Properties

Label 169.4.c.d.146.1
Level $169$
Weight $4$
Character 169.146
Analytic conductor $9.971$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [169,4,Mod(22,169)]
 
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([4]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("169.22");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 169 = 13^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 169.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(9.97132279097\)
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: no (minimal twist has level 13)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 146.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 169.146
Dual form 169.4.c.d.22.1

$q$-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} +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} -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} +(-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} +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} -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} -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} +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 \( 2 q + 4 q^{2} - 2 q^{3} - 8 q^{4} - 34 q^{5} + 8 q^{6} + 20 q^{7} + 23 q^{9} - 68 q^{10} - 32 q^{11} + 32 q^{12} + 160 q^{14} + 34 q^{15} + 64 q^{16} + 13 q^{17} + 184 q^{18} + 30 q^{19} + 136 q^{20} - 80 q^{21} + 128 q^{22} - 78 q^{23} + 328 q^{25} - 200 q^{27} + 160 q^{28} - 197 q^{29} - 136 q^{30} + 148 q^{31} - 256 q^{32} - 64 q^{33} + 104 q^{34} - 340 q^{35} + 184 q^{36} - 227 q^{37} + 240 q^{38} - 165 q^{41} - 160 q^{42} + 156 q^{43} + 512 q^{44} - 391 q^{45} + 312 q^{46} + 324 q^{47} + 128 q^{48} - 57 q^{49} + 656 q^{50} - 52 q^{51} + 186 q^{53} - 400 q^{54} + 544 q^{55} - 120 q^{57} + 788 q^{58} - 864 q^{59} - 544 q^{60} - 145 q^{61} + 296 q^{62} - 460 q^{63} - 1024 q^{64} - 512 q^{66} + 862 q^{67} + 104 q^{68} - 156 q^{69} - 2720 q^{70} + 654 q^{71} - 430 q^{73} + 908 q^{74} - 328 q^{75} + 240 q^{76} - 1280 q^{77} - 152 q^{79} - 1088 q^{80} - 421 q^{81} + 660 q^{82} - 1256 q^{83} + 320 q^{84} - 221 q^{85} + 1248 q^{86} - 394 q^{87} - 266 q^{89} - 3128 q^{90} + 1248 q^{92} - 148 q^{93} + 648 q^{94} - 510 q^{95} + 1024 q^{96} + 238 q^{97} + 228 q^{98} - 1472 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 + 3.46410i 0.707107 + 1.22474i 0.965926 + 0.258819i \(0.0833333\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(3\) −1.00000 1.73205i −0.192450 0.333333i 0.753612 0.657320i \(-0.228310\pi\)
−0.946062 + 0.323987i \(0.894977\pi\)
\(4\) −4.00000 + 6.92820i −0.500000 + 0.866025i
\(5\) −17.0000 −1.52053 −0.760263 0.649615i \(-0.774930\pi\)
−0.760263 + 0.649615i \(0.774930\pi\)
\(6\) 4.00000 6.92820i 0.272166 0.471405i
\(7\) 10.0000 17.3205i 0.539949 0.935220i −0.458957 0.888459i \(-0.651777\pi\)
0.998906 0.0467610i \(-0.0148899\pi\)
\(8\) 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 \(-0.311179\pi\)
−0.997579 + 0.0695447i \(0.977845\pi\)
\(12\) 16.0000 0.384900
\(13\) 0 0
\(14\) 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 −0.815927 0.578156i \(-0.803773\pi\)
0.908661 + 0.417535i \(0.137106\pi\)
\(18\) 92.0000 1.20470
\(19\) 15.0000 25.9808i 0.181118 0.313705i −0.761144 0.648583i \(-0.775362\pi\)
0.942261 + 0.334878i \(0.108695\pi\)
\(20\) 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 0.633304 0.773903i \(-0.281698\pi\)
−0.986872 + 0.161506i \(0.948365\pi\)
\(24\) 0 0
\(25\) 164.000 1.31200
\(26\) 0 0
\(27\) −100.000 −0.712778
\(28\) 80.0000 + 138.564i 0.539949 + 0.935220i
\(29\) −98.5000 170.607i −0.630724 1.09245i −0.987404 0.158219i \(-0.949425\pi\)
0.356680 0.934227i \(-0.383909\pi\)
\(30\) −68.0000 + 117.779i −0.413835 + 0.716783i
\(31\) 74.0000 0.428735 0.214368 0.976753i \(-0.431231\pi\)
0.214368 + 0.976753i \(0.431231\pi\)
\(32\) −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 −0.999988 0.00497814i \(-0.998415\pi\)
0.495683 0.868504i \(-0.334918\pi\)
\(38\) 120.000 0.512278
\(39\) 0 0
\(40\) 0 0
\(41\) −82.5000 142.894i −0.314252 0.544301i 0.665026 0.746820i \(-0.268420\pi\)
−0.979278 + 0.202520i \(0.935087\pi\)
\(42\) −80.0000 138.564i −0.293911 0.509069i
\(43\) 78.0000 135.100i 0.276625 0.479129i −0.693919 0.720053i \(-0.744117\pi\)
0.970544 + 0.240924i \(0.0774506\pi\)
\(44\) 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 \(-0.419114\pi\)
