Properties

Label 567.2.f.l.190.3
Level $567$
Weight $2$
Character 567.190
Analytic conductor $4.528$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [567,2,Mod(190,567)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(567, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("567.190");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 567 = 3^{4} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 567.f (of order \(3\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(4.52751779461\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.1156923.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 27x^{2} - 18x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 3 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 190.3
Root \(0.500000 - 1.51496i\) of defining polynomial
Character \(\chi\) \(=\) 567.190
Dual form 567.2.f.l.379.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.33454 + 2.31149i) q^{2} +(-2.56199 + 4.43750i) q^{4} +(-0.727452 + 1.25998i) q^{5} +(-0.500000 - 0.866025i) q^{7} -8.33816 q^{8} +O(q^{10})\) \(q+(1.33454 + 2.31149i) q^{2} +(-2.56199 + 4.43750i) q^{4} +(-0.727452 + 1.25998i) q^{5} +(-0.500000 - 0.866025i) q^{7} -8.33816 q^{8} -3.88325 q^{10} +(-0.772548 - 1.33809i) q^{11} +(-2.94163 + 5.09505i) q^{13} +(1.33454 - 2.31149i) q^{14} +(-6.00362 - 10.3986i) q^{16} +6.79306 q^{17} -6.24797 q^{19} +(-3.72745 - 6.45614i) q^{20} +(2.06199 - 3.57147i) q^{22} +(1.45490 - 2.51997i) q^{23} +(1.44163 + 2.49697i) q^{25} -15.7029 q^{26} +5.12398 q^{28} +(1.94163 + 3.36300i) q^{29} +(-1.00000 + 1.73205i) q^{31} +(7.68597 - 13.3125i) q^{32} +(9.06561 + 15.7021i) q^{34} +1.45490 q^{35} +5.00000 q^{37} +(-8.33816 - 14.4421i) q^{38} +(6.06561 - 10.5059i) q^{40} +(-1.12398 + 1.94680i) q^{41} +(3.56561 + 6.17582i) q^{43} +7.91705 q^{44} +7.76651 q^{46} +(-2.66908 - 4.62298i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-3.84782 + 6.66461i) q^{50} +(-15.0728 - 26.1069i) q^{52} +9.79306 q^{53} +2.24797 q^{55} +(4.16908 + 7.22106i) q^{56} +(-5.18236 + 8.97610i) q^{58} +(-2.33816 + 4.04981i) q^{59} +(1.18236 + 2.04790i) q^{61} -5.33816 q^{62} +17.0145 q^{64} +(-4.27979 - 7.41281i) q^{65} +(-1.68236 + 2.91393i) q^{67} +(-17.4038 + 30.1442i) q^{68} +(1.94163 + 3.36300i) q^{70} -1.36471 q^{71} -1.88325 q^{73} +(6.67270 + 11.5575i) q^{74} +(16.0072 - 27.7253i) q^{76} +(-0.772548 + 1.33809i) q^{77} +(-1.68236 - 2.91393i) q^{79} +17.4694 q^{80} -6.00000 q^{82} +(1.12398 + 1.94680i) q^{83} +(-4.94163 + 8.55915i) q^{85} +(-9.51690 + 16.4837i) q^{86} +(6.44163 + 11.1572i) q^{88} -0.793062 q^{89} +5.88325 q^{91} +(7.45490 + 12.9123i) q^{92} +(7.12398 - 12.3391i) q^{94} +(4.54510 - 7.87234i) q^{95} +(-5.12398 - 8.87500i) q^{97} -2.66908 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{4} - 3 q^{5} - 3 q^{7} - 18 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{4} - 3 q^{5} - 3 q^{7} - 18 q^{8} + 6 q^{10} - 6 q^{11} - 3 q^{13} - 12 q^{16} + 6 q^{17} - 21 q^{20} + 3 q^{22} + 6 q^{23} - 6 q^{25} - 54 q^{26} + 12 q^{28} - 3 q^{29} - 6 q^{31} + 18 q^{32} + 21 q^{34} + 6 q^{35} + 30 q^{37} - 18 q^{38} + 3 q^{40} + 12 q^{41} - 12 q^{43} - 6 q^{44} - 12 q^{46} - 3 q^{49} - 27 q^{50} - 9 q^{52} + 24 q^{53} - 24 q^{55} + 9 q^{56} - 27 q^{58} + 18 q^{59} + 3 q^{61} + 6 q^{64} + 21 q^{65} - 6 q^{67} - 39 q^{68} - 3 q^{70} + 18 q^{73} + 48 q^{76} - 6 q^{77} - 6 q^{79} + 6 q^{80} - 36 q^{82} - 12 q^{83} - 15 q^{85} - 45 q^{86} + 24 q^{88} + 30 q^{89} + 6 q^{91} + 42 q^{92} + 24 q^{94} + 30 q^{95} - 12 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(407\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.33454 + 2.31149i 0.943662 + 1.63447i 0.758408 + 0.651780i \(0.225977\pi\)
0.185254 + 0.982691i \(0.440689\pi\)
\(3\) 0 0
\(4\) −2.56199 + 4.43750i −1.28100 + 2.21875i
\(5\) −0.727452 + 1.25998i −0.325326 + 0.563482i −0.981578 0.191060i \(-0.938808\pi\)
0.656252 + 0.754542i \(0.272141\pi\)
\(6\) 0 0
\(7\) −0.500000 0.866025i −0.188982 0.327327i
\(8\) −8.33816 −2.94798
\(9\) 0 0
\(10\) −3.88325 −1.22799
\(11\) −0.772548 1.33809i −0.232932 0.403450i 0.725738 0.687972i \(-0.241499\pi\)
−0.958670 + 0.284522i \(0.908165\pi\)
\(12\) 0 0
\(13\) −2.94163 + 5.09505i −0.815861 + 1.41311i 0.0928478 + 0.995680i \(0.470403\pi\)
−0.908708 + 0.417432i \(0.862930\pi\)
\(14\) 1.33454 2.31149i 0.356671 0.617772i
\(15\) 0 0
\(16\) −6.00362 10.3986i −1.50090 2.59964i
\(17\) 6.79306 1.64756 0.823780 0.566910i \(-0.191861\pi\)
0.823780 + 0.566910i \(0.191861\pi\)
\(18\) 0 0
\(19\) −6.24797 −1.43338 −0.716691 0.697391i \(-0.754344\pi\)
−0.716691 + 0.697391i \(0.754344\pi\)
\(20\) −3.72745 6.45614i −0.833484 1.44364i
\(21\) 0 0
\(22\) 2.06199 3.57147i 0.439618 0.761441i
\(23\) 1.45490 2.51997i 0.303368 0.525450i −0.673528 0.739161i \(-0.735222\pi\)
0.976897 + 0.213712i \(0.0685554\pi\)
\(24\) 0 0
\(25\) 1.44163 + 2.49697i 0.288325 + 0.499394i
\(26\) −15.7029 −3.07959
\(27\) 0 0
\(28\) 5.12398 0.968342
\(29\) 1.94163 + 3.36300i 0.360551 + 0.624493i 0.988052 0.154123i \(-0.0492553\pi\)
−0.627501 + 0.778616i \(0.715922\pi\)
\(30\) 0 0
\(31\) −1.00000 + 1.73205i −0.179605 + 0.311086i −0.941745 0.336327i \(-0.890815\pi\)
0.762140 + 0.647412i \(0.224149\pi\)
\(32\) 7.68597 13.3125i 1.35870 2.35334i
\(33\) 0 0
\(34\) 9.06561 + 15.7021i 1.55474 + 2.69289i
\(35\) 1.45490 0.245924
\(36\) 0 0
\(37\) 5.00000 0.821995 0.410997 0.911636i \(-0.365181\pi\)
0.410997 + 0.911636i \(0.365181\pi\)
\(38\) −8.33816 14.4421i −1.35263 2.34282i
\(39\) 0 0
\(40\) 6.06561 10.5059i 0.959057 1.66114i
\(41\) −1.12398 + 1.94680i −0.175537 + 0.304038i −0.940347 0.340217i \(-0.889499\pi\)
0.764810 + 0.644256i \(0.222833\pi\)
\(42\) 0 0
\(43\) 3.56561 + 6.17582i 0.543750 + 0.941803i 0.998684 + 0.0512782i \(0.0163295\pi\)
−0.454934 + 0.890525i \(0.650337\pi\)
\(44\) 7.91705 1.19354
\(45\) 0 0
\(46\) 7.76651 1.14511
\(47\) −2.66908 4.62298i −0.389325 0.674331i 0.603034 0.797716i \(-0.293958\pi\)
