Properties

Label 1323.2.h.e.802.3
Level $1323$
Weight $2$
Character 1323.802
Analytic conductor $10.564$
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] = [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: 6.0.309123.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 802.3
Root \(0.500000 + 2.05195i\) of defining polynomial
Character \(\chi\) \(=\) 1323.802
Dual form 1323.2.h.e.226.3

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.46050 q^{2} +4.05408 q^{4} +(1.29679 - 2.24611i) q^{5} +5.05408 q^{8} +O(q^{10})\) \(q+2.46050 q^{2} +4.05408 q^{4} +(1.29679 - 2.24611i) q^{5} +5.05408 q^{8} +(3.19076 - 5.52655i) q^{10} +(2.25729 + 3.90975i) q^{11} +(0.500000 + 0.866025i) q^{13} +4.32743 q^{16} +(0.472958 - 0.819187i) q^{17} +(-2.02704 - 3.51094i) q^{19} +(5.25729 - 9.10590i) q^{20} +(5.55408 + 9.61996i) q^{22} +(-0.136673 + 0.236725i) q^{23} +(-0.863327 - 1.49533i) q^{25} +(1.23025 + 2.13086i) q^{26} +(1.23025 - 2.13086i) q^{29} -2.32743 q^{31} +0.539495 q^{32} +(1.16372 - 2.01561i) q^{34} +(-0.890369 - 1.54216i) q^{37} +(-4.98755 - 8.63868i) q^{38} +(6.55408 - 11.3520i) q^{40} +(3.20321 + 5.54812i) q^{41} +(5.21780 - 9.03749i) q^{43} +(9.15126 + 15.8505i) q^{44} +(-0.336285 + 0.582462i) q^{46} -12.1623 q^{47} +(-2.12422 - 3.67926i) q^{50} +(2.02704 + 3.51094i) q^{52} +(-3.13667 + 5.43288i) q^{53} +11.7089 q^{55} +(3.02704 - 5.24299i) q^{58} -2.72665 q^{59} +2.27335 q^{61} -5.72665 q^{62} -7.32743 q^{64} +2.59358 q^{65} -15.8171 q^{67} +(1.91741 - 3.32105i) q^{68} -3.27335 q^{71} +(-0.753696 + 1.30544i) q^{73} +(-2.19076 - 3.79450i) q^{74} +(-8.21780 - 14.2336i) q^{76} +14.7089 q^{79} +(5.61177 - 9.71987i) q^{80} +(7.88151 + 13.6512i) q^{82} +(0.472958 - 0.819187i) q^{83} +(-1.22665 - 2.12463i) q^{85} +(12.8384 - 22.2368i) q^{86} +(11.4086 + 19.7602i) q^{88} +(7.17830 + 12.4332i) q^{89} +(-0.554084 + 0.959702i) q^{92} -29.9253 q^{94} -10.5146 q^{95} +(-5.74484 + 9.95036i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 6 q + 2 q^{2} + 6 q^{4} + 5 q^{5} + 12 q^{8} - 2 q^{11} + 3 q^{13} + 6 q^{16} + 12 q^{17} - 3 q^{19} + 16 q^{20} + 15 q^{22} - 6 q^{25} + q^{26} + q^{29} + 6 q^{31} + 16 q^{32} - 3 q^{34} + 3 q^{37} - 8 q^{38} + 21 q^{40} + 22 q^{41} + 3 q^{43} + 23 q^{44} - 12 q^{46} - 18 q^{47} + 10 q^{50} + 3 q^{52} - 18 q^{53} + 12 q^{55} + 9 q^{58} - 18 q^{59} + 12 q^{61} - 36 q^{62} - 24 q^{64} + 10 q^{65} - 6 q^{68} - 18 q^{71} + 3 q^{73} + 6 q^{74} - 21 q^{76} + 30 q^{79} - 11 q^{80} + 9 q^{82} + 12 q^{83} - 9 q^{85} + 34 q^{86} + 21 q^{88} + 2 q^{89} + 15 q^{92} - 48 q^{94} - 32 q^{95} + 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.46050 1.73984 0.869920 0.493193i \(-0.164170\pi\)
0.869920 + 0.493193i \(0.164170\pi\)
\(3\) 0 0
\(4\) 4.05408 2.02704
\(5\) 1.29679 2.24611i 0.579942 1.00449i −0.415543 0.909573i \(-0.636409\pi\)
0.995485 0.0949156i \(-0.0302581\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 5.05408 1.78689
\(9\) 0 0
\(10\) 3.19076 5.52655i 1.00901 1.74765i
\(11\) 2.25729 + 3.90975i 0.680600 + 1.17883i 0.974798 + 0.223089i \(0.0716141\pi\)
−0.294198 + 0.955744i \(0.595053\pi\)
\(12\) 0 0
\(13\) 0.500000 + 0.866025i 0.138675 + 0.240192i 0.926995 0.375073i \(-0.122382\pi\)
−0.788320 + 0.615265i \(0.789049\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 4.32743 1.08186
\(17\) 0.472958 0.819187i 0.114709 0.198682i −0.802954 0.596041i \(-0.796740\pi\)
0.917663 + 0.397359i \(0.130073\pi\)
\(18\) 0 0
\(19\) −2.02704 3.51094i −0.465035 0.805465i 0.534168 0.845378i \(-0.320625\pi\)
−0.999203 + 0.0399136i \(0.987292\pi\)
\(20\) 5.25729 9.10590i 1.17557 2.03614i
\(21\) 0 0
\(22\) 5.55408 + 9.61996i 1.18413 + 2.05098i
\(23\) −0.136673 + 0.236725i −0.0284983 + 0.0493605i −0.879923 0.475117i \(-0.842406\pi\)
0.851425 + 0.524477i \(0.175739\pi\)
\(24\) 0 0
\(25\) −0.863327 1.49533i −0.172665 0.299065i
\(26\) 1.23025 + 2.13086i 0.241272 + 0.417896i
\(27\) 0 0
\(28\) 0 0
\(29\) 1.23025 2.13086i 0.228452 0.395691i −0.728897 0.684623i \(-0.759967\pi\)
0.957350 + 0.288932i \(0.0933002\pi\)
\(30\) 0 0
\(31\) −2.32743 −0.418019 −0.209009 0.977914i \(-0.567024\pi\)
−0.209009 + 0.977914i \(0.567024\pi\)
\(32\) 0.539495 0.0953702
\(33\) 0 0
\(34\) 1.16372 2.01561i 0.199576 0.345675i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.890369 1.54216i −0.146376 0.253530i 0.783510 0.621380i \(-0.213428\pi\)
−0.929885 + 0.367849i \(0.880094\pi\)
