Properties

Label 380.2.v.b.87.1
Level $380$
Weight $2$
Character 380.87
Analytic conductor $3.034$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [380,2,Mod(7,380)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(380, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([6, 3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("380.7");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 380.v (of order \(12\), degree \(4\), 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: \(3.03431527681\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 87.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 380.87
Dual form 380.2.v.b.83.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.366025 + 1.36603i) q^{2} +(-2.36603 + 0.633975i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.23205 + 1.86603i) q^{5} -3.46410i q^{6} +(3.46410 - 3.46410i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.366025 + 1.36603i) q^{2} +(-2.36603 + 0.633975i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(1.23205 + 1.86603i) q^{5} -3.46410i q^{6} +(3.46410 - 3.46410i) q^{7} +(2.00000 - 2.00000i) q^{8} +(2.59808 - 1.50000i) q^{9} +(-3.00000 + 1.00000i) q^{10} -1.73205i q^{11} +(4.73205 + 1.26795i) q^{12} +(1.36603 + 0.366025i) q^{13} +(3.46410 + 6.00000i) q^{14} +(-4.09808 - 3.63397i) q^{15} +(2.00000 + 3.46410i) q^{16} +(4.09808 - 1.09808i) q^{17} +(1.09808 + 4.09808i) q^{18} +(-2.59808 + 3.50000i) q^{19} +(-0.267949 - 4.46410i) q^{20} +(-6.00000 + 10.3923i) q^{21} +(2.36603 + 0.633975i) q^{22} +(1.26795 - 4.73205i) q^{23} +(-3.46410 + 6.00000i) q^{24} +(-1.96410 + 4.59808i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(-9.46410 + 2.53590i) q^{28} +(0.866025 - 0.500000i) q^{29} +(6.46410 - 4.26795i) q^{30} +8.66025i q^{31} +(-5.46410 + 1.46410i) q^{32} +(1.09808 + 4.09808i) q^{33} +6.00000i q^{34} +(10.7321 + 2.19615i) q^{35} -6.00000 q^{36} +(2.00000 + 2.00000i) q^{37} +(-3.83013 - 4.83013i) q^{38} -3.46410 q^{39} +(6.19615 + 1.26795i) q^{40} +(4.00000 - 6.92820i) q^{41} +(-12.0000 - 12.0000i) q^{42} +(-4.73205 + 1.26795i) q^{43} +(-1.73205 + 3.00000i) q^{44} +(6.00000 + 3.00000i) q^{45} +(6.00000 + 3.46410i) q^{46} +(11.8301 + 3.16987i) q^{47} +(-6.92820 - 6.92820i) q^{48} -17.0000i q^{49} +(-5.56218 - 4.36603i) q^{50} +(-9.00000 + 5.19615i) q^{51} +(-2.00000 - 2.00000i) q^{52} +(4.09808 + 1.09808i) q^{53} +(3.23205 - 2.13397i) q^{55} -13.8564i q^{56} +(3.92820 - 9.92820i) q^{57} +(0.366025 + 1.36603i) q^{58} +(0.866025 - 1.50000i) q^{59} +(3.46410 + 10.3923i) q^{60} +(1.50000 + 2.59808i) q^{61} +(-11.8301 - 3.16987i) q^{62} +(3.80385 - 14.1962i) q^{63} -8.00000i q^{64} +(1.00000 + 3.00000i) q^{65} -6.00000 q^{66} +(-2.36603 - 0.633975i) q^{67} +(-8.19615 - 2.19615i) q^{68} +12.0000i q^{69} +(-6.92820 + 13.8564i) q^{70} +(1.50000 + 0.866025i) q^{71} +(2.19615 - 8.19615i) q^{72} +(-2.92820 - 10.9282i) q^{73} +(-3.46410 + 2.00000i) q^{74} +(1.73205 - 12.1244i) q^{75} +(8.00000 - 3.46410i) q^{76} +(-6.00000 - 6.00000i) q^{77} +(1.26795 - 4.73205i) q^{78} +(-4.33013 + 7.50000i) q^{79} +(-4.00000 + 8.00000i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(8.00000 + 8.00000i) q^{82} +(6.92820 + 6.92820i) q^{83} +(20.7846 - 12.0000i) q^{84} +(7.09808 + 6.29423i) q^{85} -6.92820i q^{86} +(-1.73205 + 1.73205i) q^{87} +(-3.46410 - 3.46410i) q^{88} +(-0.866025 + 0.500000i) q^{89} +(-6.29423 + 7.09808i) q^{90} +(6.00000 - 3.46410i) q^{91} +(-6.92820 + 6.92820i) q^{92} +(-5.49038 - 20.4904i) q^{93} +(-8.66025 + 15.0000i) q^{94} +(-9.73205 - 0.535898i) q^{95} +(12.0000 - 6.92820i) q^{96} +(-5.46410 + 1.46410i) q^{97} +(23.2224 + 6.22243i) q^{98} +(-2.59808 - 4.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 6 q^{3} - 2 q^{5} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 6 q^{3} - 2 q^{5} + 8 q^{8} - 12 q^{10} + 12 q^{12} + 2 q^{13} - 6 q^{15} + 8 q^{16} + 6 q^{17} - 6 q^{18} - 8 q^{20} - 24 q^{21} + 6 q^{22} + 12 q^{23} + 6 q^{25} - 4 q^{26} - 24 q^{28} + 12 q^{30} - 8 q^{32} - 6 q^{33} + 36 q^{35} - 24 q^{36} + 8 q^{37} + 2 q^{38} + 4 q^{40} + 16 q^{41} - 48 q^{42} - 12 q^{43} + 24 q^{45} + 24 q^{46} + 30 q^{47} + 2 q^{50} - 36 q^{51} - 8 q^{52} + 6 q^{53} + 6 q^{55} - 12 q^{57} - 2 q^{58} + 6 q^{61} - 30 q^{62} + 36 q^{63} + 4 q^{65} - 24 q^{66} - 6 q^{67} - 12 q^{68} + 6 q^{71} - 12 q^{72} + 16 q^{73} + 32 q^{76} - 24 q^{77} + 12 q^{78} - 16 q^{80} - 18 q^{81} + 32 q^{82} + 18 q^{85} + 6 q^{90} + 24 q^{91} + 30 q^{93} - 32 q^{95} + 48 q^{96} - 8 q^{97} + 34 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\) \(191\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{4}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 + 1.36603i −0.258819 + 0.965926i