0.251384 + 0.967887i \(0.419114\pi\)
\(48\) 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
\(52\) 0 0
\(53\) 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 −0.214919 + 0.976632i \(0.568949\pi\)
−0.738328 + 0.674442i \(0.764384\pi\)
\(60\) −272.000 −0.585251
\(61\) −72.5000 + 125.574i −0.152175 + 0.263575i −0.932027 0.362389i \(-0.881961\pi\)
0.779852 + 0.625964i \(0.215294\pi\)
\(62\) 148.000 + 256.344i 0.303162 + 0.525091i
\(63\) −230.000 398.372i −0.459957 0.796668i
\(64\) −512.000 −1.00000
\(65\) 0 0
\(66\) −256.000 −0.477446
\(67\) 431.000 + 746.514i 0.785896 + 1.36121i 0.928462 + 0.371427i \(0.121131\pi\)
−0.142566 + 0.989785i \(0.545535\pi\)
\(68\) 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 −0.451917 0.892060i \(-0.649260\pi\)
0.998505 0.0546585i \(-0.0174070\pi\)
\(72\) 0 0
\(73\) −215.000 −0.344710 −0.172355 0.985035i \(-0.555138\pi\)
−0.172355 + 0.985035i \(0.555138\pi\)
\(74\) 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
\(78\) 0 0
\(79\) −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 \(-0.636307\pi\)
−0.415253 + 0.909706i \(0.636307\pi\)
\(84\) 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 \(-0.217302\pi\)
−0.934293 + 0.356505i \(0.883968\pi\)
\(90\) −1564.00 −1.83178
\(91\) 0 0
\(92\) 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 \(-0.793580\pi\)
0.921562 + 0.388231i \(0.126914\pi\)
\(98\) 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 0.994138 0.108121i \(-0.0344834\pi\)
−0.590704 + 0.806888i \(0.701150\pi\)
\(102\) −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 0.723697 0.690118i \(-0.242441\pi\)
−0.959508 + 0.281681i \(0.909108\pi\)
\(108\) 400.000 692.820i 0.356389 0.617284i
\(109\) 1634.00 1.43586 0.717930 0.696115i \(-0.245090\pi\)
0.717930 + 0.696115i \(0.245090\pi\)
\(110\) −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 −0.926022 0.377469i \(-0.876794\pi\)
0.789909 + 0.613224i \(0.210128\pi\)
\(114\) −120.000 207.846i −0.0985880 0.170759i
\(115\) 663.000 + 1148.35i 0.537609 + 0.931167i
\(116\) 1576.00 1.26145
\(117\) 0 0
\(118\) −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 0.945918 + 0.324407i \(0.105165\pi\)
−0.192014 + 0.981392i \(0.561502\pi\)
\(128\) 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 \(0.421725\pi\)
\(132\) −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 −0.478667 0.877996i \(-0.658880\pi\)
0.999701 0.0244601i \(-0.00778666\pi\)
\(138\) −624.000 −0.384916
\(139\) −456.000 + 789.815i −0.278255 + 0.481951i −0.970951 0.239278i \(-0.923089\pi\)
0.692696 + 0.721229i \(0.256423\pi\)
\(140\) −1360.00 2355.59i −0.821007 1.42203i
\(141\) −162.000 280.592i −0.0967579 0.167590i
\(142\) 2616.00 1.54598
\(143\) 0 0
\(144\) 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 0.413875 + 0.910334i \(0.364175\pi\)
−0.995310 + 0.0967407i \(0.969158\pi\)
\(150\) 656.000 1136.23i 0.357081 0.618483i
\(151\) −514.000 −0.277011 −0.138506 0.990362i \(-0.544230\pi\)
−0.138506 + 0.990362i \(0.544230\pi\)
\(152\) 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
\(156\) 0 0
\(157\) 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 −0.429835 0.902907i \(-0.641428\pi\)
0.996858 0.0792052i \(-0.0252382\pi\)
\(164\) 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 \(-0.146003\pi\)
−0.831766 + 0.555127i \(0.812670\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) −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 −0.974134 0.225972i \(-0.927444\pi\)
0.682764 + 0.730639i \(0.260778\pi\)
\(174\) −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 −0.839586 0.543227i \(-0.817202\pi\)
−0.0506550 0.998716i \(-0.516131\pi\)
\(180\) −1564.00 2708.93i −0.647632 1.12173i
\(181\) −403.000 −0.165496 −0.0827479 0.996571i \(-0.526370\pi\)
−0.0827479 + 0.996571i \(0.526370\pi\)
\(182\) 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
\(187\) −416.000 −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 −0.723553 0.690269i \(-0.757492\pi\)
0.959567 + 0.281481i \(0.0908255\pi\)
\(192\) 512.000 + 886.810i 0.192450 + 0.333333i
\(193\) 133.500 + 231.229i 0.0497904 + 0.0862394i 0.889846 0.456260i \(-0.150811\pi\)
−0.840056 + 0.542500i \(0.817478\pi\)
\(194\) 952.000 0.352318
\(195\) 0 0
\(196\) 456.000 0.166181
\(197\) 639.000 + 1106.78i 0.231101 + 0.400278i 0.958132 0.286326i \(-0.0924339\pi\)
−0.727032 + 0.686604i \(0.759101\pi\)