\(38\) −4.98755 8.63868i −0.809087 1.40138i
\(39\) 0 0
\(40\) 6.55408 11.3520i 1.03629 1.79491i
\(41\) 3.20321 + 5.54812i 0.500257 + 0.866471i 1.00000 0.000297253i \(9.46187e-5\pi\)
−0.499743 + 0.866174i \(0.666572\pi\)
\(42\) 0 0
\(43\) 5.21780 9.03749i 0.795707 1.37820i −0.126682 0.991943i \(-0.540433\pi\)
0.922389 0.386262i \(-0.126234\pi\)
\(44\) 9.15126 + 15.8505i 1.37960 + 2.38955i
\(45\) 0 0
\(46\) −0.336285 + 0.582462i −0.0495825 + 0.0858794i
\(47\) −12.1623 −1.77405 −0.887023 0.461724i \(-0.847231\pi\)
−0.887023 + 0.461724i \(0.847231\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −2.12422 3.67926i −0.300410 0.520326i
\(51\) 0 0
\(52\) 2.02704 + 3.51094i 0.281100 + 0.486880i
\(53\) −3.13667 + 5.43288i −0.430855 + 0.746263i −0.996947 0.0780790i \(-0.975121\pi\)
0.566092 + 0.824342i \(0.308455\pi\)
\(54\) 0 0
\(55\) 11.7089 1.57883
\(56\) 0 0
\(57\) 0 0
\(58\) 3.02704 5.24299i 0.397470 0.688438i
\(59\) −2.72665 −0.354980 −0.177490 0.984123i \(-0.556798\pi\)
−0.177490 + 0.984123i \(0.556798\pi\)
\(60\) 0 0
\(61\) 2.27335 0.291072 0.145536 0.989353i \(-0.453509\pi\)
0.145536 + 0.989353i \(0.453509\pi\)
\(62\) −5.72665 −0.727286
\(63\) 0 0
\(64\) −7.32743 −0.915929
\(65\) 2.59358 0.321694
\(66\) 0 0
\(67\) −15.8171 −1.93237 −0.966184 0.257854i \(-0.916985\pi\)
−0.966184 + 0.257854i \(0.916985\pi\)
\(68\) 1.91741 3.32105i 0.232520 0.402737i
\(69\) 0 0
\(70\) 0 0
\(71\) −3.27335 −0.388475 −0.194237 0.980955i \(-0.562223\pi\)
−0.194237 + 0.980955i \(0.562223\pi\)
\(72\) 0 0
\(73\) −0.753696 + 1.30544i −0.0882134 + 0.152790i −0.906756 0.421656i \(-0.861449\pi\)
0.818543 + 0.574446i \(0.194782\pi\)
\(74\) −2.19076 3.79450i −0.254670 0.441102i
\(75\) 0 0
\(76\) −8.21780 14.2336i −0.942646 1.63271i
\(77\) 0 0
\(78\) 0 0
\(79\) 14.7089 1.65489 0.827443 0.561550i \(-0.189795\pi\)
0.827443 + 0.561550i \(0.189795\pi\)
\(80\) 5.61177 9.71987i 0.627415 1.08671i
\(81\) 0 0
\(82\) 7.88151 + 13.6512i 0.870368 + 1.50752i
\(83\) 0.472958 0.819187i 0.0519139 0.0899175i −0.838901 0.544285i \(-0.816801\pi\)
0.890815 + 0.454367i \(0.150135\pi\)
\(84\) 0 0
\(85\) −1.22665 2.12463i −0.133049 0.230448i
\(86\) 12.8384 22.2368i 1.38440 2.39786i
\(87\) 0 0
\(88\) 11.4086 + 19.7602i 1.21616 + 2.10644i
\(89\) 7.17830 + 12.4332i 0.760899 + 1.31792i 0.942388 + 0.334522i \(0.108575\pi\)
−0.181489 + 0.983393i \(0.558092\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.554084 + 0.959702i −0.0577673 + 0.100056i
\(93\) 0 0
\(94\) −29.9253 −3.08656
\(95\) −10.5146 −1.07877
\(96\) 0 0
\(97\) −5.74484 + 9.95036i −0.583300 + 1.01031i 0.411785 + 0.911281i \(0.364906\pi\)
−0.995085 + 0.0990246i \(0.968428\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −3.50000 6.06218i −0.350000 0.606218i
\(101\) 1.83988 + 3.18677i 0.183075 + 0.317096i 0.942926 0.333002i \(-0.108061\pi\)
−0.759851 + 0.650097i \(0.774728\pi\)
\(102\) 0 0
\(103\) −4.86333 + 8.42353i −0.479198 + 0.829995i −0.999715 0.0238560i \(-0.992406\pi\)
0.520518 + 0.853851i \(0.325739\pi\)
\(104\) 2.52704 + 4.37697i 0.247797 + 0.429197i
\(105\) 0 0
\(106\) −7.71780 + 13.3676i −0.749619 + 1.29838i
\(107\) −0.687159 1.19019i −0.0664301 0.115060i 0.830897 0.556426i \(-0.187828\pi\)
−0.897327 + 0.441365i \(0.854494\pi\)
\(108\) 0 0
\(109\) 1.69961 2.94381i 0.162793 0.281966i −0.773076 0.634313i \(-0.781283\pi\)
0.935869 + 0.352347i \(0.114616\pi\)
\(110\) 28.8099 2.74692
\(111\) 0 0
\(112\) 0 0
\(113\) 5.19436 + 8.99689i 0.488644 + 0.846356i 0.999915 0.0130636i \(-0.00415840\pi\)
−0.511271 + 0.859420i \(0.670825\pi\)
\(114\) 0 0
\(115\) 0.354473 + 0.613964i 0.0330547 + 0.0572525i
\(116\) 4.98755 8.63868i 0.463082 0.802082i
\(117\) 0 0
\(118\) −6.70895 −0.617608
\(119\) 0 0
\(120\) 0 0
\(121\) −4.69076 + 8.12463i −0.426432 + 0.738603i
\(122\) 5.59358 0.506419
\(123\) 0 0
\(124\) −9.43560 −0.847342
\(125\) 8.48968 0.759340
\(126\) 0 0
\(127\) 0.672570 0.0596809 0.0298405 0.999555i \(-0.490500\pi\)
0.0298405 + 0.999555i \(0.490500\pi\)
\(128\) −19.1082 −1.68894
\(129\) 0 0
\(130\) 6.38151 0.559696
\(131\) −3.95691 + 6.85356i −0.345717 + 0.598799i −0.985484 0.169770i \(-0.945697\pi\)
0.639767 + 0.768569i \(0.279031\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −38.9181 −3.36201
\(135\) 0 0
\(136\) 2.39037 4.14024i 0.204972 0.355023i
\(137\) −1.83628 3.18054i −0.156884 0.271732i 0.776859 0.629674i \(-0.216812\pi\)
−0.933744 + 0.357943i \(0.883478\pi\)
\(138\) 0 0
