Properties

Label 169.4.e.c.147.2
Level $169$
Weight $4$
Character 169.147
Analytic conductor $9.971$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,4,Mod(23,169)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(169, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([5]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.23");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.e (of order \(6\), 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: \(9.97132279097\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 147.2
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 169.147
Dual form 169.4.e.c.23.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(3.46410 + 2.00000i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(4.00000 + 6.92820i) q^{4} -17.0000i q^{5} +(-6.92820 + 4.00000i) q^{6} +(17.3205 - 10.0000i) q^{7} +(11.5000 + 19.9186i) q^{9} +O(q^{10})\) \(q+(3.46410 + 2.00000i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(4.00000 + 6.92820i) q^{4} -17.0000i q^{5} +(-6.92820 + 4.00000i) q^{6} +(17.3205 - 10.0000i) q^{7} +(11.5000 + 19.9186i) q^{9} +(34.0000 - 58.8897i) q^{10} +(27.7128 + 16.0000i) q^{11} -16.0000 q^{12} +80.0000 q^{14} +(29.4449 + 17.0000i) q^{15} +(32.0000 - 55.4256i) q^{16} +(-6.50000 - 11.2583i) q^{17} +92.0000i q^{18} +(-25.9808 + 15.0000i) q^{19} +(117.779 - 68.0000i) q^{20} +40.0000i q^{21} +(64.0000 + 110.851i) q^{22} +(39.0000 - 67.5500i) q^{23} -164.000 q^{25} -100.000 q^{27} +(138.564 + 80.0000i) q^{28} +(-98.5000 + 170.607i) q^{29} +(68.0000 + 117.779i) q^{30} +74.0000i q^{31} +(221.703 - 128.000i) q^{32} +(-55.4256 + 32.0000i) q^{33} -52.0000i q^{34} +(-170.000 - 294.449i) q^{35} +(-92.0000 + 159.349i) q^{36} +(196.588 + 113.500i) q^{37} -120.000 q^{38} +(-142.894 - 82.5000i) q^{41} +(-80.0000 + 138.564i) q^{42} +(-78.0000 - 135.100i) q^{43} +256.000i q^{44} +(338.616 - 195.500i) q^{45} +(270.200 - 156.000i) q^{46} -162.000i q^{47} +(64.0000 + 110.851i) q^{48} +(28.5000 - 49.3634i) q^{49} +(-568.113 - 328.000i) q^{50} +26.0000 q^{51} +93.0000 q^{53} +(-346.410 - 200.000i) q^{54} +(272.000 - 471.118i) q^{55} -60.0000i q^{57} +(-682.428 + 394.000i) q^{58} +(-748.246 + 432.000i) q^{59} +272.000i q^{60} +(-72.5000 - 125.574i) q^{61} +(-148.000 + 256.344i) q^{62} +(398.372 + 230.000i) q^{63} +512.000 q^{64} -256.000 q^{66} +(746.514 + 431.000i) q^{67} +(52.0000 - 90.0666i) q^{68} +(78.0000 + 135.100i) q^{69} -1360.00i q^{70} +(-566.381 + 327.000i) q^{71} +215.000i q^{73} +(454.000 + 786.351i) q^{74} +(164.000 - 284.056i) q^{75} +(-207.846 - 120.000i) q^{76} +640.000 q^{77} -76.0000 q^{79} +(-942.236 - 544.000i) q^{80} +(-210.500 + 364.597i) q^{81} +(-330.000 - 571.577i) q^{82} -628.000i q^{83} +(-277.128 + 160.000i) q^{84} +(-191.392 + 110.500i) q^{85} -624.000i q^{86} +(-197.000 - 341.214i) q^{87} +(230.363 + 133.000i) q^{89} +1564.00 q^{90} +624.000 q^{92} +(-128.172 - 74.0000i) q^{93} +(324.000 - 561.184i) q^{94} +(255.000 + 441.673i) q^{95} +512.000i q^{96} +(-206.114 + 119.000i) q^{97} +(197.454 - 114.000i) q^{98} +736.000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{3} + 16 q^{4} + 46 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{3} + 16 q^{4} + 46 q^{9} + 136 q^{10} - 64 q^{12} + 320 q^{14} + 128 q^{16} - 26 q^{17} + 256 q^{22} + 156 q^{23} - 656 q^{25} - 400 q^{27} - 394 q^{29} + 272 q^{30} - 680 q^{35} - 368 q^{36} - 480 q^{38} - 320 q^{42} - 312 q^{43} + 256 q^{48} + 114 q^{49} + 104 q^{51} + 372 q^{53} + 1088 q^{55} - 290 q^{61} - 592 q^{62} + 2048 q^{64} - 1024 q^{66} + 208 q^{68} + 312 q^{69} + 1816 q^{74} + 656 q^{75} + 2560 q^{77} - 304 q^{79} - 842 q^{81} - 1320 q^{82} - 788 q^{87} + 6256 q^{90} + 2496 q^{92} + 1296 q^{94} + 1020 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/169\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.46410 + 2.00000i 1.22474 + 0.707107i 0.965926 0.258819i \(-0.0833333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(3\) −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
\(5\) 17.0000i 1.52053i −0.649615 0.760263i \(-0.725070\pi\)
0.649615 0.760263i \(-0.274930\pi\)
\(6\) −6.92820 + 4.00000i −0.471405 + 0.272166i
\(7\) 17.3205 10.0000i 0.935220 0.539949i 0.0467610 0.998906i \(-0.485110\pi\)
0.888459 + 0.458957i \(0.151777\pi\)
\(8\) 0 0
\(9\) 11.5000 + 19.9186i 0.425926 + 0.737725i
\(10\) 34.0000 58.8897i 1.07517 1.86226i
\(11\) 27.7128 + 16.0000i 0.759612 + 0.438562i 0.829156 0.559017i \(-0.188821\pi\)
−0.0695447 + 0.997579i \(0.522155\pi\)
\(12\) −16.0000 −0.384900
\(13\) 0 0
\(14\) 80.0000 1.52721
\(15\) 29.4449 + 17.0000i 0.506842 + 0.292625i
\(16\) 32.0000 55.4256i 0.500000 0.866025i
\(17\) −6.50000 11.2583i −0.0927342 0.160620i 0.815927 0.578156i \(-0.196227\pi\)
−0.908661 + 0.417535i \(0.862894\pi\)
\(18\) 92.0000i 1.20470i
\(19\) −25.9808 + 15.0000i −0.313705 + 0.181118i −0.648583 0.761144i \(-0.724638\pi\)
0.334878 + 0.942261i \(0.391305\pi\)
\(20\) 117.779 68.0000i 1.31681 0.760263i
\(21\) 40.0000i 0.415653i
\(22\) 64.0000 + 110.851i 0.620220 + 1.07425i
\(23\) 39.0000 67.5500i 0.353568 0.612398i −0.633304 0.773903i \(-0.718302\pi\)
0.986872 + 0.161506i \(0.0516350\pi\)
\(24\) 0 0
\(25\) −164.000 −1.31200
\(26\) 0 0
\(27\) −100.000 −0.712778
\(28\) 138.564 + 80.0000i 0.935220 + 0.539949i
\(29\) −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
\(31\) 74.0000i 0.428735i 0.976753 + 0.214368i \(0.0687691\pi\)
−0.976753 + 0.214368i \(0.931231\pi\)
\(32\) 221.703 128.000i 1.22474 0.707107i
\(33\) −55.4256 + 32.0000i −0.292375 + 0.168803i
\(34\) 52.0000i 0.262292i
\(35\) −170.000 294.449i −0.821007 1.42203i
\(36\) −92.0000 + 159.349i −0.425926 + 0.737725i
\(37\) 196.588 + 113.500i 0.873482 + 0.504305i 0.868504 0.495683i \(-0.165082\pi\)
0.00497814 + 0.999988i \(0.498415\pi\)
\(38\) −120.000 −0.512278
\(39\) 0 0
\(40\) 0 0
\(41\) −142.894 82.5000i −0.544301 0.314252i 0.202520 0.979278i \(-0.435087\pi\)
−0.746820 + 0.665026i \(0.768420\pi\)
\(42\) −80.0000 + 138.564i −0.293911 + 0.509069i
\(43\) −78.0000 135.100i −0.276625 0.479129i 0.693919 0.720053i \(-0.255883\pi\)
−0.970544 + 0.240924i \(0.922549\pi\)
\(44\) 256.000i 0.877124i
\(45\) 338.616 195.500i 1.12173 0.647632i
\(46\) 270.200 156.000i 0.866061 0.500021i
\(47\) 162.000i 0.502769i −0.967887 0.251384i \(-0.919114\pi\)
0.967887 0.251384i \(-0.0808858\pi\)
\(48\) 64.0000 + 110.851i 0.192450 + 0.333333i
\(49\) 28.5000 49.3634i 0.0830904 0.143917i
