Properties

Label 1323.2.h.c.226.1
Level $1323$
Weight $2$
Character 1323.226
Analytic conductor $10.564$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1323,2,Mod(226,1323)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1323, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1323.226");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (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: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - x^{3} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 226.1
Root \(-0.766044 + 0.642788i\) of defining polynomial
Character \(\chi\) \(=\) 1323.226
Dual form 1323.2.h.c.802.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-2.53209 q^{2} +4.41147 q^{4} +(-0.439693 - 0.761570i) q^{5} -6.10607 q^{8} +O(q^{10})\) \(q-2.53209 q^{2} +4.41147 q^{4} +(-0.439693 - 0.761570i) q^{5} -6.10607 q^{8} +(1.11334 + 1.92836i) q^{10} +(1.93969 - 3.35965i) q^{11} +(2.72668 - 4.72275i) q^{13} +6.63816 q^{16} +(0.826352 + 1.43128i) q^{17} +(-1.20574 + 2.08840i) q^{19} +(-1.93969 - 3.35965i) q^{20} +(-4.91147 + 8.50692i) q^{22} +(1.58125 + 2.73881i) q^{23} +(2.11334 - 3.66041i) q^{25} +(-6.90420 + 11.9584i) q^{26} +(-3.02481 - 5.23913i) q^{29} -4.55438 q^{31} -4.59627 q^{32} +(-2.09240 - 3.62414i) q^{34} +(2.27719 - 3.94421i) q^{37} +(3.05303 - 5.28801i) q^{38} +(2.68479 + 4.65020i) q^{40} +(-0.592396 + 1.02606i) q^{41} +(-0.0923963 - 0.160035i) q^{43} +(8.55690 - 14.8210i) q^{44} +(-4.00387 - 6.93491i) q^{46} +1.02229 q^{47} +(-5.35117 + 9.26849i) q^{50} +(12.0287 - 20.8343i) q^{52} +(3.64543 + 6.31407i) q^{53} -3.41147 q^{55} +(7.65910 + 13.2660i) q^{58} -6.66044 q^{59} -2.59627 q^{61} +11.5321 q^{62} -1.63816 q^{64} -4.79561 q^{65} -2.95811 q^{67} +(3.64543 + 6.31407i) q^{68} +3.68004 q^{71} +(6.39053 + 11.0687i) q^{73} +(-5.76604 + 9.98708i) q^{74} +(-5.31908 + 9.21291i) q^{76} -5.95811 q^{79} +(-2.91875 - 5.05542i) q^{80} +(1.50000 - 2.59808i) q^{82} +(-0.109470 - 0.189608i) q^{83} +(0.726682 - 1.25865i) q^{85} +(0.233956 + 0.405223i) q^{86} +(-11.8439 + 20.5142i) q^{88} +(5.51367 - 9.54996i) q^{89} +(6.97565 + 12.0822i) q^{92} -2.58853 q^{94} +2.12061 q^{95} +(-6.25150 - 10.8279i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 6 q^{2} + 6 q^{4} + 3 q^{5} - 12 q^{8} + 6 q^{11} + 3 q^{13} + 6 q^{16} + 6 q^{17} + 3 q^{19} - 6 q^{20} - 9 q^{22} + 12 q^{23} + 6 q^{25} - 3 q^{26} + 9 q^{29} - 6 q^{31} - 9 q^{34} + 3 q^{37} + 6 q^{38} + 9 q^{40} + 3 q^{43} + 15 q^{44} - 6 q^{47} - 6 q^{50} + 21 q^{52} + 6 q^{53} + 9 q^{58} + 6 q^{59} + 12 q^{61} + 60 q^{62} + 24 q^{64} - 30 q^{65} - 24 q^{67} + 6 q^{68} - 18 q^{71} + 21 q^{73} - 30 q^{74} - 15 q^{76} - 42 q^{79} - 15 q^{80} + 9 q^{82} - 18 q^{83} - 9 q^{85} + 6 q^{86} - 27 q^{88} + 12 q^{89} + 3 q^{92} - 36 q^{94} + 24 q^{95} + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.53209 −1.79046 −0.895229 0.445607i \(-0.852988\pi\)
−0.895229 + 0.445607i \(0.852988\pi\)
\(3\) 0 0
\(4\) 4.41147 2.20574
\(5\) −0.439693 0.761570i −0.196637 0.340584i 0.750799 0.660530i \(-0.229669\pi\)
−0.947436 + 0.319946i \(0.896335\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −6.10607 −2.15882
\(9\) 0 0
\(10\) 1.11334 + 1.92836i 0.352069 + 0.609802i
\(11\) 1.93969 3.35965i 0.584839 1.01297i −0.410056 0.912060i \(-0.634491\pi\)
0.994895 0.100911i \(-0.0321758\pi\)
\(12\) 0 0
\(13\) 2.72668 4.72275i 0.756245 1.30986i −0.188507 0.982072i \(-0.560365\pi\)
0.944753 0.327784i \(-0.106302\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 6.63816 1.65954
\(17\) 0.826352 + 1.43128i 0.200420 + 0.347137i 0.948664 0.316286i \(-0.102436\pi\)
−0.748244 + 0.663424i \(0.769103\pi\)
\(18\) 0 0
\(19\) −1.20574 + 2.08840i −0.276615 + 0.479111i −0.970541 0.240935i \(-0.922546\pi\)
0.693926 + 0.720046i \(0.255879\pi\)
\(20\) −1.93969 3.35965i −0.433728 0.751240i
\(21\) 0 0
\(22\) −4.91147 + 8.50692i −1.04713 + 1.81368i
\(23\) 1.58125 + 2.73881i 0.329714 + 0.571081i 0.982455 0.186500i \(-0.0597144\pi\)
−0.652741 + 0.757581i \(0.726381\pi\)
\(24\) 0 0
\(25\) 2.11334 3.66041i 0.422668 0.732083i
\(26\) −6.90420 + 11.9584i −1.35403 + 2.34524i
\(27\) 0 0
\(28\) 0 0
\(29\) −3.02481 5.23913i −0.561694 0.972883i −0.997349 0.0727688i \(-0.976816\pi\)
0.435655 0.900114i \(-0.356517\pi\)
\(30\) 0 0
\(31\) −4.55438 −0.817990 −0.408995 0.912537i \(-0.634121\pi\)
−0.408995 + 0.912537i \(0.634121\pi\)
\(32\) −4.59627 −0.812513
\(33\) 0 0
\(34\) −2.09240 3.62414i −0.358843 0.621534i
