Properties

Label 405.2.j.d.379.1
Level $405$
Weight $2$
Character 405.379
Analytic conductor $3.234$
Analytic rank $0$
Dimension $4$
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(109,405)]
 
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([2, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("405.109");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 405.j (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.23394128186\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-11})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 379.1
Root \(1.68614 + 0.396143i\) of defining polynomial
Character \(\chi\) \(=\) 405.379
Dual form 405.2.j.d.109.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.686141 - 0.396143i) q^{2} +(-0.686141 - 1.18843i) q^{4} +(2.18614 - 0.469882i) q^{5} +(3.00000 + 1.73205i) q^{7} +2.67181i q^{8} +O(q^{10})\) \(q+(-0.686141 - 0.396143i) q^{2} +(-0.686141 - 1.18843i) q^{4} +(2.18614 - 0.469882i) q^{5} +(3.00000 + 1.73205i) q^{7} +2.67181i q^{8} +(-1.68614 - 0.543620i) q^{10} +(-2.18614 + 3.78651i) q^{11} +(5.05842 - 2.92048i) q^{13} +(-1.37228 - 2.37686i) q^{14} +(-0.313859 + 0.543620i) q^{16} +0.792287i q^{17} +0.372281 q^{19} +(-2.05842 - 2.27567i) q^{20} +(3.00000 - 1.73205i) q^{22} +(-1.37228 + 0.792287i) q^{23} +(4.55842 - 2.05446i) q^{25} -4.62772 q^{26} -4.75372i q^{28} +(2.87228 - 4.97494i) q^{29} +(-3.18614 - 5.51856i) q^{31} +(5.05842 - 2.92048i) q^{32} +(0.313859 - 0.543620i) q^{34} +(7.37228 + 2.37686i) q^{35} +2.37686i q^{37} +(-0.255437 - 0.147477i) q^{38} +(1.25544 + 5.84096i) q^{40} +(2.18614 + 3.78651i) q^{41} +(3.00000 + 1.73205i) q^{43} +6.00000 q^{44} +1.25544 q^{46} +(-1.62772 - 0.939764i) q^{47} +(2.50000 + 4.33013i) q^{49} +(-3.94158 - 0.396143i) q^{50} +(-6.94158 - 4.00772i) q^{52} -11.9769i q^{53} +(-3.00000 + 9.30506i) q^{55} +(-4.62772 + 8.01544i) q^{56} +(-3.94158 + 2.27567i) q^{58} +(-0.813859 - 1.40965i) q^{59} +(-4.68614 + 8.11663i) q^{61} +5.04868i q^{62} -3.37228 q^{64} +(9.68614 - 8.76144i) q^{65} +(-10.1168 + 5.84096i) q^{67} +(0.941578 - 0.543620i) q^{68} +(-4.11684 - 4.55134i) q^{70} -13.1168 q^{71} -2.37686i q^{73} +(0.941578 - 1.63086i) q^{74} +(-0.255437 - 0.442430i) q^{76} +(-13.1168 + 7.57301i) q^{77} +(3.37228 - 5.84096i) q^{79} +(-0.430703 + 1.33591i) q^{80} -3.46410i q^{82} +(10.3723 + 5.98844i) q^{83} +(0.372281 + 1.73205i) q^{85} +(-1.37228 - 2.37686i) q^{86} +(-10.1168 - 5.84096i) q^{88} -3.00000 q^{89} +20.2337 q^{91} +(1.88316 + 1.08724i) q^{92} +(0.744563 + 1.28962i) q^{94} +(0.813859 - 0.174928i) q^{95} +(-1.11684 - 0.644810i) q^{97} -3.96143i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} + 3 q^{4} + 3 q^{5} + 12 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} + 3 q^{4} + 3 q^{5} + 12 q^{7} - q^{10} - 3 q^{11} + 3 q^{13} + 6 q^{14} - 7 q^{16} - 10 q^{19} + 9 q^{20} + 12 q^{22} + 6 q^{23} + q^{25} - 30 q^{26} - 7 q^{31} + 3 q^{32} + 7 q^{34} + 18 q^{35} - 24 q^{38} + 28 q^{40} + 3 q^{41} + 12 q^{43} + 24 q^{44} + 28 q^{46} - 18 q^{47} + 10 q^{49} - 33 q^{50} - 45 q^{52} - 12 q^{55} - 30 q^{56} - 33 q^{58} - 9 q^{59} - 13 q^{61} - 2 q^{64} + 33 q^{65} - 6 q^{67} + 21 q^{68} + 18 q^{70} - 18 q^{71} + 21 q^{74} - 24 q^{76} - 18 q^{77} + 2 q^{79} + 27 q^{80} + 30 q^{83} - 10 q^{85} + 6 q^{86} - 6 q^{88} - 12 q^{89} + 12 q^{91} + 42 q^{92} - 20 q^{94} + 9 q^{95} + 30 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(82\) \(326\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.686141 0.396143i −0.485175 0.280116i 0.237396 0.971413i \(-0.423706\pi\)
−0.722570 + 0.691297i \(0.757040\pi\)
\(3\) 0 0
\(4\) −0.686141 1.18843i −0.343070 0.594215i
\(5\) 2.18614 0.469882i 0.977672 0.210138i
\(6\) 0 0
\(7\) 3.00000 + 1.73205i 1.13389 + 0.654654i 0.944911 0.327327i \(-0.106148\pi\)
0.188982 + 0.981981i \(0.439481\pi\)
\(8\) 2.67181i 0.944629i
\(9\) 0 0
\(10\) −1.68614 0.543620i −0.533204 0.171908i
\(11\) −2.18614 + 3.78651i −0.659146 + 1.14167i 0.321691 + 0.946845i \(0.395749\pi\)
−0.980837 + 0.194830i \(0.937584\pi\)
\(12\) 0 0
\(13\) 5.05842 2.92048i 1.40295 0.809996i 0.408259 0.912866i \(-0.366136\pi\)
0.994695 + 0.102870i \(0.0328027\pi\)
\(14\) −1.37228 2.37686i −0.366758 0.635243i
\(15\) 0 0
\(16\) −0.313859 + 0.543620i −0.0784648 + 0.135905i
\(17\) 0.792287i 0.192158i 0.995374 + 0.0960789i \(0.0306301\pi\)
−0.995374 + 0.0960789i \(0.969370\pi\)
\(18\) 0 0
\(19\) 0.372281 0.0854072 0.0427036 0.999088i \(-0.486403\pi\)
0.0427036 + 0.999088i \(0.486403\pi\)
\(20\) −2.05842 2.27567i −0.460277 0.508856i
\(21\) 0 0
\(22\) 3.00000 1.73205i 0.639602 0.369274i
\(23\) −1.37228 + 0.792287i −0.286140 + 0.165203i −0.636200 0.771524i \(-0.719495\pi\)
0.350060 + 0.936727i \(0.386161\pi\)
\(24\) 0 0
\(25\) 4.55842 2.05446i 0.911684 0.410891i
\(26\) −4.62772 −0.907570
\(27\) 0 0