\(198\) −1472.00 2549.58i −0.528336 0.915104i
\(199\) −2119.00 + 3670.22i −0.754834 + 1.30741i 0.190623 + 0.981663i \(0.438949\pi\)
−0.945457 + 0.325747i \(0.894384\pi\)
\(200\) 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
\(208\) 0 0
\(209\) −960.000 −0.317725
\(210\) 1360.00 + 2355.59i 0.446900 + 0.774053i
\(211\) −1535.00 2658.70i −0.500823 0.867452i −1.00000 0.000951154i \(-0.999697\pi\)
0.499176 0.866501i \(-0.333636\pi\)
\(212\) −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
\(221\) 0 0
\(222\) −1816.00 −0.549018
\(223\) −2689.00 4657.48i −0.807483 1.39860i −0.914602 0.404356i \(-0.867496\pi\)
0.107119 0.994246i \(-0.465838\pi\)
\(224\) 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 0.414387 + 0.910101i \(0.363996\pi\)
−0.995364 + 0.0961811i \(0.969337\pi\)
\(228\) 240.000 415.692i 0.0697122 0.120745i
\(229\) 6298.00 1.81740 0.908698 0.417455i \(-0.137078\pi\)
0.908698 + 0.417455i \(0.137078\pi\)
\(230\) −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 \(0.308276\pi\)
\(234\) 0 0
\(235\) −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 \(-0.457488\pi\)
0.133158 + 0.991095i \(0.457488\pi\)
\(240\) −1088.00 + 1884.47i −0.292625 + 0.506842i
\(241\) 471.500 816.662i 0.126025 0.218281i −0.796108 0.605154i \(-0.793111\pi\)
0.922133 + 0.386873i \(0.126445\pi\)
\(242\) 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
\(247\) 0 0
\(248\) 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 −0.641777 0.766891i \(-0.721802\pi\)
0.985036 + 0.172349i \(0.0551358\pi\)
\(252\) 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 0.957441 0.288629i \(-0.0931993\pi\)
−0.728680 + 0.684854i \(0.759866\pi\)
\(258\) −624.000 1080.80i −0.150576 0.260805i
\(259\) −4540.00 −1.08920
\(260\) 0 0
\(261\) −4531.00 −1.07457
\(262\) 1460.00 + 2528.79i 0.344271 + 0.596296i
\(263\) −2016.00 3491.81i −0.472669 0.818686i 0.526842 0.849963i \(-0.323376\pi\)
−0.999511 + 0.0312769i \(0.990043\pi\)
\(264\) 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 −0.998630 0.0523292i \(-0.983335\pi\)
0.544633 + 0.838674i \(0.316669\pi\)
\(270\) 3400.00 + 5888.97i 0.766361 + 1.32738i
\(271\) −2148.00 3720.45i −0.481482 0.833952i 0.518292 0.855204i \(-0.326568\pi\)
−0.999774 + 0.0212520i \(0.993235\pi\)
\(272\) 832.000 0.185468
\(273\) 0 0
\(274\) 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 −0.390478 0.920612i \(-0.627690\pi\)
0.992513 0.122142i \(-0.0389765\pi\)
\(278\) −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 \(-0.299182\pi\)
0.589863 + 0.807504i \(0.299182\pi\)
\(282\) 648.000 1122.37i 0.136836 0.237007i
\(283\) −1560.00 2702.00i −0.327676 0.567552i 0.654374 0.756171i \(-0.272932\pi\)
−0.982050 + 0.188619i \(0.939599\pi\)
\(284\) 2616.00 + 4531.04i 0.546588 + 0.946718i
\(285\) 1020.00 0.211999
\(286\) 0 0
\(287\) −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 −0.0723887 0.997376i \(-0.523062\pi\)
0.899948 0.435998i \(-0.143604\pi\)
\(294\) −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
\(299\) 0 0
\(300\) 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 \(-0.798719\pi\)
−0.806644 + 0.591037i \(0.798719\pi\)
\(308\) 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 \(-0.692330\pi\)
−0.568123 + 0.822944i \(0.692330\pi\)
\(318\) 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
\(325\) 0 0
\(326\) 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 \(-0.739810\pi\)
0.973715 + 0.227769i \(0.0731431\pi\)
\(332\) 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 \(0.547330\pi\)
\(338\) 0 0
\(339\) 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 0.438298 + 0.898830i \(0.355581\pi\)
−0.997558 + 0.0698377i \(0.977752\pi\)
\(348\) −1576.00 2729.71i −0.242766 0.420483i
\(349\) −2629.00 4553.56i −0.403230 0.698414i 0.590884 0.806757i \(-0.298779\pi\)
−0.994114 + 0.108342i \(0.965446\pi\)
\(350\) 13120.0 2.00370
\(351\) 0 0
\(352\) 8192.00 1.24044
\(353\) 1581.50 + 2739.24i 0.238455 + 0.413017i 0.960271 0.279068i \(-0.0900256\pi\)
−0.721816 + 0.692085i \(0.756692\pi\)
\(354\) 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 \(-0.234793\pi\)
0.740068 + 0.672532i \(0.234793\pi\)
\(360\) 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
\(364\) 0 0
\(365\) 3655.00 0.524141
\(366\) 580.000 + 1004.59i 0.0828336 + 0.143472i
\(367\) −3719.00 6441.50i −0.528965 0.916195i −0.999429 0.0337755i \(-0.989247\pi\)