\(35\) 0 0
\(36\) 0 0
\(37\) 2.27719 3.94421i 0.374368 0.648424i −0.615865 0.787852i \(-0.711193\pi\)
0.990232 + 0.139428i \(0.0445265\pi\)
\(38\) 3.05303 5.28801i 0.495267 0.857828i
\(39\) 0 0
\(40\) 2.68479 + 4.65020i 0.424503 + 0.735261i
\(41\) −0.592396 + 1.02606i −0.0925168 + 0.160244i −0.908570 0.417734i \(-0.862825\pi\)
0.816053 + 0.577977i \(0.196158\pi\)
\(42\) 0 0
\(43\) −0.0923963 0.160035i −0.0140903 0.0244051i 0.858894 0.512153i \(-0.171152\pi\)
−0.872985 + 0.487748i \(0.837819\pi\)
\(44\) 8.55690 14.8210i 1.29000 2.23435i
\(45\) 0 0
\(46\) −4.00387 6.93491i −0.590338 1.02250i
\(47\) 1.02229 0.149116 0.0745581 0.997217i \(-0.476245\pi\)
0.0745581 + 0.997217i \(0.476245\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −5.35117 + 9.26849i −0.756769 + 1.31076i
\(51\) 0 0
\(52\) 12.0287 20.8343i 1.66808 2.88920i
\(53\) 3.64543 + 6.31407i 0.500738 + 0.867304i 1.00000 0.000852699i \(0.000271423\pi\)
−0.499261 + 0.866451i \(0.666395\pi\)
\(54\) 0 0
\(55\) −3.41147 −0.460003
\(56\) 0 0
\(57\) 0 0
\(58\) 7.65910 + 13.2660i 1.00569 + 1.74190i
\(59\) −6.66044 −0.867116 −0.433558 0.901126i \(-0.642742\pi\)
−0.433558 + 0.901126i \(0.642742\pi\)
\(60\) 0 0
\(61\) −2.59627 −0.332418 −0.166209 0.986091i \(-0.553153\pi\)
−0.166209 + 0.986091i \(0.553153\pi\)
\(62\) 11.5321 1.46458
\(63\) 0 0
\(64\) −1.63816 −0.204769
\(65\) −4.79561 −0.594822
\(66\) 0 0
\(67\) −2.95811 −0.361391 −0.180695 0.983539i \(-0.557835\pi\)
−0.180695 + 0.983539i \(0.557835\pi\)
\(68\) 3.64543 + 6.31407i 0.442073 + 0.765693i
\(69\) 0 0
\(70\) 0 0
\(71\) 3.68004 0.436741 0.218370 0.975866i \(-0.429926\pi\)
0.218370 + 0.975866i \(0.429926\pi\)
\(72\) 0 0
\(73\) 6.39053 + 11.0687i 0.747955 + 1.29550i 0.948801 + 0.315873i \(0.102297\pi\)
−0.200847 + 0.979623i \(0.564369\pi\)
\(74\) −5.76604 + 9.98708i −0.670289 + 1.16097i
\(75\) 0 0
\(76\) −5.31908 + 9.21291i −0.610140 + 1.05679i
\(77\) 0 0
\(78\) 0 0
\(79\) −5.95811 −0.670340 −0.335170 0.942158i \(-0.608794\pi\)
−0.335170 + 0.942158i \(0.608794\pi\)
\(80\) −2.91875 5.05542i −0.326326 0.565213i
\(81\) 0 0
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) −0.109470 0.189608i −0.0120159 0.0208122i 0.859955 0.510370i \(-0.170492\pi\)
−0.871971 + 0.489558i \(0.837158\pi\)
\(84\) 0 0
\(85\) 0.726682 1.25865i 0.0788197 0.136520i
\(86\) 0.233956 + 0.405223i 0.0252281 + 0.0436963i
\(87\) 0 0
\(88\) −11.8439 + 20.5142i −1.26256 + 2.18682i
\(89\) 5.51367 9.54996i 0.584448 1.01229i −0.410496 0.911862i \(-0.634644\pi\)
0.994944 0.100431i \(-0.0320222\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 6.97565 + 12.0822i 0.727262 + 1.25965i
\(93\) 0 0
\(94\) −2.58853 −0.266986
\(95\) 2.12061 0.217570
\(96\) 0 0
\(97\) −6.25150 10.8279i −0.634743 1.09941i −0.986569 0.163342i \(-0.947773\pi\)
0.351826 0.936065i \(-0.385561\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 9.32295 16.1478i 0.932295 1.61478i
\(101\) −4.85844 + 8.41507i −0.483433 + 0.837330i −0.999819 0.0190255i \(-0.993944\pi\)
0.516386 + 0.856356i \(0.327277\pi\)
\(102\) 0 0
\(103\) −3.29813 5.71253i −0.324975 0.562873i 0.656533 0.754298i \(-0.272022\pi\)
−0.981507 + 0.191425i \(0.938689\pi\)
\(104\) −16.6493 + 28.8374i −1.63260 + 2.82774i
\(105\) 0 0
\(106\) −9.23055 15.9878i −0.896550 1.55287i
\(107\) 1.19459 2.06910i 0.115486 0.200027i −0.802488 0.596668i \(-0.796491\pi\)
0.917974 + 0.396641i \(0.129824\pi\)
\(108\) 0 0
\(109\) −1.97906 3.42782i −0.189559 0.328326i 0.755544 0.655098i \(-0.227373\pi\)
−0.945103 + 0.326772i \(0.894039\pi\)
\(110\) 8.63816 0.823616
\(111\) 0 0
\(112\) 0 0
\(113\) 8.22668 14.2490i 0.773901 1.34044i −0.161509 0.986871i \(-0.551636\pi\)
0.935410 0.353565i \(-0.115031\pi\)
\(114\) 0 0
\(115\) 1.39053 2.40847i 0.129668 0.224591i
\(116\) −13.3439 23.1123i −1.23895 2.14592i
\(117\) 0 0
\(118\) 16.8648 1.55253
\(119\) 0 0
\(120\) 0 0
\(121\) −2.02481 3.50708i −0.184074 0.318826i
\(122\) 6.57398 0.595180
\(123\) 0 0
\(124\) −20.0915 −1.80427
\(125\) −8.11381 −0.725721
\(126\) 0 0
\(127\) 17.6536 1.56651 0.783253 0.621702i \(-0.213559\pi\)
0.783253 + 0.621702i \(0.213559\pi\)
\(128\) 13.3405 1.17914
\(129\) 0 0
\(130\) 12.1429 1.06500
\(131\) −9.59879 16.6256i −0.838650 1.45259i −0.891023 0.453958i \(-0.850012\pi\)
0.0523729 0.998628i \(-0.483322\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 7.49020 0.647055
\(135\) 0 0
\(136\) −5.04576 8.73951i −0.432670 0.749407i
