{32} +(32.0000 + 55.4256i) q^{33} -52.0000 q^{34} +(-170.000 - 294.449i) q^{35} +(92.0000 - 159.349i) q^{36} +(113.500 - 196.588i) q^{37} +120.000 q^{38} +(65.0000 - 67.5500i) q^{39} +(82.5000 - 142.894i) q^{41} +(-80.0000 + 138.564i) q^{42} +(78.0000 + 135.100i) q^{43} -256.000 q^{44} +(195.500 + 338.616i) q^{45} +(-156.000 - 270.200i) q^{46} -162.000 q^{47} +(64.0000 + 110.851i) q^{48} +(-28.5000 + 49.3634i) q^{49} +(-328.000 + 568.113i) q^{50} -26.0000 q^{51} +(104.000 + 360.267i) q^{52} +93.0000 q^{53} +(200.000 - 346.410i) q^{54} +(272.000 - 471.118i) q^{55} +60.0000 q^{57} +(-394.000 - 682.428i) q^{58} +(432.000 + 748.246i) q^{59} +272.000 q^{60} +(-72.5000 - 125.574i) q^{61} +(148.000 - 256.344i) q^{62} +(230.000 - 398.372i) q^{63} -512.000 q^{64} +(-773.500 - 191.392i) q^{65} -256.000 q^{66} +(-431.000 + 746.514i) q^{67} +(52.0000 - 90.0666i) q^{68} +(-78.0000 - 135.100i) q^{69} +1360.00 q^{70} +(-327.000 - 566.381i) q^{71} +215.000 q^{73} +(454.000 + 786.351i) q^{74} +(-164.000 + 284.056i) q^{75} +(-120.000 + 207.846i) q^{76} -640.000 q^{77} +(104.000 + 360.267i) q^{78} -76.0000 q^{79} +(544.000 - 942.236i) q^{80} +(-210.500 + 364.597i) q^{81} +(330.000 + 571.577i) q^{82} +628.000 q^{83} +(-160.000 - 277.128i) q^{84} +(110.500 + 191.392i) q^{85} -624.000 q^{86} +(-197.000 - 341.214i) q^{87} +(133.000 - 230.363i) q^{89} -1564.00 q^{90} +(260.000 + 900.666i) q^{91} +624.000 q^{92} +(74.0000 - 128.172i) q^{93} +(324.000 - 561.184i) q^{94} +(-255.000 - 441.673i) q^{95} -512.000 q^{96} +(-119.000 - 206.114i) q^{97} +(-114.000 - 197.454i) q^{98} +736.000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 4 q^{2} - 2 q^{3} - 8 q^{4} + 34 q^{5} - 8 q^{6} - 20 q^{7} + 23 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 4 q^{2} - 2 q^{3} - 8 q^{4} + 34 q^{5} - 8 q^{6} - 20 q^{7} + 23 q^{9} - 68 q^{10} + 32 q^{11} + 32 q^{12} - 91 q^{13} + 160 q^{14} - 34 q^{15} + 64 q^{16} + 13 q^{17} - 184 q^{18} - 30 q^{19} - 136 q^{20} + 80 q^{21} + 128 q^{22} - 78 q^{23} + 328 q^{25} + 260 q^{26} - 200 q^{27} - 160 q^{28} - 197 q^{29} - 136 q^{30} - 148 q^{31} + 256 q^{32} + 64 q^{33} - 104 q^{34} - 340 q^{35} + 184 q^{36} + 227 q^{37} + 240 q^{38} + 130 q^{39} + 165 q^{41} - 160 q^{42} + 156 q^{43} - 512 q^{44} + 391 q^{45} - 312 q^{46} - 324 q^{47} + 128 q^{48} - 57 q^{49} - 656 q^{50} - 52 q^{51} + 208 q^{52} + 186 q^{53} + 400 q^{54} + 544 q^{55} + 120 q^{57} - 788 q^{58} + 864 q^{59} + 544 q^{60} - 145 q^{61} + 296 q^{62} + 460 q^{63} - 1024 q^{64} - 1547 q^{65} - 512 q^{66} - 862 q^{67} + 104 q^{68} - 156 q^{69} + 2720 q^{70} - 654 q^{71} + 430 q^{73} + 908 q^{74} - 328 q^{75} - 240 q^{76} - 1280 q^{77} + 208 q^{78} - 152 q^{79} + 1088 q^{80} - 421 q^{81} + 660 q^{82} + 1256 q^{83} - 320 q^{84} + 221 q^{85} - 1248 q^{86} - 394 q^{87} + 266 q^{89} - 3128 q^{90} + 520 q^{91} + 1248 q^{92} + 148 q^{93} + 648 q^{94} - 510 q^{95} - 1024 q^{96} - 238 q^{97} - 228 q^{98} + 1472 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/13\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.00000 + 3.46410i −0.707107 + 1.22474i 0.258819 + 0.965926i \(0.416667\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) −1.00000 + 1.73205i −0.192450 + 0.333333i −0.946062 0.323987i \(-0.894977\pi\)
0.753612 + 0.657320i \(0.228310\pi\)
\(4\) −4.00000 6.92820i −0.500000 0.866025i
\(5\) 17.0000 1.52053 0.760263 0.649615i \(-0.225070\pi\)
0.760263 + 0.649615i \(0.225070\pi\)
\(6\) −4.00000 6.92820i −0.272166 0.471405i
\(7\) −10.0000 17.3205i −0.539949 0.935220i −0.998906 0.0467610i \(-0.985110\pi\)
0.458957 0.888459i \(-0.348223\pi\)
\(8\) 0 0
\(9\) 11.5000 + 19.9186i 0.425926 + 0.737725i
\(10\) −34.0000 + 58.8897i −1.07517 + 1.86226i
\(11\) 16.0000 27.7128i 0.438562 0.759612i −0.559017 0.829156i \(-0.688821\pi\)
0.997579 + 0.0695447i \(0.0221546\pi\)
\(12\) 16.0000 0.384900
\(13\) −45.5000 11.2583i −0.970725 0.240192i
\(14\) 80.0000 1.52721
\(15\) −17.0000 + 29.4449i −0.292625 + 0.506842i
\(16\) 32.0000 55.4256i 0.500000 0.866025i
\(17\) 6.50000 + 11.2583i 0.0927342 + 0.160620i 0.908661 0.417535i \(-0.137106\pi\)
−0.815927 + 0.578156i \(0.803773\pi\)
\(18\) −92.0000 −1.20470
\(19\) −15.0000 25.9808i −0.181118 0.313705i 0.761144 0.648583i \(-0.224638\pi\)
−0.942261 + 0.334878i \(0.891305\pi\)
\(20\) −68.0000 117.779i −0.760263 1.31681i
\(21\) 40.0000 0.415653
\(22\) 64.0000 + 110.851i 0.620220 + 1.07425i
\(23\) −39.0000 + 67.5500i −0.353568 + 0.612398i −0.986872 0.161506i \(-0.948365\pi\)
0.633304 + 0.773903i \(0.281698\pi\)
\(24\) 0 0
\(25\) 164.000 1.31200
\(26\) 130.000 135.100i 0.980581 1.01905i
\(27\) −100.000 −0.712778
\(28\) −80.0000 + 138.564i −0.539949 + 0.935220i
\(29\) −98.5000 + 170.607i −0.630724 + 1.09245i 0.356680 + 0.934227i \(0.383909\pi\)
−0.987404 + 0.158219i \(0.949425\pi\)
\(30\) −68.0000 117.779i −0.413835 0.716783i
\(31\) −74.0000 −0.428735 −0.214368 0.976753i \(-0.568769\pi\)
−0.214368 + 0.976753i \(0.568769\pi\)
\(32\) 128.000 + 221.703i 0.707107 + 1.22474i
\(33\) 32.0000 + 55.4256i 0.168803 + 0.292375i
\(34\) −52.0000 −0.262292
\(35\) −170.000 294.449i −0.821007 1.42203i
\(36\) 92.0000 159.349i 0.425926 0.737725i
\(37\) 113.500 196.588i 0.504305 0.873482i −0.495683 0.868504i \(-0.665082\pi\)
0.999988 0.00497814i \(-0.00158460\pi\)
\(38\) 120.000 0.512278
\(39\) 65.0000 67.5500i 0.266880 0.277350i
\(40\) 0 0
