Properties

Label 405.2.e.j.271.1
Level $405$
Weight $2$
Character 405.271
Analytic conductor $3.234$
Analytic rank $0$
Dimension $4$
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] = [405,2,Mod(136,405)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(405, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.136");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.e (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: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{13})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + 4x^{2} + 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 271.1
Root \(1.15139 + 1.99426i\) of defining polynomial
Character \(\chi\) \(=\) 405.271
Dual form 405.2.e.j.136.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.15139 - 1.99426i) q^{2} +(-1.65139 + 2.86029i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.30278 + 2.25647i) q^{7} +3.00000 q^{8} +O(q^{10})\) \(q+(-1.15139 - 1.99426i) q^{2} +(-1.65139 + 2.86029i) q^{4} +(0.500000 - 0.866025i) q^{5} +(1.30278 + 2.25647i) q^{7} +3.00000 q^{8} -2.30278 q^{10} +(2.30278 + 3.98852i) q^{11} +(-3.30278 + 5.72058i) q^{13} +(3.00000 - 5.19615i) q^{14} +(-0.151388 - 0.262211i) q^{16} -1.60555 q^{17} +3.60555 q^{19} +(1.65139 + 2.86029i) q^{20} +(5.30278 - 9.18468i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} +15.2111 q^{26} -8.60555 q^{28} +(0.697224 + 1.20763i) q^{29} +(2.80278 - 4.85455i) q^{31} +(2.65139 - 4.59234i) q^{32} +(1.84861 + 3.20189i) q^{34} +2.60555 q^{35} +2.00000 q^{37} +(-4.15139 - 7.19041i) q^{38} +(1.50000 - 2.59808i) q^{40} +(-2.30278 + 3.98852i) q^{41} +(-0.302776 - 0.524423i) q^{43} -15.2111 q^{44} +6.90833 q^{46} +(-4.60555 - 7.97705i) q^{47} +(0.105551 - 0.182820i) q^{49} +(-1.15139 + 1.99426i) q^{50} +(-10.9083 - 18.8938i) q^{52} -1.60555 q^{53} +4.60555 q^{55} +(3.90833 + 6.76942i) q^{56} +(1.60555 - 2.78090i) q^{58} +(-0.697224 + 1.20763i) q^{59} +(2.10555 + 3.64692i) q^{61} -12.9083 q^{62} -12.8167 q^{64} +(3.30278 + 5.72058i) q^{65} +(0.394449 - 0.683205i) q^{67} +(2.65139 - 4.59234i) q^{68} +(-3.00000 - 5.19615i) q^{70} -7.39445 q^{71} +12.6056 q^{73} +(-2.30278 - 3.98852i) q^{74} +(-5.95416 + 10.3129i) q^{76} +(-6.00000 + 10.3923i) q^{77} +(5.80278 + 10.0507i) q^{79} -0.302776 q^{80} +10.6056 q^{82} +(1.50000 + 2.59808i) q^{83} +(-0.802776 + 1.39045i) q^{85} +(-0.697224 + 1.20763i) q^{86} +(6.90833 + 11.9656i) q^{88} +13.8167 q^{89} -17.2111 q^{91} +(-4.95416 - 8.58086i) q^{92} +(-10.6056 + 18.3694i) q^{94} +(1.80278 - 3.12250i) q^{95} +(-4.00000 - 6.92820i) q^{97} -0.486122 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} - 3 q^{4} + 2 q^{5} - 2 q^{7} + 12 q^{8} - 2 q^{10} + 2 q^{11} - 6 q^{13} + 12 q^{14} + 3 q^{16} + 8 q^{17} + 3 q^{20} + 14 q^{22} - 6 q^{23} - 2 q^{25} + 32 q^{26} - 20 q^{28} + 10 q^{29} + 4 q^{31} + 7 q^{32} + 11 q^{34} - 4 q^{35} + 8 q^{37} - 13 q^{38} + 6 q^{40} - 2 q^{41} + 6 q^{43} - 32 q^{44} + 6 q^{46} - 4 q^{47} - 14 q^{49} - q^{50} - 22 q^{52} + 8 q^{53} + 4 q^{55} - 6 q^{56} - 8 q^{58} - 10 q^{59} - 6 q^{61} - 30 q^{62} - 8 q^{64} + 6 q^{65} + 16 q^{67} + 7 q^{68} - 12 q^{70} - 44 q^{71} + 36 q^{73} - 2 q^{74} - 13 q^{76} - 24 q^{77} + 16 q^{79} + 6 q^{80} + 28 q^{82} + 6 q^{83} + 4 q^{85} - 10 q^{86} + 6 q^{88} + 12 q^{89} - 40 q^{91} - 9 q^{92} - 28 q^{94} - 16 q^{97} - 38 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.15139 1.99426i −0.814154 1.41016i −0.909934 0.414754i \(-0.863868\pi\)
0.0957796 0.995403i \(-0.469466\pi\)
\(3\) 0 0
\(4\) −1.65139 + 2.86029i −0.825694 + 1.43014i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) 0 0
\(7\) 1.30278 + 2.25647i 0.492403 + 0.852867i 0.999962 0.00875026i \(-0.00278533\pi\)
−0.507559 + 0.861617i \(0.669452\pi\)
\(8\) 3.00000 1.06066
\(9\) 0 0
\(10\) −2.30278 −0.728202
\(11\) 2.30278 + 3.98852i 0.694313 + 1.20259i 0.970412 + 0.241456i \(0.0776250\pi\)
−0.276099 + 0.961129i \(0.589042\pi\)
\(12\) 0 0
\(13\) −3.30278 + 5.72058i −0.916025 + 1.58660i −0.110632 + 0.993861i \(0.535287\pi\)
−0.805393 + 0.592741i \(0.798046\pi\)
\(14\) 3.00000 5.19615i 0.801784 1.38873i
\(15\) 0 0
\(16\) −0.151388 0.262211i −0.0378470 0.0655528i
\(17\) −1.60555 −0.389403 −0.194702 0.980863i \(-0.562374\pi\)
−0.194702 + 0.980863i \(0.562374\pi\)
\(18\) 0 0
\(19\) 3.60555 0.827170 0.413585 0.910465i \(-0.364276\pi\)
0.413585 + 0.910465i \(0.364276\pi\)
\(20\) 1.65139 + 2.86029i 0.369262 + 0.639580i
\(21\) 0 0
\(22\) 5.30278 9.18468i 1.13056 1.95818i
\(23\) −1.50000 + 2.59808i −0.312772 + 0.541736i −0.978961 0.204046i \(-0.934591\pi\)
0.666190 + 0.745782i \(0.267924\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 15.2111 2.98314
