Properties

Label 285.2.i.d.106.2
Level $285$
Weight $2$
Character 285.106
Analytic conductor $2.276$
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] = [285,2,Mod(106,285)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(285, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("285.106");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 285 = 3 \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 285.i (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: \(2.27573645761\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 106.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 285.106
Dual form 285.2.i.d.121.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.207107 - 0.358719i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.207107 - 0.358719i) q^{6} +1.82843 q^{7} +1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.207107 - 0.358719i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.914214 + 1.58346i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.207107 - 0.358719i) q^{6} +1.82843 q^{7} +1.58579 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.207107 - 0.358719i) q^{10} -2.82843 q^{11} +1.82843 q^{12} +(0.914214 + 1.58346i) q^{13} +(0.378680 - 0.655892i) q^{14} +(-0.500000 - 0.866025i) q^{15} +(-1.50000 + 2.59808i) q^{16} +(0.585786 - 1.01461i) q^{17} -0.414214 q^{18} +(4.00000 - 1.73205i) q^{19} +1.82843 q^{20} +(0.914214 - 1.58346i) q^{21} +(-0.585786 + 1.01461i) q^{22} +(0.414214 + 0.717439i) q^{23} +(0.792893 - 1.37333i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.757359 q^{26} -1.00000 q^{27} +(1.67157 + 2.89525i) q^{28} +(-4.82843 - 8.36308i) q^{29} -0.414214 q^{30} -5.00000 q^{31} +(2.20711 + 3.82282i) q^{32} +(-1.41421 + 2.44949i) q^{33} +(-0.242641 - 0.420266i) q^{34} +(0.914214 - 1.58346i) q^{35} +(0.914214 - 1.58346i) q^{36} -2.17157 q^{37} +(0.207107 - 1.79360i) q^{38} +1.82843 q^{39} +(0.792893 - 1.37333i) q^{40} +(-1.41421 + 2.44949i) q^{41} +(-0.378680 - 0.655892i) q^{42} +(-3.91421 + 6.77962i) q^{43} +(-2.58579 - 4.47871i) q^{44} -1.00000 q^{45} +0.343146 q^{46} +(1.58579 + 2.74666i) q^{47} +(1.50000 + 2.59808i) q^{48} -3.65685 q^{49} -0.414214 q^{50} +(-0.585786 - 1.01461i) q^{51} +(-1.67157 + 2.89525i) q^{52} +(1.00000 + 1.73205i) q^{53} +(-0.207107 + 0.358719i) q^{54} +(-1.41421 + 2.44949i) q^{55} +2.89949 q^{56} +(0.500000 - 4.33013i) q^{57} -4.00000 q^{58} +(0.914214 - 1.58346i) q^{60} +(4.15685 + 7.19988i) q^{61} +(-1.03553 + 1.79360i) q^{62} +(-0.914214 - 1.58346i) q^{63} -4.17157 q^{64} +1.82843 q^{65} +(0.585786 + 1.01461i) q^{66} +(-2.74264 - 4.75039i) q^{67} +2.14214 q^{68} +0.828427 q^{69} +(-0.378680 - 0.655892i) q^{70} +(-5.00000 + 8.66025i) q^{71} +(-0.792893 - 1.37333i) q^{72} +(-4.74264 + 8.21449i) q^{73} +(-0.449747 + 0.778985i) q^{74} -1.00000 q^{75} +(6.39949 + 4.75039i) q^{76} -5.17157 q^{77} +(0.378680 - 0.655892i) q^{78} +(1.67157 - 2.89525i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.585786 + 1.01461i) q^{82} -8.00000 q^{83} +3.34315 q^{84} +(-0.585786 - 1.01461i) q^{85} +(1.62132 + 2.80821i) q^{86} -9.65685 q^{87} -4.48528 q^{88} +(-6.24264 - 10.8126i) q^{89} +(-0.207107 + 0.358719i) q^{90} +(1.67157 + 2.89525i) q^{91} +(-0.757359 + 1.31178i) q^{92} +(-2.50000 + 4.33013i) q^{93} +1.31371 q^{94} +(0.500000 - 4.33013i) q^{95} +4.41421 q^{96} +(3.00000 - 5.19615i) q^{97} +(-0.757359 + 1.31178i) q^{98} +(1.41421 + 2.44949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} + 2 q^{6} - 4 q^{7} + 12 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{12} - 2 q^{13} + 10 q^{14} - 2 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} + 16 q^{19} - 4 q^{20} - 2 q^{21} - 8 q^{22} - 4 q^{23} + 6 q^{24} - 2 q^{25} + 20 q^{26} - 4 q^{27} + 18 q^{28} - 8 q^{29} + 4 q^{30} - 20 q^{31} + 6 q^{32} + 16 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} - 2 q^{38} - 4 q^{39} + 6 q^{40} - 10 q^{42} - 10 q^{43} - 16 q^{44} - 4 q^{45} + 24 q^{46} + 12 q^{47} + 6 q^{48} + 8 q^{49} + 4 q^{50} - 8 q^{51} - 18 q^{52} + 4 q^{53} + 2 q^{54} - 28 q^{56} + 2 q^{57} - 16 q^{58} - 2 q^{60} - 6 q^{61} + 10 q^{62} + 2 q^{63} - 28 q^{64} - 4 q^{65} + 8 q^{66} + 6 q^{67} - 48 q^{68} - 8 q^{69} - 10 q^{70} - 20 q^{71} - 6 q^{72} - 2 q^{73} + 18 q^{74} - 4 q^{75} - 14 q^{76} - 32 q^{77} + 10 q^{78} + 18 q^{79} + 6 q^{80} - 2 q^{81} + 8 q^{82} - 32 q^{83} + 36 q^{84} - 8 q^{85} - 2 q^{86} - 16 q^{87} + 16 q^{88} - 8 q^{89} + 2 q^{90} + 18 q^{91} - 20 q^{92} - 10 q^{93} - 40 q^{94} + 2 q^{95} + 12 q^{96} + 12 q^{97} - 20 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/285\mathbb{Z}\right)^\times\).