\(139\) −1.02704 1.77889i −0.0871126 0.150883i 0.819177 0.573541i \(-0.194431\pi\)
−0.906289 + 0.422658i \(0.861097\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.05408 −0.675884
\(143\) −2.25729 + 3.90975i −0.188764 + 0.326950i
\(144\) 0 0
\(145\) −3.19076 5.52655i −0.264978 0.458955i
\(146\) −1.85447 + 3.21204i −0.153477 + 0.265830i
\(147\) 0 0
\(148\) −3.60963 6.25206i −0.296710 0.513917i
\(149\) −6.77188 + 11.7292i −0.554774 + 0.960897i 0.443147 + 0.896449i \(0.353862\pi\)
−0.997921 + 0.0644482i \(0.979471\pi\)
\(150\) 0 0
\(151\) −4.96410 8.59808i −0.403973 0.699702i 0.590228 0.807236i \(-0.299038\pi\)
−0.994201 + 0.107535i \(0.965704\pi\)
\(152\) −10.2448 17.7446i −0.830966 1.43928i
\(153\) 0 0
\(154\) 0 0
\(155\) −3.01819 + 5.22765i −0.242427 + 0.419895i
\(156\) 0 0
\(157\) −6.05408 −0.483169 −0.241584 0.970380i \(-0.577667\pi\)
−0.241584 + 0.970380i \(0.577667\pi\)
\(158\) 36.1914 2.87924
\(159\) 0 0
\(160\) 0.699612 1.21176i 0.0553092 0.0957983i
\(161\) 0 0
\(162\) 0 0
\(163\) −8.90856 15.4301i −0.697772 1.20858i −0.969237 0.246128i \(-0.920842\pi\)
0.271465 0.962448i \(-0.412492\pi\)
\(164\) 12.9861 + 22.4926i 1.01404 + 1.75637i
\(165\) 0 0
\(166\) 1.16372 2.01561i 0.0903218 0.156442i
\(167\) 4.23385 + 7.33325i 0.327625 + 0.567464i 0.982040 0.188672i \(-0.0604183\pi\)
−0.654415 + 0.756136i \(0.727085\pi\)
\(168\) 0 0
\(169\) 6.00000 10.3923i 0.461538 0.799408i
\(170\) −3.01819 5.22765i −0.231484 0.400943i
\(171\) 0 0
\(172\) 21.1534 36.6388i 1.61293 2.79368i
\(173\) 17.3566 1.31960 0.659799 0.751442i \(-0.270641\pi\)
0.659799 + 0.751442i \(0.270641\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 9.76829 + 16.9192i 0.736312 + 1.27533i
\(177\) 0 0
\(178\) 17.6623 + 30.5919i 1.32384 + 2.29296i
\(179\) −5.67471 + 9.82888i −0.424147 + 0.734645i −0.996340 0.0854741i \(-0.972759\pi\)
0.572193 + 0.820119i \(0.306093\pi\)
\(180\) 0 0
\(181\) −21.8889 −1.62699 −0.813495 0.581572i \(-0.802438\pi\)
−0.813495 + 0.581572i \(0.802438\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −0.690757 + 1.19643i −0.0509233 + 0.0882018i
\(185\) −4.61849 −0.339558
\(186\) 0 0
\(187\) 4.27042 0.312284
\(188\) −49.3068 −3.59607
\(189\) 0 0
\(190\) −25.8712 −1.87689
\(191\) 0.701748 0.0507767 0.0253883 0.999678i \(-0.491918\pi\)
0.0253883 + 0.999678i \(0.491918\pi\)
\(192\) 0 0
\(193\) 12.1445 0.874183 0.437092 0.899417i \(-0.356009\pi\)
0.437092 + 0.899417i \(0.356009\pi\)
\(194\) −14.1352 + 24.4829i −1.01485 + 1.75777i
\(195\) 0 0
\(196\) 0 0
\(197\) 16.4107 1.16921 0.584607 0.811317i \(-0.301249\pi\)
0.584607 + 0.811317i \(0.301249\pi\)
\(198\) 0 0
\(199\) 11.3530 19.6640i 0.804794 1.39394i −0.111637 0.993749i \(-0.535609\pi\)
0.916430 0.400194i \(-0.131057\pi\)
\(200\) −4.36333 7.55750i −0.308534 0.534396i
\(201\) 0 0
\(202\) 4.52704 + 7.84107i 0.318522 + 0.551696i
\(203\) 0 0
\(204\) 0 0
\(205\) 16.6156 1.16048
\(206\) −11.9662 + 20.7261i −0.833727 + 1.44406i
\(207\) 0 0
\(208\) 2.16372 + 3.74766i 0.150027 + 0.259854i
\(209\) 9.15126 15.8505i 0.633006 1.09640i
\(210\) 0 0
\(211\) −2.28074 3.95035i −0.157012 0.271954i 0.776778 0.629775i \(-0.216853\pi\)
−0.933790 + 0.357822i \(0.883520\pi\)
\(212\) −12.7163 + 22.0253i −0.873362 + 1.51271i
\(213\) 0 0
\(214\) −1.69076 2.92848i −0.115578 0.200187i
\(215\) −13.5328 23.4395i −0.922928 1.59856i
\(216\) 0 0
\(217\) 0 0
\(218\) 4.18190 7.24327i 0.283234 0.490576i
\(219\) 0 0
\(220\) 47.4690 3.20036
\(221\) 0.945916 0.0636292
\(222\) 0 0
\(223\) 6.66225 11.5394i 0.446137 0.772733i −0.551993 0.833849i \(-0.686133\pi\)
0.998131 + 0.0611159i \(0.0194659\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 12.7807 + 22.1369i 0.850162 + 1.47252i
\(227\) −0.690757 1.19643i −0.0458472 0.0794096i 0.842191 0.539179i \(-0.181265\pi\)
−0.888038 + 0.459769i \(0.847932\pi\)
\(228\) 0 0
\(229\) −8.98968 + 15.5706i −0.594055 + 1.02893i 0.399625 + 0.916679i \(0.369141\pi\)
−0.993679 + 0.112254i \(0.964193\pi\)
\(230\) 0.872181 + 1.51066i 0.0575099 + 0.0996101i
\(231\) 0 0
\(232\) 6.21780 10.7695i 0.408219 0.707055i
\(233\) −9.49115 16.4391i −0.621786 1.07696i −0.989153 0.146888i \(-0.953074\pi\)
0.367367 0.930076i \(-0.380259\pi\)
\(234\) 0 0
\(235\) −15.7719 + 27.3177i −1.02884 + 1.78201i
\(236\) −11.0541 −0.719560
\(237\) 0 0
\(238\) 0 0
\(239\) 2.44592 + 4.23645i 0.158213 + 0.274033i 0.934224 0.356686i \(-0.116093\pi\)
−0.776011 + 0.630719i \(0.782760\pi\)