\(41\) 82.5000 142.894i 0.314252 0.544301i −0.665026 0.746820i \(-0.731580\pi\)
0.979278 + 0.202520i \(0.0649130\pi\)
\(42\) −80.0000 + 138.564i −0.293911 + 0.509069i
\(43\) 78.0000 + 135.100i 0.276625 + 0.479129i 0.970544 0.240924i \(-0.0774506\pi\)
−0.693919 + 0.720053i \(0.744117\pi\)
\(44\) −256.000 −0.877124
\(45\) 195.500 + 338.616i 0.647632 + 1.12173i
\(46\) −156.000 270.200i −0.500021 0.866061i
\(47\) −162.000 −0.502769 −0.251384 0.967887i \(-0.580886\pi\)
−0.251384 + 0.967887i \(0.580886\pi\)
\(48\) 64.0000 + 110.851i 0.192450 + 0.333333i
\(49\) −28.5000 + 49.3634i −0.0830904 + 0.143917i
\(50\) −328.000 + 568.113i −0.927724 + 1.60687i
\(51\) −26.0000 −0.0713868
\(52\) 104.000 + 360.267i 0.277350 + 0.960769i
\(53\) 93.0000 0.241029 0.120514 0.992712i \(-0.461546\pi\)
0.120514 + 0.992712i \(0.461546\pi\)
\(54\) 200.000 346.410i 0.504010 0.872971i
\(55\) 272.000 471.118i 0.666845 1.15501i
\(56\) 0 0
\(57\) 60.0000 0.139424
\(58\) −394.000 682.428i −0.891978 1.54495i
\(59\) 432.000 + 748.246i 0.953248 + 1.65107i 0.738328 + 0.674442i \(0.235616\pi\)
0.214919 + 0.976632i \(0.431051\pi\)
\(60\) 272.000 0.585251
\(61\) −72.5000 125.574i −0.152175 0.263575i 0.779852 0.625964i \(-0.215294\pi\)
−0.932027 + 0.362389i \(0.881961\pi\)
\(62\) 148.000 256.344i 0.303162 0.525091i
\(63\) 230.000 398.372i 0.459957 0.796668i
\(64\) −512.000 −1.00000
\(65\) −773.500 191.392i −1.47601 0.365219i
\(66\) −256.000 −0.477446
\(67\) −431.000 + 746.514i −0.785896 + 1.36121i 0.142566 + 0.989785i \(0.454465\pi\)
−0.928462 + 0.371427i \(0.878869\pi\)
\(68\) 52.0000 90.0666i 0.0927342 0.160620i
\(69\) −78.0000 135.100i −0.136088 0.235712i
\(70\) 1360.00 2.32216
\(71\) −327.000 566.381i −0.546588 0.946718i −0.998505 0.0546585i \(-0.982593\pi\)
0.451917 0.892060i \(-0.350740\pi\)
\(72\) 0 0
\(73\) 215.000 0.344710 0.172355 0.985035i \(-0.444862\pi\)
0.172355 + 0.985035i \(0.444862\pi\)
\(74\) 454.000 + 786.351i 0.713195 + 1.23529i
\(75\) −164.000 + 284.056i −0.252495 + 0.437333i
\(76\) −120.000 + 207.846i −0.181118 + 0.313705i
\(77\) −640.000 −0.947205
\(78\) 104.000 + 360.267i 0.150970 + 0.522976i
\(79\) −76.0000 −0.108236 −0.0541182 0.998535i \(-0.517235\pi\)
−0.0541182 + 0.998535i \(0.517235\pi\)
\(80\) 544.000 942.236i 0.760263 1.31681i
\(81\) −210.500 + 364.597i −0.288752 + 0.500133i
\(82\) 330.000 + 571.577i 0.444420 + 0.769757i
\(83\) 628.000 0.830505 0.415253 0.909706i \(-0.363693\pi\)
0.415253 + 0.909706i \(0.363693\pi\)
\(84\) −160.000 277.128i −0.207827 0.359966i
\(85\) 110.500 + 191.392i 0.141005 + 0.244227i
\(86\) −624.000 −0.782415
\(87\) −197.000 341.214i −0.242766 0.420483i
\(88\) 0 0
\(89\) 133.000 230.363i 0.158404 0.274364i −0.775889 0.630869i \(-0.782698\pi\)
0.934293 + 0.356505i \(0.116032\pi\)
\(90\) −1564.00 −1.83178
\(91\) 260.000 + 900.666i 0.299510 + 1.03753i
\(92\) 624.000 0.707136
\(93\) 74.0000 128.172i 0.0825101 0.142912i
\(94\) 324.000 561.184i 0.355511 0.615763i
\(95\) −255.000 441.673i −0.275394 0.476997i
\(96\) −512.000 −0.544331
\(97\) −119.000 206.114i −0.124563 0.215750i 0.796999 0.603981i \(-0.206420\pi\)
−0.921562 + 0.388231i \(0.873086\pi\)
\(98\) −114.000 197.454i −0.117508 0.203529i
\(99\) 736.000 0.747180
\(100\) −656.000 1136.23i −0.656000 1.13623i
\(101\) 409.500 709.275i 0.403433 0.698767i −0.590704 0.806888i \(-0.701150\pi\)
0.994138 + 0.108121i \(0.0344834\pi\)
\(102\) 52.0000 90.0666i 0.0504781 0.0874307i
\(103\) 1638.00 1.56696 0.783480 0.621417i \(-0.213443\pi\)
0.783480 + 0.621417i \(0.213443\pi\)
\(104\) 0 0
\(105\) 680.000 0.632011
\(106\) −186.000 + 322.161i −0.170433 + 0.295199i
\(107\) −261.000 + 452.065i −0.235811 + 0.408437i −0.959508 0.281681i \(-0.909108\pi\)
0.723697 + 0.690118i \(0.242441\pi\)
\(108\) 400.000 + 692.820i 0.356389 + 0.617284i
\(109\) −1634.00 −1.43586 −0.717930 0.696115i \(-0.754910\pi\)
−0.717930 + 0.696115i \(0.754910\pi\)
\(110\) 1088.00 + 1884.47i 0.943061 + 1.63343i
\(111\) 227.000 + 393.176i 0.194107 + 0.336203i
\(112\) −1280.00 −1.07990
\(113\) −163.500 283.190i −0.136113 0.235755i 0.789909 0.613224i \(-0.210128\pi\)
−0.926022 + 0.377469i \(0.876794\pi\)
\(114\) −120.000 + 207.846i −0.0985880 + 0.170759i
\(115\) −663.000 + 1148.35i −0.537609 + 0.931167i
\(116\) 1576.00 1.26145
\(117\) −299.000 1035.77i −0.236261 0.818433i
\(118\) −3456.00 −2.69619
\(119\) 130.000 225.167i 0.100144 0.173454i
\(120\) 0 0
\(121\) 153.500 + 265.870i 0.115327 + 0.199752i
\(122\) 580.000 0.430416
\(123\) 165.000 + 285.788i 0.120956 + 0.209501i
\(124\) 296.000 + 512.687i 0.214368 + 0.371296i
\(125\) 663.000 0.474404
\(126\) 920.000 + 1593.49i 0.650477 + 1.12666i
\(127\) 1079.00 1868.88i 0.753904 1.30580i −0.192014 0.981392i \(-0.561502\pi\)
0.945918 0.324407i \(-0.105165\pi\)
\(128\) 0 0
\(129\) −312.000 −0.212946
\(130\) 2210.00 2296.70i 1.49100 1.54949i
\(131\) 730.000 0.486873 0.243437 0.969917i \(-0.421725\pi\)
0.243437 + 0.969917i \(0.421725\pi\)
\(132\) 256.000 443.405i 0.168803 0.292375i
\(133\) −300.000 + 519.615i −0.195589 + 0.338770i
\(134\) −1724.00 2986.06i −1.11142 1.92504i
\(135\) −1700.00 −1.08380
\(136\) 0 0
\(137\) −835.500 1447.13i −0.521033 0.902456i −0.999701 0.0244601i \(-0.992213\pi\)
0.478667 0.877996i \(-0.341120\pi\)
\(138\) 624.000 0.384916
\(139\) −456.000 789.815i −0.278255 0.481951i 0.692696 0.721229i \(-0.256423\pi\)
−0.970951 + 0.239278i \(0.923089\pi\)