\(27\) 0 0
\(28\) −8.60555 −1.62630
\(29\) 0.697224 + 1.20763i 0.129471 + 0.224251i 0.923472 0.383666i \(-0.125339\pi\)
−0.794001 + 0.607917i \(0.792005\pi\)
\(30\) 0 0
\(31\) 2.80278 4.85455i 0.503393 0.871903i −0.496599 0.867980i \(-0.665418\pi\)
0.999992 0.00392276i \(-0.00124866\pi\)
\(32\) 2.65139 4.59234i 0.468704 0.811818i
\(33\) 0 0
\(34\) 1.84861 + 3.20189i 0.317034 + 0.549120i
\(35\) 2.60555 0.440419
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) −4.15139 7.19041i −0.673444 1.16644i
\(39\) 0 0
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) −2.30278 + 3.98852i −0.359633 + 0.622903i −0.987899 0.155095i \(-0.950431\pi\)
0.628266 + 0.777998i \(0.283765\pi\)
\(42\) 0 0
\(43\) −0.302776 0.524423i −0.0461729 0.0799737i 0.842015 0.539454i \(-0.181369\pi\)
−0.888188 + 0.459480i \(0.848036\pi\)
\(44\) −15.2111 −2.29316
\(45\) 0 0
\(46\) 6.90833 1.01858
\(47\) −4.60555 7.97705i −0.671789 1.16357i −0.977396 0.211415i \(-0.932193\pi\)
0.305608 0.952157i \(-0.401140\pi\)
\(48\) 0 0
\(49\) 0.105551 0.182820i 0.0150788 0.0261172i
\(50\) −1.15139 + 1.99426i −0.162831 + 0.282031i
\(51\) 0 0
\(52\) −10.9083 18.8938i −1.51271 2.62010i
\(53\) −1.60555 −0.220539 −0.110270 0.993902i \(-0.535171\pi\)
−0.110270 + 0.993902i \(0.535171\pi\)
\(54\) 0 0
\(55\) 4.60555 0.621012
\(56\) 3.90833 + 6.76942i 0.522272 + 0.904602i
\(57\) 0 0
\(58\) 1.60555 2.78090i 0.210819 0.365150i
\(59\) −0.697224 + 1.20763i −0.0907709 + 0.157220i −0.907836 0.419326i \(-0.862266\pi\)
0.817065 + 0.576546i \(0.195600\pi\)
\(60\) 0 0
\(61\) 2.10555 + 3.64692i 0.269588 + 0.466940i 0.968756 0.248018i \(-0.0797791\pi\)
−0.699167 + 0.714958i \(0.746446\pi\)
\(62\) −12.9083 −1.63936
\(63\) 0 0
\(64\) −12.8167 −1.60208
\(65\) 3.30278 + 5.72058i 0.409659 + 0.709550i
\(66\) 0 0
\(67\) 0.394449 0.683205i 0.0481896 0.0834668i −0.840924 0.541153i \(-0.817988\pi\)
0.889114 + 0.457686i \(0.151322\pi\)
\(68\) 2.65139 4.59234i 0.321528 0.556903i
\(69\) 0 0
\(70\) −3.00000 5.19615i −0.358569 0.621059i
\(71\) −7.39445 −0.877560 −0.438780 0.898595i \(-0.644589\pi\)
−0.438780 + 0.898595i \(0.644589\pi\)
\(72\) 0 0
\(73\) 12.6056 1.47537 0.737684 0.675146i \(-0.235919\pi\)
0.737684 + 0.675146i \(0.235919\pi\)
\(74\) −2.30278 3.98852i −0.267692 0.463657i
\(75\) 0 0
\(76\) −5.95416 + 10.3129i −0.682989 + 1.18297i
\(77\) −6.00000 + 10.3923i −0.683763 + 1.18431i
\(78\) 0 0
\(79\) 5.80278 + 10.0507i 0.652863 + 1.13079i 0.982425 + 0.186658i \(0.0597657\pi\)
−0.329562 + 0.944134i \(0.606901\pi\)
\(80\) −0.302776 −0.0338513
\(81\) 0 0
\(82\) 10.6056 1.17119
\(83\) 1.50000 + 2.59808i 0.164646 + 0.285176i 0.936530 0.350588i \(-0.114018\pi\)
−0.771883 + 0.635764i \(0.780685\pi\)
\(84\) 0 0
\(85\) −0.802776 + 1.39045i −0.0870732 + 0.150815i
\(86\) −0.697224 + 1.20763i −0.0751836 + 0.130222i
\(87\) 0 0
\(88\) 6.90833 + 11.9656i 0.736430 + 1.27553i
\(89\) 13.8167 1.46456 0.732281 0.681002i \(-0.238456\pi\)
0.732281 + 0.681002i \(0.238456\pi\)
\(90\) 0 0
\(91\) −17.2111 −1.80421
\(92\) −4.95416 8.58086i −0.516507 0.894617i
\(93\) 0 0
\(94\) −10.6056 + 18.3694i −1.09388 + 1.89465i
\(95\) 1.80278 3.12250i 0.184961 0.320362i
\(96\) 0 0
\(97\) −4.00000 6.92820i −0.406138 0.703452i 0.588315 0.808632i \(-0.299792\pi\)
−0.994453 + 0.105180i \(0.966458\pi\)
\(98\) −0.486122 −0.0491057
\(99\) 0 0
\(100\) 3.30278 0.330278
\(101\) 6.00000 + 10.3923i 0.597022 + 1.03407i 0.993258 + 0.115924i \(0.0369830\pi\)
−0.396236 + 0.918149i \(0.629684\pi\)
\(102\) 0 0
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) −9.90833 + 17.1617i −0.971591 + 1.68285i
\(105\) 0 0
\(106\) 1.84861 + 3.20189i 0.179553 + 0.310995i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −7.00000 −0.670478 −0.335239 0.942133i \(-0.608817\pi\)
−0.335239 + 0.942133i \(0.608817\pi\)
\(110\) −5.30278 9.18468i −0.505600 0.875725i
\(111\) 0 0
\(112\) 0.394449 0.683205i 0.0372719 0.0645568i
\(113\) −7.60555 + 13.1732i −0.715470 + 1.23923i 0.247308 + 0.968937i \(0.420454\pi\)
−0.962778 + 0.270294i \(0.912879\pi\)
\(114\) 0 0
\(115\) 1.50000 + 2.59808i 0.139876 + 0.242272i
\(116\) −4.60555 −0.427615
\(117\) 0 0
\(118\) 3.21110 0.295606
\(119\) −2.09167 3.62288i −0.191743 0.332109i
\(120\) 0 0
\(121\) −5.10555 + 8.84307i −0.464141 + 0.803916i
\(122\) 4.84861 8.39804i 0.438973 0.760323i
\(123\) 0 0
\(124\) 9.25694 + 16.0335i 0.831298 + 1.43985i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −19.2111 −1.70471 −0.852355 0.522964i \(-0.824826\pi\)
−0.852355 + 0.522964i \(0.824826\pi\)
\(128\) 9.45416 + 16.3751i 0.835638 + 1.44737i
\(129\) 0 0
\(130\) 7.60555 13.1732i 0.667051 1.15537i
\(131\) 3.00000 5.19615i 0.262111 0.453990i −0.704692 0.709514i \(-0.748915\pi\)
