Properties

Label 189.4.o.a.62.10
Level $189$
Weight $4$
Character 189.62
Analytic conductor $11.151$
Analytic rank $0$
Dimension $44$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [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 62.10
Character \(\chi\) \(=\) 189.62
Dual form 189.4.o.a.125.10

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.628557 - 0.362898i) q^{2} +(-3.73661 - 6.47200i) q^{4} +(5.53318 + 9.58374i) q^{5} +(13.3114 - 12.8765i) q^{7} +11.2304i q^{8} +O(q^{10})\) \(q+(-0.628557 - 0.362898i) q^{2} +(-3.73661 - 6.47200i) q^{4} +(5.53318 + 9.58374i) q^{5} +(13.3114 - 12.8765i) q^{7} +11.2304i q^{8} -8.03191i q^{10} +(-0.219645 - 0.126812i) q^{11} +(-12.3956 + 7.15663i) q^{13} +(-13.0399 + 3.26296i) q^{14} +(-25.8174 + 44.7170i) q^{16} +92.5854 q^{17} -130.104i q^{19} +(41.3506 - 71.6214i) q^{20} +(0.0920395 + 0.159417i) q^{22} +(102.797 - 59.3500i) q^{23} +(1.26793 - 2.19612i) q^{25} +10.3885 q^{26} +(-133.077 - 38.0370i) q^{28} +(-248.320 - 143.368i) q^{29} +(214.225 - 123.683i) q^{31} +(110.262 - 63.6597i) q^{32} +(-58.1952 - 33.5990i) q^{34} +(197.060 + 56.3252i) q^{35} +188.615 q^{37} +(-47.2144 + 81.7777i) q^{38} +(-107.629 + 62.1397i) q^{40} +(-53.2437 - 92.2207i) q^{41} +(-21.5586 + 37.3406i) q^{43} +1.89539i q^{44} -86.1520 q^{46} +(68.8818 - 119.307i) q^{47} +(11.3890 - 342.811i) q^{49} +(-1.59393 + 0.920258i) q^{50} +(92.6354 + 53.4830i) q^{52} +419.280i q^{53} -2.80669i q^{55} +(144.609 + 149.493i) q^{56} +(104.056 + 180.230i) q^{58} +(217.560 + 376.825i) q^{59} +(-163.504 - 94.3989i) q^{61} -179.537 q^{62} +320.670 q^{64} +(-137.175 - 79.1977i) q^{65} +(-185.350 - 321.035i) q^{67} +(-345.956 - 599.213i) q^{68} +(-103.423 - 106.916i) q^{70} +26.1630i q^{71} +728.545i q^{73} +(-118.555 - 68.4480i) q^{74} +(-842.032 + 486.147i) q^{76} +(-4.55669 + 1.14022i) q^{77} +(-48.6779 + 84.3125i) q^{79} -571.409 q^{80} +77.2880i q^{82} +(-401.359 + 695.174i) q^{83} +(512.291 + 887.315i) q^{85} +(27.1017 - 15.6471i) q^{86} +(1.42415 - 2.46670i) q^{88} -236.618 q^{89} +(-72.8512 + 254.878i) q^{91} +(-768.227 - 443.536i) q^{92} +(-86.5924 + 49.9941i) q^{94} +(1246.88 - 719.887i) q^{95} +(1268.09 + 732.133i) q^{97} +(-131.564 + 211.343i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 44 q + 6 q^{2} + 78 q^{4} + 5 q^{7}+O(q^{10}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.628557 0.362898i −0.222229 0.128304i 0.384753 0.923019i \(-0.374287\pi\)
−0.606982 + 0.794716i \(0.707620\pi\)
\(3\) 0 0
\(4\) −3.73661 6.47200i −0.467076 0.809000i
\(5\) 5.53318 + 9.58374i 0.494902 + 0.857196i 0.999983 0.00587635i \(-0.00187051\pi\)
−0.505080 + 0.863072i \(0.668537\pi\)
\(6\) 0 0
\(7\) 13.3114 12.8765i 0.718750 0.695268i
\(8\) 11.2304i 0.496318i
\(9\) 0 0
\(10\) 8.03191i 0.253991i
\(11\) −0.219645 0.126812i −0.00602049 0.00347593i 0.496987 0.867758i \(-0.334440\pi\)
−0.503007 + 0.864282i \(0.667773\pi\)
\(12\) 0 0
\(13\) −12.3956 + 7.15663i −0.264456 + 0.152684i −0.626366 0.779529i \(-0.715458\pi\)
0.361909 + 0.932213i \(0.382125\pi\)
\(14\) −13.0399 + 3.26296i −0.248932 + 0.0622901i
\(15\) 0 0
\(16\) −25.8174 + 44.7170i −0.403397 + 0.698704i
\(17\) 92.5854 1.32090 0.660449 0.750871i \(-0.270366\pi\)
0.660449 + 0.750871i \(0.270366\pi\)
\(18\) 0 0
\(19\) 130.104i 1.57094i −0.618899 0.785470i \(-0.712421\pi\)
0.618899 0.785470i \(-0.287579\pi\)
\(20\) 41.3506 71.6214i 0.462314 0.800752i
\(21\) 0 0
\(22\) 0.0920395 + 0.159417i 0.000891950 + 0.00154490i
\(23\) 102.797 59.3500i 0.931944 0.538058i 0.0445181 0.999009i \(-0.485825\pi\)
0.887426 + 0.460951i \(0.152491\pi\)
\(24\) 0 0
\(25\) 1.26793 2.19612i 0.0101434 0.0175689i
\(26\) 10.3885 0.0783597
\(27\) 0 0
\(28\) −133.077 38.0370i −0.898183 0.256726i
\(29\) −248.320 143.368i −1.59007 0.918025i −0.993294 0.115615i \(-0.963116\pi\)
−0.596772 0.802411i \(-0.703550\pi\)
\(30\) 0 0
\(31\) 214.225 123.683i 1.24116 0.716582i 0.271827 0.962346i \(-0.412372\pi\)
0.969330 + 0.245764i \(0.0790388\pi\)
\(32\) 110.262 63.6597i 0.609117 0.351674i
\(33\) 0 0
\(34\) −58.1952 33.5990i −0.293541 0.169476i
\(35\) 197.060 + 56.3252i 0.951692 + 0.272020i
\(36\) 0 0
\(37\) 188.615 0.838058 0.419029 0.907973i \(-0.362371\pi\)
0.419029 + 0.907973i \(0.362371\pi\)
\(38\) −47.2144 + 81.7777i −0.201558 + 0.349108i
\(39\) 0 0
\(40\) −107.629 + 62.1397i −0.425442 + 0.245629i
\(41\) −53.2437 92.2207i −0.202811 0.351279i 0.746622 0.665249i \(-0.231674\pi\)
−0.949433 + 0.313969i \(0.898341\pi\)
\(42\) 0 0
\(43\) −21.5586 + 37.3406i −0.0764572 + 0.132428i −0.901719 0.432323i \(-0.857694\pi\)
0.825262 + 0.564750i \(0.191028\pi\)
\(44\) 1.89539i 0.00649410i
\(45\) 0 0
\(46\) −86.1520 −0.276139
\(47\) 68.8818 119.307i 0.213776 0.370270i −0.739118 0.673576i \(-0.764757\pi\)
0.952893 + 0.303306i \(0.0980906\pi\)
\(48\) 0 0
\(49\) 11.3890 342.811i 0.0332041 0.999449i
\(50\) −1.59393 + 0.920258i −0.00450832 + 0.00260288i
\(51\) 0 0
\(52\) 92.6354 + 53.4830i 0.247043 + 0.142630i
\(53\) 419.280i 1.08665i 0.839522 + 0.543325i \(0.182835\pi\)
−0.839522 + 0.543325i \(0.817165\pi\)
\(54\) 0 0
\(55\) 2.80669i 0.00688098i
\(56\) 144.609 + 149.493i 0.345074 + 0.356729i
\(57\) 0 0
\(58\) 104.056 + 180.230i 0.235572 + 0.408023i
\(59\) 217.560 + 376.825i 0.480066 + 0.831498i 0.999739 0.0228670i \(-0.00727943\pi\)
−0.519673 + 0.854365i \(0.673946\pi\)
\(60\) 0 0
\(61\) −163.504 94.3989i −0.343189 0.198140i 0.318493 0.947925i \(-0.396823\pi\)
−0.661681 + 0.749785i \(0.730157\pi\)
\(62\) −179.537 −0.367761
\(63\) 0 0
\(64\) 320.670 0.626310
\(65\) −137.175 79.1977i −0.261760 0.151127i
\(66\) 0 0
\(67\) −185.350 321.035i −0.337971 0.585383i 0.646080 0.763270i \(-0.276407\pi\)
−0.984051 + 0.177887i \(0.943074\pi\)
\(68\) −345.956 599.213i −0.616960 1.06861i
\(69\) 0 0
\(70\) −103.423 106.916i −0.176592 0.182556i
\(71\) 26.1630i 0.0437321i 0.999761 + 0.0218661i \(0.00696074\pi\)
−0.999761 + 0.0218661i \(0.993039\pi\)
\(72\) 0 0
\(73\) 728.545i 1.16808i 0.811725 + 0.584039i \(0.198529\pi\)