−0.992359 + 0.123385i \(0.960625\pi\)
\(48\) 0 0
\(49\) −0.500000 + 0.866025i −0.0714286 + 0.123718i
\(50\) −3.84782 + 6.66461i −0.544163 + 0.942519i
\(51\) 0 0
\(52\) −15.0728 26.1069i −2.09023 3.62038i
\(53\) 9.79306 1.34518 0.672590 0.740015i \(-0.265182\pi\)
0.672590 + 0.740015i \(0.265182\pi\)
\(54\) 0 0
\(55\) 2.24797 0.303116
\(56\) 4.16908 + 7.22106i 0.557117 + 0.964954i
\(57\) 0 0
\(58\) −5.18236 + 8.97610i −0.680477 + 1.17862i
\(59\) −2.33816 + 4.04981i −0.304402 + 0.527240i −0.977128 0.212652i \(-0.931790\pi\)
0.672726 + 0.739892i \(0.265123\pi\)
\(60\) 0 0
\(61\) 1.18236 + 2.04790i 0.151385 + 0.262207i 0.931737 0.363134i \(-0.118293\pi\)
−0.780352 + 0.625341i \(0.784960\pi\)
\(62\) −5.33816 −0.677947
\(63\) 0 0
\(64\) 17.0145 2.12681
\(65\) −4.27979 7.41281i −0.530842 0.919445i
\(66\) 0 0
\(67\) −1.68236 + 2.91393i −0.205533 + 0.355993i −0.950302 0.311329i \(-0.899226\pi\)
0.744770 + 0.667322i \(0.232559\pi\)
\(68\) −17.4038 + 30.1442i −2.11052 + 3.65552i
\(69\) 0 0
\(70\) 1.94163 + 3.36300i 0.232069 + 0.401955i
\(71\) −1.36471 −0.161962 −0.0809808 0.996716i \(-0.525805\pi\)
−0.0809808 + 0.996716i \(0.525805\pi\)
\(72\) 0 0
\(73\) −1.88325 −0.220418 −0.110209 0.993908i \(-0.535152\pi\)
−0.110209 + 0.993908i \(0.535152\pi\)
\(74\) 6.67270 + 11.5575i 0.775685 + 1.34353i
\(75\) 0 0
\(76\) 16.0072 27.7253i 1.83616 3.18032i
\(77\) −0.772548 + 1.33809i −0.0880400 + 0.152490i
\(78\) 0 0
\(79\) −1.68236 2.91393i −0.189280 0.327842i 0.755730 0.654883i \(-0.227282\pi\)
−0.945010 + 0.327040i \(0.893949\pi\)
\(80\) 17.4694 1.95314
\(81\) 0 0
\(82\) −6.00000 −0.662589
\(83\) 1.12398 + 1.94680i 0.123373 + 0.213689i 0.921096 0.389336i \(-0.127295\pi\)
−0.797723 + 0.603024i \(0.793962\pi\)
\(84\) 0 0
\(85\) −4.94163 + 8.55915i −0.535995 + 0.928370i
\(86\) −9.51690 + 16.4837i −1.02623 + 1.77749i
\(87\) 0 0
\(88\) 6.44163 + 11.1572i 0.686680 + 1.18936i
\(89\) −0.793062 −0.0840644 −0.0420322 0.999116i \(-0.513383\pi\)
−0.0420322 + 0.999116i \(0.513383\pi\)
\(90\) 0 0
\(91\) 5.88325 0.616733
\(92\) 7.45490 + 12.9123i 0.777227 + 1.34620i
\(93\) 0 0
\(94\) 7.12398 12.3391i 0.734783 1.27268i
\(95\) 4.54510 7.87234i 0.466317 0.807685i
\(96\) 0 0
\(97\) −5.12398 8.87500i −0.520262 0.901120i −0.999723 0.0235564i \(-0.992501\pi\)
0.479461 0.877563i \(-0.340832\pi\)
\(98\) −2.66908 −0.269618
\(99\) 0 0
\(100\) −14.7737 −1.47737
\(101\) 4.54510 + 7.87234i 0.452254 + 0.783327i 0.998526 0.0542812i \(-0.0172867\pi\)
−0.546272 + 0.837608i \(0.683953\pi\)
\(102\) 0 0
\(103\) −9.00724 + 15.6010i −0.887509 + 1.53721i −0.0446993 + 0.999000i \(0.514233\pi\)
−0.842810 + 0.538211i \(0.819100\pi\)
\(104\) 24.5278 42.4833i 2.40514 4.16583i
\(105\) 0 0
\(106\) 13.0692 + 22.6366i 1.26940 + 2.19866i
\(107\) 18.2214 1.76153 0.880765 0.473553i \(-0.157029\pi\)
0.880765 + 0.473553i \(0.157029\pi\)
\(108\) 0 0
\(109\) 16.3792 1.56884 0.784421 0.620229i \(-0.212960\pi\)
0.784421 + 0.620229i \(0.212960\pi\)
\(110\) 3.00000 + 5.19615i 0.286039 + 0.495434i
\(111\) 0 0
\(112\) −6.00362 + 10.3986i −0.567289 + 0.982573i
\(113\) 3.74797 6.49167i 0.352579 0.610685i −0.634122 0.773233i \(-0.718638\pi\)
0.986701 + 0.162549i \(0.0519714\pi\)
\(114\) 0 0
\(115\) 2.11675 + 3.66631i 0.197388 + 0.341885i
\(116\) −19.8977 −1.84746
\(117\) 0 0
\(118\) −12.4815 −1.14901
\(119\) −3.39653 5.88296i −0.311359 0.539290i
\(120\) 0 0
\(121\) 4.30634 7.45880i 0.391485 0.678073i
\(122\) −3.15580 + 5.46601i −0.285713 + 0.494869i
\(123\) 0 0
\(124\) −5.12398 8.87500i −0.460147 0.796998i
\(125\) −11.4694 −1.02585
\(126\) 0 0
\(127\) −7.13122 −0.632793 −0.316397 0.948627i \(-0.602473\pi\)
−0.316397 + 0.948627i \(0.602473\pi\)
\(128\) 7.33454 + 12.7038i 0.648288 + 1.12287i
\(129\) 0 0
\(130\) 11.4231 19.7854i 1.00187 1.73529i
\(131\) 9.46214 16.3889i 0.826711 1.43191i −0.0738934 0.997266i \(-0.523542\pi\)
0.900605 0.434640i \(-0.143124\pi\)
\(132\) 0 0
\(133\) 3.12398 + 5.41090i 0.270884 + 0.469184i
\(134\) −8.98068 −0.775813
\(135\) 0 0
\(136\) −56.6416 −4.85698
\(137\) −2.95490 5.11804i −0.252454 0.437264i 0.711747 0.702436i \(-0.247904\pi\)
−0.964201 + 0.265172i \(0.914571\pi\)
\(138\) 0 0
\(139\) 0.876017 1.51731i 0.0743028 0.128696i −0.826480 0.562966i \(-0.809660\pi\)
0.900783 + 0.434270i \(0.142994\pi\)
\(140\) −3.72745 + 6.45614i −0.315027 + 0.545643i
\(141\) 0 0
\(142\) −1.82126 3.15452i −0.152837 0.264721i
\(143\) 9.09019 0.760160
\(144\) 0 0
\(145\) −5.64976 −0.469187
\(146\) −2.51328 4.35312i −0.208000 0.360267i
\(147\) 0 0
\(148\) −12.8100 + 22.1875i −1.05297 + 1.82380i
\(149\) −3.04510 + 5.27426i −0.249464 + 0.432084i −0.963377 0.268150i \(-0.913588\pi\)
0.713913 + 0.700234i \(0.246921\pi\)
\(150\) 0 0
\(151\) −0.317644 0.550175i −0.0258495 0.0447726i 0.852811 0.522219i \(-0.174896\pi\)
−0.878661 + 0.477447i \(0.841562\pi\)
\(152\) 52.0965 4.22559
\(153\) 0 0
\(154\) −4.12398 −0.332320
\(155\) −1.45490 2.51997i −0.116861 0.202409i
\(156\) 0 0
\(157\) 2.57691 4.46335i 0.205660 0.356214i −0.744683 0.667419i \(-0.767399\pi\)
0.950343 + 0.311205i \(0.100733\pi\)
\(158\) 4.49034 7.77750i 0.357232 0.618745i
\(159\) 0 0
\(160\) 11.1824 + 19.3684i 0.884043 + 1.53121i
\(161\) −2.90981 −0.229325
\(162\) 0 0
\(163\) −5.36471 −0.420197 −0.210098 0.977680i \(-0.567378\pi\)
−0.210098 + 0.977680i \(0.567378\pi\)
\(164\) −5.75927 9.97535i −0.449724 0.778944i
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) 4.87602 8.44551i 0.377318 0.653533i −0.613353 0.789809i \(-0.710180\pi\)
0.990671 + 0.136275i \(0.0435132\pi\)
\(168\) 0 0
\(169\) −10.8063 18.7171i −0.831257 1.43978i
\(170\) −26.3792 −2.02319
\(171\) 0 0
\(172\) −36.5403 −2.78617
\(173\) 12.1558 + 21.0545i 0.924189 + 1.60074i 0.792861 + 0.609402i \(0.208591\pi\)
0.131327 + 0.991339i \(0.458076\pi\)
\(174\) 0 0
\(175\) 1.44163 2.49697i 0.108977 0.188753i
\(176\) −9.27617 + 16.0668i −0.699217 + 1.21108i
\(177\) 0 0