0.966803 + 0.255524i \(0.0822479\pi\)
\(132\) 0 0
\(133\) 4.69722 + 8.13583i 0.407301 + 0.705466i
\(134\) −1.81665 −0.156935
\(135\) 0 0
\(136\) −4.81665 −0.413025
\(137\) 8.40833 + 14.5636i 0.718372 + 1.24426i 0.961645 + 0.274299i \(0.0884457\pi\)
−0.243273 + 0.969958i \(0.578221\pi\)
\(138\) 0 0
\(139\) 2.00000 3.46410i 0.169638 0.293821i −0.768655 0.639664i \(-0.779074\pi\)
0.938293 + 0.345843i \(0.112407\pi\)
\(140\) −4.30278 + 7.45263i −0.363651 + 0.629862i
\(141\) 0 0
\(142\) 8.51388 + 14.7465i 0.714469 + 1.23750i
\(143\) −30.4222 −2.54403
\(144\) 0 0
\(145\) 1.39445 0.115803
\(146\) −14.5139 25.1388i −1.20118 2.08050i
\(147\) 0 0
\(148\) −3.30278 + 5.72058i −0.271486 + 0.470228i
\(149\) 11.5139 19.9426i 0.943254 1.63376i 0.184043 0.982918i \(-0.441081\pi\)
0.759211 0.650845i \(-0.225585\pi\)
\(150\) 0 0
\(151\) −7.21110 12.4900i −0.586831 1.01642i −0.994644 0.103356i \(-0.967042\pi\)
0.407813 0.913065i \(-0.366291\pi\)
\(152\) 10.8167 0.877346
\(153\) 0 0
\(154\) 27.6333 2.22676
\(155\) −2.80278 4.85455i −0.225124 0.389927i
\(156\) 0 0
\(157\) 8.90833 15.4297i 0.710962 1.23142i −0.253535 0.967326i \(-0.581593\pi\)
0.964496 0.264096i \(-0.0850735\pi\)
\(158\) 13.3625 23.1445i 1.06306 1.84128i
\(159\) 0 0
\(160\) −2.65139 4.59234i −0.209611 0.363056i
\(161\) −7.81665 −0.616039
\(162\) 0 0
\(163\) 2.00000 0.156652 0.0783260 0.996928i \(-0.475042\pi\)
0.0783260 + 0.996928i \(0.475042\pi\)
\(164\) −7.60555 13.1732i −0.593894 1.02865i
\(165\) 0 0
\(166\) 3.45416 5.98279i 0.268095 0.464354i
\(167\) −1.50000 + 2.59808i −0.116073 + 0.201045i −0.918208 0.396098i \(-0.870364\pi\)
0.802135 + 0.597143i \(0.203697\pi\)
\(168\) 0 0
\(169\) −15.3167 26.5292i −1.17820 2.04071i
\(170\) 3.69722 0.283564
\(171\) 0 0
\(172\) 2.00000 0.152499
\(173\) −5.40833 9.36750i −0.411187 0.712198i 0.583832 0.811874i \(-0.301553\pi\)
−0.995020 + 0.0996766i \(0.968219\pi\)
\(174\) 0 0
\(175\) 1.30278 2.25647i 0.0984806 0.170573i
\(176\) 0.697224 1.20763i 0.0525553 0.0910284i
\(177\) 0 0
\(178\) −15.9083 27.5540i −1.19238 2.06526i
\(179\) 21.2111 1.58539 0.792696 0.609617i \(-0.208677\pi\)
0.792696 + 0.609617i \(0.208677\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 19.8167 + 34.3235i 1.46891 + 2.54422i
\(183\) 0 0
\(184\) −4.50000 + 7.79423i −0.331744 + 0.574598i
\(185\) 1.00000 1.73205i 0.0735215 0.127343i
\(186\) 0 0
\(187\) −3.69722 6.40378i −0.270368 0.468291i
\(188\) 30.4222 2.21877
\(189\) 0 0
\(190\) −8.30278 −0.602347
\(191\) −6.21110 10.7579i −0.449420 0.778418i 0.548929 0.835869i \(-0.315036\pi\)
−0.998348 + 0.0574516i \(0.981703\pi\)
\(192\) 0 0
\(193\) −0.0916731 + 0.158782i −0.00659877 + 0.0114294i −0.869306 0.494274i \(-0.835434\pi\)
0.862707 + 0.505704i \(0.168767\pi\)
\(194\) −9.21110 + 15.9541i −0.661319 + 1.14544i
\(195\) 0 0
\(196\) 0.348612 + 0.603814i 0.0249009 + 0.0431296i
\(197\) 22.8167 1.62562 0.812810 0.582529i \(-0.197937\pi\)
0.812810 + 0.582529i \(0.197937\pi\)
\(198\) 0 0
\(199\) −1.21110 −0.0858528 −0.0429264 0.999078i \(-0.513668\pi\)
−0.0429264 + 0.999078i \(0.513668\pi\)
\(200\) −1.50000 2.59808i −0.106066 0.183712i
\(201\) 0 0
\(202\) 13.8167 23.9311i 0.972136 1.68379i
\(203\) −1.81665 + 3.14654i −0.127504 + 0.220844i
\(204\) 0 0
\(205\) 2.30278 + 3.98852i 0.160833 + 0.278571i
\(206\) −9.21110 −0.641768
\(207\) 0 0
\(208\) 2.00000 0.138675
\(209\) 8.30278 + 14.3808i 0.574315 + 0.994743i
\(210\) 0 0
\(211\) 4.40833 7.63545i 0.303482 0.525646i −0.673440 0.739242i \(-0.735184\pi\)
0.976922 + 0.213596i \(0.0685175\pi\)
\(212\) 2.65139 4.59234i 0.182098 0.315403i
\(213\) 0 0
\(214\) 0 0
\(215\) −0.605551 −0.0412983
\(216\) 0 0
\(217\) 14.6056 0.991489
\(218\) 8.05971 + 13.9598i 0.545873 + 0.945479i
\(219\) 0 0
\(220\) −7.60555 + 13.1732i −0.512766 + 0.888137i
\(221\) 5.30278 9.18468i 0.356703 0.617828i
\(222\) 0 0
\(223\) 5.00000 + 8.66025i 0.334825 + 0.579934i 0.983451 0.181173i \(-0.0579895\pi\)
−0.648626 + 0.761107i \(0.724656\pi\)
\(224\) 13.8167 0.923164
\(225\) 0 0
\(226\) 35.0278 2.33001
\(227\) −5.89445 10.2095i −0.391228 0.677627i 0.601384 0.798960i \(-0.294616\pi\)
−0.992612 + 0.121333i \(0.961283\pi\)
\(228\) 0 0
\(229\) −4.10555 + 7.11102i −0.271302 + 0.469910i −0.969196 0.246292i \(-0.920788\pi\)
0.697893 + 0.716202i \(0.254121\pi\)
\(230\) 3.45416 5.98279i 0.227761 0.394493i
\(231\) 0 0
\(232\) 2.09167 + 3.62288i 0.137325 + 0.237854i
\(233\) 18.0000 1.17922 0.589610 0.807688i \(-0.299282\pi\)
0.589610 + 0.807688i \(0.299282\pi\)
\(234\) 0 0
\(235\) −9.21110 −0.600866
\(236\) −2.30278 3.98852i −0.149898 0.259631i
\(237\) 0 0
\(238\) −4.81665 + 8.34269i −0.312217 + 0.540776i