\(28\) 4.75372i 0.898369i
\(29\) 2.87228 4.97494i 0.533369 0.923823i −0.465871 0.884853i \(-0.654259\pi\)
0.999240 0.0389701i \(-0.0124077\pi\)
\(30\) 0 0
\(31\) −3.18614 5.51856i −0.572248 0.991162i −0.996335 0.0855407i \(-0.972738\pi\)
0.424087 0.905621i \(-0.360595\pi\)
\(32\) 5.05842 2.92048i 0.894211 0.516273i
\(33\) 0 0
\(34\) 0.313859 0.543620i 0.0538264 0.0932301i
\(35\) 7.37228 + 2.37686i 1.24614 + 0.401763i
\(36\) 0 0
\(37\) 2.37686i 0.390754i 0.980728 + 0.195377i \(0.0625930\pi\)
−0.980728 + 0.195377i \(0.937407\pi\)
\(38\) −0.255437 0.147477i −0.0414374 0.0239239i
\(39\) 0 0
\(40\) 1.25544 + 5.84096i 0.198502 + 0.923537i
\(41\) 2.18614 + 3.78651i 0.341418 + 0.591353i 0.984696 0.174279i \(-0.0557596\pi\)
−0.643278 + 0.765632i \(0.722426\pi\)
\(42\) 0 0
\(43\) 3.00000 + 1.73205i 0.457496 + 0.264135i 0.710991 0.703201i \(-0.248247\pi\)
−0.253495 + 0.967337i \(0.581580\pi\)
\(44\) 6.00000 0.904534
\(45\) 0 0
\(46\) 1.25544 0.185104
\(47\) −1.62772 0.939764i −0.237427 0.137079i 0.376566 0.926390i \(-0.377105\pi\)
−0.613994 + 0.789311i \(0.710438\pi\)
\(48\) 0 0
\(49\) 2.50000 + 4.33013i 0.357143 + 0.618590i
\(50\) −3.94158 0.396143i −0.557423 0.0560232i
\(51\) 0 0
\(52\) −6.94158 4.00772i −0.962624 0.555771i
\(53\) 11.9769i 1.64515i −0.568656 0.822575i \(-0.692536\pi\)
0.568656 0.822575i \(-0.307464\pi\)
\(54\) 0 0
\(55\) −3.00000 + 9.30506i −0.404520 + 1.25469i
\(56\) −4.62772 + 8.01544i −0.618405 + 1.07111i
\(57\) 0 0
\(58\) −3.94158 + 2.27567i −0.517555 + 0.298810i
\(59\) −0.813859 1.40965i −0.105955 0.183520i 0.808173 0.588946i \(-0.200457\pi\)
−0.914128 + 0.405425i \(0.867123\pi\)
\(60\) 0 0
\(61\) −4.68614 + 8.11663i −0.599999 + 1.03923i 0.392822 + 0.919615i \(0.371499\pi\)
−0.992820 + 0.119614i \(0.961834\pi\)
\(62\) 5.04868i 0.641182i
\(63\) 0 0
\(64\) −3.37228 −0.421535
\(65\) 9.68614 8.76144i 1.20142 1.08672i
\(66\) 0 0
\(67\) −10.1168 + 5.84096i −1.23597 + 0.713587i −0.968268 0.249915i \(-0.919597\pi\)
−0.267701 + 0.963502i \(0.586264\pi\)
\(68\) 0.941578 0.543620i 0.114183 0.0659236i
\(69\) 0 0
\(70\) −4.11684 4.55134i −0.492057 0.543989i
\(71\) −13.1168 −1.55668 −0.778341 0.627841i \(-0.783939\pi\)
−0.778341 + 0.627841i \(0.783939\pi\)
\(72\) 0 0
\(73\) 2.37686i 0.278191i −0.990279 0.139095i \(-0.955581\pi\)
0.990279 0.139095i \(-0.0444194\pi\)
\(74\) 0.941578 1.63086i 0.109456 0.189584i
\(75\) 0 0
\(76\) −0.255437 0.442430i −0.0293007 0.0507503i
\(77\) −13.1168 + 7.57301i −1.49480 + 0.863025i
\(78\) 0 0
\(79\) 3.37228 5.84096i 0.379411 0.657160i −0.611565 0.791194i \(-0.709460\pi\)
0.990977 + 0.134034i \(0.0427932\pi\)
\(80\) −0.430703 + 1.33591i −0.0481541 + 0.149359i
\(81\) 0 0
\(82\) 3.46410i 0.382546i
\(83\) 10.3723 + 5.98844i 1.13851 + 0.657317i 0.946060 0.323991i \(-0.105025\pi\)
0.192446 + 0.981308i \(0.438358\pi\)
\(84\) 0 0
\(85\) 0.372281 + 1.73205i 0.0403796 + 0.187867i
\(86\) −1.37228 2.37686i −0.147977 0.256304i
\(87\) 0 0
\(88\) −10.1168 5.84096i −1.07846 0.622649i
\(89\) −3.00000 −0.317999 −0.159000 0.987279i \(-0.550827\pi\)
−0.159000 + 0.987279i \(0.550827\pi\)
\(90\) 0 0
\(91\) 20.2337 2.12107
\(92\) 1.88316 + 1.08724i 0.196333 + 0.113353i
\(93\) 0 0
\(94\) 0.744563 + 1.28962i 0.0767958 + 0.133014i
\(95\) 0.813859 0.174928i 0.0835002 0.0179473i
\(96\) 0 0
\(97\) −1.11684 0.644810i −0.113398 0.0654706i 0.442228 0.896903i \(-0.354188\pi\)
−0.555626 + 0.831432i \(0.687522\pi\)
\(98\) 3.96143i 0.400165i
\(99\) 0 0
\(100\) −5.56930 4.00772i −0.556930 0.400772i
\(101\) −8.18614 + 14.1788i −0.814551 + 1.41084i 0.0950981 + 0.995468i \(0.469684\pi\)
−0.909650 + 0.415377i \(0.863650\pi\)
\(102\) 0 0
\(103\) −6.00000 + 3.46410i −0.591198 + 0.341328i −0.765571 0.643352i \(-0.777543\pi\)
0.174373 + 0.984680i \(0.444210\pi\)
\(104\) 7.80298 + 13.5152i 0.765146 + 1.32527i
\(105\) 0 0
\(106\) −4.74456 + 8.21782i −0.460833 + 0.798186i
\(107\) 13.2665i 1.28252i −0.767323 0.641260i \(-0.778412\pi\)
0.767323 0.641260i \(-0.221588\pi\)
\(108\) 0 0
\(109\) −9.74456 −0.933360 −0.466680 0.884426i \(-0.654550\pi\)
−0.466680 + 0.884426i \(0.654550\pi\)
\(110\) 5.74456 5.19615i 0.547723 0.495434i
\(111\) 0 0
\(112\) −1.88316 + 1.08724i −0.177942 + 0.102735i
\(113\) −5.31386 + 3.06796i −0.499886 + 0.288609i −0.728666 0.684869i \(-0.759860\pi\)
0.228781 + 0.973478i \(0.426526\pi\)
\(114\) 0 0
\(115\) −2.62772 + 2.37686i −0.245036 + 0.221643i
\(116\) −7.88316 −0.731933
\(117\) 0 0
\(118\) 1.28962i 0.118719i
\(119\) −1.37228 + 2.37686i −0.125797 + 0.217886i
\(120\) 0 0
\(121\) −4.05842 7.02939i −0.368947 0.639036i
\(122\) 6.43070 3.71277i 0.582209 0.336138i
\(123\) 0 0
\(124\) −4.37228 + 7.57301i −0.392642 + 0.680077i
\(125\) 9.00000 6.63325i 0.804984 0.593296i
\(126\) 0 0
\(127\) 10.3923i 0.922168i 0.887357 + 0.461084i \(0.152539\pi\)
−0.887357 + 0.461084i \(0.847461\pi\)