\(50\) −568.113 328.000i −1.60687 0.927724i
\(51\) 26.0000 0.0713868
\(52\) 0 0
\(53\) 93.0000 0.241029 0.120514 0.992712i \(-0.461546\pi\)
0.120514 + 0.992712i \(0.461546\pi\)
\(54\) −346.410 200.000i −0.872971 0.504010i
\(55\) 272.000 471.118i 0.666845 1.15501i
\(56\) 0 0
\(57\) 60.0000i 0.139424i
\(58\) −682.428 + 394.000i −1.54495 + 0.891978i
\(59\) −748.246 + 432.000i −1.65107 + 0.953248i −0.674442 + 0.738328i \(0.735616\pi\)
−0.976632 + 0.214919i \(0.931051\pi\)
\(60\) 272.000i 0.585251i
\(61\) −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
\(63\) 398.372 + 230.000i 0.796668 + 0.459957i
\(64\) 512.000 1.00000
\(65\) 0 0
\(66\) −256.000 −0.477446
\(67\) 746.514 + 431.000i 1.36121 + 0.785896i 0.989785 0.142566i \(-0.0455354\pi\)
0.371427 + 0.928462i \(0.378869\pi\)
\(68\) 52.0000 90.0666i 0.0927342 0.160620i
\(69\) 78.0000 + 135.100i 0.136088 + 0.235712i
\(70\) 1360.00i 2.32216i
\(71\) −566.381 + 327.000i −0.946718 + 0.546588i −0.892060 0.451917i \(-0.850740\pi\)
−0.0546585 + 0.998505i \(0.517407\pi\)
\(72\) 0 0
\(73\) 215.000i 0.344710i 0.985035 + 0.172355i \(0.0551377\pi\)
−0.985035 + 0.172355i \(0.944862\pi\)
\(74\) 454.000 + 786.351i 0.713195 + 1.23529i
\(75\) 164.000 284.056i 0.252495 0.437333i
\(76\) −207.846 120.000i −0.313705 0.181118i
\(77\) 640.000 0.947205
\(78\) 0 0
\(79\) −76.0000 −0.108236 −0.0541182 0.998535i \(-0.517235\pi\)
−0.0541182 + 0.998535i \(0.517235\pi\)
\(80\) −942.236 544.000i −1.31681 0.760263i
\(81\) −210.500 + 364.597i −0.288752 + 0.500133i
\(82\) −330.000 571.577i −0.444420 0.769757i
\(83\) 628.000i 0.830505i −0.909706 0.415253i \(-0.863693\pi\)
0.909706 0.415253i \(-0.136307\pi\)
\(84\) −277.128 + 160.000i −0.359966 + 0.207827i
\(85\) −191.392 + 110.500i −0.244227 + 0.141005i
\(86\) 624.000i 0.782415i
\(87\) −197.000 341.214i −0.242766 0.420483i
\(88\) 0 0
\(89\) 230.363 + 133.000i 0.274364 + 0.158404i 0.630869 0.775889i \(-0.282698\pi\)
−0.356505 + 0.934293i \(0.616032\pi\)
\(90\) 1564.00 1.83178
\(91\) 0 0
\(92\) 624.000 0.707136
\(93\) −128.172 74.0000i −0.142912 0.0825101i
\(94\) 324.000 561.184i 0.355511 0.615763i
\(95\) 255.000 + 441.673i 0.275394 + 0.476997i
\(96\) 512.000i 0.544331i
\(97\) −206.114 + 119.000i −0.215750 + 0.124563i −0.603981 0.796999i \(-0.706420\pi\)
0.388231 + 0.921562i \(0.373086\pi\)
\(98\) 197.454 114.000i 0.203529 0.117508i
\(99\) 736.000i 0.747180i
\(100\) −656.000 1136.23i −0.656000 1.13623i
\(101\) −409.500 + 709.275i −0.403433 + 0.698767i −0.994138 0.108121i \(-0.965517\pi\)
0.590704 + 0.806888i \(0.298850\pi\)
\(102\) 90.0666 + 52.0000i 0.0874307 + 0.0504781i
\(103\) −1638.00 −1.56696 −0.783480 0.621417i \(-0.786557\pi\)
−0.783480 + 0.621417i \(0.786557\pi\)
\(104\) 0 0
\(105\) 680.000 0.632011
\(106\) 322.161 + 186.000i 0.295199 + 0.170433i
\(107\) −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
\(109\) 1634.00i 1.43586i 0.696115 + 0.717930i \(0.254910\pi\)
−0.696115 + 0.717930i \(0.745090\pi\)
\(110\) 1884.47 1088.00i 1.63343 0.943061i
\(111\) −393.176 + 227.000i −0.336203 + 0.194107i
\(112\) 1280.00i 1.07990i
\(113\) −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
\(115\) −1148.35 663.000i −0.931167 0.537609i
\(116\) −1576.00 −1.26145
\(117\) 0 0
\(118\) −3456.00 −2.69619
\(119\) −225.167 130.000i −0.173454 0.100144i
\(120\) 0 0
\(121\) −153.500 265.870i −0.115327 0.199752i
\(122\) 580.000i 0.430416i
\(123\) 285.788 165.000i 0.209501 0.120956i
\(124\) −512.687 + 296.000i −0.371296 + 0.214368i
\(125\) 663.000i 0.474404i
\(126\) 920.000 + 1593.49i 0.650477 + 1.12666i
\(127\) −1079.00 + 1868.88i −0.753904 + 1.30580i 0.192014 + 0.981392i \(0.438498\pi\)
−0.945918 + 0.324407i \(0.894835\pi\)
\(128\) 0 0
\(129\) 312.000 0.212946
\(130\) 0 0
\(131\) 730.000 0.486873 0.243437 0.969917i \(-0.421725\pi\)
0.243437 + 0.969917i \(0.421725\pi\)
\(132\) −443.405 256.000i −0.292375 0.168803i
\(133\) −300.000 + 519.615i −0.195589 + 0.338770i
\(134\) 1724.00 + 2986.06i 1.11142 + 1.92504i
\(135\) 1700.00i 1.08380i
\(136\) 0 0
\(137\) 1447.13 835.500i 0.902456 0.521033i 0.0244601 0.999701i \(-0.492213\pi\)
0.877996 + 0.478667i \(0.158880\pi\)
\(138\) 624.000i 0.384916i
\(139\) −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
\(141\) 280.592 + 162.000i 0.167590 + 0.0967579i
\(142\) −2616.00 −1.54598
\(143\) 0 0
\(144\) 1472.00 0.851852
\(145\) 2900.32 + 1674.50i 1.66109 + 0.959032i
\(146\) −430.000 + 744.782i −0.243747 + 0.422182i
\(147\) 57.0000 + 98.7269i 0.0319815 + 0.0553936i
\(148\) 1816.00i 1.00861i
\(149\) 1831.64 1057.50i 1.00707 0.581435i 0.0967407 0.995310i \(-0.469158\pi\)
0.910334 + 0.413875i \(0.135825\pi\)
\(150\) 1136.23 656.000i 0.618483 0.357081i
\(151\) 514.000i 0.277011i 0.990362 + 0.138506i \(0.0442299\pi\)
−0.990362 + 0.138506i \(0.955770\pi\)
\(152\) 0 0
\(153\) 149.500 258.942i 0.0789958 0.136825i
\(154\) 2217.03 + 1280.00i 1.16008 + 0.669775i
\(155\) 1258.00 0.651903
\(156\) 0 0
\(157\) 2901.00 1.47468 0.737341 0.675521i \(-0.236081\pi\)
0.737341 + 0.675521i \(0.236081\pi\)
\(158\) −263.272 152.000i −0.132562 0.0765346i
\(159\) −93.0000 + 161.081i −0.0463860 + 0.0803430i
\(160\) −2176.00 3768.94i −1.07517 1.86226i
\(161\) 1560.00i 0.763635i
\(162\) −1458.39 + 842.000i −0.707294 + 0.408357i
\(163\) 2043.82 1180.00i 0.982112 0.567023i 0.0792052 0.996858i \(-0.474762\pi\)
0.902907 + 0.429835i \(0.141428\pi\)
\(164\) 1320.00i 0.628504i
\(165\) 544.000 + 942.236i 0.256669 + 0.444563i
\(166\) 1256.00 2175.46i 0.587256 1.01716i
\(167\) −242.487 140.000i −0.112361 0.0648714i 0.442767 0.896637i \(-0.353997\pi\)
−0.555127 + 0.831766i \(0.687330\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −884.000 −0.398822
\(171\) −597.558 345.000i −0.267230 0.154285i
\(172\) 624.000 1080.80i 0.276625 0.479129i
\(173\) 663.000 + 1148.35i 0.291370 + 0.504667i 0.974134 0.225972i \(-0.0725557\pi\)
−0.682764 + 0.730639i \(0.739222\pi\)
\(174\) 1576.00i 0.686645i
\(175\) −2840.56 + 1640.00i −1.22701 + 0.708413i
\(176\) 1773.62 1024.00i 0.759612 0.438562i
\(177\) 1728.00i 0.733810i
\(178\) 532.000 + 921.451i 0.224017 + 0.388009i
\(179\) 2132.00 3692.73i 0.890241 1.54194i 0.0506550 0.998716i \(-0.483869\pi\)
0.839586 0.543227i \(-0.182798\pi\)
\(180\) 2708.93 + 1564.00i 1.12173 + 0.647632i
\(181\) 403.000 0.165496 0.0827479 0.996571i \(-0.473630\pi\)
0.0827479 + 0.996571i \(0.473630\pi\)
\(182\) 0 0
\(183\) 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
\(187\) 416.000i 0.162679i