\(137\) 9.07785 15.7233i 0.775573 1.34333i −0.158899 0.987295i \(-0.550794\pi\)
0.934472 0.356037i \(-0.115872\pi\)
\(138\) 0 0
\(139\) −11.0287 + 19.1022i −0.935441 + 1.62023i −0.161595 + 0.986857i \(0.551664\pi\)
−0.773846 + 0.633374i \(0.781670\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −9.31820 −0.781966
\(143\) −10.5778 18.3214i −0.884564 1.53211i
\(144\) 0 0
\(145\) −2.65998 + 4.60722i −0.220899 + 0.382608i
\(146\) −16.1814 28.0270i −1.33918 2.31953i
\(147\) 0 0
\(148\) 10.0458 17.3998i 0.825756 1.43025i
\(149\) −7.57785 13.1252i −0.620802 1.07526i −0.989337 0.145646i \(-0.953474\pi\)
0.368535 0.929614i \(-0.379859\pi\)
\(150\) 0 0
\(151\) 9.47818 16.4167i 0.771323 1.33597i −0.165515 0.986207i \(-0.552929\pi\)
0.936838 0.349764i \(-0.113738\pi\)
\(152\) 7.36231 12.7519i 0.597162 1.03432i
\(153\) 0 0
\(154\) 0 0
\(155\) 2.00253 + 3.46848i 0.160847 + 0.278595i
\(156\) 0 0
\(157\) −18.0574 −1.44114 −0.720568 0.693385i \(-0.756119\pi\)
−0.720568 + 0.693385i \(0.756119\pi\)
\(158\) 15.0865 1.20021
\(159\) 0 0
\(160\) 2.02094 + 3.50038i 0.159770 + 0.276729i
\(161\) 0 0
\(162\) 0 0
\(163\) −0.479055 + 0.829748i −0.0375225 + 0.0649909i −0.884177 0.467152i \(-0.845280\pi\)
0.846654 + 0.532143i \(0.178613\pi\)
\(164\) −2.61334 + 4.52644i −0.204068 + 0.353456i
\(165\) 0 0
\(166\) 0.277189 + 0.480105i 0.0215140 + 0.0372634i
\(167\) 9.91921 17.1806i 0.767572 1.32947i −0.171304 0.985218i \(-0.554798\pi\)
0.938876 0.344255i \(-0.111869\pi\)
\(168\) 0 0
\(169\) −8.36959 14.4965i −0.643814 1.11512i
\(170\) −1.84002 + 3.18701i −0.141123 + 0.244433i
\(171\) 0 0
\(172\) −0.407604 0.705990i −0.0310795 0.0538313i
\(173\) −22.6827 −1.72454 −0.862268 0.506452i \(-0.830957\pi\)
−0.862268 + 0.506452i \(0.830957\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 12.8760 22.3019i 0.970564 1.68107i
\(177\) 0 0
\(178\) −13.9611 + 24.1813i −1.04643 + 1.81247i
\(179\) −3.67365 6.36295i −0.274581 0.475589i 0.695448 0.718576i \(-0.255206\pi\)
−0.970029 + 0.242988i \(0.921873\pi\)
\(180\) 0 0
\(181\) −3.44562 −0.256111 −0.128056 0.991767i \(-0.540874\pi\)
−0.128056 + 0.991767i \(0.540874\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −9.65523 16.7233i −0.711793 1.23286i
\(185\) −4.00505 −0.294457
\(186\) 0 0
\(187\) 6.41147 0.468853
\(188\) 4.50980 0.328911
\(189\) 0 0
\(190\) −5.36959 −0.389551
\(191\) −5.65776 −0.409381 −0.204690 0.978827i \(-0.565619\pi\)
−0.204690 + 0.978827i \(0.565619\pi\)
\(192\) 0 0
\(193\) 9.59627 0.690754 0.345377 0.938464i \(-0.387751\pi\)
0.345377 + 0.938464i \(0.387751\pi\)
\(194\) 15.8293 + 27.4172i 1.13648 + 1.96844i
\(195\) 0 0
\(196\) 0 0
\(197\) −8.31996 −0.592772 −0.296386 0.955068i \(-0.595782\pi\)
−0.296386 + 0.955068i \(0.595782\pi\)
\(198\) 0 0
\(199\) −3.29813 5.71253i −0.233798 0.404951i 0.725124 0.688618i \(-0.241782\pi\)
−0.958923 + 0.283667i \(0.908449\pi\)
\(200\) −12.9042 + 22.3507i −0.912465 + 1.58044i
\(201\) 0 0
\(202\) 12.3020 21.3077i 0.865566 1.49920i
\(203\) 0 0
\(204\) 0 0
\(205\) 1.04189 0.0727687
\(206\) 8.35117 + 14.4646i 0.581853 + 1.00780i
\(207\) 0 0
\(208\) 18.1001 31.3504i 1.25502 2.17376i
\(209\) 4.67752 + 8.10170i 0.323551 + 0.560406i
\(210\) 0 0
\(211\) 1.68479 2.91815i 0.115986 0.200893i −0.802188 0.597072i \(-0.796331\pi\)
0.918173 + 0.396179i \(0.129664\pi\)
\(212\) 16.0817 + 27.8544i 1.10450 + 1.91304i
\(213\) 0 0
\(214\) −3.02481 + 5.23913i −0.206772 + 0.358140i
\(215\) −0.0812519 + 0.140732i −0.00554133 + 0.00959787i
\(216\) 0 0
\(217\) 0 0
\(218\) 5.01114 + 8.67956i 0.339398 + 0.587854i
\(219\) 0 0
\(220\) −15.0496 −1.01465
\(221\) 9.01279 0.606266
\(222\) 0 0
\(223\) 3.13816 + 5.43545i 0.210146 + 0.363984i 0.951760 0.306843i \(-0.0992726\pi\)
−0.741614 + 0.670827i \(0.765939\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −20.8307 + 36.0798i −1.38564 + 2.39999i
\(227\) −3.08125 + 5.33688i −0.204510 + 0.354221i −0.949976 0.312322i \(-0.898893\pi\)
0.745467 + 0.666543i \(0.232227\pi\)
\(228\) 0 0
\(229\) −11.6925 20.2521i −0.772664 1.33829i −0.936098 0.351740i \(-0.885590\pi\)
0.163434 0.986554i \(-0.447743\pi\)
\(230\) −3.52094 + 6.09845i −0.232164 + 0.402120i
\(231\) 0 0
\(232\) 18.4697 + 31.9905i 1.21260 + 2.10028i
\(233\) −4.26264 + 7.38311i −0.279255 + 0.483684i −0.971200 0.238267i \(-0.923421\pi\)
0.691945 + 0.721950i \(0.256754\pi\)
\(234\) 0 0
\(235\) −0.449493 0.778544i −0.0293217 0.0507866i
\(236\) −29.3824 −1.91263
\(237\) 0 0
\(238\) 0 0
\(239\) 7.28106 12.6112i 0.470973 0.815748i −0.528476 0.848948i \(-0.677236\pi\)