0.470464 0.882419i \(-0.344086\pi\)
\(368\) 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 −0.305242 0.952275i \(-0.598737\pi\)
0.977315 0.211790i \(-0.0679294\pi\)
\(374\) −832.000 1441.07i −0.115031 0.199240i
\(375\) 663.000 + 1148.35i 0.0912991 + 0.158135i
\(376\) 0 0
\(377\) 0 0
\(378\) −8000.00 −1.08856
\(379\) −531.000 919.719i −0.0719674 0.124651i 0.827796 0.561029i \(-0.189594\pi\)
−0.899763 + 0.436378i \(0.856261\pi\)
\(380\) −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 \(-0.909042\pi\)
0.723840 + 0.689968i \(0.242375\pi\)
\(384\) 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 \(0.756304\pi\)
\(390\) 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
\(395\) 1292.00 0.164576
\(396\) 2944.00 5099.16i 0.373590 0.647077i
\(397\) −2993.00 + 5184.03i −0.378374 + 0.655362i −0.990826 0.135145i \(-0.956850\pi\)
0.612452 + 0.790508i \(0.290183\pi\)
\(398\) −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 \(-0.0461782\pi\)
−0.619945 + 0.784646i \(0.712845\pi\)
\(402\) 6896.00 0.855575
\(403\) 0 0
\(404\) −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 −0.101023 + 0.994884i \(0.532212\pi\)
−0.811083 + 0.584931i \(0.801122\pi\)
\(410\) −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
\(416\) 0 0
\(417\) 1824.00 0.214201
\(418\) −1920.00 3325.54i −0.224666 0.389132i
\(419\) 5407.00 + 9365.20i 0.630428 + 1.09193i 0.987464 + 0.157843i \(0.0504538\pi\)
−0.357037 + 0.934090i \(0.616213\pi\)
\(420\) −2720.00 + 4711.18i −0.316006 + 0.547338i
\(421\) 6535.00 0.756524 0.378262 0.925699i \(-0.376522\pi\)
0.378262 + 0.925699i \(0.376522\pi\)
\(422\) 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
\(429\) 0 0
\(430\) −10608.0 −1.18968
\(431\) 990.000 + 1714.73i 0.110642 + 0.191637i 0.916029 0.401112i \(-0.131376\pi\)
−0.805387 + 0.592749i \(0.798043\pi\)
\(432\) −3200.00 5542.56i −0.356389 0.617284i
\(433\) 3464.50 6000.69i 0.384511 0.665993i −0.607190 0.794556i \(-0.707703\pi\)
0.991701 + 0.128564i \(0.0410368\pi\)
\(434\) 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 0.963179 0.268862i \(-0.0866476\pi\)
−0.714431 + 0.699706i \(0.753314\pi\)
\(440\) 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 \(0.656663\pi\)
\(444\) −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 \(-0.801194\pi\)
0.912013 + 0.410160i \(0.134527\pi\)
\(450\) 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
\(455\) 0 0
\(456\) 0 0
\(457\) −5880.50 10185.3i −0.601922 1.04256i −0.992530 0.122002i \(-0.961069\pi\)
0.390608 0.920557i \(-0.372265\pi\)
\(458\) 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 \(-0.818841\pi\)
0.887885 + 0.460066i \(0.152174\pi\)
\(462\) −2560.00 + 4434.05i −0.257796 + 0.446517i
\(463\) −1372.00 −0.137715 −0.0688577 0.997626i \(-0.521935\pi\)
−0.0688577 + 0.997626i \(0.521935\pi\)
\(464\) 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 \(0.602637\pi\)
\(468\) 0 0
\(469\) 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 \(-0.116819\pi\)
−0.777448 + 0.628947i \(0.783486\pi\)
\(480\) −8704.00 −0.827670
\(481\) 0 0
\(482\) 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 0.138046 0.990426i \(-0.455918\pi\)
0.788711 0.614765i \(-0.210749\pi\)
\(488\) 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 0.675280 0.737562i \(-0.264023\pi\)
−0.976387 + 0.216028i \(0.930690\pi\)
\(492\) −1320.00 2286.31i −0.120956 0.209501i
\(493\) −2561.00 −0.233959
\(494\) 0 0
\(495\) 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 \(-0.524955\pi\)
−0.0783183 + 0.996928i \(0.524955\pi\)
\(500\) 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 0.331661 + 0.943399i \(0.392391\pi\)
−0.982838 + 0.184473i \(0.940942\pi\)
\(504\) 0 0
\(505\) −6961.50 12057.7i −0.613431 1.06249i
\(506\) −9984.00 −0.877160
\(507\) 0 0
\(508\) −17264.0 −1.50781
\(509\) 4038.50 + 6994.89i 0.351677 + 0.609122i 0.986543 0.163500i \(-0.0522784\pi\)
−0.634867 + 0.772622i \(0.718945\pi\)
\(510\) 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 0.803255 0.595636i \(-0.203100\pi\)
−0.917463 + 0.397821i \(0.869767\pi\)
\(524\) −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
\(533\) 0 0
\(534\) −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 \(-0.239458\pi\)
0.730132 + 0.683306i \(0.239458\pi\)
\(542\) 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
\(546\) 0 0
