Properties

Label 189.4.o.a.62.6
Level $189$
Weight $4$
Character 189.62
Analytic conductor $11.151$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [189,4,Mod(62,189)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(189, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1, 3]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("189.62");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 189 = 3^{3} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 189.o (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: \(11.1513609911\)
Analytic rank: \(0\)
Dimension: \(44\)
Relative dimension: \(22\) over \(\Q(\zeta_{6})\)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 62.6
Character \(\chi\) \(=\) 189.62
Dual form 189.4.o.a.125.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-2.59186 - 1.49641i) q^{2} +(0.478502 + 0.828790i) q^{4} +(7.80147 + 13.5125i) q^{5} +(17.7116 + 5.41283i) q^{7} +21.0785i q^{8} +O(q^{10})\) \(q+(-2.59186 - 1.49641i) q^{2} +(0.478502 + 0.828790i) q^{4} +(7.80147 + 13.5125i) q^{5} +(17.7116 + 5.41283i) q^{7} +21.0785i q^{8} -46.6969i q^{10} +(-46.4700 - 26.8295i) q^{11} +(-29.1434 + 16.8260i) q^{13} +(-37.8062 - 40.5332i) q^{14} +(35.3701 - 61.2628i) q^{16} -43.5488 q^{17} +32.2524i q^{19} +(-7.46605 + 12.9316i) q^{20} +(80.2960 + 139.077i) q^{22} +(-129.309 + 74.6565i) q^{23} +(-59.2260 + 102.582i) q^{25} +100.714 q^{26} +(3.98894 + 17.2693i) q^{28} +(127.390 + 73.5487i) q^{29} +(-61.1678 + 35.3153i) q^{31} +(-37.3130 + 21.5427i) q^{32} +(112.873 + 65.1670i) q^{34} +(65.0355 + 281.557i) q^{35} +40.3540 q^{37} +(48.2629 - 83.5938i) q^{38} +(-284.824 + 164.443i) q^{40} +(-179.454 - 310.824i) q^{41} +(-253.886 + 439.743i) q^{43} -51.3519i q^{44} +446.867 q^{46} +(-228.160 + 395.185i) q^{47} +(284.402 + 191.740i) q^{49} +(307.011 - 177.253i) q^{50} +(-27.8904 - 16.1025i) q^{52} +213.420i q^{53} -837.238i q^{55} +(-114.094 + 373.333i) q^{56} +(-220.118 - 381.256i) q^{58} +(159.593 + 276.424i) q^{59} +(303.662 + 175.319i) q^{61} +211.385 q^{62} -436.974 q^{64} +(-454.723 - 262.535i) q^{65} +(-289.258 - 501.009i) q^{67} +(-20.8382 - 36.0928i) q^{68} +(252.762 - 827.077i) q^{70} -787.243i q^{71} +146.373i q^{73} +(-104.592 - 60.3863i) q^{74} +(-26.7305 + 15.4329i) q^{76} +(-677.836 - 726.728i) q^{77} +(-193.095 + 334.451i) q^{79} +1103.76 q^{80} +1074.15i q^{82} +(98.9043 - 171.307i) q^{83} +(-339.745 - 588.455i) q^{85} +(1316.07 - 759.835i) q^{86} +(565.524 - 979.517i) q^{88} +596.020 q^{89} +(-607.253 + 140.267i) q^{91} +(-123.749 - 71.4466i) q^{92} +(1182.72 - 682.844i) q^{94} +(-435.812 + 251.616i) q^{95} +(631.485 + 364.588i) q^{97} +(-450.210 - 922.547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7} + 18 q^{11} - 204 q^{14} - 242 q^{16} - 34 q^{22} + 102 q^{23} - 352 q^{25} + 300 q^{28} - 246 q^{29} - 1068 q^{32} + 328 q^{37} - 170 q^{43} + 968 q^{46} - 79 q^{49} - 288 q^{50} - 1212 q^{56} - 538 q^{58} - 808 q^{64} - 4350 q^{65} - 590 q^{67} + 384 q^{70} + 5304 q^{74} + 2787 q^{77} - 302 q^{79} - 612 q^{85} + 13692 q^{86} + 1294 q^{88} + 210 q^{91} + 10194 q^{92} - 6336 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/189\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(136\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.59186 1.49641i −0.916362 0.529062i −0.0338893 0.999426i \(-0.510789\pi\)
−0.882473 + 0.470364i \(0.844123\pi\)
\(3\) 0 0
\(4\) 0.478502 + 0.828790i 0.0598128 + 0.103599i
\(5\) 7.80147 + 13.5125i 0.697785 + 1.20860i 0.969233 + 0.246146i \(0.0791642\pi\)
−0.271448 + 0.962453i \(0.587502\pi\)
\(6\) 0 0
\(7\) 17.7116 + 5.41283i 0.956337 + 0.292265i
\(8\) 21.0785i 0.931545i
\(9\) 0 0
\(10\) 46.6969i 1.47669i
\(11\) −46.4700 26.8295i −1.27375 0.735400i −0.298058 0.954548i \(-0.596339\pi\)
−0.975692 + 0.219148i \(0.929672\pi\)
\(12\) 0 0
\(13\) −29.1434 + 16.8260i −0.621764 + 0.358976i −0.777555 0.628814i \(-0.783541\pi\)
0.155791 + 0.987790i \(0.450207\pi\)
\(14\) −37.8062 40.5332i −0.721725 0.773782i
\(15\) 0 0
\(16\) 35.3701 61.2628i 0.552658 0.957231i
\(17\) −43.5488 −0.621302 −0.310651 0.950524i \(-0.600547\pi\)
−0.310651 + 0.950524i \(0.600547\pi\)
\(18\) 0 0
\(19\) 32.2524i 0.389432i 0.980860 + 0.194716i \(0.0623785\pi\)
−0.980860 + 0.194716i \(0.937621\pi\)
\(20\) −7.46605 + 12.9316i −0.0834729 + 0.144579i
\(21\) 0 0
\(22\) 80.2960 + 139.077i 0.778144 + 1.34778i
\(23\) −129.309 + 74.6565i −1.17229 + 0.676824i −0.954219 0.299108i \(-0.903311\pi\)
−0.218074 + 0.975932i \(0.569977\pi\)
\(24\) 0 0
\(25\) −59.2260 + 102.582i −0.473808 + 0.820659i
\(26\) 100.714 0.759681
\(27\) 0 0
\(28\) 3.98894 + 17.2693i 0.0269228 + 0.116557i
\(29\) 127.390 + 73.5487i 0.815715 + 0.470953i 0.848937 0.528495i \(-0.177243\pi\)
−0.0332217 + 0.999448i \(0.510577\pi\)
\(30\) 0 0
\(31\) −61.1678 + 35.3153i −0.354389 + 0.204607i −0.666617 0.745401i \(-0.732258\pi\)
0.312228 + 0.950007i \(0.398925\pi\)
\(32\) −37.3130 + 21.5427i −0.206127 + 0.119008i
\(33\) 0 0
\(34\) 112.873 + 65.1670i 0.569338 + 0.328707i
\(35\) 65.0355 + 281.557i 0.314086 + 1.35977i
\(36\) 0 0
\(37\) 40.3540 0.179302 0.0896509 0.995973i \(-0.471425\pi\)
0.0896509 + 0.995973i \(0.471425\pi\)
\(38\) 48.2629 83.5938i 0.206034 0.356861i
\(39\) 0 0
\(40\) −284.824 + 164.443i −1.12586 + 0.650018i
\(41\) −179.454 310.824i −0.683562 1.18396i −0.973886 0.227036i \(-0.927096\pi\)
0.290324 0.956928i \(-0.406237\pi\)
\(42\) 0 0
\(43\) −253.886 + 439.743i −0.900400 + 1.55954i −0.0734235 + 0.997301i \(0.523392\pi\)
−0.826976 + 0.562237i \(0.809941\pi\)
\(44\) 51.3519i 0.175945i
\(45\) 0 0
\(46\) 446.867 1.43233
\(47\) −228.160 + 395.185i −0.708098 + 1.22646i 0.257464 + 0.966288i \(0.417113\pi\)
−0.965562 + 0.260174i \(0.916220\pi\)
\(48\) 0 0
\(49\) 284.402 + 191.740i 0.829162 + 0.559009i
\(50\) 307.011 177.253i 0.868359 0.501347i
\(51\) 0 0
\(52\) −27.8904 16.1025i −0.0743789 0.0429427i
\(53\) 213.420i 0.553123i 0.960996 + 0.276561i \(0.0891949\pi\)
−0.960996 + 0.276561i \(0.910805\pi\)
\(54\) 0 0
\(55\) 837.238i 2.05260i
