Properties

Label 855.2.k.f.676.1
Level $855$
Weight $2$
Character 855.676
Analytic conductor $6.827$
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] = [855,2,Mod(406,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("855.406");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 855.k (of order \(3\), degree \(2\), 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: \(6.82720937282\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 285)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 676.1
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 855.676
Dual form 855.2.k.f.406.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.207107 + 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.82843 q^{7} -1.58579 q^{8} +O(q^{10})\) \(q+(-0.207107 + 0.358719i) q^{2} +(0.914214 + 1.58346i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.82843 q^{7} -1.58579 q^{8} +(-0.207107 - 0.358719i) q^{10} +2.82843 q^{11} +(0.914214 + 1.58346i) q^{13} +(-0.378680 + 0.655892i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.585786 + 1.01461i) q^{17} +(4.00000 - 1.73205i) q^{19} -1.82843 q^{20} +(-0.585786 + 1.01461i) q^{22} +(-0.414214 - 0.717439i) q^{23} +(-0.500000 - 0.866025i) q^{25} -0.757359 q^{26} +(1.67157 + 2.89525i) q^{28} +(4.82843 + 8.36308i) q^{29} -5.00000 q^{31} +(-2.20711 - 3.82282i) q^{32} +(-0.242641 - 0.420266i) q^{34} +(-0.914214 + 1.58346i) q^{35} -2.17157 q^{37} +(-0.207107 + 1.79360i) q^{38} +(0.792893 - 1.37333i) q^{40} +(1.41421 - 2.44949i) q^{41} +(-3.91421 + 6.77962i) q^{43} +(2.58579 + 4.47871i) q^{44} +0.343146 q^{46} +(-1.58579 - 2.74666i) q^{47} -3.65685 q^{49} +0.414214 q^{50} +(-1.67157 + 2.89525i) q^{52} +(-1.00000 - 1.73205i) q^{53} +(-1.41421 + 2.44949i) q^{55} -2.89949 q^{56} -4.00000 q^{58} +(4.15685 + 7.19988i) q^{61} +(1.03553 - 1.79360i) q^{62} -4.17157 q^{64} -1.82843 q^{65} +(-2.74264 - 4.75039i) q^{67} -2.14214 q^{68} +(-0.378680 - 0.655892i) q^{70} +(5.00000 - 8.66025i) q^{71} +(-4.74264 + 8.21449i) q^{73} +(0.449747 - 0.778985i) q^{74} +(6.39949 + 4.75039i) q^{76} +5.17157 q^{77} +(1.67157 - 2.89525i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(0.585786 + 1.01461i) q^{82} +8.00000 q^{83} +(-0.585786 - 1.01461i) q^{85} +(-1.62132 - 2.80821i) q^{86} -4.48528 q^{88} +(6.24264 + 10.8126i) q^{89} +(1.67157 + 2.89525i) q^{91} +(0.757359 - 1.31178i) q^{92} +1.31371 q^{94} +(-0.500000 + 4.33013i) q^{95} +(3.00000 - 5.19615i) q^{97} +(0.757359 - 1.31178i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} - 12 q^{8} + 2 q^{10} - 2 q^{13} - 10 q^{14} - 6 q^{16} - 8 q^{17} + 16 q^{19} + 4 q^{20} - 8 q^{22} + 4 q^{23} - 2 q^{25} - 20 q^{26} + 18 q^{28} + 8 q^{29} - 20 q^{31} - 6 q^{32} + 16 q^{34} + 2 q^{35} - 20 q^{37} + 2 q^{38} + 6 q^{40} - 10 q^{43} + 16 q^{44} + 24 q^{46} - 12 q^{47} + 8 q^{49} - 4 q^{50} - 18 q^{52} - 4 q^{53} + 28 q^{56} - 16 q^{58} - 6 q^{61} - 10 q^{62} - 28 q^{64} + 4 q^{65} + 6 q^{67} + 48 q^{68} - 10 q^{70} + 20 q^{71} - 2 q^{73} - 18 q^{74} - 14 q^{76} + 32 q^{77} + 18 q^{79} - 6 q^{80} + 8 q^{82} + 32 q^{83} - 8 q^{85} + 2 q^{86} + 16 q^{88} + 8 q^{89} + 18 q^{91} + 20 q^{92} - 40 q^{94} - 2 q^{95} + 12 q^{97} + 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(496\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.207107 + 0.358719i −0.146447 + 0.253653i −0.929912 0.367783i \(-0.880117\pi\)
0.783465 + 0.621436i \(0.213450\pi\)
\(3\) 0 0
\(4\) 0.914214 + 1.58346i 0.457107 + 0.791732i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) 0 0
\(7\) 1.82843 0.691080 0.345540 0.938404i \(-0.387696\pi\)
0.345540 + 0.938404i \(0.387696\pi\)
\(8\) −1.58579 −0.560660
\(9\) 0 0
\(10\) −0.207107 0.358719i −0.0654929 0.113437i
\(11\) 2.82843 0.852803 0.426401 0.904534i \(-0.359781\pi\)
0.426401 + 0.904534i \(0.359781\pi\)
\(12\) 0 0
\(13\) 0.914214 + 1.58346i 0.253557 + 0.439174i 0.964503 0.264073i \(-0.0850661\pi\)
−0.710945 + 0.703247i \(0.751733\pi\)
\(14\) −0.378680 + 0.655892i −0.101206 + 0.175295i
\(15\) 0 0
\(16\) −1.50000 + 2.59808i −0.375000 + 0.649519i
\(17\) −0.585786 + 1.01461i −0.142074 + 0.246080i −0.928278 0.371888i \(-0.878710\pi\)
0.786203 + 0.617968i \(0.212044\pi\)
\(18\) 0 0
\(19\) 4.00000 1.73205i 0.917663 0.397360i
\(20\) −1.82843 −0.408849
\(21\) 0 0
\(22\) −0.585786 + 1.01461i −0.124890 + 0.216316i
\(23\) −0.414214 0.717439i −0.0863695 0.149596i 0.819604 0.572930i \(-0.194193\pi\)
−0.905974 + 0.423333i \(0.860860\pi\)
\(24\) 0 0
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −0.757359 −0.148530
\(27\) 0 0
\(28\) 1.67157 + 2.89525i 0.315898 + 0.547151i
\(29\) 4.82843 + 8.36308i 0.896616 + 1.55299i 0.831791 + 0.555089i \(0.187316\pi\)
0.0648251 + 0.997897i \(0.479351\pi\)