\(128\) −7.80298 4.50506i −0.689693 0.398194i
\(129\) 0 0
\(130\) −10.1168 + 2.17448i −0.887306 + 0.190715i
\(131\) 2.18614 + 3.78651i 0.191004 + 0.330829i 0.945583 0.325380i \(-0.105492\pi\)
−0.754579 + 0.656209i \(0.772159\pi\)
\(132\) 0 0
\(133\) 1.11684 + 0.644810i 0.0968427 + 0.0559121i
\(134\) 9.25544 0.799548
\(135\) 0 0
\(136\) −2.11684 −0.181518
\(137\) 12.4307 + 7.17687i 1.06203 + 0.613161i 0.925992 0.377543i \(-0.123231\pi\)
0.136034 + 0.990704i \(0.456564\pi\)
\(138\) 0 0
\(139\) 5.55842 + 9.62747i 0.471459 + 0.816591i 0.999467 0.0326483i \(-0.0103941\pi\)
−0.528008 + 0.849240i \(0.677061\pi\)
\(140\) −2.23369 10.3923i −0.188781 0.878310i
\(141\) 0 0
\(142\) 9.00000 + 5.19615i 0.755263 + 0.436051i
\(143\) 25.5383i 2.13562i
\(144\) 0 0
\(145\) 3.94158 12.2255i 0.327330 1.01528i
\(146\) −0.941578 + 1.63086i −0.0779256 + 0.134971i
\(147\) 0 0
\(148\) 2.82473 1.63086i 0.232192 0.134056i
\(149\) −5.31386 9.20387i −0.435328 0.754011i 0.561994 0.827141i \(-0.310034\pi\)
−0.997322 + 0.0731305i \(0.976701\pi\)
\(150\) 0 0
\(151\) −0.441578 + 0.764836i −0.0359351 + 0.0622414i −0.883434 0.468556i \(-0.844774\pi\)
0.847499 + 0.530798i \(0.178108\pi\)
\(152\) 0.994667i 0.0806781i
\(153\) 0 0
\(154\) 12.0000 0.966988
\(155\) −9.55842 10.5672i −0.767751 0.848781i
\(156\) 0 0
\(157\) 9.94158 5.73977i 0.793424 0.458084i −0.0477424 0.998860i \(-0.515203\pi\)
0.841167 + 0.540776i \(0.181869\pi\)
\(158\) −4.62772 + 2.67181i −0.368162 + 0.212558i
\(159\) 0 0
\(160\) 9.68614 8.76144i 0.765757 0.692653i
\(161\) −5.48913 −0.432604
\(162\) 0 0
\(163\) 15.1460i 1.18633i 0.805082 + 0.593164i \(0.202122\pi\)
−0.805082 + 0.593164i \(0.797878\pi\)
\(164\) 3.00000 5.19615i 0.234261 0.405751i
\(165\) 0 0
\(166\) −4.74456 8.21782i −0.368249 0.637827i
\(167\) 11.7446 6.78073i 0.908822 0.524708i 0.0287697 0.999586i \(-0.490841\pi\)
0.880052 + 0.474878i \(0.157508\pi\)
\(168\) 0 0
\(169\) 10.5584 18.2877i 0.812186 1.40675i
\(170\) 0.430703 1.33591i 0.0330334 0.102459i
\(171\) 0 0
\(172\) 4.75372i 0.362468i
\(173\) −9.68614 5.59230i −0.736424 0.425174i 0.0843439 0.996437i \(-0.473121\pi\)
−0.820768 + 0.571262i \(0.806454\pi\)
\(174\) 0 0
\(175\) 17.2337 + 1.73205i 1.30274 + 0.130931i
\(176\) −1.37228 2.37686i −0.103440 0.179163i
\(177\) 0 0
\(178\) 2.05842 + 1.18843i 0.154285 + 0.0890766i
\(179\) −4.88316 −0.364984 −0.182492 0.983207i \(-0.558416\pi\)
−0.182492 + 0.983207i \(0.558416\pi\)
\(180\) 0 0
\(181\) −13.8614 −1.03031 −0.515155 0.857097i \(-0.672266\pi\)
−0.515155 + 0.857097i \(0.672266\pi\)
\(182\) −13.8832 8.01544i −1.02909 0.594144i
\(183\) 0 0
\(184\) −2.11684 3.66648i −0.156056 0.270297i
\(185\) 1.11684 + 5.19615i 0.0821120 + 0.382029i
\(186\) 0 0
\(187\) −3.00000 1.73205i −0.219382 0.126660i
\(188\) 2.57924i 0.188110i
\(189\) 0 0
\(190\) −0.627719 0.202380i −0.0455395 0.0146822i
\(191\) 3.81386 6.60580i 0.275961 0.477979i −0.694416 0.719574i \(-0.744337\pi\)
0.970377 + 0.241595i \(0.0776705\pi\)
\(192\) 0 0
\(193\) 9.94158 5.73977i 0.715610 0.413158i −0.0975245 0.995233i \(-0.531092\pi\)
0.813135 + 0.582075i \(0.197759\pi\)
\(194\) 0.510875 + 0.884861i 0.0366787 + 0.0635293i
\(195\) 0 0
\(196\) 3.43070 5.94215i 0.245050 0.424439i
\(197\) 6.43087i 0.458181i 0.973405 + 0.229090i \(0.0735751\pi\)
−0.973405 + 0.229090i \(0.926425\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 5.48913 + 12.1793i 0.388140 + 0.861204i
\(201\) 0 0
\(202\) 11.2337 6.48577i 0.790400 0.456337i
\(203\) 17.2337 9.94987i 1.20957 0.698344i
\(204\) 0 0
\(205\) 6.55842 + 7.25061i 0.458060 + 0.506404i
\(206\) 5.48913 0.382445
\(207\) 0 0
\(208\) 3.66648i 0.254225i
\(209\) −0.813859 + 1.40965i −0.0562958 + 0.0975072i
\(210\) 0 0
\(211\) 0.930703 + 1.61203i 0.0640723 + 0.110976i 0.896282 0.443484i \(-0.146258\pi\)
−0.832210 + 0.554461i \(0.812925\pi\)
\(212\) −14.2337 + 8.21782i −0.977574 + 0.564402i
\(213\) 0 0
\(214\) −5.25544 + 9.10268i −0.359254 + 0.622247i
\(215\) 7.37228 + 2.37686i 0.502785 + 0.162101i
\(216\) 0 0
\(217\) 22.0742i 1.49850i
\(218\) 6.68614 + 3.86025i 0.452843 + 0.261449i
\(219\) 0 0
\(220\) 13.1168 2.81929i 0.884337 0.190077i
\(221\) 2.31386 + 4.00772i 0.155647 + 0.269589i
\(222\) 0 0
\(223\) 16.1168 + 9.30506i 1.07926 + 0.623113i 0.930698 0.365789i \(-0.119201\pi\)
0.148566 + 0.988902i \(0.452534\pi\)
\(224\) 20.2337 1.35192
\(225\) 0 0
\(226\) 4.86141 0.323376
\(227\) −11.7446 6.78073i −0.779514 0.450053i 0.0567440 0.998389i \(-0.481928\pi\)
−0.836258 + 0.548336i \(0.815261\pi\)
\(228\) 0 0
\(229\) −8.80298 15.2472i −0.581718 1.00756i −0.995276 0.0970868i \(-0.969048\pi\)
0.413558 0.910478i \(-0.364286\pi\)
\(230\) 2.74456 0.589907i 0.180971 0.0388973i
\(231\) 0 0
\(232\) 13.2921 + 7.67420i 0.872670 + 0.503836i
\(233\) 6.13592i 0.401977i −0.979594 0.200989i \(-0.935585\pi\)