\(178\) −1.05837 1.83316i −0.0793284 0.137401i
\(179\) −13.5861 −1.01547 −0.507737 0.861512i \(-0.669518\pi\)
−0.507737 + 0.861512i \(0.669518\pi\)
\(180\) 0 0
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 7.85144 + 13.5991i 0.581987 + 1.00803i
\(183\) 0 0
\(184\) −12.1312 + 21.0119i −0.894325 + 1.54902i
\(185\) −3.63726 + 6.29992i −0.267417 + 0.463179i
\(186\) 0 0
\(187\) −5.24797 9.08974i −0.383769 0.664708i
\(188\) 27.3526 1.99490
\(189\) 0 0
\(190\) 24.2624 1.76018
\(191\) 7.65580 + 13.2602i 0.553954 + 0.959477i 0.997984 + 0.0634651i \(0.0202151\pi\)
−0.444030 + 0.896012i \(0.646452\pi\)
\(192\) 0 0
\(193\) 6.18959 10.7207i 0.445537 0.771692i −0.552553 0.833478i \(-0.686346\pi\)
0.998089 + 0.0617858i \(0.0196796\pi\)
\(194\) 13.6763 23.6881i 0.981902 1.70070i
\(195\) 0 0
\(196\) −2.56199 4.43750i −0.182999 0.316964i
\(197\) 5.72942 0.408205 0.204102 0.978950i \(-0.434572\pi\)
0.204102 + 0.978950i \(0.434572\pi\)
\(198\) 0 0
\(199\) 12.0145 0.851684 0.425842 0.904798i \(-0.359978\pi\)
0.425842 + 0.904798i \(0.359978\pi\)
\(200\) −12.0205 20.8201i −0.849979 1.47221i
\(201\) 0 0
\(202\) −12.1312 + 21.0119i −0.853550 + 1.47839i
\(203\) 1.94163 3.36300i 0.136276 0.236036i
\(204\) 0 0
\(205\) −1.63529 2.83240i −0.114213 0.197823i
\(206\) −48.0821 −3.35004
\(207\) 0 0
\(208\) 70.6416 4.89812
\(209\) 4.82685 + 8.36036i 0.333880 + 0.578298i
\(210\) 0 0
\(211\) 6.56561 11.3720i 0.451995 0.782879i −0.546515 0.837450i \(-0.684046\pi\)
0.998510 + 0.0545708i \(0.0173791\pi\)
\(212\) −25.0897 + 43.4567i −1.72317 + 2.98462i
\(213\) 0 0
\(214\) 24.3172 + 42.1186i 1.66229 + 2.87917i
\(215\) −10.3752 −0.707586
\(216\) 0 0
\(217\) 2.00000 0.135769
\(218\) 21.8587 + 37.8603i 1.48046 + 2.56423i
\(219\) 0 0
\(220\) −5.75927 + 9.97535i −0.388290 + 0.672538i
\(221\) −19.9827 + 34.6110i −1.34418 + 2.32819i
\(222\) 0 0
\(223\) 0.635288 + 1.10035i 0.0425420 + 0.0736849i 0.886512 0.462705i \(-0.153121\pi\)
−0.843970 + 0.536390i \(0.819788\pi\)
\(224\) −15.3719 −1.02708
\(225\) 0 0
\(226\) 20.0072 1.33086
\(227\) −8.09743 14.0252i −0.537445 0.930882i −0.999041 0.0437919i \(-0.986056\pi\)
0.461595 0.887091i \(-0.347277\pi\)
\(228\) 0 0
\(229\) −6.18236 + 10.7082i −0.408542 + 0.707615i −0.994727 0.102562i \(-0.967296\pi\)
0.586185 + 0.810177i \(0.300629\pi\)
\(230\) −5.64976 + 9.78568i −0.372534 + 0.645248i
\(231\) 0 0
\(232\) −16.1896 28.0412i −1.06290 1.84099i
\(233\) −18.7931 −1.23117 −0.615587 0.788069i \(-0.711081\pi\)
−0.615587 + 0.788069i \(0.711081\pi\)
\(234\) 0 0
\(235\) 7.76651 0.506631
\(236\) −11.9807 20.7512i −0.779876 1.35078i
\(237\) 0 0
\(238\) 9.06561 15.7021i 0.587636 1.01782i
\(239\) 10.5656 18.3002i 0.683433 1.18374i −0.290494 0.956877i \(-0.593820\pi\)
0.973927 0.226863i \(-0.0728470\pi\)
\(240\) 0 0
\(241\) −3.18236 5.51200i −0.204994 0.355059i 0.745137 0.666911i \(-0.232384\pi\)
−0.950131 + 0.311852i \(0.899051\pi\)
\(242\) 22.9879 1.47772
\(243\) 0 0
\(244\) −12.1167 −0.775695
\(245\) −0.727452 1.25998i −0.0464752 0.0804974i
\(246\) 0 0
\(247\) 18.3792 31.8337i 1.16944 2.02553i
\(248\) 8.33816 14.4421i 0.529474 0.917075i
\(249\) 0 0
\(250\) −15.3063 26.5114i −0.968058 1.67673i
\(251\) 16.0145 1.01082 0.505412 0.862878i \(-0.331340\pi\)
0.505412 + 0.862878i \(0.331340\pi\)
\(252\) 0 0
\(253\) −4.49593 −0.282657
\(254\) −9.51690 16.4837i −0.597143 1.03428i
\(255\) 0 0
\(256\) −2.56199 + 4.43750i −0.160124 + 0.277344i
\(257\) 8.64450 14.9727i 0.539229 0.933972i −0.459717 0.888066i \(-0.652049\pi\)
0.998946 0.0459063i \(-0.0146176\pi\)
\(258\) 0 0
\(259\) −2.50000 4.33013i −0.155342 0.269061i
\(260\) 43.8591 2.72003
\(261\) 0 0
\(262\) 50.5104 3.12054
\(263\) −6.77255 11.7304i −0.417613 0.723327i 0.578086 0.815976i \(-0.303800\pi\)
−0.995699 + 0.0926488i \(0.970467\pi\)
\(264\) 0 0
\(265\) −7.12398 + 12.3391i −0.437623 + 0.757985i
\(266\) −8.33816 + 14.4421i −0.511245 + 0.885503i
\(267\) 0 0
\(268\) −8.62036 14.9309i −0.526573 0.912050i
\(269\) 12.7931 0.780007 0.390003 0.920813i \(-0.372474\pi\)
0.390003 + 0.920813i \(0.372474\pi\)
\(270\) 0 0
\(271\) −32.0145 −1.94474 −0.972370 0.233443i \(-0.925001\pi\)
−0.972370 + 0.233443i \(0.925001\pi\)
\(272\) −40.7830 70.6382i −2.47283 4.28307i
\(273\) 0 0
\(274\) 7.88687 13.6605i 0.476463 0.825259i
\(275\) 2.22745 3.85806i 0.134320 0.232650i
\(276\) 0 0
\(277\) −6.68959 11.5867i −0.401939 0.696178i 0.592021 0.805922i \(-0.298330\pi\)
−0.993960 + 0.109744i \(0.964997\pi\)
\(278\) 4.67632 0.280467
\(279\) 0 0
\(280\) −12.1312 −0.724979
\(281\) −5.38325 9.32407i −0.321138 0.556227i 0.659585 0.751630i \(-0.270732\pi\)
−0.980723 + 0.195403i \(0.937399\pi\)
\(282\) 0 0
\(283\) 14.3719 24.8929i 0.854324 1.47973i −0.0229473 0.999737i \(-0.507305\pi\)
0.877271 0.479995i \(-0.159362\pi\)
\(284\) 3.49638 6.05591i 0.207472 0.359352i
\(285\) 0 0
\(286\) 12.1312 + 21.0119i 0.717334 + 1.24246i
\(287\) 2.24797 0.132693
\(288\) 0 0
\(289\) 29.1457 1.71445
\(290\) −7.53983 13.0594i −0.442754 0.766873i
\(291\) 0 0
\(292\) 4.82488 8.35694i 0.282355 0.489053i
\(293\) 3.06561 5.30979i 0.179095 0.310201i −0.762476 0.647017i \(-0.776016\pi\)
0.941571 + 0.336815i \(0.109350\pi\)
\(294\) 0 0
\(295\) −3.40180 5.89208i −0.198060 0.343050i
\(296\) −41.6908 −2.42323
\(297\) 0 0
\(298\) −16.2552 −0.941639
\(299\) 8.55957 + 14.8256i 0.495013 + 0.857387i
\(300\) 0 0
\(301\) 3.56561 6.17582i 0.205518 0.355968i
\(302\) 0.847817 1.46846i 0.0487864 0.0845005i
\(303\) 0 0
\(304\) 37.5104 + 64.9699i 2.15137 + 3.72628i
\(305\) −3.44043 −0.196998
\(306\) 0 0
\(307\) −5.76651 −0.329112 −0.164556 0.986368i \(-0.552619\pi\)
−0.164556 + 0.986368i \(0.552619\pi\)
\(308\) −3.95852 6.85636i −0.225558 0.390678i
\(309\) 0 0
\(310\) 3.88325 6.72599i 0.220554 0.382011i
\(311\) 2.66908 4.62298i 0.151350 0.262145i −0.780374 0.625313i \(-0.784971\pi\)
0.931724 + 0.363168i \(0.118305\pi\)
\(312\) 0 0
\(313\) −3.69366 6.39761i −0.208778 0.361614i 0.742552 0.669789i \(-0.233615\pi\)