\(140\) −1360.00 + 2355.59i −0.821007 + 1.42203i
\(141\) 162.000 280.592i 0.0967579 0.167590i
\(142\) 2616.00 1.54598
\(143\) −1040.00 + 1080.80i −0.608176 + 0.632035i
\(144\) 1472.00 0.851852
\(145\) −1674.50 + 2900.32i −0.959032 + 1.66109i
\(146\) −430.000 + 744.782i −0.243747 + 0.422182i
\(147\) −57.0000 98.7269i −0.0319815 0.0553936i
\(148\) −1816.00 −1.00861
\(149\) 1057.50 + 1831.64i 0.581435 + 1.00707i 0.995310 + 0.0967407i \(0.0308418\pi\)
−0.413875 + 0.910334i \(0.635825\pi\)
\(150\) −656.000 1136.23i −0.357081 0.618483i
\(151\) 514.000 0.277011 0.138506 0.990362i \(-0.455770\pi\)
0.138506 + 0.990362i \(0.455770\pi\)
\(152\) 0 0
\(153\) −149.500 + 258.942i −0.0789958 + 0.136825i
\(154\) 1280.00 2217.03i 0.669775 1.16008i
\(155\) −1258.00 −0.651903
\(156\) −728.000 180.133i −0.373632 0.0924500i
\(157\) 2901.00 1.47468 0.737341 0.675521i \(-0.236081\pi\)
0.737341 + 0.675521i \(0.236081\pi\)
\(158\) 152.000 263.272i 0.0765346 0.132562i
\(159\) −93.0000 + 161.081i −0.0463860 + 0.0803430i
\(160\) 2176.00 + 3768.94i 1.07517 + 1.86226i
\(161\) 1560.00 0.763635
\(162\) −842.000 1458.39i −0.408357 0.707294i
\(163\) −1180.00 2043.82i −0.567023 0.982112i −0.996858 0.0792052i \(-0.974762\pi\)
0.429835 0.902907i \(-0.358572\pi\)
\(164\) −1320.00 −0.628504
\(165\) 544.000 + 942.236i 0.256669 + 0.444563i
\(166\) −1256.00 + 2175.46i −0.587256 + 1.01716i
\(167\) −140.000 + 242.487i −0.0648714 + 0.112361i −0.896637 0.442767i \(-0.853997\pi\)
0.831766 + 0.555127i \(0.187330\pi\)
\(168\) 0 0
\(169\) 1943.50 + 1024.51i 0.884615 + 0.466321i
\(170\) −884.000 −0.398822
\(171\) 345.000 597.558i 0.154285 0.267230i
\(172\) 624.000 1080.80i 0.276625 0.479129i
\(173\) −663.000 1148.35i −0.291370 0.504667i 0.682764 0.730639i \(-0.260778\pi\)
−0.974134 + 0.225972i \(0.927444\pi\)
\(174\) 1576.00 0.686645
\(175\) −1640.00 2840.56i −0.708413 1.22701i
\(176\) −1024.00 1773.62i −0.438562 0.759612i
\(177\) −1728.00 −0.733810
\(178\) 532.000 + 921.451i 0.224017 + 0.388009i
\(179\) −2132.00 + 3692.73i −0.890241 + 1.54194i −0.0506550 + 0.998716i \(0.516131\pi\)
−0.839586 + 0.543227i \(0.817202\pi\)
\(180\) 1564.00 2708.93i 0.647632 1.12173i
\(181\) −403.000 −0.165496 −0.0827479 0.996571i \(-0.526370\pi\)
−0.0827479 + 0.996571i \(0.526370\pi\)
\(182\) −3640.00 900.666i −1.48250 0.366823i
\(183\) 290.000 0.117144
\(184\) 0 0
\(185\) 1929.50 3341.99i 0.766809 1.32815i
\(186\) 296.000 + 512.687i 0.116687 + 0.202108i
\(187\) 416.000 0.162679
\(188\) 648.000 + 1122.37i 0.251384 + 0.435410i
\(189\) 1000.00 + 1732.05i 0.384864 + 0.666604i
\(190\) 2040.00 0.778932
\(191\) 623.000 + 1079.07i 0.236014 + 0.408788i 0.959567 0.281481i \(-0.0908255\pi\)
−0.723553 + 0.690269i \(0.757492\pi\)
\(192\) 512.000 886.810i 0.192450 0.333333i
\(193\) −133.500 + 231.229i −0.0497904 + 0.0862394i −0.889846 0.456260i \(-0.849189\pi\)
0.840056 + 0.542500i \(0.182522\pi\)
\(194\) 952.000 0.352318
\(195\) 1105.00 1148.35i 0.405798 0.421718i
\(196\) 456.000 0.166181
\(197\) −639.000 + 1106.78i −0.231101 + 0.400278i −0.958132 0.286326i \(-0.907566\pi\)
0.727032 + 0.686604i \(0.240899\pi\)
\(198\) −1472.00 + 2549.58i −0.528336 + 0.915104i
\(199\) −2119.00 3670.22i −0.754834 1.30741i −0.945457 0.325747i \(-0.894384\pi\)
0.190623 0.981663i \(-0.438949\pi\)
\(200\) 0 0
\(201\) −862.000 1493.03i −0.302492 0.523931i
\(202\) 1638.00 + 2837.10i 0.570541 + 0.988206i
\(203\) 3940.00 1.36224
\(204\) 104.000 + 180.133i 0.0356934 + 0.0618228i
\(205\) 1402.50 2429.20i 0.477829 0.827623i
\(206\) −3276.00 + 5674.20i −1.10801 + 1.91913i
\(207\) −1794.00 −0.602375
\(208\) −2080.00 + 2161.60i −0.693375 + 0.720577i
\(209\) −960.000 −0.317725
\(210\) −1360.00 + 2355.59i −0.446900 + 0.774053i
\(211\) −1535.00 + 2658.70i −0.500823 + 0.867452i 0.499176 + 0.866501i \(0.333636\pi\)
−1.00000 0.000951154i \(0.999697\pi\)
\(212\) −372.000 644.323i −0.120514 0.208737i
\(213\) 1308.00 0.420764
\(214\) −1044.00 1808.26i −0.333488 0.577618i
\(215\) 1326.00 + 2296.70i 0.420616 + 0.728528i
\(216\) 0 0
\(217\) 740.000 + 1281.72i 0.231495 + 0.400962i
\(218\) 3268.00 5660.34i 1.01531 1.75856i
\(219\) −215.000 + 372.391i −0.0663395 + 0.114903i
\(220\) −4352.00 −1.33369
\(221\) −169.000 585.433i −0.0514397 0.178192i
\(222\) −1816.00 −0.549018
\(223\) 2689.00 4657.48i 0.807483 1.39860i −0.107119 0.994246i \(-0.534162\pi\)
0.914602 0.404356i \(-0.132504\pi\)
\(224\) 2560.00 4434.05i 0.763604 1.32260i
\(225\) 1886.00 + 3266.65i 0.558815 + 0.967896i
\(226\) 1308.00 0.384986
\(227\) 1987.00 + 3441.58i 0.580977 + 1.00628i 0.995364 + 0.0961811i \(0.0306628\pi\)
−0.414387 + 0.910101i \(0.636004\pi\)
\(228\) −240.000 415.692i −0.0697122 0.120745i
\(229\) −6298.00 −1.81740 −0.908698 0.417455i \(-0.862922\pi\)
−0.908698 + 0.417455i \(0.862922\pi\)
\(230\) −2652.00 4593.40i −0.760294 1.31687i
\(231\) 640.000 1108.51i 0.182290 0.315735i
\(232\) 0 0
\(233\) 4030.00 1.13311 0.566554 0.824025i \(-0.308276\pi\)
0.566554 + 0.824025i \(0.308276\pi\)
\(234\) 4186.00 + 1035.77i 1.16943 + 0.289360i
\(235\) −2754.00 −0.764473
\(236\) 3456.00 5985.97i 0.953248 1.65107i
\(237\) 76.0000 131.636i 0.0208301 0.0360788i
\(238\) 520.000 + 900.666i 0.141624 + 0.245301i
\(239\) −984.000 −0.266317 −0.133158 0.991095i \(-0.542512\pi\)
−0.133158 + 0.991095i \(0.542512\pi\)
\(240\) 1088.00 + 1884.47i 0.292625 + 0.506842i