0.979594 0.200989i \(-0.0644154\pi\)
\(234\) 0 0
\(235\) −4.00000 1.28962i −0.260931 0.0841256i
\(236\) −1.11684 + 1.93443i −0.0727004 + 0.125921i
\(237\) 0 0
\(238\) 1.88316 1.08724i 0.122067 0.0704753i
\(239\) −11.4891 19.8997i −0.743170 1.28721i −0.951045 0.309052i \(-0.899988\pi\)
0.207875 0.978155i \(-0.433345\pi\)
\(240\) 0 0
\(241\) 0.755437 1.30846i 0.0486620 0.0842851i −0.840668 0.541550i \(-0.817838\pi\)
0.889330 + 0.457265i \(0.151171\pi\)
\(242\) 6.43087i 0.413392i
\(243\) 0 0
\(244\) 12.8614 0.823367
\(245\) 7.50000 + 8.29156i 0.479157 + 0.529728i
\(246\) 0 0
\(247\) 1.88316 1.08724i 0.119822 0.0691795i
\(248\) 14.7446 8.51278i 0.936281 0.540562i
\(249\) 0 0
\(250\) −8.80298 + 0.986051i −0.556750 + 0.0623633i
\(251\) 20.2337 1.27714 0.638570 0.769564i \(-0.279526\pi\)
0.638570 + 0.769564i \(0.279526\pi\)
\(252\) 0 0
\(253\) 6.92820i 0.435572i
\(254\) 4.11684 7.13058i 0.258314 0.447413i
\(255\) 0 0
\(256\) 6.94158 + 12.0232i 0.433849 + 0.751448i
\(257\) 5.56930 3.21543i 0.347403 0.200573i −0.316138 0.948713i \(-0.602386\pi\)
0.663541 + 0.748140i \(0.269053\pi\)
\(258\) 0 0
\(259\) −4.11684 + 7.13058i −0.255808 + 0.443073i
\(260\) −17.0584 5.49972i −1.05792 0.341078i
\(261\) 0 0
\(262\) 3.46410i 0.214013i
\(263\) −22.9783 13.2665i −1.41690 0.818047i −0.420874 0.907119i \(-0.638277\pi\)
−0.996025 + 0.0890715i \(0.971610\pi\)
\(264\) 0 0
\(265\) −5.62772 26.1831i −0.345708 1.60842i
\(266\) −0.510875 0.884861i −0.0313237 0.0542543i
\(267\) 0 0
\(268\) 13.8832 + 8.01544i 0.848049 + 0.489621i
\(269\) −29.2337 −1.78241 −0.891205 0.453601i \(-0.850139\pi\)
−0.891205 + 0.453601i \(0.850139\pi\)
\(270\) 0 0
\(271\) 5.25544 0.319245 0.159623 0.987178i \(-0.448972\pi\)
0.159623 + 0.987178i \(0.448972\pi\)
\(272\) −0.430703 0.248667i −0.0261152 0.0150776i
\(273\) 0 0
\(274\) −5.68614 9.84868i −0.343512 0.594981i
\(275\) −2.18614 + 21.7518i −0.131829 + 1.31168i
\(276\) 0 0
\(277\) −19.1168 11.0371i −1.14862 0.663156i −0.200069 0.979782i \(-0.564117\pi\)
−0.948551 + 0.316626i \(0.897450\pi\)
\(278\) 8.80773i 0.528253i
\(279\) 0 0
\(280\) −6.35053 + 19.6974i −0.379517 + 1.17714i
\(281\) −0.686141 + 1.18843i −0.0409317 + 0.0708958i −0.885765 0.464133i \(-0.846366\pi\)
0.844834 + 0.535029i \(0.179699\pi\)
\(282\) 0 0
\(283\) −24.0000 + 13.8564i −1.42665 + 0.823678i −0.996855 0.0792477i \(-0.974748\pi\)
−0.429797 + 0.902926i \(0.641415\pi\)
\(284\) 9.00000 + 15.5885i 0.534052 + 0.925005i
\(285\) 0 0
\(286\) 10.1168 17.5229i 0.598222 1.03615i
\(287\) 15.1460i 0.894042i
\(288\) 0 0
\(289\) 16.3723 0.963075
\(290\) −7.54755 + 6.82701i −0.443207 + 0.400896i
\(291\) 0 0
\(292\) −2.82473 + 1.63086i −0.165305 + 0.0954389i
\(293\) 0.686141 0.396143i 0.0400848 0.0231430i −0.479824 0.877365i \(-0.659299\pi\)
0.519908 + 0.854222i \(0.325966\pi\)
\(294\) 0 0
\(295\) −2.44158 2.69927i −0.142154 0.157157i
\(296\) −6.35053 −0.369117
\(297\) 0 0
\(298\) 8.42020i 0.487769i
\(299\) −4.62772 + 8.01544i −0.267628 + 0.463545i
\(300\) 0 0
\(301\) 6.00000 + 10.3923i 0.345834 + 0.599002i
\(302\) 0.605969 0.349857i 0.0348696 0.0201320i
\(303\) 0 0
\(304\) −0.116844 + 0.202380i −0.00670146 + 0.0116073i
\(305\) −6.43070 + 19.9460i −0.368221 + 1.14211i
\(306\) 0 0
\(307\) 15.1460i 0.864429i 0.901771 + 0.432215i \(0.142268\pi\)
−0.901771 + 0.432215i \(0.857732\pi\)
\(308\) 18.0000 + 10.3923i 1.02565 + 0.592157i
\(309\) 0 0
\(310\) 2.37228 + 11.0371i 0.134737 + 0.626866i
\(311\) −7.93070 13.7364i −0.449709 0.778919i 0.548658 0.836047i \(-0.315139\pi\)
−0.998367 + 0.0571282i \(0.981806\pi\)
\(312\) 0 0
\(313\) −21.1753 12.2255i −1.19690 0.691029i −0.237035 0.971501i \(-0.576176\pi\)
−0.959862 + 0.280472i \(0.909509\pi\)
\(314\) −9.09509 −0.513266
\(315\) 0 0
\(316\) −9.25544 −0.520659
\(317\) 25.5475 + 14.7499i 1.43489 + 0.828436i 0.997488 0.0708288i \(-0.0225644\pi\)
0.437405 + 0.899265i \(0.355898\pi\)
\(318\) 0 0
\(319\) 12.5584 + 21.7518i 0.703137 + 1.21787i
\(320\) −7.37228 + 1.58457i −0.412123 + 0.0885804i
\(321\) 0 0
\(322\) 3.76631 + 2.17448i 0.209888 + 0.121179i
\(323\) 0.294954i 0.0164117i
\(324\) 0 0
\(325\) 17.0584 23.7051i 0.946231 1.31492i
\(326\) 6.00000 10.3923i 0.332309 0.575577i
\(327\) 0 0
\(328\) −10.1168 + 5.84096i −0.558609 + 0.322513i
\(329\) −3.25544 5.63858i −0.179478 0.310865i
\(330\) 0 0
\(331\) −4.55842 + 7.89542i −0.250554 + 0.433971i −0.963678 0.267066i \(-0.913946\pi\)
0.713125 + 0.701037i \(0.247279\pi\)
\(332\) 16.4356i 0.902023i
\(333\) 0 0
\(334\) −10.7446 −0.587916
\(335\) −19.3723 + 17.5229i −1.05842 + 0.957378i
\(336\) 0 0
\(337\) −6.00000 + 3.46410i −0.326841 + 0.188702i −0.654438 0.756116i \(-0.727095\pi\)
0.327597 + 0.944818i \(0.393761\pi\)
\(338\) −14.4891 + 8.36530i −0.788105 + 0.455012i
\(339\) 0 0
\(340\) 1.80298 1.63086i 0.0977806 0.0884459i
\(341\) 27.8614 1.50878
\(342\) 0 0