\(547\) −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 \(-0.162490\pi\)
−0.859390 + 0.511321i \(0.829156\pi\)
\(558\) 6808.00 0.516498
\(559\) 0 0
\(560\) −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 −0.659583 0.751631i \(-0.729267\pi\)
0.980724 + 0.195400i \(0.0626006\pi\)
\(564\) 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 0.958951 + 0.283570i \(0.0915189\pi\)
−0.233897 + 0.972261i \(0.575148\pi\)
\(570\) 2040.00 + 3533.38i 0.149906 + 0.259644i
\(571\) 26624.0 1.95128 0.975639 0.219382i \(-0.0704042\pi\)
0.975639 + 0.219382i \(0.0704042\pi\)
\(572\) 0 0
\(573\) −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 \(-0.330129\pi\)
0.508694 + 0.860948i \(0.330129\pi\)
\(578\) −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
\(585\) 0 0
\(586\) 33204.0 2.34069
\(587\) 704.000 + 1219.36i 0.0495012 + 0.0857386i 0.889714 0.456518i \(-0.150904\pi\)
−0.840213 + 0.542256i \(0.817570\pi\)
\(588\) −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 \(-0.486318\pi\)
0.0429694 + 0.999076i \(0.486318\pi\)
\(594\) −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
\(598\) 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 0.999368 0.0355563i \(-0.0113203\pi\)
−0.530477 + 0.847700i \(0.677987\pi\)
\(602\) 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 −0.970512 0.241053i \(-0.922507\pi\)
0.694014 + 0.719962i \(0.255841\pi\)
\(608\) 3840.00 + 6651.08i 0.256139 + 0.443646i
\(609\) 3940.00 + 6824.28i 0.262162 + 0.454078i
\(610\) 9860.00 0.654459
\(611\) 0 0
\(612\) 2392.00 0.157992
\(613\) 11136.5 + 19289.0i 0.733767 + 1.27092i 0.955262 + 0.295760i \(0.0955728\pi\)
−0.221496 + 0.975161i \(0.571094\pi\)
\(614\) −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 0.370072 + 0.929003i \(0.379333\pi\)
−0.989576 + 0.144010i \(0.954000\pi\)
\(618\) 6552.00 11348.4i 0.426473 0.738672i
\(619\) −72.0000 −0.00467516 −0.00233758 0.999997i \(-0.500744\pi\)
−0.00233758 + 0.999997i \(0.500744\pi\)
\(620\) 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
\(624\) 0 0
\(625\) −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 0.216097 + 0.976372i \(0.430667\pi\)
−0.953611 + 0.301040i \(0.902666\pi\)
\(632\) 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
\(637\) 0 0
\(638\) −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 −0.947442 0.319927i \(-0.896342\pi\)
0.750786 + 0.660546i \(0.229675\pi\)
\(642\) −4176.00 −0.256719
\(643\) −8552.00 + 14812.5i −0.524507 + 0.908473i 0.475086 + 0.879939i \(0.342417\pi\)
−0.999593 + 0.0285332i \(0.990916\pi\)
\(644\) 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 0.740003 0.672604i \(-0.234824\pi\)
−0.952493 + 0.304560i \(0.901491\pi\)
\(648\) 0 0
\(649\) 27648.0 1.67223
\(650\) 0 0
\(651\) −2960.00 −0.178205
\(652\) 9440.00 + 16350.6i 0.567023 + 0.982112i
\(653\) 2625.00 + 4546.63i 0.157311 + 0.272471i 0.933898 0.357539i \(-0.116384\pi\)
−0.776587 + 0.630010i \(0.783051\pi\)
\(654\) 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 −0.794735 0.606956i \(-0.792390\pi\)
0.923007 + 0.384783i \(0.125724\pi\)
\(660\) 4352.00 + 7537.89i 0.256669 + 0.444563i
\(661\) −2089.50 3619.12i −0.122953 0.212961i 0.797978 0.602687i \(-0.205903\pi\)
−0.920931 + 0.389726i \(0.872570\pi\)
\(662\) 13952.0 0.819124
\(663\) 0 0
\(664\) 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 −0.981926 0.189266i \(-0.939389\pi\)
0.327054 0.945006i \(-0.393944\pi\)
\(674\) −3666.00 6349.70i −0.209509 0.362880i
\(675\) −16400.0 −0.935165
\(676\) 0 0
\(677\) 5410.00 0.307124 0.153562 0.988139i \(-0.450925\pi\)
0.153562 + 0.988139i \(0.450925\pi\)
\(678\) 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 \(-0.957527\pi\)
0.610769 + 0.791809i \(0.290861\pi\)
\(684\) 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
\(689\) 0 0
\(690\) 10608.0 0.585275
\(691\) 6372.00 + 11036.6i 0.350799 + 0.607602i 0.986390 0.164424i \(-0.0525766\pi\)
−0.635590 + 0.772026i \(0.719243\pi\)
\(692\) −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 \(0.354279\pi\)
\(702\) 0 0
\(703\) −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 \(-0.827356\pi\)
0.875262 + 0.483650i \(0.160689\pi\)
\(710\) −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
\(715\) 0 0
\(716\) 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 −0.749716 0.661760i \(-0.769810\pi\)
0.947959 + 0.318393i \(0.103143\pi\)