\(239\) −7.60555 + 13.1732i −0.491962 + 0.852104i −0.999957 0.00925650i \(-0.997054\pi\)
0.507995 + 0.861360i \(0.330387\pi\)
\(240\) 0 0
\(241\) −6.89445 11.9415i −0.444110 0.769222i 0.553879 0.832597i \(-0.313147\pi\)
−0.997990 + 0.0633751i \(0.979814\pi\)
\(242\) 23.5139 1.51153
\(243\) 0 0
\(244\) −13.9083 −0.890389
\(245\) −0.105551 0.182820i −0.00674342 0.0116800i
\(246\) 0 0
\(247\) −11.9083 + 20.6258i −0.757709 + 1.31239i
\(248\) 8.40833 14.5636i 0.533929 0.924793i
\(249\) 0 0
\(250\) 1.15139 + 1.99426i 0.0728202 + 0.126128i
\(251\) −27.6333 −1.74420 −0.872099 0.489329i \(-0.837242\pi\)
−0.872099 + 0.489329i \(0.837242\pi\)
\(252\) 0 0
\(253\) −13.8167 −0.868646
\(254\) 22.1194 + 38.3120i 1.38790 + 2.40391i
\(255\) 0 0
\(256\) 8.95416 15.5091i 0.559635 0.969317i
\(257\) 0.591673 1.02481i 0.0369076 0.0639258i −0.846982 0.531622i \(-0.821583\pi\)
0.883889 + 0.467696i \(0.154916\pi\)
\(258\) 0 0
\(259\) 2.60555 + 4.51295i 0.161901 + 0.280421i
\(260\) −21.8167 −1.35301
\(261\) 0 0
\(262\) −13.8167 −0.853596
\(263\) −1.39445 2.41526i −0.0859854 0.148931i 0.819825 0.572614i \(-0.194071\pi\)
−0.905811 + 0.423683i \(0.860737\pi\)
\(264\) 0 0
\(265\) −0.802776 + 1.39045i −0.0493141 + 0.0854146i
\(266\) 10.8167 18.7350i 0.663212 1.14872i
\(267\) 0 0
\(268\) 1.30278 + 2.25647i 0.0795797 + 0.137836i
\(269\) 3.21110 0.195784 0.0978922 0.995197i \(-0.468790\pi\)
0.0978922 + 0.995197i \(0.468790\pi\)
\(270\) 0 0
\(271\) 31.2389 1.89763 0.948813 0.315839i \(-0.102286\pi\)
0.948813 + 0.315839i \(0.102286\pi\)
\(272\) 0.243061 + 0.420994i 0.0147377 + 0.0255265i
\(273\) 0 0
\(274\) 19.3625 33.5368i 1.16973 2.02603i
\(275\) 2.30278 3.98852i 0.138863 0.240517i
\(276\) 0 0
\(277\) −3.51388 6.08622i −0.211128 0.365685i 0.740939 0.671572i \(-0.234381\pi\)
−0.952068 + 0.305887i \(0.901047\pi\)
\(278\) −9.21110 −0.552445
\(279\) 0 0
\(280\) 7.81665 0.467134
\(281\) −9.90833 17.1617i −0.591081 1.02378i −0.994087 0.108585i \(-0.965368\pi\)
0.403006 0.915197i \(-0.367965\pi\)
\(282\) 0 0
\(283\) −1.69722 + 2.93968i −0.100890 + 0.174746i −0.912051 0.410076i \(-0.865502\pi\)
0.811162 + 0.584822i \(0.198836\pi\)
\(284\) 12.2111 21.1503i 0.724596 1.25504i
\(285\) 0 0
\(286\) 35.0278 + 60.6699i 2.07123 + 3.58748i
\(287\) −12.0000 −0.708338
\(288\) 0 0
\(289\) −14.4222 −0.848365
\(290\) −1.60555 2.78090i −0.0942812 0.163300i
\(291\) 0 0
\(292\) −20.8167 + 36.0555i −1.21820 + 2.10999i
\(293\) −3.59167 + 6.22096i −0.209828 + 0.363432i −0.951660 0.307153i \(-0.900624\pi\)
0.741832 + 0.670585i \(0.233957\pi\)
\(294\) 0 0
\(295\) 0.697224 + 1.20763i 0.0405940 + 0.0703108i
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) −53.0278 −3.07182
\(299\) −9.90833 17.1617i −0.573013 0.992488i
\(300\) 0 0
\(301\) 0.788897 1.36641i 0.0454713 0.0787586i
\(302\) −16.6056 + 28.7617i −0.955542 + 1.65505i
\(303\) 0 0
\(304\) −0.545837 0.945417i −0.0313059 0.0542234i
\(305\) 4.21110 0.241127
\(306\) 0 0
\(307\) 8.42221 0.480681 0.240340 0.970689i \(-0.422741\pi\)
0.240340 + 0.970689i \(0.422741\pi\)
\(308\) −19.8167 34.3235i −1.12916 1.95576i
\(309\) 0 0
\(310\) −6.45416 + 11.1789i −0.366572 + 0.634921i
\(311\) −3.90833 + 6.76942i −0.221621 + 0.383859i −0.955300 0.295637i \(-0.904468\pi\)
0.733679 + 0.679496i \(0.237801\pi\)
\(312\) 0 0
\(313\) 9.81665 + 17.0029i 0.554870 + 0.961063i 0.997914 + 0.0645631i \(0.0205654\pi\)
−0.443044 + 0.896500i \(0.646101\pi\)
\(314\) −41.0278 −2.31533
\(315\) 0 0
\(316\) −38.3305 −2.15626
\(317\) −3.80278 6.58660i −0.213585 0.369940i 0.739249 0.673432i \(-0.235181\pi\)
−0.952834 + 0.303492i \(0.901847\pi\)
\(318\) 0 0
\(319\) −3.21110 + 5.56179i −0.179787 + 0.311401i
\(320\) −6.40833 + 11.0995i −0.358236 + 0.620484i
\(321\) 0 0
\(322\) 9.00000 + 15.5885i 0.501550 + 0.868711i
\(323\) −5.78890 −0.322103
\(324\) 0 0
\(325\) 6.60555 0.366410
\(326\) −2.30278 3.98852i −0.127539 0.220904i
\(327\) 0 0
\(328\) −6.90833 + 11.9656i −0.381449 + 0.660688i
\(329\) 12.0000 20.7846i 0.661581 1.14589i
\(330\) 0 0
\(331\) −14.6056 25.2976i −0.802794 1.39048i −0.917770 0.397111i \(-0.870013\pi\)
0.114977 0.993368i \(-0.463321\pi\)
\(332\) −9.90833 −0.543790
\(333\) 0 0
\(334\) 6.90833 0.378007
\(335\) −0.394449 0.683205i −0.0215510 0.0373275i
\(336\) 0 0
\(337\) −3.30278 + 5.72058i −0.179914 + 0.311620i −0.941851 0.336031i \(-0.890915\pi\)
0.761937 + 0.647651i \(0.224249\pi\)
\(338\) −35.2708 + 61.0908i −1.91848 + 3.32290i
\(339\) 0 0
\(340\) −2.65139 4.59234i −0.143792 0.249055i
\(341\) 25.8167 1.39805
\(342\) 0 0
\(343\) 18.7889 1.01451
\(344\) −0.908327 1.57327i −0.0489737 0.0848249i
\(345\) 0 0
\(346\) −12.4542 + 21.5712i −0.669540 + 1.15968i