\(241\) −471.500 816.662i −0.126025 0.218281i 0.796108 0.605154i \(-0.206889\pi\)
−0.922133 + 0.386873i \(0.873555\pi\)
\(242\) −1228.00 −0.326194
\(243\) −1771.00 3067.46i −0.467530 0.809785i
\(244\) −580.000 + 1004.59i −0.152175 + 0.263575i
\(245\) −484.500 + 839.179i −0.126341 + 0.218829i
\(246\) −1320.00 −0.342114
\(247\) 390.000 + 1351.00i 0.100466 + 0.348024i
\(248\) 0 0
\(249\) −628.000 + 1087.73i −0.159831 + 0.276835i
\(250\) −1326.00 + 2296.70i −0.335454 + 0.581024i
\(251\) 1365.00 + 2364.25i 0.343259 + 0.594542i 0.985036 0.172349i \(-0.0551358\pi\)
−0.641777 + 0.766891i \(0.721802\pi\)
\(252\) −3680.00 −0.919914
\(253\) 1248.00 + 2161.60i 0.310123 + 0.537149i
\(254\) 4316.00 + 7475.53i 1.06618 + 1.84668i
\(255\) −442.000 −0.108546
\(256\) −2048.00 3547.24i −0.500000 0.866025i
\(257\) 942.500 1632.46i 0.228761 0.396225i −0.728680 0.684854i \(-0.759866\pi\)
0.957441 + 0.288629i \(0.0931993\pi\)
\(258\) 624.000 1080.80i 0.150576 0.260805i
\(259\) −4540.00 −1.08920
\(260\) 1768.00 + 6124.53i 0.421718 + 1.46087i
\(261\) −4531.00 −1.07457
\(262\) −1460.00 + 2528.79i −0.344271 + 0.596296i
\(263\) −2016.00 + 3491.81i −0.472669 + 0.818686i −0.999511 0.0312769i \(-0.990043\pi\)
0.526842 + 0.849963i \(0.323376\pi\)
\(264\) 0 0
\(265\) 1581.00 0.366491
\(266\) −1200.00 2078.46i −0.276604 0.479093i
\(267\) 266.000 + 460.726i 0.0609698 + 0.105603i
\(268\) 6896.00 1.57179
\(269\) −2003.00 3469.30i −0.453997 0.786345i 0.544633 0.838674i \(-0.316669\pi\)
−0.998630 + 0.0523292i \(0.983335\pi\)
\(270\) 3400.00 5888.97i 0.766361 1.32738i
\(271\) 2148.00 3720.45i 0.481482 0.833952i −0.518292 0.855204i \(-0.673432\pi\)
0.999774 + 0.0212520i \(0.00676523\pi\)
\(272\) 832.000 0.185468
\(273\) −1820.00 450.333i −0.403485 0.0998367i
\(274\) 6684.00 1.47371
\(275\) 2624.00 4544.90i 0.575393 0.996610i
\(276\) −624.000 + 1080.80i −0.136088 + 0.235712i
\(277\) 2775.50 + 4807.31i 0.602035 + 1.04275i 0.992513 + 0.122142i \(0.0389765\pi\)
−0.390478 + 0.920612i \(0.627690\pi\)
\(278\) 3648.00 0.787023
\(279\) −851.000 1473.98i −0.182609 0.316289i
\(280\) 0 0
\(281\) −5557.00 −1.17973 −0.589863 0.807504i \(-0.700818\pi\)
−0.589863 + 0.807504i \(0.700818\pi\)
\(282\) 648.000 + 1122.37i 0.136836 + 0.237007i
\(283\) −1560.00 + 2702.00i −0.327676 + 0.567552i −0.982050 0.188619i \(-0.939599\pi\)
0.654374 + 0.756171i \(0.272932\pi\)
\(284\) −2616.00 + 4531.04i −0.546588 + 0.946718i
\(285\) 1020.00 0.211999
\(286\) −1664.00 5764.27i −0.344036 1.19178i
\(287\) −3300.00 −0.678721
\(288\) −2944.00 + 5099.16i −0.602350 + 1.04330i
\(289\) 2372.00 4108.42i 0.482801 0.836235i
\(290\) −6698.00 11601.3i −1.35628 2.34914i
\(291\) 476.000 0.0958887
\(292\) −860.000 1489.56i −0.172355 0.298528i
\(293\) −4150.50 7188.88i −0.827559 1.43337i −0.899948 0.435998i \(-0.856396\pi\)
0.0723887 0.997376i \(-0.476938\pi\)
\(294\) 456.000 0.0904573
\(295\) 7344.00 + 12720.2i 1.44944 + 2.51050i
\(296\) 0 0
\(297\) −1600.00 + 2771.28i −0.312597 + 0.541435i
\(298\) −8460.00 −1.64455
\(299\) 2535.00 2634.45i 0.490310 0.509546i
\(300\) 2624.00 0.504989
\(301\) 1560.00 2702.00i 0.298727 0.517411i
\(302\) −1028.00 + 1780.55i −0.195877 + 0.339268i
\(303\) 819.000 + 1418.55i 0.155282 + 0.268956i
\(304\) −1920.00 −0.362235
\(305\) −1232.50 2134.75i −0.231386 0.400772i
\(306\) −598.000 1035.77i −0.111717 0.193499i
\(307\) 8678.00 1.61329 0.806644 0.591037i \(-0.201281\pi\)
0.806644 + 0.591037i \(0.201281\pi\)
\(308\) 2560.00 + 4434.05i 0.473602 + 0.820303i
\(309\) −1638.00 + 2837.10i −0.301562 + 0.522320i
\(310\) 2516.00 4357.84i 0.460965 0.798415i
\(311\) 8658.00 1.57862 0.789309 0.613996i \(-0.210439\pi\)
0.789309 + 0.613996i \(0.210439\pi\)
\(312\) 0 0
\(313\) −5250.00 −0.948075 −0.474038 0.880505i \(-0.657204\pi\)
−0.474038 + 0.880505i \(0.657204\pi\)
\(314\) −5802.00 + 10049.4i −1.04276 + 1.80611i
\(315\) 3910.00 6772.32i 0.699376 1.21136i
\(316\) 304.000 + 526.543i 0.0541182 + 0.0937354i
\(317\) 6413.00 1.13625 0.568123 0.822944i \(-0.307670\pi\)
0.568123 + 0.822944i \(0.307670\pi\)
\(318\) −372.000 644.323i −0.0655998 0.113622i
\(319\) 3152.00 + 5459.42i 0.553223 + 0.958210i
\(320\) −8704.00 −1.52053
\(321\) −522.000 904.131i −0.0907639 0.157208i
\(322\) −3120.00 + 5404.00i −0.539971 + 0.935258i
\(323\) 195.000 337.750i 0.0335916 0.0581824i
\(324\) 3368.00 0.577503
\(325\) −7462.00 1846.37i −1.27359 0.315132i
\(326\) 9440.00 1.60378
\(327\) 1634.00 2830.17i 0.276332 0.478620i
\(328\) 0 0
\(329\) 1620.00 + 2805.92i 0.271470 + 0.470199i
\(330\) −4352.00 −0.725969
\(331\) −1744.00 3020.70i −0.289604 0.501609i 0.684111 0.729378i \(-0.260190\pi\)
−0.973715 + 0.227769i \(0.926857\pi\)
\(332\) −2512.00 4350.91i −0.415253 0.719239i
\(333\) 5221.00 0.859186
\(334\) −560.000 969.948i −0.0917420 0.158902i
\(335\) −7327.00 + 12690.7i −1.19498 + 2.06976i
\(336\) 1280.00 2217.03i 0.207827 0.359966i
\(337\) −1833.00 −0.296290 −0.148145 0.988966i \(-0.547330\pi\)
−0.148145 + 0.988966i \(0.547330\pi\)
\(338\) −7436.00 + 4683.47i −1.19664 + 0.753689i
\(339\) 654.000 0.104780
\(340\) 884.000 1531.13i 0.141005 0.244227i
\(341\) −1184.00 + 2050.75i −0.188027 + 0.325672i
\(342\) 1380.00 + 2390.23i 0.218193 + 0.377921i
\(343\) −5720.00 −0.900440
\(344\) 0 0
\(345\) −1326.00 2296.70i −0.206926 0.358406i
\(346\) 5304.00 0.824118
\(347\) −3615.00 6261.36i −0.559260 0.968667i −0.997558 0.0698377i \(-0.977752\pi\)