−0.951330 + 0.308174i \(0.900282\pi\)
\(314\) 13.7560 0.776295
\(315\) 0 0
\(316\) 17.2407 0.969867
\(317\) 5.51328 + 9.54928i 0.309656 + 0.536341i 0.978287 0.207254i \(-0.0664526\pi\)
−0.668631 + 0.743595i \(0.733119\pi\)
\(318\) 0 0
\(319\) 3.00000 5.19615i 0.167968 0.290929i
\(320\) −12.3772 + 21.4380i −0.691907 + 1.19842i
\(321\) 0 0
\(322\) −3.88325 6.72599i −0.216405 0.374825i
\(323\) −42.4428 −2.36158
\(324\) 0 0
\(325\) −16.9629 −0.940933
\(326\) −7.15942 12.4005i −0.396524 0.686799i
\(327\) 0 0
\(328\) 9.37195 16.2327i 0.517479 0.896301i
\(329\) −2.66908 + 4.62298i −0.147151 + 0.254873i
\(330\) 0 0
\(331\) 15.7665 + 27.3084i 0.866606 + 1.50101i 0.865444 + 0.501006i \(0.167036\pi\)
0.00116169 + 0.999999i \(0.499630\pi\)
\(332\) −11.5185 −0.632162
\(333\) 0 0
\(334\) 26.0289 1.42424
\(335\) −2.44767 4.23948i −0.133730 0.231628i
\(336\) 0 0
\(337\) −17.3249 + 30.0076i −0.943746 + 1.63462i −0.185505 + 0.982643i \(0.559392\pi\)
−0.758242 + 0.651973i \(0.773941\pi\)
\(338\) 28.8430 49.9575i 1.56885 2.71733i
\(339\) 0 0
\(340\) −25.3208 43.8569i −1.37321 2.37848i
\(341\) 3.09019 0.167343
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −29.7306 51.4949i −1.60297 2.77642i
\(345\) 0 0
\(346\) −32.4448 + 56.1960i −1.74424 + 3.02112i
\(347\) 1.34420 2.32822i 0.0721603 0.124985i −0.827688 0.561189i \(-0.810344\pi\)
0.899848 + 0.436204i \(0.143677\pi\)
\(348\) 0 0
\(349\) 2.24073 + 3.88106i 0.119943 + 0.207748i 0.919745 0.392516i \(-0.128395\pi\)
−0.799802 + 0.600264i \(0.795062\pi\)
\(350\) 7.69563 0.411349
\(351\) 0 0
\(352\) −23.7511 −1.26594
\(353\) 15.5523 + 26.9374i 0.827767 + 1.43373i 0.899786 + 0.436332i \(0.143723\pi\)
−0.0720188 + 0.997403i \(0.522944\pi\)
\(354\) 0 0
\(355\) 0.992763 1.71952i 0.0526904 0.0912624i
\(356\) 2.03182 3.51921i 0.107686 0.186518i
\(357\) 0 0
\(358\) −18.1312 31.4042i −0.958265 1.65976i
\(359\) 18.2214 0.961689 0.480845 0.876806i \(-0.340330\pi\)
0.480845 + 0.876806i \(0.340330\pi\)
\(360\) 0 0
\(361\) 20.0371 1.05458
\(362\) 2.66908 + 4.62298i 0.140284 + 0.242978i
\(363\) 0 0
\(364\) −15.0728 + 26.1069i −0.790032 + 1.36838i
\(365\) 1.36998 2.37287i 0.0717079 0.124202i
\(366\) 0 0
\(367\) 14.1312 + 24.4760i 0.737644 + 1.27764i 0.953554 + 0.301223i \(0.0973949\pi\)
−0.215910 + 0.976413i \(0.569272\pi\)
\(368\) −34.9388 −1.82131
\(369\) 0 0
\(370\) −19.4163 −1.00940
\(371\) −4.89653 8.48104i −0.254215 0.440314i
\(372\) 0 0
\(373\) 1.07691 1.86527i 0.0557605 0.0965801i −0.836798 0.547512i \(-0.815575\pi\)
0.892558 + 0.450932i \(0.148908\pi\)
\(374\) 14.0072 24.2612i 0.724297 1.25452i
\(375\) 0 0
\(376\) 22.2552 + 38.5471i 1.14772 + 1.98792i
\(377\) −22.8462 −1.17664
\(378\) 0 0
\(379\) −7.67237 −0.394103 −0.197052 0.980393i \(-0.563137\pi\)
−0.197052 + 0.980393i \(0.563137\pi\)
\(380\) 23.2890 + 40.3377i 1.19470 + 2.06928i
\(381\) 0 0
\(382\) −20.4339 + 35.3926i −1.04549 + 1.81084i
\(383\) −8.90981 + 15.4322i −0.455270 + 0.788551i −0.998704 0.0509014i \(-0.983791\pi\)
0.543434 + 0.839452i \(0.317124\pi\)
\(384\) 0 0
\(385\) −1.12398 1.94680i −0.0572835 0.0992179i
\(386\) 33.0410 1.68174
\(387\) 0 0
\(388\) 52.5104 2.66581
\(389\) −0.0901918 0.156217i −0.00457291 0.00792051i 0.863730 0.503955i \(-0.168122\pi\)
−0.868303 + 0.496035i \(0.834789\pi\)
\(390\) 0 0
\(391\) 9.88325 17.1183i 0.499818 0.865710i
\(392\) 4.16908 7.22106i 0.210570 0.364718i
\(393\) 0 0
\(394\) 7.64614 + 13.2435i 0.385207 + 0.667198i
\(395\) 4.89533 0.246311
\(396\) 0 0
\(397\) −22.3937 −1.12391 −0.561953 0.827169i \(-0.689950\pi\)
−0.561953 + 0.827169i \(0.689950\pi\)
\(398\) 16.0338 + 27.7713i 0.803701 + 1.39205i
\(399\) 0 0
\(400\) 17.3100 29.9817i 0.865498 1.49909i
\(401\) −6.04510 + 10.4704i −0.301878 + 0.522867i −0.976561 0.215240i \(-0.930947\pi\)
0.674684 + 0.738107i \(0.264280\pi\)
\(402\) 0 0
\(403\) −5.88325 10.1901i −0.293066 0.507605i
\(404\) −46.5780 −2.31734
\(405\) 0 0
\(406\) 10.3647 0.514392
\(407\) −3.86274 6.69046i −0.191469 0.331634i
\(408\) 0 0
\(409\) 10.1824 17.6364i 0.503485 0.872062i −0.496507 0.868033i \(-0.665384\pi\)
0.999992 0.00402894i \(-0.00128246\pi\)
\(410\) 4.36471 7.55990i 0.215558 0.373357i
\(411\) 0 0
\(412\) −46.1529 79.9392i −2.27379 3.93832i
\(413\) 4.67632 0.230106
\(414\) 0 0
\(415\) −3.27058 −0.160546
\(416\) 45.2185 + 78.3208i 2.21702 + 3.83999i
\(417\) 0 0
\(418\) −12.8833 + 22.3145i −0.630141 + 1.09144i
\(419\) −5.48870 + 9.50670i −0.268140 + 0.464433i −0.968382 0.249474i \(-0.919742\pi\)
0.700241 + 0.713906i \(0.253076\pi\)
\(420\) 0 0
\(421\) −3.86471 6.69388i −0.188355 0.326240i 0.756347 0.654170i \(-0.226982\pi\)
−0.944702 + 0.327931i \(0.893649\pi\)
\(422\) 35.0483 1.70612
\(423\) 0 0
\(424\) −81.6561 −3.96557
\(425\) 9.79306 + 16.9621i 0.475033 + 0.822782i
\(426\) 0 0
\(427\) 1.18236 2.04790i 0.0572182 0.0991049i
\(428\) −46.6831 + 80.8575i −2.25651 + 3.90840i
\(429\) 0 0
\(430\) −13.8462 23.9823i −0.667722 1.15653i
\(431\) 27.1722 1.30884 0.654421 0.756131i \(-0.272913\pi\)
0.654421 + 0.756131i \(0.272913\pi\)
\(432\) 0 0
\(433\) 4.59820 0.220976 0.110488 0.993877i \(-0.464759\pi\)
0.110488 + 0.993877i \(0.464759\pi\)
\(434\) 2.66908 + 4.62298i 0.128120 + 0.221910i
\(435\) 0 0
\(436\) −41.9633 + 72.6826i −2.00968 + 3.48087i
\(437\) −9.09019 + 15.7447i −0.434843 + 0.753170i
\(438\) 0 0
\(439\) 12.1240 + 20.9994i 0.578646 + 1.00224i 0.995635 + 0.0933329i \(0.0297521\pi\)
−0.416989 + 0.908912i \(0.636915\pi\)
\(440\) −18.7439 −0.893580
\(441\) 0 0
\(442\) −106.671 −5.07380
\(443\) −15.0410 26.0518i −0.714621 1.23776i −0.963106 0.269124i \(-0.913266\pi\)
0.248485 0.968636i \(-0.420067\pi\)
\(444\) 0 0
\(445\) 0.576915 0.999246i 0.0273484 0.0473688i
\(446\) −1.69563 + 2.93692i −0.0802906 + 0.139067i
\(447\) 0 0
\(448\) −8.50724 14.7350i −0.401929 0.696162i
\(449\) −29.3792 −1.38649 −0.693245 0.720702i \(-0.743820\pi\)
−0.693245 + 0.720702i \(0.743820\pi\)
\(450\) 0 0