\(n\) \(172\) \(191\) \(211\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.783465 0.621436i \(-0.786550\pi\)
0.929912 + 0.367783i \(0.119883\pi\)
\(3\) 0.500000 0.866025i 0.288675 0.500000i
\(4\) 0.914214 + 1.58346i 0.457107 + 0.791732i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −0.207107 0.358719i −0.0845510 0.146447i
\(7\) 1.82843 0.691080 0.345540 0.938404i \(-0.387696\pi\)
0.345540 + 0.938404i \(0.387696\pi\)
\(8\) 1.58579 0.560660
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.207107 0.358719i −0.0654929 0.113437i
\(11\) −2.82843 −0.852803 −0.426401 0.904534i \(-0.640219\pi\)
−0.426401 + 0.904534i \(0.640219\pi\)
\(12\) 1.82843 0.527821
\(13\) 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
\(15\) −0.500000 0.866025i −0.129099 0.223607i
\(16\) −1.50000 + 2.59808i −0.375000 + 0.649519i
\(17\) 0.585786 1.01461i 0.142074 0.246080i −0.786203 0.617968i \(-0.787956\pi\)
0.928278 + 0.371888i \(0.121290\pi\)
\(18\) −0.414214 −0.0976311
\(19\) 4.00000 1.73205i 0.917663 0.397360i
\(20\) 1.82843 0.408849
\(21\) 0.914214 1.58346i 0.199498 0.345540i
\(22\) −0.585786 + 1.01461i −0.124890 + 0.216316i
\(23\) 0.414214 + 0.717439i 0.0863695 + 0.149596i 0.905974 0.423333i \(-0.139140\pi\)
−0.819604 + 0.572930i \(0.805807\pi\)
\(24\) 0.792893 1.37333i 0.161849 0.280330i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0.757359 0.148530
\(27\) −1.00000 −0.192450
\(28\) 1.67157 + 2.89525i 0.315898 + 0.547151i
\(29\) −4.82843 8.36308i −0.896616 1.55299i −0.831791 0.555089i \(-0.812684\pi\)
−0.0648251 0.997897i \(-0.520649\pi\)
\(30\) −0.414214 −0.0756247
\(31\) −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
\(33\) −1.41421 + 2.44949i −0.246183 + 0.426401i
\(34\) −0.242641 0.420266i −0.0416125 0.0720750i
\(35\) 0.914214 1.58346i 0.154530 0.267654i
\(36\) 0.914214 1.58346i 0.152369 0.263911i
\(37\) −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
\(39\) 1.82843 0.292783
\(40\) 0.792893 1.37333i 0.125367 0.217143i
\(41\) −1.41421 + 2.44949i −0.220863 + 0.382546i −0.955070 0.296379i \(-0.904221\pi\)
0.734207 + 0.678925i \(0.237554\pi\)
\(42\) −0.378680 0.655892i −0.0584315 0.101206i
\(43\) −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
\(45\) −1.00000 −0.149071
\(46\) 0.343146 0.0505941
\(47\) 1.58579 + 2.74666i 0.231311 + 0.400642i 0.958194 0.286119i \(-0.0923653\pi\)
−0.726883 + 0.686761i \(0.759032\pi\)
\(48\) 1.50000 + 2.59808i 0.216506 + 0.375000i
\(49\) −3.65685 −0.522408
\(50\) −0.414214 −0.0585786
\(51\) −0.585786 1.01461i −0.0820265 0.142074i
\(52\) −1.67157 + 2.89525i −0.231805 + 0.401499i
\(53\) 1.00000 + 1.73205i 0.137361 + 0.237915i 0.926497 0.376303i \(-0.122805\pi\)
−0.789136 + 0.614218i \(0.789471\pi\)
\(54\) −0.207107 + 0.358719i −0.0281837 + 0.0488155i
\(55\) −1.41421 + 2.44949i −0.190693 + 0.330289i
\(56\) 2.89949 0.387461
\(57\) 0.500000 4.33013i 0.0662266 0.573539i
\(58\) −4.00000 −0.525226
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 0.914214 1.58346i 0.118024 0.204424i
\(61\) 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
\(63\) −0.914214 1.58346i −0.115180 0.199498i
\(64\) −4.17157 −0.521447
\(65\) 1.82843 0.226788
\(66\) 0.585786 + 1.01461i 0.0721053 + 0.124890i
\(67\) −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
\(69\) 0.828427 0.0997309
\(70\) −0.378680 0.655892i −0.0452609 0.0783941i
\(71\) −5.00000 + 8.66025i −0.593391 + 1.02778i 0.400381 + 0.916349i \(0.368878\pi\)
−0.993772 + 0.111434i \(0.964456\pi\)
\(72\) −0.792893 1.37333i −0.0934434 0.161849i
\(73\) −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
\(75\) −1.00000 −0.115470
\(76\) 6.39949 + 4.75039i 0.734072 + 0.544907i
\(77\) −5.17157 −0.589355
\(78\) 0.378680 0.655892i 0.0428770 0.0742652i
\(79\) 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
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0.585786 + 1.01461i 0.0646893 + 0.112045i
\(83\) −8.00000 −0.878114 −0.439057 0.898459i \(-0.644687\pi\)
−0.439057 + 0.898459i \(0.644687\pi\)
\(84\) 3.34315 0.364767
\(85\) −0.585786 1.01461i −0.0635375 0.110050i
\(86\) 1.62132 + 2.80821i 0.174831 + 0.302817i
\(87\) −9.65685 −1.03532
\(88\) −4.48528 −0.478133
\(89\) −6.24264 10.8126i −0.661719 1.14613i −0.980164 0.198189i \(-0.936494\pi\)
0.318445 0.947941i \(-0.396839\pi\)
\(90\) −0.207107 + 0.358719i −0.0218310 + 0.0378124i
\(91\) 1.67157 + 2.89525i 0.175228 + 0.303505i
\(92\) −0.757359 + 1.31178i −0.0789602 + 0.136763i
\(93\) −2.50000 + 4.33013i −0.259238 + 0.449013i
\(94\) 1.31371 0.135499
\(95\) 0.500000 4.33013i 0.0512989 0.444262i
\(96\) 4.41421 0.450524
\(97\) 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
\(99\) 1.41421 + 2.44949i 0.142134 + 0.246183i
\(100\) 0.914214 1.58346i 0.0914214 0.158346i
\(101\) −6.07107 10.5154i −0.604094 1.04632i −0.992194 0.124704i \(-0.960202\pi\)
0.388100 0.921617i \(-0.373131\pi\)
\(102\) −0.485281 −0.0480500
\(103\) 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
\(105\) −0.914214 1.58346i −0.0892181 0.154530i
\(106\) 0.828427 0.0804640
\(107\) 14.0000 1.35343 0.676716 0.736245i \(-0.263403\pi\)