\(720\) −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 \(-0.479270\pi\)
0.0650786 + 0.997880i \(0.479270\pi\)
\(734\) 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 \(-0.134320\pi\)
−0.810834 + 0.585276i \(0.800986\pi\)
\(740\) −30872.0 −1.53362
\(741\) 0 0
\(742\) 7440.00 0.368101
\(743\) −17028.0 29493.4i −0.840776 1.45627i −0.889239 0.457442i \(-0.848766\pi\)
0.0484632 0.998825i \(-0.484568\pi\)
\(744\) 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 0.870413 0.492322i \(-0.163852\pi\)
−0.861570 + 0.507639i \(0.830518\pi\)
\(752\) 5184.00 + 8978.95i 0.251384 + 0.435410i
\(753\) −5460.00 −0.264241
\(754\) 0 0
\(755\) 8738.00 0.421203
\(756\) −8000.00 13856.4i −0.384864 0.666604i
\(757\) 3457.00 + 5987.70i 0.165980 + 0.287486i 0.937003 0.349322i \(-0.113588\pi\)
−0.771023 + 0.636807i \(0.780255\pi\)
\(758\) 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 \(-0.725268\pi\)
0.983101 + 0.183062i \(0.0586011\pi\)
\(762\) 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
\(767\) 0 0
\(768\) 8192.00 0.384900
\(769\) −9033.00 15645.6i −0.423587 0.733674i 0.572700 0.819765i \(-0.305896\pi\)
−0.996287 + 0.0860907i \(0.972563\pi\)
\(770\) 21760.0 + 37689.4i 1.01841 + 1.76394i
\(771\) 1885.00 3264.92i 0.0880501 0.152507i
\(772\) −2136.00 −0.0995807
\(773\) 7217.00 12500.2i 0.335805 0.581632i −0.647834 0.761782i \(-0.724325\pi\)
0.983639 + 0.180150i \(0.0576583\pi\)
\(774\) 7176.00 12429.2i 0.333251 0.577207i
\(775\) 12136.0 0.562501
\(776\) 0 0
\(777\) 4540.00 + 7863.51i 0.209616 + 0.363065i
\(778\) −22126.0 38323.4i −1.01961 1.76601i
\(779\) −4950.00 −0.227666
\(780\) 0 0
\(781\) −20928.0 −0.958851
\(782\) −2028.00 3512.60i −0.0927380 0.160627i
\(783\) 9850.00 + 17060.7i 0.449566 + 0.778671i
\(784\) 1824.00 3159.26i 0.0830904 0.143917i
\(785\) −49317.0 −2.24229
\(786\) 2920.00 5057.59i 0.132510 0.229514i
\(787\) −7699.00 + 13335.1i −0.348716 + 0.603994i −0.986022 0.166617i \(-0.946716\pi\)
0.637305 + 0.770611i \(0.280049\pi\)
\(788\) −10224.0 −0.462202
\(789\) −4032.00 + 6983.63i −0.181930 + 0.315113i
\(790\) 2584.00 + 4475.62i 0.116373 + 0.201564i
\(791\) 3270.00 + 5663.81i 0.146988 + 0.254591i
\(792\) 0 0
\(793\) 0 0
\(794\) −23944.0 −1.07020
\(795\) 1581.00 + 2738.37i 0.0705312 + 0.122164i
\(796\) −16952.0 29361.7i −0.754834 1.30741i
\(797\) 18421.0 31906.1i 0.818702 1.41803i −0.0879373 0.996126i \(-0.528028\pi\)
0.906639 0.421907i \(-0.138639\pi\)
\(798\) −4800.00 −0.212930
\(799\) 1053.00 1823.85i 0.0466239 0.0807549i
\(800\) −20992.0 + 36359.2i −0.927724 + 1.60687i
\(801\) −6118.00 −0.269874
\(802\) −11870.0 + 20559.4i −0.522624 + 0.905211i
\(803\) 3440.00 + 5958.25i 0.151177 + 0.261846i
\(804\) 6896.00 + 11944.2i 0.302492 + 0.523931i
\(805\) 26520.0 1.16113
\(806\) 0 0
\(807\) 8012.00 0.349487
\(808\) 0 0
\(809\) −20755.5 35949.6i −0.902008 1.56232i −0.824884 0.565302i \(-0.808760\pi\)
−0.0771242 0.997021i \(-0.524574\pi\)
\(810\) −14314.0 + 24792.6i −0.620917 + 1.07546i
\(811\) −23066.0 −0.998714 −0.499357 0.866396i \(-0.666430\pi\)
−0.499357 + 0.866396i \(0.666430\pi\)
\(812\) 15760.0 27297.1i 0.681118 1.17973i
\(813\) −4296.00 + 7440.89i −0.185323 + 0.320988i
\(814\) −29056.0 −1.25112
\(815\) −20060.0 + 34744.9i −0.862173 + 1.49333i
\(816\) −832.000 1441.07i −0.0356934 0.0618228i
\(817\) −2340.00 4053.00i −0.100203 0.173558i
\(818\) −60356.0 −2.57983
\(819\) 0 0
\(820\) −22440.0 −0.955657
\(821\) 14419.0 + 24974.4i 0.612943 + 1.06165i 0.990742 + 0.135761i \(0.0433480\pi\)
−0.377798 + 0.925888i \(0.623319\pi\)
\(822\) −6684.00 11577.0i −0.283615 0.491235i
\(823\) −13728.0 + 23777.6i −0.581443 + 1.00709i 0.413865 + 0.910338i \(0.364179\pi\)
−0.995309 + 0.0967514i \(0.969155\pi\)
\(824\) 0 0
\(825\) −5248.00 + 9089.80i −0.221469 + 0.383596i
\(826\) −34560.0 + 59859.7i −1.45581 + 2.52153i
\(827\) 33572.0 1.41162 0.705812 0.708399i \(-0.250582\pi\)
0.705812 + 0.708399i \(0.250582\pi\)
\(828\) 7176.00 12429.2i 0.301187 0.521672i
\(829\) 22899.5 + 39663.1i 0.959388 + 1.66171i 0.723991 + 0.689809i \(0.242306\pi\)
0.235396 + 0.971899i \(0.424361\pi\)
\(830\) 21352.0 + 36982.7i 0.892938 + 1.54661i
\(831\) −11102.0 −0.463447
\(832\) 0 0
\(833\) −741.000 −0.0308213
\(834\) 3648.00 + 6318.52i 0.151463 + 0.262341i
\(835\) −2380.00 4122.28i −0.0986387 0.170847i
\(836\) 3840.00 6651.08i 0.158863 0.275158i
\(837\) −7400.00 −0.305593