\(451\) 3.47332 0.163552
\(452\) 19.2045 + 33.2632i 0.903304 + 1.56457i
\(453\) 0 0
\(454\) 21.6127 37.4343i 1.01433 1.75688i
\(455\) −4.27979 + 7.41281i −0.200639 + 0.347518i
\(456\) 0 0
\(457\) 0.500000 + 0.866025i 0.0233890 + 0.0405110i 0.877483 0.479608i \(-0.159221\pi\)
−0.854094 + 0.520119i \(0.825888\pi\)
\(458\) −33.0024 −1.54210
\(459\) 0 0
\(460\) −21.6923 −1.01141
\(461\) −4.25520 7.37023i −0.198185 0.343266i 0.749755 0.661715i \(-0.230171\pi\)
−0.947940 + 0.318449i \(0.896838\pi\)
\(462\) 0 0
\(463\) −11.6968 + 20.2595i −0.543598 + 0.941539i 0.455096 + 0.890442i \(0.349605\pi\)
−0.998694 + 0.0510966i \(0.983728\pi\)
\(464\) 23.3136 40.3803i 1.08231 1.87461i
\(465\) 0 0
\(466\) −25.0801 43.4400i −1.16181 2.01232i
\(467\) −25.8872 −1.19792 −0.598958 0.800780i \(-0.704419\pi\)
−0.598958 + 0.800780i \(0.704419\pi\)
\(468\) 0 0
\(469\) 3.36471 0.155368
\(470\) 10.3647 + 17.9522i 0.478089 + 0.828074i
\(471\) 0 0
\(472\) 19.4959 33.7679i 0.897373 1.55430i
\(473\) 5.50921 9.54223i 0.253314 0.438752i
\(474\) 0 0
\(475\) −9.00724 15.6010i −0.413280 0.715823i
\(476\) 34.8075 1.59540
\(477\) 0 0
\(478\) 56.4009 2.57972
\(479\) 5.90981 + 10.2361i 0.270026 + 0.467699i 0.968868 0.247577i \(-0.0796344\pi\)
−0.698842 + 0.715276i \(0.746301\pi\)
\(480\) 0 0
\(481\) −14.7081 + 25.4752i −0.670633 + 1.16157i
\(482\) 8.49396 14.7120i 0.386889 0.670112i
\(483\) 0 0
\(484\) 22.0656 + 38.2188i 1.00298 + 1.73722i
\(485\) 14.9098 0.677020
\(486\) 0 0
\(487\) 31.8606 1.44374 0.721872 0.692027i \(-0.243282\pi\)
0.721872 + 0.692027i \(0.243282\pi\)
\(488\) −9.85867 17.0757i −0.446281 0.772982i
\(489\) 0 0
\(490\) 1.94163 3.36300i 0.0877138 0.151925i
\(491\) −7.76651 + 13.4520i −0.350498 + 0.607080i −0.986337 0.164742i \(-0.947321\pi\)
0.635839 + 0.771822i \(0.280654\pi\)
\(492\) 0 0
\(493\) 13.1896 + 22.8450i 0.594029 + 1.02889i
\(494\) 98.1110 4.41422
\(495\) 0 0
\(496\) 24.0145 1.07828
\(497\) 0.682356 + 1.18188i 0.0306079 + 0.0530144i
\(498\) 0 0
\(499\) −12.3792 + 21.4414i −0.554169 + 0.959848i 0.443799 + 0.896126i \(0.353630\pi\)
−0.997968 + 0.0637218i \(0.979703\pi\)
\(500\) 29.3845 50.8954i 1.31411 2.27611i
\(501\) 0 0
\(502\) 21.3719 + 37.0173i 0.953877 + 1.65216i
\(503\) −35.2995 −1.57393 −0.786964 0.616999i \(-0.788348\pi\)
−0.786964 + 0.616999i \(0.788348\pi\)
\(504\) 0 0
\(505\) −13.2254 −0.588521
\(506\) −6.00000 10.3923i −0.266733 0.461994i
\(507\) 0 0
\(508\) 18.2701 31.6448i 0.810606 1.40401i
\(509\) 0.0901918 0.156217i 0.00399768 0.00692419i −0.864020 0.503458i \(-0.832061\pi\)
0.868017 + 0.496534i \(0.165394\pi\)
\(510\) 0 0
\(511\) 0.941627 + 1.63095i 0.0416551 + 0.0721488i
\(512\) 15.6618 0.692162
\(513\) 0 0
\(514\) 46.1457 2.03540
\(515\) −13.1047 22.6979i −0.577461 1.00019i
\(516\) 0 0
\(517\) −4.12398 + 7.14295i −0.181373 + 0.314147i
\(518\) 6.67270 11.5575i 0.293182 0.507805i
\(519\) 0 0
\(520\) 35.6855 + 61.8091i 1.56491 + 2.71051i
\(521\) −10.8567 −0.475641 −0.237820 0.971309i \(-0.576433\pi\)
−0.237820 + 0.971309i \(0.576433\pi\)
\(522\) 0 0
\(523\) −40.7439 −1.78161 −0.890803 0.454389i \(-0.849857\pi\)
−0.890803 + 0.454389i \(0.849857\pi\)
\(524\) 48.4839 + 83.9765i 2.11803 + 3.66853i
\(525\) 0 0
\(526\) 18.0765 31.3094i 0.788171 1.36515i
\(527\) −6.79306 + 11.7659i −0.295910 + 0.512532i
\(528\) 0 0
\(529\) 7.26651 + 12.5860i 0.315935 + 0.547216i
\(530\) −38.0289 −1.65187
\(531\) 0 0
\(532\) −32.0145 −1.38800
\(533\) −6.61268 11.4535i −0.286427 0.496106i
\(534\) 0 0
\(535\) −13.2552 + 22.9587i −0.573072 + 0.992591i
\(536\) 14.0278 24.2968i 0.605907 1.04946i
\(537\) 0 0
\(538\) 17.0728 + 29.5710i 0.736063 + 1.27490i
\(539\) 1.54510 0.0665520
\(540\) 0 0
\(541\) −17.2335 −0.740926 −0.370463 0.928847i \(-0.620801\pi\)
−0.370463 + 0.928847i \(0.620801\pi\)
\(542\) −42.7246 74.0011i −1.83518 3.17862i
\(543\) 0 0
\(544\) 52.2113 90.4326i 2.23854 3.87727i
\(545\) −11.9151 + 20.6375i −0.510386 + 0.884014i
\(546\) 0 0
\(547\) 19.9303 + 34.5203i 0.852159 + 1.47598i 0.879256 + 0.476350i \(0.158040\pi\)
−0.0270967 + 0.999633i \(0.508626\pi\)
\(548\) 30.2818 1.29357
\(549\) 0 0
\(550\) 11.8905 0.507012
\(551\) −12.1312 21.0119i −0.516807 0.895137i
\(552\) 0 0
\(553\) −1.68236 + 2.91393i −0.0715411 + 0.123913i
\(554\) 17.8551 30.9259i 0.758589 1.31391i
\(555\) 0 0
\(556\) 4.48870 + 7.77465i 0.190363 + 0.329719i
\(557\) −28.5861 −1.21123 −0.605616 0.795757i \(-0.707073\pi\)
−0.605616 + 0.795757i \(0.707073\pi\)
\(558\) 0 0
\(559\) −41.9548 −1.77450
\(560\) −8.73469 15.1289i −0.369108 0.639314i
\(561\) 0 0
\(562\) 14.3683 24.8867i 0.606091 1.04978i
\(563\) 12.0410 20.8557i 0.507469 0.878962i −0.492494 0.870316i \(-0.663915\pi\)
0.999963 0.00864587i \(-0.00275210\pi\)
\(564\) 0 0
\(565\) 5.45293 + 9.44475i 0.229407 + 0.397344i
\(566\) 76.7197 3.22477
\(567\) 0 0
\(568\) 11.3792 0.477460
\(569\) −0.526554 0.912018i −0.0220743 0.0382338i 0.854777 0.518995i \(-0.173694\pi\)
−0.876852 + 0.480761i \(0.840360\pi\)
\(570\) 0 0
\(571\) 8.13122 14.0837i 0.340281 0.589384i −0.644204 0.764854i \(-0.722811\pi\)
0.984485 + 0.175470i \(0.0561445\pi\)
\(572\) −23.2890 + 40.3377i −0.973762 + 1.68660i
\(573\) 0 0
\(574\) 3.00000 + 5.19615i 0.125218 + 0.216883i
\(575\) 8.38972 0.349875
\(576\) 0 0
\(577\) 38.3937 1.59835 0.799175 0.601099i \(-0.205270\pi\)
0.799175 + 0.601099i \(0.205270\pi\)
\(578\) 38.8961 + 67.3700i 1.61786 + 2.80222i
\(579\) 0 0
\(580\) 14.4746 25.0708i 0.601027 1.04101i
\(581\) 1.12398 1.94680i 0.0466307 0.0807667i
\(582\) 0 0
\(583\) −7.56561 13.1040i −0.313336 0.542713i
\(584\) 15.7029 0.649789
\(585\) 0 0
\(586\) 16.3647 0.676020
\(587\) −13.9774 24.2096i −0.576909 0.999235i −0.995831 0.0912132i \(-0.970926\pi\)
0.418923 0.908022i \(-0.362408\pi\)
\(588\) 0 0
\(589\) 6.24797 10.8218i 0.257443 0.445904i
\(590\) 9.07966 15.7264i 0.373804 0.647447i
\(591\) 0 0
\(592\) −30.0181 51.9929i −1.23374 2.13689i
\(593\) −3.52249 −0.144651 −0.0723256 0.997381i \(-0.523042\pi\)