\(30\) 0 0
\(31\) −5.00000 −0.898027 −0.449013 0.893525i \(-0.648224\pi\)
−0.449013 + 0.893525i \(0.648224\pi\)
\(32\) −2.20711 3.82282i −0.390165 0.675786i
\(33\) 0 0
\(34\) −0.242641 0.420266i −0.0416125 0.0720750i
\(35\) −0.914214 + 1.58346i −0.154530 + 0.267654i
\(36\) 0 0
\(37\) −2.17157 −0.357004 −0.178502 0.983940i \(-0.557125\pi\)
−0.178502 + 0.983940i \(0.557125\pi\)
\(38\) −0.207107 + 1.79360i −0.0335972 + 0.290960i
\(39\) 0 0
\(40\) 0.792893 1.37333i 0.125367 0.217143i
\(41\) 1.41421 2.44949i 0.220863 0.382546i −0.734207 0.678925i \(-0.762446\pi\)
0.955070 + 0.296379i \(0.0957793\pi\)
\(42\) 0 0
\(43\) −3.91421 + 6.77962i −0.596912 + 1.03388i 0.396362 + 0.918094i \(0.370273\pi\)
−0.993274 + 0.115788i \(0.963061\pi\)
\(44\) 2.58579 + 4.47871i 0.389822 + 0.675191i
\(45\) 0 0
\(46\) 0.343146 0.0505941
\(47\) −1.58579 2.74666i −0.231311 0.400642i 0.726883 0.686761i \(-0.240968\pi\)
−0.958194 + 0.286119i \(0.907635\pi\)
\(48\) 0 0
\(49\) −3.65685 −0.522408
\(50\) 0.414214 0.0585786
\(51\) 0 0
\(52\) −1.67157 + 2.89525i −0.231805 + 0.401499i
\(53\) −1.00000 1.73205i −0.137361 0.237915i 0.789136 0.614218i \(-0.210529\pi\)
−0.926497 + 0.376303i \(0.877195\pi\)
\(54\) 0 0
\(55\) −1.41421 + 2.44949i −0.190693 + 0.330289i
\(56\) −2.89949 −0.387461
\(57\) 0 0
\(58\) −4.00000 −0.525226
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0 0
\(61\) 4.15685 + 7.19988i 0.532231 + 0.921851i 0.999292 + 0.0376256i \(0.0119794\pi\)
−0.467061 + 0.884225i \(0.654687\pi\)
\(62\) 1.03553 1.79360i 0.131513 0.227787i
\(63\) 0 0
\(64\) −4.17157 −0.521447
\(65\) −1.82843 −0.226788
\(66\) 0 0
\(67\) −2.74264 4.75039i −0.335067 0.580353i 0.648431 0.761274i \(-0.275426\pi\)
−0.983498 + 0.180921i \(0.942092\pi\)
\(68\) −2.14214 −0.259772
\(69\) 0 0
\(70\) −0.378680 0.655892i −0.0452609 0.0783941i
\(71\) 5.00000 8.66025i 0.593391 1.02778i −0.400381 0.916349i \(-0.631122\pi\)
0.993772 0.111434i \(-0.0355445\pi\)
\(72\) 0 0
\(73\) −4.74264 + 8.21449i −0.555084 + 0.961434i 0.442813 + 0.896614i \(0.353981\pi\)
−0.997897 + 0.0648198i \(0.979353\pi\)
\(74\) 0.449747 0.778985i 0.0522821 0.0905552i
\(75\) 0 0
\(76\) 6.39949 + 4.75039i 0.734072 + 0.544907i
\(77\) 5.17157 0.589355
\(78\) 0 0
\(79\) 1.67157 2.89525i 0.188067 0.325741i −0.756539 0.653949i \(-0.773111\pi\)
0.944606 + 0.328208i \(0.106445\pi\)
\(80\) −1.50000 2.59808i −0.167705 0.290474i
\(81\) 0 0
\(82\) 0.585786 + 1.01461i 0.0646893 + 0.112045i
\(83\) 8.00000 0.878114 0.439057 0.898459i \(-0.355313\pi\)
0.439057 + 0.898459i \(0.355313\pi\)
\(84\) 0 0
\(85\) −0.585786 1.01461i −0.0635375 0.110050i
\(86\) −1.62132 2.80821i −0.174831 0.302817i
\(87\) 0 0
\(88\) −4.48528 −0.478133
\(89\) 6.24264 + 10.8126i 0.661719 + 1.14613i 0.980164 + 0.198189i \(0.0635060\pi\)
−0.318445 + 0.947941i \(0.603161\pi\)
\(90\) 0 0
\(91\) 1.67157 + 2.89525i 0.175228 + 0.303505i
\(92\) 0.757359 1.31178i 0.0789602 0.136763i
\(93\) 0 0
\(94\) 1.31371 0.135499
\(95\) −0.500000 + 4.33013i −0.0512989 + 0.444262i
\(96\) 0 0
\(97\) 3.00000 5.19615i 0.304604 0.527589i −0.672569 0.740034i \(-0.734809\pi\)
0.977173 + 0.212445i \(0.0681426\pi\)
\(98\) 0.757359 1.31178i 0.0765048 0.132510i
\(99\) 0 0
\(100\) 0.914214 1.58346i 0.0914214 0.158346i
\(101\) 6.07107 + 10.5154i 0.604094 + 1.04632i 0.992194 + 0.124704i \(0.0397981\pi\)
−0.388100 + 0.921617i \(0.626869\pi\)
\(102\) 0 0
\(103\) 9.82843 0.968424 0.484212 0.874951i \(-0.339106\pi\)
0.484212 + 0.874951i \(0.339106\pi\)
\(104\) −1.44975 2.51104i −0.142159 0.246227i
\(105\) 0 0
\(106\) 0.828427 0.0804640
\(107\) −14.0000 −1.35343 −0.676716 0.736245i \(-0.736597\pi\)
−0.676716 + 0.736245i \(0.736597\pi\)
\(108\) 0 0
\(109\) 8.65685 14.9941i 0.829176 1.43618i −0.0695090 0.997581i \(-0.522143\pi\)
0.898685 0.438594i \(-0.144523\pi\)
\(110\) −0.585786 1.01461i −0.0558525 0.0967394i
\(111\) 0 0
\(112\) −2.74264 + 4.75039i −0.259155 + 0.448870i
\(113\) −4.00000 −0.376288 −0.188144 0.982141i \(-0.560247\pi\)
−0.188144 + 0.982141i \(0.560247\pi\)
\(114\) 0 0
\(115\) 0.828427 0.0772512
\(116\) −8.82843 + 15.2913i −0.819699 + 1.41976i
\(117\) 0 0
\(118\) 0 0
\(119\) −1.07107 + 1.85514i −0.0981846 + 0.170061i
\(120\) 0 0
\(121\) −3.00000 −0.272727
\(122\) −3.44365 −0.311773
\(123\) 0 0
\(124\) −4.57107 7.91732i −0.410494 0.710996i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −6.48528 11.2328i −0.575476 0.996753i −0.995990 0.0894671i \(-0.971484\pi\)
0.420514 0.907286i \(-0.361850\pi\)
\(128\) 5.27817 9.14207i 0.466529 0.808052i
\(129\) 0 0
\(130\) 0.378680 0.655892i 0.0332124 0.0575256i
\(131\) 3.24264 5.61642i 0.283311 0.490709i −0.688887 0.724868i \(-0.741901\pi\)
0.972198 + 0.234160i \(0.0752339\pi\)