\(343\) 6.92820i 0.374088i
\(344\) −4.62772 + 8.01544i −0.249510 + 0.432164i
\(345\) 0 0
\(346\) 4.43070 + 7.67420i 0.238196 + 0.412568i
\(347\) −2.48913 + 1.43710i −0.133623 + 0.0771474i −0.565321 0.824871i \(-0.691248\pi\)
0.431698 + 0.902018i \(0.357915\pi\)
\(348\) 0 0
\(349\) −13.3030 + 23.0414i −0.712092 + 1.23338i 0.251978 + 0.967733i \(0.418919\pi\)
−0.964070 + 0.265647i \(0.914414\pi\)
\(350\) −11.1386 8.01544i −0.595383 0.428443i
\(351\) 0 0
\(352\) 25.5383i 1.36120i
\(353\) −1.62772 0.939764i −0.0866347 0.0500186i 0.456057 0.889951i \(-0.349261\pi\)
−0.542692 + 0.839932i \(0.682595\pi\)
\(354\) 0 0
\(355\) −28.6753 + 6.16337i −1.52193 + 0.327118i
\(356\) 2.05842 + 3.56529i 0.109096 + 0.188960i
\(357\) 0 0
\(358\) 3.35053 + 1.93443i 0.177081 + 0.102238i
\(359\) −10.8832 −0.574391 −0.287196 0.957872i \(-0.592723\pi\)
−0.287196 + 0.957872i \(0.592723\pi\)
\(360\) 0 0
\(361\) −18.8614 −0.992706
\(362\) 9.51087 + 5.49111i 0.499880 + 0.288606i
\(363\) 0 0
\(364\) −13.8832 24.0463i −0.727675 1.26037i
\(365\) −1.11684 5.19615i −0.0584583 0.271979i
\(366\) 0 0
\(367\) −14.2337 8.21782i −0.742992 0.428967i 0.0801639 0.996782i \(-0.474456\pi\)
−0.823156 + 0.567815i \(0.807789\pi\)
\(368\) 0.994667i 0.0518506i
\(369\) 0 0
\(370\) 1.29211 4.00772i 0.0671736 0.208352i
\(371\) 20.7446 35.9306i 1.07700 1.86543i
\(372\) 0 0
\(373\) 7.11684 4.10891i 0.368496 0.212751i −0.304305 0.952575i \(-0.598424\pi\)
0.672801 + 0.739823i \(0.265091\pi\)
\(374\) 1.37228 + 2.37686i 0.0709590 + 0.122905i
\(375\) 0 0
\(376\) 2.51087 4.34896i 0.129488 0.224281i
\(377\) 33.5538i 1.72811i
\(378\) 0 0
\(379\) 1.48913 0.0764912 0.0382456 0.999268i \(-0.487823\pi\)
0.0382456 + 0.999268i \(0.487823\pi\)
\(380\) −0.766312 0.847190i −0.0393110 0.0434599i
\(381\) 0 0
\(382\) −5.23369 + 3.02167i −0.267779 + 0.154602i
\(383\) −9.60597 + 5.54601i −0.490842 + 0.283388i −0.724924 0.688829i \(-0.758125\pi\)
0.234082 + 0.972217i \(0.424792\pi\)
\(384\) 0 0
\(385\) −25.1168 + 22.7190i −1.28007 + 1.15787i
\(386\) −9.09509 −0.462928
\(387\) 0 0
\(388\) 1.76972i 0.0898440i
\(389\) 0.255437 0.442430i 0.0129512 0.0224321i −0.859477 0.511174i \(-0.829211\pi\)
0.872428 + 0.488742i \(0.162544\pi\)
\(390\) 0 0
\(391\) −0.627719 1.08724i −0.0317451 0.0549841i
\(392\) −11.5693 + 6.67954i −0.584338 + 0.337368i
\(393\) 0 0
\(394\) 2.54755 4.41248i 0.128344 0.222298i
\(395\) 4.62772 14.3537i 0.232846 0.722215i
\(396\) 0 0
\(397\) 17.5229i 0.879449i −0.898133 0.439724i \(-0.855076\pi\)
0.898133 0.439724i \(-0.144924\pi\)
\(398\) 10.9783 + 6.33830i 0.550290 + 0.317710i
\(399\) 0 0
\(400\) −0.313859 + 3.12286i −0.0156930 + 0.156143i
\(401\) 12.6861 + 21.9730i 0.633516 + 1.09728i 0.986828 + 0.161776i \(0.0517221\pi\)
−0.353312 + 0.935506i \(0.614945\pi\)
\(402\) 0 0
\(403\) −32.2337 18.6101i −1.60567 0.927037i
\(404\) 22.4674 1.11779
\(405\) 0 0
\(406\) −15.7663 −0.782469
\(407\) −9.00000 5.19615i −0.446113 0.257564i
\(408\) 0 0
\(409\) 11.4307 + 19.7986i 0.565212 + 0.978976i 0.997030 + 0.0770150i \(0.0245389\pi\)
−0.431818 + 0.901961i \(0.642128\pi\)
\(410\) −1.62772 7.57301i −0.0803873 0.374004i
\(411\) 0 0
\(412\) 8.23369 + 4.75372i 0.405645 + 0.234199i
\(413\) 5.63858i 0.277457i
\(414\) 0 0
\(415\) 25.4891 + 8.21782i 1.25121 + 0.403397i
\(416\) 17.0584 29.5461i 0.836358 1.44861i
\(417\) 0 0
\(418\) 1.11684 0.644810i 0.0546266 0.0315387i
\(419\) 8.74456 + 15.1460i 0.427200 + 0.739932i 0.996623 0.0821127i \(-0.0261667\pi\)
−0.569423 + 0.822045i \(0.692833\pi\)
\(420\) 0 0
\(421\) 10.8723 18.8313i 0.529883 0.917784i −0.469510 0.882927i \(-0.655569\pi\)
0.999392 0.0348563i \(-0.0110973\pi\)
\(422\) 1.47477i 0.0717906i
\(423\) 0 0
\(424\) 32.0000 1.55406
\(425\) 1.62772 + 3.61158i 0.0789560 + 0.175187i
\(426\) 0 0
\(427\) −28.1168 + 16.2333i −1.36067 + 0.785583i
\(428\) −15.7663 + 9.10268i −0.762093 + 0.439995i
\(429\) 0 0
\(430\) −4.11684 4.55134i −0.198532 0.219485i
\(431\) 33.3505 1.60644 0.803219 0.595683i \(-0.203119\pi\)
0.803219 + 0.595683i \(0.203119\pi\)
\(432\) 0 0
\(433\) 12.7692i 0.613647i −0.951766 0.306823i \(-0.900734\pi\)
0.951766 0.306823i \(-0.0992661\pi\)
\(434\) −8.74456 + 15.1460i −0.419752 + 0.727033i
\(435\) 0 0
\(436\) 6.68614 + 11.5807i 0.320208 + 0.554617i
\(437\) −0.510875 + 0.294954i −0.0244385 + 0.0141095i
\(438\) 0 0
\(439\) 15.9307 27.5928i 0.760331 1.31693i −0.182349 0.983234i \(-0.558370\pi\)
0.942680 0.333698i \(-0.108297\pi\)
\(440\) −24.8614 8.01544i −1.18522 0.382121i
\(441\) 0 0
\(442\) 3.66648i 0.174397i
\(443\) 18.6060 + 10.7422i 0.883996 + 0.510375i 0.871974 0.489552i \(-0.162840\pi\)
0.0120223 + 0.999928i \(0.496173\pi\)
\(444\) 0 0
\(445\) −6.55842 + 1.40965i −0.310899 + 0.0668236i
\(446\) −7.37228 12.7692i −0.349088 0.604638i
\(447\) 0 0
\(448\) −10.1168 5.84096i −0.477976 0.275960i