−0.0723256 + 0.997381i \(0.523042\pi\)
\(594\) 0 0
\(595\) 9.88325 0.405174
\(596\) −15.6030 27.0252i −0.639125 1.10700i
\(597\) 0 0
\(598\) −22.8462 + 39.5707i −0.934249 + 1.61817i
\(599\) 2.97949 5.16062i 0.121738 0.210857i −0.798715 0.601710i \(-0.794486\pi\)
0.920453 + 0.390852i \(0.127820\pi\)
\(600\) 0 0
\(601\) 0.430322 + 0.745340i 0.0175532 + 0.0304031i 0.874669 0.484721i \(-0.161079\pi\)
−0.857115 + 0.515125i \(0.827746\pi\)
\(602\) 19.0338 0.775759
\(603\) 0 0
\(604\) 3.25520 0.132452
\(605\) 6.26531 + 10.8518i 0.254721 + 0.441190i
\(606\) 0 0
\(607\) 16.4887 28.5593i 0.669256 1.15918i −0.308857 0.951108i \(-0.599946\pi\)
0.978113 0.208076i \(-0.0667202\pi\)
\(608\) −48.0217 + 83.1760i −1.94754 + 3.37323i
\(609\) 0 0
\(610\) −4.59139 7.95252i −0.185900 0.321988i
\(611\) 31.4057 1.27054
\(612\) 0 0
\(613\) −27.9203 −1.12769 −0.563846 0.825880i \(-0.690679\pi\)
−0.563846 + 0.825880i \(0.690679\pi\)
\(614\) −7.69563 13.3292i −0.310570 0.537924i
\(615\) 0 0
\(616\) 6.44163 11.1572i 0.259541 0.449537i
\(617\) −20.6855 + 35.8284i −0.832768 + 1.44240i 0.0630670 + 0.998009i \(0.479912\pi\)
−0.895835 + 0.444387i \(0.853422\pi\)
\(618\) 0 0
\(619\) 5.64252 + 9.77314i 0.226792 + 0.392816i 0.956856 0.290564i \(-0.0938428\pi\)
−0.730063 + 0.683379i \(0.760509\pi\)
\(620\) 14.9098 0.598792
\(621\) 0 0
\(622\) 14.2480 0.571291
\(623\) 0.396531 + 0.686812i 0.0158867 + 0.0275165i
\(624\) 0 0
\(625\) 1.13529 1.96638i 0.0454115 0.0786550i
\(626\) 9.85867 17.0757i 0.394032 0.682483i
\(627\) 0 0
\(628\) 13.2041 + 22.8701i 0.526900 + 0.912617i
\(629\) 33.9653 1.35429
\(630\) 0 0
\(631\) 32.2624 1.28435 0.642174 0.766559i \(-0.278033\pi\)
0.642174 + 0.766559i \(0.278033\pi\)
\(632\) 14.0278 + 24.2968i 0.557994 + 0.966474i
\(633\) 0 0
\(634\) −14.7154 + 25.4878i −0.584422 + 1.01225i
\(635\) 5.18762 8.98522i 0.205864 0.356568i
\(636\) 0 0
\(637\) −2.94163 5.09505i −0.116552 0.201873i
\(638\) 16.0145 0.634019
\(639\) 0 0
\(640\) −21.3421 −0.843621
\(641\) −18.9694 32.8559i −0.749245 1.29773i −0.948185 0.317719i \(-0.897083\pi\)
0.198939 0.980012i \(-0.436250\pi\)
\(642\) 0 0
\(643\) −19.4018 + 33.6049i −0.765132 + 1.32525i 0.175045 + 0.984561i \(0.443993\pi\)
−0.940177 + 0.340687i \(0.889340\pi\)
\(644\) 7.45490 12.9123i 0.293764 0.508815i
\(645\) 0 0
\(646\) −56.6416 98.1062i −2.22854 3.85994i
\(647\) 43.7279 1.71912 0.859560 0.511035i \(-0.170738\pi\)
0.859560 + 0.511035i \(0.170738\pi\)
\(648\) 0 0
\(649\) 7.22536 0.283620
\(650\) −22.6377 39.2096i −0.887923 1.53793i
\(651\) 0 0
\(652\) 13.7443 23.8059i 0.538270 0.932311i
\(653\) −17.5994 + 30.4831i −0.688718 + 1.19289i 0.283535 + 0.958962i \(0.408493\pi\)
−0.972253 + 0.233932i \(0.924841\pi\)
\(654\) 0 0
\(655\) 13.7665 + 23.8443i 0.537902 + 0.931674i
\(656\) 26.9919 1.05386
\(657\) 0 0
\(658\) −14.2480 −0.555444
\(659\) −2.18642 3.78700i −0.0851710 0.147520i 0.820293 0.571943i \(-0.193810\pi\)
−0.905464 + 0.424423i \(0.860477\pi\)
\(660\) 0 0
\(661\) 11.3063 19.5832i 0.439766 0.761696i −0.557905 0.829904i \(-0.688395\pi\)
0.997671 + 0.0682081i \(0.0217282\pi\)
\(662\) −42.0821 + 72.8883i −1.63557 + 2.83288i
\(663\) 0 0
\(664\) −9.37195 16.2327i −0.363702 0.629951i
\(665\) −9.09019 −0.352503
\(666\) 0 0
\(667\) 11.2995 0.437519
\(668\) 24.9846 + 43.2746i 0.966684 + 1.67435i
\(669\) 0 0
\(670\) 6.53302 11.3155i 0.252392 0.437157i
\(671\) 1.82685 3.16420i 0.0705249 0.122153i
\(672\) 0 0
\(673\) −12.8647 22.2823i −0.495898 0.858921i 0.504091 0.863651i \(-0.331828\pi\)
−0.999989 + 0.00472987i \(0.998494\pi\)
\(674\) −92.4830 −3.56231
\(675\) 0 0
\(676\) 110.743 4.25935
\(677\) 17.0676 + 29.5619i 0.655960 + 1.13616i 0.981652 + 0.190681i \(0.0610696\pi\)
−0.325692 + 0.945476i \(0.605597\pi\)
\(678\) 0 0
\(679\) −5.12398 + 8.87500i −0.196640 + 0.340591i
\(680\) 41.2041 71.3675i 1.58010 2.73682i
\(681\) 0 0
\(682\) 4.12398 + 7.14295i 0.157915 + 0.273518i
\(683\) 13.8075 0.528331 0.264165 0.964477i \(-0.414904\pi\)
0.264165 + 0.964477i \(0.414904\pi\)
\(684\) 0 0
\(685\) 8.59820 0.328520
\(686\) 1.33454 + 2.31149i 0.0509530 + 0.0882531i
\(687\) 0 0
\(688\) 42.8131 74.1545i 1.63224 2.82711i
\(689\) −28.8075 + 49.8961i −1.09748 + 1.90089i
\(690\) 0 0
\(691\) 0.635288 + 1.10035i 0.0241675 + 0.0418593i 0.877856 0.478924i \(-0.158973\pi\)
−0.853689 + 0.520784i \(0.825640\pi\)
\(692\) −124.572 −4.73553
\(693\) 0 0
\(694\) 7.17554 0.272380
\(695\) 1.27452 + 2.20753i 0.0483453 + 0.0837365i
\(696\) 0 0
\(697\) −7.63529 + 13.2247i −0.289207 + 0.500921i
\(698\) −5.98068 + 10.3588i −0.226372 + 0.392088i
\(699\) 0 0
\(700\) 7.38687 + 12.7944i 0.279198 + 0.483584i
\(701\) 15.0000 0.566542 0.283271 0.959040i \(-0.408580\pi\)
0.283271 + 0.959040i \(0.408580\pi\)
\(702\) 0 0
\(703\) −31.2398 −1.17823
\(704\) −13.1445 22.7669i −0.495402 0.858061i
\(705\) 0 0
\(706\) −41.5104 + 71.8981i −1.56226 + 2.70592i
\(707\) 4.54510 7.87234i 0.170936 0.296070i
\(708\) 0 0
\(709\) 15.5000 + 26.8468i 0.582115 + 1.00825i 0.995228 + 0.0975728i \(0.0311079\pi\)
−0.413114 + 0.910679i \(0.635559\pi\)
\(710\) 5.29952 0.198888
\(711\) 0 0
\(712\) 6.61268 0.247821
\(713\) 2.90981 + 5.03994i 0.108973 + 0.188747i
\(714\) 0 0
\(715\) −6.61268 + 11.4535i −0.247300 + 0.428336i
\(716\) 34.8075 60.2884i 1.30082 2.25308i
\(717\) 0 0
\(718\) 24.3172 + 42.1186i 0.907510 + 1.57185i
\(719\) −36.4428 −1.35909 −0.679544 0.733635i \(-0.737822\pi\)
−0.679544 + 0.733635i \(0.737822\pi\)
\(720\) 0 0
\(721\) 18.0145 0.670894
\(722\) 26.7403 + 46.3155i 0.995170 + 1.72369i
\(723\) 0 0
\(724\) −5.12398 + 8.87500i −0.190431 + 0.329837i
\(725\) −5.59820 + 9.69637i −0.207912 + 0.360114i
\(726\) 0 0
\(727\) 7.89049 + 13.6667i 0.292642 + 0.506871i 0.974434 0.224676i \(-0.0721322\pi\)
−0.681792 + 0.731547i \(0.738799\pi\)
\(728\) −49.0555 −1.81812
\(729\) 0 0
\(730\) 7.31315 0.270672
\(731\) 24.2214 + 41.9527i 0.895861 + 1.55168i
\(732\) 0 0