0.676716 + 0.736245i \(0.263403\pi\)
\(108\) −0.914214 1.58346i −0.0879702 0.152369i
\(109\) 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
\(111\) −1.08579 + 1.88064i −0.103058 + 0.178502i
\(112\) −2.74264 + 4.75039i −0.259155 + 0.448870i
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) −1.44975 1.07616i −0.135781 0.100791i
\(115\) 0.828427 0.0772512
\(116\) 8.82843 15.2913i 0.819699 1.41976i
\(117\) 0.914214 1.58346i 0.0845191 0.146391i
\(118\) 0 0
\(119\) 1.07107 1.85514i 0.0981846 0.170061i
\(120\) −0.792893 1.37333i −0.0723809 0.125367i
\(121\) −3.00000 −0.272727
\(122\) 3.44365 0.311773
\(123\) 1.41421 + 2.44949i 0.127515 + 0.220863i
\(124\) −4.57107 7.91732i −0.410494 0.710996i
\(125\) −1.00000 −0.0894427
\(126\) −0.757359 −0.0674709
\(127\) −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
\(129\) 3.91421 + 6.77962i 0.344627 + 0.596912i
\(130\) 0.378680 0.655892i 0.0332124 0.0575256i
\(131\) −3.24264 + 5.61642i −0.283311 + 0.490709i −0.972198 0.234160i \(-0.924766\pi\)
0.688887 + 0.724868i \(0.258099\pi\)
\(132\) −5.17157 −0.450128
\(133\) 7.31371 3.16693i 0.634179 0.274608i
\(134\) −2.27208 −0.196278
\(135\) −0.500000 + 0.866025i −0.0430331 + 0.0745356i
\(136\) 0.928932 1.60896i 0.0796553 0.137967i
\(137\) 5.24264 + 9.08052i 0.447909 + 0.775801i 0.998250 0.0591390i \(-0.0188355\pi\)
−0.550341 + 0.834940i \(0.685502\pi\)
\(138\) 0.171573 0.297173i 0.0146053 0.0252970i
\(139\) 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
\(141\) 3.17157 0.267095
\(142\) 2.07107 + 3.58719i 0.173800 + 0.301031i
\(143\) −2.58579 4.47871i −0.216234 0.374529i
\(144\) 3.00000 0.250000
\(145\) −9.65685 −0.801958
\(146\) 1.96447 + 3.40256i 0.162580 + 0.281597i
\(147\) −1.82843 + 3.16693i −0.150806 + 0.261204i
\(148\) −1.98528 3.43861i −0.163189 0.282652i
\(149\) 0.585786 1.01461i 0.0479895 0.0831202i −0.841033 0.540984i \(-0.818052\pi\)
0.889022 + 0.457864i \(0.151385\pi\)
\(150\) −0.207107 + 0.358719i −0.0169102 + 0.0292893i
\(151\) 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
\(153\) −1.17157 −0.0947161
\(154\) −1.07107 + 1.85514i −0.0863091 + 0.149492i
\(155\) −2.50000 + 4.33013i −0.200805 + 0.347804i
\(156\) 1.67157 + 2.89525i 0.133833 + 0.231805i
\(157\) 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
\(159\) 2.00000 0.158610
\(160\) 4.41421 0.348974
\(161\) 0.757359 + 1.31178i 0.0596883 + 0.103383i
\(162\) 0.207107 + 0.358719i 0.0162718 + 0.0281837i
\(163\) 15.1421 1.18602 0.593012 0.805194i \(-0.297939\pi\)
0.593012 + 0.805194i \(0.297939\pi\)
\(164\) −5.17157 −0.403832
\(165\) 1.41421 + 2.44949i 0.110096 + 0.190693i
\(166\) −1.65685 + 2.86976i −0.128597 + 0.222736i
\(167\) 12.4853 + 21.6251i 0.966140 + 1.67340i 0.706520 + 0.707693i \(0.250264\pi\)
0.259620 + 0.965711i \(0.416403\pi\)
\(168\) 1.44975 2.51104i 0.111850 0.193731i
\(169\) 4.82843 8.36308i 0.371417 0.643314i
\(170\) −0.485281 −0.0372194
\(171\) −3.50000 2.59808i −0.267652 0.198680i
\(172\) −14.3137 −1.09141
\(173\) −3.65685 + 6.33386i −0.278025 + 0.481554i −0.970894 0.239510i \(-0.923013\pi\)
0.692868 + 0.721064i \(0.256347\pi\)
\(174\) −2.00000 + 3.46410i −0.151620 + 0.262613i
\(175\) −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 \(-0.293868\pi\)
0.603260 + 0.797545i \(0.293868\pi\)
\(180\) −0.914214 1.58346i −0.0681415 0.118024i
\(181\) −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
\(183\) 8.31371 0.614567
\(184\) 0.656854 + 1.13770i 0.0484239 + 0.0838727i
\(185\) −1.08579 + 1.88064i −0.0798286 + 0.138267i
\(186\) 1.03553 + 1.79360i 0.0759290 + 0.131513i
\(187\) −1.65685 + 2.86976i −0.121161 + 0.209857i
\(188\) −2.89949 + 5.02207i −0.211467 + 0.366272i
\(189\) −1.82843 −0.132999
\(190\) −1.44975 1.07616i −0.105176 0.0780727i
\(191\) −16.8284 −1.21766 −0.608831 0.793300i \(-0.708361\pi\)
−0.608831 + 0.793300i \(0.708361\pi\)
\(192\) −2.08579 + 3.61269i −0.150529 + 0.260723i
\(193\) 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
\(195\) 0.914214 1.58346i 0.0654682 0.113394i
\(196\) −3.34315 5.79050i −0.238796 0.413607i
\(197\) 17.6569 1.25800 0.628999 0.777406i \(-0.283465\pi\)
0.628999 + 0.777406i \(0.283465\pi\)
\(198\) 1.17157 0.0832601
\(199\) 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
\(201\) −5.48528 −0.386902
\(202\) −5.02944 −0.353870
\(203\) −8.82843 15.2913i −0.619634 1.07324i
\(204\) 1.07107 1.85514i 0.0749897 0.129886i
\(205\) 1.41421 + 2.44949i 0.0987730 + 0.171080i
\(206\) 2.03553 3.52565i 0.141822 0.245644i
\(207\) 0.414214 0.717439i 0.0287898 0.0498655i
\(208\) −5.48528 −0.380336
\(209\) −11.3137 + 4.89898i −0.782586 + 0.338869i
\(210\) −0.757359 −0.0522628
\(211\) 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
\(213\) 5.00000 + 8.66025i 0.342594 + 0.593391i
\(214\) 2.89949 5.02207i 0.198205 0.343302i
\(215\) 3.91421 + 6.77962i 0.266947 + 0.462366i
\(216\) −1.58579 −0.107899
\(217\) −9.14214 −0.620609
\(218\) −3.58579 6.21076i −0.242860 0.420646i
\(219\) 4.74264 + 8.21449i 0.320478 + 0.555084i
\(220\) −5.17157 −0.348667
\(221\) 2.14214 0.144096