\(188\) 1122.37 648.000i 0.435410 0.251384i
\(189\) −1732.05 + 1000.00i −0.666604 + 0.384864i
\(190\) 2040.00i 0.778932i
\(191\) 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
\(193\) −231.229 133.500i −0.0862394 0.0497904i 0.456260 0.889846i \(-0.349189\pi\)
−0.542500 + 0.840056i \(0.682522\pi\)
\(194\) −952.000 −0.352318
\(195\) 0 0
\(196\) 456.000 0.166181
\(197\) 1106.78 + 639.000i 0.400278 + 0.231101i 0.686604 0.727032i \(-0.259101\pi\)
−0.286326 + 0.958132i \(0.592434\pi\)
\(198\) −1472.00 + 2549.58i −0.528336 + 0.915104i
\(199\) 2119.00 + 3670.22i 0.754834 + 1.30741i 0.945457 + 0.325747i \(0.105616\pi\)
−0.190623 + 0.981663i \(0.561051\pi\)
\(200\) 0 0
\(201\) −1493.03 + 862.000i −0.523931 + 0.302492i
\(202\) −2837.10 + 1638.00i −0.988206 + 0.570541i
\(203\) 3940.00i 1.36224i
\(204\) 104.000 + 180.133i 0.0356934 + 0.0618228i
\(205\) −1402.50 + 2429.20i −0.477829 + 0.827623i
\(206\) −5674.20 3276.00i −1.91913 1.10801i
\(207\) 1794.00 0.602375
\(208\) 0 0
\(209\) −960.000 −0.317725
\(210\) 2355.59 + 1360.00i 0.774053 + 0.446900i
\(211\) −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
\(213\) 1308.00i 0.420764i
\(214\) −1808.26 + 1044.00i −0.577618 + 0.333488i
\(215\) −2296.70 + 1326.00i −0.728528 + 0.420616i
\(216\) 0 0
\(217\) 740.000 + 1281.72i 0.231495 + 0.400962i
\(218\) −3268.00 + 5660.34i −1.01531 + 1.75856i
\(219\) −372.391 215.000i −0.114903 0.0663395i
\(220\) 4352.00 1.33369
\(221\) 0 0
\(222\) −1816.00 −0.549018
\(223\) −4657.48 2689.00i −1.39860 0.807483i −0.404356 0.914602i \(-0.632504\pi\)
−0.994246 + 0.107119i \(0.965838\pi\)
\(224\) 2560.00 4434.05i 0.763604 1.32260i
\(225\) −1886.00 3266.65i −0.558815 0.967896i
\(226\) 1308.00i 0.384986i
\(227\) 3441.58 1987.00i 1.00628 0.580977i 0.0961811 0.995364i \(-0.469337\pi\)
0.910101 + 0.414387i \(0.136004\pi\)
\(228\) 415.692 240.000i 0.120745 0.0697122i
\(229\) 6298.00i 1.81740i −0.417455 0.908698i \(-0.637078\pi\)
0.417455 0.908698i \(-0.362922\pi\)
\(230\) −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 \(-0.691724\pi\)
−0.566554 + 0.824025i \(0.691724\pi\)
\(234\) 0 0
\(235\) −2754.00 −0.764473
\(236\) −5985.97 3456.00i −1.65107 0.953248i
\(237\) 76.0000 131.636i 0.0208301 0.0360788i
\(238\) −520.000 900.666i −0.141624 0.245301i
\(239\) 984.000i 0.266317i 0.991095 + 0.133158i \(0.0425119\pi\)
−0.991095 + 0.133158i \(0.957488\pi\)
\(240\) 1884.47 1088.00i 0.506842 0.292625i
\(241\) 816.662 471.500i 0.218281 0.126025i −0.386873 0.922133i \(-0.626445\pi\)
0.605154 + 0.796108i \(0.293111\pi\)
\(242\) 1228.00i 0.326194i
\(243\) −1771.00 3067.46i −0.467530 0.809785i
\(244\) 580.000 1004.59i 0.152175 0.263575i
\(245\) −839.179 484.500i −0.218829 0.126341i
\(246\) 1320.00 0.342114
\(247\) 0 0
\(248\) 0 0
\(249\) 1087.73 + 628.000i 0.276835 + 0.159831i
\(250\) −1326.00 + 2296.70i −0.335454 + 0.581024i
\(251\) −1365.00 2364.25i −0.343259 0.594542i 0.641777 0.766891i \(-0.278198\pi\)
−0.985036 + 0.172349i \(0.944864\pi\)
\(252\) 3680.00i 0.919914i
\(253\) 2161.60 1248.00i 0.537149 0.310123i
\(254\) −7475.53 + 4316.00i −1.84668 + 1.06618i
\(255\) 442.000i 0.108546i
\(256\) −2048.00 3547.24i −0.500000 0.866025i
\(257\) −942.500 + 1632.46i −0.228761 + 0.396225i −0.957441 0.288629i \(-0.906801\pi\)
0.728680 + 0.684854i \(0.240134\pi\)
\(258\) 1080.80 + 624.000i 0.260805 + 0.150576i
\(259\) 4540.00 1.08920
\(260\) 0 0
\(261\) −4531.00 −1.07457
\(262\) 2528.79 + 1460.00i 0.596296 + 0.344271i
\(263\) −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
\(265\) 1581.00i 0.366491i
\(266\) −2078.46 + 1200.00i −0.479093 + 0.276604i
\(267\) −460.726 + 266.000i −0.105603 + 0.0609698i
\(268\) 6896.00i 1.57179i
\(269\) −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
\(271\) 3720.45 + 2148.00i 0.833952 + 0.481482i 0.855204 0.518292i \(-0.173432\pi\)
−0.0212520 + 0.999774i \(0.506765\pi\)
\(272\) −832.000 −0.185468
\(273\) 0 0
\(274\) 6684.00 1.47371
\(275\) −4544.90 2624.00i −0.996610 0.575393i
\(276\) −624.000 + 1080.80i −0.136088 + 0.235712i
\(277\) −2775.50 4807.31i −0.602035 1.04275i −0.992513 0.122142i \(-0.961024\pi\)
0.390478 0.920612i \(-0.372310\pi\)
\(278\) 3648.00i 0.787023i
\(279\) −1473.98 + 851.000i −0.316289 + 0.182609i
\(280\) 0 0
\(281\) 5557.00i 1.17973i −0.807504 0.589863i \(-0.799182\pi\)
0.807504 0.589863i \(-0.200818\pi\)
\(282\) 648.000 + 1122.37i 0.136836 + 0.237007i
\(283\) 1560.00 2702.00i 0.327676 0.567552i −0.654374 0.756171i \(-0.727068\pi\)
0.982050 + 0.188619i \(0.0604012\pi\)
\(284\) −4531.04 2616.00i −0.946718 0.546588i
\(285\) −1020.00 −0.211999
\(286\) 0 0
\(287\) −3300.00 −0.678721
\(288\) 5099.16 + 2944.00i 1.04330 + 0.602350i
\(289\) 2372.00 4108.42i 0.482801 0.836235i
\(290\) 6698.00 + 11601.3i 1.35628 + 2.34914i
\(291\) 476.000i 0.0958887i
\(292\) −1489.56 + 860.000i −0.298528 + 0.172355i
\(293\) 7188.88 4150.50i 1.43337 0.827559i 0.435998 0.899948i \(-0.356396\pi\)
0.997376 + 0.0723887i \(0.0230622\pi\)
\(294\) 456.000i 0.0904573i
\(295\) 7344.00 + 12720.2i 1.44944 + 2.51050i
\(296\) 0 0
\(297\) −2771.28 1600.00i −0.541435 0.312597i
\(298\) 8460.00 1.64455
\(299\) 0 0
\(300\) 2624.00 0.504989
\(301\) −2702.00 1560.00i −0.517411 0.298727i
\(302\) −1028.00 + 1780.55i −0.195877 + 0.339268i
\(303\) −819.000 1418.55i −0.155282 0.268956i
\(304\) 1920.00i 0.362235i
\(305\) −2134.75 + 1232.50i −0.400772 + 0.231386i
\(306\) 1035.77 598.000i 0.193499 0.111717i
\(307\) 8678.00i 1.61329i 0.591037 + 0.806644i \(0.298719\pi\)
−0.591037 + 0.806644i \(0.701281\pi\)
\(308\) 2560.00 + 4434.05i 0.473602 + 0.820303i
\(309\) 1638.00 2837.10i 0.301562 0.522320i
\(310\) 4357.84 + 2516.00i 0.798415 + 0.460965i
\(311\) −8658.00 −1.57862 −0.789309 0.613996i \(-0.789561\pi\)
−0.789309 + 0.613996i \(0.789561\pi\)
\(312\) 0 0
\(313\) −5250.00 −0.948075 −0.474038 0.880505i \(-0.657204\pi\)
−0.474038 + 0.880505i \(0.657204\pi\)
\(314\) 10049.4 + 5802.00i 1.80611 + 1.04276i
\(315\) 3910.00 6772.32i 0.699376 1.21136i
\(316\) −304.000 526.543i −0.0541182 0.0937354i
\(317\) 6413.00i 1.13625i −0.822944 0.568123i \(-0.807670\pi\)
0.822944 0.568123i \(-0.192330\pi\)
\(318\) −644.323 + 372.000i −0.113622 + 0.0655998i
\(319\) −5459.42 + 3152.00i −0.958210 + 0.553223i
\(320\) 8704.00i 1.52053i
\(321\) −522.000 904.131i −0.0907639 0.157208i
\(322\) 3120.00 5404.00i 0.539971 0.935258i
\(323\) 337.750 + 195.000i 0.0581824 + 0.0335916i
\(324\) −3368.00 −0.577503
\(325\) 0 0