−0.811725 + 0.584039i \(0.801471\pi\)
\(74\) −118.555 68.4480i −0.186240 0.107526i
\(75\) 0 0
\(76\) −842.032 + 486.147i −1.27089 + 0.733749i
\(77\) −4.55669 + 1.14022i −0.00674393 + 0.00168753i
\(78\) 0 0
\(79\) −48.6779 + 84.3125i −0.0693251 + 0.120075i −0.898604 0.438760i \(-0.855418\pi\)
0.829279 + 0.558834i \(0.188751\pi\)
\(80\) −571.409 −0.798568
\(81\) 0 0
\(82\) 77.2880i 0.104086i
\(83\) −401.359 + 695.174i −0.530781 + 0.919340i 0.468573 + 0.883425i \(0.344768\pi\)
−0.999355 + 0.0359157i \(0.988565\pi\)
\(84\) 0 0
\(85\) 512.291 + 887.315i 0.653715 + 1.13227i
\(86\) 27.1017 15.6471i 0.0339819 0.0196195i
\(87\) 0 0
\(88\) 1.42415 2.46670i 0.00172517 0.00298808i
\(89\) −236.618 −0.281814 −0.140907 0.990023i \(-0.545002\pi\)
−0.140907 + 0.990023i \(0.545002\pi\)
\(90\) 0 0
\(91\) −72.8512 + 254.878i −0.0839218 + 0.293610i
\(92\) −768.227 443.536i −0.870578 0.502628i
\(93\) 0 0
\(94\) −86.5924 + 49.9941i −0.0950141 + 0.0548564i
\(95\) 1246.88 719.887i 1.34660 0.777462i
\(96\) 0 0
\(97\) 1268.09 + 732.133i 1.32737 + 0.766360i 0.984893 0.173165i \(-0.0553995\pi\)
0.342481 + 0.939525i \(0.388733\pi\)
\(98\) −131.564 + 211.343i −0.135612 + 0.217846i
\(99\) 0 0
\(100\) −18.9510 −0.0189510
\(101\) −783.722 + 1357.45i −0.772112 + 1.33734i 0.164292 + 0.986412i \(0.447466\pi\)
−0.936404 + 0.350925i \(0.885867\pi\)
\(102\) 0 0
\(103\) −86.8588 + 50.1479i −0.0830918 + 0.0479730i −0.540970 0.841042i \(-0.681943\pi\)
0.457878 + 0.889015i \(0.348609\pi\)
\(104\) −80.3717 139.208i −0.0757798 0.131254i
\(105\) 0 0
\(106\) 152.156 263.541i 0.139421 0.241485i
\(107\) 553.381i 0.499976i 0.968249 + 0.249988i \(0.0804266\pi\)
−0.968249 + 0.249988i \(0.919573\pi\)
\(108\) 0 0
\(109\) −400.600 −0.352023 −0.176012 0.984388i \(-0.556320\pi\)
−0.176012 + 0.984388i \(0.556320\pi\)
\(110\) −1.01854 + 1.76417i −0.000882856 + 0.00152915i
\(111\) 0 0
\(112\) 232.134 + 927.687i 0.195845 + 0.782663i
\(113\) 617.417 356.466i 0.513997 0.296756i −0.220478 0.975392i \(-0.570762\pi\)
0.734475 + 0.678635i \(0.237428\pi\)
\(114\) 0 0
\(115\) 1137.59 + 656.788i 0.922442 + 0.532572i
\(116\) 2142.84i 1.71515i
\(117\) 0 0
\(118\) 315.808i 0.246377i
\(119\) 1232.45 1192.18i 0.949396 0.918378i
\(120\) 0 0
\(121\) −665.468 1152.62i −0.499976 0.865984i
\(122\) 68.5143 + 118.670i 0.0508442 + 0.0880648i
\(123\) 0 0
\(124\) −1600.95 924.307i −1.15943 0.669397i
\(125\) 1411.36 1.00988
\(126\) 0 0
\(127\) 102.170 0.0713865 0.0356932 0.999363i \(-0.488636\pi\)
0.0356932 + 0.999363i \(0.488636\pi\)
\(128\) −1083.65 625.648i −0.748300 0.432031i
\(129\) 0 0
\(130\) 57.4814 + 99.5606i 0.0387804 + 0.0671696i
\(131\) −236.423 409.496i −0.157682 0.273113i 0.776350 0.630302i \(-0.217069\pi\)
−0.934032 + 0.357188i \(0.883735\pi\)
\(132\) 0 0
\(133\) −1675.29 1731.87i −1.09222 1.12911i
\(134\) 269.052i 0.173452i
\(135\) 0 0
\(136\) 1039.77i 0.655585i
\(137\) −2268.47 1309.70i −1.41466 0.816756i −0.418840 0.908060i \(-0.637563\pi\)
−0.995823 + 0.0913039i \(0.970897\pi\)
\(138\) 0 0
\(139\) 1075.92 621.185i 0.656537 0.379052i −0.134419 0.990925i \(-0.542917\pi\)
0.790956 + 0.611873i \(0.209583\pi\)
\(140\) −371.800 1485.84i −0.224449 0.896973i
\(141\) 0 0
\(142\) 9.49451 16.4450i 0.00561100 0.00971853i
\(143\) 3.63018 0.00212287
\(144\) 0 0
\(145\) 3173.12i 1.81733i
\(146\) 264.387 457.932i 0.149869 0.259581i
\(147\) 0 0
\(148\) −704.781 1220.72i −0.391437 0.677989i
\(149\) −973.891 + 562.276i −0.535465 + 0.309151i −0.743239 0.669026i \(-0.766711\pi\)
0.207774 + 0.978177i \(0.433378\pi\)
\(150\) 0 0
\(151\) 237.798 411.879i 0.128157 0.221975i −0.794805 0.606864i \(-0.792427\pi\)
0.922963 + 0.384889i \(0.125760\pi\)
\(152\) 1461.12 0.779686
\(153\) 0 0
\(154\) 3.27792 + 0.936921i 0.00171521 + 0.000490255i
\(155\) 2370.68 + 1368.71i 1.22850 + 0.709276i
\(156\) 0 0
\(157\) 1674.30 966.660i 0.851108 0.491388i −0.00991644 0.999951i \(-0.503157\pi\)
0.861025 + 0.508563i \(0.169823\pi\)
\(158\) 61.1936 35.3302i 0.0308121 0.0177893i
\(159\) 0 0
\(160\) 1220.20 + 704.481i 0.602906 + 0.348088i
\(161\) 604.156 2113.71i 0.295740 1.03468i
\(162\) 0 0
\(163\) −743.323 −0.357187 −0.178594 0.983923i \(-0.557155\pi\)
−0.178594 + 0.983923i \(0.557155\pi\)
\(164\) −397.902 + 689.186i −0.189457 + 0.328149i
\(165\) 0 0
\(166\) 504.554 291.304i 0.235910 0.136202i
\(167\) 1811.60 + 3137.78i 0.839435 + 1.45394i 0.890368 + 0.455242i \(0.150447\pi\)
−0.0509327 + 0.998702i \(0.516219\pi\)
\(168\) 0 0
\(169\) −996.065 + 1725.24i −0.453375 + 0.785269i
\(170\) 743.638i 0.335496i
\(171\) 0 0
\(172\) 322.225 0.142845
\(173\) 1648.50 2855.29i 0.724470 1.25482i −0.234722 0.972063i \(-0.575418\pi\)
0.959192 0.282756i \(-0.0912488\pi\)
\(174\) 0 0
\(175\) −11.4005 45.5601i −0.00492453 0.0196801i
\(176\) 11.3413 6.54791i 0.00485729 0.00280436i
\(177\) 0 0
\(178\) 148.728 + 85.8680i 0.0626270 + 0.0361577i
\(179\) 2746.77i 1.14695i −0.819225 0.573473i \(-0.805596\pi\)
0.819225 0.573473i \(-0.194404\pi\)
\(180\) 0 0
\(181\) 738.434i 0.303245i −0.988438 0.151622i \(-0.951550\pi\)
0.988438 0.151622i \(-0.0484498\pi\)
\(182\) 138.286 133.768i 0.0563210 0.0544810i
\(183\) 0 0
\(184\) 666.524 + 1154.45i 0.267048 + 0.462541i
\(185\) 1043.64 + 1807.64i 0.414757 + 0.718380i
\(186\) 0 0
\(187\) −20.3359 11.7409i −0.00795245 0.00459135i
\(188\) −1029.54 −0.399398
\(189\) 0 0
\(190\) −1044.98 −0.399005
\(191\) 2879.69 + 1662.59i 1.09093 + 0.629848i 0.933823 0.357734i \(-0.116451\pi\)
0.157105 + 0.987582i \(0.449784\pi\)
\(192\) 0 0
\(193\) 1660.75 + 2876.50i 0.619394 + 1.07282i 0.989596 + 0.143871i \(0.0459550\pi\)
−0.370202 + 0.928951i \(0.620712\pi\)
\(194\) −531.379 920.376i −0.196654 0.340614i
\(195\) 0 0
\(196\) −2261.23 + 1207.24i −0.824063 + 0.439957i
\(197\) 501.482i 0.181366i −0.995880 0.0906830i \(-0.971095\pi\)
0.995880 0.0906830i \(-0.0289050\pi\)
\(198\) 0 0
\(199\) 4067.59i 1.44896i 0.689294 + 0.724482i \(0.257921\pi\)
−0.689294 + 0.724482i \(0.742079\pi\)