\(240\) 0 0
\(241\) −13.0797 22.6546i −0.842535 1.45931i −0.887745 0.460336i \(-0.847729\pi\)
0.0452094 0.998978i \(-0.485604\pi\)
\(242\) −11.5416 + 19.9907i −0.741924 + 1.28505i
\(243\) 0 0
\(244\) 9.21634 0.590016
\(245\) 0 0
\(246\) 0 0
\(247\) 2.02704 3.51094i 0.128978 0.223396i
\(248\) −11.7630 −0.746953
\(249\) 0 0
\(250\) 20.8889 1.32113
\(251\) 18.4576 1.16503 0.582516 0.812819i \(-0.302068\pi\)
0.582516 + 0.812819i \(0.302068\pi\)
\(252\) 0 0
\(253\) −1.23405 −0.0775838
\(254\) 1.65486 0.103835
\(255\) 0 0
\(256\) −32.3609 −2.02256
\(257\) 5.86693 10.1618i 0.365969 0.633876i −0.622962 0.782252i \(-0.714071\pi\)
0.988931 + 0.148375i \(0.0474044\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 10.5146 0.652087
\(261\) 0 0
\(262\) −9.73599 + 16.8632i −0.601491 + 1.04181i
\(263\) −3.76089 6.51406i −0.231907 0.401674i 0.726463 0.687206i \(-0.241163\pi\)
−0.958369 + 0.285532i \(0.907830\pi\)
\(264\) 0 0
\(265\) 8.13521 + 14.0906i 0.499742 + 0.865579i
\(266\) 0 0
\(267\) 0 0
\(268\) −64.1239 −3.91699
\(269\) 9.41741 16.3114i 0.574190 0.994526i −0.421939 0.906624i \(-0.638651\pi\)
0.996129 0.0879017i \(-0.0280161\pi\)
\(270\) 0 0
\(271\) −11.9911 20.7693i −0.728410 1.26164i −0.957555 0.288251i \(-0.906926\pi\)
0.229145 0.973392i \(-0.426407\pi\)
\(272\) 2.04669 3.54498i 0.124099 0.214946i
\(273\) 0 0
\(274\) −4.51819 7.82573i −0.272954 0.472770i
\(275\) 3.89757 6.75078i 0.235032 0.407088i
\(276\) 0 0
\(277\) −3.58113 6.20269i −0.215169 0.372684i 0.738156 0.674630i \(-0.235697\pi\)
−0.953325 + 0.301947i \(0.902364\pi\)
\(278\) −2.52704 4.37697i −0.151562 0.262513i
\(279\) 0 0
\(280\) 0 0
\(281\) 7.44085 12.8879i 0.443884 0.768830i −0.554090 0.832457i \(-0.686933\pi\)
0.997974 + 0.0636271i \(0.0202668\pi\)
\(282\) 0 0
\(283\) −19.9971 −1.18870 −0.594351 0.804205i \(-0.702591\pi\)
−0.594351 + 0.804205i \(0.702591\pi\)
\(284\) −13.2704 −0.787455
\(285\) 0 0
\(286\) −5.55408 + 9.61996i −0.328420 + 0.568840i
\(287\) 0 0
\(288\) 0 0
\(289\) 8.05262 + 13.9475i 0.473684 + 0.820444i
\(290\) −7.85087 13.5981i −0.461019 0.798509i
\(291\) 0 0
\(292\) −3.05555 + 5.29236i −0.178812 + 0.309712i
\(293\) −7.53278 13.0472i −0.440070 0.762223i 0.557625 0.830093i \(-0.311713\pi\)
−0.997694 + 0.0678705i \(0.978380\pi\)
\(294\) 0 0
\(295\) −3.53590 + 6.12435i −0.205868 + 0.356574i
\(296\) −4.50000 7.79423i −0.261557 0.453030i
\(297\) 0 0
\(298\) −16.6623 + 28.8599i −0.965218 + 1.67181i
\(299\) −0.273346 −0.0158080
\(300\) 0 0
\(301\) 0 0
\(302\) −12.2142 21.1556i −0.702848 1.21737i
\(303\) 0 0
\(304\) −8.77188 15.1933i −0.503102 0.871398i
\(305\) 2.94805 5.10618i 0.168805 0.292379i
\(306\) 0 0
\(307\) 27.2704 1.55641 0.778203 0.628013i \(-0.216132\pi\)
0.778203 + 0.628013i \(0.216132\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −7.42627 + 12.8627i −0.421784 + 0.730551i
\(311\) −15.9823 −0.906273 −0.453136 0.891441i \(-0.649695\pi\)
−0.453136 + 0.891441i \(0.649695\pi\)
\(312\) 0 0
\(313\) −11.5979 −0.655549 −0.327775 0.944756i \(-0.606299\pi\)
−0.327775 + 0.944756i \(0.606299\pi\)
\(314\) −14.8961 −0.840636
\(315\) 0 0
\(316\) 59.6313 3.35452
\(317\) 2.01771 0.113326 0.0566629 0.998393i \(-0.481954\pi\)
0.0566629 + 0.998393i \(0.481954\pi\)
\(318\) 0 0
\(319\) 11.1082 0.621938
\(320\) −9.50214 + 16.4582i −0.531186 + 0.920040i
\(321\) 0 0
\(322\) 0 0
\(323\) −3.83482 −0.213375
\(324\) 0 0
\(325\) 0.863327 1.49533i 0.0478888 0.0829458i
\(326\) −21.9195 37.9658i −1.21401 2.10273i
\(327\) 0 0
\(328\) 16.1893 + 28.0407i 0.893904 + 1.54829i
\(329\) 0 0
\(330\) 0 0
\(331\) −19.7089 −1.08330 −0.541651 0.840604i \(-0.682200\pi\)
−0.541651 + 0.840604i \(0.682200\pi\)
\(332\) 1.91741 3.32105i 0.105232 0.182266i
\(333\) 0 0
\(334\) 10.4174 + 18.0435i 0.570015 + 0.987296i
\(335\) −20.5115 + 35.5269i −1.12066 + 1.94104i
\(336\) 0 0
\(337\) 14.5256 + 25.1590i 0.791259 + 1.37050i 0.925188 + 0.379509i \(0.123907\pi\)
−0.133929 + 0.990991i \(0.542759\pi\)
\(338\) 14.7630 25.5703i 0.803003 1.39084i
\(339\) 0 0
\(340\) −4.97296 8.61342i −0.269697 0.467128i
\(341\) −5.25370 9.09967i −0.284504 0.492775i
\(342\) 0 0
\(343\) 0 0
\(344\) 26.3712 45.6763i 1.42184 2.46270i
\(345\) 0 0
\(346\) 42.7060 2.29589
\(347\) −29.0833 −1.56127 −0.780636 0.624986i \(-0.785105\pi\)
−0.780636 + 0.624986i \(0.785105\pi\)
\(348\) 0 0
\(349\) 12.3815 21.4454i 0.662767 1.14795i −0.317118 0.948386i \(-0.602715\pi\)