\(347\) 15.2111 26.3464i 0.816575 1.41435i −0.0916168 0.995794i \(-0.529203\pi\)
0.908192 0.418555i \(-0.137463\pi\)
\(348\) 0 0
\(349\) 15.9222 + 27.5781i 0.852296 + 1.47622i 0.879131 + 0.476580i \(0.158124\pi\)
−0.0268349 + 0.999640i \(0.508543\pi\)
\(350\) −6.00000 −0.320713
\(351\) 0 0
\(352\) 24.4222 1.30171
\(353\) 10.8167 + 18.7350i 0.575712 + 0.997163i 0.995964 + 0.0897554i \(0.0286085\pi\)
−0.420251 + 0.907408i \(0.638058\pi\)
\(354\) 0 0
\(355\) −3.69722 + 6.40378i −0.196228 + 0.339877i
\(356\) −22.8167 + 39.5196i −1.20928 + 2.09453i
\(357\) 0 0
\(358\) −24.4222 42.3005i −1.29075 2.23565i
\(359\) 9.63331 0.508427 0.254213 0.967148i \(-0.418183\pi\)
0.254213 + 0.967148i \(0.418183\pi\)
\(360\) 0 0
\(361\) −6.00000 −0.315789
\(362\) 8.05971 + 13.9598i 0.423609 + 0.733713i
\(363\) 0 0
\(364\) 28.4222 49.2287i 1.48973 2.58029i
\(365\) 6.30278 10.9167i 0.329902 0.571408i
\(366\) 0 0
\(367\) 1.30278 + 2.25647i 0.0680043 + 0.117787i 0.898023 0.439949i \(-0.145003\pi\)
−0.830018 + 0.557736i \(0.811670\pi\)
\(368\) 0.908327 0.0473498
\(369\) 0 0
\(370\) −4.60555 −0.239431
\(371\) −2.09167 3.62288i −0.108594 0.188091i
\(372\) 0 0
\(373\) 12.6056 21.8335i 0.652691 1.13049i −0.329777 0.944059i \(-0.606973\pi\)
0.982467 0.186434i \(-0.0596932\pi\)
\(374\) −8.51388 + 14.7465i −0.440242 + 0.762522i
\(375\) 0 0
\(376\) −13.8167 23.9311i −0.712540 1.23415i
\(377\) −9.21110 −0.474396
\(378\) 0 0
\(379\) 21.6056 1.10980 0.554901 0.831916i \(-0.312756\pi\)
0.554901 + 0.831916i \(0.312756\pi\)
\(380\) 5.95416 + 10.3129i 0.305442 + 0.529041i
\(381\) 0 0
\(382\) −14.3028 + 24.7731i −0.731794 + 1.26750i
\(383\) 12.3167 21.3331i 0.629352 1.09007i −0.358330 0.933595i \(-0.616654\pi\)
0.987682 0.156474i \(-0.0500128\pi\)
\(384\) 0 0
\(385\) 6.00000 + 10.3923i 0.305788 + 0.529641i
\(386\) 0.422205 0.0214897
\(387\) 0 0
\(388\) 26.4222 1.34138
\(389\) 12.9083 + 22.3579i 0.654478 + 1.13359i 0.982024 + 0.188754i \(0.0604450\pi\)
−0.327546 + 0.944835i \(0.606222\pi\)
\(390\) 0 0
\(391\) 2.40833 4.17134i 0.121794 0.210954i
\(392\) 0.316654 0.548461i 0.0159934 0.0277014i
\(393\) 0 0
\(394\) −26.2708 45.5024i −1.32350 2.29238i
\(395\) 11.6056 0.583939
\(396\) 0 0
\(397\) −5.39445 −0.270740 −0.135370 0.990795i \(-0.543222\pi\)
−0.135370 + 0.990795i \(0.543222\pi\)
\(398\) 1.39445 + 2.41526i 0.0698974 + 0.121066i
\(399\) 0 0
\(400\) −0.151388 + 0.262211i −0.00756939 + 0.0131106i
\(401\) −15.0000 + 25.9808i −0.749064 + 1.29742i 0.199207 + 0.979957i \(0.436163\pi\)
−0.948272 + 0.317460i \(0.897170\pi\)
\(402\) 0 0
\(403\) 18.5139 + 32.0670i 0.922242 + 1.59737i
\(404\) −39.6333 −1.97183
\(405\) 0 0
\(406\) 8.36669 0.415232
\(407\) 4.60555 + 7.97705i 0.228289 + 0.395408i
\(408\) 0 0
\(409\) −2.50000 + 4.33013i −0.123617 + 0.214111i −0.921192 0.389109i \(-0.872783\pi\)
0.797574 + 0.603220i \(0.206116\pi\)
\(410\) 5.30278 9.18468i 0.261885 0.453599i
\(411\) 0 0
\(412\) 6.60555 + 11.4412i 0.325432 + 0.563665i
\(413\) −3.63331 −0.178783
\(414\) 0 0
\(415\) 3.00000 0.147264
\(416\) 17.5139 + 30.3349i 0.858689 + 1.48729i
\(417\) 0 0
\(418\) 19.1194 33.1158i 0.935162 1.61975i
\(419\) 11.5139 19.9426i 0.562490 0.974261i −0.434789 0.900533i \(-0.643177\pi\)
0.997278 0.0737283i \(-0.0234898\pi\)
\(420\) 0 0
\(421\) −2.71110 4.69577i −0.132131 0.228858i 0.792367 0.610045i \(-0.208849\pi\)
−0.924498 + 0.381187i \(0.875515\pi\)
\(422\) −20.3028 −0.988324
\(423\) 0 0
\(424\) −4.81665 −0.233917
\(425\) 0.802776 + 1.39045i 0.0389403 + 0.0674466i
\(426\) 0 0
\(427\) −5.48612 + 9.50224i −0.265492 + 0.459846i
\(428\) 0 0
\(429\) 0 0
\(430\) 0.697224 + 1.20763i 0.0336231 + 0.0582370i
\(431\) −4.18335 −0.201505 −0.100752 0.994912i \(-0.532125\pi\)
−0.100752 + 0.994912i \(0.532125\pi\)
\(432\) 0 0
\(433\) 22.2389 1.06873 0.534366 0.845253i \(-0.320551\pi\)
0.534366 + 0.845253i \(0.320551\pi\)
\(434\) −16.8167 29.1273i −0.807225 1.39816i
\(435\) 0 0
\(436\) 11.5597 20.0220i 0.553610 0.958881i
\(437\) −5.40833 + 9.36750i −0.258715 + 0.448108i
\(438\) 0 0
\(439\) −13.8028 23.9071i −0.658771 1.14102i −0.980934 0.194340i \(-0.937743\pi\)
0.322164 0.946684i \(-0.395590\pi\)
\(440\) 13.8167 0.658683
\(441\) 0 0
\(442\) −24.4222 −1.16165
\(443\) −12.3167 21.3331i −0.585182 1.01356i −0.994853 0.101331i \(-0.967690\pi\)
0.409671 0.912233i \(-0.365644\pi\)
\(444\) 0 0
\(445\) 6.90833 11.9656i 0.327486 0.567223i
\(446\) 11.5139 19.9426i 0.545198 0.944311i
\(447\) 0 0
\(448\) −16.6972 28.9204i −0.788870 1.36636i
\(449\) −38.2389 −1.80460 −0.902302 0.431105i \(-0.858124\pi\)
−0.902302 + 0.431105i \(0.858124\pi\)
\(450\) 0 0
\(451\) −21.2111 −0.998792
\(452\) −25.1194 43.5081i −1.18152 2.04645i