\(3\) −2.36603 + 0.633975i −1.36603 + 0.366025i −0.866025 0.500000i \(-0.833333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) 1.23205 + 1.86603i 0.550990 + 0.834512i
\(6\) 3.46410i 1.41421i
\(7\) 3.46410 3.46410i 1.30931 1.30931i 0.387392 0.921915i \(-0.373376\pi\)
0.921915 0.387392i \(-0.126624\pi\)
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) 2.59808 1.50000i 0.866025 0.500000i
\(10\) −3.00000 + 1.00000i −0.948683 + 0.316228i
\(11\) 1.73205i 0.522233i −0.965307 0.261116i \(-0.915909\pi\)
0.965307 0.261116i \(-0.0840907\pi\)
\(12\) 4.73205 + 1.26795i 1.36603 + 0.366025i
\(13\) 1.36603 + 0.366025i 0.378867 + 0.101517i 0.443227 0.896410i \(-0.353834\pi\)
−0.0643593 + 0.997927i \(0.520500\pi\)
\(14\) 3.46410 + 6.00000i 0.925820 + 1.60357i
\(15\) −4.09808 3.63397i −1.05812 0.938288i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) 4.09808 1.09808i 0.993929 0.266323i 0.275029 0.961436i \(-0.411312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) 1.09808 + 4.09808i 0.258819 + 0.965926i
\(19\) −2.59808 + 3.50000i −0.596040 + 0.802955i
\(20\) −0.267949 4.46410i −0.0599153 0.998203i
\(21\) −6.00000 + 10.3923i −1.30931 + 2.26779i
\(22\) 2.36603 + 0.633975i 0.504438 + 0.135164i
\(23\) 1.26795 4.73205i 0.264386 0.986701i −0.698240 0.715864i \(-0.746033\pi\)
0.962625 0.270837i \(-0.0873003\pi\)
\(24\) −3.46410 + 6.00000i −0.707107 + 1.22474i
\(25\) −1.96410 + 4.59808i −0.392820 + 0.919615i
\(26\) −1.00000 + 1.73205i −0.196116 + 0.339683i
\(27\) 0 0
\(28\) −9.46410 + 2.53590i −1.78855 + 0.479240i
\(29\) 0.866025 0.500000i 0.160817 0.0928477i −0.417432 0.908708i \(-0.637070\pi\)
0.578249 + 0.815861i \(0.303736\pi\)
\(30\) 6.46410 4.26795i 1.18018 0.779217i
\(31\) 8.66025i 1.55543i 0.628619 + 0.777714i \(0.283621\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −5.46410 + 1.46410i −0.965926 + 0.258819i
\(33\) 1.09808 + 4.09808i 0.191151 + 0.713384i
\(34\) 6.00000i 1.02899i
\(35\) 10.7321 + 2.19615i 1.81405 + 0.371218i
\(36\) −6.00000 −1.00000
\(37\) 2.00000 + 2.00000i 0.328798 + 0.328798i 0.852129 0.523331i \(-0.175311\pi\)
−0.523331 + 0.852129i \(0.675311\pi\)
\(38\) −3.83013 4.83013i −0.621329 0.783550i
\(39\) −3.46410 −0.554700
\(40\) 6.19615 + 1.26795i 0.979698 + 0.200480i
\(41\) 4.00000 6.92820i 0.624695 1.08200i −0.363905 0.931436i \(-0.618557\pi\)
0.988600 0.150567i \(-0.0481100\pi\)
\(42\) −12.0000 12.0000i −1.85164 1.85164i
\(43\) −4.73205 + 1.26795i −0.721631 + 0.193360i −0.600899 0.799325i \(-0.705191\pi\)
−0.120732 + 0.992685i \(0.538524\pi\)
\(44\) −1.73205 + 3.00000i −0.261116 + 0.452267i
\(45\) 6.00000 + 3.00000i 0.894427 + 0.447214i
\(46\) 6.00000 + 3.46410i 0.884652 + 0.510754i
\(47\) 11.8301 + 3.16987i 1.72560 + 0.462373i 0.979162 0.203080i \(-0.0650952\pi\)
0.746439 + 0.665454i \(0.231762\pi\)
\(48\) −6.92820 6.92820i −1.00000 1.00000i
\(49\) 17.0000i 2.42857i
\(50\) −5.56218 4.36603i −0.786611 0.617449i
\(51\) −9.00000 + 5.19615i −1.26025 + 0.727607i
\(52\) −2.00000 2.00000i −0.277350 0.277350i
\(53\) 4.09808 + 1.09808i 0.562914 + 0.150832i 0.529045 0.848594i \(-0.322550\pi\)
0.0338693 + 0.999426i \(0.489217\pi\)
\(54\) 0 0
\(55\) 3.23205 2.13397i 0.435810 0.287745i
\(56\) 13.8564i 1.85164i
\(57\) 3.92820 9.92820i 0.520303 1.31502i
\(58\) 0.366025 + 1.36603i 0.0480615 + 0.179368i
\(59\) 0.866025 1.50000i 0.112747 0.195283i −0.804130 0.594454i \(-0.797368\pi\)
0.916877 + 0.399170i \(0.130702\pi\)
\(60\) 3.46410 + 10.3923i 0.447214 + 1.34164i
\(61\) 1.50000 + 2.59808i 0.192055 + 0.332650i 0.945931 0.324367i \(-0.105151\pi\)
−0.753876 + 0.657017i \(0.771818\pi\)
\(62\) −11.8301 3.16987i −1.50243 0.402574i
\(63\) 3.80385 14.1962i 0.479240 1.78855i
\(64\) 8.00000i 1.00000i
\(65\) 1.00000 + 3.00000i 0.124035 + 0.372104i
\(66\) −6.00000 −0.738549