\(449\) −10.8832 −0.513608 −0.256804 0.966464i \(-0.582669\pi\)
−0.256804 + 0.966464i \(0.582669\pi\)
\(450\) 0 0
\(451\) −19.1168 −0.900177
\(452\) 7.29211 + 4.21010i 0.342992 + 0.198027i
\(453\) 0 0
\(454\) 5.37228 + 9.30506i 0.252134 + 0.436708i
\(455\) 44.2337 9.50744i 2.07371 0.445716i
\(456\) 0 0
\(457\) 18.1753 + 10.4935i 0.850203 + 0.490865i 0.860719 0.509080i \(-0.170014\pi\)
−0.0105163 + 0.999945i \(0.503348\pi\)
\(458\) 13.9490i 0.651793i
\(459\) 0 0
\(460\) 4.62772 + 1.49200i 0.215768 + 0.0695649i
\(461\) 12.0475 20.8670i 0.561110 0.971871i −0.436290 0.899806i \(-0.643708\pi\)
0.997400 0.0720652i \(-0.0229590\pi\)
\(462\) 0 0
\(463\) 12.0000 6.92820i 0.557687 0.321981i −0.194529 0.980897i \(-0.562318\pi\)
0.752217 + 0.658916i \(0.228985\pi\)
\(464\) 1.80298 + 3.12286i 0.0837015 + 0.144975i
\(465\) 0 0
\(466\) −2.43070 + 4.21010i −0.112600 + 0.195029i
\(467\) 18.3152i 0.847525i 0.905773 + 0.423763i \(0.139291\pi\)
−0.905773 + 0.423763i \(0.860709\pi\)
\(468\) 0 0
\(469\) −40.4674 −1.86861
\(470\) 2.23369 + 2.46943i 0.103032 + 0.113907i
\(471\) 0 0
\(472\) 3.76631 2.17448i 0.173359 0.100089i
\(473\) −13.1168 + 7.57301i −0.603113 + 0.348208i
\(474\) 0 0
\(475\) 1.69702 0.764836i 0.0778644 0.0350931i
\(476\) 3.76631 0.172629
\(477\) 0 0
\(478\) 18.2054i 0.832694i
\(479\) −9.30298 + 16.1132i −0.425064 + 0.736233i −0.996426 0.0844652i \(-0.973082\pi\)
0.571362 + 0.820698i \(0.306415\pi\)
\(480\) 0 0
\(481\) 6.94158 + 12.0232i 0.316509 + 0.548209i
\(482\) −1.03667 + 0.598523i −0.0472191 + 0.0272620i
\(483\) 0 0
\(484\) −5.56930 + 9.64630i −0.253150 + 0.438468i
\(485\) −2.74456 0.884861i −0.124624 0.0401795i
\(486\) 0 0
\(487\) 9.50744i 0.430823i 0.976523 + 0.215412i \(0.0691093\pi\)
−0.976523 + 0.215412i \(0.930891\pi\)
\(488\) −21.6861 12.5205i −0.981685 0.566776i
\(489\) 0 0
\(490\) −1.86141 8.66025i −0.0840898 0.391230i
\(491\) −15.8139 27.3904i −0.713669 1.23611i −0.963470 0.267815i \(-0.913699\pi\)
0.249801 0.968297i \(-0.419635\pi\)
\(492\) 0 0
\(493\) 3.94158 + 2.27567i 0.177520 + 0.102491i
\(494\) −1.72281 −0.0775130
\(495\) 0 0
\(496\) 4.00000 0.179605
\(497\) −39.3505 22.7190i −1.76511 1.01909i
\(498\) 0 0
\(499\) −12.1861 21.1070i −0.545527 0.944880i −0.998574 0.0533931i \(-0.982996\pi\)
0.453047 0.891487i \(-0.350337\pi\)
\(500\) −14.0584 6.14453i −0.628712 0.274792i
\(501\) 0 0
\(502\) −13.8832 8.01544i −0.619636 0.357747i
\(503\) 3.16915i 0.141305i 0.997501 + 0.0706527i \(0.0225082\pi\)
−0.997501 + 0.0706527i \(0.977492\pi\)
\(504\) 0 0
\(505\) −11.2337 + 34.8434i −0.499893 + 1.55051i
\(506\) −2.74456 + 4.75372i −0.122011 + 0.211329i
\(507\) 0 0
\(508\) 12.3505 7.13058i 0.547966 0.316368i
\(509\) −0.255437 0.442430i −0.0113221 0.0196104i 0.860309 0.509773i \(-0.170271\pi\)
−0.871631 + 0.490163i \(0.836937\pi\)
\(510\) 0 0
\(511\) 4.11684 7.13058i 0.182118 0.315438i
\(512\) 7.02078i 0.310277i
\(513\) 0 0
\(514\) −5.09509 −0.224735
\(515\) −11.4891 + 10.3923i −0.506271 + 0.457940i
\(516\) 0 0
\(517\) 7.11684 4.10891i 0.312998 0.180710i
\(518\) 5.64947 3.26172i 0.248223 0.143312i
\(519\) 0 0
\(520\) 23.4090 + 25.8796i 1.02655 + 1.13489i
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) 4.75372i 0.207866i −0.994584 0.103933i \(-0.966857\pi\)
0.994584 0.103933i \(-0.0331427\pi\)
\(524\) 3.00000 5.19615i 0.131056 0.226995i
\(525\) 0 0
\(526\) 10.5109 + 18.2054i 0.458296 + 0.793792i
\(527\) 4.37228 2.52434i 0.190460 0.109962i
\(528\) 0 0
\(529\) −10.2446 + 17.7441i −0.445416 + 0.771483i
\(530\) −6.51087 + 20.1947i −0.282814 + 0.877202i
\(531\) 0 0
\(532\) 1.76972i 0.0767272i
\(533\) 22.1168 + 12.7692i 0.957987 + 0.553094i
\(534\) 0 0
\(535\) −6.23369 29.0024i −0.269506 1.25388i
\(536\) −15.6060 27.0303i −0.674075 1.16753i
\(537\) 0 0
\(538\) 20.0584 + 11.5807i 0.864780 + 0.499281i
\(539\) −21.8614 −0.941637
\(540\) 0 0
\(541\) 19.2337 0.826921 0.413460 0.910522i \(-0.364320\pi\)
0.413460 + 0.910522i \(0.364320\pi\)
\(542\) −3.60597 2.08191i −0.154890 0.0894256i
\(543\) 0 0
\(544\) 2.31386 + 4.00772i 0.0992059 + 0.171830i
\(545\) −21.3030 + 4.57879i −0.912520 + 0.196134i
\(546\) 0 0
\(547\) −6.00000 3.46410i −0.256541 0.148114i 0.366214 0.930531i \(-0.380654\pi\)
−0.622756 + 0.782416i \(0.713987\pi\)
\(548\) 19.6974i 0.841430i
\(549\) 0 0
\(550\) 10.1168 14.0588i 0.431384 0.599469i
\(551\) 1.06930 1.85208i 0.0455536 0.0789011i
\(552\) 0 0
\(553\) 20.2337 11.6819i 0.860424 0.496766i
\(554\) 8.74456 + 15.1460i 0.371521 + 0.643493i
\(555\) 0 0
\(556\) 7.62772 13.2116i 0.323487 0.560296i
\(557\) 25.0410i 1.06102i 0.847678 + 0.530511i \(0.178000\pi\)
−0.847678 + 0.530511i \(0.822000\pi\)
\(558\) 0 0
\(559\) 20.2337 0.855794
\(560\) −3.60597 + 3.26172i −0.152380 + 0.137833i
\(561\) 0 0
\(562\) 0.941578 0.543620i 0.0397181 0.0229312i