\(56\) −114.094 + 373.333i −0.272258 + 0.890871i
\(57\) 0 0
\(58\) −220.118 381.256i −0.498327 0.863127i
\(59\) 159.593 + 276.424i 0.352157 + 0.609954i 0.986627 0.162993i \(-0.0521149\pi\)
−0.634470 + 0.772947i \(0.718782\pi\)
\(60\) 0 0
\(61\) 303.662 + 175.319i 0.637375 + 0.367989i 0.783603 0.621262i \(-0.213380\pi\)
−0.146227 + 0.989251i \(0.546713\pi\)
\(62\) 211.385 0.432998
\(63\) 0 0
\(64\) −436.974 −0.853466
\(65\) −454.723 262.535i −0.867715 0.500976i
\(66\) 0 0
\(67\) −289.258 501.009i −0.527440 0.913553i −0.999489 0.0319801i \(-0.989819\pi\)
0.472049 0.881572i \(-0.343515\pi\)
\(68\) −20.8382 36.0928i −0.0371618 0.0643662i
\(69\) 0 0
\(70\) 252.762 827.077i 0.431584 1.41221i
\(71\) 787.243i 1.31589i −0.753064 0.657947i \(-0.771425\pi\)
0.753064 0.657947i \(-0.228575\pi\)
\(72\) 0 0
\(73\) 146.373i 0.234681i 0.993092 + 0.117340i \(0.0374368\pi\)
−0.993092 + 0.117340i \(0.962563\pi\)
\(74\) −104.592 60.3863i −0.164305 0.0948617i
\(75\) 0 0
\(76\) −26.7305 + 15.4329i −0.0403447 + 0.0232930i
\(77\) −677.836 726.728i −1.00320 1.07556i
\(78\) 0 0
\(79\) −193.095 + 334.451i −0.274999 + 0.476312i −0.970135 0.242566i \(-0.922011\pi\)
0.695136 + 0.718878i \(0.255344\pi\)
\(80\) 1103.76 1.54254
\(81\) 0 0
\(82\) 1074.15i 1.44659i
\(83\) 98.9043 171.307i 0.130797 0.226547i −0.793187 0.608978i \(-0.791580\pi\)
0.923984 + 0.382431i \(0.124913\pi\)
\(84\) 0 0
\(85\) −339.745 588.455i −0.433535 0.750905i
\(86\) 1316.07 759.835i 1.65018 0.952734i
\(87\) 0 0
\(88\) 565.524 979.517i 0.685058 1.18656i
\(89\) 596.020 0.709865 0.354932 0.934892i \(-0.384504\pi\)
0.354932 + 0.934892i \(0.384504\pi\)
\(90\) 0 0
\(91\) −607.253 + 140.267i −0.699532 + 0.161582i
\(92\) −123.749 71.4466i −0.140236 0.0809654i
\(93\) 0 0
\(94\) 1182.72 682.844i 1.29775 0.749255i
\(95\) −435.812 + 251.616i −0.470667 + 0.271740i
\(96\) 0 0
\(97\) 631.485 + 364.588i 0.661006 + 0.381632i 0.792660 0.609664i \(-0.208696\pi\)
−0.131654 + 0.991296i \(0.542029\pi\)
\(98\) −450.210 922.547i −0.464062 0.950932i
\(99\) 0 0
\(100\) −113.359 −0.113359
\(101\) 286.723 496.619i 0.282476 0.489262i −0.689518 0.724268i \(-0.742178\pi\)
0.971994 + 0.235006i \(0.0755111\pi\)
\(102\) 0 0
\(103\) −1420.04 + 819.860i −1.35845 + 0.784303i −0.989415 0.145111i \(-0.953646\pi\)
−0.369038 + 0.929414i \(0.620313\pi\)
\(104\) −354.665 614.298i −0.334402 0.579201i
\(105\) 0 0
\(106\) 319.365 553.156i 0.292636 0.506861i
\(107\) 377.596i 0.341155i 0.985344 + 0.170577i \(0.0545633\pi\)
−0.985344 + 0.170577i \(0.945437\pi\)
\(108\) 0 0
\(109\) −1166.06 −1.02467 −0.512334 0.858787i \(-0.671219\pi\)
−0.512334 + 0.858787i \(0.671219\pi\)
\(110\) −1252.85 + 2170.01i −1.08595 + 1.88093i
\(111\) 0 0
\(112\) 958.067 893.611i 0.808293 0.753913i
\(113\) 279.069 161.121i 0.232324 0.134132i −0.379320 0.925266i \(-0.623842\pi\)
0.611644 + 0.791133i \(0.290509\pi\)
\(114\) 0 0
\(115\) −2017.60 1164.86i −1.63602 0.944555i
\(116\) 140.773i 0.112676i
\(117\) 0 0
\(118\) 955.269i 0.745252i
\(119\) −771.320 235.722i −0.594175 0.181585i
\(120\) 0 0
\(121\) 774.144 + 1340.86i 0.581626 + 1.00741i
\(122\) −524.700 908.806i −0.389378 0.674422i
\(123\) 0 0
\(124\) −58.5379 33.7969i −0.0423940 0.0244762i
\(125\) 102.169 0.0731064
\(126\) 0 0
\(127\) 1356.31 0.947663 0.473832 0.880615i \(-0.342871\pi\)
0.473832 + 0.880615i \(0.342871\pi\)
\(128\) 1431.08 + 826.236i 0.988211 + 0.570544i
\(129\) 0 0
\(130\) 785.720 + 1360.91i 0.530094 + 0.918150i
\(131\) 978.999 + 1695.68i 0.652943 + 1.13093i 0.982405 + 0.186762i \(0.0597992\pi\)
−0.329462 + 0.944169i \(0.606867\pi\)
\(132\) 0 0
\(133\) −174.577 + 571.242i −0.113818 + 0.372428i
\(134\) 1731.40i 1.11619i
\(135\) 0 0
\(136\) 917.942i 0.578771i
\(137\) 859.395 + 496.172i 0.535935 + 0.309422i 0.743430 0.668814i \(-0.233198\pi\)
−0.207495 + 0.978236i \(0.566531\pi\)
\(138\) 0 0
\(139\) 722.161 416.940i 0.440668 0.254420i −0.263213 0.964738i \(-0.584782\pi\)
0.703881 + 0.710318i \(0.251449\pi\)
\(140\) −202.232 + 188.627i −0.122084 + 0.113870i
\(141\) 0 0
\(142\) −1178.04 + 2040.43i −0.696190 + 1.20584i
\(143\) 1805.73 1.05596
\(144\) 0 0
\(145\) 2295.15i 1.31450i
\(146\) 219.035 379.379i 0.124161 0.215052i
\(147\) 0 0
\(148\) 19.3095 + 33.4450i 0.0107245 + 0.0185754i
\(149\) −1324.03 + 764.428i −0.727978 + 0.420298i −0.817682 0.575670i \(-0.804741\pi\)
0.0897042 + 0.995968i \(0.471408\pi\)
\(150\) 0 0
\(151\) −373.571 + 647.044i −0.201330 + 0.348713i −0.948957 0.315405i \(-0.897860\pi\)
0.747627 + 0.664118i \(0.231193\pi\)
\(152\) −679.831 −0.362774
\(153\) 0 0
\(154\) 669.373 + 2897.90i 0.350257 + 1.51636i
\(155\) −954.398 551.022i −0.494575 0.285543i
\(156\) 0 0
\(157\) 1193.21 688.900i 0.606551 0.350192i −0.165064 0.986283i \(-0.552783\pi\)
0.771614 + 0.636091i \(0.219450\pi\)
\(158\) 1000.95 577.901i 0.503997 0.290983i
\(159\) 0 0
\(160\) −582.193 336.129i −0.287665 0.166083i
\(161\) −2694.37 + 622.360i −1.31892 + 0.304651i
\(162\) 0 0
\(163\) 1900.28 0.913139 0.456569 0.889688i \(-0.349078\pi\)
0.456569 + 0.889688i \(0.349078\pi\)
\(164\) 171.739 297.460i 0.0817715 0.141632i
\(165\) 0 0
\(166\) −512.693 + 296.003i −0.239715 + 0.138399i
\(167\) −836.404 1448.69i −0.387562 0.671277i 0.604559 0.796560i \(-0.293349\pi\)
−0.992121 + 0.125283i \(0.960016\pi\)
\(168\) 0 0
\(169\) −532.274 + 921.925i −0.242273 + 0.419629i
\(170\) 2033.59i 0.917468i
\(171\) 0 0
\(172\) −485.939 −0.215422
\(173\) 496.398 859.787i 0.218153 0.377852i −0.736090 0.676883i \(-0.763330\pi\)
0.954243 + 0.299031i \(0.0966635\pi\)
\(174\) 0 0
\(175\) −1604.25 + 1496.32i −0.692970 + 0.646349i
\(176\) −3287.30 + 1897.92i −1.40790 + 0.812849i
\(177\) 0 0
\(178\) −1544.80 891.891i −0.650493 0.375562i
\(179\) 145.772i 0.0608687i −0.999537 0.0304343i \(-0.990311\pi\)
0.999537 0.0304343i \(-0.00968905\pi\)
\(180\) 0 0
\(181\) 2253.56i 0.925448i −0.886502 0.462724i \(-0.846872\pi\)
0.886502 0.462724i \(-0.153128\pi\)
\(182\) 1783.81 + 545.150i 0.726511 + 0.222029i
\(183\) 0 0
\(184\) −1573.64 2725.63i −0.630492 1.09204i
\(185\) 314.821 + 545.286i 0.125114 + 0.216704i