\(838\) −21628.0 + 37460.8i −0.891560 + 1.54423i
\(839\) 16143.0 27960.5i 0.664265 1.15054i −0.315219 0.949019i \(-0.602078\pi\)
0.979484 0.201522i \(-0.0645886\pi\)
\(840\) 0 0
\(841\) −7210.00 + 12488.1i −0.295625 + 0.512038i
\(842\) 13070.0 + 22637.9i 0.534943 + 0.926548i
\(843\) −5557.00 9625.01i −0.227038 0.393242i
\(844\) 24560.0 1.00165
\(845\) 0 0
\(846\) 14904.0 0.605686
\(847\) −3070.00 5317.40i −0.124541 0.215712i
\(848\) 2976.00 + 5154.58i 0.120514 + 0.208737i
\(849\) −3120.00 + 5404.00i −0.126123 + 0.218451i
\(850\) 8528.00 0.344127
\(851\) −8853.00 + 15333.8i −0.356612 + 0.617670i
\(852\) 5232.00 9062.09i 0.210382 0.364392i
\(853\) −20937.0 −0.840409 −0.420205 0.907429i \(-0.638042\pi\)
−0.420205 + 0.907429i \(0.638042\pi\)
\(854\) −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 \(-0.545763\pi\)
−0.143274 + 0.989683i \(0.545763\pi\)
\(858\) 0 0
\(859\) −32498.0 −1.29082 −0.645412 0.763835i \(-0.723314\pi\)
−0.645412 + 0.763835i \(0.723314\pi\)
\(860\) −10608.0 18373.6i −0.420616 0.728528i
\(861\) 3300.00 + 5715.77i 0.130620 + 0.226240i
\(862\) −3960.00 + 6858.92i −0.156471 + 0.271016i
\(863\) −8428.00 −0.332436 −0.166218 0.986089i \(-0.553156\pi\)
−0.166218 + 0.986089i \(0.553156\pi\)
\(864\) 12800.0 22170.3i 0.504010 0.872971i
\(865\) 11271.0 19521.9i 0.443035 0.767360i
\(866\) 27716.0 1.08756
\(867\) 4744.00 8216.85i 0.185830 0.321867i
\(868\) 5920.00 + 10253.7i 0.231495 + 0.400962i
\(869\) 1216.00 + 2106.17i 0.0474683 + 0.0822176i
\(870\) 26792.0 1.04406
\(871\) 0 0
\(872\) 0 0
\(873\) −2737.00 4740.62i −0.106109 0.183787i
\(874\) −4680.00 8106.00i −0.181125 0.313718i
\(875\) −6630.00 + 11483.5i −0.256154 + 0.443672i
\(876\) −3440.00 −0.132679
\(877\) −3423.50 + 5929.68i −0.131817 + 0.228313i −0.924377 0.381480i \(-0.875414\pi\)
0.792560 + 0.609794i \(0.208748\pi\)
\(878\) −9152.00 + 15851.7i −0.351783 + 0.609305i
\(879\) −16602.0 −0.637055
\(880\) −17408.0 + 30151.5i −0.666845 + 1.15501i
\(881\) −14865.5 25747.8i −0.568481 0.984637i −0.996717 0.0809703i \(-0.974198\pi\)
0.428236 0.903667i \(-0.359135\pi\)
\(882\) −2622.00 4541.44i −0.100099 0.173377i
\(883\) −23738.0 −0.904697 −0.452348 0.891841i \(-0.649414\pi\)
−0.452348 + 0.891841i \(0.649414\pi\)
\(884\) 0 0
\(885\) −29376.0 −1.11578
\(886\) −17624.0 30525.7i −0.668273 1.15748i
\(887\) −13794.0 23891.9i −0.522161 0.904410i −0.999668 0.0257817i \(-0.991793\pi\)
0.477506 0.878628i \(-0.341541\pi\)
\(888\) 0 0
\(889\) 43160.0 1.62828
\(890\) −9044.00 + 15664.7i −0.340624 + 0.589978i
\(891\) −6736.00 + 11667.1i −0.253271 + 0.438678i
\(892\) 43024.0 1.61497
\(893\) 2430.00 4208.88i 0.0910603 0.157721i
\(894\) 8460.00 + 14653.1i 0.316493 + 0.548182i
\(895\) 36244.0 + 62776.4i 1.35363 + 2.34456i
\(896\) 0 0
\(897\) 0 0
\(898\) 7672.00 0.285098
\(899\) −7289.00 12624.9i −0.270414 0.468370i
\(900\) 15088.0 + 26133.2i 0.558815 + 0.967896i
\(901\) 604.500 1047.02i 0.0223516 0.0387142i
\(902\) −21120.0 −0.779622
\(903\) −3120.00 + 5404.00i −0.114980 + 0.199152i
\(904\) 0 0
\(905\) 6851.00 0.251641
\(906\) −2056.00 + 3561.10i −0.0753930 + 0.130584i
\(907\) 18564.0 + 32153.8i 0.679611 + 1.17712i 0.975098 + 0.221775i \(0.0711849\pi\)
−0.295487 + 0.955347i \(0.595482\pi\)
\(908\) −15896.0 27532.7i −0.580977 1.00628i
\(909\) 18837.0 0.687331
\(910\) 0 0
\(911\) 20516.0 0.746131 0.373066 0.927805i \(-0.378307\pi\)
0.373066 + 0.927805i \(0.378307\pi\)
\(912\) −1920.00 3325.54i −0.0697122 0.120745i
\(913\) 10048.0 + 17403.6i 0.364228 + 0.630862i
\(914\) 23522.0 40741.3i 0.851246 1.47440i
\(915\) −4930.00 −0.178121
\(916\) −25192.0 + 43633.8i −0.908698 + 1.57391i
\(917\) 7300.00 12644.0i 0.262887 0.455333i
\(918\) −5200.00 −0.186956
\(919\) 10503.0 18191.7i 0.376999 0.652981i −0.613625 0.789597i \(-0.710289\pi\)
0.990624 + 0.136616i \(0.0436227\pi\)
\(920\) 0 0
\(921\) 8678.00 + 15030.7i 0.310478 + 0.537763i
\(922\) 3604.00 0.128733
\(923\) 0 0
\(924\) −10240.0 −0.364579
\(925\) −18614.0 32240.4i −0.661648 1.14601i
\(926\) −2744.00 4752.75i −0.0973795 0.168666i
\(927\) 18837.0 32626.6i 0.667409 1.15599i
\(928\) 50432.0 1.78396
\(929\) 10213.5 17690.3i 0.360704 0.624758i −0.627373 0.778719i \(-0.715870\pi\)
0.988077 + 0.153961i \(0.0492031\pi\)
\(930\) −5032.00 + 8715.68i −0.177426 + 0.307310i
\(931\) −1710.00 −0.0601965
\(932\) −16120.0 + 27920.7i −0.566554 + 0.981300i