\(200\) 24.6633 + 14.2393i 0.00871978 + 0.00503437i
\(201\) 0 0
\(202\) 985.229 568.822i 0.343171 0.198130i
\(203\) −5151.58 + 1289.08i −1.78113 + 0.445692i
\(204\) 0 0
\(205\) 589.213 1020.55i 0.200744 0.347698i
\(206\) 72.7943 0.0246205
\(207\) 0 0
\(208\) 739.062i 0.246369i
\(209\) −16.4987 + 28.5766i −0.00546048 + 0.00945783i
\(210\) 0 0
\(211\) −2456.95 4255.56i −0.801628 1.38846i −0.918544 0.395319i \(-0.870634\pi\)
0.116916 0.993142i \(-0.462699\pi\)
\(212\) 2713.58 1566.68i 0.879100 0.507549i
\(213\) 0 0
\(214\) 200.821 347.832i 0.0641487 0.111109i
\(215\) −477.150 −0.151355
\(216\) 0 0
\(217\) 1259.03 4404.87i 0.393865 1.37798i
\(218\) 251.800 + 145.377i 0.0782296 + 0.0451659i
\(219\) 0 0
\(220\) −18.1649 + 10.4875i −0.00556672 + 0.00321394i
\(221\) −1147.66 + 662.599i −0.349320 + 0.201680i
\(222\) 0 0
\(223\) −1033.31 596.580i −0.310293 0.179148i 0.336765 0.941589i \(-0.390667\pi\)
−0.647058 + 0.762441i \(0.724001\pi\)
\(224\) 648.027 2267.20i 0.193295 0.676265i
\(225\) 0 0
\(226\) −517.443 −0.152300
\(227\) −2804.31 + 4857.22i −0.819951 + 1.42020i 0.0857665 + 0.996315i \(0.472666\pi\)
−0.905718 + 0.423882i \(0.860667\pi\)
\(228\) 0 0
\(229\) −4618.56 + 2666.53i −1.33276 + 0.769472i −0.985722 0.168378i \(-0.946147\pi\)
−0.347042 + 0.937850i \(0.612814\pi\)
\(230\) −476.694 825.658i −0.136662 0.236706i
\(231\) 0 0
\(232\) 1610.08 2788.73i 0.455632 0.789179i
\(233\) 111.828i 0.0314424i 0.999876 + 0.0157212i \(0.00500442\pi\)
−0.999876 + 0.0157212i \(0.994996\pi\)
\(234\) 0 0
\(235\) 1524.54 0.423192
\(236\) 1625.87 2816.09i 0.448455 0.776746i
\(237\) 0 0
\(238\) −1207.30 + 302.102i −0.328814 + 0.0822789i
\(239\) −4132.66 + 2385.99i −1.11849 + 0.645762i −0.941016 0.338363i \(-0.890127\pi\)
−0.177477 + 0.984125i \(0.556794\pi\)
\(240\) 0 0
\(241\) 4621.37 + 2668.15i 1.23522 + 0.713156i 0.968114 0.250510i \(-0.0805984\pi\)
0.267109 + 0.963666i \(0.413932\pi\)
\(242\) 965.987i 0.256595i
\(243\) 0 0
\(244\) 1410.93i 0.370186i
\(245\) 3348.43 1787.68i 0.873156 0.466167i
\(246\) 0 0
\(247\) 931.104 + 1612.72i 0.239857 + 0.415445i
\(248\) 1389.00 + 2405.83i 0.355653 + 0.616008i
\(249\) 0 0
\(250\) −887.119 512.178i −0.224425 0.129572i
\(251\) −3081.73 −0.774970 −0.387485 0.921876i \(-0.626656\pi\)
−0.387485 + 0.921876i \(0.626656\pi\)
\(252\) 0 0
\(253\) −30.1052 −0.00748101
\(254\) −64.2194 37.0771i −0.0158641 0.00915915i
\(255\) 0 0
\(256\) −828.589 1435.16i −0.202292 0.350381i
\(257\) −1067.55 1849.05i −0.259113 0.448797i 0.706892 0.707322i \(-0.250097\pi\)
−0.966005 + 0.258525i \(0.916764\pi\)
\(258\) 0 0
\(259\) 2510.74 2428.71i 0.602354 0.582675i
\(260\) 1183.72i 0.282352i
\(261\) 0 0
\(262\) 343.189i 0.0809248i
\(263\) 1429.14 + 825.115i 0.335075 + 0.193455i 0.658092 0.752938i \(-0.271364\pi\)
−0.323017 + 0.946393i \(0.604697\pi\)
\(264\) 0 0
\(265\) −4018.27 + 2319.95i −0.931473 + 0.537786i
\(266\) 424.523 + 1696.54i 0.0978541 + 0.391058i
\(267\) 0 0
\(268\) −1385.16 + 2399.16i −0.315716 + 0.546837i
\(269\) −5477.73 −1.24157 −0.620787 0.783979i \(-0.713187\pi\)
−0.620787 + 0.783979i \(0.713187\pi\)
\(270\) 0 0
\(271\) 3607.16i 0.808558i 0.914636 + 0.404279i \(0.132477\pi\)
−0.914636 + 0.404279i \(0.867523\pi\)
\(272\) −2390.31 + 4140.15i −0.532846 + 0.922916i
\(273\) 0 0
\(274\) 950.577 + 1646.45i 0.209586 + 0.363013i
\(275\) −0.556988 + 0.321577i −0.000122137 + 7.05158e-5i
\(276\) 0 0
\(277\) −1488.99 + 2579.00i −0.322977 + 0.559413i −0.981101 0.193497i \(-0.938017\pi\)
0.658124 + 0.752910i \(0.271350\pi\)
\(278\) −901.707 −0.194535
\(279\) 0 0
\(280\) −632.554 + 2213.06i −0.135008 + 0.472342i
\(281\) 4936.36 + 2850.01i 1.04797 + 0.605043i 0.922079 0.387002i \(-0.126489\pi\)
0.125886 + 0.992045i \(0.459823\pi\)
\(282\) 0 0
\(283\) 476.719 275.234i 0.100134 0.0578125i −0.449097 0.893483i \(-0.648254\pi\)
0.549231 + 0.835671i \(0.314921\pi\)
\(284\) 169.327 97.7611i 0.0353793 0.0204262i
\(285\) 0 0
\(286\) −2.28178 1.31739i −0.000471763 0.000272373i
\(287\) −1896.23 541.996i −0.390004 0.111474i
\(288\) 0 0
\(289\) 3659.06 0.744771
\(290\) −1151.52 + 1994.49i −0.233170 + 0.403863i
\(291\) 0 0
\(292\) 4715.14 2722.29i 0.944976 0.545582i
\(293\) −3915.00 6780.98i −0.780603 1.35204i −0.931591 0.363508i \(-0.881579\pi\)
0.150988 0.988536i \(-0.451754\pi\)
\(294\) 0 0
\(295\) −2407.59 + 4170.08i −0.475171 + 0.823021i
\(296\) 2118.22i 0.415943i
\(297\) 0 0
\(298\) 816.195 0.158661
\(299\) −849.492 + 1471.36i −0.164306 + 0.284586i
\(300\) 0 0
\(301\) 193.842 + 774.658i 0.0371192 + 0.148341i
\(302\) −298.940 + 172.593i −0.0569604 + 0.0328861i
\(303\) 0 0
\(304\) 5817.86 + 3358.94i 1.09762 + 0.633712i
\(305\) 2089.30i 0.392240i
\(306\) 0 0
\(307\) 5845.06i 1.08663i 0.839529 + 0.543315i \(0.182831\pi\)
−0.839529 + 0.543315i \(0.817169\pi\)
\(308\) 24.4060 + 25.2303i 0.00451514 + 0.00466764i
\(309\) 0 0
\(310\) −993.407 1720.63i −0.182006 0.315243i
\(311\) 2909.85 + 5040.01i 0.530554 + 0.918947i 0.999364 + 0.0356482i \(0.0113496\pi\)
−0.468810 + 0.883299i \(0.655317\pi\)
\(312\) 0 0
\(313\) −5754.23 3322.21i −1.03913 0.599943i −0.119545 0.992829i \(-0.538143\pi\)
−0.919587 + 0.392886i \(0.871477\pi\)
\(314\) −1403.19 −0.252187
\(315\) 0 0
\(316\) 727.561 0.129521
\(317\) −5206.82 3006.16i −0.922536 0.532626i −0.0380927 0.999274i \(-0.512128\pi\)
−0.884443 + 0.466648i \(0.845462\pi\)
\(318\) 0 0
\(319\) 36.3615 + 62.9800i 0.00638198 + 0.0110539i
\(320\) 1774.33 + 3073.22i 0.309962 + 0.536870i
\(321\) 0 0
\(322\) −1146.81 + 1109.34i −0.198475 + 0.191991i
\(323\) 12045.7i 2.07505i
\(324\) 0 0
\(325\) 36.2964i 0.00619496i
\(326\) 467.221 + 269.750i 0.0793772 + 0.0458285i
\(327\) 0 0
\(328\) 1035.68 597.947i 0.174346 0.100659i
\(329\) −619.344 2475.11i −0.103786 0.414763i
\(330\) 0 0
\(331\) 1371.24 2375.06i 0.227705 0.394397i −0.729422 0.684064i \(-0.760211\pi\)
0.957128 + 0.289667i \(0.0935444\pi\)
\(332\) 5998.89 0.991662
\(333\) 0 0
\(334\) 2629.70i 0.430811i
\(335\) 2051.14 3552.68i 0.334525 0.579414i