\(733\) −17.3864 + 30.1142i −0.642182 + 1.11229i 0.342762 + 0.939422i \(0.388637\pi\)
−0.984945 + 0.172870i \(0.944696\pi\)
\(734\) −37.7173 + 65.3284i −1.39217 + 2.41131i
\(735\) 0 0
\(736\) −22.3647 38.7368i −0.824374 1.42786i
\(737\) 5.19880 0.191500
\(738\) 0 0
\(739\) 0.635288 0.0233694 0.0116847 0.999932i \(-0.496281\pi\)
0.0116847 + 0.999932i \(0.496281\pi\)
\(740\) −18.6373 32.2807i −0.685119 1.18666i
\(741\) 0 0
\(742\) 13.0692 22.6366i 0.479786 0.831015i
\(743\) 24.9448 43.2057i 0.915136 1.58506i 0.108434 0.994104i \(-0.465417\pi\)
0.806702 0.590958i \(-0.201250\pi\)
\(744\) 0 0
\(745\) −4.43032 7.67354i −0.162314 0.281137i
\(746\) 5.74874 0.210476
\(747\) 0 0
\(748\) 53.7810 1.96643
\(749\) −9.11071 15.7802i −0.332898 0.576596i
\(750\) 0 0
\(751\) 9.08415 15.7342i 0.331485 0.574150i −0.651318 0.758805i \(-0.725784\pi\)
0.982803 + 0.184655i \(0.0591169\pi\)
\(752\) −32.0483 + 55.5092i −1.16868 + 2.02421i
\(753\) 0 0
\(754\) −30.4891 52.8087i −1.11035 1.92318i
\(755\) 0.924283 0.0336381
\(756\) 0 0
\(757\) −14.4959 −0.526864 −0.263432 0.964678i \(-0.584854\pi\)
−0.263432 + 0.964678i \(0.584854\pi\)
\(758\) −10.2391 17.7346i −0.371900 0.644150i
\(759\) 0 0
\(760\) −37.8977 + 65.6408i −1.37470 + 2.38104i
\(761\) 11.0020 19.0560i 0.398821 0.690779i −0.594760 0.803904i \(-0.702753\pi\)
0.993581 + 0.113125i \(0.0360861\pi\)
\(762\) 0 0
\(763\) −8.18959 14.1848i −0.296483 0.513524i
\(764\) −78.4564 −2.83845
\(765\) 0 0
\(766\) −47.5620 −1.71848
\(767\) −13.7560 23.8261i −0.496700 0.860309i
\(768\) 0 0
\(769\) −13.8176 + 23.9329i −0.498277 + 0.863041i −0.999998 0.00198843i \(-0.999367\pi\)
0.501721 + 0.865029i \(0.332700\pi\)
\(770\) 3.00000 5.19615i 0.108112 0.187256i
\(771\) 0 0
\(772\) 31.7154 + 54.9326i 1.14146 + 1.97707i
\(773\) 22.0636 0.793574 0.396787 0.917911i \(-0.370125\pi\)
0.396787 + 0.917911i \(0.370125\pi\)
\(774\) 0 0
\(775\) −5.76651 −0.207139
\(776\) 42.7246 + 74.0011i 1.53372 + 2.65649i
\(777\) 0 0
\(778\) 0.240729 0.416955i 0.00863056 0.0149486i
\(779\) 7.02261 12.1635i 0.251611 0.435803i
\(780\) 0 0
\(781\) 1.05431 + 1.82611i 0.0377260 + 0.0653434i
\(782\) 52.7584 1.88664
\(783\) 0 0
\(784\) 12.0072 0.428830
\(785\) 3.74916 + 6.49374i 0.133813 + 0.231772i
\(786\) 0 0
\(787\) 13.0072 22.5292i 0.463658 0.803079i −0.535482 0.844547i \(-0.679870\pi\)
0.999140 + 0.0414676i \(0.0132033\pi\)
\(788\) −14.6787 + 25.4243i −0.522908 + 0.905704i
\(789\) 0 0
\(790\) 6.53302 + 11.3155i 0.232434 + 0.402588i
\(791\) −7.49593 −0.266525
\(792\) 0 0
\(793\) −13.9122 −0.494037
\(794\) −29.8852 51.7627i −1.06059 1.83699i
\(795\) 0 0
\(796\) −30.7810 + 53.3142i −1.09100 + 1.88967i
\(797\) 15.4376 26.7386i 0.546826 0.947131i −0.451663 0.892189i \(-0.649169\pi\)
0.998490 0.0549426i \(-0.0174976\pi\)
\(798\) 0 0
\(799\) −18.1312 31.4042i −0.641436 1.11100i
\(800\) 44.3212 1.56699
\(801\) 0 0
\(802\) −32.2697 −1.13948
\(803\) 1.45490 + 2.51997i 0.0513425 + 0.0889277i
\(804\) 0 0
\(805\) 2.11675 3.66631i 0.0746055 0.129221i
\(806\) 15.7029 27.1982i 0.553110 0.958015i
\(807\) 0 0
\(808\) −37.8977 65.6408i −1.33324 2.30923i
\(809\) −43.8567 −1.54192 −0.770960 0.636884i \(-0.780223\pi\)
−0.770960 + 0.636884i \(0.780223\pi\)
\(810\) 0 0
\(811\) 11.2706 0.395763 0.197882 0.980226i \(-0.436594\pi\)
0.197882 + 0.980226i \(0.436594\pi\)
\(812\) 9.94886 + 17.2319i 0.349137 + 0.604722i
\(813\) 0 0
\(814\) 10.3100 17.8574i 0.361364 0.625901i
\(815\) 3.90257 6.75945i 0.136701 0.236773i
\(816\) 0 0
\(817\) −22.2778 38.5863i −0.779402 1.34996i
\(818\) 54.3550 1.90048
\(819\) 0 0
\(820\) 16.7584 0.585228
\(821\) 17.2029 + 29.7962i 0.600384 + 1.03990i 0.992763 + 0.120092i \(0.0383190\pi\)
−0.392378 + 0.919804i \(0.628348\pi\)
\(822\) 0 0
\(823\) −1.27058 + 2.20070i −0.0442895 + 0.0767116i −0.887320 0.461154i \(-0.847436\pi\)
0.843031 + 0.537865i \(0.180769\pi\)
\(824\) 75.1038 130.084i 2.61636 4.53167i
\(825\) 0 0
\(826\) 6.24073 + 10.8093i 0.217143 + 0.376102i
\(827\) −7.90586 −0.274914 −0.137457 0.990508i \(-0.543893\pi\)
−0.137457 + 0.990508i \(0.543893\pi\)
\(828\) 0 0
\(829\) −40.2624 −1.39837 −0.699186 0.714940i \(-0.746454\pi\)
−0.699186 + 0.714940i \(0.746454\pi\)
\(830\) −4.36471 7.55990i −0.151501 0.262408i
\(831\) 0 0
\(832\) −50.0502 + 86.6896i −1.73518 + 3.00542i
\(833\) −3.39653 + 5.88296i −0.117683 + 0.203833i
\(834\) 0 0
\(835\) 7.09414 + 12.2874i 0.245503 + 0.425223i
\(836\) −49.4654 −1.71080
\(837\) 0 0
\(838\) −29.2995 −1.01214
\(839\) −10.5258 18.2312i −0.363390 0.629410i 0.625126 0.780524i \(-0.285047\pi\)
−0.988516 + 0.151113i \(0.951714\pi\)
\(840\) 0 0
\(841\) 6.96017 12.0554i 0.240006 0.415702i
\(842\) 10.3152 17.8665i 0.355486 0.615720i
\(843\) 0 0
\(844\) 33.6421 + 58.2698i 1.15801 + 2.00573i
\(845\) 31.4444 1.08172
\(846\) 0 0
\(847\) −8.61268 −0.295935
\(848\) −58.7938 101.834i −2.01899 3.49699i
\(849\) 0 0
\(850\) −26.1385 + 45.2731i −0.896542 + 1.55286i
\(851\) 7.27452 12.5998i 0.249367 0.431917i
\(852\) 0 0
\(853\) 12.7367 + 22.0605i 0.436095 + 0.755339i 0.997384 0.0722810i \(-0.0230278\pi\)
−0.561289 + 0.827620i \(0.689694\pi\)
\(854\) 6.31160 0.215979
\(855\) 0 0
\(856\) −151.933 −5.19296
\(857\) −17.6445 30.5612i −0.602725 1.04395i −0.992407 0.123000i \(-0.960748\pi\)
0.389682 0.920949i \(-0.372585\pi\)
\(858\) 0 0
\(859\) 12.0145 20.8097i 0.409929 0.710017i −0.584953 0.811067i \(-0.698887\pi\)
0.994881 + 0.101050i \(0.0322203\pi\)
\(860\) 26.5813 46.0401i 0.906414 1.56996i
\(861\) 0 0
\(862\) 36.2624 + 62.8084i 1.23510 + 2.13926i
\(863\) −39.8365 −1.35605 −0.678025 0.735039i \(-0.737164\pi\)
−0.678025 + 0.735039i \(0.737164\pi\)
\(864\) 0 0
\(865\) −35.3711 −1.20265
\(866\) 6.13649 + 10.6287i 0.208526 + 0.361178i
\(867\) 0 0
\(868\) −5.12398 + 8.87500i −0.173919 + 0.301237i
\(869\) −2.59940 + 4.50230i −0.0881787 + 0.152730i
\(870\) 0 0
\(871\) −9.89773 17.1434i −0.335372 0.580881i
\(872\) −136.572 −4.62492
\(873\) 0 0
\(874\) −48.5249 −1.64138