\(222\) 0.449747 + 0.778985i 0.0301851 + 0.0522821i
\(223\) −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
\(225\) −0.500000 + 0.866025i −0.0333333 + 0.0577350i
\(226\) 0.828427 1.43488i 0.0551062 0.0954467i
\(227\) −18.9706 −1.25912 −0.629560 0.776952i \(-0.716765\pi\)
−0.629560 + 0.776952i \(0.716765\pi\)
\(228\) 7.31371 3.16693i 0.484362 0.209735i
\(229\) −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
\(231\) −2.58579 + 4.47871i −0.170132 + 0.294678i
\(232\) −7.65685 13.2621i −0.502697 0.870697i
\(233\) 12.6569 21.9223i 0.829178 1.43618i −0.0695057 0.997582i \(-0.522142\pi\)
0.898684 0.438597i \(-0.144524\pi\)
\(234\) −0.378680 0.655892i −0.0247551 0.0428770i
\(235\) 3.17157 0.206891
\(236\) 0 0
\(237\) −1.67157 2.89525i −0.108580 0.188067i
\(238\) −0.443651 0.768426i −0.0287576 0.0498096i
\(239\) −24.6274 −1.59302 −0.796508 0.604629i \(-0.793322\pi\)
−0.796508 + 0.604629i \(0.793322\pi\)
\(240\) 3.00000 0.193649
\(241\) −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
\(243\) 0.500000 + 0.866025i 0.0320750 + 0.0555556i
\(244\) −7.60051 + 13.1645i −0.486572 + 0.842768i
\(245\) −1.82843 + 3.16693i −0.116814 + 0.202328i
\(246\) 1.17157 0.0746968
\(247\) 6.39949 + 4.75039i 0.407190 + 0.302260i
\(248\) −7.92893 −0.503488
\(249\) −4.00000 + 6.92820i −0.253490 + 0.439057i
\(250\) −0.207107 + 0.358719i −0.0130986 + 0.0226874i
\(251\) 8.17157 + 14.1536i 0.515785 + 0.893366i 0.999832 + 0.0183240i \(0.00583304\pi\)
−0.484047 + 0.875042i \(0.660834\pi\)
\(252\) 1.67157 2.89525i 0.105299 0.182384i
\(253\) −1.17157 2.02922i −0.0736562 0.127576i
\(254\) −5.37258 −0.337106
\(255\) −1.17157 −0.0733667
\(256\) −1.98528 3.43861i −0.124080 0.214913i
\(257\) 8.41421 + 14.5738i 0.524864 + 0.909091i 0.999581 + 0.0289528i \(0.00921724\pi\)
−0.474717 + 0.880139i \(0.657449\pi\)
\(258\) 3.24264 0.201878
\(259\) −3.97056 −0.246719
\(260\) 1.67157 + 2.89525i 0.103667 + 0.179556i
\(261\) −4.82843 + 8.36308i −0.298872 + 0.517662i
\(262\) 1.34315 + 2.32640i 0.0829798 + 0.143725i
\(263\) −12.8995 + 22.3426i −0.795417 + 1.37770i 0.127157 + 0.991883i \(0.459415\pi\)
−0.922574 + 0.385820i \(0.873919\pi\)
\(264\) −2.24264 + 3.88437i −0.138025 + 0.239066i
\(265\) 2.00000 0.122859
\(266\) 0.378680 3.27946i 0.0232183 0.201077i
\(267\) −12.4853 −0.764087
\(268\) 5.01472 8.68575i 0.306323 0.530566i
\(269\) −0.828427 + 1.43488i −0.0505101 + 0.0874860i −0.890175 0.455619i \(-0.849418\pi\)
0.839665 + 0.543105i \(0.182751\pi\)
\(270\) 0.207107 + 0.358719i 0.0126041 + 0.0218310i
\(271\) −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
\(273\) 3.34315 0.202336
\(274\) 4.34315 0.262379
\(275\) 1.41421 + 2.44949i 0.0852803 + 0.147710i
\(276\) 0.757359 + 1.31178i 0.0455877 + 0.0789602i
\(277\) 6.00000 0.360505 0.180253 0.983620i \(-0.442309\pi\)
0.180253 + 0.983620i \(0.442309\pi\)
\(278\) 6.75736 0.405279
\(279\) 2.50000 + 4.33013i 0.149671 + 0.259238i
\(280\) 1.44975 2.51104i 0.0866390 0.150063i
\(281\) 3.48528 + 6.03668i 0.207914 + 0.360118i 0.951057 0.309014i \(-0.0999991\pi\)
−0.743143 + 0.669133i \(0.766666\pi\)
\(282\) 0.656854 1.13770i 0.0391151 0.0677493i
\(283\) 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
\(285\) −3.50000 2.59808i −0.207322 0.153897i
\(286\) −2.14214 −0.126667
\(287\) −2.58579 + 4.47871i −0.152634 + 0.264370i
\(288\) 2.20711 3.82282i 0.130055 0.225262i
\(289\) 7.81371 + 13.5337i 0.459630 + 0.796102i
\(290\) −2.00000 + 3.46410i −0.117444 + 0.203419i
\(291\) −3.00000 5.19615i −0.175863 0.304604i
\(292\) −17.3431 −1.01493
\(293\) −5.31371 −0.310430 −0.155215 0.987881i \(-0.549607\pi\)
−0.155215 + 0.987881i \(0.549607\pi\)
\(294\) 0.757359 + 1.31178i 0.0441701 + 0.0765048i
\(295\) 0 0
\(296\) −3.44365 −0.200158
\(297\) 2.82843 0.164122
\(298\) −0.242641 0.420266i −0.0140558 0.0243454i
\(299\) −0.757359 + 1.31178i −0.0437992 + 0.0758625i
\(300\) −0.914214 1.58346i −0.0527821 0.0914214i
\(301\) −7.15685 + 12.3960i −0.412514 + 0.714496i
\(302\) 2.14214 3.71029i 0.123266 0.213503i
\(303\) −12.1421 −0.697547
\(304\) −1.50000 + 12.9904i −0.0860309 + 0.745049i
\(305\) 8.31371 0.476042
\(306\) −0.242641 + 0.420266i −0.0138708 + 0.0240250i
\(307\) 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
\(309\) 4.91421 8.51167i 0.279560 0.484212i
\(310\) 1.03553 + 1.79360i 0.0588144 + 0.101869i
\(311\) −4.00000 −0.226819 −0.113410 0.993548i \(-0.536177\pi\)
−0.113410 + 0.993548i \(0.536177\pi\)
\(312\) 2.89949 0.164152
\(313\) 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
\(315\) −1.82843 −0.103020
\(316\) 6.11270 0.343866
\(317\) −2.65685 4.60181i −0.149224 0.258463i 0.781717 0.623633i \(-0.214344\pi\)
−0.930941 + 0.365170i \(0.881011\pi\)
\(318\) 0.414214 0.717439i 0.0232279 0.0402320i
\(319\) 13.6569 + 23.6544i 0.764637 + 1.32439i
\(320\) −2.08579 + 3.61269i −0.116599 + 0.201955i
\(321\) 7.00000 12.1244i 0.390702 0.676716i
\(322\) 0.627417 0.0349646
\(323\) 0.585786 5.07306i 0.0325940 0.282273i
\(324\) −1.82843 −0.101579
\(325\) 0.914214 1.58346i 0.0507114 0.0878348i
\(326\) 3.13604 5.43178i 0.173689 0.300838i
\(327\) −8.65685 14.9941i −0.478725 0.829176i