\(326\) 9440.00 1.60378
\(327\) −2830.17 1634.00i −0.478620 0.276332i
\(328\) 0 0
\(329\) −1620.00 2805.92i −0.271470 0.470199i
\(330\) 4352.00i 0.725969i
\(331\) −3020.70 + 1744.00i −0.501609 + 0.289604i −0.729378 0.684111i \(-0.760190\pi\)
0.227769 + 0.973715i \(0.426857\pi\)
\(332\) 4350.91 2512.00i 0.719239 0.415253i
\(333\) 5221.00i 0.859186i
\(334\) −560.000 969.948i −0.0917420 0.158902i
\(335\) 7327.00 12690.7i 1.19498 2.06976i
\(336\) 2217.03 + 1280.00i 0.359966 + 0.207827i
\(337\) 1833.00 0.296290 0.148145 0.988966i \(-0.452670\pi\)
0.148145 + 0.988966i \(0.452670\pi\)
\(338\) 0 0
\(339\) 654.000 0.104780
\(340\) −1531.13 884.000i −0.244227 0.141005i
\(341\) −1184.00 + 2050.75i −0.188027 + 0.325672i
\(342\) −1380.00 2390.23i −0.218193 0.377921i
\(343\) 5720.00i 0.900440i
\(344\) 0 0
\(345\) 2296.70 1326.00i 0.358406 0.206926i
\(346\) 5304.00i 0.824118i
\(347\) −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
\(349\) 4553.56 + 2629.00i 0.698414 + 0.403230i 0.806757 0.590884i \(-0.201221\pi\)
−0.108342 + 0.994114i \(0.534554\pi\)
\(350\) −13120.0 −2.00370
\(351\) 0 0
\(352\) 8192.00 1.24044
\(353\) 2739.24 + 1581.50i 0.413017 + 0.238455i 0.692085 0.721816i \(-0.256692\pi\)
−0.279068 + 0.960271i \(0.590026\pi\)
\(354\) 3456.00 5985.97i 0.518882 0.898730i
\(355\) 5559.00 + 9628.47i 0.831102 + 1.43951i
\(356\) 2128.00i 0.316808i
\(357\) 450.333 260.000i 0.0667624 0.0385453i
\(358\) 14770.9 8528.00i 2.18064 1.25899i
\(359\) 10068.0i 1.48014i −0.672532 0.740068i \(-0.734793\pi\)
0.672532 0.740068i \(-0.265207\pi\)
\(360\) 0 0
\(361\) −2979.50 + 5160.65i −0.434393 + 0.752390i
\(362\) 1396.03 + 806.000i 0.202690 + 0.117023i
\(363\) 614.000 0.0887786
\(364\) 0 0
\(365\) 3655.00 0.524141
\(366\) 1004.59 + 580.000i 0.143472 + 0.0828336i
\(367\) −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
\(369\) 3795.00i 0.535392i
\(370\) 13368.0 7718.00i 1.87829 1.08443i
\(371\) 1610.81 930.000i 0.225415 0.130143i
\(372\) 1184.00i 0.165020i
\(373\) 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
\(375\) −1148.35 663.000i −0.158135 0.0912991i
\(376\) 0 0
\(377\) 0 0
\(378\) −8000.00 −1.08856
\(379\) −919.719 531.000i −0.124651 0.0719674i 0.436378 0.899763i \(-0.356261\pi\)
−0.561029 + 0.827796i \(0.689594\pi\)
\(380\) −2040.00 + 3533.38i −0.275394 + 0.476997i
\(381\) −2158.00 3737.77i −0.290178 0.502602i
\(382\) 4984.00i 0.667549i
\(383\) 3058.80 1766.00i 0.408087 0.235609i −0.281880 0.959450i \(-0.590958\pi\)
0.689968 + 0.723840i \(0.257625\pi\)
\(384\) 0 0
\(385\) 10880.0i 1.44025i
\(386\) −534.000 924.915i −0.0704142 0.121961i
\(387\) 1794.00 3107.30i 0.235644 0.408147i
\(388\) −1648.91 952.000i −0.215750 0.124563i
\(389\) 11063.0 1.44194 0.720972 0.692964i \(-0.243696\pi\)
0.720972 + 0.692964i \(0.243696\pi\)
\(390\) 0 0
\(391\) −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
\(395\) 1292.00i 0.164576i
\(396\) −5099.16 + 2944.00i −0.647077 + 0.373590i
\(397\) −5184.03 + 2993.00i −0.655362 + 0.378374i −0.790508 0.612452i \(-0.790183\pi\)
0.135145 + 0.990826i \(0.456850\pi\)
\(398\) 16952.0i 2.13499i
\(399\) −600.000 1039.23i −0.0752821 0.130392i
\(400\) −5248.00 + 9089.80i −0.656000 + 1.13623i
\(401\) −5139.86 2967.50i −0.640081 0.369551i 0.144565 0.989495i \(-0.453822\pi\)
−0.784646 + 0.619945i \(0.787155\pi\)
\(402\) −6896.00 −0.855575
\(403\) 0 0
\(404\) −6552.00 −0.806867
\(405\) 6198.14 + 3578.50i 0.760465 + 0.439055i
\(406\) −7880.00 + 13648.6i −0.963246 + 1.66839i
\(407\) 3632.00 + 6290.81i 0.442338 + 0.766152i
\(408\) 0 0
\(409\) 13067.5 7544.50i 1.57981 0.912106i 0.584931 0.811083i \(-0.301122\pi\)
0.994884 0.101023i \(-0.0322116\pi\)
\(410\) −9716.81 + 5610.00i −1.17044 + 0.675752i
\(411\) 3342.00i 0.401092i
\(412\) −6552.00 11348.4i −0.783480 1.35703i
\(413\) −8640.00 + 14964.9i −1.02941 + 1.78299i
\(414\) 6214.60 + 3588.00i 0.737756 + 0.425943i
\(415\) −10676.0 −1.26281
\(416\) 0 0
\(417\) 1824.00 0.214201
\(418\) −3325.54 1920.00i −0.389132 0.224666i
\(419\) 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
\(421\) 6535.00i 0.756524i 0.925699 + 0.378262i \(0.123478\pi\)
−0.925699 + 0.378262i \(0.876522\pi\)
\(422\) −10634.8 + 6140.00i −1.22676 + 0.708271i
\(423\) 3226.81 1863.00i 0.370905 0.214142i
\(424\) 0 0
\(425\) 1066.00 + 1846.37i 0.121667 + 0.210734i
\(426\) 2616.00 4531.04i 0.297525 0.515328i
\(427\) −2511.47 1450.00i −0.284634 0.164334i
\(428\) −4176.00 −0.471623
\(429\) 0 0
\(430\) −10608.0 −1.18968
\(431\) 1714.73 + 990.000i 0.191637 + 0.110642i 0.592749 0.805387i \(-0.298043\pi\)
−0.401112 + 0.916029i \(0.631376\pi\)
\(432\) −3200.00 + 5542.56i −0.356389 + 0.617284i
\(433\) −3464.50 6000.69i −0.384511 0.665993i 0.607190 0.794556i \(-0.292297\pi\)
−0.991701 + 0.128564i \(0.958963\pi\)
\(434\) 5920.00i 0.654767i
\(435\) −5800.64 + 3349.00i −0.639355 + 0.369132i
\(436\) −11320.7 + 6536.00i −1.24349 + 0.717930i
\(437\) 2340.00i 0.256150i
\(438\) −860.000 1489.56i −0.0938182 0.162498i
\(439\) −2288.00 + 3962.93i −0.248748 + 0.430844i −0.963179 0.268862i \(-0.913352\pi\)
0.714431 + 0.699706i \(0.246686\pi\)
\(440\) 0 0
\(441\) 1311.00 0.141561
\(442\) 0 0
\(443\) −8812.00 −0.945081 −0.472540 0.881309i \(-0.656663\pi\)
−0.472540 + 0.881309i \(0.656663\pi\)
\(444\) −3145.40 1816.00i −0.336203 0.194107i
\(445\) 2261.00 3916.17i 0.240858 0.417178i
\(446\) −10756.0 18629.9i −1.14195 1.97792i
\(447\) 4230.00i 0.447589i
\(448\) 8868.10 5120.00i 0.935220 0.539949i
\(449\) 1661.04 959.000i 0.174586 0.100797i −0.410160 0.912013i \(-0.634527\pi\)
0.584747 + 0.811216i \(0.301194\pi\)
\(450\) 15088.0i 1.58057i
\(451\) −2640.00 4572.61i −0.275638 0.477419i
\(452\) 1308.00 2265.52i 0.136113 0.235755i
\(453\) −890.274 514.000i −0.0923371 0.0533109i
\(454\) 15896.0 1.64325
\(455\) 0 0
\(456\) 0 0
\(457\) −10185.3 5880.50i −1.04256 0.601922i −0.122002 0.992530i \(-0.538931\pi\)
−0.920557 + 0.390608i \(0.872265\pi\)
\(458\) 12596.0 21816.9i 1.28509 2.22585i
\(459\) 650.000 + 1125.83i 0.0660989 + 0.114487i
\(460\) 10608.0i 1.07522i
\(461\) −780.289 + 450.500i −0.0788323 + 0.0455138i −0.538898 0.842371i \(-0.681159\pi\)
0.460066 + 0.887885i \(0.347826\pi\)
\(462\) −4434.05 + 2560.00i −0.446517 + 0.257796i
\(463\) 1372.00i 0.137715i 0.997626 + 0.0688577i \(0.0219354\pi\)
−0.997626 + 0.0688577i \(0.978065\pi\)
\(464\) 6304.00 + 10918.8i 0.630724 + 1.09245i
\(465\) −1258.00 + 2178.92i −0.125459 + 0.217301i
\(466\) −13960.3 8060.00i −1.38777 0.801228i