0.979885 0.199561i \(-0.0639515\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 1.21780 + 2.10929i 0.0649089 + 0.112426i
\(353\) 16.6513 + 28.8408i 0.886257 + 1.53504i 0.844266 + 0.535925i \(0.180037\pi\)
0.0419914 + 0.999118i \(0.486630\pi\)
\(354\) 0 0
\(355\) −4.24484 + 7.35228i −0.225293 + 0.390219i
\(356\) 29.1015 + 50.4052i 1.54237 + 2.67147i
\(357\) 0 0
\(358\) −13.9626 + 24.1840i −0.737949 + 1.27816i
\(359\) 12.7683 + 22.1153i 0.673884 + 1.16720i 0.976794 + 0.214182i \(0.0687087\pi\)
−0.302909 + 0.953019i \(0.597958\pi\)
\(360\) 0 0
\(361\) 1.28220 2.22084i 0.0674842 0.116886i
\(362\) −53.8578 −2.83070
\(363\) 0 0
\(364\) 0 0
\(365\) 1.95477 + 3.38576i 0.102317 + 0.177219i
\(366\) 0 0
\(367\) 13.7252 + 23.7727i 0.716449 + 1.24093i 0.962398 + 0.271644i \(0.0875672\pi\)
−0.245949 + 0.969283i \(0.579100\pi\)
\(368\) −0.591443 + 1.02441i −0.0308311 + 0.0534011i
\(369\) 0 0
\(370\) −11.3638 −0.590776
\(371\) 0 0
\(372\) 0 0
\(373\) −8.16372 + 14.1400i −0.422701 + 0.732140i −0.996203 0.0870646i \(-0.972251\pi\)
0.573502 + 0.819204i \(0.305585\pi\)
\(374\) 10.5074 0.543324
\(375\) 0 0
\(376\) −61.4690 −3.17002
\(377\) 2.46050 0.126722
\(378\) 0 0
\(379\) 12.0364 0.618267 0.309134 0.951019i \(-0.399961\pi\)
0.309134 + 0.951019i \(0.399961\pi\)
\(380\) −42.6270 −2.18672
\(381\) 0 0
\(382\) 1.72665 0.0883433
\(383\) 6.21780 10.7695i 0.317715 0.550298i −0.662296 0.749242i \(-0.730418\pi\)
0.980011 + 0.198944i \(0.0637512\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 29.8817 1.52094
\(387\) 0 0
\(388\) −23.2901 + 40.3396i −1.18237 + 2.04793i
\(389\) 10.3004 + 17.8408i 0.522250 + 0.904564i 0.999665 + 0.0258860i \(0.00824070\pi\)
−0.477414 + 0.878678i \(0.658426\pi\)
\(390\) 0 0
\(391\) 0.129281 + 0.223922i 0.00653803 + 0.0113242i
\(392\) 0 0
\(393\) 0 0
\(394\) 40.3786 2.03424
\(395\) 19.0744 33.0378i 0.959738 1.66231i
\(396\) 0 0
\(397\) −11.8186 20.4704i −0.593157 1.02738i −0.993804 0.111146i \(-0.964548\pi\)
0.400647 0.916233i \(-0.368785\pi\)
\(398\) 27.9341 48.3833i 1.40021 2.42524i
\(399\) 0 0
\(400\) −3.73599 6.47092i −0.186799 0.323546i
\(401\) −1.28220 + 2.22084i −0.0640300 + 0.110903i −0.896263 0.443522i \(-0.853729\pi\)
0.832233 + 0.554426i \(0.187062\pi\)
\(402\) 0 0
\(403\) −1.16372 2.01561i −0.0579688 0.100405i
\(404\) 7.45904 + 12.9194i 0.371101 + 0.642766i
\(405\) 0 0
\(406\) 0 0
\(407\) 4.01965 6.96224i 0.199247 0.345105i
\(408\) 0 0
\(409\) 34.3245 1.69724 0.848619 0.529005i \(-0.177435\pi\)
0.848619 + 0.529005i \(0.177435\pi\)
\(410\) 40.8827 2.01905
\(411\) 0 0
\(412\) −19.7163 + 34.1497i −0.971354 + 1.68243i
\(413\) 0 0
\(414\) 0 0
\(415\) −1.22665 2.12463i −0.0602141 0.104294i
\(416\) 0.269748 + 0.467216i 0.0132255 + 0.0229072i
\(417\) 0 0
\(418\) 22.5167 39.0001i 1.10133 1.90756i
\(419\) −2.02850 3.51347i −0.0990989 0.171644i 0.812213 0.583361i \(-0.198263\pi\)
−0.911312 + 0.411717i \(0.864929\pi\)
\(420\) 0 0
\(421\) 10.5344 18.2462i 0.513417 0.889264i −0.486462 0.873702i \(-0.661713\pi\)
0.999879 0.0155624i \(-0.00495387\pi\)
\(422\) −5.61177 9.71987i −0.273177 0.473156i
\(423\) 0 0
\(424\) −15.8530 + 27.4582i −0.769890 + 1.33349i
\(425\) −1.63327 −0.0792252
\(426\) 0 0
\(427\) 0 0
\(428\) −2.78580 4.82515i −0.134657 0.233232i
\(429\) 0 0
\(430\) −33.2975 57.6729i −1.60575 2.78123i
\(431\) 11.3092 19.5882i 0.544747 0.943530i −0.453876 0.891065i \(-0.649959\pi\)
0.998623 0.0524646i \(-0.0167077\pi\)
\(432\) 0 0
\(433\) −2.41789 −0.116196 −0.0580982 0.998311i \(-0.518504\pi\)
−0.0580982 + 0.998311i \(0.518504\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 6.89037 11.9345i 0.329989 0.571557i
\(437\) 1.10817 0.0530109
\(438\) 0 0
\(439\) 23.4897 1.12110 0.560551 0.828120i \(-0.310589\pi\)
0.560551 + 0.828120i \(0.310589\pi\)
\(440\) 59.1780 2.82120
\(441\) 0 0
\(442\) 2.32743 0.110705
\(443\) 13.4179 0.637503 0.318752 0.947838i \(-0.396736\pi\)
0.318752 + 0.947838i \(0.396736\pi\)
\(444\) 0 0
\(445\) 37.2350 1.76511
\(446\) 16.3925 28.3927i 0.776208 1.34443i
\(447\) 0 0
\(448\) 0 0
\(449\) 9.16225 0.432393 0.216197 0.976350i \(-0.430635\pi\)
0.216197 + 0.976350i \(0.430635\pi\)
\(450\) 0 0
\(451\) −14.4612 + 25.0475i −0.680950 + 1.17944i
\(452\) 21.0584 + 36.4741i 0.990502 + 1.71560i
\(453\) 0 0
\(454\) −1.69961 2.94381i −0.0797667 0.138160i
\(455\) 0 0
\(456\) 0 0
\(457\) 8.81711 0.412447 0.206224 0.978505i \(-0.433883\pi\)
0.206224 + 0.978505i \(0.433883\pi\)