\(328\) −2.24264 + 3.88437i −0.123829 + 0.214478i
\(329\) 2.89949 + 5.02207i 0.159854 + 0.276876i
\(330\) 1.17157 0.0644930
\(331\) −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
\(333\) 1.08579 + 1.88064i 0.0595007 + 0.103058i
\(334\) 10.3431 0.565952
\(335\) −5.48528 −0.299693
\(336\) 2.74264 + 4.75039i 0.149623 + 0.259155i
\(337\) −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
\(339\) 2.00000 3.46410i 0.108625 0.188144i
\(340\) 1.07107 1.85514i 0.0580868 0.100609i
\(341\) 14.1421 0.765840
\(342\) −1.65685 + 0.717439i −0.0895924 + 0.0387947i
\(343\) −19.4853 −1.05211
\(344\) −6.20711 + 10.7510i −0.334665 + 0.579656i
\(345\) 0.414214 0.717439i 0.0223005 0.0386256i
\(346\) 1.51472 + 2.62357i 0.0814318 + 0.141044i
\(347\) 17.7279 30.7057i 0.951685 1.64837i 0.209906 0.977722i \(-0.432684\pi\)
0.741779 0.670645i \(-0.233982\pi\)
\(348\) −8.82843 15.2913i −0.473253 0.819699i
\(349\) −31.6274 −1.69298 −0.846488 0.532407i \(-0.821288\pi\)
−0.846488 + 0.532407i \(0.821288\pi\)
\(350\) −0.757359 −0.0404826
\(351\) −0.914214 1.58346i −0.0487971 0.0845191i
\(352\) −6.24264 10.8126i −0.332734 0.576312i
\(353\) −1.31371 −0.0699216 −0.0349608 0.999389i \(-0.511131\pi\)
−0.0349608 + 0.999389i \(0.511131\pi\)
\(354\) 0 0
\(355\) 5.00000 + 8.66025i 0.265372 + 0.459639i
\(356\) 11.4142 19.7700i 0.604952 1.04781i
\(357\) −1.07107 1.85514i −0.0566869 0.0981846i
\(358\) 3.34315 5.79050i 0.176691 0.306037i
\(359\) −4.58579 + 7.94282i −0.242029 + 0.419206i −0.961292 0.275532i \(-0.911146\pi\)
0.719263 + 0.694737i \(0.244479\pi\)
\(360\) −1.58579 −0.0835783
\(361\) 13.0000 13.8564i 0.684211 0.729285i
\(362\) −10.4853 −0.551094
\(363\) −1.50000 + 2.59808i −0.0787296 + 0.136364i
\(364\) −3.05635 + 5.29375i −0.160196 + 0.277468i
\(365\) 4.74264 + 8.21449i 0.248241 + 0.429966i
\(366\) 1.72183 2.98229i 0.0900013 0.155887i
\(367\) 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
\(369\) 2.82843 0.147242
\(370\) 0.449747 + 0.778985i 0.0233813 + 0.0404975i
\(371\) 1.82843 + 3.16693i 0.0949272 + 0.164419i
\(372\) −9.14214 −0.473998
\(373\) −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
\(375\) −0.500000 + 0.866025i −0.0258199 + 0.0447214i
\(376\) 2.51472 + 4.35562i 0.129687 + 0.224624i
\(377\) 8.82843 15.2913i 0.454687 0.787541i
\(378\) −0.378680 + 0.655892i −0.0194772 + 0.0337355i
\(379\) 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
\(381\) −12.9706 −0.664502
\(382\) −3.48528 + 6.03668i −0.178323 + 0.308864i
\(383\) 16.9706 29.3939i 0.867155 1.50196i 0.00226413 0.999997i \(-0.499279\pi\)
0.864891 0.501960i \(-0.167387\pi\)
\(384\) 5.27817 + 9.14207i 0.269351 + 0.466529i
\(385\) −2.58579 + 4.47871i −0.131784 + 0.228256i
\(386\) −5.13604 8.89588i −0.261418 0.452788i
\(387\) 7.82843 0.397941
\(388\) 10.9706 0.556946
\(389\) 7.72792 + 13.3852i 0.391821 + 0.678654i 0.992690 0.120694i \(-0.0385118\pi\)
−0.600869 + 0.799348i \(0.705179\pi\)
\(390\) −0.378680 0.655892i −0.0191752 0.0332124i
\(391\) 0.970563 0.0490835
\(392\) −5.79899 −0.292893
\(393\) 3.24264 + 5.61642i 0.163570 + 0.283311i
\(394\) 3.65685 6.33386i 0.184230 0.319095i
\(395\) −1.67157 2.89525i −0.0841060 0.145676i
\(396\) −2.58579 + 4.47871i −0.129941 + 0.225064i
\(397\) 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
\(399\) 0.914214 7.91732i 0.0457679 0.396362i
\(400\) 3.00000 0.150000
\(401\) 11.3137 19.5959i 0.564980 0.978573i −0.432072 0.901839i \(-0.642217\pi\)
0.997052 0.0767343i \(-0.0244493\pi\)
\(402\) −1.13604 + 1.96768i −0.0566605 + 0.0981388i
\(403\) −4.57107 7.91732i −0.227701 0.394390i
\(404\) 11.1005 19.2266i 0.552271 0.956561i
\(405\) 0.500000 + 0.866025i 0.0248452 + 0.0430331i
\(406\) −7.31371 −0.362973
\(407\) 6.14214 0.304454
\(408\) −0.928932 1.60896i −0.0459890 0.0796553i
\(409\) −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
\(411\) 10.4853 0.517201
\(412\) 8.98528 + 15.5630i 0.442673 + 0.766732i
\(413\) 0 0
\(414\) −0.171573 0.297173i −0.00843235 0.0146053i
\(415\) −4.00000 + 6.92820i −0.196352 + 0.340092i
\(416\) −4.03553 + 6.98975i −0.197858 + 0.342701i
\(417\) 16.3137 0.798886
\(418\) −0.585786 + 5.07306i −0.0286518 + 0.248131i
\(419\) 3.31371 0.161885 0.0809426 0.996719i \(-0.474207\pi\)
0.0809426 + 0.996719i \(0.474207\pi\)
\(420\) 1.67157 2.89525i 0.0815644 0.141274i
\(421\) 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
\(423\) 1.58579 2.74666i 0.0771036 0.133547i
\(424\) 1.58579 + 2.74666i 0.0770126 + 0.133390i
\(425\) −1.17157 −0.0568296
\(426\) 4.14214 0.200687
\(427\) 7.60051 + 13.1645i 0.367814 + 0.637073i
\(428\) 12.7990 + 22.1685i 0.618663 + 1.07155i
\(429\) −5.17157 −0.249686
\(430\) 3.24264 0.156374
\(431\) 1.24264 + 2.15232i 0.0598559 + 0.103673i 0.894401 0.447267i \(-0.147603\pi\)
−0.834545 + 0.550940i \(0.814269\pi\)
\(432\) 1.50000 2.59808i 0.0721688 0.125000i
\(433\) 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
\(435\) −4.82843 + 8.36308i −0.231505 + 0.400979i
\(436\) 31.6569 1.51609
\(437\) 2.89949 + 2.15232i 0.138702 + 0.102959i
\(438\) 3.92893 0.187732