\(467\) 6396.00 0.633772 0.316886 0.948464i \(-0.397363\pi\)
0.316886 + 0.948464i \(0.397363\pi\)
\(468\) 0 0
\(469\) 17240.0 1.69738
\(470\) −9540.14 5508.00i −0.936284 0.540564i
\(471\) −2901.00 + 5024.68i −0.283803 + 0.491561i
\(472\) 0 0
\(473\) 4992.00i 0.485269i
\(474\) 526.543 304.000i 0.0510231 0.0294582i
\(475\) 4260.84 2460.00i 0.411581 0.237626i
\(476\) 2080.00i 0.200287i
\(477\) 1069.50 + 1852.43i 0.102660 + 0.177813i
\(478\) −1968.00 + 3408.68i −0.188314 + 0.326170i
\(479\) −2831.90 1635.00i −0.270131 0.155960i 0.358816 0.933408i \(-0.383181\pi\)
−0.628947 + 0.777448i \(0.716514\pi\)
\(480\) 8704.00 0.827670
\(481\) 0 0
\(482\) 3772.00 0.356452
\(483\) 2702.00 + 1560.00i 0.254545 + 0.146962i
\(484\) 1228.00 2126.96i 0.115327 0.199752i
\(485\) 2023.00 + 3503.94i 0.189401 + 0.328053i
\(486\) 14168.0i 1.32237i
\(487\) −17251.2 + 9960.00i −1.60519 + 0.926757i −0.614765 + 0.788711i \(0.710749\pi\)
−0.990426 + 0.138046i \(0.955918\pi\)
\(488\) 0 0
\(489\) 4720.00i 0.436494i
\(490\) −1938.00 3356.71i −0.178673 0.309471i
\(491\) 3276.00 5674.20i 0.301108 0.521534i −0.675280 0.737562i \(-0.735977\pi\)
0.976387 + 0.216028i \(0.0693103\pi\)
\(492\) 2286.31 + 1320.00i 0.209501 + 0.120956i
\(493\) 2561.00 0.233959
\(494\) 0 0
\(495\) 12512.0 1.13611
\(496\) 4101.50 + 2368.00i 0.371296 + 0.214368i
\(497\) −6540.00 + 11327.6i −0.590260 + 1.02236i
\(498\) 2512.00 + 4350.91i 0.226035 + 0.391504i
\(499\) 1746.00i 0.156637i −0.996928 0.0783183i \(-0.975045\pi\)
0.996928 0.0783183i \(-0.0249551\pi\)
\(500\) −4593.40 + 2652.00i −0.410846 + 0.237202i
\(501\) 484.974 280.000i 0.0432476 0.0249690i
\(502\) 10920.0i 0.970883i
\(503\) −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
\(505\) 12057.7 + 6961.50i 1.06249 + 0.613431i
\(506\) 9984.00 0.877160
\(507\) 0 0
\(508\) −17264.0 −1.50781
\(509\) 6994.89 + 4038.50i 0.609122 + 0.351677i 0.772622 0.634867i \(-0.218945\pi\)
−0.163500 + 0.986543i \(0.552278\pi\)
\(510\) 884.000 1531.13i 0.0767533 0.132941i
\(511\) 2150.00 + 3723.91i 0.186126 + 0.322380i
\(512\) 16384.0i 1.41421i
\(513\) 2598.08 1500.00i 0.223602 0.129097i
\(514\) −6529.83 + 3770.00i −0.560347 + 0.323517i
\(515\) 27846.0i 2.38260i
\(516\) 1248.00 + 2161.60i 0.106473 + 0.184417i
\(517\) 2592.00 4489.48i 0.220495 0.381909i
\(518\) 15727.0 + 9080.00i 1.33399 + 0.770178i
\(519\) −2652.00 −0.224296
\(520\) 0 0
\(521\) 11247.0 0.945758 0.472879 0.881127i \(-0.343215\pi\)
0.472879 + 0.881127i \(0.343215\pi\)
\(522\) −15695.8 9062.00i −1.31607 0.759833i
\(523\) −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
\(525\) 6560.00i 0.545337i
\(526\) −13967.3 + 8064.00i −1.15780 + 0.668455i
\(527\) 833.116 481.000i 0.0688636 0.0397584i
\(528\) 4096.00i 0.337605i
\(529\) 3041.50 + 5268.03i 0.249979 + 0.432977i
\(530\) 3162.00 5476.74i 0.259148 0.448858i
\(531\) −17209.7 9936.00i −1.40647 0.812026i
\(532\) −4800.00 −0.391177
\(533\) 0 0
\(534\) −2128.00 −0.172449
\(535\) 7685.11 + 4437.00i 0.621040 + 0.358557i
\(536\) 0 0
\(537\) 4264.00 + 7385.46i 0.342654 + 0.593494i
\(538\) 16024.0i 1.28410i
\(539\) 1579.63 912.000i 0.126233 0.0728806i
\(540\) −11777.9 + 6800.00i −0.938596 + 0.541899i
\(541\) 18375.0i 1.46026i −0.683306 0.730132i \(-0.739458\pi\)
0.683306 0.730132i \(-0.260542\pi\)
\(542\) 8592.00 + 14881.8i 0.680919 + 1.17939i
\(543\) −403.000 + 698.016i −0.0318497 + 0.0551653i
\(544\) −2882.13 1664.00i −0.227151 0.131146i
\(545\) 27778.0 2.18326
\(546\) 0 0
\(547\) −10346.0 −0.808708 −0.404354 0.914603i \(-0.632504\pi\)
−0.404354 + 0.914603i \(0.632504\pi\)
\(548\) 11577.0 + 6684.00i 0.902456 + 0.521033i
\(549\) 1667.50 2888.19i 0.129631 0.224527i
\(550\) −10496.0 18179.6i −0.813729 1.40942i
\(551\) 5910.00i 0.456941i
\(552\) 0 0
\(553\) −1316.36 + 760.000i −0.101225 + 0.0584421i
\(554\) 22204.0i 1.70281i
\(555\) 3859.00 + 6683.98i 0.295145 + 0.511206i
\(556\) 3648.00 6318.52i 0.278255 0.481951i
\(557\) −298.779 172.500i −0.0227283 0.0131222i 0.488593 0.872512i \(-0.337510\pi\)
−0.511321 + 0.859390i \(0.670844\pi\)
\(558\) −6808.00 −0.516498
\(559\) 0 0
\(560\) −21760.0 −1.64201
\(561\) 720.533 + 416.000i 0.0542263 + 0.0313075i
\(562\) 11114.0 19250.0i 0.834192 1.44486i
\(563\) −4290.00 7430.50i −0.321140 0.556231i 0.659583 0.751631i \(-0.270733\pi\)
−0.980724 + 0.195400i \(0.937399\pi\)
\(564\) 2592.00i 0.193516i
\(565\) −4814.24 + 2779.50i −0.358472 + 0.206964i
\(566\) 10808.0 6240.00i 0.802640 0.463404i
\(567\) 8420.00i 0.623645i
\(568\) 0 0
\(569\) −9841.00 + 17045.1i −0.725055 + 1.25583i 0.233897 + 0.972261i \(0.424852\pi\)
−0.958951 + 0.283570i \(0.908481\pi\)
\(570\) −3533.38 2040.00i −0.259644 0.149906i
\(571\) −26624.0 −1.95128 −0.975639 0.219382i \(-0.929596\pi\)
−0.975639 + 0.219382i \(0.929596\pi\)
\(572\) 0 0
\(573\) −2492.00 −0.181684
\(574\) −11431.5 6600.00i −0.831260 0.479928i
\(575\) −6396.00 + 11078.2i −0.463881 + 0.803466i
\(576\) 5888.00 + 10198.3i 0.425926 + 0.737725i
\(577\) 14101.0i 1.01739i 0.860948 + 0.508694i \(0.169871\pi\)
−0.860948 + 0.508694i \(0.830129\pi\)
\(578\) 16433.7 9488.00i 1.18262 0.682783i
\(579\) 462.458 267.000i 0.0331936 0.0191643i
\(580\) 26792.0i 1.91806i
\(581\) −6280.00 10877.3i −0.448431 0.776705i
\(582\) 952.000 1648.91i 0.0678036 0.117439i
\(583\) 2577.29 + 1488.00i 0.183088 + 0.105706i
\(584\) 0 0
\(585\) 0 0
\(586\) 33204.0 2.34069
\(587\) 1219.36 + 704.000i 0.0857386 + 0.0495012i 0.542256 0.840213i \(-0.317570\pi\)
−0.456518 + 0.889714i \(0.650904\pi\)
\(588\) −456.000 + 789.815i −0.0319815 + 0.0553936i
\(589\) −1110.00 1922.58i −0.0776515 0.134496i
\(590\) 58752.0i 4.09963i
\(591\) −2213.56 + 1278.00i −0.154067 + 0.0889508i
\(592\) 12581.6 7264.00i 0.873482 0.504305i
\(593\) 1241.00i 0.0859389i −0.999076 0.0429694i \(-0.986318\pi\)
0.999076 0.0429694i \(-0.0136818\pi\)
\(594\) −6400.00 11085.1i −0.442079 0.765704i
\(595\) −2210.00 + 3827.83i −0.152271 + 0.263741i
\(596\) 14653.1 + 8460.00i 1.00707 + 0.581435i
\(597\) −8476.00 −0.581071
\(598\) 0 0
\(599\) 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
\(603\) 19826.0i 1.33893i
\(604\) −3561.10 + 2056.00i −0.239899 + 0.138506i
\(605\) −4519.79 + 2609.50i −0.303728 + 0.175357i
\(606\) 6552.00i 0.439203i
\(607\) −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
\(609\) −6824.28 3940.00i −0.454078 0.262162i
\(610\) −9860.00 −0.654459
\(611\) 0 0
\(612\) 2392.00 0.157992
\(613\) 19289.0 + 11136.5i 1.27092 + 0.733767i 0.975161 0.221496i \(-0.0710938\pi\)