\(458\) −22.1192 + 38.3115i −1.03356 + 1.79018i
\(459\) 0 0
\(460\) 1.43706 + 2.48906i 0.0670033 + 0.116053i
\(461\) 2.82957 4.90095i 0.131786 0.228260i −0.792579 0.609769i \(-0.791262\pi\)
0.924365 + 0.381509i \(0.124595\pi\)
\(462\) 0 0
\(463\) −7.86333 13.6197i −0.365440 0.632960i 0.623407 0.781898i \(-0.285748\pi\)
−0.988847 + 0.148937i \(0.952415\pi\)
\(464\) 5.32383 9.22115i 0.247153 0.428081i
\(465\) 0 0
\(466\) −23.3530 40.4486i −1.08181 1.87375i
\(467\) 10.9985 + 19.0500i 0.508952 + 0.881530i 0.999946 + 0.0103675i \(0.00330013\pi\)
−0.490995 + 0.871163i \(0.663367\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −38.8068 + 67.2153i −1.79002 + 3.10041i
\(471\) 0 0
\(472\) −13.7807 −0.634310
\(473\) 47.1124 2.16623
\(474\) 0 0
\(475\) −3.50000 + 6.06218i −0.160591 + 0.278152i
\(476\) 0 0
\(477\) 0 0
\(478\) 6.01819 + 10.4238i 0.275265 + 0.476774i
\(479\) −12.4875 21.6291i −0.570571 0.988257i −0.996507 0.0835043i \(-0.973389\pi\)
0.425937 0.904753i \(-0.359945\pi\)
\(480\) 0 0
\(481\) 0.890369 1.54216i 0.0405973 0.0703166i
\(482\) −32.1826 55.7419i −1.46588 2.53897i
\(483\) 0 0
\(484\) −19.0167 + 32.9379i −0.864397 + 1.49718i
\(485\) 14.8997 + 25.8070i 0.676561 + 1.17184i
\(486\) 0 0
\(487\) 8.79893 15.2402i 0.398717 0.690599i −0.594851 0.803836i \(-0.702789\pi\)
0.993568 + 0.113238i \(0.0361221\pi\)
\(488\) 11.4897 0.520114
\(489\) 0 0
\(490\) 0 0
\(491\) 6.89757 + 11.9469i 0.311283 + 0.539158i 0.978640 0.205580i \(-0.0659080\pi\)
−0.667358 + 0.744737i \(0.732575\pi\)
\(492\) 0 0
\(493\) −1.16372 2.01561i −0.0524111 0.0907787i
\(494\) 4.98755 8.63868i 0.224400 0.388673i
\(495\) 0 0
\(496\) −10.0718 −0.452237
\(497\) 0 0
\(498\) 0 0
\(499\) −6.54377 + 11.3341i −0.292939 + 0.507386i −0.974503 0.224373i \(-0.927967\pi\)
0.681564 + 0.731758i \(0.261300\pi\)
\(500\) 34.4179 1.53921
\(501\) 0 0
\(502\) 45.4150 2.02697
\(503\) −22.3068 −0.994611 −0.497305 0.867576i \(-0.665677\pi\)
−0.497305 + 0.867576i \(0.665677\pi\)
\(504\) 0 0
\(505\) 9.54377 0.424692
\(506\) −3.03638 −0.134983
\(507\) 0 0
\(508\) 2.72665 0.120976
\(509\) 7.94659 13.7639i 0.352226 0.610074i −0.634413 0.772994i \(-0.718758\pi\)
0.986639 + 0.162920i \(0.0520914\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −41.4078 −1.82998
\(513\) 0 0
\(514\) 14.4356 25.0032i 0.636727 1.10284i
\(515\) 12.6134 + 21.8471i 0.555814 + 0.962698i
\(516\) 0 0
\(517\) −27.4538 47.5514i −1.20742 2.09131i
\(518\) 0 0
\(519\) 0 0
\(520\) 13.1082 0.574831
\(521\) −2.20895 + 3.82600i −0.0967756 + 0.167620i −0.910348 0.413843i \(-0.864186\pi\)
0.813573 + 0.581463i \(0.197520\pi\)
\(522\) 0 0
\(523\) 12.6367 + 21.8874i 0.552563 + 0.957067i 0.998089 + 0.0617982i \(0.0196835\pi\)
−0.445526 + 0.895269i \(0.646983\pi\)
\(524\) −16.0416 + 27.7849i −0.700782 + 1.21379i
\(525\) 0 0
\(526\) −9.25370 16.0279i −0.403480 0.698848i
\(527\) −1.10078 + 1.90660i −0.0479506 + 0.0830528i
\(528\) 0 0
\(529\) 11.4626 + 19.8539i 0.498376 + 0.863212i
\(530\) 20.0167 + 34.6700i 0.869471 + 1.50597i
\(531\) 0 0
\(532\) 0 0
\(533\) −3.20321 + 5.54812i −0.138746 + 0.240316i
\(534\) 0 0
\(535\) −3.56440 −0.154103
\(536\) −79.9410 −3.45293
\(537\) 0 0
\(538\) 23.1716 40.1344i 0.998998 1.73032i
\(539\) 0 0
\(540\) 0 0
\(541\) 1.71926 + 2.97785i 0.0739168 + 0.128028i 0.900615 0.434618i \(-0.143117\pi\)
−0.826698 + 0.562646i \(0.809783\pi\)
\(542\) −29.5043 51.1029i −1.26732 2.19506i
\(543\) 0 0
\(544\) 0.255158 0.441947i 0.0109398 0.0189483i
\(545\) −4.40808 7.63501i −0.188821 0.327048i
\(546\) 0 0
\(547\) 3.46410 6.00000i 0.148114 0.256542i −0.782416 0.622756i \(-0.786013\pi\)
0.930531 + 0.366214i \(0.119346\pi\)
\(548\) −7.44445 12.8942i −0.318011 0.550812i
\(549\) 0 0
\(550\) 9.58998 16.6103i 0.408918 0.708267i
\(551\) −9.97509 −0.424953
\(552\) 0 0
\(553\) 0 0
\(554\) −8.81138 15.2618i −0.374360 0.648410i
\(555\) 0 0
\(556\) −4.16372 7.21177i −0.176581 0.305847i
\(557\) 16.7917 29.0841i 0.711488 1.23233i −0.252810 0.967516i \(-0.581355\pi\)
0.964298 0.264818i \(-0.0853119\pi\)
\(558\) 0 0
\(559\) 10.4356 0.441379
\(560\) 0 0
\(561\) 0 0
\(562\) 18.3083 31.7108i 0.772287 1.33764i
\(563\) 42.4792 1.79028 0.895142 0.445781i \(-0.147074\pi\)
0.895142 + 0.445781i \(0.147074\pi\)
\(564\) 0 0
\(565\) 26.9439 1.13354
\(566\) −49.2029 −2.06815
\(567\) 0 0
\(568\) −16.5438 −0.694161
\(569\) −10.4035 −0.436137 −0.218069 0.975933i \(-0.569976\pi\)
−0.218069 + 0.975933i \(0.569976\pi\)