\(453\) 0 0
\(454\) −13.5736 + 23.5102i −0.637040 + 1.10339i
\(455\) −8.60555 + 14.9053i −0.403434 + 0.698769i
\(456\) 0 0
\(457\) 6.60555 + 11.4412i 0.308995 + 0.535194i 0.978143 0.207935i \(-0.0666741\pi\)
−0.669148 + 0.743129i \(0.733341\pi\)
\(458\) 18.9083 0.883528
\(459\) 0 0
\(460\) −9.90833 −0.461978
\(461\) 10.8167 + 18.7350i 0.503782 + 0.872576i 0.999990 + 0.00437236i \(0.00139177\pi\)
−0.496209 + 0.868203i \(0.665275\pi\)
\(462\) 0 0
\(463\) 0.394449 0.683205i 0.0183316 0.0317512i −0.856714 0.515792i \(-0.827498\pi\)
0.875046 + 0.484040i \(0.160831\pi\)
\(464\) 0.211103 0.365640i 0.00980019 0.0169744i
\(465\) 0 0
\(466\) −20.7250 35.8967i −0.960066 1.66288i
\(467\) −12.2111 −0.565062 −0.282531 0.959258i \(-0.591174\pi\)
−0.282531 + 0.959258i \(0.591174\pi\)
\(468\) 0 0
\(469\) 2.05551 0.0949148
\(470\) 10.6056 + 18.3694i 0.489198 + 0.847315i
\(471\) 0 0
\(472\) −2.09167 + 3.62288i −0.0962771 + 0.166757i
\(473\) 1.39445 2.41526i 0.0641168 0.111054i
\(474\) 0 0
\(475\) −1.80278 3.12250i −0.0827170 0.143270i
\(476\) 13.8167 0.633285
\(477\) 0 0
\(478\) 35.0278 1.60213
\(479\) −18.9083 32.7502i −0.863944 1.49639i −0.868092 0.496403i \(-0.834654\pi\)
0.00414888 0.999991i \(-0.498679\pi\)
\(480\) 0 0
\(481\) −6.60555 + 11.4412i −0.301187 + 0.521672i
\(482\) −15.8764 + 27.4987i −0.723149 + 1.25253i
\(483\) 0 0
\(484\) −16.8625 29.2067i −0.766477 1.32758i
\(485\) −8.00000 −0.363261
\(486\) 0 0
\(487\) −29.8167 −1.35112 −0.675561 0.737304i \(-0.736098\pi\)
−0.675561 + 0.737304i \(0.736098\pi\)
\(488\) 6.31665 + 10.9408i 0.285941 + 0.495265i
\(489\) 0 0
\(490\) −0.243061 + 0.420994i −0.0109804 + 0.0190186i
\(491\) 13.6056 23.5655i 0.614010 1.06350i −0.376547 0.926397i \(-0.622889\pi\)
0.990557 0.137099i \(-0.0437779\pi\)
\(492\) 0 0
\(493\) −1.11943 1.93891i −0.0504166 0.0873241i
\(494\) 54.8444 2.46757
\(495\) 0 0
\(496\) −1.69722 −0.0762076
\(497\) −9.63331 16.6854i −0.432113 0.748442i
\(498\) 0 0
\(499\) 10.1972 17.6621i 0.456490 0.790665i −0.542282 0.840196i \(-0.682440\pi\)
0.998773 + 0.0495318i \(0.0157729\pi\)
\(500\) 1.65139 2.86029i 0.0738523 0.127916i
\(501\) 0 0
\(502\) 31.8167 + 55.1081i 1.42005 + 2.45959i
\(503\) −2.57779 −0.114938 −0.0574691 0.998347i \(-0.518303\pi\)
−0.0574691 + 0.998347i \(0.518303\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 15.9083 + 27.5540i 0.707211 + 1.22493i
\(507\) 0 0
\(508\) 31.7250 54.9493i 1.40757 2.43798i
\(509\) −12.4222 + 21.5159i −0.550605 + 0.953675i 0.447626 + 0.894221i \(0.352269\pi\)
−0.998231 + 0.0594544i \(0.981064\pi\)
\(510\) 0 0
\(511\) 16.4222 + 28.4441i 0.726476 + 1.25829i
\(512\) −3.42221 −0.151242
\(513\) 0 0
\(514\) −2.72498 −0.120194
\(515\) −2.00000 3.46410i −0.0881305 0.152647i
\(516\) 0 0
\(517\) 21.2111 36.7387i 0.932863 1.61577i
\(518\) 6.00000 10.3923i 0.263625 0.456612i
\(519\) 0 0
\(520\) 9.90833 + 17.1617i 0.434509 + 0.752591i
\(521\) 28.6056 1.25323 0.626616 0.779328i \(-0.284439\pi\)
0.626616 + 0.779328i \(0.284439\pi\)
\(522\) 0 0
\(523\) 30.6056 1.33829 0.669144 0.743133i \(-0.266661\pi\)
0.669144 + 0.743133i \(0.266661\pi\)
\(524\) 9.90833 + 17.1617i 0.432847 + 0.749713i
\(525\) 0 0
\(526\) −3.21110 + 5.56179i −0.140011 + 0.242506i
\(527\) −4.50000 + 7.79423i −0.196023 + 0.339522i
\(528\) 0 0
\(529\) 7.00000 + 12.1244i 0.304348 + 0.527146i
\(530\) 3.69722 0.160597
\(531\) 0 0
\(532\) −31.0278 −1.34522
\(533\) −15.2111 26.3464i −0.658866 1.14119i
\(534\) 0 0
\(535\) 0 0
\(536\) 1.18335 2.04962i 0.0511128 0.0885299i
\(537\) 0 0
\(538\) −3.69722 6.40378i −0.159399 0.276087i
\(539\) 0.972244 0.0418775
\(540\) 0 0
\(541\) −40.4222 −1.73789 −0.868943 0.494912i \(-0.835200\pi\)
−0.868943 + 0.494912i \(0.835200\pi\)
\(542\) −35.9680 62.2985i −1.54496 2.67595i
\(543\) 0 0
\(544\) −4.25694 + 7.37323i −0.182515 + 0.316125i
\(545\) −3.50000 + 6.06218i −0.149924 + 0.259675i
\(546\) 0 0
\(547\) −0.302776 0.524423i −0.0129458 0.0224227i 0.859480 0.511169i \(-0.170788\pi\)
−0.872426 + 0.488747i \(0.837454\pi\)
\(548\) −55.5416 −2.37262
\(549\) 0 0
\(550\) −10.6056 −0.452222
\(551\) 2.51388 + 4.35416i 0.107095 + 0.185494i
\(552\) 0 0
\(553\) −15.1194 + 26.1876i −0.642944 + 1.11361i
\(554\) −8.09167 + 14.0152i −0.343782 + 0.595448i
\(555\) 0 0
\(556\) 6.60555 + 11.4412i 0.280138 + 0.485213i
\(557\) −9.63331 −0.408176 −0.204088 0.978953i \(-0.565423\pi\)
−0.204088 + 0.978953i \(0.565423\pi\)
\(558\) 0 0
\(559\) 4.00000 0.169182
\(560\) −0.394449 0.683205i −0.0166685 0.0288707i
\(561\) 0 0
\(562\) −22.8167 + 39.5196i −0.962462 + 1.66703i
\(563\) 12.0000 20.7846i 0.505740 0.875967i −0.494238 0.869326i \(-0.664553\pi\)
0.999978 0.00664037i \(-0.00211371\pi\)
\(564\) 0 0