\(67\) −2.36603 0.633975i −0.289056 0.0774523i 0.111377 0.993778i \(-0.464474\pi\)
−0.400433 + 0.916326i \(0.631140\pi\)
\(68\) −8.19615 2.19615i −0.993929 0.266323i
\(69\) 12.0000i 1.44463i
\(70\) −6.92820 + 13.8564i −0.828079 + 1.65616i
\(71\) 1.50000 + 0.866025i 0.178017 + 0.102778i 0.586361 0.810050i \(-0.300560\pi\)
−0.408344 + 0.912828i \(0.633893\pi\)
\(72\) 2.19615 8.19615i 0.258819 0.965926i
\(73\) −2.92820 10.9282i −0.342720 1.27905i −0.895253 0.445558i \(-0.853005\pi\)
0.552533 0.833491i \(-0.313661\pi\)
\(74\) −3.46410 + 2.00000i −0.402694 + 0.232495i
\(75\) 1.73205 12.1244i 0.200000 1.40000i
\(76\) 8.00000 3.46410i 0.917663 0.397360i
\(77\) −6.00000 6.00000i −0.683763 0.683763i
\(78\) 1.26795 4.73205i 0.143567 0.535799i
\(79\) −4.33013 + 7.50000i −0.487177 + 0.843816i −0.999891 0.0147436i \(-0.995307\pi\)
0.512714 + 0.858559i \(0.328640\pi\)
\(80\) −4.00000 + 8.00000i −0.447214 + 0.894427i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 8.00000 + 8.00000i 0.883452 + 0.883452i
\(83\) 6.92820 + 6.92820i 0.760469 + 0.760469i 0.976407 0.215938i \(-0.0692809\pi\)
−0.215938 + 0.976407i \(0.569281\pi\)
\(84\) 20.7846 12.0000i 2.26779 1.30931i
\(85\) 7.09808 + 6.29423i 0.769894 + 0.682705i
\(86\) 6.92820i 0.747087i
\(87\) −1.73205 + 1.73205i −0.185695 + 0.185695i
\(88\) −3.46410 3.46410i −0.369274 0.369274i
\(89\) −0.866025 + 0.500000i −0.0917985 + 0.0529999i −0.545197 0.838308i \(-0.683545\pi\)
0.453398 + 0.891308i \(0.350212\pi\)
\(90\) −6.29423 + 7.09808i −0.663470 + 0.748203i
\(91\) 6.00000 3.46410i 0.628971 0.363137i
\(92\) −6.92820 + 6.92820i −0.722315 + 0.722315i
\(93\) −5.49038 20.4904i −0.569326 2.12475i
\(94\) −8.66025 + 15.0000i −0.893237 + 1.54713i
\(95\) −9.73205 0.535898i −0.998487 0.0549820i
\(96\) 12.0000 6.92820i 1.22474 0.707107i
\(97\) −5.46410 + 1.46410i −0.554795 + 0.148657i −0.525314 0.850908i \(-0.676052\pi\)
−0.0294813 + 0.999565i \(0.509386\pi\)
\(98\) 23.2224 + 6.22243i 2.34582 + 0.628561i
\(99\) −2.59808 4.50000i −0.261116 0.452267i
\(100\) 8.00000 6.00000i 0.800000 0.600000i
\(101\) 0.500000 + 0.866025i 0.0497519 + 0.0861727i 0.889829 0.456294i \(-0.150824\pi\)
−0.840077 + 0.542467i \(0.817490\pi\)
\(102\) −3.80385 14.1962i −0.376637 1.40563i
\(103\) 3.46410 + 3.46410i 0.341328 + 0.341328i 0.856866 0.515538i \(-0.172408\pi\)
−0.515538 + 0.856866i \(0.672408\pi\)
\(104\) 3.46410 2.00000i 0.339683 0.196116i
\(105\) −26.7846 + 1.60770i −2.61391 + 0.156895i
\(106\) −3.00000 + 5.19615i −0.291386 + 0.504695i
\(107\) 10.3923 10.3923i 1.00466 1.00466i 0.00467295 0.999989i \(-0.498513\pi\)
0.999989 0.00467295i \(-0.00148745\pi\)
\(108\) 0 0
\(109\) −2.59808 1.50000i −0.248851 0.143674i 0.370387 0.928877i \(-0.379225\pi\)
−0.619238 + 0.785203i \(0.712558\pi\)
\(110\) 1.73205 + 5.19615i 0.165145 + 0.495434i
\(111\) −6.00000 3.46410i −0.569495 0.328798i
\(112\) 18.9282 + 5.07180i 1.78855 + 0.479240i
\(113\) −1.00000 + 1.00000i −0.0940721 + 0.0940721i −0.752577 0.658505i \(-0.771189\pi\)
0.658505 + 0.752577i \(0.271189\pi\)
\(114\) 12.1244 + 9.00000i 1.13555 + 0.842927i
\(115\) 10.3923 3.46410i 0.969087 0.323029i
\(116\) −2.00000 −0.185695
\(117\) 4.09808 1.09808i 0.378867 0.101517i
\(118\) 1.73205 + 1.73205i 0.159448 + 0.159448i
\(119\) 10.3923 18.0000i 0.952661 1.65006i
\(120\) −15.4641 + 0.928203i −1.41167 + 0.0847330i
\(121\) 8.00000 0.727273
\(122\) −4.09808 + 1.09808i −0.371022 + 0.0994151i
\(123\) −5.07180 + 18.9282i −0.457309 + 1.70670i
\(124\) 8.66025 15.0000i 0.777714 1.34704i
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 18.0000 + 10.3923i 1.60357 + 0.925820i
\(127\) −16.5622 4.43782i −1.46966 0.393793i −0.566843 0.823826i \(-0.691835\pi\)
−0.902813 + 0.430033i \(0.858502\pi\)
\(128\) 10.9282 + 2.92820i 0.965926 + 0.258819i
\(129\) 10.3923 6.00000i 0.914991 0.528271i
\(130\) −4.46410 + 0.267949i −0.391528 + 0.0235007i
\(131\) −18.0000 10.3923i −1.57267 0.907980i −0.995841 0.0911134i \(-0.970957\pi\)
−0.576827 0.816866i \(-0.695709\pi\)
\(132\) 2.19615 8.19615i 0.191151 0.713384i
\(133\) 3.12436 + 21.1244i 0.270916 + 1.83171i
\(134\) 1.73205 3.00000i 0.149626 0.259161i
\(135\) 0 0
\(136\) 6.00000 10.3923i 0.514496 0.891133i
\(137\) −3.66025 + 13.6603i −0.312717 + 1.16707i 0.613380 + 0.789788i \(0.289809\pi\)