0.438298 0.898830i \(-0.355581\pi\)
\(348\) −1576.00 + 2729.71i −0.242766 + 0.420483i
\(349\) 2629.00 4553.56i 0.403230 0.698414i −0.590884 0.806757i \(-0.701221\pi\)
0.994114 + 0.108342i \(0.0345543\pi\)
\(350\) 13120.0 2.00370
\(351\) 4550.00 + 1125.83i 0.691912 + 0.171204i
\(352\) 8192.00 1.24044
\(353\) −1581.50 + 2739.24i −0.238455 + 0.413017i −0.960271 0.279068i \(-0.909974\pi\)
0.721816 + 0.692085i \(0.243308\pi\)
\(354\) 3456.00 5985.97i 0.518882 0.898730i
\(355\) −5559.00 9628.47i −0.831102 1.43951i
\(356\) −2128.00 −0.316808
\(357\) 260.000 + 450.333i 0.0385453 + 0.0667624i
\(358\) −8528.00 14770.9i −1.25899 2.18064i
\(359\) −10068.0 −1.48014 −0.740068 0.672532i \(-0.765207\pi\)
−0.740068 + 0.672532i \(0.765207\pi\)
\(360\) 0 0
\(361\) 2979.50 5160.65i 0.434393 0.752390i
\(362\) 806.000 1396.03i 0.117023 0.202690i
\(363\) −614.000 −0.0887786
\(364\) 5200.00 5404.00i 0.748775 0.778150i
\(365\) 3655.00 0.524141
\(366\) −580.000 + 1004.59i −0.0828336 + 0.143472i
\(367\) −3719.00 + 6441.50i −0.528965 + 0.916195i 0.470464 + 0.882419i \(0.344086\pi\)
−0.999429 + 0.0337755i \(0.989247\pi\)
\(368\) 2496.00 + 4323.20i 0.353568 + 0.612398i
\(369\) 3795.00 0.535392
\(370\) 7718.00 + 13368.0i 1.08443 + 1.87829i
\(371\) −930.000 1610.81i −0.130143 0.225415i
\(372\) −1184.00 −0.165020
\(373\) 4841.50 + 8385.72i 0.672073 + 1.16407i 0.977315 + 0.211790i \(0.0679294\pi\)
−0.305242 + 0.952275i \(0.598737\pi\)
\(374\) −832.000 + 1441.07i −0.115031 + 0.199240i
\(375\) −663.000 + 1148.35i −0.0912991 + 0.158135i
\(376\) 0 0
\(377\) 6402.50 6653.67i 0.874657 0.908970i
\(378\) −8000.00 −1.08856
\(379\) 531.000 919.719i 0.0719674 0.124651i −0.827796 0.561029i \(-0.810406\pi\)
0.899763 + 0.436378i \(0.143739\pi\)
\(380\) −2040.00 + 3533.38i −0.275394 + 0.476997i
\(381\) 2158.00 + 3737.77i 0.290178 + 0.502602i
\(382\) −4984.00 −0.667549
\(383\) 1766.00 + 3058.80i 0.235609 + 0.408087i 0.959450 0.281880i \(-0.0909581\pi\)
−0.723840 + 0.689968i \(0.757625\pi\)
\(384\) 0 0
\(385\) −10880.0 −1.44025
\(386\) −534.000 924.915i −0.0704142 0.121961i
\(387\) −1794.00 + 3107.30i −0.235644 + 0.408147i
\(388\) −952.000 + 1648.91i −0.124563 + 0.215750i
\(389\) −11063.0 −1.44194 −0.720972 0.692964i \(-0.756304\pi\)
−0.720972 + 0.692964i \(0.756304\pi\)
\(390\) 1768.00 + 6124.53i 0.229554 + 0.795199i
\(391\) −1014.00 −0.131151
\(392\) 0 0
\(393\) −730.000 + 1264.40i −0.0936988 + 0.162291i
\(394\) −2556.00 4427.12i −0.326826 0.566079i
\(395\) −1292.00 −0.164576
\(396\) −2944.00 5099.16i −0.373590 0.647077i
\(397\) 2993.00 + 5184.03i 0.378374 + 0.655362i 0.990826 0.135145i \(-0.0431501\pi\)
−0.612452 + 0.790508i \(0.709817\pi\)
\(398\) 16952.0 2.13499
\(399\) −600.000 1039.23i −0.0752821 0.130392i
\(400\) 5248.00 9089.80i 0.656000 1.13623i
\(401\) −2967.50 + 5139.86i −0.369551 + 0.640081i −0.989495 0.144565i \(-0.953822\pi\)
0.619945 + 0.784646i \(0.287155\pi\)
\(402\) 6896.00 0.855575
\(403\) 3367.00 + 833.116i 0.416184 + 0.102979i
\(404\) −6552.00 −0.806867
\(405\) −3578.50 + 6198.14i −0.439055 + 0.760465i
\(406\) −7880.00 + 13648.6i −0.963246 + 1.66839i
\(407\) −3632.00 6290.81i −0.442338 0.766152i
\(408\) 0 0
\(409\) 7544.50 + 13067.5i 0.912106 + 1.57981i 0.811083 + 0.584931i \(0.198878\pi\)
0.101023 + 0.994884i \(0.467788\pi\)
\(410\) 5610.00 + 9716.81i 0.675752 + 1.17044i
\(411\) 3342.00 0.401092
\(412\) −6552.00 11348.4i −0.783480 1.35703i
\(413\) 8640.00 14964.9i 1.02941 1.78299i
\(414\) 3588.00 6214.60i 0.425943 0.737756i
\(415\) 10676.0 1.26281
\(416\) −3328.00 11528.5i −0.392232 1.35873i
\(417\) 1824.00 0.214201
\(418\) 1920.00 3325.54i 0.224666 0.389132i
\(419\) 5407.00 9365.20i 0.630428 1.09193i −0.357037 0.934090i \(-0.616213\pi\)
0.987464 0.157843i \(-0.0504538\pi\)
\(420\) −2720.00 4711.18i −0.316006 0.547338i
\(421\) −6535.00 −0.756524 −0.378262 0.925699i \(-0.623478\pi\)
−0.378262 + 0.925699i \(0.623478\pi\)
\(422\) −6140.00 10634.8i −0.708271 1.22676i
\(423\) −1863.00 3226.81i −0.214142 0.370905i
\(424\) 0 0
\(425\) 1066.00 + 1846.37i 0.121667 + 0.210734i
\(426\) −2616.00 + 4531.04i −0.297525 + 0.515328i
\(427\) −1450.00 + 2511.47i −0.164334 + 0.284634i
\(428\) 4176.00 0.471623
\(429\) −832.000 2882.13i −0.0936348 0.324361i
\(430\) −10608.0 −1.18968
\(431\) −990.000 + 1714.73i −0.110642 + 0.191637i −0.916029 0.401112i \(-0.868624\pi\)
0.805387 + 0.592749i \(0.201957\pi\)
\(432\) −3200.00 + 5542.56i −0.356389 + 0.617284i
\(433\) 3464.50 + 6000.69i 0.384511 + 0.665993i 0.991701 0.128564i \(-0.0410368\pi\)
−0.607190 + 0.794556i \(0.707703\pi\)
\(434\) −5920.00 −0.654767
\(435\) −3349.00 5800.64i −0.369132 0.639355i
\(436\) 6536.00 + 11320.7i 0.717930 + 1.24349i
\(437\) 2340.00 0.256150
\(438\) −860.000 1489.56i −0.0938182 0.162498i
\(439\) 2288.00 3962.93i 0.248748 0.430844i −0.714431 0.699706i \(-0.753314\pi\)
0.963179 + 0.268862i \(0.0866476\pi\)
\(440\) 0 0
\(441\) −1311.00 −0.141561
\(442\) 2366.00 + 585.433i 0.254613 + 0.0630005i
\(443\) −8812.00 −0.945081 −0.472540 0.881309i \(-0.656663\pi\)
−0.472540 + 0.881309i \(0.656663\pi\)
\(444\) 1816.00 3145.40i 0.194107 0.336203i
\(445\) 2261.00 3916.17i 0.240858 0.417178i
\(446\) 10756.0 + 18629.9i 1.14195 + 1.97792i
\(447\) −4230.00 −0.447589
\(448\) 5120.00 + 8868.10i 0.539949 + 0.935220i
\(449\) −959.000 1661.04i −0.100797 0.174586i 0.811216 0.584747i \(-0.198806\pi\)