\(186\) 0 0
\(187\) 2023.72 + 1168.39i 0.791384 + 0.456906i
\(188\) −436.701 −0.169413
\(189\) 0 0
\(190\) 1506.09 0.575069
\(191\) −3201.45 1848.36i −1.21282 0.700222i −0.249448 0.968388i \(-0.580249\pi\)
−0.963373 + 0.268166i \(0.913583\pi\)
\(192\) 0 0
\(193\) 2194.75 + 3801.42i 0.818559 + 1.41779i 0.906744 + 0.421681i \(0.138560\pi\)
−0.0881856 + 0.996104i \(0.528107\pi\)
\(194\) −1091.15 1889.92i −0.403814 0.699426i
\(195\) 0 0
\(196\) −22.8250 + 327.458i −0.00831814 + 0.119336i
\(197\) 2110.35i 0.763229i −0.924322 0.381615i \(-0.875368\pi\)
0.924322 0.381615i \(-0.124632\pi\)
\(198\) 0 0
\(199\) 3443.20i 1.22654i −0.789873 0.613271i \(-0.789854\pi\)
0.789873 0.613271i \(-0.210146\pi\)
\(200\) −2162.28 1248.39i −0.764481 0.441373i
\(201\) 0 0
\(202\) −1486.29 + 858.113i −0.517700 + 0.298894i
\(203\) 1858.18 + 1992.21i 0.642455 + 0.688795i
\(204\) 0 0
\(205\) 2800.02 4849.77i 0.953959 1.65231i
\(206\) 4907.40 1.65978
\(207\) 0 0
\(208\) 2380.54i 0.793562i
\(209\) 865.316 1498.77i 0.286388 0.496039i
\(210\) 0 0
\(211\) −1865.08 3230.41i −0.608518 1.05398i −0.991485 0.130223i \(-0.958431\pi\)
0.382966 0.923762i \(-0.374903\pi\)
\(212\) −176.881 + 102.122i −0.0573028 + 0.0330838i
\(213\) 0 0
\(214\) 565.039 978.676i 0.180492 0.312621i
\(215\) −7922.73 −2.51314
\(216\) 0 0
\(217\) −1274.54 + 294.399i −0.398715 + 0.0920973i
\(218\) 3022.28 + 1744.91i 0.938966 + 0.542112i
\(219\) 0 0
\(220\) 693.895 400.620i 0.212647 0.122772i
\(221\) 1269.16 732.751i 0.386303 0.223032i
\(222\) 0 0
\(223\) 2359.66 + 1362.35i 0.708585 + 0.409101i 0.810537 0.585688i \(-0.199176\pi\)
−0.101952 + 0.994789i \(0.532509\pi\)
\(224\) −777.481 + 179.587i −0.231909 + 0.0535675i
\(225\) 0 0
\(226\) −964.411 −0.283857
\(227\) 2832.72 4906.41i 0.828256 1.43458i −0.0711495 0.997466i \(-0.522667\pi\)
0.899405 0.437116i \(-0.144000\pi\)
\(228\) 0 0
\(229\) 366.827 211.787i 0.105854 0.0611149i −0.446138 0.894964i \(-0.647201\pi\)
0.551992 + 0.833849i \(0.313868\pi\)
\(230\) 3486.22 + 6038.32i 0.999456 + 1.73111i
\(231\) 0 0
\(232\) −1550.29 + 2685.18i −0.438714 + 0.759875i
\(233\) 234.803i 0.0660192i −0.999455 0.0330096i \(-0.989491\pi\)
0.999455 0.0330096i \(-0.0105092\pi\)
\(234\) 0 0
\(235\) −7119.95 −1.97640
\(236\) −152.731 + 264.539i −0.0421270 + 0.0729661i
\(237\) 0 0
\(238\) 1646.42 + 1765.17i 0.448409 + 0.480753i
\(239\) −1575.90 + 909.844i −0.426511 + 0.246246i −0.697859 0.716235i \(-0.745864\pi\)
0.271348 + 0.962481i \(0.412531\pi\)
\(240\) 0 0
\(241\) 2358.44 + 1361.65i 0.630377 + 0.363948i 0.780898 0.624659i \(-0.214762\pi\)
−0.150521 + 0.988607i \(0.548095\pi\)
\(242\) 4633.75i 1.23086i
\(243\) 0 0
\(244\) 335.562i 0.0880417i
\(245\) −372.137 + 5338.86i −0.0970407 + 1.39219i
\(246\) 0 0
\(247\) −542.678 939.946i −0.139797 0.242135i
\(248\) −744.391 1289.32i −0.190600 0.330129i
\(249\) 0 0
\(250\) −264.809 152.887i −0.0669919 0.0386778i
\(251\) 4214.66 1.05987 0.529934 0.848039i \(-0.322217\pi\)
0.529934 + 0.848039i \(0.322217\pi\)
\(252\) 0 0
\(253\) 8011.98 1.99094
\(254\) −3515.38 2029.60i −0.868403 0.501372i
\(255\) 0 0
\(256\) −724.881 1255.53i −0.176973 0.306526i
\(257\) 1388.99 + 2405.80i 0.337132 + 0.583929i 0.983892 0.178764i \(-0.0572099\pi\)
−0.646760 + 0.762693i \(0.723877\pi\)
\(258\) 0 0
\(259\) 714.735 + 218.430i 0.171473 + 0.0524037i
\(260\) 502.494i 0.119859i
\(261\) 0 0
\(262\) 5859.95i 1.38179i
\(263\) 2737.40 + 1580.44i 0.641808 + 0.370548i 0.785311 0.619102i \(-0.212503\pi\)
−0.143503 + 0.989650i \(0.545837\pi\)
\(264\) 0 0
\(265\) −2883.85 + 1664.99i −0.668504 + 0.385961i
\(266\) 1307.29 1219.34i 0.301336 0.281063i
\(267\) 0 0
\(268\) 276.821 479.468i 0.0630953 0.109284i
\(269\) −4337.32 −0.983088 −0.491544 0.870853i \(-0.663567\pi\)
−0.491544 + 0.870853i \(0.663567\pi\)
\(270\) 0 0
\(271\) 8399.64i 1.88281i −0.337276 0.941406i \(-0.609505\pi\)
0.337276 0.941406i \(-0.390495\pi\)
\(272\) −1540.33 + 2667.92i −0.343368 + 0.594730i
\(273\) 0 0
\(274\) −1484.96 2572.02i −0.327407 0.567085i
\(275\) 5504.47 3178.01i 1.20702 0.696876i
\(276\) 0 0
\(277\) 1826.45 3163.50i 0.396176 0.686197i −0.597075 0.802186i \(-0.703670\pi\)
0.993250 + 0.115989i \(0.0370038\pi\)
\(278\) −2495.66 −0.538415
\(279\) 0 0
\(280\) −5934.79 + 1370.85i −1.26668 + 0.292585i
\(281\) 7198.88 + 4156.27i 1.52829 + 0.882358i 0.999434 + 0.0336451i \(0.0107116\pi\)
0.528854 + 0.848713i \(0.322622\pi\)
\(282\) 0 0
\(283\) 1294.63 747.458i 0.271937 0.157003i −0.357831 0.933786i \(-0.616484\pi\)
0.629767 + 0.776784i \(0.283150\pi\)
\(284\) 652.459 376.697i 0.136325 0.0787073i
\(285\) 0 0
\(286\) −4680.20 2702.12i −0.967644 0.558669i
\(287\) −1495.99 6476.55i −0.307684 1.33205i
\(288\) 0 0
\(289\) −3016.50 −0.613983
\(290\) 3434.49 5948.72i 0.695450 1.20455i
\(291\) 0 0
\(292\) −121.313 + 70.0399i −0.0243126 + 0.0140369i
\(293\) 139.838 + 242.207i 0.0278820 + 0.0482931i 0.879630 0.475659i \(-0.157790\pi\)
−0.851748 + 0.523952i \(0.824457\pi\)
\(294\) 0 0
\(295\) −2490.12 + 4313.02i −0.491460 + 0.851233i
\(296\) 850.601i 0.167028i
\(297\) 0 0
\(298\) 4575.60 0.889455
\(299\) 2512.33 4351.49i 0.485926 0.841649i
\(300\) 0 0
\(301\) −6876.98 + 6414.31i −1.31688 + 1.22829i
\(302\) 1936.49 1118.03i 0.368982 0.213032i
\(303\) 0 0
\(304\) 1975.87 + 1140.77i 0.372777 + 0.215223i
\(305\) 5470.99i 1.02711i
\(306\) 0 0
\(307\) 10727.5i 1.99430i 0.0754451 + 0.997150i \(0.475962\pi\)
−0.0754451 + 0.997150i \(0.524038\pi\)
\(308\) 277.959 909.525i 0.0514227 0.168263i
\(309\) 0 0
\(310\) 1649.11 + 2856.35i 0.302140 + 0.523321i
\(311\) 4776.34 + 8272.87i 0.870873 + 1.50840i 0.861095 + 0.508445i \(0.169779\pi\)
0.00977881 + 0.999952i \(0.496887\pi\)
\(312\) 0 0
\(313\) 3195.36 + 1844.84i 0.577037 + 0.333153i 0.759955 0.649976i \(-0.225221\pi\)
−0.182918 + 0.983128i \(0.558554\pi\)
\(314\) −4123.51 −0.741093
\(315\) 0 0
\(316\) −369.586 −0.0657938
\(317\) 652.484 + 376.712i 0.115606 + 0.0667453i 0.556688 0.830722i \(-0.312072\pi\)
−0.441082 + 0.897467i \(0.645405\pi\)
\(318\) 0 0
\(319\) −3946.55 6835.62i −0.692678 1.19975i