−0.926097 + 0.377286i \(0.876857\pi\)
\(138\) −16.3923 4.39230i −1.39541 0.373898i
\(139\) 5.19615 + 9.00000i 0.440732 + 0.763370i 0.997744 0.0671344i \(-0.0213856\pi\)
−0.557012 + 0.830504i \(0.688052\pi\)
\(140\) −16.3923 14.5359i −1.38540 1.22851i
\(141\) −30.0000 −2.52646
\(142\) −1.73205 + 1.73205i −0.145350 + 0.145350i
\(143\) 0.633975 2.36603i 0.0530156 0.197857i
\(144\) 10.3923 + 6.00000i 0.866025 + 0.500000i
\(145\) 2.00000 + 1.00000i 0.166091 + 0.0830455i
\(146\) 16.0000 1.32417
\(147\) 10.7776 + 40.2224i 0.888919 + 3.31749i
\(148\) −1.46410 5.46410i −0.120348 0.449146i
\(149\) 11.2583 + 6.50000i 0.922318 + 0.532501i 0.884374 0.466779i \(-0.154586\pi\)
0.0379444 + 0.999280i \(0.487919\pi\)
\(150\) 15.9282 + 6.80385i 1.30053 + 0.555532i
\(151\) 8.66025i 0.704761i 0.935857 + 0.352381i \(0.114628\pi\)
−0.935857 + 0.352381i \(0.885372\pi\)
\(152\) 1.80385 + 12.1962i 0.146311 + 0.989239i
\(153\) 9.00000 9.00000i 0.727607 0.727607i
\(154\) 10.3923 6.00000i 0.837436 0.483494i
\(155\) −16.1603 + 10.6699i −1.29802 + 0.857025i
\(156\) 6.00000 + 3.46410i 0.480384 + 0.277350i
\(157\) 6.83013 1.83013i 0.545103 0.146060i 0.0242497 0.999706i \(-0.492280\pi\)
0.520854 + 0.853646i \(0.325614\pi\)
\(158\) −8.66025 8.66025i −0.688973 0.688973i
\(159\) −10.3923 −0.824163
\(160\) −9.46410 8.39230i −0.748203 0.663470i
\(161\) −12.0000 20.7846i −0.945732 1.63806i
\(162\) −9.00000 9.00000i −0.707107 0.707107i
\(163\) −8.66025 8.66025i −0.678323 0.678323i 0.281297 0.959621i \(-0.409235\pi\)
−0.959621 + 0.281297i \(0.909235\pi\)
\(164\) −13.8564 + 8.00000i −1.08200 + 0.624695i
\(165\) −6.29423 + 7.09808i −0.490005 + 0.552584i
\(166\) −12.0000 + 6.92820i −0.931381 + 0.537733i
\(167\) 0 0 0.258819 0.965926i \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(168\) 8.78461 + 32.7846i 0.677747 + 2.52939i
\(169\) −9.52628 5.50000i −0.732791 0.423077i
\(170\) −11.1962 + 7.39230i −0.858706 + 0.566964i
\(171\) −1.50000 + 12.9904i −0.114708 + 0.993399i
\(172\) 9.46410 + 2.53590i 0.721631 + 0.193360i
\(173\) −2.92820 10.9282i −0.222627 0.830856i −0.983341 0.181769i \(-0.941818\pi\)
0.760714 0.649087i \(-0.224849\pi\)
\(174\) −1.73205 3.00000i −0.131306 0.227429i
\(175\) 9.12436 + 22.7321i 0.689736 + 1.71838i
\(176\) 6.00000 3.46410i 0.452267 0.261116i
\(177\) −1.09808 + 4.09808i −0.0825365 + 0.308030i
\(178\) −0.366025 1.36603i −0.0274348 0.102388i
\(179\) −8.66025 −0.647298 −0.323649 0.946177i \(-0.604910\pi\)
−0.323649 + 0.946177i \(0.604910\pi\)
\(180\) −7.39230 11.1962i −0.550990 0.834512i
\(181\) −6.00000 10.3923i −0.445976 0.772454i 0.552143 0.833749i \(-0.313810\pi\)
−0.998120 + 0.0612954i \(0.980477\pi\)
\(182\) 2.53590 + 9.46410i 0.187973 + 0.701526i
\(183\) −5.19615 5.19615i −0.384111 0.384111i
\(184\) −6.92820 12.0000i −0.510754 0.884652i
\(185\) −1.26795 + 6.19615i −0.0932215 + 0.455550i
\(186\) 30.0000 2.19971
\(187\) −1.90192 7.09808i −0.139082 0.519063i
\(188\) −17.3205 17.3205i −1.26323 1.26323i
\(189\) 0 0
\(190\) 4.29423 13.0981i 0.311536 0.950234i
\(191\) 8.66025i 0.626634i −0.949649 0.313317i \(-0.898560\pi\)
0.949649 0.313317i \(-0.101440\pi\)
\(192\) 5.07180 + 18.9282i 0.366025 + 1.36603i
\(193\) −2.92820 10.9282i −0.210777 0.786629i −0.987611 0.156924i \(-0.949842\pi\)
0.776834 0.629705i \(-0.216824\pi\)
\(194\) 8.00000i 0.574367i
\(195\) −4.26795 6.46410i −0.305634 0.462904i
\(196\) −17.0000 + 29.4449i −1.21429 + 2.10320i
\(197\) 1.00000 + 1.00000i 0.0712470 + 0.0712470i 0.741832 0.670585i \(-0.233957\pi\)
−0.670585 + 0.741832i \(0.733957\pi\)
\(198\) 7.09808 1.90192i 0.504438 0.135164i
\(199\) −9.52628 16.5000i −0.675300 1.16965i −0.976381 0.216055i \(-0.930681\pi\)
0.301081 0.953599i \(-0.402653\pi\)
\(200\) 5.26795 + 13.1244i 0.372500 + 0.928032i
\(201\) 6.00000 0.423207
\(202\) −1.36603 + 0.366025i −0.0961132 + 0.0257535i
\(203\) 1.26795 4.73205i 0.0889926 0.332125i
\(204\) 20.7846 1.45521
\(205\) 17.8564 1.07180i 1.24715 0.0748575i
\(206\) −6.00000 + 3.46410i −0.418040 + 0.241355i
\(207\) −3.80385 14.1962i −0.264386 0.986701i
\(208\) 1.46410 + 5.46410i 0.101517 + 0.378867i
\(209\) 6.06218 + 4.50000i 0.419330 + 0.311272i
\(210\) 7.60770 37.1769i 0.524981 2.56545i
\(211\) 13.5000 + 7.79423i 0.929378 + 0.536577i 0.886615 0.462508i \(-0.153050\pi\)