\(132\) 0 0
\(133\) 7.31371 3.16693i 0.634179 0.274608i
\(134\) 2.27208 0.196278
\(135\) 0 0
\(136\) 0.928932 1.60896i 0.0796553 0.137967i
\(137\) −5.24264 9.08052i −0.447909 0.775801i 0.550341 0.834940i \(-0.314498\pi\)
−0.998250 + 0.0591390i \(0.981164\pi\)
\(138\) 0 0
\(139\) 8.15685 + 14.1281i 0.691855 + 1.19833i 0.971229 + 0.238146i \(0.0765398\pi\)
−0.279374 + 0.960182i \(0.590127\pi\)
\(140\) −3.34315 −0.282547
\(141\) 0 0
\(142\) 2.07107 + 3.58719i 0.173800 + 0.301031i
\(143\) 2.58579 + 4.47871i 0.216234 + 0.374529i
\(144\) 0 0
\(145\) −9.65685 −0.801958
\(146\) −1.96447 3.40256i −0.162580 0.281597i
\(147\) 0 0
\(148\) −1.98528 3.43861i −0.163189 0.282652i
\(149\) −0.585786 + 1.01461i −0.0479895 + 0.0831202i −0.889022 0.457864i \(-0.848615\pi\)
0.841033 + 0.540984i \(0.181948\pi\)
\(150\) 0 0
\(151\) 10.3431 0.841713 0.420857 0.907127i \(-0.361730\pi\)
0.420857 + 0.907127i \(0.361730\pi\)
\(152\) −6.34315 + 2.74666i −0.514497 + 0.222784i
\(153\) 0 0
\(154\) −1.07107 + 1.85514i −0.0863091 + 0.149492i
\(155\) 2.50000 4.33013i 0.200805 0.347804i
\(156\) 0 0
\(157\) 9.91421 17.1719i 0.791240 1.37047i −0.133959 0.990987i \(-0.542769\pi\)
0.925199 0.379482i \(-0.123898\pi\)
\(158\) 0.692388 + 1.19925i 0.0550834 + 0.0954073i
\(159\) 0 0
\(160\) 4.41421 0.348974
\(161\) −0.757359 1.31178i −0.0596883 0.103383i
\(162\) 0 0
\(163\) 15.1421 1.18602 0.593012 0.805194i \(-0.297939\pi\)
0.593012 + 0.805194i \(0.297939\pi\)
\(164\) 5.17157 0.403832
\(165\) 0 0
\(166\) −1.65685 + 2.86976i −0.128597 + 0.222736i
\(167\) −12.4853 21.6251i −0.966140 1.67340i −0.706520 0.707693i \(-0.749736\pi\)
−0.259620 0.965711i \(-0.583597\pi\)
\(168\) 0 0
\(169\) 4.82843 8.36308i 0.371417 0.643314i
\(170\) 0.485281 0.0372194
\(171\) 0 0
\(172\) −14.3137 −1.09141
\(173\) 3.65685 6.33386i 0.278025 0.481554i −0.692868 0.721064i \(-0.743653\pi\)
0.970894 + 0.239510i \(0.0769867\pi\)
\(174\) 0 0
\(175\) −0.914214 1.58346i −0.0691080 0.119699i
\(176\) −4.24264 + 7.34847i −0.319801 + 0.553912i
\(177\) 0 0
\(178\) −5.17157 −0.387626
\(179\) −16.1421 −1.20652 −0.603260 0.797545i \(-0.706132\pi\)
−0.603260 + 0.797545i \(0.706132\pi\)
\(180\) 0 0
\(181\) −12.6569 21.9223i −0.940777 1.62947i −0.763994 0.645223i \(-0.776765\pi\)
−0.176782 0.984250i \(-0.556569\pi\)
\(182\) −1.38478 −0.102646
\(183\) 0 0
\(184\) 0.656854 + 1.13770i 0.0484239 + 0.0838727i
\(185\) 1.08579 1.88064i 0.0798286 0.138267i
\(186\) 0 0
\(187\) −1.65685 + 2.86976i −0.121161 + 0.209857i
\(188\) 2.89949 5.02207i 0.211467 0.366272i
\(189\) 0 0
\(190\) −1.44975 1.07616i −0.105176 0.0780727i
\(191\) 16.8284 1.21766 0.608831 0.793300i \(-0.291639\pi\)
0.608831 + 0.793300i \(0.291639\pi\)
\(192\) 0 0
\(193\) 12.3995 21.4766i 0.892535 1.54592i 0.0557094 0.998447i \(-0.482258\pi\)
0.836826 0.547469i \(-0.184409\pi\)
\(194\) 1.24264 + 2.15232i 0.0892164 + 0.154527i
\(195\) 0 0
\(196\) −3.34315 5.79050i −0.238796 0.413607i
\(197\) −17.6569 −1.25800 −0.628999 0.777406i \(-0.716535\pi\)
−0.628999 + 0.777406i \(0.716535\pi\)
\(198\) 0 0
\(199\) 8.50000 + 14.7224i 0.602549 + 1.04365i 0.992434 + 0.122782i \(0.0391815\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) 0.792893 + 1.37333i 0.0560660 + 0.0971092i
\(201\) 0 0
\(202\) −5.02944 −0.353870
\(203\) 8.82843 + 15.2913i 0.619634 + 1.07324i
\(204\) 0 0
\(205\) 1.41421 + 2.44949i 0.0987730 + 0.171080i
\(206\) −2.03553 + 3.52565i −0.141822 + 0.245644i
\(207\) 0 0
\(208\) −5.48528 −0.380336
\(209\) 11.3137 4.89898i 0.782586 0.338869i
\(210\) 0 0
\(211\) 0.156854 0.271680i 0.0107983 0.0187032i −0.860576 0.509322i \(-0.829896\pi\)
0.871374 + 0.490619i \(0.163229\pi\)
\(212\) 1.82843 3.16693i 0.125577 0.217506i
\(213\) 0 0
\(214\) 2.89949 5.02207i 0.198205 0.343302i
\(215\) −3.91421 6.77962i −0.266947 0.462366i
\(216\) 0 0
\(217\) −9.14214 −0.620609
\(218\) 3.58579 + 6.21076i 0.242860 + 0.420646i
\(219\) 0 0
\(220\) −5.17157 −0.348667
\(221\) −2.14214 −0.144096
\(222\) 0 0
\(223\) −2.91421 + 5.04757i −0.195150 + 0.338010i −0.946950 0.321382i \(-0.895853\pi\)
0.751800 + 0.659392i \(0.229186\pi\)
\(224\) −4.03553 6.98975i −0.269635 0.467022i
\(225\) 0 0
\(226\) 0.828427 1.43488i 0.0551062 0.0954467i
\(227\) 18.9706 1.25912 0.629560 0.776952i \(-0.283235\pi\)
0.629560 + 0.776952i \(0.283235\pi\)
\(228\) 0 0
\(229\) −4.65685 −0.307734 −0.153867 0.988092i \(-0.549173\pi\)
−0.153867 + 0.988092i \(0.549173\pi\)
\(230\) −0.171573 + 0.297173i −0.0113132 + 0.0195950i
\(231\) 0 0
\(232\) −7.65685 13.2621i −0.502697 0.870697i
\(233\) −12.6569 + 21.9223i −0.829178 + 1.43618i 0.0695057 + 0.997582i \(0.477858\pi\)
−0.898684 + 0.438597i \(0.855476\pi\)
\(234\) 0 0
\(235\) 3.17157 0.206891
\(236\) 0 0
\(237\) 0 0