\(320\) −3409.04 5904.64i −0.595536 1.03150i
\(321\) 0 0
\(322\) 7914.74 + 2418.82i 1.36979 + 0.418620i
\(323\) 1404.55i 0.241955i
\(324\) 0 0
\(325\) 3986.14i 0.680342i
\(326\) −4925.27 2843.61i −0.836766 0.483107i
\(327\) 0 0
\(328\) 6551.69 3782.62i 1.10292 0.636769i
\(329\) −6180.16 + 5764.38i −1.03563 + 0.965959i
\(330\) 0 0
\(331\) −3119.34 + 5402.86i −0.517989 + 0.897184i 0.481792 + 0.876285i \(0.339986\pi\)
−0.999782 + 0.0208983i \(0.993347\pi\)
\(332\) 189.304 0.0312933
\(333\) 0 0
\(334\) 5006.42i 0.820177i
\(335\) 4513.27 7817.22i 0.736079 1.27493i
\(336\) 0 0
\(337\) −3929.76 6806.55i −0.635216 1.10023i −0.986469 0.163946i \(-0.947578\pi\)
0.351254 0.936280i \(-0.385756\pi\)
\(338\) 2759.16 1593.00i 0.444020 0.256355i
\(339\) 0 0
\(340\) 325.137 563.155i 0.0518619 0.0898275i
\(341\) 3789.96 0.601871
\(342\) 0 0
\(343\) 3999.37 + 4935.45i 0.629579 + 0.776936i
\(344\) −9269.10 5351.52i −1.45278 0.838763i
\(345\) 0 0
\(346\) −2573.19 + 1485.63i −0.399814 + 0.230833i
\(347\) −1142.47 + 659.607i −0.176747 + 0.102045i −0.585763 0.810482i \(-0.699205\pi\)
0.409016 + 0.912527i \(0.365872\pi\)
\(348\) 0 0
\(349\) −4291.07 2477.45i −0.658153 0.379985i 0.133420 0.991060i \(-0.457404\pi\)
−0.791573 + 0.611075i \(0.790738\pi\)
\(350\) 6397.10 1477.64i 0.976970 0.225666i
\(351\) 0 0
\(352\) 2311.92 0.350073
\(353\) −2690.76 + 4660.53i −0.405707 + 0.702706i −0.994404 0.105648i \(-0.966308\pi\)
0.588696 + 0.808354i \(0.299641\pi\)
\(354\) 0 0
\(355\) 10637.7 6141.65i 1.59039 0.918211i
\(356\) 285.197 + 493.975i 0.0424590 + 0.0735411i
\(357\) 0 0
\(358\) −218.135 + 377.820i −0.0322033 + 0.0557777i
\(359\) 3814.03i 0.560715i 0.959896 + 0.280357i \(0.0904530\pi\)
−0.959896 + 0.280357i \(0.909547\pi\)
\(360\) 0 0
\(361\) 5818.78 0.848343
\(362\) −3372.26 + 5840.93i −0.489619 + 0.848046i
\(363\) 0 0
\(364\) −406.824 436.168i −0.0585806 0.0628060i
\(365\) −1977.88 + 1141.93i −0.283635 + 0.163757i
\(366\) 0 0
\(367\) −10883.1 6283.37i −1.54794 0.893704i −0.998299 0.0583038i \(-0.981431\pi\)
−0.549642 0.835400i \(-0.685236\pi\)
\(368\) 10562.4i 1.49621i
\(369\) 0 0
\(370\) 1884.41i 0.264772i
\(371\) −1155.21 + 3780.01i −0.161659 + 0.528972i
\(372\) 0 0
\(373\) 2338.60 + 4050.58i 0.324633 + 0.562281i 0.981438 0.191779i \(-0.0614258\pi\)
−0.656805 + 0.754061i \(0.728092\pi\)
\(374\) −3496.80 6056.63i −0.483463 0.837382i
\(375\) 0 0
\(376\) −8329.90 4809.27i −1.14250 0.659625i
\(377\) −4950.11 −0.676243
\(378\) 0 0
\(379\) −4851.71 −0.657561 −0.328780 0.944406i \(-0.606638\pi\)
−0.328780 + 0.944406i \(0.606638\pi\)
\(380\) −417.074 240.798i −0.0563038 0.0325070i
\(381\) 0 0
\(382\) 5531.81 + 9581.38i 0.740922 + 1.28331i
\(383\) −2456.18 4254.22i −0.327689 0.567573i 0.654364 0.756180i \(-0.272936\pi\)
−0.982053 + 0.188606i \(0.939603\pi\)
\(384\) 0 0
\(385\) 4531.83 14828.8i 0.599905 1.96298i
\(386\) 13137.0i 1.73227i
\(387\) 0 0
\(388\) 697.825i 0.0913059i
\(389\) 4621.95 + 2668.48i 0.602421 + 0.347808i 0.769994 0.638052i \(-0.220259\pi\)
−0.167572 + 0.985860i \(0.553593\pi\)
\(390\) 0 0
\(391\) 5631.24 3251.20i 0.728349 0.420512i
\(392\) −4041.58 + 5994.77i −0.520742 + 0.772401i
\(393\) 0 0
\(394\) −3157.95 + 5469.74i −0.403795 + 0.699394i
\(395\) −6025.71 −0.767561
\(396\) 0 0
\(397\) 1308.17i 0.165378i 0.996575 + 0.0826889i \(0.0263508\pi\)
−0.996575 + 0.0826889i \(0.973649\pi\)
\(398\) −5152.44 + 8924.29i −0.648916 + 1.12396i
\(399\) 0 0
\(400\) 4189.66 + 7256.70i 0.523707 + 0.907087i
\(401\) 1742.21 1005.86i 0.216962 0.125263i −0.387581 0.921836i \(-0.626689\pi\)
0.604543 + 0.796573i \(0.293356\pi\)
\(402\) 0 0
\(403\) 1188.43 2058.42i 0.146898 0.254434i
\(404\) 548.791 0.0675826
\(405\) 0 0
\(406\) −1834.98 7944.12i −0.224306 0.971084i
\(407\) −1875.25 1082.68i −0.228386 0.131858i
\(408\) 0 0
\(409\) 61.5250 35.5215i 0.00743818 0.00429444i −0.496276 0.868165i \(-0.665300\pi\)
0.503714 + 0.863870i \(0.331966\pi\)
\(410\) −14514.5 + 8379.96i −1.74834 + 1.00941i
\(411\) 0 0
\(412\) −1358.98 784.610i −0.162506 0.0938227i
\(413\) 1330.42 + 5759.76i 0.158512 + 0.686245i
\(414\) 0 0
\(415\) 3086.40 0.365073
\(416\) 724.953 1255.66i 0.0854417 0.147989i
\(417\) 0 0
\(418\) −4485.56 + 2589.74i −0.524871 + 0.303034i
\(419\) 1825.15 + 3161.25i 0.212803 + 0.368585i 0.952591 0.304255i \(-0.0984076\pi\)
−0.739788 + 0.672840i \(0.765074\pi\)
\(420\) 0 0
\(421\) −2970.12 + 5144.40i −0.343836 + 0.595541i −0.985142 0.171744i \(-0.945060\pi\)
0.641306 + 0.767285i \(0.278393\pi\)
\(422\) 11163.7i 1.28778i
\(423\) 0 0
\(424\) −4498.57 −0.515259
\(425\) 2579.22 4467.34i 0.294378 0.509877i
\(426\) 0 0
\(427\) 4429.37 + 4748.85i 0.501995 + 0.538204i
\(428\) −312.948 + 180.680i −0.0353432 + 0.0204054i
\(429\) 0 0
\(430\) 20534.6 + 11855.7i 2.30295 + 1.32961i
\(431\) 7508.08i 0.839098i −0.907733 0.419549i \(-0.862188\pi\)
0.907733 0.419549i \(-0.137812\pi\)
\(432\) 0 0
\(433\) 6880.95i 0.763689i 0.924227 + 0.381845i \(0.124711\pi\)
−0.924227 + 0.381845i \(0.875289\pi\)
\(434\) 3743.97 + 1144.19i 0.414092 + 0.126550i
\(435\) 0 0
\(436\) −557.964 966.423i −0.0612882 0.106154i
\(437\) −2407.85 4170.52i −0.263577 0.456529i
\(438\) 0 0
\(439\) 4495.14 + 2595.27i 0.488705 + 0.282154i 0.724037 0.689761i \(-0.242285\pi\)
−0.235332 + 0.971915i \(0.575618\pi\)
\(440\) 17647.7 1.91209
\(441\) 0 0
\(442\) −4385.99 −0.471992
\(443\) 878.510 + 507.208i 0.0942196 + 0.0543977i 0.546369 0.837544i \(-0.316009\pi\)
−0.452150 + 0.891942i \(0.649343\pi\)
\(444\) 0 0
\(445\) 4649.83 + 8053.74i 0.495333 + 0.857942i
\(446\) −4077.27 7062.04i −0.432880 0.749770i
\(447\) 0 0
\(448\) −7739.52 2365.27i −0.816201 0.249439i
\(449\) 6361.05i 0.668589i 0.942469 + 0.334295i \(0.108498\pi\)
−0.942469 + 0.334295i \(0.891502\pi\)
\(450\) 0 0
\(451\) 19258.7i 2.01077i
\(452\) 267.070 + 154.193i 0.0277919 + 0.0160456i
\(453\) 0 0
\(454\) −14684.0 + 8477.83i −1.51796 + 0.876397i
\(455\) −6632.83 7111.25i −0.683410 0.732705i
\(456\) 0 0
\(457\) −2808.03 + 4863.65i −0.287427 + 0.497838i −0.973195 0.229982i \(-0.926133\pi\)