\(336\) 0 0
\(337\) 1953.27 + 3383.16i 0.315731 + 0.546862i 0.979593 0.200993i \(-0.0644169\pi\)
−0.663862 + 0.747856i \(0.731084\pi\)
\(338\) 1252.17 722.940i 0.201506 0.116339i
\(339\) 0 0
\(340\) 3828.47 6631.10i 0.610670 1.05771i
\(341\) −62.7377 −0.00996316
\(342\) 0 0
\(343\) −4262.62 4709.96i −0.671019 0.741440i
\(344\) −419.350 242.112i −0.0657262 0.0379471i
\(345\) 0 0
\(346\) −2072.36 + 1196.48i −0.321996 + 0.185904i
\(347\) 509.871 294.374i 0.0788799 0.0455413i −0.460041 0.887898i \(-0.652165\pi\)
0.538921 + 0.842356i \(0.318832\pi\)
\(348\) 0 0
\(349\) −6360.33 3672.14i −0.975532 0.563224i −0.0746138 0.997213i \(-0.523772\pi\)
−0.900918 + 0.433989i \(0.857106\pi\)
\(350\) −9.36780 + 32.7743i −0.00143066 + 0.00500532i
\(351\) 0 0
\(352\) −32.2913 −0.00488957
\(353\) 4370.77 7570.40i 0.659016 1.14145i −0.321855 0.946789i \(-0.604306\pi\)
0.980871 0.194660i \(-0.0623604\pi\)
\(354\) 0 0
\(355\) −250.740 + 144.765i −0.0374870 + 0.0216431i
\(356\) 884.148 + 1531.39i 0.131628 + 0.227987i
\(357\) 0 0
\(358\) −996.797 + 1726.50i −0.147157 + 0.254884i
\(359\) 7817.81i 1.14933i 0.818390 + 0.574663i \(0.194867\pi\)
−0.818390 + 0.574663i \(0.805133\pi\)
\(360\) 0 0
\(361\) −10068.0 −1.46785
\(362\) −267.976 + 464.148i −0.0389075 + 0.0673897i
\(363\) 0 0
\(364\) 1921.79 480.887i 0.276728 0.0692454i
\(365\) −6982.19 + 4031.17i −1.00127 + 0.578085i
\(366\) 0 0
\(367\) −2084.12 1203.27i −0.296431 0.171145i 0.344407 0.938820i \(-0.388080\pi\)
−0.640839 + 0.767676i \(0.721413\pi\)
\(368\) 6129.05i 0.868204i
\(369\) 0 0
\(370\) 1514.94i 0.212859i
\(371\) 5398.87 + 5581.22i 0.755514 + 0.781031i
\(372\) 0 0
\(373\) −2185.08 3784.67i −0.303322 0.525370i 0.673564 0.739129i \(-0.264763\pi\)
−0.976886 + 0.213759i \(0.931429\pi\)
\(374\) 8.52152 + 14.7597i 0.00117817 + 0.00204066i
\(375\) 0 0
\(376\) 1339.86 + 773.570i 0.183772 + 0.106101i
\(377\) 4104.12 0.560671
\(378\) 0 0
\(379\) 11260.9 1.52620 0.763102 0.646278i \(-0.223675\pi\)
0.763102 + 0.646278i \(0.223675\pi\)
\(380\) −9318.22 5379.88i −1.25793 0.726268i
\(381\) 0 0
\(382\) −1206.70 2090.07i −0.161624 0.279940i
\(383\) −1486.57 2574.82i −0.198330 0.343517i 0.749657 0.661826i \(-0.230218\pi\)
−0.947987 + 0.318309i \(0.896885\pi\)
\(384\) 0 0
\(385\) −36.1405 37.3611i −0.00478413 0.00494571i
\(386\) 2410.72i 0.317882i
\(387\) 0 0
\(388\) 10942.8i 1.43179i
\(389\) 5714.27 + 3299.13i 0.744794 + 0.430007i 0.823810 0.566866i \(-0.191844\pi\)
−0.0790159 + 0.996873i \(0.525178\pi\)
\(390\) 0 0
\(391\) 9517.53 5494.95i 1.23100 0.710720i
\(392\) 3849.90 + 127.903i 0.496044 + 0.0164798i
\(393\) 0 0
\(394\) −181.987 + 315.210i −0.0232699 + 0.0403047i
\(395\) −1077.37 −0.137237
\(396\) 0 0
\(397\) 5908.48i 0.746947i 0.927641 + 0.373474i \(0.121833\pi\)
−0.927641 + 0.373474i \(0.878167\pi\)
\(398\) 1476.12 2556.71i 0.185907 0.322001i
\(399\) 0 0
\(400\) 65.4693 + 113.396i 0.00818366 + 0.0141745i
\(401\) 4847.53 2798.72i 0.603676 0.348532i −0.166811 0.985989i \(-0.553347\pi\)
0.770486 + 0.637457i \(0.220014\pi\)
\(402\) 0 0
\(403\) −1770.30 + 3066.25i −0.218821 + 0.379009i
\(404\) 11713.9 1.44254
\(405\) 0 0
\(406\) 3705.87 + 1059.24i 0.453003 + 0.129481i
\(407\) −41.4283 23.9187i −0.00504552 0.00291303i
\(408\) 0 0
\(409\) −948.568 + 547.656i −0.114679 + 0.0662099i −0.556242 0.831020i \(-0.687757\pi\)
0.441563 + 0.897230i \(0.354424\pi\)
\(410\) −740.708 + 427.648i −0.0892219 + 0.0515123i
\(411\) 0 0
\(412\) 649.115 + 374.767i 0.0776204 + 0.0448141i
\(413\) 7748.24 + 2214.66i 0.923162 + 0.263865i
\(414\) 0 0
\(415\) −8883.16 −1.05074
\(416\) −911.178 + 1578.21i −0.107390 + 0.186005i
\(417\) 0 0
\(418\) 20.7408 11.9747i 0.00242695 0.00140120i
\(419\) 6796.78 + 11772.4i 0.792468 + 1.37260i 0.924434 + 0.381341i \(0.124538\pi\)
−0.131966 + 0.991254i \(0.542129\pi\)
\(420\) 0 0
\(421\) 2842.13 4922.72i 0.329019 0.569878i −0.653298 0.757101i \(-0.726615\pi\)
0.982318 + 0.187222i \(0.0599485\pi\)
\(422\) 3566.49i 0.411407i
\(423\) 0 0
\(424\) −4708.68 −0.539324
\(425\) 117.392 203.329i 0.0133984 0.0232068i
\(426\) 0 0
\(427\) −3392.00 + 848.778i −0.384427 + 0.0961949i
\(428\) 3581.48 2067.77i 0.404480 0.233527i
\(429\) 0 0
\(430\) 299.916 + 173.157i 0.0336355 + 0.0194194i
\(431\) 4806.22i 0.537140i −0.963260 0.268570i \(-0.913449\pi\)
0.963260 0.268570i \(-0.0865511\pi\)
\(432\) 0 0
\(433\) 9621.49i 1.06785i −0.845532 0.533925i \(-0.820716\pi\)
0.845532 0.533925i \(-0.179284\pi\)
\(434\) −2389.89 + 2311.81i −0.264328 + 0.255692i
\(435\) 0 0
\(436\) 1496.89 + 2592.68i 0.164422 + 0.284787i
\(437\) −7721.67 13374.3i −0.845257 1.46403i
\(438\) 0 0
\(439\) 11200.0 + 6466.31i 1.21764 + 0.703007i 0.964413 0.264399i \(-0.0851737\pi\)
0.253230 + 0.967406i \(0.418507\pi\)
\(440\) 31.5202 0.00341516
\(441\) 0 0
\(442\) 961.823 0.103505
\(443\) −11401.0 6582.35i −1.22275 0.705953i −0.257244 0.966347i \(-0.582814\pi\)
−0.965502 + 0.260394i \(0.916148\pi\)
\(444\) 0 0
\(445\) −1309.25 2267.68i −0.139470 0.241569i
\(446\) 432.995 + 749.969i 0.0459706 + 0.0796235i
\(447\) 0 0
\(448\) 4268.59 4129.13i 0.450160 0.435453i
\(449\) 7787.86i 0.818557i −0.912410 0.409278i \(-0.865781\pi\)
0.912410 0.409278i \(-0.134219\pi\)
\(450\) 0 0
\(451\) 27.0077i 0.00281983i
\(452\) −4614.09 2663.95i −0.480152 0.277216i
\(453\) 0 0
\(454\) 3525.34 2035.36i 0.364433 0.210406i
\(455\) −2845.78 + 712.098i −0.293214 + 0.0733707i
\(456\) 0 0
\(457\) −2408.56 + 4171.76i −0.246538 + 0.427017i −0.962563 0.271058i \(-0.912626\pi\)
0.716025 + 0.698075i \(0.245960\pi\)
\(458\) 3870.71 0.394904
\(459\) 0 0
\(460\) 9816.65i 0.995008i
\(461\) 25.6446 44.4177i 0.00259086 0.00448750i −0.864727 0.502242i \(-0.832509\pi\)
0.867318 + 0.497755i \(0.165842\pi\)
\(462\) 0 0
\(463\) 4787.43 + 8292.07i 0.480542 + 0.832322i 0.999751 0.0223247i \(-0.00710677\pi\)
−0.519209 + 0.854647i \(0.673773\pi\)
\(464\) 12822.0 7402.77i 1.28286 0.740657i
\(465\) 0 0
\(466\) 40.5820 70.2901i 0.00403418 0.00698740i