\(439\) −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
\(441\) 1.82843 + 3.16693i 0.0870680 + 0.150806i
\(442\) 0.443651 0.768426i 0.0211023 0.0365503i
\(443\) −9.07107 15.7116i −0.430979 0.746478i 0.565978 0.824420i \(-0.308499\pi\)
−0.996958 + 0.0779417i \(0.975165\pi\)
\(444\) −3.97056 −0.188435
\(445\) −12.4853 −0.591859
\(446\) 1.20711 + 2.09077i 0.0571582 + 0.0990008i
\(447\) −0.585786 1.01461i −0.0277067 0.0479895i
\(448\) −7.62742 −0.360362
\(449\) 13.1716 0.621605 0.310802 0.950475i \(-0.399402\pi\)
0.310802 + 0.950475i \(0.399402\pi\)
\(450\) 0.207107 + 0.358719i 0.00976311 + 0.0169102i
\(451\) 4.00000 6.92820i 0.188353 0.326236i
\(452\) 3.65685 + 6.33386i 0.172004 + 0.297920i
\(453\) 5.17157 8.95743i 0.242982 0.420857i
\(454\) −3.92893 + 6.80511i −0.184394 + 0.319380i
\(455\) 3.34315 0.156729
\(456\) 0.792893 6.86666i 0.0371306 0.321561i
\(457\) −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
\(459\) −0.585786 + 1.01461i −0.0273422 + 0.0473580i
\(460\) 0.757359 + 1.31178i 0.0353121 + 0.0611623i
\(461\) −15.0711 + 26.1039i −0.701930 + 1.21578i 0.265859 + 0.964012i \(0.414345\pi\)
−0.967788 + 0.251766i \(0.918989\pi\)
\(462\) 1.07107 + 1.85514i 0.0498306 + 0.0863091i
\(463\) −22.7990 −1.05956 −0.529779 0.848135i \(-0.677725\pi\)
−0.529779 + 0.848135i \(0.677725\pi\)
\(464\) 28.9706 1.34492
\(465\) 2.50000 + 4.33013i 0.115935 + 0.200805i
\(466\) −5.24264 9.08052i −0.242861 0.420647i
\(467\) 23.7990 1.10129 0.550643 0.834741i \(-0.314383\pi\)
0.550643 + 0.834741i \(0.314383\pi\)
\(468\) 3.34315 0.154537
\(469\) −5.01472 8.68575i −0.231558 0.401071i
\(470\) 0.656854 1.13770i 0.0302984 0.0524784i
\(471\) −9.91421 17.1719i −0.456823 0.791240i
\(472\) 0 0
\(473\) 11.0711 19.1757i 0.509048 0.881697i
\(474\) −1.38478 −0.0636049
\(475\) −3.50000 2.59808i −0.160591 0.119208i
\(476\) 3.91674 0.179523
\(477\) 1.00000 1.73205i 0.0457869 0.0793052i
\(478\) −5.10051 + 8.83433i −0.233292 + 0.404073i
\(479\) −1.24264 2.15232i −0.0567777 0.0983419i 0.836240 0.548364i \(-0.184749\pi\)
−0.893017 + 0.450022i \(0.851416\pi\)
\(480\) 2.20711 3.82282i 0.100740 0.174487i
\(481\) −1.98528 3.43861i −0.0905210 0.156787i
\(482\) −2.07107 −0.0943346
\(483\) 1.51472 0.0689221
\(484\) −2.74264 4.75039i −0.124665 0.215927i
\(485\) −3.00000 5.19615i −0.136223 0.235945i
\(486\) 0.414214 0.0187891
\(487\) −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
\(489\) 7.57107 13.1135i 0.342376 0.593012i
\(490\) 0.757359 + 1.31178i 0.0342140 + 0.0592604i
\(491\) −11.8284 + 20.4874i −0.533809 + 0.924585i 0.465411 + 0.885095i \(0.345907\pi\)
−0.999220 + 0.0394901i \(0.987427\pi\)
\(492\) −2.58579 + 4.47871i −0.116576 + 0.201916i
\(493\) −11.3137 −0.509544
\(494\) 3.02944 1.31178i 0.136301 0.0590200i
\(495\) 2.82843 0.127128
\(496\) 7.50000 12.9904i 0.336760 0.583285i
\(497\) −9.14214 + 15.8346i −0.410081 + 0.710281i
\(498\) 1.65685 + 2.86976i 0.0742454 + 0.128597i
\(499\) 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
\(501\) 24.9706 1.11560
\(502\) 6.76955 0.302140
\(503\) −6.92893 12.0013i −0.308946 0.535110i 0.669186 0.743095i \(-0.266643\pi\)
−0.978132 + 0.207985i \(0.933310\pi\)
\(504\) −1.44975 2.51104i −0.0645769 0.111850i
\(505\) −12.1421 −0.540318
\(506\) −0.970563 −0.0431468
\(507\) −4.82843 8.36308i −0.214438 0.371417i
\(508\) 11.8579 20.5384i 0.526108 0.911245i
\(509\) −16.5563 28.6764i −0.733847 1.27106i −0.955227 0.295873i \(-0.904389\pi\)
0.221380 0.975188i \(-0.428944\pi\)
\(510\) −0.242641 + 0.420266i −0.0107443 + 0.0186097i
\(511\) −8.67157 + 15.0196i −0.383608 + 0.664428i
\(512\) −22.7574 −1.00574
\(513\) −4.00000 + 1.73205i −0.176604 + 0.0764719i
\(514\) 6.97056 0.307458
\(515\) 4.91421 8.51167i 0.216546 0.375069i
\(516\) −7.15685 + 12.3960i −0.315063 + 0.545705i
\(517\) −4.48528 7.76874i −0.197262 0.341669i
\(518\) −0.822330 + 1.42432i −0.0361311 + 0.0625809i
\(519\) 3.65685 + 6.33386i 0.160518 + 0.278025i
\(520\) 2.89949 0.127151
\(521\) 6.34315 0.277898 0.138949 0.990300i \(-0.455628\pi\)
0.138949 + 0.990300i \(0.455628\pi\)
\(522\) 2.00000 + 3.46410i 0.0875376 + 0.151620i
\(523\) 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
\(525\) −1.82843 −0.0797991
\(526\) 5.34315 + 9.25460i 0.232972 + 0.403520i
\(527\) −2.92893 + 5.07306i −0.127586 + 0.220986i
\(528\) −4.24264 7.34847i −0.184637 0.319801i
\(529\) 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
\(534\) −2.58579 + 4.47871i −0.111898 + 0.193813i
\(535\) 7.00000 12.1244i 0.302636 0.524182i
\(536\) −4.34924 7.53311i −0.187859 0.325381i
\(537\) 8.07107 13.9795i 0.348292 0.603260i
\(538\) 0.343146 + 0.594346i 0.0147941 + 0.0256241i
\(539\) 10.3431 0.445511
\(540\) −1.82843 −0.0786830
\(541\) −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
\(543\) −25.3137 −1.08632
\(544\) 5.17157 0.221729
\(545\) −8.65685 14.9941i −0.370819 0.642277i
\(546\) 0.692388 1.19925i 0.0296315 0.0513232i
\(547\) 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
\(549\) 4.15685 7.19988i 0.177410 0.307284i
\(550\) 1.17157 0.0499560
\(551\) −33.7990 25.0892i −1.43989 1.06884i
\(552\) 1.31371 0.0559151