−0.912013 + 0.410160i \(0.865473\pi\)
\(450\) −15088.0 −1.58057
\(451\) −2640.00 4572.61i −0.275638 0.477419i
\(452\) −1308.00 + 2265.52i −0.136113 + 0.235755i
\(453\) −514.000 + 890.274i −0.0533109 + 0.0923371i
\(454\) −15896.0 −1.64325
\(455\) 4420.00 + 15311.3i 0.455413 + 1.57760i
\(456\) 0 0
\(457\) 5880.50 10185.3i 0.601922 1.04256i −0.390608 0.920557i \(-0.627735\pi\)
0.992530 0.122002i \(-0.0389314\pi\)
\(458\) 12596.0 21816.9i 1.28509 2.22585i
\(459\) −650.000 1125.83i −0.0660989 0.114487i
\(460\) 10608.0 1.07522
\(461\) −450.500 780.289i −0.0455138 0.0788323i 0.842371 0.538898i \(-0.181159\pi\)
−0.887885 + 0.460066i \(0.847826\pi\)
\(462\) 2560.00 + 4434.05i 0.257796 + 0.446517i
\(463\) 1372.00 0.137715 0.0688577 0.997626i \(-0.478065\pi\)
0.0688577 + 0.997626i \(0.478065\pi\)
\(464\) 6304.00 + 10918.8i 0.630724 + 1.09245i
\(465\) 1258.00 2178.92i 0.125459 0.217301i
\(466\) −8060.00 + 13960.3i −0.801228 + 1.38777i
\(467\) −6396.00 −0.633772 −0.316886 0.948464i \(-0.602637\pi\)
−0.316886 + 0.948464i \(0.602637\pi\)
\(468\) −5980.00 + 6214.60i −0.590653 + 0.613825i
\(469\) 17240.0 1.69738
\(470\) 5508.00 9540.14i 0.540564 0.936284i
\(471\) −2901.00 + 5024.68i −0.283803 + 0.491561i
\(472\) 0 0
\(473\) 4992.00 0.485269
\(474\) 304.000 + 526.543i 0.0294582 + 0.0510231i
\(475\) −2460.00 4260.84i −0.237626 0.411581i
\(476\) −2080.00 −0.200287
\(477\) 1069.50 + 1852.43i 0.102660 + 0.177813i
\(478\) 1968.00 3408.68i 0.188314 0.326170i
\(479\) −1635.00 + 2831.90i −0.155960 + 0.270131i −0.933408 0.358816i \(-0.883181\pi\)
0.777448 + 0.628947i \(0.216514\pi\)
\(480\) −8704.00 −0.827670
\(481\) −7377.50 + 7666.92i −0.699345 + 0.726781i
\(482\) 3772.00 0.356452
\(483\) −1560.00 + 2702.00i −0.146962 + 0.254545i
\(484\) 1228.00 2126.96i 0.115327 0.199752i
\(485\) −2023.00 3503.94i −0.189401 0.328053i
\(486\) 14168.0 1.32237
\(487\) −9960.00 17251.2i −0.926757 1.60519i −0.788711 0.614765i \(-0.789251\pi\)
−0.138046 0.990426i \(-0.544082\pi\)
\(488\) 0 0
\(489\) 4720.00 0.436494
\(490\) −1938.00 3356.71i −0.178673 0.309471i
\(491\) −3276.00 + 5674.20i −0.301108 + 0.521534i −0.976387 0.216028i \(-0.930690\pi\)
0.675280 + 0.737562i \(0.264023\pi\)
\(492\) 1320.00 2286.31i 0.120956 0.209501i
\(493\) −2561.00 −0.233959
\(494\) −5460.00 1351.00i −0.497281 0.123045i
\(495\) 12512.0 1.13611
\(496\) −2368.00 + 4101.50i −0.214368 + 0.371296i
\(497\) −6540.00 + 11327.6i −0.590260 + 1.02236i
\(498\) −2512.00 4350.91i −0.226035 0.391504i
\(499\) 1746.00 0.156637 0.0783183 0.996928i \(-0.475045\pi\)
0.0783183 + 0.996928i \(0.475045\pi\)
\(500\) −2652.00 4593.40i −0.237202 0.410846i
\(501\) −280.000 484.974i −0.0249690 0.0432476i
\(502\) −10920.0 −0.970883
\(503\) −7346.00 12723.6i −0.651177 1.12787i −0.982838 0.184473i \(-0.940942\pi\)
0.331661 0.943399i \(-0.392391\pi\)
\(504\) 0 0
\(505\) 6961.50 12057.7i 0.613431 1.06249i
\(506\) −9984.00 −0.877160
\(507\) −3718.00 + 2341.73i −0.325685 + 0.205128i
\(508\) −17264.0 −1.50781
\(509\) −4038.50 + 6994.89i −0.351677 + 0.609122i −0.986543 0.163500i \(-0.947722\pi\)
0.634867 + 0.772622i \(0.281055\pi\)
\(510\) 884.000 1531.13i 0.0767533 0.132941i
\(511\) −2150.00 3723.91i −0.186126 0.322380i
\(512\) 16384.0 1.41421
\(513\) 1500.00 + 2598.08i 0.129097 + 0.223602i
\(514\) 3770.00 + 6529.83i 0.323517 + 0.560347i
\(515\) 27846.0 2.38260
\(516\) 1248.00 + 2161.60i 0.106473 + 0.184417i
\(517\) −2592.00 + 4489.48i −0.220495 + 0.381909i
\(518\) 9080.00 15727.0i 0.770178 1.33399i
\(519\) 2652.00 0.224296
\(520\) 0 0
\(521\) 11247.0 0.945758 0.472879 0.881127i \(-0.343215\pi\)
0.472879 + 0.881127i \(0.343215\pi\)
\(522\) 9062.00 15695.8i 0.759833 1.31607i
\(523\) −1366.00 + 2365.98i −0.114208 + 0.197815i −0.917463 0.397821i \(-0.869767\pi\)
0.803255 + 0.595636i \(0.203100\pi\)
\(524\) −2920.00 5057.59i −0.243437 0.421645i
\(525\) 6560.00 0.545337
\(526\) −8064.00 13967.3i −0.668455 1.15780i
\(527\) −481.000 833.116i −0.0397584 0.0688636i
\(528\) 4096.00 0.337605
\(529\) 3041.50 + 5268.03i 0.249979 + 0.432977i
\(530\) −3162.00 + 5476.74i −0.259148 + 0.448858i
\(531\) −9936.00 + 17209.7i −0.812026 + 1.40647i
\(532\) 4800.00 0.391177
\(533\) −5362.50 + 5572.87i −0.435789 + 0.452885i
\(534\) −2128.00 −0.172449
\(535\) −4437.00 + 7685.11i −0.358557 + 0.621040i
\(536\) 0 0
\(537\) −4264.00 7385.46i −0.342654 0.593494i
\(538\) 16024.0 1.28410
\(539\) 912.000 + 1579.63i 0.0728806 + 0.126233i
\(540\) 6800.00 + 11777.9i 0.541899 + 0.938596i
\(541\) −18375.0 −1.46026 −0.730132 0.683306i \(-0.760542\pi\)
−0.730132 + 0.683306i \(0.760542\pi\)
\(542\) 8592.00 + 14881.8i 0.680919 + 1.17939i
\(543\) 403.000 698.016i 0.0318497 0.0551653i
\(544\) −1664.00 + 2882.13i −0.131146 + 0.227151i
\(545\) −27778.0 −2.18326
\(546\) 5200.00 5404.00i 0.407581 0.423571i
\(547\) −10346.0 −0.808708 −0.404354 0.914603i \(-0.632504\pi\)
−0.404354 + 0.914603i \(0.632504\pi\)
\(548\) −6684.00 + 11577.0i −0.521033 + 0.902456i
\(549\) 1667.50 2888.19i 0.129631 0.224527i
\(550\) 10496.0 + 18179.6i 0.813729 + 1.40942i
\(551\) 5910.00 0.456941
\(552\) 0 0
\(553\) 760.000 + 1316.36i 0.0584421 + 0.101225i
\(554\) −22204.0 −1.70281
\(555\) 3859.00 + 6683.98i 0.295145 + 0.511206i
\(556\) −3648.00 + 6318.52i −0.278255 + 0.481951i
\(557\) −172.500 + 298.779i −0.0131222 + 0.0227283i −0.872512 0.488593i \(-0.837510\pi\)