\(933\) −8658.00 14996.1i −0.303805 0.526206i
\(934\) −12792.0 22156.4i −0.448145 0.776209i
\(935\) 7072.00 0.247357
\(936\) 0 0
\(937\) 33191.0 1.15721 0.578603 0.815609i \(-0.303598\pi\)
0.578603 + 0.815609i \(0.303598\pi\)
\(938\) 34480.0 + 59721.1i 1.20023 + 2.07885i
\(939\) 5250.00 + 9093.27i 0.182457 + 0.316025i
\(940\) 11016.0 19080.3i 0.382236 0.662053i
\(941\) 36422.0 1.26177 0.630884 0.775877i \(-0.282692\pi\)
0.630884 + 0.775877i \(0.282692\pi\)
\(942\) 11604.0 20098.7i 0.401357 0.695172i
\(943\) −6435.00 + 11145.7i −0.222219 + 0.384894i
\(944\) −55296.0 −1.90650
\(945\) 17000.0 29444.9i 0.585196 1.01359i
\(946\) −9984.00 17292.8i −0.343137 0.594331i
\(947\) −19815.0 34320.6i −0.679938 1.17769i −0.974999 0.222208i \(-0.928673\pi\)
0.295062 0.955478i \(-0.404660\pi\)
\(948\) −1216.00 −0.0416602
\(949\) 0 0
\(950\) 19680.0 0.672109
\(951\) 6413.00 + 11107.6i 0.218671 + 0.378749i
\(952\) 0 0
\(953\) −28821.0 + 49919.4i −0.979647 + 1.69680i −0.315989 + 0.948763i \(0.602336\pi\)
−0.663658 + 0.748036i \(0.730997\pi\)
\(954\) 8556.00 0.290368
\(955\) −10591.0 + 18344.2i −0.358866 + 0.621574i
\(956\) −3936.00 + 6817.35i −0.133158 + 0.230637i
\(957\) 12608.0 0.425871
\(958\) −6540.00 + 11327.6i −0.220561 + 0.382024i
\(959\) −16710.0 28942.6i −0.562663 0.974561i
\(960\) −8704.00 15075.8i −0.292625 0.506842i
\(961\) −24315.0 −0.816186
\(962\) 0 0
\(963\) −12006.0 −0.401753
\(964\) 3772.00 + 6533.30i 0.126025 + 0.218281i
\(965\) −2269.50 3930.89i −0.0757076 0.131129i
\(966\) −6240.00 + 10808.0i −0.207835 + 0.359981i
\(967\) −2162.00 −0.0718979 −0.0359489 0.999354i \(-0.511445\pi\)
−0.0359489 + 0.999354i \(0.511445\pi\)
\(968\) 0 0
\(969\) −390.000 + 675.500i −0.0129294 + 0.0223944i
\(970\) −16184.0 −0.535708
\(971\) 9879.00 17110.9i 0.326501 0.565516i −0.655314 0.755356i \(-0.727464\pi\)
0.981815 + 0.189841i \(0.0607971\pi\)
\(972\) −14168.0 24539.7i −0.467530 0.809785i
\(973\) 9120.00 + 15796.3i 0.300487 + 0.520459i
\(974\) 79680.0 2.62126
\(975\) 0 0
\(976\) −9280.00 −0.304350
\(977\) −6244.50 10815.8i −0.204482 0.354174i 0.745485 0.666522i \(-0.232218\pi\)
−0.949968 + 0.312348i \(0.898884\pi\)
\(978\) −9440.00 16350.6i −0.308648 0.534594i
\(979\) −4256.00 + 7371.61i −0.138940 + 0.240651i
\(980\) −7752.00 −0.252682
\(981\) 18791.0 32547.0i 0.611570 1.05927i
\(982\) 13104.0 22696.8i 0.425830 0.737560i
\(983\) 28658.0 0.929856 0.464928 0.885349i \(-0.346080\pi\)
0.464928 + 0.885349i \(0.346080\pi\)
\(984\) 0 0
\(985\) −10863.0 18815.3i −0.351395 0.608634i
\(986\) −5122.00 8871.56i −0.165434 0.286540i
\(987\) −6480.00 −0.208977
\(988\) 0 0
\(989\) −12168.0 −0.391223
\(990\) 25024.0 + 43342.8i 0.803348 + 1.39144i
\(991\) 21397.0 + 37060.7i 0.685871 + 1.18796i 0.973162 + 0.230120i \(0.0739119\pi\)
−0.287291 + 0.957843i \(0.592755\pi\)
\(992\) −9472.00 + 16406.0i −0.303162 + 0.525091i
\(993\) −6976.00 −0.222937
\(994\) 26160.0 45310.4i 0.834753 1.44584i
\(995\) 36023.0 62393.7i 1.14774 1.98795i
\(996\) −10048.0 −0.319662
\(997\) 26291.5 45538.2i 0.835166 1.44655i −0.0587298 0.998274i \(-0.518705\pi\)
0.893895 0.448275i \(-0.147962\pi\)
\(998\) −3492.00 6048.32i −0.110759 0.191840i
\(999\) 11350.0 + 19658.8i 0.359458 + 0.622599i
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.c.d.146.1 2
13.2 odd 12 169.4.b.c.168.2 2
13.3 even 3 169.4.a.a.1.1 1
13.4 even 6 13.4.c.a.9.1 yes 2
13.5 odd 4 169.4.e.c.23.2 4
13.6 odd 12 169.4.e.c.147.1 4
13.7 odd 12 169.4.e.c.147.2 4
13.8 odd 4 169.4.e.c.23.1 4
13.9 even 3 inner 169.4.c.d.22.1 2
13.10 even 6 169.4.a.d.1.1 1
13.11 odd 12 169.4.b.c.168.1 2
13.12 even 2 13.4.c.a.3.1 2
39.17 odd 6 117.4.g.c.100.1 2
39.23 odd 6 1521.4.a.b.1.1 1
39.29 odd 6 1521.4.a.k.1.1 1
39.38 odd 2 117.4.g.c.55.1 2
52.43 odd 6 208.4.i.b.113.1 2
52.51 odd 2 208.4.i.b.81.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
13.4.c.a.3.1 2 13.12 even 2
13.4.c.a.9.1 yes 2 13.4 even 6
117.4.g.c.55.1 2 39.38 odd 2
117.4.g.c.100.1 2 39.17 odd 6
169.4.a.a.1.1 1 13.3 even 3
169.4.a.d.1.1 1 13.10 even 6
169.4.b.c.168.1 2 13.11 odd 12
169.4.b.c.168.2 2 13.2 odd 12
169.4.c.d.22.1 2 13.9 even 3 inner
169.4.c.d.146.1 2 1.1 even 1 trivial
169.4.e.c.23.1 4 13.8 odd 4
169.4.e.c.23.2 4 13.5 odd 4
169.4.e.c.147.1 4 13.6 odd 12
169.4.e.c.147.2 4 13.7 odd 12
208.4.i.b.81.1 2 52.51 odd 2
208.4.i.b.113.1 2 52.43 odd 6
1521.4.a.b.1.1 1 39.23 odd 6
1521.4.a.k.1.1 1 39.29 odd 6