0.0427634 + 0.999085i \(0.486384\pi\)
\(212\) −6.00000 6.00000i −0.412082 0.412082i
\(213\) −4.09808 1.09808i −0.280796 0.0752389i
\(214\) 10.3923 + 18.0000i 0.710403 + 1.23045i
\(215\) −8.19615 7.26795i −0.558973 0.495670i
\(216\) 0 0
\(217\) 30.0000 + 30.0000i 2.03653 + 2.03653i
\(218\) 3.00000 3.00000i 0.203186 0.203186i
\(219\) 13.8564 + 24.0000i 0.936329 + 1.62177i
\(220\) −7.73205 + 0.464102i −0.521295 + 0.0312897i
\(221\) 6.00000 0.403604
\(222\) 6.92820 6.92820i 0.464991 0.464991i
\(223\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(224\) −13.8564 + 24.0000i −0.925820 + 1.60357i
\(225\) 1.79423 + 14.8923i 0.119615 + 0.992820i
\(226\) −1.00000 1.73205i −0.0665190 0.115214i
\(227\) −3.46410 + 3.46410i −0.229920 + 0.229920i −0.812659 0.582739i \(-0.801981\pi\)
0.582739 + 0.812659i \(0.301981\pi\)
\(228\) −16.7321 + 13.2679i −1.10811 + 0.878691i
\(229\) 1.00000i 0.0660819i 0.999454 + 0.0330409i \(0.0105192\pi\)
−0.999454 + 0.0330409i \(0.989481\pi\)
\(230\) 0.928203 + 15.4641i 0.0612039 + 1.01967i
\(231\) 18.0000 + 10.3923i 1.18431 + 0.683763i
\(232\) 0.732051 2.73205i 0.0480615 0.179368i
\(233\) 5.49038 + 20.4904i 0.359687 + 1.34237i 0.874483 + 0.485057i \(0.161201\pi\)
−0.514796 + 0.857313i \(0.672132\pi\)
\(234\) 6.00000i 0.392232i
\(235\) 8.66025 + 25.9808i 0.564933 + 1.69480i
\(236\) −3.00000 + 1.73205i −0.195283 + 0.112747i
\(237\) 5.49038 20.4904i 0.356639 1.33099i
\(238\) 20.7846 + 20.7846i 1.34727 + 1.34727i
\(239\) 1.73205 0.112037 0.0560185 0.998430i \(-0.482159\pi\)
0.0560185 + 0.998430i \(0.482159\pi\)
\(240\) 4.39230 21.4641i 0.283522 1.38550i
\(241\) −9.50000 16.4545i −0.611949 1.05993i −0.990912 0.134515i \(-0.957053\pi\)
0.378963 0.925412i \(-0.376281\pi\)
\(242\) −2.92820 + 10.9282i −0.188232 + 0.702492i
\(243\) 5.70577 21.2942i 0.366025 1.36603i
\(244\) 6.00000i 0.384111i
\(245\) 31.7224 20.9449i 2.02667 1.33812i
\(246\) −24.0000 13.8564i −1.53018 0.883452i
\(247\) −4.83013 + 3.83013i −0.307334 + 0.243705i
\(248\) 17.3205 + 17.3205i 1.09985 + 1.09985i
\(249\) −20.7846 12.0000i −1.31717 0.760469i
\(250\) 1.29423 15.7583i 0.0818542 0.996644i
\(251\) −4.50000 + 2.59808i −0.284037 + 0.163989i −0.635250 0.772307i \(-0.719103\pi\)
0.351212 + 0.936296i \(0.385770\pi\)
\(252\) −20.7846 + 20.7846i −1.30931 + 1.30931i
\(253\) −8.19615 2.19615i −0.515288 0.138071i
\(254\) 12.1244 21.0000i 0.760750 1.31766i
\(255\) −20.7846 10.3923i −1.30158 0.650791i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −4.02628 + 15.0263i −0.251152 + 0.937314i 0.719038 + 0.694971i \(0.244583\pi\)
−0.970191 + 0.242343i \(0.922084\pi\)
\(258\) 4.39230 + 16.3923i 0.273453 + 1.02054i
\(259\) 13.8564 0.860995
\(260\) 1.26795 6.19615i 0.0786349 0.384269i
\(261\) 1.50000 2.59808i 0.0928477 0.160817i
\(262\) 20.7846 20.7846i 1.28408 1.28408i
\(263\) −16.5622 + 4.43782i −1.02127 + 0.273648i −0.730330 0.683094i \(-0.760634\pi\)
−0.290937 + 0.956742i \(0.593967\pi\)
\(264\) 10.3923 + 6.00000i 0.639602 + 0.369274i
\(265\) 3.00000 + 9.00000i 0.184289 + 0.552866i
\(266\) −30.0000 3.46410i −1.83942 0.212398i
\(267\) 1.73205 1.73205i 0.106000 0.106000i
\(268\) 3.46410 + 3.46410i 0.211604 + 0.211604i
\(269\) −21.6506 12.5000i −1.32006 0.762138i −0.336324 0.941746i \(-0.609184\pi\)
−0.983738 + 0.179608i \(0.942517\pi\)
\(270\) 0 0
\(271\) 13.5000 + 7.79423i 0.820067 + 0.473466i 0.850439 0.526073i \(-0.176336\pi\)
−0.0303728 + 0.999539i \(0.509669\pi\)
\(272\) 12.0000 + 12.0000i 0.727607 + 0.727607i
\(273\) −12.0000 + 12.0000i −0.726273 + 0.726273i
\(274\) −17.3205 10.0000i −1.04637 0.604122i
\(275\) 7.96410 + 3.40192i 0.480253 + 0.205144i
\(276\) 12.0000 20.7846i 0.722315 1.25109i
\(277\) −16.0000 16.0000i −0.961347 0.961347i 0.0379334 0.999280i \(-0.487923\pi\)
−0.999280 + 0.0379334i \(0.987923\pi\)
\(278\) −14.1962 + 3.80385i −0.851429 + 0.228140i
\(279\) 12.9904 + 22.5000i 0.777714 + 1.34704i
\(280\) 25.8564 17.0718i 1.54522 1.02023i
\(281\) −1.00000 1.73205i −0.0596550 0.103325i 0.834656 0.550772i \(-0.185667\pi\)
−0.894311 + 0.447447i \(0.852333\pi\)
\(282\) 10.9808 40.9808i 0.653895 2.44037i
\(283\) 21.2942 5.70577i 1.26581 0.339173i 0.437386 0.899274i \(-0.355904\pi\)
0.828424 + 0.560101i \(0.189238\pi\)