\(238\) −0.443651 0.768426i −0.0287576 0.0498096i
\(239\) 24.6274 1.59302 0.796508 0.604629i \(-0.206678\pi\)
0.796508 + 0.604629i \(0.206678\pi\)
\(240\) 0 0
\(241\) −2.50000 4.33013i −0.161039 0.278928i 0.774202 0.632938i \(-0.218151\pi\)
−0.935242 + 0.354010i \(0.884818\pi\)
\(242\) 0.621320 1.07616i 0.0399400 0.0691781i
\(243\) 0 0
\(244\) −7.60051 + 13.1645i −0.486572 + 0.842768i
\(245\) 1.82843 3.16693i 0.116814 0.202328i
\(246\) 0 0
\(247\) 6.39949 + 4.75039i 0.407190 + 0.302260i
\(248\) 7.92893 0.503488
\(249\) 0 0
\(250\) −0.207107 + 0.358719i −0.0130986 + 0.0226874i
\(251\) −8.17157 14.1536i −0.515785 0.893366i −0.999832 0.0183240i \(-0.994167\pi\)
0.484047 0.875042i \(-0.339166\pi\)
\(252\) 0 0
\(253\) −1.17157 2.02922i −0.0736562 0.127576i
\(254\) 5.37258 0.337106
\(255\) 0 0
\(256\) −1.98528 3.43861i −0.124080 0.214913i
\(257\) −8.41421 14.5738i −0.524864 0.909091i −0.999581 0.0289528i \(-0.990783\pi\)
0.474717 0.880139i \(-0.342551\pi\)
\(258\) 0 0
\(259\) −3.97056 −0.246719
\(260\) −1.67157 2.89525i −0.103667 0.179556i
\(261\) 0 0
\(262\) 1.34315 + 2.32640i 0.0829798 + 0.143725i
\(263\) 12.8995 22.3426i 0.795417 1.37770i −0.127157 0.991883i \(-0.540585\pi\)
0.922574 0.385820i \(-0.126081\pi\)
\(264\) 0 0
\(265\) 2.00000 0.122859
\(266\) −0.378680 + 3.27946i −0.0232183 + 0.201077i
\(267\) 0 0
\(268\) 5.01472 8.68575i 0.306323 0.530566i
\(269\) 0.828427 1.43488i 0.0505101 0.0874860i −0.839665 0.543105i \(-0.817249\pi\)
0.890175 + 0.455619i \(0.150582\pi\)
\(270\) 0 0
\(271\) −6.82843 + 11.8272i −0.414797 + 0.718450i −0.995407 0.0957318i \(-0.969481\pi\)
0.580610 + 0.814182i \(0.302814\pi\)
\(272\) −1.75736 3.04384i −0.106556 0.184560i
\(273\) 0 0
\(274\) 4.34315 0.262379
\(275\) −1.41421 2.44949i −0.0852803 0.147710i
\(276\) 0 0
\(277\) 6.00000 0.360505 0.180253 0.983620i \(-0.442309\pi\)
0.180253 + 0.983620i \(0.442309\pi\)
\(278\) −6.75736 −0.405279
\(279\) 0 0
\(280\) 1.44975 2.51104i 0.0866390 0.150063i
\(281\) −3.48528 6.03668i −0.207914 0.360118i 0.743143 0.669133i \(-0.233334\pi\)
−0.951057 + 0.309014i \(0.900001\pi\)
\(282\) 0 0
\(283\) 10.4853 18.1610i 0.623285 1.07956i −0.365584 0.930778i \(-0.619131\pi\)
0.988870 0.148784i \(-0.0475358\pi\)
\(284\) 18.2843 1.08497
\(285\) 0 0
\(286\) −2.14214 −0.126667
\(287\) 2.58579 4.47871i 0.152634 0.264370i
\(288\) 0 0
\(289\) 7.81371 + 13.5337i 0.459630 + 0.796102i
\(290\) 2.00000 3.46410i 0.117444 0.203419i
\(291\) 0 0
\(292\) −17.3431 −1.01493
\(293\) 5.31371 0.310430 0.155215 0.987881i \(-0.450393\pi\)
0.155215 + 0.987881i \(0.450393\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 3.44365 0.200158
\(297\) 0 0
\(298\) −0.242641 0.420266i −0.0140558 0.0243454i
\(299\) 0.757359 1.31178i 0.0437992 0.0758625i
\(300\) 0 0
\(301\) −7.15685 + 12.3960i −0.412514 + 0.714496i
\(302\) −2.14214 + 3.71029i −0.123266 + 0.213503i
\(303\) 0 0
\(304\) −1.50000 + 12.9904i −0.0860309 + 0.745049i
\(305\) −8.31371 −0.476042
\(306\) 0 0
\(307\) 8.82843 15.2913i 0.503865 0.872720i −0.496125 0.868251i \(-0.665244\pi\)
0.999990 0.00446862i \(-0.00142241\pi\)
\(308\) 4.72792 + 8.18900i 0.269398 + 0.466612i
\(309\) 0 0
\(310\) 1.03553 + 1.79360i 0.0588144 + 0.101869i
\(311\) 4.00000 0.226819 0.113410 0.993548i \(-0.463823\pi\)
0.113410 + 0.993548i \(0.463823\pi\)
\(312\) 0 0
\(313\) 3.00000 + 5.19615i 0.169570 + 0.293704i 0.938269 0.345907i \(-0.112429\pi\)
−0.768699 + 0.639611i \(0.779095\pi\)
\(314\) 4.10660 + 7.11284i 0.231749 + 0.401401i
\(315\) 0 0
\(316\) 6.11270 0.343866
\(317\) 2.65685 + 4.60181i 0.149224 + 0.258463i 0.930941 0.365170i \(-0.118989\pi\)
−0.781717 + 0.623633i \(0.785656\pi\)
\(318\) 0 0
\(319\) 13.6569 + 23.6544i 0.764637 + 1.32439i
\(320\) 2.08579 3.61269i 0.116599 0.201955i
\(321\) 0 0
\(322\) 0.627417 0.0349646
\(323\) −0.585786 + 5.07306i −0.0325940 + 0.282273i
\(324\) 0 0
\(325\) 0.914214 1.58346i 0.0507114 0.0878348i
\(326\) −3.13604 + 5.43178i −0.173689 + 0.300838i
\(327\) 0 0
\(328\) −2.24264 + 3.88437i −0.123829 + 0.214478i
\(329\) −2.89949 5.02207i −0.159854 0.276876i
\(330\) 0 0
\(331\) −5.34315 −0.293686 −0.146843 0.989160i \(-0.546911\pi\)
−0.146843 + 0.989160i \(0.546911\pi\)
\(332\) 7.31371 + 12.6677i 0.401392 + 0.695231i
\(333\) 0 0
\(334\) 10.3431 0.565952
\(335\) 5.48528 0.299693
\(336\) 0 0
\(337\) −8.74264 + 15.1427i −0.476242 + 0.824875i −0.999629 0.0272195i \(-0.991335\pi\)
0.523387 + 0.852095i \(0.324668\pi\)
\(338\) 2.00000 + 3.46410i 0.108786 + 0.188422i
\(339\) 0 0
\(340\) 1.07107 1.85514i 0.0580868 0.100609i
\(341\) −14.1421 −0.765840
\(342\) 0 0
\(343\) −19.4853 −1.05211
\(344\) 6.20711 10.7510i 0.334665 0.579656i
\(345\) 0 0
\(346\) 1.51472 + 2.62357i 0.0814318 + 0.141044i