\(570\) 0 0
\(571\) 17.8496 0.746983 0.373491 0.927634i \(-0.378161\pi\)
0.373491 + 0.927634i \(0.378161\pi\)
\(572\) −9.15126 + 15.8505i −0.382633 + 0.662741i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.471974 0.0196827
\(576\) 0 0
\(577\) 5.97150 10.3429i 0.248597 0.430582i −0.714540 0.699595i \(-0.753364\pi\)
0.963137 + 0.269013i \(0.0866973\pi\)
\(578\) 19.8135 + 34.3180i 0.824134 + 1.42744i
\(579\) 0 0
\(580\) −12.9356 22.4051i −0.537122 0.930322i
\(581\) 0 0
\(582\) 0 0
\(583\) −28.3216 −1.17296
\(584\) −3.80924 + 6.59780i −0.157628 + 0.273019i
\(585\) 0 0
\(586\) −18.5344 32.1026i −0.765650 1.32615i
\(587\) −11.9299 + 20.6631i −0.492398 + 0.852859i −0.999962 0.00875568i \(-0.997213\pi\)
0.507563 + 0.861614i \(0.330546\pi\)
\(588\) 0 0
\(589\) 4.71780 + 8.17147i 0.194394 + 0.336699i
\(590\) −8.70009 + 15.0690i −0.358177 + 0.620381i
\(591\) 0 0
\(592\) −3.85301 6.67361i −0.158358 0.274284i
\(593\) −9.79007 16.9569i −0.402030 0.696336i 0.591941 0.805981i \(-0.298362\pi\)
−0.993971 + 0.109645i \(0.965029\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −27.4538 + 47.5514i −1.12455 + 1.94778i
\(597\) 0 0
\(598\) −0.672570 −0.0275034
\(599\) −18.5467 −0.757797 −0.378899 0.925438i \(-0.623697\pi\)
−0.378899 + 0.925438i \(0.623697\pi\)
\(600\) 0 0
\(601\) −9.09931 + 15.7605i −0.371169 + 0.642883i −0.989746 0.142841i \(-0.954376\pi\)
0.618577 + 0.785724i \(0.287710\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −20.1249 34.8573i −0.818870 1.41832i
\(605\) 12.1659 + 21.0719i 0.494612 + 0.856693i
\(606\) 0 0
\(607\) −11.1549 + 19.3208i −0.452762 + 0.784206i −0.998556 0.0537125i \(-0.982895\pi\)
0.545795 + 0.837919i \(0.316228\pi\)
\(608\) −1.09358 1.89413i −0.0443505 0.0768173i
\(609\) 0 0
\(610\) 7.25370 12.5638i 0.293694 0.508692i
\(611\) −6.08113 10.5328i −0.246016 0.426112i
\(612\) 0 0
\(613\) −5.11849 + 8.86548i −0.206734 + 0.358073i −0.950684 0.310162i \(-0.899617\pi\)
0.743950 + 0.668235i \(0.232950\pi\)
\(614\) 67.0990 2.70790
\(615\) 0 0
\(616\) 0 0
\(617\) −5.66372 9.80984i −0.228013 0.394929i 0.729206 0.684294i \(-0.239889\pi\)
−0.957219 + 0.289364i \(0.906556\pi\)
\(618\) 0 0
\(619\) 4.31663 + 7.47663i 0.173500 + 0.300511i 0.939641 0.342161i \(-0.111159\pi\)
−0.766141 + 0.642672i \(0.777826\pi\)
\(620\) −12.2360 + 21.1934i −0.491409 + 0.851145i
\(621\) 0 0
\(622\) −39.3245 −1.57677
\(623\) 0 0
\(624\) 0 0
\(625\) 15.3260 26.5454i 0.613039 1.06181i
\(626\) −28.5366 −1.14055
\(627\) 0 0
\(628\) −24.5438 −0.979403
\(629\) −1.68443 −0.0671626
\(630\) 0 0
\(631\) −14.8535 −0.591308 −0.295654 0.955295i \(-0.595538\pi\)
−0.295654 + 0.955295i \(0.595538\pi\)
\(632\) 74.3402 2.95710
\(633\) 0 0
\(634\) 4.96458 0.197169
\(635\) 0.872181 1.51066i 0.0346115 0.0599488i
\(636\) 0 0
\(637\) 0 0
\(638\) 27.3317 1.08207
\(639\) 0 0
\(640\) −24.7793 + 42.9190i −0.979487 + 1.69652i
\(641\) −17.0797 29.5828i −0.674606 1.16845i −0.976584 0.215137i \(-0.930980\pi\)
0.301978 0.953315i \(-0.402353\pi\)
\(642\) 0 0
\(643\) −5.41741 9.38323i −0.213642 0.370039i 0.739210 0.673475i \(-0.235199\pi\)
−0.952852 + 0.303437i \(0.901866\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −9.43560 −0.371239
\(647\) −16.4846 + 28.5522i −0.648077 + 1.12250i 0.335504 + 0.942039i \(0.391093\pi\)
−0.983582 + 0.180464i \(0.942240\pi\)
\(648\) 0 0
\(649\) −6.15486 10.6605i −0.241599 0.418462i
\(650\) 2.12422 3.67926i 0.0833188 0.144312i
\(651\) 0 0
\(652\) −36.1160 62.5548i −1.41441 2.44984i
\(653\) −1.96557 + 3.40446i −0.0769185 + 0.133227i −0.901919 0.431905i \(-0.857841\pi\)
0.825000 + 0.565132i \(0.191175\pi\)
\(654\) 0 0
\(655\) 10.2626 + 17.7753i 0.400991 + 0.694537i
\(656\) 13.8617 + 24.0091i 0.541207 + 0.937399i
\(657\) 0 0
\(658\) 0 0
\(659\) 8.40856 14.5640i 0.327551 0.567335i −0.654474 0.756084i \(-0.727110\pi\)
0.982025 + 0.188749i \(0.0604434\pi\)
\(660\) 0 0
\(661\) 17.0216 0.662063 0.331032 0.943620i \(-0.392603\pi\)
0.331032 + 0.943620i \(0.392603\pi\)
\(662\) −48.4940 −1.88477
\(663\) 0 0
\(664\) 2.39037 4.14024i 0.0927643 0.160672i
\(665\) 0 0
\(666\) 0 0
\(667\) 0.336285 + 0.582462i 0.0130210 + 0.0225530i
\(668\) 17.1644 + 29.7296i 0.664110 + 1.15027i
\(669\) 0 0
\(670\) −50.4686 + 87.4141i −1.94977 + 3.37710i
\(671\) 5.13161 + 8.88821i 0.198104 + 0.343126i
\(672\) 0 0
\(673\) −14.3727 + 24.8942i −0.554025 + 0.959600i 0.443953 + 0.896050i \(0.353576\pi\)