0.859390 + 0.511321i \(0.170844\pi\)
\(558\) 6808.00 0.516498
\(559\) −2028.00 7025.20i −0.153444 0.531546i
\(560\) −21760.0 −1.64201
\(561\) −416.000 + 720.533i −0.0313075 + 0.0542263i
\(562\) 11114.0 19250.0i 0.834192 1.44486i
\(563\) 4290.00 + 7430.50i 0.321140 + 0.556231i 0.980724 0.195400i \(-0.0626006\pi\)
−0.659583 + 0.751631i \(0.729267\pi\)
\(564\) −2592.00 −0.193516
\(565\) −2779.50 4814.24i −0.206964 0.358472i
\(566\) −6240.00 10808.0i −0.463404 0.802640i
\(567\) 8420.00 0.623645
\(568\) 0 0
\(569\) 9841.00 17045.1i 0.725055 1.25583i −0.233897 0.972261i \(-0.575148\pi\)
0.958951 0.283570i \(-0.0915189\pi\)
\(570\) −2040.00 + 3533.38i −0.149906 + 0.259644i
\(571\) 26624.0 1.95128 0.975639 0.219382i \(-0.0704042\pi\)
0.975639 + 0.219382i \(0.0704042\pi\)
\(572\) 11648.0 + 2882.13i 0.851446 + 0.210678i
\(573\) −2492.00 −0.181684
\(574\) 6600.00 11431.5i 0.479928 0.831260i
\(575\) −6396.00 + 11078.2i −0.463881 + 0.803466i
\(576\) −5888.00 10198.3i −0.425926 0.737725i
\(577\) −14101.0 −1.01739 −0.508694 0.860948i \(-0.669871\pi\)
−0.508694 + 0.860948i \(0.669871\pi\)
\(578\) 9488.00 + 16433.7i 0.682783 + 1.18262i
\(579\) −267.000 462.458i −0.0191643 0.0331936i
\(580\) 26792.0 1.91806
\(581\) −6280.00 10877.3i −0.448431 0.776705i
\(582\) −952.000 + 1648.91i −0.0678036 + 0.117439i
\(583\) 1488.00 2577.29i 0.105706 0.183088i
\(584\) 0 0
\(585\) −5083.00 17608.0i −0.359241 1.24445i
\(586\) 33204.0 2.34069
\(587\) −704.000 + 1219.36i −0.0495012 + 0.0857386i −0.889714 0.456518i \(-0.849096\pi\)
0.840213 + 0.542256i \(0.182430\pi\)
\(588\) −456.000 + 789.815i −0.0319815 + 0.0553936i
\(589\) 1110.00 + 1922.58i 0.0776515 + 0.134496i
\(590\) −58752.0 −4.09963
\(591\) −1278.00 2213.56i −0.0889508 0.154067i
\(592\) −7264.00 12581.6i −0.504305 0.873482i
\(593\) −1241.00 −0.0859389 −0.0429694 0.999076i \(-0.513682\pi\)
−0.0429694 + 0.999076i \(0.513682\pi\)
\(594\) −6400.00 11085.1i −0.442079 0.765704i
\(595\) 2210.00 3827.83i 0.152271 0.263741i
\(596\) 8460.00 14653.1i 0.581435 1.00707i
\(597\) 8476.00 0.581071
\(598\) 4056.00 + 14050.4i 0.277361 + 0.960808i
\(599\) 11078.0 0.755651 0.377825 0.925877i \(-0.376672\pi\)
0.377825 + 0.925877i \(0.376672\pi\)
\(600\) 0 0
\(601\) 6908.50 11965.9i 0.468891 0.812143i −0.530477 0.847700i \(-0.677987\pi\)
0.999368 + 0.0355563i \(0.0113203\pi\)
\(602\) 6240.00 + 10808.0i 0.422464 + 0.731729i
\(603\) −19826.0 −1.33893
\(604\) −2056.00 3561.10i −0.138506 0.239899i
\(605\) 2609.50 + 4519.79i 0.175357 + 0.303728i
\(606\) −6552.00 −0.439203
\(607\) −4135.00 7162.03i −0.276498 0.478909i 0.694014 0.719962i \(-0.255841\pi\)
−0.970512 + 0.241053i \(0.922507\pi\)
\(608\) 3840.00 6651.08i 0.256139 0.443646i
\(609\) −3940.00 + 6824.28i −0.262162 + 0.454078i
\(610\) 9860.00 0.654459
\(611\) 7371.00 + 1823.85i 0.488050 + 0.120761i
\(612\) 2392.00 0.157992
\(613\) −11136.5 + 19289.0i −0.733767 + 1.27092i 0.221496 + 0.975161i \(0.428906\pi\)
−0.955262 + 0.295760i \(0.904427\pi\)
\(614\) −17356.0 + 30061.5i −1.14077 + 1.97587i
\(615\) 2805.00 + 4858.40i 0.183916 + 0.318552i
\(616\) 0 0
\(617\) 9494.50 + 16445.0i 0.619504 + 1.07301i 0.989576 + 0.144010i \(0.0459997\pi\)
−0.370072 + 0.929003i \(0.620667\pi\)
\(618\) −6552.00 11348.4i −0.426473 0.738672i
\(619\) 72.0000 0.00467516 0.00233758 0.999997i \(-0.499256\pi\)
0.00233758 + 0.999997i \(0.499256\pi\)
\(620\) 5032.00 + 8715.68i 0.325952 + 0.564565i
\(621\) 3900.00 6755.00i 0.252015 0.436504i
\(622\) −17316.0 + 29992.2i −1.11625 + 1.93340i
\(623\) −5320.00 −0.342121
\(624\) −1664.00 5764.27i −0.106752 0.369800i
\(625\) −9229.00 −0.590656
\(626\) 10500.0 18186.5i 0.670390 1.16115i
\(627\) 960.000 1662.77i 0.0611463 0.105908i
\(628\) −11604.0 20098.7i −0.737341 1.27711i
\(629\) 2951.00 0.187065
\(630\) 15640.0 + 27089.3i 0.989067 + 1.71312i
\(631\) 11690.0 + 20247.7i 0.737514 + 1.27741i 0.953611 + 0.301040i \(0.0973339\pi\)
−0.216097 + 0.976372i \(0.569333\pi\)
\(632\) 0 0
\(633\) −3070.00 5317.40i −0.192767 0.333882i
\(634\) −12826.0 + 22215.3i −0.803447 + 1.39161i
\(635\) 18343.0 31771.0i 1.14633 1.98550i
\(636\) 1488.00 0.0927721
\(637\) 1852.50 1925.17i 0.115226 0.119746i
\(638\) −25216.0 −1.56475
\(639\) 7521.00 13026.8i 0.465612 0.806464i
\(640\) 0 0
\(641\) −3191.50 5527.84i −0.196656 0.340619i 0.750786 0.660546i \(-0.229675\pi\)
−0.947442 + 0.319927i \(0.896342\pi\)
\(642\) 4176.00 0.256719
\(643\) 8552.00 + 14812.5i 0.524507 + 0.908473i 0.999593 + 0.0285332i \(0.00908365\pi\)
−0.475086 + 0.879939i \(0.657583\pi\)
\(644\) −6240.00 10808.0i −0.381817 0.661327i
\(645\) −5304.00 −0.323790
\(646\) 780.000 + 1351.00i 0.0475057 + 0.0822823i
\(647\) −3497.00 + 6056.98i −0.212490 + 0.368044i −0.952493 0.304560i \(-0.901491\pi\)
0.740003 + 0.672604i \(0.234824\pi\)
\(648\) 0 0
\(649\) 27648.0 1.67223
\(650\) 21320.0 22156.4i 1.28652 1.33699i
\(651\) −2960.00 −0.178205
\(652\) −9440.00 + 16350.6i −0.567023 + 0.982112i
\(653\) 2625.00 4546.63i 0.157311 0.272471i −0.776587 0.630010i \(-0.783051\pi\)
0.933898 + 0.357539i \(0.116384\pi\)
\(654\) 6536.00 + 11320.7i 0.390792 + 0.676871i
\(655\) 12410.0 0.740304
\(656\) −5280.00 9145.23i −0.314252 0.544301i
\(657\) 2472.50 + 4282.50i 0.146821 + 0.254301i
\(658\) −12960.0 −0.767832
\(659\) 2170.00 + 3758.55i 0.128272 + 0.222173i 0.923007 0.384783i \(-0.125724\pi\)
−0.794735 + 0.606956i \(0.792390\pi\)