\(347\) −17.7279 + 30.7057i −0.951685 + 1.64837i −0.209906 + 0.977722i \(0.567316\pi\)
−0.741779 + 0.670645i \(0.766018\pi\)
\(348\) 0 0
\(349\) −31.6274 −1.69298 −0.846488 0.532407i \(-0.821288\pi\)
−0.846488 + 0.532407i \(0.821288\pi\)
\(350\) 0.757359 0.0404826
\(351\) 0 0
\(352\) −6.24264 10.8126i −0.332734 0.576312i
\(353\) 1.31371 0.0699216 0.0349608 0.999389i \(-0.488869\pi\)
0.0349608 + 0.999389i \(0.488869\pi\)
\(354\) 0 0
\(355\) 5.00000 + 8.66025i 0.265372 + 0.459639i
\(356\) −11.4142 + 19.7700i −0.604952 + 1.04781i
\(357\) 0 0
\(358\) 3.34315 5.79050i 0.176691 0.306037i
\(359\) 4.58579 7.94282i 0.242029 0.419206i −0.719263 0.694737i \(-0.755521\pi\)
0.961292 + 0.275532i \(0.0888539\pi\)
\(360\) 0 0
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) 10.4853 0.551094
\(363\) 0 0
\(364\) −3.05635 + 5.29375i −0.160196 + 0.277468i
\(365\) −4.74264 8.21449i −0.248241 0.429966i
\(366\) 0 0
\(367\) 17.0563 + 29.5425i 0.890334 + 1.54210i 0.839475 + 0.543398i \(0.182863\pi\)
0.0508591 + 0.998706i \(0.483804\pi\)
\(368\) 2.48528 0.129554
\(369\) 0 0
\(370\) 0.449747 + 0.778985i 0.0233813 + 0.0404975i
\(371\) −1.82843 3.16693i −0.0949272 0.164419i
\(372\) 0 0
\(373\) −11.6569 −0.603569 −0.301785 0.953376i \(-0.597582\pi\)
−0.301785 + 0.953376i \(0.597582\pi\)
\(374\) −0.686292 1.18869i −0.0354873 0.0614658i
\(375\) 0 0
\(376\) 2.51472 + 4.35562i 0.129687 + 0.224624i
\(377\) −8.82843 + 15.2913i −0.454687 + 0.787541i
\(378\) 0 0
\(379\) 1.68629 0.0866190 0.0433095 0.999062i \(-0.486210\pi\)
0.0433095 + 0.999062i \(0.486210\pi\)
\(380\) −7.31371 + 3.16693i −0.375185 + 0.162460i
\(381\) 0 0
\(382\) −3.48528 + 6.03668i −0.178323 + 0.308864i
\(383\) −16.9706 + 29.3939i −0.867155 + 1.50196i −0.00226413 + 0.999997i \(0.500721\pi\)
−0.864891 + 0.501960i \(0.832613\pi\)
\(384\) 0 0
\(385\) −2.58579 + 4.47871i −0.131784 + 0.228256i
\(386\) 5.13604 + 8.89588i 0.261418 + 0.452788i
\(387\) 0 0
\(388\) 10.9706 0.556946
\(389\) −7.72792 13.3852i −0.391821 0.678654i 0.600869 0.799348i \(-0.294821\pi\)
−0.992690 + 0.120694i \(0.961488\pi\)
\(390\) 0 0
\(391\) 0.970563 0.0490835
\(392\) 5.79899 0.292893
\(393\) 0 0
\(394\) 3.65685 6.33386i 0.184230 0.319095i
\(395\) 1.67157 + 2.89525i 0.0841060 + 0.145676i
\(396\) 0 0
\(397\) 11.9142 20.6360i 0.597957 1.03569i −0.395165 0.918610i \(-0.629313\pi\)
0.993122 0.117082i \(-0.0373541\pi\)
\(398\) −7.04163 −0.352965
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) −11.3137 + 19.5959i −0.564980 + 0.978573i 0.432072 + 0.901839i \(0.357783\pi\)
−0.997052 + 0.0767343i \(0.975551\pi\)
\(402\) 0 0
\(403\) −4.57107 7.91732i −0.227701 0.394390i
\(404\) −11.1005 + 19.2266i −0.552271 + 0.956561i
\(405\) 0 0
\(406\) −7.31371 −0.362973
\(407\) −6.14214 −0.304454
\(408\) 0 0
\(409\) −3.00000 5.19615i −0.148340 0.256933i 0.782274 0.622935i \(-0.214060\pi\)
−0.930614 + 0.366002i \(0.880726\pi\)
\(410\) −1.17157 −0.0578599
\(411\) 0 0
\(412\) 8.98528 + 15.5630i 0.442673 + 0.766732i
\(413\) 0 0
\(414\) 0 0
\(415\) −4.00000 + 6.92820i −0.196352 + 0.340092i
\(416\) 4.03553 6.98975i 0.197858 0.342701i
\(417\) 0 0
\(418\) −0.585786 + 5.07306i −0.0286518 + 0.248131i
\(419\) −3.31371 −0.161885 −0.0809426 0.996719i \(-0.525793\pi\)
−0.0809426 + 0.996719i \(0.525793\pi\)
\(420\) 0 0
\(421\) 3.82843 6.63103i 0.186586 0.323177i −0.757524 0.652808i \(-0.773591\pi\)
0.944110 + 0.329631i \(0.106924\pi\)
\(422\) 0.0649712 + 0.112533i 0.00316275 + 0.00547804i
\(423\) 0 0
\(424\) 1.58579 + 2.74666i 0.0770126 + 0.133390i
\(425\) 1.17157 0.0568296
\(426\) 0 0
\(427\) 7.60051 + 13.1645i 0.367814 + 0.637073i
\(428\) −12.7990 22.1685i −0.618663 1.07155i
\(429\) 0 0
\(430\) 3.24264 0.156374
\(431\) −1.24264 2.15232i −0.0598559 0.103673i 0.834545 0.550940i \(-0.185731\pi\)
−0.894401 + 0.447267i \(0.852397\pi\)
\(432\) 0 0
\(433\) 19.9142 + 34.4924i 0.957016 + 1.65760i 0.729686 + 0.683783i \(0.239666\pi\)
0.227330 + 0.973818i \(0.427000\pi\)
\(434\) 1.89340 3.27946i 0.0908860 0.157419i
\(435\) 0 0
\(436\) 31.6569 1.51609
\(437\) −2.89949 2.15232i −0.138702 0.102959i
\(438\) 0 0
\(439\) −8.50000 + 14.7224i −0.405683 + 0.702663i −0.994401 0.105675i \(-0.966300\pi\)
0.588718 + 0.808339i \(0.299633\pi\)
\(440\) 2.24264 3.88437i 0.106914 0.185180i
\(441\) 0 0
\(442\) 0.443651 0.768426i 0.0211023 0.0365503i
\(443\) 9.07107 + 15.7116i 0.430979 + 0.746478i 0.996958 0.0779417i \(-0.0248348\pi\)
−0.565978 + 0.824420i \(0.691501\pi\)
\(444\) 0 0
\(445\) −12.4853 −0.591859
\(446\) −1.20711 2.09077i −0.0571582 0.0990008i
\(447\) 0 0
\(448\) −7.62742 −0.360362
\(449\) −13.1716 −0.621605 −0.310802 0.950475i \(-0.600598\pi\)
−0.310802 + 0.950475i \(0.600598\pi\)
\(450\) 0 0
\(451\) 4.00000 6.92820i 0.188353 0.326236i