\(284\) −1.73205 3.00000i −0.102778 0.178017i
\(285\) 23.3660 4.90192i 1.38408 0.290365i
\(286\) 3.00000 + 1.73205i 0.177394 + 0.102418i
\(287\) −10.1436 37.8564i −0.598757 2.23459i
\(288\) −12.0000 + 12.0000i −0.707107 + 0.707107i
\(289\) 0.866025 0.500000i 0.0509427 0.0294118i
\(290\) −2.09808 + 2.36603i −0.123203 + 0.138938i
\(291\) 12.0000 6.92820i 0.703452 0.406138i
\(292\) −5.85641 + 21.8564i −0.342720 + 1.27905i
\(293\) 4.00000 4.00000i 0.233682 0.233682i −0.580545 0.814228i \(-0.697161\pi\)
0.814228 + 0.580545i \(0.197161\pi\)
\(294\) −58.8897 −3.43452
\(295\) 3.86603 0.232051i 0.225089 0.0135105i
\(296\) 8.00000 0.464991
\(297\) 0 0
\(298\) −13.0000 + 13.0000i −0.753070 + 0.753070i
\(299\) 3.46410 6.00000i 0.200334 0.346989i
\(300\) −15.1244 + 19.2679i −0.873205 + 1.11244i
\(301\) −12.0000 + 20.7846i −0.691669 + 1.19800i
\(302\) −11.8301 3.16987i −0.680747 0.182406i
\(303\) −1.73205 1.73205i −0.0995037 0.0995037i
\(304\) −17.3205 2.00000i −0.993399 0.114708i
\(305\) −3.00000 + 6.00000i −0.171780 + 0.343559i
\(306\) 9.00000 + 15.5885i 0.514496 + 0.891133i
\(307\) 0.633975 + 2.36603i 0.0361828 + 0.135036i 0.981655 0.190668i \(-0.0610654\pi\)
−0.945472 + 0.325704i \(0.894399\pi\)
\(308\) 4.39230 + 16.3923i 0.250275 + 0.934038i
\(309\) −10.3923 6.00000i −0.591198 0.341328i
\(310\) −8.66025 25.9808i −0.491869 1.47561i
\(311\) 13.8564i 0.785725i 0.919597 + 0.392862i \(0.128515\pi\)
−0.919597 + 0.392862i \(0.871485\pi\)
\(312\) −6.92820 + 6.92820i −0.392232 + 0.392232i
\(313\) −6.83013 1.83013i −0.386062 0.103445i 0.0605675 0.998164i \(-0.480709\pi\)
−0.446629 + 0.894719i \(0.647376\pi\)
\(314\) 10.0000i 0.564333i
\(315\) 31.1769 10.3923i 1.75662 0.585540i
\(316\) 15.0000 8.66025i 0.843816 0.487177i
\(317\) 4.39230 16.3923i 0.246696 0.920684i −0.725827 0.687878i \(-0.758543\pi\)
0.972523 0.232806i \(-0.0747907\pi\)
\(318\) 3.80385 14.1962i 0.213309 0.796081i
\(319\) −0.866025 1.50000i −0.0484881 0.0839839i
\(320\) 14.9282 9.85641i 0.834512 0.550990i
\(321\) −18.0000 + 31.1769i −1.00466 + 1.74013i
\(322\) 32.7846 8.78461i 1.82701 0.489547i
\(323\) −6.80385 + 17.1962i −0.378576 + 0.956820i
\(324\) 15.5885 9.00000i 0.866025 0.500000i
\(325\) −4.36603 + 5.56218i −0.242184 + 0.308534i
\(326\) 15.0000 8.66025i 0.830773 0.479647i
\(327\) 7.09808 + 1.90192i 0.392525 + 0.105177i
\(328\) −5.85641 21.8564i −0.323366 1.20682i
\(329\) 51.9615 30.0000i 2.86473 1.65395i
\(330\) −7.39230 11.1962i −0.406933 0.616328i
\(331\) 20.7846i 1.14243i 0.820802 + 0.571213i \(0.193527\pi\)
−0.820802 + 0.571213i \(0.806473\pi\)
\(332\) −5.07180 18.9282i −0.278351 1.03882i
\(333\) 8.19615 + 2.19615i 0.449146 + 0.120348i
\(334\) 0 0
\(335\) −1.73205 5.19615i −0.0946320 0.283896i
\(336\) −48.0000 −2.61861
\(337\) −19.1244 + 5.12436i −1.04177 + 0.279141i −0.738847 0.673874i \(-0.764629\pi\)
−0.302923 + 0.953015i \(0.597963\pi\)
\(338\) 11.0000 11.0000i 0.598321 0.598321i
\(339\) 1.73205 3.00000i 0.0940721 0.162938i
\(340\) −6.00000 18.0000i −0.325396 0.976187i
\(341\) 15.0000 0.812296
\(342\) −17.1962 6.80385i −0.929861 0.367910i
\(343\) −34.6410 34.6410i −1.87044 1.87044i
\(344\) −6.92820 + 12.0000i −0.373544 + 0.646997i
\(345\) −22.3923 + 14.7846i −1.20556 + 0.795977i
\(346\) 16.0000 0.860165
\(347\) −5.07180 18.9282i −0.272268 1.01612i −0.957650 0.287935i \(-0.907031\pi\)
0.685382 0.728184i \(-0.259635\pi\)
\(348\) 4.73205 1.26795i 0.253665 0.0679692i
\(349\) 24.0000i 1.28469i 0.766415 + 0.642345i \(0.222038\pi\)
−0.766415 + 0.642345i \(0.777962\pi\)
\(350\) −34.3923 + 4.14359i −1.83835 + 0.221484i
\(351\) 0 0
\(352\) 2.53590 + 9.46410i 0.135164 + 0.504438i
\(353\) 6.00000 6.00000i 0.319348 0.319348i −0.529169 0.848517i \(-0.677496\pi\)
0.848517 + 0.529169i \(0.177496\pi\)
\(354\) −5.19615 3.00000i −0.276172 0.159448i
\(355\) 0.232051 + 3.86603i 0.0123160 + 0.205187i
\(356\) 2.00000 0.106000
\(357\) −13.1769 + 49.1769i −0.697396 + 2.60272i
\(358\) 3.16987 11.8301i 0.167533 0.625242i
\(359\) −3.46410 + 6.00000i −0.182828 + 0.316668i −0.942843 0.333238i \(-0.891859\pi\)
0.760014 + 0.649906i \(0.225192\pi\)
\(360\) 18.0000 6.00000i 0.948683 0.316228i
\(361\) −5.50000 18.1865i −0.289474 0.957186i
\(362\) 16.3923 4.39230i 0.861560 0.230854i
\(363\) −18.9282 + 5.07180i −0.993473 + 0.266200i