0.685768 + 0.727820i \(0.259467\pi\)
\(458\) −1267.69 −0.129334
\(459\) 0 0
\(460\) 2229.55i 0.225986i
\(461\) −2311.52 + 4003.68i −0.233532 + 0.404490i −0.958845 0.283929i \(-0.908362\pi\)
0.725313 + 0.688420i \(0.241695\pi\)
\(462\) 0 0
\(463\) 2180.04 + 3775.94i 0.218823 + 0.379012i 0.954448 0.298376i \(-0.0964450\pi\)
−0.735626 + 0.677388i \(0.763112\pi\)
\(464\) 9011.59 5202.85i 0.901622 0.520552i
\(465\) 0 0
\(466\) −351.363 + 608.578i −0.0349283 + 0.0604975i
\(467\) 10923.9 1.08243 0.541216 0.840884i \(-0.317964\pi\)
0.541216 + 0.840884i \(0.317964\pi\)
\(468\) 0 0
\(469\) −2411.34 10439.4i −0.237410 1.02782i
\(470\) 18453.9 + 10654.4i 1.81110 + 1.04564i
\(471\) 0 0
\(472\) −5826.58 + 3363.98i −0.568200 + 0.328050i
\(473\) 23596.1 13623.2i 2.29377 1.32431i
\(474\) 0 0
\(475\) −3308.53 1910.18i −0.319591 0.184516i
\(476\) −173.714 752.056i −0.0167272 0.0724169i
\(477\) 0 0
\(478\) 5446.01 0.521118
\(479\) −4797.57 + 8309.64i −0.457634 + 0.792645i −0.998835 0.0482479i \(-0.984636\pi\)
0.541202 + 0.840893i \(0.317970\pi\)
\(480\) 0 0
\(481\) −1176.06 + 678.996i −0.111483 + 0.0643649i
\(482\) −4075.18 7058.41i −0.385102 0.667016i
\(483\) 0 0
\(484\) −740.859 + 1283.21i −0.0695773 + 0.120511i
\(485\) 11377.3i 1.06519i
\(486\) 0 0
\(487\) −8240.46 −0.766758 −0.383379 0.923591i \(-0.625240\pi\)
−0.383379 + 0.923591i \(0.625240\pi\)
\(488\) −3695.46 + 6400.72i −0.342798 + 0.593744i
\(489\) 0 0
\(490\) 8953.66 13280.7i 0.825480 1.22441i
\(491\) −1742.44 + 1006.00i −0.160153 + 0.0924645i −0.577935 0.816083i \(-0.696141\pi\)
0.417781 + 0.908548i \(0.362808\pi\)
\(492\) 0 0
\(493\) −5547.68 3202.96i −0.506806 0.292604i
\(494\) 3248.28i 0.295844i
\(495\) 0 0
\(496\) 4996.42i 0.452310i
\(497\) 4261.21 13943.3i 0.384591 1.25844i
\(498\) 0 0
\(499\) −7186.51 12447.4i −0.644714 1.11668i −0.984367 0.176127i \(-0.943643\pi\)
0.339653 0.940551i \(-0.389690\pi\)
\(500\) 48.8883 + 84.6769i 0.00437270 + 0.00757374i
\(501\) 0 0
\(502\) −10923.8 6306.87i −0.971222 0.560735i
\(503\) −12261.8 −1.08693 −0.543467 0.839430i \(-0.682889\pi\)
−0.543467 + 0.839430i \(0.682889\pi\)
\(504\) 0 0
\(505\) 8947.46 0.788429
\(506\) −20766.0 11989.2i −1.82443 1.05333i
\(507\) 0 0
\(508\) 648.998 + 1124.10i 0.0566824 + 0.0981768i
\(509\) 10985.2 + 19026.9i 0.956602 + 1.65688i 0.730658 + 0.682744i \(0.239213\pi\)
0.225945 + 0.974140i \(0.427453\pi\)
\(510\) 0 0
\(511\) −792.294 + 2592.51i −0.0685891 + 0.224434i
\(512\) 8880.88i 0.766569i
\(513\) 0 0
\(514\) 8314.01i 0.713454i
\(515\) −22156.8 12792.2i −1.89582 1.09455i
\(516\) 0 0
\(517\) 21205.3 12242.9i 1.80388 1.04147i
\(518\) −1525.63 1635.68i −0.129406 0.138741i
\(519\) 0 0
\(520\) 5533.82 9584.87i 0.466681 0.808316i
\(521\) 9869.79 0.829949 0.414974 0.909833i \(-0.363791\pi\)
0.414974 + 0.909833i \(0.363791\pi\)
\(522\) 0 0
\(523\) 4243.21i 0.354766i −0.984142 0.177383i \(-0.943237\pi\)
0.984142 0.177383i \(-0.0567632\pi\)
\(524\) −936.906 + 1622.77i −0.0781087 + 0.135288i
\(525\) 0 0
\(526\) −4729.98 8192.57i −0.392086 0.679112i
\(527\) 2663.79 1537.94i 0.220183 0.127123i
\(528\) 0 0
\(529\) 5063.67 8770.54i 0.416181 0.720846i
\(530\) 9966.06 0.816788
\(531\) 0 0
\(532\) −556.976 + 128.653i −0.0453909 + 0.0104846i
\(533\) 10459.8 + 6038.99i 0.850029 + 0.490765i
\(534\) 0 0
\(535\) −5102.28 + 2945.80i −0.412319 + 0.238053i
\(536\) 10560.5 6097.11i 0.851015 0.491334i
\(537\) 0 0
\(538\) 11241.7 + 6490.41i 0.900865 + 0.520115i
\(539\) −8071.91 16540.5i −0.645050 1.32180i
\(540\) 0 0
\(541\) 3649.63 0.290037 0.145018 0.989429i \(-0.453676\pi\)
0.145018 + 0.989429i \(0.453676\pi\)
\(542\) −12569.3 + 21770.7i −0.996124 + 1.72534i
\(543\) 0 0
\(544\) 1624.94 938.158i 0.128067 0.0739397i
\(545\) −9097.02 15756.5i −0.714997 1.23841i
\(546\) 0 0
\(547\) 758.912 1314.47i 0.0593212 0.102747i −0.834840 0.550493i \(-0.814440\pi\)
0.894161 + 0.447746i \(0.147773\pi\)
\(548\) 949.678i 0.0740296i
\(549\) 0 0
\(550\) −19022.4 −1.47476
\(551\) −2372.12 + 4108.64i −0.183404 + 0.317666i
\(552\) 0 0
\(553\) −5230.36 + 4878.47i −0.402201 + 0.375142i
\(554\) −9467.81 + 5466.24i −0.726081 + 0.419203i
\(555\) 0 0
\(556\) 691.111 + 399.013i 0.0527152 + 0.0304351i
\(557\) 3101.35i 0.235922i −0.993018 0.117961i \(-0.962364\pi\)
0.993018 0.117961i \(-0.0376357\pi\)
\(558\) 0 0
\(559\) 17087.5i 1.29289i
\(560\) 19549.3 + 5974.44i 1.47519 + 0.450833i
\(561\) 0 0
\(562\) −12439.0 21545.0i −0.933643 1.61712i
\(563\) 488.465 + 846.047i 0.0365655 + 0.0633333i 0.883729 0.467999i \(-0.155025\pi\)
−0.847164 + 0.531332i \(0.821692\pi\)
\(564\) 0 0
\(565\) 4354.30 + 2513.96i 0.324224 + 0.187191i
\(566\) −4474.02 −0.332256
\(567\) 0 0
\(568\) 16593.9 1.22581
\(569\) −14997.0 8658.53i −1.10493 0.637934i −0.167421 0.985885i \(-0.553544\pi\)
−0.937513 + 0.347952i \(0.886877\pi\)
\(570\) 0 0
\(571\) −9602.72 16632.4i −0.703785 1.21899i −0.967128 0.254289i \(-0.918158\pi\)
0.263343 0.964702i \(-0.415175\pi\)
\(572\) 864.045 + 1496.57i 0.0631601 + 0.109396i
\(573\) 0 0
\(574\) −5814.20 + 19024.9i −0.422787 + 1.38343i
\(575\) 17686.4i 1.28274i
\(576\) 0 0
\(577\) 19299.1i 1.39243i 0.717832 + 0.696216i \(0.245134\pi\)
−0.717832 + 0.696216i \(0.754866\pi\)
\(578\) 7818.36 + 4513.93i 0.562631 + 0.324835i
\(579\) 0 0
\(580\) −1902.20 + 1098.24i −0.136180 + 0.0786237i
\(581\) 2679.01 2498.78i 0.191298 0.178428i
\(582\) 0 0
\(583\) 5725.95 9917.64i 0.406766 0.704540i
\(584\) −3085.32 −0.218616
\(585\) 0 0
\(586\) 837.023i 0.0590053i
\(587\) 4690.62 8124.39i 0.329817 0.571260i −0.652658 0.757652i \(-0.726346\pi\)
0.982475 + 0.186392i \(0.0596796\pi\)
\(588\) 0 0
\(589\) −1139.00 1972.81i −0.0796804 0.138011i
\(590\) 12908.1 7452.51i 0.900710 0.520025i
\(591\) 0 0
\(592\) 1427.33 2472.20i 0.0990925 0.171633i
\(593\) 21351.5 1.47859 0.739294 0.673383i \(-0.235159\pi\)
0.739294 + 0.673383i \(0.235159\pi\)
\(594\) 0 0
\(595\) −2832.22 12261.5i −0.195142 0.844826i
\(596\) −1267.10 731.562i −0.0870847 0.0502784i
\(597\) 0 0
\(598\) −13023.2 + 7518.98i −0.890569 + 0.514170i