\(660\) 4352.00 7537.89i 0.256669 0.444563i
\(661\) 2089.50 3619.12i 0.122953 0.212961i −0.797978 0.602687i \(-0.794097\pi\)
0.920931 + 0.389726i \(0.127430\pi\)
\(662\) 13952.0 0.819124
\(663\) 1183.00 + 292.717i 0.0692970 + 0.0171466i
\(664\) 0 0
\(665\) −5100.00 + 8833.46i −0.297398 + 0.515108i
\(666\) −10442.0 + 18086.1i −0.607536 + 1.05228i
\(667\) −7683.00 13307.3i −0.446007 0.772508i
\(668\) 2240.00 0.129743
\(669\) 5378.00 + 9314.97i 0.310800 + 0.538322i
\(670\) −29308.0 50762.9i −1.68995 2.92708i
\(671\) −4640.00 −0.266953
\(672\) 5120.00 + 8868.10i 0.293911 + 0.509069i
\(673\) −11433.5 + 19803.4i −0.654872 + 1.13427i 0.327054 + 0.945006i \(0.393944\pi\)
−0.981926 + 0.189266i \(0.939389\pi\)
\(674\) 3666.00 6349.70i 0.209509 0.362880i
\(675\) −16400.0 −0.935165
\(676\) −676.000 17563.0i −0.0384615 0.999260i
\(677\) 5410.00 0.307124 0.153562 0.988139i \(-0.450925\pi\)
0.153562 + 0.988139i \(0.450925\pi\)
\(678\) −1308.00 + 2265.52i −0.0740906 + 0.128329i
\(679\) −2380.00 + 4122.28i −0.134515 + 0.232988i
\(680\) 0 0
\(681\) −7948.00 −0.447236
\(682\) −4736.00 8202.99i −0.265910 0.460570i
\(683\) 6789.00 + 11758.9i 0.380342 + 0.658772i 0.991111 0.133037i \(-0.0424728\pi\)
−0.610769 + 0.791809i \(0.709139\pi\)
\(684\) −5520.00 −0.308571
\(685\) −14203.5 24601.2i −0.792245 1.37221i
\(686\) 11440.0 19814.7i 0.636707 1.10281i
\(687\) 6298.00 10908.5i 0.349758 0.605798i
\(688\) 9984.00 0.553251
\(689\) −4231.50 1047.02i −0.233973 0.0578933i
\(690\) 10608.0 0.585275
\(691\) −6372.00 + 11036.6i −0.350799 + 0.607602i −0.986390 0.164424i \(-0.947423\pi\)
0.635590 + 0.772026i \(0.280757\pi\)
\(692\) −5304.00 + 9186.80i −0.291370 + 0.504667i
\(693\) −7360.00 12747.9i −0.403439 0.698777i
\(694\) 28920.0 1.58183
\(695\) −7752.00 13426.9i −0.423094 0.732820i
\(696\) 0 0
\(697\) 2145.00 0.116568
\(698\) 10516.0 + 18214.2i 0.570253 + 0.987707i
\(699\) −4030.00 + 6980.16i −0.218067 + 0.377703i
\(700\) −13120.0 + 22724.5i −0.708413 + 1.22701i
\(701\) 16406.0 0.883946 0.441973 0.897028i \(-0.354279\pi\)
0.441973 + 0.897028i \(0.354279\pi\)
\(702\) −13000.0 + 13510.0i −0.698936 + 0.726356i
\(703\) −6810.00 −0.365354
\(704\) −8192.00 + 14189.0i −0.438562 + 0.759612i
\(705\) 2754.00 4770.07i 0.147123 0.254824i
\(706\) −6326.00 10957.0i −0.337227 0.584094i
\(707\) −16380.0 −0.871334
\(708\) 6912.00 + 11971.9i 0.366905 + 0.635498i
\(709\) −354.500 614.012i −0.0187779 0.0325243i 0.856484 0.516174i \(-0.172644\pi\)
−0.875262 + 0.483650i \(0.839311\pi\)
\(710\) 44472.0 2.35071
\(711\) −874.000 1513.81i −0.0461006 0.0798487i
\(712\) 0 0
\(713\) 2886.00 4998.70i 0.151587 0.262556i
\(714\) −2080.00 −0.109022
\(715\) −17680.0 + 18373.6i −0.924748 + 0.961026i
\(716\) 34112.0 1.78048
\(717\) 984.000 1704.34i 0.0512527 0.0887722i
\(718\) 20136.0 34876.6i 1.04661 1.81279i
\(719\) 3822.00 + 6619.90i 0.198243 + 0.343367i 0.947959 0.318393i \(-0.103143\pi\)
−0.749716 + 0.661760i \(0.769810\pi\)
\(720\) 25024.0 1.29526
\(721\) −16380.0 28371.0i −0.846079 1.46545i
\(722\) 11918.0 + 20642.6i 0.614324 + 1.06404i
\(723\) 1886.00 0.0970140
\(724\) 1612.00 + 2792.07i 0.0827479 + 0.143324i
\(725\) −16154.0 + 27979.5i −0.827510 + 1.43329i
\(726\) 1228.00 2126.96i 0.0627760 0.108731i
\(727\) −15808.0 −0.806446 −0.403223 0.915102i \(-0.632110\pi\)
−0.403223 + 0.915102i \(0.632110\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) −7310.00 + 12661.3i −0.370624 + 0.641939i
\(731\) −1014.00 + 1756.30i −0.0513053 + 0.0888633i
\(732\) −1160.00 2009.18i −0.0585722 0.101450i
\(733\) −2583.00 −0.130157 −0.0650786 0.997880i \(-0.520730\pi\)
−0.0650786 + 0.997880i \(0.520730\pi\)
\(734\) −14876.0 25766.0i −0.748070 1.29569i
\(735\) −969.000 1678.36i −0.0486287 0.0842274i
\(736\) −19968.0 −1.00004
\(737\) 13792.0 + 23888.4i 0.689328 + 1.19395i
\(738\) −7590.00 + 13146.3i −0.378580 + 0.655719i
\(739\) −2038.00 + 3529.92i −0.101447 + 0.175711i −0.912281 0.409565i \(-0.865680\pi\)
0.810834 + 0.585276i \(0.199014\pi\)
\(740\) −30872.0 −1.53362
\(741\) −2730.00 675.500i −0.135343 0.0334887i
\(742\) 7440.00 0.368101
\(743\) 17028.0 29493.4i 0.840776 1.45627i −0.0484632 0.998825i \(-0.515432\pi\)
0.889239 0.457442i \(-0.151234\pi\)
\(744\) 0 0
\(745\) 17977.5 + 31137.9i 0.884087 + 1.53128i
\(746\) −38732.0 −1.90091
\(747\) 7222.00 + 12508.9i 0.353734 + 0.612685i
\(748\) −1664.00 2882.13i −0.0813394 0.140884i
\(749\) 10440.0 0.509305
\(750\) −2652.00 4593.40i −0.129116 0.223636i
\(751\) 182.000 315.233i 0.00884324 0.0153169i −0.861570 0.507639i \(-0.830518\pi\)
0.870413 + 0.492322i \(0.163852\pi\)
\(752\) −5184.00 + 8978.95i −0.251384 + 0.435410i
\(753\) −5460.00 −0.264241
\(754\) 10244.0 + 35486.3i 0.494780 + 1.71397i
\(755\) 8738.00 0.421203
\(756\) 8000.00 13856.4i 0.384864 0.666604i
\(757\) 3457.00 5987.70i 0.165980 0.287486i −0.771023 0.636807i \(-0.780255\pi\)
0.937003 + 0.349322i \(0.113588\pi\)
\(758\) 2124.00 + 3678.88i 0.101777 + 0.176283i
\(759\) −4992.00 −0.238733
\(760\) 0 0
\(761\) −6991.00 12108.8i −0.333014 0.576797i 0.650087 0.759859i \(-0.274732\pi\)
−0.983101 + 0.183062i \(0.941399\pi\)
\(762\) −17264.0 −0.820746
\(763\) 16340.0 + 28301.7i 0.775292 + 1.34284i
\(764\) 4984.00 8632.54i 0.236014 0.408788i
\(765\) −2541.50 + 4402.01i −0.120115 + 0.208046i
\(766\) −14128.0 −0.666404
\(767\) −11232.0 38908.8i −0.528767 1.83170i
\(768\) 8192.00 0.384900