\(364\) −13.8564 −0.726273
\(365\) 16.7846 18.9282i 0.878547 0.990747i
\(366\) 9.00000 5.19615i 0.470438 0.271607i
\(367\) −9.46410 2.53590i −0.494022 0.132373i 0.00320218 0.999995i \(-0.498981\pi\)
−0.497224 + 0.867622i \(0.665647\pi\)
\(368\) 18.9282 5.07180i 0.986701 0.264386i
\(369\) 24.0000i 1.24939i
\(370\) −8.00000 4.00000i −0.415900 0.207950i
\(371\) 18.0000 10.3923i 0.934513 0.539542i
\(372\) −10.9808 + 40.9808i −0.569326 + 2.12475i
\(373\) 10.0000 10.0000i 0.517780 0.517780i −0.399119 0.916899i \(-0.630684\pi\)
0.916899 + 0.399119i \(0.130684\pi\)
\(374\) 10.3923 0.537373
\(375\) 24.7583 11.7058i 1.27851 0.604483i
\(376\) 30.0000 17.3205i 1.54713 0.893237i
\(377\) 1.36603 0.366025i 0.0703539 0.0188513i
\(378\) 0 0
\(379\) −36.3731 −1.86836 −0.934179 0.356803i \(-0.883867\pi\)
−0.934179 + 0.356803i \(0.883867\pi\)
\(380\) 16.3205 + 10.6603i 0.837224 + 0.546859i
\(381\) 42.0000 2.15173
\(382\) 11.8301 + 3.16987i 0.605282 + 0.162185i
\(383\) 7.09808 1.90192i 0.362695 0.0971838i −0.0728693 0.997341i \(-0.523216\pi\)
0.435564 + 0.900158i \(0.356549\pi\)
\(384\) −27.7128 −1.41421
\(385\) 3.80385 18.5885i 0.193862 0.947356i
\(386\) 16.0000 0.814379
\(387\) −10.3923 + 10.3923i −0.528271 + 0.528271i
\(388\) 10.9282 + 2.92820i 0.554795 + 0.148657i
\(389\) −4.33013 + 2.50000i −0.219546 + 0.126755i −0.605740 0.795663i \(-0.707123\pi\)
0.386194 + 0.922418i \(0.373790\pi\)
\(390\) 10.3923 3.46410i 0.526235 0.175412i
\(391\) 20.7846i 1.05112i
\(392\) −34.0000 34.0000i −1.71726 1.71726i
\(393\) 49.1769 + 13.1769i 2.48065 + 0.664687i
\(394\) −1.73205 + 1.00000i −0.0872595 + 0.0503793i
\(395\) −19.3301 + 1.16025i −0.972604 + 0.0583787i
\(396\) 10.3923i 0.522233i
\(397\) −30.0526 + 8.05256i −1.50829 + 0.404146i −0.915868 0.401478i \(-0.868496\pi\)
−0.592426 + 0.805625i \(0.701830\pi\)
\(398\) 26.0263 6.97372i 1.30458 0.349561i
\(399\) −20.7846 48.0000i −1.04053 2.40301i
\(400\) −19.8564 + 2.39230i −0.992820 + 0.119615i
\(401\) −5.50000 + 9.52628i −0.274657 + 0.475720i −0.970049 0.242911i \(-0.921898\pi\)
0.695392 + 0.718631i \(0.255231\pi\)
\(402\) −2.19615 + 8.19615i −0.109534 + 0.408787i
\(403\) −3.16987 + 11.8301i −0.157903 + 0.589301i
\(404\) 2.00000i 0.0995037i
\(405\) −20.0885 + 1.20577i −0.998203 + 0.0599153i
\(406\) 6.00000 + 3.46410i 0.297775 + 0.171920i
\(407\) 3.46410 3.46410i 0.171709 0.171709i
\(408\) −7.60770 + 28.3923i −0.376637 + 1.40563i
\(409\) −7.79423 + 4.50000i −0.385400 + 0.222511i −0.680165 0.733059i \(-0.738092\pi\)
0.294765 + 0.955570i \(0.404759\pi\)
\(410\) −5.07180 + 24.7846i −0.250478 + 1.22402i
\(411\) 34.6410i 1.70872i
\(412\) −2.53590 9.46410i −0.124935 0.466263i
\(413\) −2.19615 8.19615i −0.108066 0.403306i
\(414\) 20.7846 1.02151
\(415\) −4.39230 + 21.4641i −0.215610 + 1.05363i
\(416\) −8.00000 −0.392232
\(417\) −18.0000 18.0000i −0.881464 0.881464i
\(418\) −8.36603 + 6.63397i −0.409196 + 0.324478i
\(419\) −5.19615 −0.253849 −0.126924 0.991912i \(-0.540511\pi\)
−0.126924 + 0.991912i \(0.540511\pi\)
\(420\) 48.0000 + 24.0000i 2.34216 + 1.17108i
\(421\) −11.5000 + 19.9186i −0.560476 + 0.970772i 0.436979 + 0.899472i \(0.356048\pi\)
−0.997455 + 0.0713008i \(0.977285\pi\)
\(422\) −15.5885 + 15.5885i −0.758834 + 0.758834i
\(423\) 35.4904 9.50962i 1.72560 0.462373i
\(424\) 10.3923 6.00000i 0.504695 0.291386i
\(425\) −3.00000 + 21.0000i −0.145521 + 1.01865i
\(426\) 3.00000 5.19615i 0.145350 0.251754i
\(427\) 14.1962 + 3.80385i 0.687000 + 0.184081i
\(428\) −28.3923 + 7.60770i −1.37239 + 0.367732i
\(429\) 6.00000i 0.289683i
\(430\) 12.9282 8.53590i 0.623453 0.411638i
\(431\) 10.5000 6.06218i 0.505767 0.292005i −0.225325 0.974284i \(-0.572344\pi\)
0.731092 + 0.682279i \(0.239011\pi\)
\(432\) 0 0
\(433\) 30.0526 + 8.05256i 1.44423 + 0.386981i 0.894014 0.448039i \(-0.147877\pi\)
0.550220 + 0.835020i \(0.314544\pi\)
\(434\) −51.9615 + 30.0000i −2.49423 + 1.44005i
\(435\) −5.36603 1.09808i −0.257281 0.0526487i
\(436\) 3.00000 + 5.19615i 0.143674 + 0.248851i
\(437\) 13.2679 + 16.7321i 0.634692 + 0.800403i
\(438\) −37.8564 + 10.1436i −1.80885 + 0.484680i
\(439\) 16.4545 28.5000i 0.785330 1.36023i −0.143472 0.989654i \(-0.545827\pi\)
0.928802 0.370576i \(-0.120840\pi\)
\(440\) 2.19615 10.7321i 0.104697 0.511630i