0.295760 + 0.955262i \(0.404427\pi\)
\(614\) −17356.0 + 30061.5i −1.14077 + 1.97587i
\(615\) −2805.00 4858.40i −0.183916 0.318552i
\(616\) 0 0
\(617\) 16445.0 9494.50i 1.07301 0.619504i 0.144010 0.989576i \(-0.454000\pi\)
0.929003 + 0.370072i \(0.120667\pi\)
\(618\) 11348.4 6552.00i 0.738672 0.426473i
\(619\) 72.0000i 0.00467516i 0.999997 + 0.00233758i \(0.000744076\pi\)
−0.999997 + 0.00233758i \(0.999256\pi\)
\(620\) 5032.00 + 8715.68i 0.325952 + 0.564565i
\(621\) −3900.00 + 6755.00i −0.252015 + 0.436504i
\(622\) −29992.2 17316.0i −1.93340 1.11625i
\(623\) 5320.00 0.342121
\(624\) 0 0
\(625\) −9229.00 −0.590656
\(626\) −18186.5 10500.0i −1.16115 0.670390i
\(627\) 960.000 1662.77i 0.0611463 0.105908i
\(628\) 11604.0 + 20098.7i 0.737341 + 1.27711i
\(629\) 2951.00i 0.187065i
\(630\) 27089.3 15640.0i 1.71312 0.989067i
\(631\) −20247.7 + 11690.0i −1.27741 + 0.737514i −0.976372 0.216097i \(-0.930667\pi\)
−0.301040 + 0.953611i \(0.597334\pi\)
\(632\) 0 0
\(633\) −3070.00 5317.40i −0.192767 0.333882i
\(634\) 12826.0 22215.3i 0.803447 1.39161i
\(635\) 31771.0 + 18343.0i 1.98550 + 1.14633i
\(636\) −1488.00 −0.0927721
\(637\) 0 0
\(638\) −25216.0 −1.56475
\(639\) −13026.8 7521.00i −0.806464 0.465612i
\(640\) 0 0
\(641\) 3191.50 + 5527.84i 0.196656 + 0.340619i 0.947442 0.319927i \(-0.103658\pi\)
−0.750786 + 0.660546i \(0.770325\pi\)
\(642\) 4176.00i 0.256719i
\(643\) 14812.5 8552.00i 0.908473 0.524507i 0.0285332 0.999593i \(-0.490916\pi\)
0.879939 + 0.475086i \(0.157583\pi\)
\(644\) 10808.0 6240.00i 0.661327 0.381817i
\(645\) 5304.00i 0.323790i
\(646\) 780.000 + 1351.00i 0.0475057 + 0.0822823i
\(647\) 3497.00 6056.98i 0.212490 0.368044i −0.740003 0.672604i \(-0.765176\pi\)
0.952493 + 0.304560i \(0.0985093\pi\)
\(648\) 0 0
\(649\) −27648.0 −1.67223
\(650\) 0 0
\(651\) −2960.00 −0.178205
\(652\) 16350.6 + 9440.00i 0.982112 + 0.567023i
\(653\) 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
\(655\) 12410.0i 0.740304i
\(656\) −9145.23 + 5280.00i −0.544301 + 0.314252i
\(657\) −4282.50 + 2472.50i −0.254301 + 0.146821i
\(658\) 12960.0i 0.767832i
\(659\) 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
\(661\) 3619.12 + 2089.50i 0.212961 + 0.122953i 0.602687 0.797978i \(-0.294097\pi\)
−0.389726 + 0.920931i \(0.627430\pi\)
\(662\) −13952.0 −0.819124
\(663\) 0 0
\(664\) 0 0
\(665\) 8833.46 + 5100.00i 0.515108 + 0.297398i
\(666\) −10442.0 + 18086.1i −0.607536 + 1.05228i
\(667\) 7683.00 + 13307.3i 0.446007 + 0.772508i
\(668\) 2240.00i 0.129743i
\(669\) 9314.97 5378.00i 0.538322 0.310800i
\(670\) 50762.9 29308.0i 2.92708 1.68995i
\(671\) 4640.00i 0.266953i
\(672\) 5120.00 + 8868.10i 0.293911 + 0.509069i
\(673\) 11433.5 19803.4i 0.654872 1.13427i −0.327054 0.945006i \(-0.606056\pi\)
0.981926 0.189266i \(-0.0606109\pi\)
\(674\) 6349.70 + 3666.00i 0.362880 + 0.209509i
\(675\) 16400.0 0.935165
\(676\) 0 0
\(677\) 5410.00 0.307124 0.153562 0.988139i \(-0.450925\pi\)
0.153562 + 0.988139i \(0.450925\pi\)
\(678\) 2265.52 + 1308.00i 0.128329 + 0.0740906i
\(679\) −2380.00 + 4122.28i −0.134515 + 0.232988i
\(680\) 0 0
\(681\) 7948.00i 0.447236i
\(682\) −8202.99 + 4736.00i −0.460570 + 0.265910i
\(683\) −11758.9 + 6789.00i −0.658772 + 0.380342i −0.791809 0.610769i \(-0.790861\pi\)
0.133037 + 0.991111i \(0.457527\pi\)
\(684\) 5520.00i 0.308571i
\(685\) −14203.5 24601.2i −0.792245 1.37221i
\(686\) −11440.0 + 19814.7i −0.636707 + 1.10281i
\(687\) 10908.5 + 6298.00i 0.605798 + 0.349758i
\(688\) −9984.00 −0.553251
\(689\) 0 0
\(690\) 10608.0 0.585275
\(691\) 11036.6 + 6372.00i 0.607602 + 0.350799i 0.772026 0.635590i \(-0.219243\pi\)
−0.164424 + 0.986390i \(0.552577\pi\)
\(692\) −5304.00 + 9186.80i −0.291370 + 0.504667i
\(693\) 7360.00 + 12747.9i 0.403439 + 0.698777i
\(694\) 28920.0i 1.58183i
\(695\) −13426.9 + 7752.00i −0.732820 + 0.423094i
\(696\) 0 0
\(697\) 2145.00i 0.116568i
\(698\) 10516.0 + 18214.2i 0.570253 + 0.987707i
\(699\) 4030.00 6980.16i 0.218067 0.377703i
\(700\) −22724.5 13120.0i −1.22701 0.708413i
\(701\) −16406.0 −0.883946 −0.441973 0.897028i \(-0.645721\pi\)
−0.441973 + 0.897028i \(0.645721\pi\)
\(702\) 0 0
\(703\) −6810.00 −0.365354
\(704\) 14189.0 + 8192.00i 0.759612 + 0.438562i
\(705\) 2754.00 4770.07i 0.147123 0.254824i
\(706\) 6326.00 + 10957.0i 0.337227 + 0.584094i
\(707\) 16380.0i 0.871334i
\(708\) 11971.9 6912.00i 0.635498 0.366905i
\(709\) 614.012 354.500i 0.0325243 0.0187779i −0.483650 0.875262i \(-0.660689\pi\)
0.516174 + 0.856484i \(0.327356\pi\)
\(710\) 44472.0i 2.35071i
\(711\) −874.000 1513.81i −0.0461006 0.0798487i
\(712\) 0 0
\(713\) 4998.70 + 2886.00i 0.262556 + 0.151587i
\(714\) 2080.00 0.109022
\(715\) 0 0
\(716\) 34112.0 1.78048
\(717\) −1704.34 984.000i −0.0887722 0.0512527i
\(718\) 20136.0 34876.6i 1.04661 1.81279i
\(719\) −3822.00 6619.90i −0.198243 0.343367i 0.749716 0.661760i \(-0.230190\pi\)
−0.947959 + 0.318393i \(0.896857\pi\)
\(720\) 25024.0i 1.29526i
\(721\) −28371.0 + 16380.0i −1.46545 + 0.846079i
\(722\) −20642.6 + 11918.0i −1.06404 + 0.614324i
\(723\) 1886.00i 0.0970140i
\(724\) 1612.00 + 2792.07i 0.0827479 + 0.143324i
\(725\) 16154.0 27979.5i 0.827510 1.43329i
\(726\) 2126.96 + 1228.00i 0.108731 + 0.0627760i
\(727\) 15808.0 0.806446 0.403223 0.915102i \(-0.367890\pi\)
0.403223 + 0.915102i \(0.367890\pi\)
\(728\) 0 0
\(729\) −4283.00 −0.217599
\(730\) 12661.3 + 7310.00i 0.641939 + 0.370624i
\(731\) −1014.00 + 1756.30i −0.0513053 + 0.0888633i
\(732\) 1160.00 + 2009.18i 0.0585722 + 0.101450i
\(733\) 2583.00i 0.130157i 0.997880 + 0.0650786i \(0.0207298\pi\)
−0.997880 + 0.0650786i \(0.979270\pi\)
\(734\) −25766.0 + 14876.0i −1.29569 + 0.748070i
\(735\) 1678.36 969.000i 0.0842274 0.0486287i
\(736\) 19968.0i 1.00004i
\(737\) 13792.0 + 23888.4i 0.689328 + 1.19395i
\(738\) 7590.00 13146.3i 0.378580 0.655719i
\(739\) −3529.92 2038.00i −0.175711 0.101447i 0.409565 0.912281i \(-0.365680\pi\)
−0.585276 + 0.810834i \(0.699014\pi\)
\(740\) 30872.0 1.53362
\(741\) 0 0
\(742\) 7440.00 0.368101
\(743\) −29493.4 17028.0i −1.45627 0.840776i −0.457442 0.889239i \(-0.651234\pi\)
−0.998825 + 0.0484632i \(0.984568\pi\)
\(744\) 0 0
\(745\) −17977.5 31137.9i −0.884087 1.53128i
\(746\) 38732.0i 1.90091i
\(747\) 12508.9 7222.00i 0.612685 0.353734i
\(748\) 2882.13 1664.00i 0.140884 0.0813394i
\(749\) 10440.0i 0.509305i
\(750\) −2652.00 4593.40i −0.129116 0.223636i
\(751\) −182.000 + 315.233i −0.00884324 + 0.0153169i −0.870413 0.492322i \(-0.836148\pi\)