\(563\) 27.8614 16.0858i 1.17422 0.677935i 0.219548 0.975602i \(-0.429542\pi\)
0.954670 + 0.297666i \(0.0962083\pi\)
\(564\) 0 0
\(565\) −10.1753 + 9.20387i −0.428077 + 0.387210i
\(566\) 21.9565 0.922901
\(567\) 0 0
\(568\) 35.0458i 1.47049i
\(569\) −10.2446 + 17.7441i −0.429474 + 0.743871i −0.996827 0.0796038i \(-0.974634\pi\)
0.567352 + 0.823475i \(0.307968\pi\)
\(570\) 0 0
\(571\) −2.06930 3.58413i −0.0865974 0.149991i 0.819473 0.573117i \(-0.194266\pi\)
−0.906071 + 0.423126i \(0.860933\pi\)
\(572\) 30.3505 17.5229i 1.26902 0.732669i
\(573\) 0 0
\(574\) 6.00000 10.3923i 0.250435 0.433766i
\(575\) −4.62772 + 6.43087i −0.192989 + 0.268186i
\(576\) 0 0
\(577\) 18.4077i 0.766325i −0.923681 0.383162i \(-0.874835\pi\)
0.923681 0.383162i \(-0.125165\pi\)
\(578\) −11.2337 6.48577i −0.467260 0.269773i
\(579\) 0 0
\(580\) −17.2337 + 3.70415i −0.715590 + 0.153807i
\(581\) 20.7446 + 35.9306i 0.860629 + 1.49065i
\(582\) 0 0
\(583\) 45.3505 + 26.1831i 1.87823 + 1.08439i
\(584\) 6.35053 0.262787
\(585\) 0 0
\(586\) −0.627719 −0.0259308
\(587\) 14.4891 + 8.36530i 0.598030 + 0.345273i 0.768266 0.640130i \(-0.221120\pi\)
−0.170236 + 0.985403i \(0.554453\pi\)
\(588\) 0 0
\(589\) −1.18614 2.05446i −0.0488741 0.0846524i
\(590\) 0.605969 + 2.81929i 0.0249474 + 0.116068i
\(591\) 0 0
\(592\) −1.29211 0.746000i −0.0531054 0.0306604i
\(593\) 1.67715i 0.0688722i 0.999407 + 0.0344361i \(0.0109635\pi\)
−0.999407 + 0.0344361i \(0.989036\pi\)
\(594\) 0 0
\(595\) −1.88316 + 5.84096i −0.0772019 + 0.239456i
\(596\) −7.29211 + 12.6303i −0.298696 + 0.517357i
\(597\) 0 0
\(598\) 6.35053 3.66648i 0.259693 0.149934i
\(599\) −0.813859 1.40965i −0.0332534 0.0575966i 0.848920 0.528522i \(-0.177254\pi\)
−0.882173 + 0.470925i \(0.843920\pi\)
\(600\) 0 0
\(601\) 8.98913 15.5696i 0.366674 0.635098i −0.622369 0.782724i \(-0.713830\pi\)
0.989043 + 0.147626i \(0.0471631\pi\)
\(602\) 9.50744i 0.387494i
\(603\) 0 0
\(604\) 1.21194 0.0493131
\(605\) −12.1753 13.4603i −0.494995 0.547238i
\(606\) 0 0
\(607\) 37.4674 21.6318i 1.52075 0.878008i 0.521054 0.853524i \(-0.325539\pi\)
0.999700 0.0244837i \(-0.00779419\pi\)
\(608\) 1.88316 1.08724i 0.0763721 0.0440934i
\(609\) 0 0
\(610\) 12.3139 11.1383i 0.498574 0.450977i
\(611\) −10.9783 −0.444132
\(612\) 0 0
\(613\) 30.2921i 1.22348i −0.791057 0.611742i \(-0.790469\pi\)
0.791057 0.611742i \(-0.209531\pi\)
\(614\) 6.00000 10.3923i 0.242140 0.419399i
\(615\) 0 0
\(616\) −20.2337 35.0458i −0.815239 1.41203i
\(617\) 17.9198 10.3460i 0.721425 0.416515i −0.0938519 0.995586i \(-0.529918\pi\)
0.815277 + 0.579071i \(0.196585\pi\)
\(618\) 0 0
\(619\) 2.00000 3.46410i 0.0803868 0.139234i −0.823029 0.567999i \(-0.807718\pi\)
0.903416 + 0.428765i \(0.141051\pi\)
\(620\) −6.00000 + 18.6101i −0.240966 + 0.747401i
\(621\) 0 0
\(622\) 12.5668i 0.503882i
\(623\) −9.00000 5.19615i −0.360577 0.208179i
\(624\) 0 0
\(625\) 16.5584 18.7302i 0.662337 0.749206i
\(626\) 9.68614 + 16.7769i 0.387136 + 0.670539i
\(627\) 0 0
\(628\) −13.6426 7.87658i −0.544401 0.314310i
\(629\) −1.88316 −0.0750863
\(630\) 0 0
\(631\) 6.37228 0.253677 0.126838 0.991923i \(-0.459517\pi\)
0.126838 + 0.991923i \(0.459517\pi\)
\(632\) 15.6060 + 9.01011i 0.620772 + 0.358403i
\(633\) 0 0
\(634\) −11.6861 20.2410i −0.464116 0.803872i
\(635\) 4.88316 + 22.7190i 0.193782 + 0.901578i
\(636\) 0 0
\(637\) 25.2921 + 14.6024i 1.00211 + 0.578568i
\(638\) 19.8997i 0.787839i
\(639\) 0 0
\(640\) −19.1753 6.18220i −0.757969 0.244373i
\(641\) 3.98913 6.90937i 0.157561 0.272904i −0.776428 0.630206i \(-0.782970\pi\)
0.933989 + 0.357303i \(0.116304\pi\)
\(642\) 0 0
\(643\) −1.11684 + 0.644810i −0.0440440 + 0.0254288i −0.521860 0.853031i \(-0.674762\pi\)
0.477816 + 0.878460i \(0.341428\pi\)
\(644\) 3.76631 + 6.52344i 0.148413 + 0.257060i
\(645\) 0 0
\(646\) 0.116844 0.202380i 0.00459716 0.00796252i
\(647\) 28.7075i 1.12861i 0.825567 + 0.564304i \(0.190855\pi\)
−0.825567 + 0.564304i \(0.809145\pi\)
\(648\) 0 0
\(649\) 7.11684 0.279361
\(650\) −21.0951 + 9.50744i −0.827418 + 0.372913i
\(651\) 0 0
\(652\) 18.0000 10.3923i 0.704934 0.406994i
\(653\) −5.48913 + 3.16915i −0.214806 + 0.124018i −0.603543 0.797330i \(-0.706245\pi\)
0.388737 + 0.921349i \(0.372911\pi\)
\(654\) 0 0
\(655\) 6.55842 + 7.25061i 0.256259 + 0.283305i
\(656\) −2.74456 −0.107157
\(657\) 0 0
\(658\) 5.15848i 0.201099i
\(659\) −10.6277 + 18.4077i −0.413997 + 0.717064i −0.995323 0.0966070i \(-0.969201\pi\)
0.581325 + 0.813671i \(0.302534\pi\)
\(660\) 0 0
\(661\) 7.61684 + 13.1928i 0.296261 + 0.513139i 0.975277 0.220984i \(-0.0709269\pi\)
−0.679017 + 0.734123i \(0.737594\pi\)
\(662\) 6.25544 3.61158i 0.243124 0.140368i
\(663\) 0 0
\(664\) −16.0000 + 27.7128i −0.620920 + 1.07547i
\(665\) 2.74456 + 0.884861i 0.106430 + 0.0343134i
\(666\) 0 0
\(667\) 9.10268i 0.352457i
\(668\) −16.1168 9.30506i −0.623579 0.360024i
\(669\) 0 0