\(565\) 7.60555 + 13.1732i 0.319968 + 0.554201i
\(566\) 7.81665 0.328558
\(567\) 0 0
\(568\) −22.1833 −0.930793
\(569\) 8.09167 + 14.0152i 0.339221 + 0.587547i 0.984286 0.176580i \(-0.0565034\pi\)
−0.645066 + 0.764127i \(0.723170\pi\)
\(570\) 0 0
\(571\) −14.2250 + 24.6384i −0.595297 + 1.03108i 0.398208 + 0.917295i \(0.369632\pi\)
−0.993505 + 0.113789i \(0.963701\pi\)
\(572\) 50.2389 87.0163i 2.10059 3.63833i
\(573\) 0 0
\(574\) 13.8167 + 23.9311i 0.576696 + 0.998867i
\(575\) 3.00000 0.125109
\(576\) 0 0
\(577\) 6.18335 0.257416 0.128708 0.991683i \(-0.458917\pi\)
0.128708 + 0.991683i \(0.458917\pi\)
\(578\) 16.6056 + 28.7617i 0.690700 + 1.19633i
\(579\) 0 0
\(580\) −2.30278 + 3.98852i −0.0956176 + 0.165614i
\(581\) −3.90833 + 6.76942i −0.162145 + 0.280843i
\(582\) 0 0
\(583\) −3.69722 6.40378i −0.153123 0.265217i
\(584\) 37.8167 1.56486
\(585\) 0 0
\(586\) 16.5416 0.683329
\(587\) 10.5000 + 18.1865i 0.433381 + 0.750639i 0.997162 0.0752860i \(-0.0239870\pi\)
−0.563781 + 0.825925i \(0.690654\pi\)
\(588\) 0 0
\(589\) 10.1056 17.5033i 0.416392 0.721212i
\(590\) 1.60555 2.78090i 0.0660995 0.114488i
\(591\) 0 0
\(592\) −0.302776 0.524423i −0.0124440 0.0215536i
\(593\) 29.2389 1.20070 0.600348 0.799739i \(-0.295029\pi\)
0.600348 + 0.799739i \(0.295029\pi\)
\(594\) 0 0
\(595\) −4.18335 −0.171500
\(596\) 38.0278 + 65.8660i 1.55768 + 2.69798i
\(597\) 0 0
\(598\) −22.8167 + 39.5196i −0.933042 + 1.61608i
\(599\) −11.3028 + 19.5770i −0.461819 + 0.799894i −0.999052 0.0435402i \(-0.986136\pi\)
0.537233 + 0.843434i \(0.319470\pi\)
\(600\) 0 0
\(601\) 5.31665 + 9.20871i 0.216871 + 0.375631i 0.953850 0.300285i \(-0.0970816\pi\)
−0.736979 + 0.675916i \(0.763748\pi\)
\(602\) −3.63331 −0.148083
\(603\) 0 0
\(604\) 47.6333 1.93817
\(605\) 5.10555 + 8.84307i 0.207570 + 0.359522i
\(606\) 0 0
\(607\) −12.3028 + 21.3090i −0.499354 + 0.864907i −1.00000 0.000745477i \(-0.999763\pi\)
0.500645 + 0.865652i \(0.333096\pi\)
\(608\) 9.55971 16.5579i 0.387698 0.671512i
\(609\) 0 0
\(610\) −4.84861 8.39804i −0.196315 0.340027i
\(611\) 60.8444 2.46150
\(612\) 0 0
\(613\) −28.8444 −1.16501 −0.582507 0.812825i \(-0.697928\pi\)
−0.582507 + 0.812825i \(0.697928\pi\)
\(614\) −9.69722 16.7961i −0.391348 0.677835i
\(615\) 0 0
\(616\) −18.0000 + 31.1769i −0.725241 + 1.25615i
\(617\) 19.2250 33.2986i 0.773969 1.34055i −0.161404 0.986888i \(-0.551602\pi\)
0.935372 0.353664i \(-0.115065\pi\)
\(618\) 0 0
\(619\) −17.8167 30.8593i −0.716112 1.24034i −0.962529 0.271178i \(-0.912587\pi\)
0.246417 0.969164i \(-0.420747\pi\)
\(620\) 18.5139 0.743535
\(621\) 0 0
\(622\) 18.0000 0.721734
\(623\) 18.0000 + 31.1769i 0.721155 + 1.24908i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 22.6056 39.1540i 0.903500 1.56491i
\(627\) 0 0
\(628\) 29.4222 + 50.9608i 1.17407 + 2.03356i
\(629\) −3.21110 −0.128035
\(630\) 0 0
\(631\) −6.02776 −0.239961 −0.119981 0.992776i \(-0.538283\pi\)
−0.119981 + 0.992776i \(0.538283\pi\)
\(632\) 17.4083 + 30.1521i 0.692466 + 1.19939i
\(633\) 0 0
\(634\) −8.75694 + 15.1675i −0.347782 + 0.602377i
\(635\) −9.60555 + 16.6373i −0.381185 + 0.660231i
\(636\) 0 0
\(637\) 0.697224 + 1.20763i 0.0276250 + 0.0478480i
\(638\) 14.7889 0.585498
\(639\) 0 0
\(640\) 18.9083 0.747417
\(641\) −12.0000 20.7846i −0.473972 0.820943i 0.525584 0.850741i \(-0.323847\pi\)
−0.999556 + 0.0297987i \(0.990513\pi\)
\(642\) 0 0
\(643\) −6.51388 + 11.2824i −0.256882 + 0.444933i −0.965405 0.260755i \(-0.916029\pi\)
0.708523 + 0.705688i \(0.249362\pi\)
\(644\) 12.9083 22.3579i 0.508659 0.881024i
\(645\) 0 0
\(646\) 6.66527 + 11.5446i 0.262241 + 0.454215i
\(647\) −23.7889 −0.935238 −0.467619 0.883930i \(-0.654888\pi\)
−0.467619 + 0.883930i \(0.654888\pi\)
\(648\) 0 0
\(649\) −6.42221 −0.252094
\(650\) −7.60555 13.1732i −0.298314 0.516695i
\(651\) 0 0
\(652\) −3.30278 + 5.72058i −0.129347 + 0.224035i
\(653\) −11.6194 + 20.1254i −0.454703 + 0.787569i −0.998671 0.0515368i \(-0.983588\pi\)
0.543968 + 0.839106i \(0.316921\pi\)
\(654\) 0 0
\(655\) −3.00000 5.19615i −0.117220 0.203030i
\(656\) 1.39445 0.0544441
\(657\) 0 0
\(658\) −55.2666 −2.15452
\(659\) −6.69722 11.5999i −0.260887 0.451869i 0.705591 0.708619i \(-0.250682\pi\)
−0.966478 + 0.256750i \(0.917348\pi\)
\(660\) 0 0
\(661\) 17.4222 30.1761i 0.677645 1.17372i −0.298043 0.954552i \(-0.596334\pi\)
0.975688 0.219164i \(-0.0703328\pi\)
\(662\) −33.6333 + 58.2546i −1.30720 + 2.26413i
\(663\) 0 0
\(664\) 4.50000 + 7.79423i 0.174634 + 0.302475i
\(665\) 9.39445 0.364301
\(666\) 0 0
\(667\) −4.18335 −0.161980
\(668\) −4.95416 8.58086i −0.191682 0.332004i
\(669\) 0 0
\(670\) −0.908327 + 1.57327i −0.0350917 + 0.0607807i
\(671\) −9.69722 + 16.7961i −0.374357 + 0.648406i