\(467\) −12806.5 −1.26898 −0.634492 0.772929i \(-0.718791\pi\)
−0.634492 + 0.772929i \(0.718791\pi\)
\(468\) 0 0
\(469\) −6601.09 1886.77i −0.649915 0.185764i
\(470\) −958.262 553.253i −0.0940453 0.0542971i
\(471\) 0 0
\(472\) −4231.89 + 2443.28i −0.412688 + 0.238265i
\(473\) 9.47047 5.46778i 0.000920619 0.000531520i
\(474\) 0 0
\(475\) −285.723 164.962i −0.0275998 0.0159347i
\(476\) −12321.0 3521.67i −1.18641 0.339108i
\(477\) 0 0
\(478\) 3463.49 0.331415
\(479\) 2542.79 4404.24i 0.242553 0.420114i −0.718888 0.695126i \(-0.755348\pi\)
0.961441 + 0.275012i \(0.0886818\pi\)
\(480\) 0 0
\(481\) −2338.01 + 1349.85i −0.221630 + 0.127958i
\(482\) −1936.53 3354.17i −0.183001 0.316967i
\(483\) 0 0
\(484\) −4973.19 + 8613.81i −0.467054 + 0.808961i
\(485\) 16204.1i 1.51709i
\(486\) 0 0
\(487\) 16991.3 1.58100 0.790501 0.612461i \(-0.209820\pi\)
0.790501 + 0.612461i \(0.209820\pi\)
\(488\) 1060.14 1836.21i 0.0983405 0.170331i
\(489\) 0 0
\(490\) −2753.43 91.4755i −0.253851 0.00843355i
\(491\) −8055.59 + 4650.90i −0.740415 + 0.427479i −0.822220 0.569170i \(-0.807265\pi\)
0.0818052 + 0.996648i \(0.473931\pi\)
\(492\) 0 0
\(493\) −22990.8 13273.8i −2.10032 1.21262i
\(494\) 1351.58i 0.123098i
\(495\) 0 0
\(496\) 12772.6i 1.15627i
\(497\) 336.890 + 348.268i 0.0304056 + 0.0314325i
\(498\) 0 0
\(499\) 250.332 + 433.588i 0.0224577 + 0.0388979i 0.877036 0.480425i \(-0.159518\pi\)
−0.854578 + 0.519323i \(0.826184\pi\)
\(500\) −5273.69 9134.30i −0.471693 0.816997i
\(501\) 0 0
\(502\) 1937.05 + 1118.35i 0.172220 + 0.0994315i
\(503\) 3581.09 0.317441 0.158721 0.987324i \(-0.449263\pi\)
0.158721 + 0.987324i \(0.449263\pi\)
\(504\) 0 0
\(505\) −17345.9 −1.52848
\(506\) 18.9228 + 10.9251i 0.00166249 + 0.000959842i
\(507\) 0 0
\(508\) −381.768 661.241i −0.0333429 0.0577516i
\(509\) 5085.37 + 8808.13i 0.442839 + 0.767020i 0.997899 0.0647904i \(-0.0206379\pi\)
−0.555060 + 0.831811i \(0.687305\pi\)
\(510\) 0 0
\(511\) 9381.15 + 9697.99i 0.812128 + 0.839557i
\(512\) 11213.1i 0.967882i
\(513\) 0 0
\(514\) 1549.65i 0.132981i
\(515\) −961.210 554.955i −0.0822446 0.0474839i
\(516\) 0 0
\(517\) −30.2591 + 17.4701i −0.00257407 + 0.00148614i
\(518\) −2459.52 + 615.443i −0.208620 + 0.0522027i
\(519\) 0 0
\(520\) 889.422 1540.52i 0.0750072 0.129916i
\(521\) 389.899 0.0327865 0.0163933 0.999866i \(-0.494782\pi\)
0.0163933 + 0.999866i \(0.494782\pi\)
\(522\) 0 0
\(523\) 14306.4i 1.19613i 0.801448 + 0.598065i \(0.204063\pi\)
−0.801448 + 0.598065i \(0.795937\pi\)
\(524\) −1766.84 + 3060.25i −0.147299 + 0.255130i
\(525\) 0 0
\(526\) −598.865 1037.26i −0.0496421 0.0859827i
\(527\) 19834.1 11451.2i 1.63944 0.946532i
\(528\) 0 0
\(529\) 961.351 1665.11i 0.0790130 0.136854i
\(530\) 3367.62 0.276000
\(531\) 0 0
\(532\) −4948.76 + 17313.8i −0.403301 + 1.41099i
\(533\) 1319.98 + 762.090i 0.107269 + 0.0619320i
\(534\) 0 0
\(535\) −5303.46 + 3061.96i −0.428577 + 0.247439i
\(536\) 3605.35 2081.55i 0.290536 0.167741i
\(537\) 0 0
\(538\) 3443.07 + 1987.86i 0.275913 + 0.159299i
\(539\) −45.9740 + 73.8523i −0.00367392 + 0.00590175i
\(540\) 0 0
\(541\) 21775.6 1.73051 0.865257 0.501328i \(-0.167155\pi\)
0.865257 + 0.501328i \(0.167155\pi\)
\(542\) 1309.03 2267.30i 0.103741 0.179685i
\(543\) 0 0
\(544\) 10208.6 5893.96i 0.804581 0.464525i
\(545\) −2216.59 3839.25i −0.174217 0.301753i
\(546\) 0 0
\(547\) 8960.85 15520.7i 0.700436 1.21319i −0.267878 0.963453i \(-0.586322\pi\)
0.968314 0.249738i \(-0.0803444\pi\)
\(548\) 19575.4i 1.52595i
\(549\) 0 0
\(550\) 0.466799 3.61897e−5
\(551\) −18652.7 + 32307.4i −1.44216 + 2.49790i
\(552\) 0 0
\(553\) 437.682 + 1749.12i 0.0336566 + 0.134503i
\(554\) 1871.83 1080.70i 0.143550 0.0828783i
\(555\) 0 0
\(556\) −8040.62 4642.25i −0.613306 0.354092i
\(557\) 19309.8i 1.46891i 0.678657 + 0.734455i \(0.262562\pi\)
−0.678657 + 0.734455i \(0.737438\pi\)
\(558\) 0 0
\(559\) 617.148i 0.0466951i
\(560\) −7606.28 + 7357.77i −0.573971 + 0.555219i
\(561\) 0 0
\(562\) −2068.52 3582.78i −0.155259 0.268916i
\(563\) −3232.24 5598.41i −0.241959 0.419085i 0.719313 0.694686i \(-0.244457\pi\)
−0.961272 + 0.275601i \(0.911123\pi\)
\(564\) 0 0
\(565\) 6832.55 + 3944.78i 0.508757 + 0.293731i
\(566\) −399.527 −0.0296702
\(567\) 0 0
\(568\) −293.821 −0.0217050
\(569\) −17286.9 9980.61i −1.27365 0.735341i −0.297975 0.954574i \(-0.596311\pi\)
−0.975673 + 0.219233i \(0.929645\pi\)
\(570\) 0 0
\(571\) 6257.56 + 10838.4i 0.458617 + 0.794349i 0.998888 0.0471426i \(-0.0150115\pi\)
−0.540271 + 0.841491i \(0.681678\pi\)
\(572\) −13.5646 23.4945i −0.000991545 0.00171741i
\(573\) 0 0
\(574\) 995.203 + 1028.82i 0.0723675 + 0.0748117i
\(575\) 301.007i 0.0218310i
\(576\) 0 0
\(577\) 547.118i 0.0394746i −0.999805 0.0197373i \(-0.993717\pi\)
0.999805 0.0197373i \(-0.00628298\pi\)
\(578\) −2299.93 1327.87i −0.165509 0.0955569i
\(579\) 0 0
\(580\) −20536.4 + 11856.7i −1.47022 + 0.848832i
\(581\) 3608.77 + 14421.9i 0.257689 + 1.02981i
\(582\) 0 0
\(583\) 53.1697 92.0926i 0.00377712 0.00654217i
\(584\) −8181.85 −0.579739
\(585\) 0 0
\(586\) 5682.98i 0.400617i
\(587\) −902.414 + 1563.03i −0.0634525 + 0.109903i −0.896006 0.444041i \(-0.853544\pi\)
0.832554 + 0.553944i \(0.186878\pi\)
\(588\) 0 0
\(589\) −16091.6 27871.4i −1.12571 1.94978i
\(590\) 3026.62 1747.42i 0.211193 0.121933i
\(591\) 0 0
\(592\) −4869.55 + 8434.31i −0.338070 + 0.585554i
\(593\) −20359.7 −1.40990 −0.704951 0.709256i \(-0.749031\pi\)
−0.704951 + 0.709256i \(0.749031\pi\)
\(594\) 0 0
\(595\) 18244.9 + 5214.89i 1.25709 + 0.359311i
\(596\) 7278.10 + 4202.01i 0.500206 + 0.288794i
\(597\) 0 0
\(598\) 1067.91 616.557i 0.0730268 0.0421620i
\(599\) 3739.33 2158.90i 0.255067 0.147263i −0.367015 0.930215i \(-0.619620\pi\)
0.622082 + 0.782952i \(0.286287\pi\)
\(600\) 0 0
\(601\) 6928.17 + 3999.98i 0.470227 + 0.271485i 0.716335 0.697757i \(-0.245818\pi\)
−0.246108 + 0.969242i \(0.579152\pi\)
\(602\) 159.281 557.262i 0.0107837 0.0377281i
\(603\) 0 0
\(604\) −3554.24 −0.239437
\(605\) 7364.30 12755.3i 0.494878 0.857154i