0.861570 + 0.507639i \(0.169482\pi\)
\(752\) −8978.95 5184.00i −0.435410 0.251384i
\(753\) 5460.00 0.264241
\(754\) 0 0
\(755\) 8738.00 0.421203
\(756\) −13856.4 8000.00i −0.666604 0.384864i
\(757\) 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
\(759\) 4992.00i 0.238733i
\(760\) 0 0
\(761\) 12108.8 6991.00i 0.576797 0.333014i −0.183062 0.983101i \(-0.558601\pi\)
0.759859 + 0.650087i \(0.225268\pi\)
\(762\) 17264.0i 0.820746i
\(763\) 16340.0 + 28301.7i 0.775292 + 1.34284i
\(764\) −4984.00 + 8632.54i −0.236014 + 0.408788i
\(765\) −4402.01 2541.50i −0.208046 0.120115i
\(766\) 14128.0 0.666404
\(767\) 0 0
\(768\) 8192.00 0.384900
\(769\) −15645.6 9033.00i −0.733674 0.423587i 0.0860907 0.996287i \(-0.472563\pi\)
−0.819765 + 0.572700i \(0.805896\pi\)
\(770\) 21760.0 37689.4i 1.01841 1.76394i
\(771\) −1885.00 3264.92i −0.0880501 0.152507i
\(772\) 2136.00i 0.0995807i
\(773\) −12500.2 + 7217.00i −0.581632 + 0.335805i −0.761782 0.647834i \(-0.775675\pi\)
0.180150 + 0.983639i \(0.442342\pi\)
\(774\) 12429.2 7176.00i 0.577207 0.333251i
\(775\) 12136.0i 0.562501i
\(776\) 0 0
\(777\) −4540.00 + 7863.51i −0.209616 + 0.363065i
\(778\) 38323.4 + 22126.0i 1.76601 + 1.01961i
\(779\) 4950.00 0.227666
\(780\) 0 0
\(781\) −20928.0 −0.958851
\(782\) −3512.60 2028.00i −0.160627 0.0927380i
\(783\) 9850.00 17060.7i 0.449566 0.778671i
\(784\) −1824.00 3159.26i −0.0830904 0.143917i
\(785\) 49317.0i 2.24229i
\(786\) −5057.59 + 2920.00i −0.229514 + 0.132510i
\(787\) −13335.1 + 7699.00i −0.603994 + 0.348716i −0.770611 0.637305i \(-0.780049\pi\)
0.166617 + 0.986022i \(0.446716\pi\)
\(788\) 10224.0i 0.462202i
\(789\) −4032.00 6983.63i −0.181930 0.315113i
\(790\) −2584.00 + 4475.62i −0.116373 + 0.201564i
\(791\) −5663.81 3270.00i −0.254591 0.146988i
\(792\) 0 0
\(793\) 0 0
\(794\) −23944.0 −1.07020
\(795\) 2738.37 + 1581.00i 0.122164 + 0.0705312i
\(796\) −16952.0 + 29361.7i −0.754834 + 1.30741i
\(797\) −18421.0 31906.1i −0.818702 1.41803i −0.906639 0.421907i \(-0.861361\pi\)
0.0879373 0.996126i \(-0.471972\pi\)
\(798\) 4800.00i 0.212930i
\(799\) −1823.85 + 1053.00i −0.0807549 + 0.0466239i
\(800\) −36359.2 + 20992.0i −1.60687 + 0.927724i
\(801\) 6118.00i 0.269874i
\(802\) −11870.0 20559.4i −0.522624 0.905211i
\(803\) −3440.00 + 5958.25i −0.151177 + 0.261846i
\(804\) −11944.2 6896.00i −0.523931 0.302492i
\(805\) −26520.0 −1.16113
\(806\) 0 0
\(807\) 8012.00 0.349487
\(808\) 0 0
\(809\) −20755.5 + 35949.6i −0.902008 + 1.56232i −0.0771242 + 0.997021i \(0.524574\pi\)
−0.824884 + 0.565302i \(0.808760\pi\)
\(810\) 14314.0 + 24792.6i 0.620917 + 1.07546i
\(811\) 23066.0i 0.998714i −0.866396 0.499357i \(-0.833570\pi\)
0.866396 0.499357i \(-0.166430\pi\)
\(812\) −27297.1 + 15760.0i −1.17973 + 0.681118i
\(813\) −7440.89 + 4296.00i −0.320988 + 0.185323i
\(814\) 29056.0i 1.25112i
\(815\) −20060.0 34744.9i −0.862173 1.49333i
\(816\) 832.000 1441.07i 0.0356934 0.0618228i
\(817\) 4053.00 + 2340.00i 0.173558 + 0.100203i
\(818\) 60356.0 2.57983
\(819\) 0 0
\(820\) −22440.0 −0.955657
\(821\) 24974.4 + 14419.0i 1.06165 + 0.612943i 0.925888 0.377798i \(-0.123319\pi\)
0.135761 + 0.990742i \(0.456652\pi\)
\(822\) −6684.00 + 11577.0i −0.283615 + 0.491235i
\(823\) 13728.0 + 23777.6i 0.581443 + 1.00709i 0.995309 + 0.0967514i \(0.0308452\pi\)
−0.413865 + 0.910338i \(0.635821\pi\)
\(824\) 0 0
\(825\) 9089.80 5248.00i 0.383596 0.221469i
\(826\) −59859.7 + 34560.0i −2.52153 + 1.45581i
\(827\) 33572.0i 1.41162i −0.708399 0.705812i \(-0.750582\pi\)
0.708399 0.705812i \(-0.249418\pi\)
\(828\) 7176.00 + 12429.2i 0.301187 + 0.521672i
\(829\) −22899.5 + 39663.1i −0.959388 + 1.66171i −0.235396 + 0.971899i \(0.575639\pi\)
−0.723991 + 0.689809i \(0.757694\pi\)
\(830\) −36982.7 21352.0i −1.54661 0.892938i
\(831\) 11102.0 0.463447
\(832\) 0 0
\(833\) −741.000 −0.0308213
\(834\) 6318.52 + 3648.00i 0.262341 + 0.151463i
\(835\) −2380.00 + 4122.28i −0.0986387 + 0.170847i
\(836\) −3840.00 6651.08i −0.158863 0.275158i
\(837\) 7400.00i 0.305593i
\(838\) 37460.8 21628.0i 1.54423 0.891560i
\(839\) 27960.5 16143.0i 1.15054 0.664265i 0.201522 0.979484i \(-0.435411\pi\)
0.949019 + 0.315219i \(0.102078\pi\)
\(840\) 0 0
\(841\) −7210.00 12488.1i −0.295625 0.512038i
\(842\) −13070.0 + 22637.9i −0.534943 + 0.926548i
\(843\) 9625.01 + 5557.00i 0.393242 + 0.227038i
\(844\) −24560.0 −1.00165
\(845\) 0 0
\(846\) 14904.0 0.605686
\(847\) −5317.40 3070.00i −0.215712 0.124541i
\(848\) 2976.00 5154.58i 0.120514 0.208737i
\(849\) 3120.00 + 5404.00i 0.126123 + 0.218451i
\(850\) 8528.00i 0.344127i
\(851\) 15333.8 8853.00i 0.617670 0.356612i
\(852\) 9062.09 5232.00i 0.364392 0.210382i
\(853\) 20937.0i 0.840409i 0.907429 + 0.420205i \(0.138042\pi\)
−0.907429 + 0.420205i \(0.861958\pi\)
\(854\) −5800.00 10045.9i −0.232403 0.402533i
\(855\) −5865.00 + 10158.5i −0.234595 + 0.406331i
\(856\) 0 0
\(857\) 7189.00 0.286548 0.143274 0.989683i \(-0.454237\pi\)
0.143274 + 0.989683i \(0.454237\pi\)
\(858\) 0 0
\(859\) −32498.0 −1.29082 −0.645412 0.763835i \(-0.723314\pi\)
−0.645412 + 0.763835i \(0.723314\pi\)
\(860\) −18373.6 10608.0i −0.728528 0.420616i
\(861\) 3300.00 5715.77i 0.130620 0.226240i
\(862\) 3960.00 + 6858.92i 0.156471 + 0.271016i
\(863\) 8428.00i 0.332436i −0.986089 0.166218i \(-0.946844\pi\)
0.986089 0.166218i \(-0.0531556\pi\)
\(864\) −22170.3 + 12800.0i −0.872971 + 0.504010i
\(865\) 19521.9 11271.0i 0.767360 0.443035i
\(866\) 27716.0i 1.08756i
\(867\) 4744.00 + 8216.85i 0.185830 + 0.321867i
\(868\) −5920.00 + 10253.7i −0.231495 + 0.400962i
\(869\) −2106.17 1216.00i −0.0822176 0.0474683i
\(870\) −26792.0 −1.04406
\(871\) 0 0
\(872\) 0 0
\(873\) −4740.62 2737.00i −0.183787 0.106109i
\(874\) −4680.00 + 8106.00i −0.181125 + 0.313718i
\(875\) 6630.00 + 11483.5i 0.256154 + 0.443672i
\(876\) 3440.00i 0.132679i
\(877\) 5929.68 3423.50i 0.228313 0.131817i −0.381480 0.924377i \(-0.624586\pi\)
0.609794 + 0.792560i \(0.291252\pi\)
\(878\) −15851.7 + 9152.00i −0.609305 + 0.351783i
\(879\) 16602.0i 0.637055i
\(880\) −17408.0 30151.5i −0.666845 1.15501i
\(881\) 14865.5 25747.8i 0.568481 0.984637i −0.428236 0.903667i \(-0.640865\pi\)
0.996717 0.0809703i \(-0.0258019\pi\)
\(882\) 4541.44 + 2622.00i 0.173377 + 0.100099i
\(883\) 23738.0 0.904697 0.452348 0.891841i \(-0.350586\pi\)
0.452348 + 0.891841i \(0.350586\pi\)
\(884\) 0 0
\(885\) −29376.0 −1.11578
\(886\) −30525.7 17624.0i −1.15748 0.668273i
\(887\) −13794.0 + 23891.9i −0.522161 + 0.904410i 0.477506 + 0.878628i \(0.341541\pi\)