0.999449 + 0.0331997i \(0.0105697\pi\)
\(240\) 0 0
\(241\) 2.70187 4.67977i 0.174043 0.301451i −0.765787 0.643094i \(-0.777650\pi\)
0.939830 + 0.341644i \(0.110984\pi\)
\(242\) 5.12701 + 8.88024i 0.329577 + 0.570844i
\(243\) 0 0
\(244\) −11.4534 −0.733226
\(245\) 0 0
\(246\) 0 0
\(247\) 6.57532 + 11.3888i 0.418378 + 0.724651i
\(248\) 27.8093 1.76589
\(249\) 0 0
\(250\) 20.5449 1.29937
\(251\) 12.0669 0.761654 0.380827 0.924646i \(-0.375639\pi\)
0.380827 + 0.924646i \(0.375639\pi\)
\(252\) 0 0
\(253\) 12.2686 0.771318
\(254\) −44.7006 −2.80476
\(255\) 0 0
\(256\) −30.5030 −1.90644
\(257\) 5.28312 + 9.15063i 0.329552 + 0.570801i 0.982423 0.186668i \(-0.0597690\pi\)
−0.652871 + 0.757469i \(0.726436\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −21.1557 −1.31202
\(261\) 0 0
\(262\) 24.3050 + 42.0975i 1.50157 + 2.60079i
\(263\) −14.1766 + 24.5547i −0.874169 + 1.51411i −0.0165240 + 0.999863i \(0.505260\pi\)
−0.857645 + 0.514242i \(0.828073\pi\)
\(264\) 0 0
\(265\) 3.20574 5.55250i 0.196927 0.341087i
\(266\) 0 0
\(267\) 0 0
\(268\) −13.0496 −0.797133
\(269\) 3.74170 + 6.48081i 0.228135 + 0.395142i 0.957255 0.289244i \(-0.0934038\pi\)
−0.729120 + 0.684386i \(0.760070\pi\)
\(270\) 0 0
\(271\) −6.81908 + 11.8110i −0.414229 + 0.717467i −0.995347 0.0963530i \(-0.969282\pi\)
0.581118 + 0.813819i \(0.302616\pi\)
\(272\) 5.48545 + 9.50108i 0.332604 + 0.576088i
\(273\) 0 0
\(274\) −22.9859 + 39.8128i −1.38863 + 2.40518i
\(275\) −8.19846 14.2002i −0.494386 0.856302i
\(276\) 0 0
\(277\) 3.07532 5.32661i 0.184778 0.320045i −0.758724 0.651413i \(-0.774177\pi\)
0.943502 + 0.331368i \(0.107510\pi\)
\(278\) 27.9256 48.3686i 1.67487 2.90095i
\(279\) 0 0
\(280\) 0 0
\(281\) 1.65611 + 2.86846i 0.0987951 + 0.171118i 0.911186 0.411995i \(-0.135168\pi\)
−0.812391 + 0.583113i \(0.801835\pi\)
\(282\) 0 0
\(283\) 29.0232 1.72525 0.862626 0.505843i \(-0.168818\pi\)
0.862626 + 0.505843i \(0.168818\pi\)
\(284\) 16.2344 0.963336
\(285\) 0 0
\(286\) 26.7841 + 46.3913i 1.58377 + 2.74318i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.13429 12.3569i 0.419664 0.726879i
\(290\) 6.73530 11.6659i 0.395510 0.685044i
\(291\) 0 0
\(292\) 28.1917 + 48.8294i 1.64979 + 2.85752i
\(293\) −4.20961 + 7.29125i −0.245928 + 0.425960i −0.962392 0.271664i \(-0.912426\pi\)
0.716464 + 0.697624i \(0.245759\pi\)
\(294\) 0 0
\(295\) 2.92855 + 5.07239i 0.170507 + 0.295326i
\(296\) −13.9047 + 24.0836i −0.808192 + 1.39983i
\(297\) 0 0
\(298\) 19.1878 + 33.2342i 1.11152 + 1.92521i
\(299\) 17.2463 0.997378
\(300\) 0 0
\(301\) 0 0
\(302\) −23.9996 + 41.5685i −1.38102 + 2.39200i
\(303\) 0 0
\(304\) −8.00387 + 13.8631i −0.459053 + 0.795104i
\(305\) 1.14156 + 1.97724i 0.0653655 + 0.113216i
\(306\) 0 0
\(307\) −12.6878 −0.724130 −0.362065 0.932153i \(-0.617928\pi\)
−0.362065 + 0.932153i \(0.617928\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −5.07057 8.78249i −0.287989 0.498812i
\(311\) 16.4902 0.935073 0.467537 0.883974i \(-0.345142\pi\)
0.467537 + 0.883974i \(0.345142\pi\)
\(312\) 0 0
\(313\) 28.5185 1.61196 0.805980 0.591943i \(-0.201639\pi\)
0.805980 + 0.591943i \(0.201639\pi\)
\(314\) 45.7229 2.58029
\(315\) 0 0
\(316\) −26.2841 −1.47859
\(317\) 25.8949 1.45440 0.727200 0.686425i \(-0.240821\pi\)
0.727200 + 0.686425i \(0.240821\pi\)
\(318\) 0 0
\(319\) −23.4688 −1.31400
\(320\) 0.720285 + 1.24757i 0.0402652 + 0.0697413i
\(321\) 0 0
\(322\) 0 0
\(323\) −3.98545 −0.221756
\(324\) 0 0
\(325\) −11.5248 19.9616i −0.639282 1.10727i
\(326\) 1.21301 2.10100i 0.0671825 0.116363i
\(327\) 0 0
\(328\) 3.61721 6.26519i 0.199727 0.345937i
\(329\) 0 0
\(330\) 0 0
\(331\) 8.21894 0.451754 0.225877 0.974156i \(-0.427475\pi\)
0.225877 + 0.974156i \(0.427475\pi\)
\(332\) −0.482926 0.836452i −0.0265040 0.0459063i
\(333\) 0 0
\(334\) −25.1163 + 43.5028i −1.37430 + 2.38037i
\(335\) 1.30066 + 2.25281i 0.0710626 + 0.123084i
\(336\) 0 0
\(337\) −2.28564 + 3.95885i −0.124507 + 0.215652i −0.921540 0.388283i \(-0.873068\pi\)
0.797033 + 0.603936i \(0.206402\pi\)
\(338\) 21.1925 + 36.7065i 1.15272 + 1.99657i
\(339\) 0 0
\(340\) 3.20574 5.55250i 0.173856 0.301127i
\(341\) −8.83409 + 15.3011i −0.478393 + 0.828601i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.564178 + 0.977185i 0.0304184 + 0.0526863i
\(345\) 0 0
\(346\) 57.4347 3.08771
\(347\) −22.4662 −1.20605 −0.603023 0.797724i \(-0.706037\pi\)
−0.603023 + 0.797724i \(0.706037\pi\)
\(348\) 0 0