\(553\) 3.05635 5.29375i 0.129969 0.225113i
\(554\) 1.24264 2.15232i 0.0527947 0.0914432i
\(555\) 1.08579 + 1.88064i 0.0460891 + 0.0798286i
\(556\) −14.9142 + 25.8322i −0.632504 + 1.09553i
\(557\) 4.51472 + 7.81972i 0.191295 + 0.331332i 0.945680 0.325100i \(-0.105398\pi\)
−0.754385 + 0.656432i \(0.772065\pi\)
\(558\) 2.07107 0.0876753
\(559\) −14.3137 −0.605405
\(560\) 2.74264 + 4.75039i 0.115898 + 0.200741i
\(561\) 1.65685 + 2.86976i 0.0699524 + 0.121161i
\(562\) 2.88730 0.121793
\(563\) −12.1421 −0.511730 −0.255865 0.966713i \(-0.582360\pi\)
−0.255865 + 0.966713i \(0.582360\pi\)
\(564\) 2.89949 + 5.02207i 0.122091 + 0.211467i
\(565\) 2.00000 3.46410i 0.0841406 0.145736i
\(566\) −4.34315 7.52255i −0.182556 0.316196i
\(567\) −0.914214 + 1.58346i −0.0383934 + 0.0664993i
\(568\) −7.92893 + 13.7333i −0.332691 + 0.576237i
\(569\) 4.97056 0.208377 0.104188 0.994558i \(-0.466776\pi\)
0.104188 + 0.994558i \(0.466776\pi\)
\(570\) −1.65685 + 0.717439i −0.0693980 + 0.0300502i
\(571\) 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
\(573\) −8.41421 + 14.5738i −0.351509 + 0.608831i
\(574\) 1.07107 + 1.85514i 0.0447055 + 0.0774322i
\(575\) 0.414214 0.717439i 0.0172739 0.0299193i
\(576\) 2.08579 + 3.61269i 0.0869078 + 0.150529i
\(577\) −36.3431 −1.51298 −0.756492 0.654002i \(-0.773089\pi\)
−0.756492 + 0.654002i \(0.773089\pi\)
\(578\) 6.47309 0.269245
\(579\) −12.3995 21.4766i −0.515305 0.892535i
\(580\) −8.82843 15.2913i −0.366580 0.634936i
\(581\) −14.6274 −0.606848
\(582\) −2.48528 −0.103018
\(583\) −2.82843 4.89898i −0.117141 0.202895i
\(584\) −7.52082 + 13.0264i −0.311214 + 0.539038i
\(585\) −0.914214 1.58346i −0.0377981 0.0654682i
\(586\) −1.10051 + 1.90613i −0.0454614 + 0.0787415i
\(587\) −5.31371 + 9.20361i −0.219320 + 0.379874i −0.954600 0.297890i \(-0.903717\pi\)
0.735280 + 0.677763i \(0.237051\pi\)
\(588\) −6.68629 −0.275738
\(589\) −20.0000 + 8.66025i −0.824086 + 0.356840i
\(590\) 0 0
\(591\) 8.82843 15.2913i 0.363153 0.628999i
\(592\) 3.25736 5.64191i 0.133877 0.231881i
\(593\) 4.92893 + 8.53716i 0.202407 + 0.350579i 0.949303 0.314361i \(-0.101790\pi\)
−0.746896 + 0.664940i \(0.768457\pi\)
\(594\) 0.585786 1.01461i 0.0240351 0.0416300i
\(595\) −1.07107 1.85514i −0.0439095 0.0760535i
\(596\) 2.14214 0.0877453
\(597\) 17.0000 0.695764
\(598\) 0.313708 + 0.543359i 0.0128285 + 0.0222196i
\(599\) 8.48528 + 14.6969i 0.346699 + 0.600501i 0.985661 0.168738i \(-0.0539691\pi\)
−0.638962 + 0.769238i \(0.720636\pi\)
\(600\) −1.58579 −0.0647395
\(601\) −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
\(603\) −2.74264 + 4.75039i −0.111689 + 0.193451i
\(604\) 9.45584 + 16.3780i 0.384753 + 0.666411i
\(605\) −1.50000 + 2.59808i −0.0609837 + 0.105627i
\(606\) −2.51472 + 4.35562i −0.102153 + 0.176935i
\(607\) −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
\(609\) −17.6569 −0.715492
\(610\) 1.72183 2.98229i 0.0697147 0.120749i
\(611\) −2.89949 + 5.02207i −0.117301 + 0.203171i
\(612\) −1.07107 1.85514i −0.0432954 0.0749897i
\(613\) −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
\(615\) 2.82843 0.114053
\(616\) −8.20101 −0.330428
\(617\) −12.8284 22.2195i −0.516453 0.894523i −0.999818 0.0191037i \(-0.993919\pi\)
0.483364 0.875419i \(-0.339415\pi\)
\(618\) −2.03553 3.52565i −0.0818812 0.141822i
\(619\) 15.6863 0.630485 0.315243 0.949011i \(-0.397914\pi\)
0.315243 + 0.949011i \(0.397914\pi\)
\(620\) −9.14214 −0.367157
\(621\) −0.414214 0.717439i −0.0166218 0.0287898i
\(622\) −0.828427 + 1.43488i −0.0332169 + 0.0575334i
\(623\) −11.4142 19.7700i −0.457301 0.792068i
\(624\) −2.74264 + 4.75039i −0.109793 + 0.190168i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 2.48528 0.0993318
\(627\) −1.41421 + 12.2474i −0.0564782 + 0.489116i
\(628\) 36.2548 1.44673
\(629\) −1.27208 + 2.20330i −0.0507211 + 0.0878515i
\(630\) −0.378680 + 0.655892i −0.0150870 + 0.0261314i
\(631\) 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
\(633\) −0.156854 0.271680i −0.00623440 0.0107983i
\(634\) −2.20101 −0.0874133
\(635\) −12.9706 −0.514721
\(636\) 1.82843 + 3.16693i 0.0725019 + 0.125577i
\(637\) −3.34315 5.79050i −0.132460 0.229428i
\(638\) 11.3137 0.447914
\(639\) 10.0000 0.395594
\(640\) 5.27817 + 9.14207i 0.208638 + 0.361372i
\(641\) −14.0711 + 24.3718i −0.555774 + 0.962628i 0.442069 + 0.896981i \(0.354245\pi\)
−0.997843 + 0.0656474i \(0.979089\pi\)
\(642\) −2.89949 5.02207i −0.114434 0.198205i
\(643\) −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
\(645\) 7.82843 0.308244
\(646\) −1.69848 1.26080i −0.0668260 0.0496054i
\(647\) −32.2843 −1.26923 −0.634613 0.772830i \(-0.718840\pi\)
−0.634613 + 0.772830i \(0.718840\pi\)
\(648\) −0.792893 + 1.37333i −0.0311478 + 0.0539496i
\(649\) 0 0
\(650\) −0.378680 0.655892i −0.0148530 0.0257262i
\(651\) −4.57107 + 7.91732i −0.179154 + 0.310304i
\(652\) 13.8431 + 23.9770i 0.542139 + 0.939013i
\(653\) 39.9411 1.56302 0.781509 0.623895i \(-0.214451\pi\)
0.781509 + 0.623895i \(0.214451\pi\)
\(654\) −7.17157 −0.280431
\(655\) 3.24264 + 5.61642i 0.126700 + 0.219452i
\(656\) −4.24264 7.34847i −0.165647 0.286910i