\(672\) 0 0
\(673\) −12.5139 21.6747i −0.482375 0.835497i 0.517421 0.855731i \(-0.326892\pi\)
−0.999795 + 0.0202339i \(0.993559\pi\)
\(674\) 15.2111 0.585910
\(675\) 0 0
\(676\) 101.175 3.89134
\(677\) 10.8167 + 18.7350i 0.415718 + 0.720044i 0.995504 0.0947247i \(-0.0301971\pi\)
−0.579786 + 0.814769i \(0.696864\pi\)
\(678\) 0 0
\(679\) 10.4222 18.0518i 0.399968 0.692764i
\(680\) −2.40833 + 4.17134i −0.0923551 + 0.159964i
\(681\) 0 0
\(682\) −29.7250 51.4852i −1.13823 1.97147i
\(683\) 9.00000 0.344375 0.172188 0.985064i \(-0.444916\pi\)
0.172188 + 0.985064i \(0.444916\pi\)
\(684\) 0 0
\(685\) 16.8167 0.642531
\(686\) −21.6333 37.4700i −0.825964 1.43061i
\(687\) 0 0
\(688\) −0.0916731 + 0.158782i −0.00349500 + 0.00605352i
\(689\) 5.30278 9.18468i 0.202020 0.349908i
\(690\) 0 0
\(691\) −4.80278 8.31865i −0.182706 0.316456i 0.760095 0.649812i \(-0.225152\pi\)
−0.942801 + 0.333356i \(0.891819\pi\)
\(692\) 35.7250 1.35806
\(693\) 0 0
\(694\) −70.0555 −2.65927
\(695\) −2.00000 3.46410i −0.0758643 0.131401i
\(696\) 0 0
\(697\) 3.69722 6.40378i 0.140042 0.242560i
\(698\) 36.6653 63.5061i 1.38780 2.40374i
\(699\) 0 0
\(700\) 4.30278 + 7.45263i 0.162630 + 0.281683i
\(701\) −11.5778 −0.437287 −0.218644 0.975805i \(-0.570163\pi\)
−0.218644 + 0.975805i \(0.570163\pi\)
\(702\) 0 0
\(703\) 7.21110 0.271972
\(704\) −29.5139 51.1195i −1.11235 1.92664i
\(705\) 0 0
\(706\) 24.9083 43.1425i 0.937437 1.62369i
\(707\) −15.6333 + 27.0777i −0.587951 + 1.01836i
\(708\) 0 0
\(709\) 11.4222 + 19.7838i 0.428970 + 0.742998i 0.996782 0.0801605i \(-0.0255433\pi\)
−0.567812 + 0.823158i \(0.692210\pi\)
\(710\) 17.0278 0.639040
\(711\) 0 0
\(712\) 41.4500 1.55340
\(713\) 8.40833 + 14.5636i 0.314894 + 0.545413i
\(714\) 0 0
\(715\) −15.2111 + 26.3464i −0.568863 + 0.985300i
\(716\) −35.0278 + 60.6699i −1.30905 + 2.26734i
\(717\) 0 0
\(718\) −11.0917 19.2113i −0.413938 0.716961i
\(719\) −37.2666 −1.38981 −0.694905 0.719101i \(-0.744554\pi\)
−0.694905 + 0.719101i \(0.744554\pi\)
\(720\) 0 0
\(721\) 10.4222 0.388143
\(722\) 6.90833 + 11.9656i 0.257101 + 0.445313i
\(723\) 0 0
\(724\) 11.5597 20.0220i 0.429613 0.744112i
\(725\) 0.697224 1.20763i 0.0258943 0.0448502i
\(726\) 0 0
\(727\) −17.8167 30.8593i −0.660783 1.14451i −0.980410 0.196967i \(-0.936891\pi\)
0.319627 0.947543i \(-0.396442\pi\)
\(728\) −51.6333 −1.91366
\(729\) 0 0
\(730\) −29.0278 −1.07437
\(731\) 0.486122 + 0.841988i 0.0179799 + 0.0311420i
\(732\) 0 0
\(733\) −16.0000 + 27.7128i −0.590973 + 1.02360i 0.403128 + 0.915144i \(0.367923\pi\)
−0.994102 + 0.108453i \(0.965410\pi\)
\(734\) 3.00000 5.19615i 0.110732 0.191793i
\(735\) 0 0
\(736\) 7.95416 + 13.7770i 0.293194 + 0.507828i
\(737\) 3.63331 0.133835
\(738\) 0 0
\(739\) −6.02776 −0.221735 −0.110867 0.993835i \(-0.535363\pi\)
−0.110867 + 0.993835i \(0.535363\pi\)
\(740\) 3.30278 + 5.72058i 0.121412 + 0.210293i
\(741\) 0 0
\(742\) −4.81665 + 8.34269i −0.176825 + 0.306270i
\(743\) −2.78890 + 4.83051i −0.102315 + 0.177214i −0.912638 0.408769i \(-0.865958\pi\)
0.810323 + 0.585983i \(0.199292\pi\)
\(744\) 0 0
\(745\) −11.5139 19.9426i −0.421836 0.730641i
\(746\) −58.0555 −2.12556
\(747\) 0 0
\(748\) 24.4222 0.892964
\(749\) 0 0
\(750\) 0 0
\(751\) 15.0139 26.0048i 0.547864 0.948929i −0.450556 0.892748i \(-0.648774\pi\)
0.998421 0.0561807i \(-0.0178923\pi\)
\(752\) −1.39445 + 2.41526i −0.0508503 + 0.0880753i
\(753\) 0 0
\(754\) 10.6056 + 18.3694i 0.386231 + 0.668972i
\(755\) −14.4222 −0.524878
\(756\) 0 0
\(757\) 16.7889 0.610203 0.305101 0.952320i \(-0.401310\pi\)
0.305101 + 0.952320i \(0.401310\pi\)
\(758\) −24.8764 43.0871i −0.903550 1.56500i
\(759\) 0 0
\(760\) 5.40833 9.36750i 0.196181 0.339795i
\(761\) 5.72498 9.91596i 0.207530 0.359453i −0.743406 0.668841i \(-0.766791\pi\)
0.950936 + 0.309388i \(0.100124\pi\)
\(762\) 0 0
\(763\) −9.11943 15.7953i −0.330146 0.571829i
\(764\) 41.0278 1.48433
\(765\) 0 0
\(766\) −56.7250 −2.04956
\(767\) −4.60555 7.97705i −0.166297 0.288035i
\(768\) 0 0
\(769\) −20.5000 + 35.5070i −0.739249 + 1.28042i 0.213585 + 0.976924i \(0.431486\pi\)
−0.952834 + 0.303492i \(0.901847\pi\)
\(770\) 13.8167 23.9311i 0.497918 0.862419i
\(771\) 0 0
\(772\) −0.302776 0.524423i −0.0108971 0.0188744i
\(773\) 4.81665 0.173243 0.0866215 0.996241i \(-0.472393\pi\)
0.0866215 + 0.996241i \(0.472393\pi\)
\(774\) 0 0
\(775\) −5.60555 −0.201357
\(776\) −12.0000 20.7846i −0.430775 0.746124i
\(777\) 0 0
\(778\) 29.7250 51.4852i 1.06569 1.84583i
\(779\) −8.30278 + 14.3808i −0.297478 + 0.515247i
\(780\) 0 0
\(781\) −17.0278 29.4929i −0.609301 1.05534i
\(782\) −11.0917 −0.396637
\(783\) 0 0
\(784\) −0.0639167 −0.00228274
\(785\) −8.90833