\(875\) 5.73469 + 9.93277i 0.193868 + 0.335789i
\(876\) 0 0
\(877\) 9.50000 16.4545i 0.320792 0.555628i −0.659860 0.751389i \(-0.729384\pi\)
0.980652 + 0.195761i \(0.0627176\pi\)
\(878\) −32.3599 + 56.0489i −1.09209 + 1.89156i
\(879\) 0 0
\(880\) −13.4959 23.3756i −0.454948 0.787993i
\(881\) −1.28505 −0.0432944 −0.0216472 0.999766i \(-0.506891\pi\)
−0.0216472 + 0.999766i \(0.506891\pi\)
\(882\) 0 0
\(883\) −25.9348 −0.872776 −0.436388 0.899759i \(-0.643742\pi\)
−0.436388 + 0.899759i \(0.643742\pi\)
\(884\) −102.391 177.346i −3.44377 5.96479i
\(885\) 0 0
\(886\) 40.1457 69.5344i 1.34872 2.33605i
\(887\) −20.5596 + 35.6102i −0.690323 + 1.19567i 0.281409 + 0.959588i \(0.409198\pi\)
−0.971732 + 0.236086i \(0.924135\pi\)
\(888\) 0 0
\(889\) 3.56561 + 6.17582i 0.119587 + 0.207130i
\(890\) 3.07966 0.103231
\(891\) 0 0
\(892\) −6.51041 −0.217985
\(893\) 16.6763 + 28.8842i 0.558052 + 0.966574i
\(894\) 0 0
\(895\) 9.88325 17.1183i 0.330361 0.572202i
\(896\) 7.33454 12.7038i 0.245030 0.424404i
\(897\) 0 0
\(898\) −39.2077 67.9097i −1.30838 2.26618i
\(899\) −7.76651 −0.259028
\(900\) 0 0
\(901\) 66.5249 2.21627
\(902\) 4.63529 + 8.02855i 0.154338 + 0.267322i
\(903\) 0 0
\(904\) −31.2511 + 54.1286i −1.03940 + 1.80029i
\(905\) −1.45490 + 2.51997i −0.0483626 + 0.0837666i
\(906\) 0 0
\(907\) −16.6824 28.8947i −0.553929 0.959432i −0.997986 0.0634341i \(-0.979795\pi\)
0.444057 0.895998i \(-0.353539\pi\)
\(908\) 82.9822 2.75386
\(909\) 0 0
\(910\) −22.8462 −0.757343
\(911\) 10.4959 + 18.1795i 0.347746 + 0.602313i 0.985849 0.167638i \(-0.0536139\pi\)
−0.638103 + 0.769951i \(0.720281\pi\)
\(912\) 0 0
\(913\) 1.73666 3.00799i 0.0574751 0.0995498i
\(914\) −1.33454 + 2.31149i −0.0441426 + 0.0764573i
\(915\) 0 0
\(916\) −31.6783 54.8684i −1.04668 1.81290i
\(917\) −18.9243 −0.624935
\(918\) 0 0
\(919\) 24.6353 0.812643 0.406322 0.913730i \(-0.366811\pi\)
0.406322 + 0.913730i \(0.366811\pi\)
\(920\) −17.6498 30.5703i −0.581895 1.00787i
\(921\) 0 0
\(922\) 11.3575 19.6717i 0.374039 0.647854i
\(923\) 4.01447 6.95327i 0.132138 0.228870i
\(924\) 0 0
\(925\) 7.20814 + 12.4849i 0.237002 + 0.410500i
\(926\) −62.4395 −2.05189
\(927\) 0 0
\(928\) 59.6932 1.95952
\(929\) −23.4940 40.6927i −0.770812 1.33509i −0.937119 0.349011i \(-0.886518\pi\)
0.166307 0.986074i \(-0.446816\pi\)
\(930\) 0 0
\(931\) 3.12398 5.41090i 0.102384 0.177335i
\(932\) 48.1477 83.3942i 1.57713 2.73167i
\(933\) 0 0
\(934\) −34.5475 59.8380i −1.13043 1.95796i
\(935\) 15.2706 0.499401
\(936\) 0 0
\(937\) 58.6416 1.91574 0.957869 0.287205i \(-0.0927260\pi\)
0.957869 + 0.287205i \(0.0927260\pi\)
\(938\) 4.49034 + 7.77750i 0.146615 + 0.253944i
\(939\) 0 0
\(940\) −19.8977 + 34.4639i −0.648992 + 1.12409i
\(941\) 11.8659 20.5524i 0.386818 0.669988i −0.605202 0.796072i \(-0.706908\pi\)
0.992020 + 0.126084i \(0.0402410\pi\)
\(942\) 0 0
\(943\) 3.27058 + 5.66480i 0.106505 + 0.184471i
\(944\) 56.1496 1.82752
\(945\) 0 0
\(946\) 29.4090 0.956170
\(947\) 8.06758 + 13.9735i 0.262161 + 0.454077i 0.966816 0.255474i \(-0.0822314\pi\)
−0.704655 + 0.709550i \(0.748898\pi\)
\(948\) 0 0
\(949\) 5.53983 9.59527i 0.179831 0.311476i
\(950\) 24.0410 41.6403i 0.779994 1.35099i
\(951\) 0 0
\(952\) 28.3208 + 49.0531i 0.917883 + 1.58982i
\(953\) 20.3792 0.660147 0.330073 0.943955i \(-0.392927\pi\)
0.330073 + 0.943955i \(0.392927\pi\)
\(954\) 0 0
\(955\) −22.2769 −0.720864
\(956\) 54.1380 + 93.7698i 1.75095 + 3.03273i
\(957\) 0 0
\(958\) −15.7737 + 27.3209i −0.509627 + 0.882699i
\(959\) −2.95490 + 5.11804i −0.0954188 + 0.165270i
\(960\) 0 0
\(961\) 13.5000 + 23.3827i 0.435484 + 0.754280i
\(962\) −78.5144 −2.53140
\(963\) 0 0
\(964\) 32.6127 1.05038
\(965\) 9.00526 + 15.5976i 0.289890 + 0.502104i
\(966\) 0 0
\(967\) −12.1167 + 20.9868i −0.389648 + 0.674891i −0.992402 0.123037i \(-0.960737\pi\)
0.602754 + 0.797927i \(0.294070\pi\)
\(968\) −35.9069 + 62.1926i −1.15409 + 1.99895i
\(969\) 0 0
\(970\) 19.8977 + 34.4639i 0.638878 + 1.10657i
\(971\) 48.3445 1.55145 0.775724 0.631072i \(-0.217385\pi\)
0.775724 + 0.631072i \(0.217385\pi\)
\(972\) 0 0
\(973\) −1.75203 −0.0561676
\(974\) 42.5193 + 73.6456i 1.36241 + 2.35976i
\(975\) 0 0
\(976\) 14.1968 24.5896i 0.454429 0.787095i
\(977\) 13.6763 23.6881i 0.437544 0.757849i −0.559955 0.828523i \(-0.689182\pi\)
0.997499 + 0.0706741i \(0.0225150\pi\)
\(978\) 0 0
\(979\) 0.612679 + 1.06119i 0.0195813 + 0.0339158i
\(980\) 7.45490 0.238138
\(981\) 0 0
\(982\) −41.4588 −1.32301
\(983\) 8.53786 + 14.7880i 0.272315 + 0.471664i 0.969454 0.245272i \(-0.0788773\pi\)
−0.697139 + 0.716936i \(0.745544\pi\)
\(984\) 0 0
\(985\) −4.16788 + 7.21898i −0.132800 + 0.230016i
\(986\) −35.2041 + 60.9752i −1.12113 + 1.94185i
\(987\) 0 0
\(988\) 94.1746 + 163.115i 2.99609 + 5.18939i
\(989\) 20.7505 0.659827
\(990\) 0 0
\(991\) 38.1231 1.21102 0.605510 0.795838i \(-0.292969\pi\)
0.605510 + 0.795838i \(0.292969\pi\)
\(992\) 15.3719 + 26.6250i 0.488060 + 0.845345i
\(993\) 0 0
\(994\) −1.82126 + 3.15452i −0.0577669 + 0.100055i
\(995\) −8.73995 + 15.1380i −0.277075 + 0.479908i
\(996\) 0 0
\(997\) −3.82488 6.62489i −0.121135 0.209812i 0.799080 0.601224i \(-0.205320\pi\)
−0.920216 + 0.391412i \(0.871987\pi\)
\(998\) −66.0821 −2.09179
\(999\) 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 567.2.f.l.190.3 6
3.2 odd 2 567.2.f.m.190.1 6
9.2 odd 6 567.2.f.m.379.1 6
9.4 even 3 567.2.a.f.1.1 yes 3
9.5 odd 6 567.2.a.e.1.3 3
9.7 even 3 inner 567.2.f.l.379.3 6
36.23 even 6 9072.2.a.bu.1.2 3
36.31 odd 6 9072.2.a.cb.1.2 3
63.13 odd 6 3969.2.a.n.1.1 3
63.41 even 6 3969.2.a.o.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
567.2.a.e.1.3 3 9.5 odd 6
567.2.a.f.1.1 yes 3 9.4 even 3
567.2.f.l.190.3 6 1.1 even 1 trivial
567.2.f.l.379.3 6 9.7 even 3 inner
567.2.f.m.190.1 6 3.2 odd 2
567.2.f.m.379.1 6 9.2 odd 6
3969.2.a.n.1.1 3 63.13 odd 6
3969.2.a.o.1.3 3 63.41 even 6
9072.2.a.bu.1.2 3 36.23 even 6
9072.2.a.cb.1.2 3 36.31 odd 6