\(599\) −15576.0 + 8992.82i −1.06247 + 0.613417i −0.926114 0.377243i \(-0.876872\pi\)
−0.136355 + 0.990660i \(0.543539\pi\)
\(600\) 0 0
\(601\) 14051.1 + 8112.39i 0.953669 + 0.550601i 0.894219 0.447630i \(-0.147732\pi\)
0.0594502 + 0.998231i \(0.481065\pi\)
\(602\) 27422.6 6334.22i 1.85658 0.428843i
\(603\) 0 0
\(604\) −715.019 −0.0481684
\(605\) −12078.9 + 20921.3i −0.811699 + 1.40590i
\(606\) 0 0
\(607\) −9689.02 + 5593.96i −0.647883 + 0.374055i −0.787645 0.616130i \(-0.788700\pi\)
0.139762 + 0.990185i \(0.455366\pi\)
\(608\) −694.803 1203.43i −0.0463454 0.0802726i
\(609\) 0 0
\(610\) 8186.86 14180.1i 0.543404 0.941203i
\(611\) 15356.1i 1.01676i
\(612\) 0 0
\(613\) 26379.5 1.73810 0.869052 0.494720i \(-0.164729\pi\)
0.869052 + 0.494720i \(0.164729\pi\)
\(614\) 16052.7 27804.2i 1.05511 1.82750i
\(615\) 0 0
\(616\) 15318.3 14287.7i 1.00194 0.934528i
\(617\) −18989.8 + 10963.8i −1.23906 + 0.715371i −0.968902 0.247445i \(-0.920409\pi\)
−0.270157 + 0.962816i \(0.587076\pi\)
\(618\) 0 0
\(619\) 15019.6 + 8671.59i 0.975267 + 0.563071i 0.900838 0.434156i \(-0.142953\pi\)
0.0744291 + 0.997226i \(0.476287\pi\)
\(620\) 1054.66i 0.0683165i
\(621\) 0 0
\(622\) 28589.5i 1.84298i
\(623\) 10556.5 + 3226.15i 0.678870 + 0.207469i
\(624\) 0 0
\(625\) 8200.32 + 14203.4i 0.524820 + 0.909015i
\(626\) −5521.30 9563.17i −0.352517 0.610577i
\(627\) 0 0
\(628\) 1141.91 + 659.280i 0.0725590 + 0.0418919i
\(629\) −1757.37 −0.111401
\(630\) 0 0
\(631\) −30543.8 −1.92699 −0.963495 0.267727i \(-0.913727\pi\)
−0.963495 + 0.267727i \(0.913727\pi\)
\(632\) −7049.71 4070.15i −0.443706 0.256174i
\(633\) 0 0
\(634\) −1127.43 1952.77i −0.0706248 0.122326i
\(635\) 10581.2 + 18327.2i 0.661265 + 1.14534i
\(636\) 0 0
\(637\) −11514.7 802.614i −0.716213 0.0499226i
\(638\) 23622.7i 1.46588i
\(639\) 0 0
\(640\) 25783.4i 1.59247i
\(641\) 513.438 + 296.433i 0.0316374 + 0.0182659i 0.515735 0.856748i \(-0.327519\pi\)
−0.484098 + 0.875014i \(0.660852\pi\)
\(642\) 0 0
\(643\) −27553.5 + 15908.0i −1.68990 + 0.975661i −0.735307 + 0.677735i \(0.762962\pi\)
−0.954589 + 0.297927i \(0.903705\pi\)
\(644\) −1805.07 1935.27i −0.110450 0.118416i
\(645\) 0 0
\(646\) −2101.79 + 3640.41i −0.128009 + 0.221718i
\(647\) −14337.8 −0.871218 −0.435609 0.900136i \(-0.643467\pi\)
−0.435609 + 0.900136i \(0.643467\pi\)
\(648\) 0 0
\(649\) 17127.2i 1.03591i
\(650\) −5964.90 + 10331.5i −0.359943 + 0.623439i
\(651\) 0 0
\(652\) 909.290 + 1574.94i 0.0546174 + 0.0946001i
\(653\) −1310.50 + 756.617i −0.0785356 + 0.0453426i −0.538754 0.842463i \(-0.681105\pi\)
0.460218 + 0.887806i \(0.347771\pi\)
\(654\) 0 0
\(655\) −15275.3 + 26457.5i −0.911228 + 1.57829i
\(656\) −25389.3 −1.51110
\(657\) 0 0
\(658\) 24644.0 5692.40i 1.46007 0.337254i
\(659\) −2743.47 1583.94i −0.162171 0.0936293i 0.416718 0.909036i \(-0.363180\pi\)
−0.578889 + 0.815406i \(0.696514\pi\)
\(660\) 0 0
\(661\) 4954.29 2860.36i 0.291527 0.168313i −0.347103 0.937827i \(-0.612835\pi\)
0.638630 + 0.769514i \(0.279501\pi\)
\(662\) 16169.8 9335.64i 0.949331 0.548097i
\(663\) 0 0
\(664\) 3610.89 + 2084.75i 0.211039 + 0.121843i
\(665\) −9080.90 + 2097.55i −0.529537 + 0.122315i
\(666\) 0 0
\(667\) −21963.5 −1.27501
\(668\) 800.442 1386.41i 0.0463623 0.0803019i
\(669\) 0 0
\(670\) −23395.6 + 13507.4i −1.34903 + 0.778863i
\(671\) −9407.45 16294.2i −0.541238 0.937451i
\(672\) 0 0
\(673\) 3370.28 5837.50i 0.193038 0.334352i −0.753217 0.657772i \(-0.771499\pi\)
0.946256 + 0.323420i \(0.104833\pi\)
\(674\) 23522.2i 1.34427i
\(675\) 0 0
\(676\) −1018.78 −0.0579641
\(677\) −2209.63 + 3827.20i −0.125440 + 0.217269i −0.921905 0.387416i \(-0.873368\pi\)
0.796465 + 0.604685i \(0.206701\pi\)
\(678\) 0 0
\(679\) 9211.16 + 9875.56i 0.520607 + 0.558158i
\(680\) 12403.7 7161.30i 0.699502 0.403858i
\(681\) 0 0
\(682\) −9823.06 5671.35i −0.551532 0.318427i
\(683\) 25188.7i 1.41115i 0.708633 + 0.705577i \(0.249312\pi\)
−0.708633 + 0.705577i \(0.750688\pi\)
\(684\) 0 0
\(685\) 15483.5i 0.863640i
\(686\) −2980.35 18776.7i −0.165875 1.04504i
\(687\) 0 0
\(688\) 17959.9 + 31107.5i 0.995225 + 1.72378i
\(689\) −3591.00 6219.79i −0.198558 0.343912i
\(690\) 0 0
\(691\) −21.1593 12.2163i −0.00116489 0.000672548i 0.499417 0.866361i \(-0.333547\pi\)
−0.500582 + 0.865689i \(0.666881\pi\)
\(692\) 950.111 0.0521933
\(693\) 0 0
\(694\) 3948.18 0.215952
\(695\) 11267.8 + 6505.49i 0.614983 + 0.355061i
\(696\) 0 0
\(697\) 7815.02 + 13536.0i 0.424699 + 0.735600i
\(698\) 7414.57 + 12842.4i 0.402071 + 0.696408i
\(699\) 0 0
\(700\) −2007.77 613.593i −0.108409 0.0331309i
\(701\) 5989.84i 0.322729i 0.986895 + 0.161365i \(0.0515895\pi\)
−0.986895 + 0.161365i \(0.948411\pi\)
\(702\) 0 0
\(703\) 1301.52i 0.0698259i
\(704\) 20306.2 + 11723.8i 1.08710 + 0.627639i
\(705\) 0 0
\(706\) 13948.2 8052.98i 0.743550 0.429289i
\(707\) 7766.45 7243.94i 0.413136 0.385342i
\(708\) 0 0
\(709\) −2214.14 + 3835.00i −0.117283 + 0.203140i −0.918690 0.394979i \(-0.870752\pi\)
0.801407 + 0.598119i \(0.204085\pi\)
\(710\) −36761.8 −1.94316
\(711\) 0 0
\(712\) 12563.2i 0.661271i
\(713\) 5273.02 9133.15i 0.276965 0.479718i
\(714\) 0 0
\(715\) 14087.3 + 24400.0i 0.736835 + 1.27624i
\(716\) 120.814 69.7521i 0.00630592 0.00364073i
\(717\) 0 0
\(718\) 5707.36 9885.44i 0.296653 0.513818i
\(719\) 28053.6 1.45511 0.727554 0.686050i \(-0.240657\pi\)
0.727554 + 0.686050i \(0.240657\pi\)
\(720\) 0 0
\(721\) −29589.0 + 6834.61i −1.52836 + 0.353030i
\(722\) −15081.5 8707.30i −0.777389 0.448826i
\(723\) 0 0
\(724\) 1867.73 1078.34i 0.0958753 0.0553536i
\(725\) −15089.6 + 8711.98i −0.772984 + 0.446282i
\(726\) 0 0
\(727\) −13620.1 7863.54i −0.694828 0.401159i 0.110590 0.993866i \(-0.464726\pi\)
−0.805418 + 0.592707i \(0.798059\pi\)
\(728\) −2956.60 12800.0i −0.150521 0.651646i
\(729\) 0 0
\(730\) 6835.18 0.346550
\(731\) 11056.4 19150.3i 0.559420 0.968945i
\(732\) 0 0
\(733\) 28543.9 16479.8i 1.43833 0.830418i 0.440593 0.897707i \(-0.354768\pi\)
0.997734 + 0.0672892i \(0.0214350\pi\)
\(734\) 18805.0 + 32571.3i 0.945649 + 1.63791i
\(735\) 0 0
\(736\) 3216.60 5571.32i 0.161094 0.279024i