\(349\) −13.0496 22.6026i −0.698531 1.20989i −0.968976 0.247155i \(-0.920504\pi\)
0.270445 0.962735i \(-0.412829\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −8.91534 + 15.4418i −0.475189 + 0.823052i
\(353\) −0.177519 + 0.307471i −0.00944836 + 0.0163650i −0.870711 0.491795i \(-0.836341\pi\)
0.861263 + 0.508160i \(0.169674\pi\)
\(354\) 0 0
\(355\) −1.61809 2.80261i −0.0858792 0.148747i
\(356\) 24.3234 42.1294i 1.28914 2.23285i
\(357\) 0 0
\(358\) 9.30200 + 16.1115i 0.491626 + 0.851522i
\(359\) 2.72803 4.72508i 0.143980 0.249380i −0.785012 0.619480i \(-0.787343\pi\)
0.928992 + 0.370100i \(0.120677\pi\)
\(360\) 0 0
\(361\) 6.59240 + 11.4184i 0.346968 + 0.600967i
\(362\) 8.72462 0.458556
\(363\) 0 0
\(364\) 0 0
\(365\) 5.61974 9.73367i 0.294150 0.509484i
\(366\) 0 0
\(367\) −5.46198 + 9.46043i −0.285113 + 0.493830i −0.972637 0.232332i \(-0.925364\pi\)
0.687523 + 0.726162i \(0.258698\pi\)
\(368\) 10.4966 + 18.1806i 0.547173 + 0.947731i
\(369\) 0 0
\(370\) 10.1411 0.527213
\(371\) 0 0
\(372\) 0 0
\(373\) −0.865715 1.49946i −0.0448250 0.0776392i 0.842742 0.538317i \(-0.180940\pi\)
−0.887567 + 0.460678i \(0.847606\pi\)
\(374\) −16.2344 −0.839462
\(375\) 0 0
\(376\) −6.24216 −0.321915
\(377\) −32.9908 −1.69911
\(378\) 0 0
\(379\) −12.1334 −0.623251 −0.311626 0.950205i \(-0.600873\pi\)
−0.311626 + 0.950205i \(0.600873\pi\)
\(380\) 9.35504 0.479903
\(381\) 0 0
\(382\) 14.3259 0.732979
\(383\) −4.35591 7.54467i −0.222577 0.385514i 0.733013 0.680215i \(-0.238113\pi\)
−0.955590 + 0.294700i \(0.904780\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −24.2986 −1.23677
\(387\) 0 0
\(388\) −27.5783 47.7670i −1.40008 2.42500i
\(389\) 1.82160 3.15511i 0.0923590 0.159970i −0.816144 0.577848i \(-0.803893\pi\)
0.908503 + 0.417878i \(0.137226\pi\)
\(390\) 0 0
\(391\) −2.61334 + 4.52644i −0.132162 + 0.228912i
\(392\) 0 0
\(393\) 0 0
\(394\) 21.0669 1.06133
\(395\) 2.61974 + 4.53752i 0.131813 + 0.228307i
\(396\) 0 0
\(397\) 7.72281 13.3763i 0.387597 0.671337i −0.604529 0.796583i \(-0.706639\pi\)
0.992126 + 0.125246i \(0.0399720\pi\)
\(398\) 8.35117 + 14.4646i 0.418606 + 0.725047i
\(399\) 0 0
\(400\) 14.0287 24.2984i 0.701434 1.21492i
\(401\) 9.21095 + 15.9538i 0.459973 + 0.796697i 0.998959 0.0456182i \(-0.0145258\pi\)
−0.538986 + 0.842315i \(0.681192\pi\)
\(402\) 0 0
\(403\) −12.4183 + 21.5092i −0.618601 + 1.07145i
\(404\) −21.4329 + 37.1228i −1.06633 + 1.84693i
\(405\) 0 0
\(406\) 0 0
\(407\) −8.83409 15.3011i −0.437890 0.758447i
\(408\) 0 0
\(409\) −28.6364 −1.41598 −0.707989 0.706223i \(-0.750398\pi\)
−0.707989 + 0.706223i \(0.750398\pi\)
\(410\) −2.63816 −0.130289
\(411\) 0 0
\(412\) −14.5496 25.2007i −0.716809 1.24155i
\(413\) 0 0
\(414\) 0 0
\(415\) −0.0962667 + 0.166739i −0.00472554 + 0.00818488i
\(416\) −12.5326 + 21.7070i −0.614459 + 1.06427i
\(417\) 0 0
\(418\) −11.8439 20.5142i −0.579304 1.00338i
\(419\) −17.3478 + 30.0472i −0.847494 + 1.46790i 0.0359442 + 0.999354i \(0.488556\pi\)
−0.883438 + 0.468548i \(0.844777\pi\)
\(420\) 0 0
\(421\) 13.7010 + 23.7308i 0.667745 + 1.15657i 0.978533 + 0.206090i \(0.0660738\pi\)
−0.310788 + 0.950479i \(0.600593\pi\)
\(422\) −4.26604 + 7.38901i −0.207668 + 0.359691i
\(423\) 0 0
\(424\) −22.2592 38.5541i −1.08100 1.87235i
\(425\) 6.98545 0.338844
\(426\) 0 0
\(427\) 0 0
\(428\) 5.26991 9.12776i 0.254731 0.441207i
\(429\) 0 0
\(430\) 0.205737 0.356347i 0.00992152 0.0171846i
\(431\) 13.2961 + 23.0295i 0.640449 + 1.10929i 0.985333 + 0.170645i \(0.0545852\pi\)
−0.344883 + 0.938646i \(0.612081\pi\)
\(432\) 0 0
\(433\) 37.1830 1.78690 0.893451 0.449160i \(-0.148277\pi\)
0.893451 + 0.449160i \(0.148277\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −8.73055 15.1218i −0.418118 0.724201i
\(437\) −7.62630 −0.364815
\(438\) 0 0
\(439\) 25.0746 1.19675 0.598373 0.801218i \(-0.295814\pi\)
0.598373 + 0.801218i \(0.295814\pi\)
\(440\) 20.8307 0.993064
\(441\) 0 0
\(442\) −22.8212 −1.08549
\(443\) −2.04458 −0.0971408 −0.0485704 0.998820i \(-0.515467\pi\)
−0.0485704 + 0.998820i \(0.515467\pi\)
\(444\) 0 0
\(445\) −9.69728 −0.459695
\(446\) −7.94609 13.7630i −0.376258 0.651698i
\(447\) 0 0
\(448\) 0 0
\(449\) 10.2344 0.482992 0.241496 0.970402i \(-0.422362\pi\)
0.241496 + 0.970402i \(0.422362\pi\)
\(450\) 0 0
\(451\) 2.29813 + 3.98048i 0.108215 + 0.187434i
\(452\) 36.2918 62.8592i 1.70702 2.95665i
\(453\) 0 0
\(454\) 7.80200 13.5135i 0.366166 0.634218i
\(455\) 0 0
\(456\) 0 0
\(457\) −42.5945 −1.99249 −0.996244 0.0865948i \(-0.972401\pi\)