\(606\) 0 0
\(607\) −3079.67 + 1778.05i −0.205931 + 0.118894i −0.599419 0.800435i \(-0.704602\pi\)
0.393488 + 0.919330i \(0.371268\pi\)
\(608\) −8282.37 14345.5i −0.552458 0.956886i
\(609\) 0 0
\(610\) −758.204 + 1313.25i −0.0503258 + 0.0871669i
\(611\) 1971.85i 0.130560i
\(612\) 0 0
\(613\) −7113.75 −0.468714 −0.234357 0.972151i \(-0.575298\pi\)
−0.234357 + 0.972151i \(0.575298\pi\)
\(614\) 2121.16 3673.96i 0.139419 0.241480i
\(615\) 0 0
\(616\) −12.8051 51.1734i −0.000837551 0.00334714i
\(617\) −790.942 + 456.650i −0.0516080 + 0.0297959i −0.525582 0.850743i \(-0.676152\pi\)
0.473974 + 0.880539i \(0.342819\pi\)
\(618\) 0 0
\(619\) −819.836 473.333i −0.0532342 0.0307348i 0.473147 0.880984i \(-0.343118\pi\)
−0.526381 + 0.850249i \(0.676451\pi\)
\(620\) 20457.4i 1.32514i
\(621\) 0 0
\(622\) 4223.91i 0.272288i
\(623\) −3149.72 + 3046.82i −0.202554 + 0.195936i
\(624\) 0 0
\(625\) 7650.79 + 13251.6i 0.489651 + 0.848100i
\(626\) 2411.24 + 4176.39i 0.153950 + 0.266649i
\(627\) 0 0
\(628\) −12512.4 7224.06i −0.795065 0.459031i
\(629\) 17463.0 1.10699
\(630\) 0 0
\(631\) 3209.46 0.202482 0.101241 0.994862i \(-0.467719\pi\)
0.101241 + 0.994862i \(0.467719\pi\)
\(632\) −946.863 546.671i −0.0595952 0.0344073i
\(633\) 0 0
\(634\) 2181.85 + 3779.08i 0.136676 + 0.236730i
\(635\) 565.322 + 979.167i 0.0353293 + 0.0611922i
\(636\) 0 0
\(637\) 2312.20 + 4330.87i 0.143819 + 0.269380i
\(638\) 52.7820i 0.00327533i
\(639\) 0 0
\(640\) 13847.3i 0.855253i
\(641\) −12387.1 7151.71i −0.763279 0.440679i 0.0671928 0.997740i \(-0.478596\pi\)
−0.830472 + 0.557061i \(0.811929\pi\)
\(642\) 0 0
\(643\) −844.276 + 487.443i −0.0517807 + 0.0298956i −0.525667 0.850691i \(-0.676184\pi\)
0.473886 + 0.880586i \(0.342851\pi\)
\(644\) −15937.4 + 3988.01i −0.975190 + 0.244021i
\(645\) 0 0
\(646\) −4371.36 + 7571.43i −0.266237 + 0.461136i
\(647\) 12668.5 0.769783 0.384891 0.922962i \(-0.374239\pi\)
0.384891 + 0.922962i \(0.374239\pi\)
\(648\) 0 0
\(649\) 110.357i 0.00667470i
\(650\) 13.1719 22.8144i 0.000794836 0.00137670i
\(651\) 0 0
\(652\) 2777.51 + 4810.78i 0.166834 + 0.288964i
\(653\) 13746.7 7936.65i 0.823812 0.475628i −0.0279172 0.999610i \(-0.508887\pi\)
0.851729 + 0.523982i \(0.175554\pi\)
\(654\) 0 0
\(655\) 2616.34 4531.63i 0.156074 0.270329i
\(656\) 5498.45 0.327254
\(657\) 0 0
\(658\) −508.918 + 1780.50i −0.0301515 + 0.105488i
\(659\) 26410.9 + 15248.4i 1.56119 + 0.901353i 0.997137 + 0.0756145i \(0.0240918\pi\)
0.564053 + 0.825739i \(0.309241\pi\)
\(660\) 0 0
\(661\) 14464.7 8351.23i 0.851155 0.491415i −0.00988528 0.999951i \(-0.503147\pi\)
0.861040 + 0.508536i \(0.169813\pi\)
\(662\) −1723.81 + 995.243i −0.101205 + 0.0584308i
\(663\) 0 0
\(664\) −7807.08 4507.42i −0.456285 0.263436i
\(665\) 7328.13 25638.3i 0.427327 1.49505i
\(666\) 0 0
\(667\) −34035.5 −1.97580
\(668\) 13538.5 23449.3i 0.784160 1.35821i
\(669\) 0 0
\(670\) −2578.52 + 1488.71i −0.148682 + 0.0858416i
\(671\) 23.9418 + 41.4685i 0.00137744 + 0.00238580i
\(672\) 0 0
\(673\) −12445.2 + 21555.7i −0.712820 + 1.23464i 0.250975 + 0.967994i \(0.419249\pi\)
−0.963794 + 0.266646i \(0.914084\pi\)
\(674\) 2835.35i 0.162038i
\(675\) 0 0
\(676\) 14887.6 0.847043
\(677\) 756.276 1309.91i 0.0429336 0.0743632i −0.843760 0.536721i \(-0.819663\pi\)
0.886694 + 0.462357i \(0.152996\pi\)
\(678\) 0 0
\(679\) 26307.5 6582.90i 1.48688 0.372060i
\(680\) −9964.90 + 5753.23i −0.561965 + 0.324451i
\(681\) 0 0
\(682\) 39.4342 + 22.7674i 0.00221410 + 0.00127831i
\(683\) 2180.44i 0.122156i −0.998133 0.0610778i \(-0.980546\pi\)
0.998133 0.0610778i \(-0.0194538\pi\)
\(684\) 0 0
\(685\) 28987.3i 1.61686i
\(686\) 970.066 + 4507.37i 0.0539902 + 0.250863i
\(687\) 0 0
\(688\) −1113.17 1928.08i −0.0616852 0.106842i
\(689\) −3000.63 5197.24i −0.165914 0.287372i
\(690\) 0 0
\(691\) 24166.2 + 13952.4i 1.33043 + 0.768124i 0.985365 0.170455i \(-0.0545237\pi\)
0.345064 + 0.938579i \(0.387857\pi\)
\(692\) −24639.2 −1.35353
\(693\) 0 0
\(694\) −427.311 −0.0233725
\(695\) 11906.6 + 6874.25i 0.649844 + 0.375187i
\(696\) 0 0
\(697\) −4929.59 8538.30i −0.267893 0.464004i
\(698\) 2665.22 + 4616.30i 0.144527 + 0.250329i
\(699\) 0 0
\(700\) −252.266 + 244.024i −0.0136211 + 0.0131761i
\(701\) 15696.6i 0.845722i −0.906195 0.422861i \(-0.861026\pi\)
0.906195 0.422861i \(-0.138974\pi\)
\(702\) 0 0
\(703\) 24539.6i 1.31654i
\(704\) −70.4336 40.6648i −0.00377069 0.00217701i
\(705\) 0 0
\(706\) −5494.56 + 3172.29i −0.292904 + 0.169108i
\(707\) 7046.76 + 28161.2i 0.374852 + 1.49804i
\(708\) 0 0
\(709\) 9253.46 16027.5i 0.490157 0.848976i −0.509779 0.860305i \(-0.670273\pi\)
0.999936 + 0.0113291i \(0.00360624\pi\)
\(710\) 210.139 0.0111076
\(711\) 0 0
\(712\) 2657.31i 0.139869i
\(713\) 14681.1 25428.5i 0.771126 1.33563i
\(714\) 0 0
\(715\) 20.0864 + 34.7907i 0.00105062 + 0.00181972i
\(716\) −17777.1 + 10263.6i −0.927879 + 0.535711i
\(717\) 0 0
\(718\) 2837.06 4913.94i 0.147463 0.255413i
\(719\) 12998.8 0.674232 0.337116 0.941463i \(-0.390549\pi\)
0.337116 + 0.941463i \(0.390549\pi\)
\(720\) 0 0
\(721\) −510.483 + 1785.98i −0.0263681 + 0.0922517i
\(722\) 6328.32 + 3653.66i 0.326199 + 0.188331i
\(723\) 0 0
\(724\) −4779.14 + 2759.24i −0.245325 + 0.141639i
\(725\) −629.705 + 363.561i −0.0322575 + 0.0186239i
\(726\) 0 0
\(727\) −1646.14 950.399i −0.0839779 0.0484846i 0.457423 0.889249i \(-0.348773\pi\)
−0.541401 + 0.840765i \(0.682106\pi\)
\(728\) −2862.38 818.148i −0.145724 0.0416519i
\(729\) 0 0
\(730\) 5851.61 0.296682
\(731\) −1996.01 + 3457.20i −0.100992 + 0.174923i
\(732\) 0 0
\(733\) −4804.26 + 2773.74i −0.242087 + 0.139769i −0.616135 0.787640i \(-0.711303\pi\)
0.374049 + 0.927409i \(0.377969\pi\)
\(734\) 873.327 + 1512.65i 0.0439170 + 0.0760665i
\(735\) 0 0
\(736\) 7556.41 13088.1i 0.378442 0.655480i
\(737\) 94.0181i 0.00469905i
\(738\) 0 0
\(739\) −15681.5 −0.780586 −0.390293 0.920691i \(-0.627626\pi\)
−0.390293 + 0.920691i \(0.627626\pi\)
\(740\) 7799.36 13508.9i 0.387446 0.671076i
\(741\) 0 0