\(452\) −3.65685 6.33386i −0.172004 0.297920i
\(453\) 0 0
\(454\) −3.92893 + 6.80511i −0.184394 + 0.319380i
\(455\) −3.34315 −0.156729
\(456\) 0 0
\(457\) −4.17157 −0.195138 −0.0975690 0.995229i \(-0.531107\pi\)
−0.0975690 + 0.995229i \(0.531107\pi\)
\(458\) 0.964466 1.67050i 0.0450665 0.0780575i
\(459\) 0 0
\(460\) 0.757359 + 1.31178i 0.0353121 + 0.0611623i
\(461\) 15.0711 26.1039i 0.701930 1.21578i −0.265859 0.964012i \(-0.585655\pi\)
0.967788 0.251766i \(-0.0810112\pi\)
\(462\) 0 0
\(463\) −22.7990 −1.05956 −0.529779 0.848135i \(-0.677725\pi\)
−0.529779 + 0.848135i \(0.677725\pi\)
\(464\) −28.9706 −1.34492
\(465\) 0 0
\(466\) −5.24264 9.08052i −0.242861 0.420647i
\(467\) −23.7990 −1.10129 −0.550643 0.834741i \(-0.685617\pi\)
−0.550643 + 0.834741i \(0.685617\pi\)
\(468\) 0 0
\(469\) −5.01472 8.68575i −0.231558 0.401071i
\(470\) −0.656854 + 1.13770i −0.0302984 + 0.0524784i
\(471\) 0 0
\(472\) 0 0
\(473\) −11.0711 + 19.1757i −0.509048 + 0.881697i
\(474\) 0 0
\(475\) −3.50000 2.59808i −0.160591 0.119208i
\(476\) −3.91674 −0.179523
\(477\) 0 0
\(478\) −5.10051 + 8.83433i −0.233292 + 0.404073i
\(479\) 1.24264 + 2.15232i 0.0567777 + 0.0983419i 0.893017 0.450022i \(-0.148584\pi\)
−0.836240 + 0.548364i \(0.815251\pi\)
\(480\) 0 0
\(481\) −1.98528 3.43861i −0.0905210 0.156787i
\(482\) 2.07107 0.0943346
\(483\) 0 0
\(484\) −2.74264 4.75039i −0.124665 0.215927i
\(485\) 3.00000 + 5.19615i 0.136223 + 0.235945i
\(486\) 0 0
\(487\) −6.34315 −0.287435 −0.143718 0.989619i \(-0.545906\pi\)
−0.143718 + 0.989619i \(0.545906\pi\)
\(488\) −6.59188 11.4175i −0.298401 0.516845i
\(489\) 0 0
\(490\) 0.757359 + 1.31178i 0.0342140 + 0.0592604i
\(491\) 11.8284 20.4874i 0.533809 0.924585i −0.465411 0.885095i \(-0.654093\pi\)
0.999220 0.0394901i \(-0.0125734\pi\)
\(492\) 0 0
\(493\) −11.3137 −0.509544
\(494\) −3.02944 + 1.31178i −0.136301 + 0.0590200i
\(495\) 0 0
\(496\) 7.50000 12.9904i 0.336760 0.583285i
\(497\) 9.14214 15.8346i 0.410081 0.710281i
\(498\) 0 0
\(499\) 3.67157 6.35935i 0.164362 0.284684i −0.772066 0.635542i \(-0.780777\pi\)
0.936429 + 0.350858i \(0.114110\pi\)
\(500\) 0.914214 + 1.58346i 0.0408849 + 0.0708147i
\(501\) 0 0
\(502\) 6.76955 0.302140
\(503\) 6.92893 + 12.0013i 0.308946 + 0.535110i 0.978132 0.207985i \(-0.0666905\pi\)
−0.669186 + 0.743095i \(0.733357\pi\)
\(504\) 0 0
\(505\) −12.1421 −0.540318
\(506\) 0.970563 0.0431468
\(507\) 0 0
\(508\) 11.8579 20.5384i 0.526108 0.911245i
\(509\) 16.5563 + 28.6764i 0.733847 + 1.27106i 0.955227 + 0.295873i \(0.0956106\pi\)
−0.221380 + 0.975188i \(0.571056\pi\)
\(510\) 0 0
\(511\) −8.67157 + 15.0196i −0.383608 + 0.664428i
\(512\) 22.7574 1.00574
\(513\) 0 0
\(514\) 6.97056 0.307458
\(515\) −4.91421 + 8.51167i −0.216546 + 0.375069i
\(516\) 0 0
\(517\) −4.48528 7.76874i −0.197262 0.341669i
\(518\) 0.822330 1.42432i 0.0361311 0.0625809i
\(519\) 0 0
\(520\) 2.89949 0.127151
\(521\) −6.34315 −0.277898 −0.138949 0.990300i \(-0.544372\pi\)
−0.138949 + 0.990300i \(0.544372\pi\)
\(522\) 0 0
\(523\) 14.8848 + 25.7812i 0.650866 + 1.12733i 0.982913 + 0.184070i \(0.0589273\pi\)
−0.332047 + 0.943263i \(0.607739\pi\)
\(524\) 11.8579 0.518013
\(525\) 0 0
\(526\) 5.34315 + 9.25460i 0.232972 + 0.403520i
\(527\) 2.92893 5.07306i 0.127586 0.220986i
\(528\) 0 0
\(529\) 11.1569 19.3242i 0.485081 0.840184i
\(530\) −0.414214 + 0.717439i −0.0179923 + 0.0311636i
\(531\) 0 0
\(532\) 11.7010 + 8.68575i 0.507303 + 0.376575i
\(533\) 5.17157 0.224006
\(534\) 0 0
\(535\) 7.00000 12.1244i 0.302636 0.524182i
\(536\) 4.34924 + 7.53311i 0.187859 + 0.325381i
\(537\) 0 0
\(538\) 0.343146 + 0.594346i 0.0147941 + 0.0256241i
\(539\) −10.3431 −0.445511
\(540\) 0 0
\(541\) −8.15685 14.1281i −0.350691 0.607414i 0.635680 0.771953i \(-0.280720\pi\)
−0.986371 + 0.164539i \(0.947386\pi\)
\(542\) −2.82843 4.89898i −0.121491 0.210429i
\(543\) 0 0
\(544\) 5.17157 0.221729
\(545\) 8.65685 + 14.9941i 0.370819 + 0.642277i
\(546\) 0 0
\(547\) 6.57107 + 11.3814i 0.280959 + 0.486635i 0.971621 0.236543i \(-0.0760143\pi\)
−0.690663 + 0.723177i \(0.742681\pi\)
\(548\) 9.58579 16.6031i 0.409485 0.709248i
\(549\) 0 0
\(550\) 1.17157 0.0499560
\(551\) 33.7990 + 25.0892i 1.43989 + 1.06884i
\(552\) 0 0
\(553\) 3.05635 5.29375i 0.129969 0.225113i
\(554\) −1.24264 + 2.15232i −0.0527947 + 0.0914432i
\(555\) 0 0
\(556\) −14.9142 + 25.8322i −0.632504 + 1.09553i
\(557\) −4.51472 7.81972i −0.191295 0.331332i 0.754385 0.656432i \(-0.227935\pi\)
−0.945680 + 0.325100i \(0.894602\pi\)
\(558\) 0 0
\(559\) −14.3137 −0.605405
\(560\) −2.74264 4.75039i −0.115898 0.200741i
\(561\) 0 0
\(562\) 2.88730 0.121793
\(563\) 12.1421 0.511730 0.255865 0.966713i \(-0.417640\pi\)
0.255865 + 0.966713i \(0.417640\pi\)