−0.996244 + 0.0865948i \(0.972401\pi\)
\(458\) 29.6065 + 51.2800i 1.38342 + 2.39616i
\(459\) 0 0
\(460\) 6.13429 10.6249i 0.286013 0.495388i
\(461\) 0.252374 + 0.437124i 0.0117542 + 0.0203589i 0.871843 0.489786i \(-0.162925\pi\)
−0.860088 + 0.510145i \(0.829592\pi\)
\(462\) 0 0
\(463\) −1.34002 + 2.32099i −0.0622761 + 0.107865i −0.895482 0.445097i \(-0.853169\pi\)
0.833206 + 0.552962i \(0.186503\pi\)
\(464\) −20.0792 34.7782i −0.932153 1.61454i
\(465\) 0 0
\(466\) 10.7934 18.6947i 0.499994 0.866015i
\(467\) −15.7083 + 27.2075i −0.726892 + 1.25901i 0.231299 + 0.972883i \(0.425702\pi\)
−0.958191 + 0.286131i \(0.907631\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 1.13816 + 1.97134i 0.0524992 + 0.0909313i
\(471\) 0 0
\(472\) 40.6691 1.87195
\(473\) −0.716881 −0.0329622
\(474\) 0 0
\(475\) 5.09627 + 8.82699i 0.233833 + 0.405010i
\(476\) 0 0
\(477\) 0 0
\(478\) −18.4363 + 31.9326i −0.843256 + 1.46056i
\(479\) −8.22028 + 14.2380i −0.375594 + 0.650549i −0.990416 0.138118i \(-0.955895\pi\)
0.614821 + 0.788666i \(0.289228\pi\)
\(480\) 0 0
\(481\) −12.4183 21.5092i −0.566227 0.980735i
\(482\) −6.84137 + 11.8496i −0.311616 + 0.539734i
\(483\) 0 0
\(484\) −8.93242 15.4714i −0.406019 0.703246i
\(485\) −5.49747 + 9.52190i −0.249627 + 0.432367i
\(486\) 0 0
\(487\) 1.48767 + 2.57673i 0.0674129 + 0.116763i 0.897762 0.440481i \(-0.145192\pi\)
−0.830349 + 0.557244i \(0.811859\pi\)
\(488\) 15.8530 0.717631
\(489\) 0 0
\(490\) 0 0
\(491\) −13.2430 + 22.9376i −0.597650 + 1.03516i 0.395517 + 0.918459i \(0.370565\pi\)
−0.993167 + 0.116702i \(0.962768\pi\)
\(492\) 0 0
\(493\) 4.99912 8.65873i 0.225149 0.389970i
\(494\) −16.6493 28.8374i −0.749087 1.29746i
\(495\) 0 0
\(496\) −30.2327 −1.35749
\(497\) 0 0
\(498\) 0 0
\(499\) 6.72193 + 11.6427i 0.300915 + 0.521200i 0.976343 0.216225i \(-0.0693746\pi\)
−0.675428 + 0.737426i \(0.736041\pi\)
\(500\) −35.7939 −1.60075
\(501\) 0 0
\(502\) −30.5544 −1.36371
\(503\) 22.6631 1.01050 0.505250 0.862973i \(-0.331400\pi\)
0.505250 + 0.862973i \(0.331400\pi\)
\(504\) 0 0
\(505\) 8.54488 0.380242
\(506\) −31.0651 −1.38101
\(507\) 0 0
\(508\) 77.8786 3.45530
\(509\) 4.77379 + 8.26844i 0.211594 + 0.366492i 0.952214 0.305433i \(-0.0988011\pi\)
−0.740619 + 0.671925i \(0.765468\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 50.5553 2.23425
\(513\) 0 0
\(514\) −13.3773 23.1702i −0.590049 1.02199i
\(515\) −2.90033 + 5.02352i −0.127804 + 0.221363i
\(516\) 0 0
\(517\) 1.98293 3.43453i 0.0872090 0.151050i
\(518\) 0 0
\(519\) 0 0
\(520\) 29.2823 1.28411
\(521\) −1.55644 2.69583i −0.0681887 0.118106i 0.829915 0.557889i \(-0.188389\pi\)
−0.898104 + 0.439783i \(0.855055\pi\)
\(522\) 0 0
\(523\) 8.07444 13.9853i 0.353071 0.611537i −0.633715 0.773567i \(-0.718471\pi\)
0.986786 + 0.162030i \(0.0518041\pi\)
\(524\) −42.3448 73.3434i −1.84984 3.20402i
\(525\) 0 0
\(526\) 35.8965 62.1746i 1.56516 2.71094i
\(527\) −3.76352 6.51860i −0.163941 0.283955i
\(528\) 0 0
\(529\) 6.49928 11.2571i 0.282578 0.489439i
\(530\) −8.11721 + 14.0594i −0.352589 + 0.610702i
\(531\) 0 0
\(532\) 0 0
\(533\) 3.23055 + 5.59548i 0.139931 + 0.242367i
\(534\) 0 0
\(535\) −2.10101 −0.0908348
\(536\) 18.0624 0.780178
\(537\) 0 0
\(538\) −9.47431 16.4100i −0.408466 0.707485i
\(539\) 0 0
\(540\) 0 0
\(541\) 2.50774 4.34353i 0.107816 0.186743i −0.807069 0.590457i \(-0.798948\pi\)
0.914885 + 0.403714i \(0.132281\pi\)
\(542\) 17.2665 29.9065i 0.741660 1.28459i
\(543\) 0 0
\(544\) −3.79813 6.57856i −0.162844 0.282053i
\(545\) −1.74035 + 3.01438i −0.0745485 + 0.129122i
\(546\) 0 0
\(547\) −8.23901 14.2704i −0.352275 0.610157i 0.634373 0.773027i \(-0.281258\pi\)
−0.986648 + 0.162870i \(0.947925\pi\)
\(548\) 40.0467 69.3629i 1.71071 2.96304i
\(549\) 0 0
\(550\) 20.7592 + 35.9561i 0.885177 + 1.53317i
\(551\) 14.5885 0.621492
\(552\) 0 0
\(553\) 0 0
\(554\) −7.78699 + 13.4875i −0.330837 + 0.573027i
\(555\) 0 0
\(556\) −48.6528 + 84.2691i −2.06334 + 3.57380i
\(557\) −17.2815 29.9325i −0.732242 1.26828i −0.955923 0.293618i \(-0.905141\pi\)
0.223681 0.974662i \(-0.428193\pi\)
\(558\) 0 0
\(559\) −1.00774 −0.0426229
\(560\) 0 0
\(561\) 0 0
\(562\) −4.19341 7.26320i −0.176888 0.306380i
\(563\) 37.2104 1.56823 0.784115 0.620615i \(-0.213117\pi\)
0.784115 + 0.620615i \(0.213117\pi\)
\(564\) 0 0
\(565\) −14.4688 −0.608709
\(566\) −73.4894 −3.08899
\(567\) 0 0
\(568\) −22.4706 −0.942845
\(569\) −0.404667 −0.0169645 −0.00848226 0.999964i \(-0.502700\pi\)