−0.999668 + 0.0257817i \(0.991793\pi\)
\(888\) 0 0
\(889\) 43160.0i 1.62828i
\(890\) 15664.7 9044.00i 0.589978 0.340624i
\(891\) −11667.1 + 6736.00i −0.438678 + 0.253271i
\(892\) 43024.0i 1.61497i
\(893\) 2430.00 + 4208.88i 0.0910603 + 0.157721i
\(894\) −8460.00 + 14653.1i −0.316493 + 0.548182i
\(895\) −62776.4 36244.0i −2.34456 1.35363i
\(896\) 0 0
\(897\) 0 0
\(898\) 7672.00 0.285098
\(899\) −12624.9 7289.00i −0.468370 0.270414i
\(900\) 15088.0 26133.2i 0.558815 0.967896i
\(901\) −604.500 1047.02i −0.0223516 0.0387142i
\(902\) 21120.0i 0.779622i
\(903\) 5404.00 3120.00i 0.199152 0.114980i
\(904\) 0 0
\(905\) 6851.00i 0.251641i
\(906\) −2056.00 3561.10i −0.0753930 0.130584i
\(907\) −18564.0 + 32153.8i −0.679611 + 1.17712i 0.295487 + 0.955347i \(0.404518\pi\)
−0.975098 + 0.221775i \(0.928815\pi\)
\(908\) 27532.7 + 15896.0i 1.00628 + 0.580977i
\(909\) −18837.0 −0.687331
\(910\) 0 0
\(911\) 20516.0 0.746131 0.373066 0.927805i \(-0.378307\pi\)
0.373066 + 0.927805i \(0.378307\pi\)
\(912\) −3325.54 1920.00i −0.120745 0.0697122i
\(913\) 10048.0 17403.6i 0.364228 0.630862i
\(914\) −23522.0 40741.3i −0.851246 1.47440i
\(915\) 4930.00i 0.178121i
\(916\) 43633.8 25192.0i 1.57391 0.908698i
\(917\) 12644.0 7300.00i 0.455333 0.262887i
\(918\) 5200.00i 0.186956i
\(919\) 10503.0 + 18191.7i 0.376999 + 0.652981i 0.990624 0.136616i \(-0.0436227\pi\)
−0.613625 + 0.789597i \(0.710289\pi\)
\(920\) 0 0
\(921\) −15030.7 8678.00i −0.537763 0.310478i
\(922\) −3604.00 −0.128733
\(923\) 0 0
\(924\) −10240.0 −0.364579
\(925\) −32240.4 18614.0i −1.14601 0.661648i
\(926\) −2744.00 + 4752.75i −0.0973795 + 0.168666i
\(927\) −18837.0 32626.6i −0.667409 1.15599i
\(928\) 50432.0i 1.78396i
\(929\) −17690.3 + 10213.5i −0.624758 + 0.360704i −0.778719 0.627373i \(-0.784130\pi\)
0.153961 + 0.988077i \(0.450797\pi\)
\(930\) −8715.68 + 5032.00i −0.307310 + 0.177426i
\(931\) 1710.00i 0.0601965i
\(932\) −16120.0 27920.7i −0.566554 0.981300i
\(933\) 8658.00 14996.1i 0.303805 0.526206i
\(934\) 22156.4 + 12792.0i 0.776209 + 0.448145i
\(935\) −7072.00 −0.247357
\(936\) 0 0
\(937\) 33191.0 1.15721 0.578603 0.815609i \(-0.303598\pi\)
0.578603 + 0.815609i \(0.303598\pi\)
\(938\) 59721.1 + 34480.0i 2.07885 + 1.20023i
\(939\) 5250.00 9093.27i 0.182457 0.316025i
\(940\) −11016.0 19080.3i −0.382236 0.662053i
\(941\) 36422.0i 1.26177i 0.775877 + 0.630884i \(0.217308\pi\)
−0.775877 + 0.630884i \(0.782692\pi\)
\(942\) −20098.7 + 11604.0i −0.695172 + 0.401357i
\(943\) −11145.7 + 6435.00i −0.384894 + 0.222219i
\(944\) 55296.0i 1.90650i
\(945\) 17000.0 + 29444.9i 0.585196 + 1.01359i
\(946\) 9984.00 17292.8i 0.343137 0.594331i
\(947\) 34320.6 + 19815.0i 1.17769 + 0.679938i 0.955478 0.295062i \(-0.0953401\pi\)
0.222208 + 0.974999i \(0.428673\pi\)
\(948\) 1216.00 0.0416602
\(949\) 0 0
\(950\) 19680.0 0.672109
\(951\) 11107.6 + 6413.00i 0.378749 + 0.218671i
\(952\) 0 0
\(953\) 28821.0 + 49919.4i 0.979647 + 1.69680i 0.663658 + 0.748036i \(0.269003\pi\)
0.315989 + 0.948763i \(0.397664\pi\)
\(954\) 8556.00i 0.290368i
\(955\) 18344.2 10591.0i 0.621574 0.358866i
\(956\) −6817.35 + 3936.00i −0.230637 + 0.133158i
\(957\) 12608.0i 0.425871i
\(958\) −6540.00 11327.6i −0.220561 0.382024i
\(959\) 16710.0 28942.6i 0.562663 0.974561i
\(960\) 15075.8 + 8704.00i 0.506842 + 0.292625i
\(961\) 24315.0 0.816186
\(962\) 0 0
\(963\) −12006.0 −0.401753
\(964\) 6533.30 + 3772.00i 0.218281 + 0.126025i
\(965\) −2269.50 + 3930.89i −0.0757076 + 0.131129i
\(966\) 6240.00 + 10808.0i 0.207835 + 0.359981i
\(967\) 2162.00i 0.0718979i −0.999354 0.0359489i \(-0.988555\pi\)
0.999354 0.0359489i \(-0.0114454\pi\)
\(968\) 0 0
\(969\) −675.500 + 390.000i −0.0223944 + 0.0129294i
\(970\) 16184.0i 0.535708i
\(971\) 9879.00 + 17110.9i 0.326501 + 0.565516i 0.981815 0.189841i \(-0.0607971\pi\)
−0.655314 + 0.755356i \(0.727464\pi\)
\(972\) 14168.0 24539.7i 0.467530 0.809785i
\(973\) −15796.3 9120.00i −0.520459 0.300487i
\(974\) −79680.0 −2.62126
\(975\) 0 0
\(976\) −9280.00 −0.304350
\(977\) −10815.8 6244.50i −0.354174 0.204482i 0.312348 0.949968i \(-0.398884\pi\)
−0.666522 + 0.745485i \(0.732218\pi\)
\(978\) −9440.00 + 16350.6i −0.308648 + 0.534594i
\(979\) 4256.00 + 7371.61i 0.138940 + 0.240651i
\(980\) 7752.00i 0.252682i
\(981\) −32547.0 + 18791.0i −1.05927 + 0.611570i
\(982\) 22696.8 13104.0i 0.737560 0.425830i
\(983\) 28658.0i 0.929856i −0.885349 0.464928i \(-0.846080\pi\)
0.885349 0.464928i \(-0.153920\pi\)
\(984\) 0 0
\(985\) 10863.0 18815.3i 0.351395 0.608634i
\(986\) 8871.56 + 5122.00i 0.286540 + 0.165434i
\(987\) 6480.00 0.208977
\(988\) 0 0
\(989\) −12168.0 −0.391223
\(990\) 43342.8 + 25024.0i 1.39144 + 0.803348i
\(991\) 21397.0 37060.7i 0.685871 1.18796i −0.287291 0.957843i \(-0.592755\pi\)
0.973162 0.230120i \(-0.0739119\pi\)
\(992\) 9472.00 + 16406.0i 0.303162 + 0.525091i
\(993\) 6976.00i 0.222937i
\(994\) −45310.4 + 26160.0i −1.44584 + 0.834753i
\(995\) 62393.7 36023.0i 1.98795 1.14774i
\(996\) 10048.0i 0.319662i
\(997\) 26291.5 + 45538.2i 0.835166 + 1.44655i 0.893895 + 0.448275i \(0.147962\pi\)
−0.0587298 + 0.998274i \(0.518705\pi\)
\(998\) 3492.00 6048.32i 0.110759 0.191840i
\(999\) −19658.8 11350.0i −0.622599 0.359458i
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 169.4.e.c.147.2 4
13.2 odd 12 169.4.c.d.146.1 2
13.3 even 3 inner 169.4.e.c.23.1 4
13.4 even 6 169.4.b.c.168.2 2
13.5 odd 4 169.4.c.d.22.1 2
13.6 odd 12 169.4.a.a.1.1 1
13.7 odd 12 169.4.a.d.1.1 1
13.8 odd 4 13.4.c.a.9.1 yes 2
13.9 even 3 169.4.b.c.168.1 2
13.10 even 6 inner 169.4.e.c.23.2 4
13.11 odd 12 13.4.c.a.3.1 2
13.12 even 2 inner 169.4.e.c.147.1 4
39.8 even 4 117.4.g.c.100.1 2
39.11 even 12 117.4.g.c.55.1 2
39.20 even 12 1521.4.a.b.1.1 1
39.32 even 12 1521.4.a.k.1.1 1
52.11 even 12 208.4.i.b.81.1 2
52.47 even 4 208.4.i.b.113.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.4.c.a.3.1 2 13.11 odd 12
13.4.c.a.9.1 yes 2 13.8 odd 4
117.4.g.c.55.1 2 39.11 even 12
117.4.g.c.100.1 2 39.8 even 4
169.4.a.a.1.1 1 13.6 odd 12
169.4.a.d.1.1 1 13.7 odd 12
169.4.b.c.168.1 2 13.9 even 3
169.4.b.c.168.2 2 13.4 even 6
169.4.c.d.22.1 2 13.5 odd 4
169.4.c.d.146.1 2 13.2 odd 12
169.4.e.c.23.1 4 13.3 even 3 inner
169.4.e.c.23.2 4 13.10 even 6 inner
169.4.e.c.147.1 4 13.12 even 2 inner
169.4.e.c.147.2 4 1.1 even 1 trivial
208.4.i.b.81.1 2 52.11 even 12
208.4.i.b.113.1 2 52.47 even 4
1521.4.a.b.1.1 1 39.20 even 12
1521.4.a.k.1.1 1 39.32 even 12