\(742\) −1368.09 5467.35i −0.0676876 0.270503i
\(743\) −15659.4 + 9040.97i −0.773201 + 0.446408i −0.834015 0.551741i \(-0.813964\pi\)
0.0608145 + 0.998149i \(0.480630\pi\)
\(744\) 0 0
\(745\) −10777.4 6222.35i −0.530006 0.305999i
\(746\) 3171.84i 0.155669i
\(747\) 0 0
\(748\) 175.485i 0.00857804i
\(749\) 7125.64 + 7366.30i 0.347617 + 0.359358i
\(750\) 0 0
\(751\) −11091.4 19210.8i −0.538921 0.933438i −0.998962 0.0455407i \(-0.985499\pi\)
0.460042 0.887897i \(-0.347834\pi\)
\(752\) 3556.70 + 6160.39i 0.172473 + 0.298732i
\(753\) 0 0
\(754\) −2579.67 1489.38i −0.124597 0.0719361i
\(755\) 5263.12 0.253701
\(756\) 0 0
\(757\) −2531.12 −0.121526 −0.0607630 0.998152i \(-0.519353\pi\)
−0.0607630 + 0.998152i \(0.519353\pi\)
\(758\) −7078.10 4086.54i −0.339166 0.195818i
\(759\) 0 0
\(760\) 8084.62 + 14003.0i 0.385868 + 0.668344i
\(761\) 1897.02 + 3285.73i 0.0903637 + 0.156514i 0.907664 0.419697i \(-0.137864\pi\)
−0.817301 + 0.576212i \(0.804530\pi\)
\(762\) 0 0
\(763\) −5332.57 + 5158.35i −0.253017 + 0.244751i
\(764\) 24849.8i 1.17675i
\(765\) 0 0
\(766\) 2157.89i 0.101786i
\(767\) −5393.59 3113.99i −0.253913 0.146597i
\(768\) 0 0
\(769\) −5524.12 + 3189.35i −0.259044 + 0.149559i −0.623898 0.781506i \(-0.714452\pi\)
0.364854 + 0.931065i \(0.381119\pi\)
\(770\) 9.15811 + 36.5989i 0.000428617 + 0.00171290i
\(771\) 0 0
\(772\) 12411.1 21496.7i 0.578609 1.00218i
\(773\) 29728.9 1.38328 0.691638 0.722244i \(-0.256889\pi\)
0.691638 + 0.722244i \(0.256889\pi\)
\(774\) 0 0
\(775\) 627.283i 0.0290744i
\(776\) −8222.15 + 14241.2i −0.380358 + 0.658799i
\(777\) 0 0
\(778\) −2394.50 4147.39i −0.110343 0.191120i
\(779\) −11998.3 + 6927.20i −0.551839 + 0.318604i
\(780\) 0 0
\(781\) 3.31779 5.74657i 0.000152010 0.000263289i
\(782\) −7976.42 −0.364752
\(783\) 0 0
\(784\) 15035.5 + 9359.77i 0.684924 + 0.426374i
\(785\) 18528.4 + 10697.4i 0.842431 + 0.486378i
\(786\) 0 0
\(787\) 3237.27 1869.04i 0.146628 0.0846556i −0.424891 0.905244i \(-0.639688\pi\)
0.571519 + 0.820589i \(0.306354\pi\)
\(788\) −3245.59 + 1873.84i −0.146725 + 0.0847117i
\(789\) 0 0
\(790\) 677.190 + 390.976i 0.0304979 + 0.0176080i
\(791\) 3628.66 12695.3i 0.163110 0.570660i
\(792\) 0 0
\(793\) 2702.31 0.121011
\(794\) 2144.17 3713.82i 0.0958361 0.165993i
\(795\) 0 0
\(796\) 26325.4 15199.0i 1.17221 0.676776i
\(797\) 5377.39 + 9313.91i 0.238992 + 0.413947i 0.960425 0.278537i \(-0.0898496\pi\)
−0.721433 + 0.692484i \(0.756516\pi\)
\(798\) 0 0
\(799\) 6377.45 11046.1i 0.282376 0.489089i
\(800\) 322.864i 0.0142687i
\(801\) 0 0
\(802\) −4062.60 −0.178872
\(803\) 92.3882 160.021i 0.00406016 0.00703241i
\(804\) 0 0
\(805\) 23600.1 5905.44i 1.03329 0.258558i
\(806\) 2225.47 1284.88i 0.0972566 0.0561511i
\(807\) 0 0
\(808\) −15244.7 8801.51i −0.663744 0.383213i
\(809\) 31037.7i 1.34886i 0.738340 + 0.674429i \(0.235610\pi\)
−0.738340 + 0.674429i \(0.764390\pi\)
\(810\) 0 0
\(811\) 3943.22i 0.170734i 0.996350 + 0.0853669i \(0.0272062\pi\)
−0.996350 + 0.0853669i \(0.972794\pi\)
\(812\) 27592.4 + 28524.3i 1.19249 + 1.23277i
\(813\) 0 0
\(814\) 17.3601 + 30.0685i 0.000747506 + 0.00129472i
\(815\) −4112.93 7123.81i −0.176773 0.306179i
\(816\) 0 0
\(817\) 4858.16 + 2804.86i 0.208036 + 0.120110i
\(818\) 794.973 0.0339799
\(819\) 0 0
\(820\) −8806.64 −0.375050
\(821\) −25087.6 14484.3i −1.06646 0.615720i −0.139247 0.990258i \(-0.544468\pi\)
−0.927212 + 0.374537i \(0.877802\pi\)
\(822\) 0 0
\(823\) −18643.1 32290.8i −0.789622 1.36766i −0.926199 0.377035i \(-0.876944\pi\)
0.136577 0.990629i \(-0.456390\pi\)
\(824\) −563.181 975.458i −0.0238099 0.0412399i
\(825\) 0 0
\(826\) −4066.52 4203.86i −0.171298 0.177084i
\(827\) 13151.6i 0.552992i −0.961015 0.276496i \(-0.910827\pi\)
0.961015 0.276496i \(-0.0891732\pi\)
\(828\) 0 0
\(829\) 27671.1i 1.15929i 0.814867 + 0.579647i \(0.196810\pi\)
−0.814867 + 0.579647i \(0.803190\pi\)
\(830\) 5583.57 + 3223.68i 0.233504 + 0.134814i
\(831\) 0 0
\(832\) −3974.92 + 2294.92i −0.165632 + 0.0956274i
\(833\) 1054.46 31739.3i 0.0438592 1.32017i
\(834\) 0 0
\(835\) −20047.8 + 34723.8i −0.830877 + 1.43912i
\(836\) 246.597 0.0102018
\(837\) 0 0
\(838\) 9866.14i 0.406707i
\(839\) 8498.72 14720.2i 0.349712 0.605719i −0.636486 0.771288i \(-0.719613\pi\)
0.986198 + 0.165569i \(0.0529461\pi\)
\(840\) 0 0
\(841\) 28914.2 + 50080.8i 1.18554 + 2.05342i
\(842\) −3572.89 + 2062.81i −0.146235 + 0.0844288i
\(843\) 0 0
\(844\) −18361.3 + 31802.8i −0.748843 + 1.29703i
\(845\) −22045.6 −0.897506
\(846\) 0 0
\(847\) −23700.2 6774.16i −0.961449 0.274809i
\(848\) −18748.9 10824.7i −0.759247 0.438351i
\(849\) 0 0
\(850\) −147.575 + 85.2024i −0.00595503 + 0.00343814i
\(851\) 19389.1 11194.3i 0.781023 0.450924i
\(852\) 0 0
\(853\) −13130.3 7580.75i −0.527047 0.304291i 0.212766 0.977103i \(-0.431753\pi\)
−0.739813 + 0.672812i \(0.765086\pi\)
\(854\) 2440.09 + 697.445i 0.0977729 + 0.0279462i
\(855\) 0 0
\(856\) −6214.69 −0.248147
\(857\) −14186.9 + 24572.4i −0.565477 + 0.979436i 0.431528 + 0.902100i \(0.357975\pi\)
−0.997005 + 0.0773360i \(0.975359\pi\)
\(858\) 0 0
\(859\) −33411.7 + 19290.2i −1.32712 + 0.766210i −0.984853 0.173394i \(-0.944527\pi\)
−0.342263 + 0.939604i \(0.611193\pi\)
\(860\) 1782.93 + 3088.12i 0.0706945 + 0.122446i
\(861\) 0 0
\(862\) −1744.17 + 3020.98i −0.0689171 + 0.119368i
\(863\) 112.649i 0.00444337i 0.999998 + 0.00222168i \(0.000707185\pi\)
−0.999998 + 0.00222168i \(0.999293\pi\)
\(864\) 0 0
\(865\) 36485.8 1.43417
\(866\) −3491.62 + 6047.66i −0.137009 + 0.237307i
\(867\) 0 0
\(868\) −33212.8 + 8310.81i −1.29875 + 0.324985i
\(869\) 21.3837 12.3459i 0.000834742 0.000481939i
\(870\) 0 0
\(871\) 4595.05 + 2652.95i 0.178757 + 0.103205i
\(872\) 4498.90i 0.174716i
\(873\) 0 0
\(874\) 11208.7i 0.433799i
\(875\) 18787.2 18173.4i 0.725855 0.702141i
\(876\) 0 0
\(877\) 10379.3 + 17977.5i 0.399639 + 0.692196i 0.993681 0.112238i \(-0.0358020\pi\)
−0.594042 + 0.804434i \(0.702469\pi\)
\(878\) −4693.22 8128.89i −0.180397 0.312456i
\(879\) 0 0
\(880\) 125.507 + 72.4615i 0.00480777 + 0.00277577i