−0.00848226 + 0.999964i \(0.502700\pi\)
\(570\) 0 0
\(571\) −37.7793 −1.58101 −0.790507 0.612453i \(-0.790183\pi\)
−0.790507 + 0.612453i \(0.790183\pi\)
\(572\) −46.6639 80.8243i −1.95112 3.37943i
\(573\) 0 0
\(574\) 0 0
\(575\) 13.3669 0.557438
\(576\) 0 0
\(577\) 1.10560 + 1.91496i 0.0460267 + 0.0797206i 0.888121 0.459610i \(-0.152011\pi\)
−0.842094 + 0.539330i \(0.818677\pi\)
\(578\) −18.0646 + 31.2889i −0.751390 + 1.30145i
\(579\) 0 0
\(580\) −11.7344 + 20.3246i −0.487245 + 0.843934i
\(581\) 0 0
\(582\) 0 0
\(583\) 28.2841 1.17141
\(584\) −39.0210 67.5864i −1.61470 2.79674i
\(585\) 0 0
\(586\) 10.6591 18.4621i 0.440323 0.762662i
\(587\) 12.1049 + 20.9663i 0.499622 + 0.865371i 1.00000 0.000436347i \(-0.000138894\pi\)
−0.500378 + 0.865807i \(0.666806\pi\)
\(588\) 0 0
\(589\) 5.49138 9.51135i 0.226268 0.391908i
\(590\) −7.41534 12.8438i −0.305285 0.528769i
\(591\) 0 0
\(592\) 15.1163 26.1823i 0.621277 1.07608i
\(593\) 6.11927 10.5989i 0.251288 0.435244i −0.712592 0.701578i \(-0.752479\pi\)
0.963881 + 0.266334i \(0.0858124\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −33.4295 57.9016i −1.36932 2.37174i
\(597\) 0 0
\(598\) −43.6691 −1.78576
\(599\) −39.6168 −1.61870 −0.809349 0.587328i \(-0.800180\pi\)
−0.809349 + 0.587328i \(0.800180\pi\)
\(600\) 0 0
\(601\) 15.0039 + 25.9875i 0.612021 + 1.06005i 0.990899 + 0.134605i \(0.0429764\pi\)
−0.378879 + 0.925446i \(0.623690\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 41.8127 72.4218i 1.70134 2.94680i
\(605\) −1.78059 + 3.08408i −0.0723914 + 0.125386i
\(606\) 0 0
\(607\) 9.74216 + 16.8739i 0.395422 + 0.684891i 0.993155 0.116804i \(-0.0372650\pi\)
−0.597733 + 0.801695i \(0.703932\pi\)
\(608\) 5.54189 9.59883i 0.224753 0.389284i
\(609\) 0 0
\(610\) −2.89053 5.00654i −0.117034 0.202709i
\(611\) 2.78746 4.82802i 0.112768 0.195321i
\(612\) 0 0
\(613\) 9.26382 + 16.0454i 0.374162 + 0.648068i 0.990201 0.139648i \(-0.0445970\pi\)
−0.616039 + 0.787716i \(0.711264\pi\)
\(614\) 32.1266 1.29652
\(615\) 0 0
\(616\) 0 0
\(617\) 13.9201 24.1103i 0.560402 0.970644i −0.437059 0.899433i \(-0.643980\pi\)
0.997461 0.0712118i \(-0.0226866\pi\)
\(618\) 0 0
\(619\) 22.4907 38.9550i 0.903976 1.56573i 0.0816906 0.996658i \(-0.473968\pi\)
0.822286 0.569075i \(-0.192699\pi\)
\(620\) 8.83409 + 15.3011i 0.354786 + 0.614507i
\(621\) 0 0
\(622\) −41.7547 −1.67421
\(623\) 0 0
\(624\) 0 0
\(625\) −6.99912 12.1228i −0.279965 0.484913i
\(626\) −72.2113 −2.88614
\(627\) 0 0
\(628\) −79.6596 −3.17877
\(629\) 7.52704 0.300123
\(630\) 0 0
\(631\) 9.43613 0.375646 0.187823 0.982203i \(-0.439857\pi\)
0.187823 + 0.982203i \(0.439857\pi\)
\(632\) 36.3806 1.44714
\(633\) 0 0
\(634\) −65.5681 −2.60404
\(635\) −7.76217 13.4445i −0.308032 0.533528i
\(636\) 0 0
\(637\) 0 0
\(638\) 59.4252 2.35267
\(639\) 0 0
\(640\) −5.86571 10.1597i −0.231863 0.401598i
\(641\) 18.6951 32.3808i 0.738410 1.27896i −0.214800 0.976658i \(-0.568910\pi\)
0.953211 0.302306i \(-0.0977566\pi\)
\(642\) 0 0
\(643\) −0.805874 + 1.39581i −0.0317806 + 0.0550456i −0.881478 0.472225i \(-0.843451\pi\)
0.849698 + 0.527270i \(0.176784\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 10.0915 0.397046
\(647\) −20.5881 35.6597i −0.809402 1.40193i −0.913278 0.407336i \(-0.866458\pi\)
0.103876 0.994590i \(-0.466875\pi\)
\(648\) 0 0
\(649\) −12.9192 + 22.3767i −0.507124 + 0.878364i
\(650\) 29.1819 + 50.5445i 1.14461 + 1.98252i
\(651\) 0 0
\(652\) −2.11334 + 3.66041i −0.0827648 + 0.143353i
\(653\) 1.52600 + 2.64310i 0.0597169 + 0.103433i 0.894338 0.447391i \(-0.147647\pi\)
−0.834621 + 0.550824i \(0.814314\pi\)
\(654\) 0 0
\(655\) −8.44104 + 14.6203i −0.329819 + 0.571263i
\(656\) −3.93242 + 6.81115i −0.153535 + 0.265931i
\(657\) 0 0
\(658\) 0 0
\(659\) 20.8175 + 36.0569i 0.810934 + 1.40458i 0.912211 + 0.409721i \(0.134374\pi\)
−0.101277 + 0.994858i \(0.532293\pi\)
\(660\) 0 0
\(661\) 20.3010 0.789616 0.394808 0.918764i \(-0.370811\pi\)
0.394808 + 0.918764i \(0.370811\pi\)
\(662\) −20.8111 −0.808846
\(663\) 0 0
\(664\) 0.668434 + 1.15776i 0.0259403 + 0.0449298i
\(665\) 0 0
\(666\) 0 0
\(667\) 9.56599 16.5688i 0.370397 0.641546i
\(668\) 43.7584 75.7917i 1.69306 2.93247i
\(669\) 0 0
\(670\) −3.29339 5.70431i −0.127235 0.220377i
\(671\) −5.03596 + 8.72254i −0.194411 + 0.336730i
\(672\) 0 0
\(673\) 0.415345 + 0.719398i 0.0160104 + 0.0277307i 0.873920 0.486071i \(-0.161570\pi\)
−0.857909 + 0.513801i \(0.828237\pi\)
\(674\) 5.78746 10.0242i 0.222924 0.386117i