\(564\) 0 0
\(565\) 2.00000 3.46410i 0.0841406 0.145736i
\(566\) 4.34315 + 7.52255i 0.182556 + 0.316196i
\(567\) 0 0
\(568\) −7.92893 + 13.7333i −0.332691 + 0.576237i
\(569\) −4.97056 −0.208377 −0.104188 0.994558i \(-0.533224\pi\)
−0.104188 + 0.994558i \(0.533224\pi\)
\(570\) 0 0
\(571\) 14.3137 0.599010 0.299505 0.954095i \(-0.403178\pi\)
0.299505 + 0.954095i \(0.403178\pi\)
\(572\) −4.72792 + 8.18900i −0.197684 + 0.342399i
\(573\) 0 0
\(574\) 1.07107 + 1.85514i 0.0447055 + 0.0774322i
\(575\) −0.414214 + 0.717439i −0.0172739 + 0.0299193i
\(576\) 0 0
\(577\) −36.3431 −1.51298 −0.756492 0.654002i \(-0.773089\pi\)
−0.756492 + 0.654002i \(0.773089\pi\)
\(578\) −6.47309 −0.269245
\(579\) 0 0
\(580\) −8.82843 15.2913i −0.366580 0.634936i
\(581\) 14.6274 0.606848
\(582\) 0 0
\(583\) −2.82843 4.89898i −0.117141 0.202895i
\(584\) 7.52082 13.0264i 0.311214 0.539038i
\(585\) 0 0
\(586\) −1.10051 + 1.90613i −0.0454614 + 0.0787415i
\(587\) 5.31371 9.20361i 0.219320 0.379874i −0.735280 0.677763i \(-0.762949\pi\)
0.954600 + 0.297890i \(0.0962827\pi\)
\(588\) 0 0
\(589\) −20.0000 + 8.66025i −0.824086 + 0.356840i
\(590\) 0 0
\(591\) 0 0
\(592\) 3.25736 5.64191i 0.133877 0.231881i
\(593\) −4.92893 8.53716i −0.202407 0.350579i 0.746896 0.664940i \(-0.231543\pi\)
−0.949303 + 0.314361i \(0.898210\pi\)
\(594\) 0 0
\(595\) −1.07107 1.85514i −0.0439095 0.0760535i
\(596\) −2.14214 −0.0877453
\(597\) 0 0
\(598\) 0.313708 + 0.543359i 0.0128285 + 0.0222196i
\(599\) −8.48528 14.6969i −0.346699 0.600501i 0.638962 0.769238i \(-0.279364\pi\)
−0.985661 + 0.168738i \(0.946031\pi\)
\(600\) 0 0
\(601\) −35.3431 −1.44168 −0.720838 0.693103i \(-0.756243\pi\)
−0.720838 + 0.693103i \(0.756243\pi\)
\(602\) −2.96447 5.13461i −0.120823 0.209271i
\(603\) 0 0
\(604\) 9.45584 + 16.3780i 0.384753 + 0.666411i
\(605\) 1.50000 2.59808i 0.0609837 0.105627i
\(606\) 0 0
\(607\) −6.17157 −0.250496 −0.125248 0.992125i \(-0.539973\pi\)
−0.125248 + 0.992125i \(0.539973\pi\)
\(608\) −15.4497 11.4685i −0.626570 0.465108i
\(609\) 0 0
\(610\) 1.72183 2.98229i 0.0697147 0.120749i
\(611\) 2.89949 5.02207i 0.117301 0.203171i
\(612\) 0 0
\(613\) −16.7990 + 29.0967i −0.678505 + 1.17520i 0.296926 + 0.954900i \(0.404038\pi\)
−0.975431 + 0.220304i \(0.929295\pi\)
\(614\) 3.65685 + 6.33386i 0.147579 + 0.255614i
\(615\) 0 0
\(616\) −8.20101 −0.330428
\(617\) 12.8284 + 22.2195i 0.516453 + 0.894523i 0.999818 + 0.0191037i \(0.00608126\pi\)
−0.483364 + 0.875419i \(0.660585\pi\)
\(618\) 0 0
\(619\) 15.6863 0.630485 0.315243 0.949011i \(-0.397914\pi\)
0.315243 + 0.949011i \(0.397914\pi\)
\(620\) 9.14214 0.367157
\(621\) 0 0
\(622\) −0.828427 + 1.43488i −0.0332169 + 0.0575334i
\(623\) 11.4142 + 19.7700i 0.457301 + 0.792068i
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −2.48528 −0.0993318
\(627\) 0 0
\(628\) 36.2548 1.44673
\(629\) 1.27208 2.20330i 0.0507211 0.0878515i
\(630\) 0 0
\(631\) 6.64214 + 11.5045i 0.264419 + 0.457988i 0.967411 0.253210i \(-0.0814864\pi\)
−0.702992 + 0.711198i \(0.748153\pi\)
\(632\) −2.65076 + 4.59125i −0.105441 + 0.182630i
\(633\) 0 0
\(634\) −2.20101 −0.0874133
\(635\) 12.9706 0.514721
\(636\) 0 0
\(637\) −3.34315 5.79050i −0.132460 0.229428i
\(638\) −11.3137 −0.447914
\(639\) 0 0
\(640\) 5.27817 + 9.14207i 0.208638 + 0.361372i
\(641\) 14.0711 24.3718i 0.555774 0.962628i −0.442069 0.896981i \(-0.645755\pi\)
0.997843 0.0656474i \(-0.0209113\pi\)
\(642\) 0 0
\(643\) −2.91421 + 5.04757i −0.114925 + 0.199057i −0.917750 0.397159i \(-0.869996\pi\)
0.802825 + 0.596215i \(0.203330\pi\)
\(644\) 1.38478 2.39850i 0.0545678 0.0945143i
\(645\) 0 0
\(646\) −1.69848 1.26080i −0.0668260 0.0496054i
\(647\) 32.2843 1.26923 0.634613 0.772830i \(-0.281160\pi\)
0.634613 + 0.772830i \(0.281160\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0.378680 + 0.655892i 0.0148530 + 0.0257262i
\(651\) 0 0
\(652\) 13.8431 + 23.9770i 0.542139 + 0.939013i
\(653\) −39.9411 −1.56302 −0.781509 0.623895i \(-0.785549\pi\)
−0.781509 + 0.623895i \(0.785549\pi\)
\(654\) 0 0
\(655\) 3.24264 + 5.61642i 0.126700 + 0.219452i
\(656\) 4.24264 + 7.34847i 0.165647 + 0.286910i
\(657\) 0 0
\(658\) 2.40202 0.0936405
\(659\) 3.75736 + 6.50794i 0.146366 + 0.253513i 0.929882 0.367859i \(-0.119909\pi\)
−0.783516 + 0.621372i \(0.786576\pi\)
\(660\) 0 0
\(661\) 3.48528 + 6.03668i 0.135562 + 0.234800i 0.925812 0.377985i \(-0.123383\pi\)
−0.790250 + 0.612784i \(0.790049\pi\)
\(662\) 1.10660 1.91669i 0.0430093 0.0744943i
\(663\) 0 0
\(664\) −12.6863 −0.492324
\(665\) −0.914214 + 7.91732i −0.0354517 + 0.307021i
\(666\) 0 0
\(667\) 4.00000 6.92820i 0.154881 0.268261i
\(668\) 22.8284 39.5400i 0.883258 1.52985i
\(669\) 0 0
\(670\) −1.13604 + 1.96768i −0.0438890 + 0.0760180i