−0.997979 + 0.0635501i \(0.979758\pi\)
\(674\) 35.7403 + 61.9039i 1.37666 + 2.38445i
\(675\) 0 0
\(676\) 24.3245 42.1313i 0.935558 1.62043i
\(677\) −6.03638 −0.231997 −0.115998 0.993249i \(-0.537007\pi\)
−0.115998 + 0.993249i \(0.537007\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −6.19961 10.7380i −0.237744 0.411785i
\(681\) 0 0
\(682\) −12.9267 22.3898i −0.494991 0.857349i
\(683\) 10.2556 17.7633i 0.392421 0.679693i −0.600347 0.799739i \(-0.704971\pi\)
0.992768 + 0.120046i \(0.0383043\pi\)
\(684\) 0 0
\(685\) −9.52510 −0.363935
\(686\) 0 0
\(687\) 0 0
\(688\) 22.5797 39.1091i 0.860842 1.49102i
\(689\) −6.27335 −0.238995
\(690\) 0 0
\(691\) 15.0029 0.570738 0.285369 0.958418i \(-0.407884\pi\)
0.285369 + 0.958418i \(0.407884\pi\)
\(692\) 70.3652 2.67488
\(693\) 0 0
\(694\) −71.5595 −2.71636
\(695\) −5.32743 −0.202081
\(696\) 0 0
\(697\) 6.05993 0.229536
\(698\) 30.4648 52.7665i 1.15311 1.99724i
\(699\) 0 0
\(700\) 0 0
\(701\) −38.5113 −1.45455 −0.727275 0.686346i \(-0.759214\pi\)
−0.727275 + 0.686346i \(0.759214\pi\)
\(702\) 0 0
\(703\) −3.60963 + 6.25206i −0.136140 + 0.235801i
\(704\) −16.5402 28.6484i −0.623381 1.07973i
\(705\) 0 0
\(706\) 40.9705 + 70.9630i 1.54195 + 2.67073i
\(707\) 0 0
\(708\) 0 0
\(709\) 7.64008 0.286929 0.143465 0.989655i \(-0.454176\pi\)
0.143465 + 0.989655i \(0.454176\pi\)
\(710\) −10.4445 + 18.0903i −0.391973 + 0.678918i
\(711\) 0 0
\(712\) 36.2798 + 62.8384i 1.35964 + 2.35497i
\(713\) 0.318097 0.550960i 0.0119128 0.0206336i
\(714\) 0 0
\(715\) 5.85447 + 10.1402i 0.218945 + 0.379224i
\(716\) −23.0057 + 39.8471i −0.859765 + 1.48916i
\(717\) 0 0
\(718\) 31.4164 + 54.4148i 1.17245 + 2.03074i
\(719\) 15.0182 + 26.0123i 0.560084 + 0.970094i 0.997488 + 0.0708289i \(0.0225644\pi\)
−0.437405 + 0.899265i \(0.644102\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 3.15486 5.46438i 0.117412 0.203363i
\(723\) 0 0
\(724\) −88.7395 −3.29798
\(725\) −4.24844 −0.157783
\(726\) 0 0
\(727\) 1.72812 2.99319i 0.0640923 0.111011i −0.832199 0.554478i \(-0.812918\pi\)
0.896291 + 0.443466i \(0.146251\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 4.80972 + 8.33068i 0.178016 + 0.308332i
\(731\) −4.93560 8.54871i −0.182550 0.316185i
\(732\) 0 0
\(733\) 19.2630 33.3645i 0.711496 1.23235i −0.252799 0.967519i \(-0.581351\pi\)
0.964295 0.264829i \(-0.0853155\pi\)
\(734\) 33.7709 + 58.4929i 1.24651 + 2.15901i
\(735\) 0 0
\(736\) −0.0737345 + 0.127712i −0.00271789 + 0.00470752i
\(737\) −35.7039 61.8409i −1.31517 2.27794i
\(738\) 0 0
\(739\) −22.5620 + 39.0785i −0.829955 + 1.43752i 0.0681179 + 0.997677i \(0.478301\pi\)
−0.898073 + 0.439847i \(0.855033\pi\)
\(740\) −18.7237 −0.688298
\(741\) 0 0
\(742\) 0 0
\(743\) 4.74338 + 8.21577i 0.174018 + 0.301407i 0.939821 0.341668i \(-0.110992\pi\)
−0.765803 + 0.643075i \(0.777658\pi\)
\(744\) 0 0
\(745\) 17.5634 + 30.4207i 0.643474 + 1.11453i
\(746\) −20.0869 + 34.7915i −0.735432 + 1.27381i
\(747\) 0 0
\(748\) 17.3126 0.633013
\(749\) 0 0
\(750\) 0 0
\(751\) 4.91595 8.51467i 0.179386 0.310705i −0.762285 0.647242i \(-0.775922\pi\)
0.941670 + 0.336537i \(0.109256\pi\)
\(752\) −52.6313 −1.91927
\(753\) 0 0
\(754\) 6.05408 0.220477
\(755\) −25.7496 −0.937124
\(756\) 0 0
\(757\) −41.8171 −1.51987 −0.759934 0.650000i \(-0.774769\pi\)
−0.759934 + 0.650000i \(0.774769\pi\)
\(758\) 29.6156 1.07569
\(759\) 0 0
\(760\) −53.1416 −1.92765
\(761\) −11.4897 + 19.9007i −0.416501 + 0.721400i −0.995585 0.0938675i \(-0.970077\pi\)
0.579084 + 0.815268i \(0.303410\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 2.84494 0.102926
\(765\) 0 0
\(766\) 15.2989 26.4985i 0.552773 0.957430i
\(767\) −1.36333 2.36135i −0.0492269 0.0852635i
\(768\) 0 0
\(769\) 3.04329 + 5.27113i 0.109744 + 0.190082i 0.915666 0.401939i \(-0.131664\pi\)
−0.805923 + 0.592021i \(0.798330\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 49.2350 1.77201
\(773\) 20.9107 36.2184i 0.752105 1.30268i −0.194695 0.980864i \(-0.562372\pi\)
0.946801 0.321821i \(-0.104295\pi\)
\(774\) 0 0
\(775\) 2.00933 + 3.48027i 0.0721774 + 0.125015i
\(776\) −29.0349 + 50.2899i −1.04229 + 1.80530i
\(777\) 0 0
\(778\) 25.3442 + 43.8974i 0.908632 + 1.57380i
\(779\) 12.9861 22.4926i 0.465275 0.805880i
\(780\) 0 0
\(781\) −7.38891 12.7980i −0.264396 0.457947i
\(782\) 0.318097 + 0.550960i 0.0113751 + 0.0197023i
\(783\) 0 0
\(784\) 0 0
\(785\) −7.85087 + 13.5981i −0.280210 + 0.485337i
\(786\) 0 0
\(787\) −32.2920 −1.15109