\(737\) 31042.6i 1.55152i
\(738\) 0 0
\(739\) 18483.4 0.920056 0.460028 0.887905i \(-0.347839\pi\)
0.460028 + 0.887905i \(0.347839\pi\)
\(740\) −301.285 + 521.841i −0.0149668 + 0.0259233i
\(741\) 0 0
\(742\) 8650.60 8068.61i 0.427997 0.399202i
\(743\) −27952.9 + 16138.6i −1.38020 + 0.796861i −0.992183 0.124790i \(-0.960174\pi\)
−0.388020 + 0.921651i \(0.626841\pi\)
\(744\) 0 0
\(745\) −20658.8 11927.3i −1.01594 0.586555i
\(746\) 13998.0i 0.687004i
\(747\) 0 0
\(748\) 2236.31i 0.109315i
\(749\) −2043.86 + 6687.83i −0.0997077 + 0.326259i
\(750\) 0 0
\(751\) 12875.3 + 22300.7i 0.625601 + 1.08357i 0.988424 + 0.151715i \(0.0484796\pi\)
−0.362823 + 0.931858i \(0.618187\pi\)
\(752\) 16140.1 + 27955.5i 0.782672 + 1.35563i
\(753\) 0 0
\(754\) 12830.0 + 7407.41i 0.619683 + 0.357774i
\(755\) −11657.6 −0.561939
\(756\) 0 0
\(757\) 14678.2 0.704741 0.352371 0.935861i \(-0.385376\pi\)
0.352371 + 0.935861i \(0.385376\pi\)
\(758\) 12575.0 + 7260.16i 0.602564 + 0.347890i
\(759\) 0 0
\(760\) −5303.68 9186.25i −0.253138 0.438448i
\(761\) −15248.7 26411.6i −0.726369 1.25811i −0.958408 0.285401i \(-0.907873\pi\)
0.232039 0.972706i \(-0.425460\pi\)
\(762\) 0 0
\(763\) −20652.9 6311.71i −0.979927 0.299475i
\(764\) 3537.77i 0.167529i
\(765\) 0 0
\(766\) 14701.8i 0.693470i
\(767\) −9302.19 5370.62i −0.437917 0.252832i
\(768\) 0 0
\(769\) −30619.6 + 17678.2i −1.43585 + 0.828989i −0.997558 0.0698425i \(-0.977750\pi\)
−0.438294 + 0.898832i \(0.644417\pi\)
\(770\) −33936.0 + 31652.8i −1.58827 + 1.48141i
\(771\) 0 0
\(772\) −2100.39 + 3637.98i −0.0979205 + 0.169603i
\(773\) 4097.47 0.190654 0.0953272 0.995446i \(-0.469610\pi\)
0.0953272 + 0.995446i \(0.469610\pi\)
\(774\) 0 0
\(775\) 8366.32i 0.387777i
\(776\) −7684.95 + 13310.7i −0.355507 + 0.615757i
\(777\) 0 0
\(778\) −7986.30 13832.7i −0.368024 0.637436i
\(779\) 10024.8 5787.84i 0.461074 0.266201i
\(780\) 0 0
\(781\) −21121.3 + 36583.2i −0.967709 + 1.67612i
\(782\) −19460.6 −0.889908
\(783\) 0 0
\(784\) 21805.9 10641.4i 0.993343 0.484759i
\(785\) 18617.6 + 10748.9i 0.846484 + 0.488718i
\(786\) 0 0
\(787\) 29205.4 16861.7i 1.32282 0.763730i 0.338642 0.940915i \(-0.390032\pi\)
0.984178 + 0.177185i \(0.0566990\pi\)
\(788\) 1749.04 1009.81i 0.0790696 0.0456509i
\(789\) 0 0
\(790\) 15617.8 + 9016.95i 0.703363 + 0.406087i
\(791\) 5814.88 1343.15i 0.261382 0.0603754i
\(792\) 0 0
\(793\) −11799.7 −0.528396
\(794\) 1957.56 3390.59i 0.0874950 0.151546i
\(795\) 0 0
\(796\) 2853.69 1647.58i 0.127068 0.0733628i
\(797\) 7132.81 + 12354.4i 0.317010 + 0.549077i 0.979863 0.199672i \(-0.0639878\pi\)
−0.662853 + 0.748750i \(0.730654\pi\)
\(798\) 0 0
\(799\) 9936.12 17209.9i 0.439943 0.762004i
\(800\) 5103.54i 0.225547i
\(801\) 0 0
\(802\) −6020.75 −0.265087
\(803\) 3927.12 6801.97i 0.172584 0.298925i
\(804\) 0 0
\(805\) −29429.7 31552.5i −1.28852 1.38146i
\(806\) −6160.48 + 3556.75i −0.269223 + 0.155436i
\(807\) 0 0
\(808\) 10468.0 + 6043.68i 0.455770 + 0.263139i
\(809\) 13916.9i 0.604812i −0.953179 0.302406i \(-0.902210\pi\)
0.953179 0.302406i \(-0.0977898\pi\)
\(810\) 0 0
\(811\) 7296.14i 0.315909i −0.987446 0.157954i \(-0.949510\pi\)
0.987446 0.157954i \(-0.0504899\pi\)
\(812\) −761.980 + 2493.31i −0.0329313 + 0.107756i
\(813\) 0 0
\(814\) 3240.27 + 5612.31i 0.139523 + 0.241660i
\(815\) 14825.0 + 25677.7i 0.637175 + 1.10362i
\(816\) 0 0
\(817\) −14182.8 8188.42i −0.607334 0.350645i
\(818\) −212.619 −0.00908809
\(819\) 0 0
\(820\) 5359.26 0.228236
\(821\) −30269.4 17476.0i −1.28673 0.742897i −0.308664 0.951171i \(-0.599882\pi\)
−0.978070 + 0.208274i \(0.933215\pi\)
\(822\) 0 0
\(823\) −11765.3 20378.1i −0.498314 0.863105i 0.501684 0.865051i \(-0.332714\pi\)
−0.999998 + 0.00194598i \(0.999381\pi\)
\(824\) −17281.4 29932.2i −0.730614 1.26546i
\(825\) 0 0
\(826\) 5170.71 16919.4i 0.217811 0.712712i
\(827\) 40158.9i 1.68859i −0.535880 0.844294i \(-0.680020\pi\)
0.535880 0.844294i \(-0.319980\pi\)
\(828\) 0 0
\(829\) 10739.4i 0.449934i 0.974366 + 0.224967i \(0.0722275\pi\)
−0.974366 + 0.224967i \(0.927773\pi\)
\(830\) −7999.52 4618.52i −0.334539 0.193146i
\(831\) 0 0
\(832\) 12734.9 7352.52i 0.530654 0.306373i
\(833\) −12385.4 8350.05i −0.515160 0.347313i
\(834\) 0 0
\(835\) 13050.4 22603.9i 0.540870 0.936814i
\(836\) 1656.22 0.0685187
\(837\) 0 0
\(838\) 10924.7i 0.450343i
\(839\) 9285.04 16082.2i 0.382068 0.661762i −0.609289 0.792948i \(-0.708545\pi\)
0.991358 + 0.131186i \(0.0418786\pi\)
\(840\) 0 0
\(841\) −1375.69 2382.76i −0.0564062 0.0976983i
\(842\) 15396.3 8889.05i 0.630156 0.363821i
\(843\) 0 0
\(844\) 1784.89 3091.52i 0.0727944 0.126084i
\(845\) −16610.1 −0.676218
\(846\) 0 0
\(847\) 6453.50 + 27939.0i 0.261801 + 1.13341i
\(848\) 13074.7 + 7548.69i 0.529466 + 0.305688i
\(849\) 0 0
\(850\) −13370.0 + 7719.16i −0.539513 + 0.311488i
\(851\) −5218.13 + 3012.69i −0.210194 + 0.121356i
\(852\) 0 0
\(853\) 4663.07 + 2692.22i 0.187175 + 0.108066i 0.590659 0.806921i \(-0.298868\pi\)
−0.403484 + 0.914987i \(0.632201\pi\)
\(854\) −4374.06 18936.5i −0.175266 0.758776i
\(855\) 0 0
\(856\) −7959.13 −0.317801
\(857\) 5528.79 9576.15i 0.220373 0.381698i −0.734548 0.678557i \(-0.762606\pi\)
0.954921 + 0.296859i \(0.0959391\pi\)
\(858\) 0 0
\(859\) 14136.9 8161.94i 0.561519 0.324193i −0.192236 0.981349i \(-0.561574\pi\)
0.753755 + 0.657156i \(0.228241\pi\)
\(860\) −3791.04 6566.28i −0.150318 0.260358i
\(861\) 0 0
\(862\) −11235.2 + 19459.9i −0.443935 + 0.768917i
\(863\) 37617.5i 1.48379i 0.670515 + 0.741896i \(0.266073\pi\)
−0.670515 + 0.741896i \(0.733927\pi\)
\(864\) 0 0
\(865\) 15490.5 0.608895
\(866\) 10296.7 17834.5i 0.404039 0.699816i
\(867\) 0 0
\(868\) −853.864 915.453i −0.0333894 0.0357978i
\(869\) 17946.3 10361.3i 0.700560 0.404468i
\(870\) 0 0
\(871\) 16859.9 + 9734.08i 0.655886 + 0.378676i
\(872\) 24578.8i 0.954523i
\(873\) 0 0
\(874\) 14412.6i 0.557794i
\(875\) 1809.58 + 553.025i 0.0699144 + 0.0213665i
\(876\) 0 0
\(877\) −21070.2 36494.6i −0.811275 1.40517i −0.911972 0.410253i \(-0.865440\pi\)
0.100696 0.994917i \(-0.467893\pi\)