\(671\) 11.7574 + 20.3643i 0.453888 + 0.786157i
\(672\) 0 0
\(673\) −23.8284 −0.918518 −0.459259 0.888302i \(-0.651885\pi\)
−0.459259 + 0.888302i \(0.651885\pi\)
\(674\) −3.62132 6.27231i −0.139488 0.241600i
\(675\) 0 0
\(676\) 17.6569 0.679110
\(677\) 23.4558 0.901481 0.450741 0.892655i \(-0.351160\pi\)
0.450741 + 0.892655i \(0.351160\pi\)
\(678\) 0 0
\(679\) 5.48528 9.50079i 0.210506 0.364607i
\(680\) 0.928932 + 1.60896i 0.0356229 + 0.0617007i
\(681\) 0 0
\(682\) 2.92893 5.07306i 0.112155 0.194257i
\(683\) −44.1421 −1.68905 −0.844526 0.535515i \(-0.820118\pi\)
−0.844526 + 0.535515i \(0.820118\pi\)
\(684\) 0 0
\(685\) 10.4853 0.400622
\(686\) 4.03553 6.98975i 0.154077 0.266870i
\(687\) 0 0
\(688\) −11.7426 20.3389i −0.447684 0.775411i
\(689\) 1.82843 3.16693i 0.0696575 0.120650i
\(690\) 0 0
\(691\) 31.3137 1.19123 0.595615 0.803270i \(-0.296908\pi\)
0.595615 + 0.803270i \(0.296908\pi\)
\(692\) 13.3726 0.508349
\(693\) 0 0
\(694\) −7.34315 12.7187i −0.278742 0.482795i
\(695\) −16.3137 −0.618814
\(696\) 0 0
\(697\) 1.65685 + 2.86976i 0.0627578 + 0.108700i
\(698\) 6.55025 11.3454i 0.247931 0.429429i
\(699\) 0 0
\(700\) 1.67157 2.89525i 0.0631795 0.109430i
\(701\) 16.0711 27.8359i 0.606996 1.05135i −0.384737 0.923026i \(-0.625708\pi\)
0.991733 0.128321i \(-0.0409589\pi\)
\(702\) 0 0
\(703\) −8.68629 + 3.76127i −0.327610 + 0.141859i
\(704\) −11.7990 −0.444691
\(705\) 0 0
\(706\) −0.272078 + 0.471253i −0.0102398 + 0.0177358i
\(707\) 11.1005 + 19.2266i 0.417477 + 0.723092i
\(708\) 0 0
\(709\) −15.8137 27.3901i −0.593896 1.02866i −0.993702 0.112058i \(-0.964256\pi\)
0.399805 0.916600i \(-0.369078\pi\)
\(710\) −4.14214 −0.155452
\(711\) 0 0
\(712\) −9.89949 17.1464i −0.370999 0.642590i
\(713\) 2.07107 + 3.58719i 0.0775621 + 0.134341i
\(714\) 0 0
\(715\) −5.17157 −0.193406
\(716\) −14.7574 25.5605i −0.551508 0.955241i
\(717\) 0 0
\(718\) 1.89949 + 3.29002i 0.0708885 + 0.122783i
\(719\) −11.5858 + 20.0672i −0.432077 + 0.748379i −0.997052 0.0767288i \(-0.975552\pi\)
0.564975 + 0.825108i \(0.308886\pi\)
\(720\) 0 0
\(721\) 17.9706 0.669259
\(722\) 2.27817 + 7.53311i 0.0847849 + 0.280353i
\(723\) 0 0
\(724\) 23.1421 40.0834i 0.860071 1.48969i
\(725\) 4.82843 8.36308i 0.179323 0.310597i
\(726\) 0 0
\(727\) −18.0858 + 31.3255i −0.670765 + 1.16180i 0.306923 + 0.951734i \(0.400701\pi\)
−0.977688 + 0.210064i \(0.932633\pi\)
\(728\) −2.65076 4.59125i −0.0982436 0.170163i
\(729\) 0 0
\(730\) 3.92893 0.145416
\(731\) −4.58579 7.94282i −0.169611 0.293776i
\(732\) 0 0
\(733\) 3.65685 0.135069 0.0675345 0.997717i \(-0.478487\pi\)
0.0675345 + 0.997717i \(0.478487\pi\)
\(734\) −14.1299 −0.521546
\(735\) 0 0
\(736\) −1.82843 + 3.16693i −0.0673967 + 0.116735i
\(737\) −7.75736 13.4361i −0.285746 0.494927i
\(738\) 0 0
\(739\) 20.8137 36.0504i 0.765645 1.32614i −0.174260 0.984700i \(-0.555753\pi\)
0.939905 0.341436i \(-0.110913\pi\)
\(740\) 3.97056 0.145961
\(741\) 0 0
\(742\) 1.51472 0.0556071
\(743\) 17.0711 29.5680i 0.626277 1.08474i −0.362016 0.932172i \(-0.617911\pi\)
0.988292 0.152571i \(-0.0487553\pi\)
\(744\) 0 0
\(745\) −0.585786 1.01461i −0.0214616 0.0371725i
\(746\) 2.41421 4.18154i 0.0883906 0.153097i
\(747\) 0 0
\(748\) −6.05887 −0.221534
\(749\) −25.5980 −0.935330
\(750\) 0 0
\(751\) −13.1569 22.7883i −0.480100 0.831558i 0.519639 0.854386i \(-0.326066\pi\)
−0.999739 + 0.0228276i \(0.992733\pi\)
\(752\) 9.51472 0.346966
\(753\) 0 0
\(754\) −3.65685 6.33386i −0.133175 0.230665i
\(755\) −5.17157 + 8.95743i −0.188213 + 0.325994i
\(756\) 0 0
\(757\) 16.5711 28.7019i 0.602286 1.04319i −0.390188 0.920735i \(-0.627590\pi\)
0.992474 0.122454i \(-0.0390765\pi\)
\(758\) −0.349242 + 0.604906i −0.0126851 + 0.0219712i
\(759\) 0 0
\(760\) 0.792893 6.86666i 0.0287613 0.249080i
\(761\) −51.5980 −1.87043 −0.935213 0.354087i \(-0.884792\pi\)
−0.935213 + 0.354087i \(0.884792\pi\)
\(762\) 0 0
\(763\) 15.8284 27.4156i 0.573028 0.992513i
\(764\) 15.3848 + 26.6472i 0.556602 + 0.964062i
\(765\) 0 0
\(766\) −7.02944 12.1753i −0.253984 0.439913i
\(767\) 0 0
\(768\) 0 0
\(769\) −7.15685 12.3960i −0.258083 0.447012i 0.707646 0.706568i \(-0.249757\pi\)
−0.965728 + 0.259555i \(0.916424\pi\)
\(770\) −1.07107 1.85514i −0.0385986 0.0668547i
\(771\) 0 0
\(772\) 45.3431 1.63194
\(773\) −11.0000 19.0526i −0.395643 0.685273i 0.597540 0.801839i \(-0.296145\pi\)
−0.993183 + 0.116566i \(0.962811\pi\)
\(774\) 0 0
\(775\) 2.50000 + 4.33013i 0.0898027 + 0.155543i
\(776\) −4.75736 + 8.23999i −0.170779 + 0.295798i
\(777\) 0 0
\(778\) 6.40202 0.229524
\(779\) 1.41421 12.2474i 0.0506695 0.438810i
\(780\) 0 0
\(781\) 14.1421 24.4949i 0.506045 0.876496i
\(782\) −0.201010 + 0.348160i −0.00718811 + 0.0124502i
\(783\)