\(675\) 0 0
\(676\) −36.9222 63.9511i −1.42008 2.45966i
\(677\) −10.8672 −0.417660 −0.208830 0.977952i \(-0.566966\pi\)
−0.208830 + 0.977952i \(0.566966\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −4.43717 + 7.68540i −0.170158 + 0.294722i
\(681\) 0 0
\(682\) 22.3687 38.7437i 0.856542 1.48357i
\(683\) 16.3473 + 28.3143i 0.625512 + 1.08342i 0.988442 + 0.151602i \(0.0484432\pi\)
−0.362930 + 0.931817i \(0.618223\pi\)
\(684\) 0 0
\(685\) −15.9659 −0.610024
\(686\) 0 0
\(687\) 0 0
\(688\) −0.613341 1.06234i −0.0233834 0.0405012i
\(689\) 39.7597 1.51472
\(690\) 0 0
\(691\) 14.9982 0.570560 0.285280 0.958444i \(-0.407913\pi\)
0.285280 + 0.958444i \(0.407913\pi\)
\(692\) −100.064 −3.80387
\(693\) 0 0
\(694\) 56.8863 2.15937
\(695\) 19.3969 0.735767
\(696\) 0 0
\(697\) −1.95811 −0.0741687
\(698\) 33.0428 + 57.2318i 1.25069 + 2.16626i
\(699\) 0 0
\(700\) 0 0
\(701\) −26.4688 −0.999714 −0.499857 0.866108i \(-0.666614\pi\)
−0.499857 + 0.866108i \(0.666614\pi\)
\(702\) 0 0
\(703\) 5.49138 + 9.51135i 0.207111 + 0.358727i
\(704\) −3.17752 + 5.50362i −0.119757 + 0.207426i
\(705\) 0 0
\(706\) 0.449493 0.778544i 0.0169169 0.0293009i
\(707\) 0 0
\(708\) 0 0
\(709\) 15.3601 0.576860 0.288430 0.957501i \(-0.406867\pi\)
0.288430 + 0.957501i \(0.406867\pi\)
\(710\) 4.09714 + 7.09646i 0.153763 + 0.266325i
\(711\) 0 0
\(712\) −33.6668 + 58.3127i −1.26172 + 2.18536i
\(713\) −7.20162 12.4736i −0.269703 0.467139i
\(714\) 0 0
\(715\) −9.30200 + 16.1115i −0.347875 + 0.602538i
\(716\) −16.2062 28.0700i −0.605654 1.04902i
\(717\) 0 0
\(718\) −6.90760 + 11.9643i −0.257789 + 0.446504i
\(719\) 13.3653 23.1494i 0.498442 0.863326i −0.501557 0.865125i \(-0.667239\pi\)
0.999998 + 0.00179839i \(0.000572447\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −16.6925 28.9123i −0.621232 1.07600i
\(723\) 0 0
\(724\) −15.2003 −0.564914
\(725\) −25.5699 −0.949641
\(726\) 0 0
\(727\) 22.8221 + 39.5290i 0.846424 + 1.46605i 0.884379 + 0.466770i \(0.154582\pi\)
−0.0379552 + 0.999279i \(0.512084\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −14.2297 + 24.6465i −0.526664 + 0.912209i
\(731\) 0.152704 0.264490i 0.00564795 0.00978253i
\(732\) 0 0
\(733\) −2.98751 5.17452i −0.110346 0.191125i 0.805564 0.592509i \(-0.201863\pi\)
−0.915910 + 0.401384i \(0.868529\pi\)
\(734\) 13.8302 23.9546i 0.510483 0.884182i
\(735\) 0 0
\(736\) −7.26786 12.5883i −0.267897 0.464011i
\(737\) −5.73783 + 9.93821i −0.211356 + 0.366079i
\(738\) 0 0
\(739\) 17.7981 + 30.8273i 0.654715 + 1.13400i 0.981965 + 0.189062i \(0.0605447\pi\)
−0.327250 + 0.944938i \(0.606122\pi\)
\(740\) −17.6682 −0.649495
\(741\) 0 0
\(742\) 0 0
\(743\) −14.6544 + 25.3821i −0.537616 + 0.931178i 0.461416 + 0.887184i \(0.347342\pi\)
−0.999032 + 0.0439943i \(0.985992\pi\)
\(744\) 0 0
\(745\) −6.66385 + 11.5421i −0.244145 + 0.422871i
\(746\) 2.19207 + 3.79677i 0.0802573 + 0.139010i
\(747\) 0 0
\(748\) 28.2841 1.03417
\(749\) 0 0
\(750\) 0 0
\(751\) 8.66684 + 15.0114i 0.316258 + 0.547774i 0.979704 0.200450i \(-0.0642403\pi\)
−0.663446 + 0.748224i \(0.730907\pi\)
\(752\) 6.78611 0.247464
\(753\) 0 0
\(754\) 83.5357 3.04219
\(755\) −16.6699 −0.606681
\(756\) 0 0
\(757\) −2.77156 −0.100734 −0.0503671 0.998731i \(-0.516039\pi\)
−0.0503671 + 0.998731i \(0.516039\pi\)
\(758\) 30.7229 1.11590
\(759\) 0 0
\(760\) −12.9486 −0.469696
\(761\) 3.75372 + 6.50163i 0.136072 + 0.235684i 0.926007 0.377508i \(-0.123219\pi\)
−0.789934 + 0.613191i \(0.789885\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −24.9590 −0.902987
\(765\) 0 0
\(766\) 11.0296 + 19.1038i 0.398514 + 0.690247i
\(767\) −18.1609 + 31.4556i −0.655752 + 1.13580i
\(768\) 0 0
\(769\) −1.02182 + 1.76985i −0.0368478 + 0.0638223i −0.883861 0.467749i \(-0.845065\pi\)
0.847013 + 0.531572i \(0.178398\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 42.3337 1.52362
\(773\) −12.4709 21.6002i −0.448547 0.776907i 0.549744 0.835333i \(-0.314725\pi\)
−0.998292 + 0.0584263i \(0.981392\pi\)
\(774\) 0 0
\(775\) −9.62495 + 16.6709i −0.345738 + 0.598837i
\(776\) 38.1721 + 66.1159i 1.37030 + 2.37342i
\(777\) 0 0
\(778\) −4.61246 + 7.98902i −0.165365 + 0.286420i
\(779\) −1.42855 2.47432i −0.0511831 0.0886516i
\(780\) 0 0
\(781\) 7.13816 12.3636i 0.255423 0.442406i
\(782\) 6.61721 11.4613i 0.236631 0.409857i
\(783\) 0 0
\(784\) 0 0
\(785\) 7.93969 + 13.7520i 0.283380 + 0.490828i
\(786\) 0 0
\(787\) 7.10700 0.253337 0.126669 0.991945i \(-0.459572\pi\)
0.126669