\(878\) −7767.19 13453.2i −0.298553 0.517110i
\(879\) 0 0
\(880\) −51291.6 29613.2i −1.96482 1.13439i
\(881\) −17255.0 −0.659861 −0.329930 0.944005i \(-0.607025\pi\)
−0.329930 + 0.944005i \(0.607025\pi\)
\(882\) 0 0
\(883\) −26461.1 −1.00848 −0.504240 0.863564i \(-0.668227\pi\)
−0.504240 + 0.863564i \(0.668227\pi\)
\(884\) 1214.59 + 701.246i 0.0462118 + 0.0266804i
\(885\) 0 0
\(886\) −1517.98 2629.23i −0.0575595 0.0996959i
\(887\) 9683.24 + 16771.9i 0.366552 + 0.634886i 0.989024 0.147756i \(-0.0472050\pi\)
−0.622472 + 0.782642i \(0.713872\pi\)
\(888\) 0 0
\(889\) 24022.5 + 7341.49i 0.906286 + 0.276969i
\(890\) 27832.3i 1.04825i
\(891\) 0 0
\(892\) 2607.55i 0.0978780i
\(893\) −12745.7 7358.72i −0.477624 0.275756i
\(894\) 0 0
\(895\) 1969.75 1137.23i 0.0735658 0.0424732i
\(896\) 20874.5 + 22380.2i 0.778313 + 0.834452i
\(897\) 0 0
\(898\) 9518.76 16487.0i 0.353725 0.612670i
\(899\) −10389.6 −0.385441
\(900\) 0 0
\(901\) 9294.19i 0.343656i
\(902\) 28818.9 49915.9i 1.06382 1.84259i
\(903\) 0 0
\(904\) 3396.17 + 5882.34i 0.124950 + 0.216420i
\(905\) 30451.4 17581.1i 1.11850 0.645764i
\(906\) 0 0
\(907\) 569.688 986.728i 0.0208558 0.0361232i −0.855409 0.517953i \(-0.826694\pi\)
0.876265 + 0.481830i \(0.160028\pi\)
\(908\) 5421.85 0.198161
\(909\) 0 0
\(910\) 6550.01 + 28356.8i 0.238605 + 1.03299i
\(911\) 7531.25 + 4348.17i 0.273898 + 0.158135i 0.630658 0.776061i \(-0.282785\pi\)
−0.356760 + 0.934196i \(0.616118\pi\)
\(912\) 0 0
\(913\) −9192.18 + 5307.10i −0.333205 + 0.192376i
\(914\) 14556.1 8403.95i 0.526775 0.304133i
\(915\) 0 0
\(916\) 351.055 + 202.682i 0.0126629 + 0.00731090i
\(917\) 8161.24 + 35332.3i 0.293902 + 1.27238i
\(918\) 0 0
\(919\) −2297.46 −0.0824659 −0.0412330 0.999150i \(-0.513129\pi\)
−0.0412330 + 0.999150i \(0.513129\pi\)
\(920\) 24553.5 42527.8i 0.879895 1.52402i
\(921\) 0 0
\(922\) 11982.3 6917.99i 0.428000 0.247106i
\(923\) 13246.1 + 22942.9i 0.472374 + 0.818176i
\(924\) 0 0
\(925\) −2390.01 + 4139.61i −0.0849545 + 0.147146i
\(926\) 13048.9i 0.463083i
\(927\) 0 0
\(928\) −6337.74 −0.224188
\(929\) −24197.9 + 41911.9i −0.854581 + 1.48018i 0.0224522 + 0.999748i \(0.492853\pi\)
−0.877033 + 0.480430i \(0.840481\pi\)
\(930\) 0 0
\(931\) −6184.08 + 9172.67i −0.217696 + 0.322902i
\(932\) 194.603 112.354i 0.00683951 0.00394879i
\(933\) 0 0
\(934\) −28313.1 16346.6i −0.991900 0.572673i
\(935\) 36460.7i 1.27529i
\(936\) 0 0
\(937\) 23667.6i 0.825172i 0.910919 + 0.412586i \(0.135374\pi\)
−0.910919 + 0.412586i \(0.864626\pi\)
\(938\) −9371.76 + 30665.8i −0.326225 + 1.06746i
\(939\) 0 0
\(940\) −3406.91 5900.94i −0.118214 0.204753i
\(941\) −5099.48 8832.56i −0.176661 0.305987i 0.764074 0.645129i \(-0.223196\pi\)
−0.940735 + 0.339143i \(0.889863\pi\)
\(942\) 0 0
\(943\) 46410.0 + 26794.9i 1.60267 + 0.925303i
\(944\) 22579.3 0.778489
\(945\) 0 0
\(946\) −81544.0 −2.80256
\(947\) 2943.58 + 1699.47i 0.101007 + 0.0583163i 0.549652 0.835393i \(-0.314760\pi\)
−0.448646 + 0.893710i \(0.648093\pi\)
\(948\) 0 0
\(949\) −2462.87 4265.82i −0.0842447 0.145916i
\(950\) 5716.84 + 9901.85i 0.195241 + 0.338167i
\(951\) 0 0
\(952\) 4968.67 16258.2i 0.169155 0.553500i
\(953\) 27410.8i 0.931714i −0.884860 0.465857i \(-0.845746\pi\)
0.884860 0.465857i \(-0.154254\pi\)
\(954\) 0 0
\(955\) 57679.7i 1.95442i
\(956\) −1508.14 870.725i −0.0510217 0.0294574i
\(957\) 0 0
\(958\) 24869.3 14358.3i 0.838716 0.484233i
\(959\) 12535.6 + 13439.8i 0.422101 + 0.452547i
\(960\) 0 0
\(961\) −12401.2 + 21479.4i −0.416272 + 0.721005i
\(962\) 4064.23 0.136212
\(963\) 0 0
\(964\) 2606.21i 0.0870750i
\(965\) −34244.6 + 59313.4i −1.14236 + 1.97862i
\(966\) 0 0
\(967\) 18511.5 + 32062.9i 0.615606 + 1.06626i 0.990278 + 0.139103i \(0.0444221\pi\)
−0.374672 + 0.927158i \(0.622245\pi\)
\(968\) −28263.2 + 16317.8i −0.938443 + 0.541810i
\(969\) 0 0
\(970\) 17025.1 29488.4i 0.563550 0.976098i
\(971\) 17050.2 0.563509 0.281754 0.959487i \(-0.409084\pi\)
0.281754 + 0.959487i \(0.409084\pi\)
\(972\) 0 0
\(973\) 15047.5 3475.74i 0.495786 0.114519i
\(974\) 21358.2 + 12331.1i 0.702628 + 0.405662i
\(975\) 0 0
\(976\) 21481.1 12402.1i 0.704501 0.406744i
\(977\) 14180.0 8186.83i 0.464338 0.268086i −0.249528 0.968367i \(-0.580276\pi\)
0.713867 + 0.700282i \(0.246942\pi\)
\(978\) 0 0
\(979\) −27697.1 15990.9i −0.904190 0.522034i
\(980\) −4602.86 + 2246.23i −0.150034 + 0.0732176i
\(981\) 0 0
\(982\) 6021.56 0.195678
\(983\) −10769.1 + 18652.7i −0.349423 + 0.605218i −0.986147 0.165874i \(-0.946956\pi\)
0.636724 + 0.771092i \(0.280289\pi\)
\(984\) 0 0
\(985\) 28516.2 16463.8i 0.922438 0.532570i
\(986\) 9585.89 + 16603.3i 0.309612 + 0.536263i
\(987\) 0 0
\(988\) 519.345 899.533i 0.0167233 0.0289655i
\(989\) 75816.8i 2.43765i
\(990\) 0 0
\(991\) 39248.1 1.25808 0.629040 0.777373i \(-0.283448\pi\)
0.629040 + 0.777373i \(0.283448\pi\)
\(992\) 1521.57 2635.44i 0.0486995 0.0843500i
\(993\) 0 0
\(994\) −31909.5 + 29762.7i −1.01822 + 0.949713i
\(995\) 46526.3 26862.0i 1.48240 0.855862i
\(996\) 0 0
\(997\) 3452.73 + 1993.43i 0.109678 + 0.0633226i 0.553836 0.832626i \(-0.313164\pi\)
−0.444158 + 0.895949i \(0.646497\pi\)
\(998\) 43015.9i 1.36437i
\(999\) 0 0
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 189.4.o.a.62.6 44
3.2 odd 2 63.4.o.a.20.17 44
7.6 odd 2 inner 189.4.o.a.62.5 44
9.2 odd 6 567.4.c.c.566.37 44
9.4 even 3 63.4.o.a.41.18 yes 44
9.5 odd 6 inner 189.4.o.a.125.5 44
9.7 even 3 567.4.c.c.566.8 44
21.20 even 2 63.4.o.a.20.18 yes 44
63.13 odd 6 63.4.o.a.41.17 yes 44
63.20 even 6 567.4.c.c.566.7 44
63.34 odd 6 567.4.c.c.566.38 44
63.41 even 6 inner 189.4.o.a.125.6 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.o.a.20.17 44 3.2 odd 2
63.4.o.a.20.18 yes 44 21.20 even 2
63.4.o.a.41.17 yes 44 63.13 odd 6
63.4.o.a.41.18 yes 44 9.4 even 3
189.4.o.a.62.5 44 7.6 odd 2 inner
189.4.o.a.62.6 44 1.1 even 1 trivial
189.4.o.a.125.5 44 9.5 odd 6 inner
189.4.o.a.125.6 44 63.41 even 6 inner
567.4.c.c.566.7 44 63.20 even 6
567.4.c.c.566.8 44 9.7 even 3
567.4.c.c.566.37 44 9.2 odd 6
567.4.c.c.566.38 44 63.34 odd 6