\(657\) 9.48528 0.370056
\(658\) 2.40202 0.0936405
\(659\) −3.75736 6.50794i −0.146366 0.253513i 0.783516 0.621372i \(-0.213424\pi\)
−0.929882 + 0.367859i \(0.880091\pi\)
\(660\) −2.58579 + 4.47871i −0.100652 + 0.174334i
\(661\) 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
\(663\) 1.07107 1.85514i 0.0415968 0.0720478i
\(664\) −12.6863 −0.492324
\(665\) 0.914214 7.91732i 0.0354517 0.307021i
\(666\) 0.899495 0.0348547
\(667\) 4.00000 6.92820i 0.154881 0.268261i
\(668\) −22.8284 + 39.5400i −0.883258 + 1.52985i
\(669\) 2.91421 + 5.04757i 0.112670 + 0.195150i
\(670\) −1.13604 + 1.96768i −0.0438890 + 0.0760180i
\(671\) −11.7574 20.3643i −0.453888 0.786157i
\(672\) 8.07107 0.311348
\(673\) −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
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 17.6569 0.679110
\(677\) −23.4558 −0.901481 −0.450741 0.892655i \(-0.648840\pi\)
−0.450741 + 0.892655i \(0.648840\pi\)
\(678\) −0.828427 1.43488i −0.0318156 0.0551062i
\(679\) 5.48528 9.50079i 0.210506 0.364607i
\(680\) −0.928932 1.60896i −0.0356229 0.0617007i
\(681\) −9.48528 + 16.4290i −0.363477 + 0.629560i
\(682\) 2.92893 5.07306i 0.112155 0.194257i
\(683\) 44.1421 1.68905 0.844526 0.535515i \(-0.179882\pi\)
0.844526 + 0.535515i \(0.179882\pi\)
\(684\) 0.914214 7.91732i 0.0349558 0.302726i
\(685\) 10.4853 0.400622
\(686\) −4.03553 + 6.98975i −0.154077 + 0.266870i
\(687\) −2.32843 + 4.03295i −0.0888350 + 0.153867i
\(688\) −11.7426 20.3389i −0.447684 0.775411i
\(689\) −1.82843 + 3.16693i −0.0696575 + 0.120650i
\(690\) −0.171573 0.297173i −0.00653167 0.0113132i
\(691\) 31.3137 1.19123 0.595615 0.803270i \(-0.296908\pi\)
0.595615 + 0.803270i \(0.296908\pi\)
\(692\) −13.3726 −0.508349
\(693\) 2.58579 + 4.47871i 0.0982259 + 0.170132i
\(694\) −7.34315 12.7187i −0.278742 0.482795i
\(695\) 16.3137 0.618814
\(696\) −15.3137 −0.580465
\(697\) 1.65685 + 2.86976i 0.0627578 + 0.108700i
\(698\) −6.55025 + 11.3454i −0.247931 + 0.429429i
\(699\) −12.6569 21.9223i −0.478726 0.829178i
\(700\) 1.67157 2.89525i 0.0631795 0.109430i
\(701\) −16.0711 + 27.8359i −0.606996 + 1.05135i 0.384737 + 0.923026i \(0.374292\pi\)
−0.991733 + 0.128321i \(0.959041\pi\)
\(702\) −0.757359 −0.0285847
\(703\) −8.68629 + 3.76127i −0.327610 + 0.141859i
\(704\) 11.7990 0.444691
\(705\) 1.58579 2.74666i 0.0597242 0.103445i
\(706\) −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
\(711\) −3.34315 −0.125378
\(712\) −9.89949 17.1464i −0.370999 0.642590i
\(713\) −2.07107 3.58719i −0.0775621 0.134341i
\(714\) −0.887302 −0.0332064
\(715\) −5.17157 −0.193406
\(716\) 14.7574 + 25.5605i 0.551508 + 0.955241i
\(717\) −12.3137 + 21.3280i −0.459864 + 0.796508i
\(718\) 1.89949 + 3.29002i 0.0708885 + 0.122783i
\(719\) 11.5858 20.0672i 0.432077 0.748379i −0.564975 0.825108i \(-0.691114\pi\)
0.997052 + 0.0767288i \(0.0244476\pi\)
\(720\) 1.50000 2.59808i 0.0559017 0.0968246i
\(721\) 17.9706 0.669259
\(722\) −2.27817 7.53311i −0.0847849 0.280353i
\(723\) −5.00000 −0.185952
\(724\) 23.1421 40.0834i 0.860071 1.48969i
\(725\) −4.82843 + 8.36308i −0.179323 + 0.310597i
\(726\) 0.621320 + 1.07616i 0.0230594 + 0.0399400i
\(727\) −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
\(729\) 1.00000 0.0370370
\(730\) 3.92893 0.145416
\(731\) 4.58579 + 7.94282i 0.169611 + 0.293776i
\(732\) 7.60051 + 13.1645i 0.280923 + 0.486572i
\(733\) 3.65685 0.135069 0.0675345 0.997717i \(-0.478487\pi\)
0.0675345 + 0.997717i \(0.478487\pi\)
\(734\) 14.1299 0.521546
\(735\) 1.82843 + 3.16693i 0.0674426 + 0.116814i
\(736\) −1.82843 + 3.16693i −0.0673967 + 0.116735i
\(737\) 7.75736 + 13.4361i 0.285746 + 0.494927i
\(738\) 0.585786 1.01461i 0.0215631 0.0373484i
\(739\) 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
\(741\) 7.31371 3.16693i 0.268676 0.116340i
\(742\) 1.51472 0.0556071
\(743\) −17.0711 + 29.5680i −0.626277 + 1.08474i 0.362016 + 0.932172i \(0.382089\pi\)
−0.988292 + 0.152571i \(0.951245\pi\)
\(744\) −3.96447 + 6.86666i −0.145344 + 0.251744i
\(745\) −0.585786 1.01461i −0.0214616 0.0371725i
\(746\) −2.41421 + 4.18154i −0.0883906 + 0.153097i
\(747\) 4.00000 + 6.92820i 0.146352 + 0.253490i
\(748\) −6.05887 −0.221534
\(749\) 25.5980 0.935330
\(750\) 0.207107 + 0.358719i 0.00756247 + 0.0130986i
\(751\) −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
\(753\) 16.3431 0.595577
\(754\) −3.65685 6.33386i −0.133175 0.230665i
\(755\) 5.17157 8.95743i 0.188213 0.325994i
\(756\) −1.67157 2.89525i −0.0607945 0.105299i
\(757\) 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
\(759\) −2.34315 −0.0850508
\(760\) 0.792893 6.86666i 0.0287613 0.249080i
\(761\) 51.5980 1.87043 0.935213 0.354087i \(-0.115208\pi\)
0.935213 + 0.354087i \(0.115208\pi\)
\(762\) −2.68629 + 4.65279i −0.0973141 + 0.168553i
\(763\) 15.8284 27.4156i 0.573028 0.992513i
\(764\) −15.3848 26.6472i −0.556602 0.964062i
\(765\) −0.585786 + 1.01461i −0.0211792 + 0.0366834i
\(766\) −7.02944 12.1753i −0.253984 0.439913i
\(767\) 0 0
\(768\) −3.97056 −0.143275
\(769\) −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
\(771\)