\(670\) 20.2337 4.34896i 0.781696 0.168015i
\(671\) −20.4891 35.4882i −0.790974 1.37001i
\(672\) 0 0
\(673\) 9.17527 + 5.29734i 0.353681 + 0.204198i 0.666305 0.745679i \(-0.267875\pi\)
−0.312625 + 0.949877i \(0.601208\pi\)
\(674\) 5.48913 0.211433
\(675\) 0 0
\(676\) −28.9783 −1.11455
\(677\) −22.9783 13.2665i −0.883126 0.509873i −0.0114381 0.999935i \(-0.503641\pi\)
−0.871688 + 0.490062i \(0.836974\pi\)
\(678\) 0 0
\(679\) −2.23369 3.86886i −0.0857211 0.148473i
\(680\) −4.62772 + 0.994667i −0.177465 + 0.0381437i
\(681\) 0 0
\(682\) −19.1168 11.0371i −0.732022 0.422633i
\(683\) 27.1229i 1.03783i −0.854826 0.518915i \(-0.826336\pi\)
0.854826 0.518915i \(-0.173664\pi\)
\(684\) 0 0
\(685\) 30.5475 + 9.84868i 1.16716 + 0.376299i
\(686\) −2.74456 + 4.75372i −0.104788 + 0.181498i
\(687\) 0 0
\(688\) −1.88316 + 1.08724i −0.0717947 + 0.0414507i
\(689\) −34.9783 60.5841i −1.33257 2.30807i
\(690\) 0 0
\(691\) −22.8614 + 39.5971i −0.869689 + 1.50635i −0.00737407 + 0.999973i \(0.502347\pi\)
−0.862315 + 0.506373i \(0.830986\pi\)
\(692\) 15.3484i 0.583459i
\(693\) 0 0
\(694\) 2.27719 0.0864408
\(695\) 16.6753 + 18.4352i 0.632529 + 0.699287i
\(696\) 0 0
\(697\) −3.00000 + 1.73205i −0.113633 + 0.0656061i
\(698\) 18.2554 10.5398i 0.690978 0.398937i
\(699\) 0 0
\(700\) −9.76631 21.6695i −0.369132 0.819029i
\(701\) −17.2337 −0.650907 −0.325454 0.945558i \(-0.605517\pi\)
−0.325454 + 0.945558i \(0.605517\pi\)
\(702\) 0 0
\(703\) 0.884861i 0.0333732i
\(704\) 7.37228 12.7692i 0.277853 0.481256i
\(705\) 0 0
\(706\) 0.744563 + 1.28962i 0.0280220 + 0.0485355i
\(707\) −49.1168 + 28.3576i −1.84723 + 1.06650i
\(708\) 0 0
\(709\) 26.1753 45.3369i 0.983033 1.70266i 0.332661 0.943046i \(-0.392053\pi\)
0.650372 0.759616i \(-0.274613\pi\)
\(710\) 22.1168 + 7.13058i 0.830030 + 0.267606i
\(711\) 0 0
\(712\) 8.01544i 0.300391i
\(713\) 8.74456 + 5.04868i 0.327486 + 0.189074i
\(714\) 0 0
\(715\) 12.0000 + 55.8304i 0.448775 + 2.08794i
\(716\) 3.35053 + 5.80329i 0.125215 + 0.216879i
\(717\) 0 0
\(718\) 7.46738 + 4.31129i 0.278680 + 0.160896i
\(719\) 10.8832 0.405873 0.202937 0.979192i \(-0.434951\pi\)
0.202937 + 0.979192i \(0.434951\pi\)
\(720\) 0 0
\(721\) −24.0000 −0.893807
\(722\) 12.9416 + 7.47182i 0.481636 + 0.278072i
\(723\) 0 0
\(724\) 9.51087 + 16.4733i 0.353469 + 0.612226i
\(725\) 2.87228 28.5788i 0.106674 1.06139i
\(726\) 0 0
\(727\) 42.3505 + 24.4511i 1.57069 + 0.906841i 0.996084 + 0.0884137i \(0.0281798\pi\)
0.574610 + 0.818427i \(0.305154\pi\)
\(728\) 54.0607i 2.00362i
\(729\) 0 0
\(730\) −1.29211 + 4.00772i −0.0478231 + 0.148332i
\(731\) −1.37228 + 2.37686i −0.0507557 + 0.0879114i
\(732\) 0 0
\(733\) −14.2337 + 8.21782i −0.525733 + 0.303532i −0.739277 0.673401i \(-0.764833\pi\)
0.213544 + 0.976933i \(0.431499\pi\)
\(734\) 6.51087 + 11.2772i 0.240321 + 0.416248i
\(735\) 0 0
\(736\) −4.62772 + 8.01544i −0.170580 + 0.295453i
\(737\) 51.0767i 1.88143i
\(738\) 0 0
\(739\) −5.62772 −0.207019 −0.103509 0.994628i \(-0.533007\pi\)
−0.103509 + 0.994628i \(0.533007\pi\)
\(740\) 5.40895 4.89258i 0.198837 0.179855i
\(741\) 0 0
\(742\) −28.4674 + 16.4356i −1.04507 + 0.603372i
\(743\) −8.13859 + 4.69882i −0.298576 + 0.172383i −0.641803 0.766870i \(-0.721813\pi\)
0.343227 + 0.939252i \(0.388480\pi\)
\(744\) 0 0
\(745\) −15.9416 17.6241i −0.584054 0.645696i
\(746\) −6.51087 −0.238380
\(747\) 0 0
\(748\) 4.75372i 0.173813i
\(749\) 22.9783 39.7995i 0.839607 1.45424i
\(750\) 0 0
\(751\) −10.8614 18.8125i −0.396338 0.686478i 0.596933 0.802291i \(-0.296386\pi\)
−0.993271 + 0.115813i \(0.963053\pi\)
\(752\) 1.02175 0.589907i 0.0372594 0.0215117i
\(753\) 0 0
\(754\) −13.2921 + 23.0226i −0.484070 + 0.838434i
\(755\) −0.605969 + 1.87953i −0.0220535 + 0.0684030i
\(756\) 0 0
\(757\) 41.5692i 1.51086i 0.655230 + 0.755429i \(0.272572\pi\)
−0.655230 + 0.755429i \(0.727428\pi\)
\(758\) −1.02175 0.589907i −0.0371116 0.0214264i
\(759\) 0 0
\(760\) 0.467376 + 2.17448i 0.0169535 + 0.0788767i
\(761\) 16.2446 + 28.1364i 0.588865 + 1.01994i 0.994381 + 0.105856i \(0.0337583\pi\)
−0.405517 + 0.914088i \(0.632908\pi\)
\(762\) 0 0
\(763\) −29.2337 16.8781i −1.05833 0.611027i
\(764\) −10.4674 −0.378696
\(765\) 0 0
\(766\) 8.78806 0.317526
\(767\) −8.23369 4.75372i −0.297301 0.171647i
\(768\) 0 0
\(769\) −8.24456 14.2800i −0.297307 0.514950i 0.678212 0.734866i \(-0.262755\pi\)
−0.975519 + 0.219916i \(0.929422\pi\)
\(770\) 26.2337 5.63858i 0.945396 0.203200i
\(771\) 0 0
\(772\) −13.6426 7.87658i −0.491009 0.283484i
\(773\) 21.5769i 0.776067i 0.921645 + 0.388034i \(0.126846\pi\)
−0.921645 + 0.388034i \(0.873154\pi\)
\(774\) 0 0
\(775\) −25.8614 18.6101i −0.928969 0.668496i
\(776\) 1.72281 2.98400i 0.0618454 0.107119i
\(777\) 0 0
\(778\) −0.350532 + 0.202380i −0.0125672 + 0.00725566i
\(779\) 0.813859 + 1.40965i 0.0291595 + 0.0505058i
\(780\) 0 0