\(881\) −18603.4 −0.711425 −0.355712 0.934595i \(-0.615762\pi\)
−0.355712 + 0.934595i \(0.615762\pi\)
\(882\) 0 0
\(883\) 17188.8 0.655096 0.327548 0.944835i \(-0.393778\pi\)
0.327548 + 0.944835i \(0.393778\pi\)
\(884\) 8576.68 + 4951.75i 0.326318 + 0.188400i
\(885\) 0 0
\(886\) 4777.44 + 8274.77i 0.181153 + 0.313766i
\(887\) 6615.31 + 11458.1i 0.250417 + 0.433736i 0.963641 0.267201i \(-0.0860988\pi\)
−0.713223 + 0.700937i \(0.752765\pi\)
\(888\) 0 0
\(889\) 1360.02 1315.59i 0.0513090 0.0496327i
\(890\) 1900.49i 0.0715782i
\(891\) 0 0
\(892\) 8916.74i 0.334703i
\(893\) −15522.3 8961.79i −0.581672 0.335829i
\(894\) 0 0
\(895\) 26324.3 15198.4i 0.983157 0.567626i
\(896\) −22481.2 + 5625.45i −0.838219 + 0.209747i
\(897\) 0 0
\(898\) −2826.20 + 4895.12i −0.105024 + 0.181907i
\(899\) −70928.4 −2.63136
\(900\) 0 0
\(901\) 38819.2i 1.43535i
\(902\) 9.80104 16.9759i 0.000361795 0.000626647i
\(903\) 0 0
\(904\) 4003.25 + 6933.83i 0.147286 + 0.255106i
\(905\) 7076.96 4085.88i 0.259940 0.150077i
\(906\) 0 0
\(907\) 21753.0 37677.2i 0.796356 1.37933i −0.125618 0.992079i \(-0.540091\pi\)
0.921975 0.387251i \(-0.126575\pi\)
\(908\) 41914.5 1.53192
\(909\) 0 0
\(910\) 2047.16 + 585.134i 0.0745743 + 0.0213154i
\(911\) −14899.7 8602.33i −0.541875 0.312852i 0.203964 0.978978i \(-0.434618\pi\)
−0.745838 + 0.666127i \(0.767951\pi\)
\(912\) 0 0
\(913\) 176.313 101.794i 0.00639113 0.00368992i
\(914\) 3027.84 1748.13i 0.109576 0.0632635i
\(915\) 0 0
\(916\) 34515.5 + 19927.5i 1.24500 + 0.718804i
\(917\) −8420.02 2406.68i −0.303221 0.0866690i
\(918\) 0 0
\(919\) 18441.8 0.661956 0.330978 0.943639i \(-0.392621\pi\)
0.330978 + 0.943639i \(0.392621\pi\)
\(920\) −7375.99 + 12775.6i −0.264325 + 0.457825i
\(921\) 0 0
\(922\) −32.2382 + 18.6127i −0.00115153 + 0.000664834i
\(923\) −187.239 324.308i −0.00667719 0.0115652i
\(924\) 0 0
\(925\) 239.151 414.221i 0.00850079 0.0147238i
\(926\) 6949.39i 0.246621i
\(927\) 0 0
\(928\) −36507.0 −1.29138
\(929\) −17234.7 + 29851.4i −0.608668 + 1.05424i 0.382792 + 0.923835i \(0.374963\pi\)
−0.991460 + 0.130410i \(0.958371\pi\)
\(930\) 0 0
\(931\) −44601.0 1481.75i −1.57007 0.0521617i
\(932\) 723.749 417.857i 0.0254369 0.0146860i
\(933\) 0 0
\(934\) 8049.64 + 4647.46i 0.282005 + 0.162815i
\(935\) 259.859i 0.00908908i
\(936\) 0 0
\(937\) 8204.91i 0.286065i 0.989718 + 0.143032i \(0.0456853\pi\)
−0.989718 + 0.143032i \(0.954315\pi\)
\(938\) 3464.46 + 3581.47i 0.120595 + 0.124668i
\(939\) 0 0
\(940\) −5696.62 9866.83i −0.197663 0.342362i
\(941\) 11955.6 + 20707.8i 0.414179 + 0.717380i 0.995342 0.0964079i \(-0.0307353\pi\)
−0.581163 + 0.813787i \(0.697402\pi\)
\(942\) 0 0
\(943\) −10946.6 6320.03i −0.378017 0.218249i
\(944\) −22467.3 −0.774628
\(945\) 0 0
\(946\) −7.93698 −0.000272784
\(947\) 34519.4 + 19929.8i 1.18451 + 0.683877i 0.957054 0.289911i \(-0.0936257\pi\)
0.227456 + 0.973788i \(0.426959\pi\)
\(948\) 0 0
\(949\) −5213.93 9030.78i −0.178347 0.308906i
\(950\) 119.729 + 207.377i 0.00408897 + 0.00708231i
\(951\) 0 0
\(952\) 13388.7 + 13840.8i 0.455808 + 0.471202i
\(953\) 10983.4i 0.373334i 0.982423 + 0.186667i \(0.0597685\pi\)
−0.982423 + 0.186667i \(0.940232\pi\)
\(954\) 0 0
\(955\) 36797.6i 1.24685i
\(956\) 30884.3 + 17831.1i 1.04484 + 0.603240i
\(957\) 0 0
\(958\) −3196.58 + 1845.54i −0.107804 + 0.0622409i
\(959\) −47061.1 + 11776.1i −1.58465 + 0.396527i
\(960\) 0 0
\(961\) 15699.3 27191.9i 0.526980 0.912756i
\(962\) 1959.43 0.0656699
\(963\) 0 0
\(964\) 39879.3i 1.33239i
\(965\) −18378.4 + 31832.3i −0.613079 + 1.06188i
\(966\) 0 0
\(967\) −7413.81 12841.1i −0.246548 0.427034i 0.716018 0.698082i \(-0.245963\pi\)
−0.962566 + 0.271048i \(0.912630\pi\)
\(968\) 12944.4 7473.47i 0.429803 0.248147i
\(969\) 0 0
\(970\) 5880.43 10185.2i 0.194649 0.337141i
\(971\) −8249.56 −0.272648 −0.136324 0.990664i \(-0.543529\pi\)
−0.136324 + 0.990664i \(0.543529\pi\)
\(972\) 0 0
\(973\) 6323.38 22123.1i 0.208344 0.728913i
\(974\) −10680.0 6166.09i −0.351344 0.202848i
\(975\) 0 0
\(976\) 8442.48 4874.27i 0.276882 0.159858i
\(977\) −4134.88 + 2387.28i −0.135401 + 0.0781737i −0.566170 0.824288i \(-0.691576\pi\)
0.430769 + 0.902462i \(0.358242\pi\)
\(978\) 0 0
\(979\) 51.9718 + 30.0059i 0.00169666 + 0.000979564i
\(980\) −24081.7 14991.1i −0.784960 0.488648i
\(981\) 0 0
\(982\) 6751.20 0.219389
\(983\) 8970.02 15536.5i 0.291047 0.504108i −0.683011 0.730409i \(-0.739330\pi\)
0.974058 + 0.226300i \(0.0726630\pi\)
\(984\) 0 0
\(985\) 4806.07 2774.79i 0.155466 0.0897584i
\(986\) 9634.04 + 16686.6i 0.311167 + 0.538957i
\(987\) 0 0
\(988\) 6958.35 12052.2i 0.224063 0.388089i
\(989\) 5118.02i 0.164554i
\(990\) 0 0
\(991\) 1714.50 0.0549574 0.0274787 0.999622i \(-0.491252\pi\)
0.0274787 + 0.999622i \(0.491252\pi\)
\(992\) 15747.2 27274.9i 0.504006 0.872964i
\(993\) 0 0
\(994\) −85.3688 341.163i −0.00272408 0.0108863i
\(995\) −38982.7 + 22506.7i −1.24205 + 0.717095i
\(996\) 0 0
\(997\) 29996.8 + 17318.7i 0.952867 + 0.550138i 0.893970 0.448126i \(-0.147908\pi\)
0.0588968 + 0.998264i \(0.481242\pi\)
\(998\) 363.380i 0.0115256i
\(999\) 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.62.10 44
3.2 odd 2 63.4.o.a.20.13 44
7.6 odd 2 inner 189.4.o.a.62.9 44
9.2 odd 6 567.4.c.c.566.11 44
9.4 even 3 63.4.o.a.41.14 yes 44
9.5 odd 6 inner 189.4.o.a.125.9 44
9.7 even 3 567.4.c.c.566.34 44
21.20 even 2 63.4.o.a.20.14 yes 44
63.13 odd 6 63.4.o.a.41.13 yes 44
63.20 even 6 567.4.c.c.566.33 44
63.34 odd 6 567.4.c.c.566.12 44
63.41 even 6 inner 189.4.o.a.125.10 44
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.o.a.20.13 44 3.2 odd 2
63.4.o.a.20.14 yes 44 21.20 even 2
63.4.o.a.41.13 yes 44 63.13 odd 6
63.4.o.a.41.14 yes 44 9.4 even 3
189.4.o.a.62.9 44 7.6 odd 2 inner
189.4.o.a.62.10 44 1.1 even 1 trivial
189.4.o.a.125.9 44 9.5 odd 6 inner
189.4.o.a.125.10 44 63.41 even 6 inner
567.4.c.c.566.11 44 9.2 odd 6
567.4.c.c.566.12 44 63.34 odd 6
567.4.c.c.566.33 44 63.20 even 6
567.4.c.c.566.34 44 9.7 even 3