\(441\) −25.5000 44.1673i −1.21429 2.10320i
\(442\) −2.19615 + 8.19615i −0.104460 + 0.389851i
\(443\) −3.80385 + 14.1962i −0.180726 + 0.674480i 0.814779 + 0.579772i \(0.196858\pi\)
−0.995505 + 0.0947077i \(0.969808\pi\)
\(444\) 6.92820 + 12.0000i 0.328798 + 0.569495i
\(445\) −2.00000 1.00000i −0.0948091 0.0474045i
\(446\) 0 0
\(447\) −30.7583 8.24167i −1.45482 0.389818i
\(448\) −27.7128 27.7128i −1.30931 1.30931i
\(449\) 41.0000i 1.93491i 0.253044 + 0.967455i \(0.418568\pi\)
−0.253044 + 0.967455i \(0.581432\pi\)
\(450\) −21.0000 3.00000i −0.989949 0.141421i
\(451\) −12.0000 6.92820i −0.565058 0.326236i
\(452\) 2.73205 0.732051i 0.128505 0.0344328i
\(453\) −5.49038 20.4904i −0.257961 0.962722i
\(454\) −3.46410 6.00000i −0.162578 0.281594i
\(455\) 13.8564 + 6.92820i 0.649598 + 0.324799i
\(456\) −12.0000 27.7128i −0.561951 1.29777i
\(457\) 13.0000 + 13.0000i 0.608114 + 0.608114i 0.942453 0.334339i \(-0.108513\pi\)
−0.334339 + 0.942453i \(0.608513\pi\)
\(458\) −1.36603 0.366025i −0.0638302 0.0171032i
\(459\) 0 0
\(460\) −21.4641 4.39230i −1.00077 0.204792i
\(461\) −0.500000 + 0.866025i −0.0232873 + 0.0403348i −0.877434 0.479697i \(-0.840747\pi\)
0.854147 + 0.520032i \(0.174080\pi\)
\(462\) −20.7846 + 20.7846i −0.966988 + 0.966988i
\(463\) −6.92820 6.92820i −0.321981 0.321981i 0.527546 0.849527i \(-0.323112\pi\)
−0.849527 + 0.527546i \(0.823112\pi\)
\(464\) 3.46410 + 2.00000i 0.160817 + 0.0928477i
\(465\) 31.4711 35.4904i 1.45944 1.64583i
\(466\) −30.0000 −1.38972
\(467\) −17.3205 + 17.3205i −0.801498 + 0.801498i −0.983330 0.181832i \(-0.941797\pi\)
0.181832 + 0.983330i \(0.441797\pi\)
\(468\) −8.19615 2.19615i −0.378867 0.101517i
\(469\) −10.3923 + 6.00000i −0.479872 + 0.277054i
\(470\) −38.6603 + 2.32051i −1.78326 + 0.107037i
\(471\) −15.0000 + 8.66025i −0.691164 + 0.399043i
\(472\) −1.26795 4.73205i −0.0583621 0.217810i
\(473\) 2.19615 + 8.19615i 0.100979 + 0.376859i
\(474\) 25.9808 + 15.0000i 1.19334 + 0.688973i
\(475\) −10.9904 18.8205i −0.504273 0.863544i
\(476\) −36.0000 + 20.7846i −1.65006 + 0.952661i
\(477\) 12.2942 3.29423i 0.562914 0.150832i
\(478\) −0.633975 + 2.36603i −0.0289973 + 0.108219i
\(479\) 6.06218 + 10.5000i 0.276988 + 0.479757i 0.970635 0.240558i \(-0.0773304\pi\)
−0.693647 + 0.720315i \(0.743997\pi\)
\(480\) 27.7128 + 13.8564i 1.26491 + 0.632456i
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) 25.9545 6.95448i 1.18219 0.316768i
\(483\) 41.5692 + 41.5692i 1.89146 + 1.89146i
\(484\) −13.8564 8.00000i −0.629837 0.363636i
\(485\) −9.46410 8.39230i −0.429743 0.381075i
\(486\) 27.0000 + 15.5885i 1.22474 + 0.707107i
\(487\) 5.19615 5.19615i 0.235460 0.235460i −0.579507 0.814967i \(-0.696755\pi\)
0.814967 + 0.579507i \(0.196755\pi\)
\(488\) 8.19615 + 2.19615i 0.371022 + 0.0994151i
\(489\) 25.9808 + 15.0000i 1.17489 + 0.678323i
\(490\) 17.0000 + 51.0000i 0.767982 + 2.30395i
\(491\) 28.5000 + 16.4545i 1.28619 + 0.742580i 0.977972 0.208736i \(-0.0669350\pi\)
0.308215 + 0.951317i \(0.400268\pi\)
\(492\) 27.7128 27.7128i 1.24939 1.24939i
\(493\) 3.00000 3.00000i 0.135113 0.135113i
\(494\) −3.46410 8.00000i −0.155857 0.359937i
\(495\) 5.19615 10.3923i 0.233550 0.467099i
\(496\) −30.0000 + 17.3205i −1.34704 + 0.777714i
\(497\) 8.19615 2.19615i 0.367648 0.0985109i
\(498\) 24.0000 24.0000i 1.07547 1.07547i
\(499\) −13.8564 + 24.0000i −0.620298 + 1.07439i 0.369132 + 0.929377i \(0.379655\pi\)
−0.989430 + 0.145011i \(0.953678\pi\)
\(500\) 21.0526 + 7.53590i 0.941499 + 0.337016i
\(501\) 0 0
\(502\) −1.90192 7.09808i −0.0848870 0.316803i
\(503\) 0.633975 2.36603i 0.0282675 0.105496i −0.950351 0.311181i \(-0.899276\pi\)
0.978618 + 0.205685i \(0.0659422\pi\)
\(504\) −20.7846 36.0000i −0.925820 1.60357i
\(505\) −1.00000 + 2.00000i −0.0444994 + 0.0889988i
\(506\) 6.00000 10.3923i 0.266733 0.461994i
\(507\) 26.0263 + 6.97372i 1.15587 + 0.309714i
\(508\) 24.2487 + 24.2487i 1.07586 + 1.07586i
\(509\) −34.6410 + 20.0000i −1.53544 + 0.886484i −0.536339 + 0.844003i \(0.680193\pi\)
−0.999097 + 0.0424816i \(0.986474\pi\)
\(510\) 21.8038 24.5885i 0.965491 1.08880i
\(511\) −48.0000 27.7128i −2.12339 1.22594i
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 0 0
\(514\) −19.0526 11.0000i −0.840372 0.485189i
\(515\) −2.19615 + 10.7321i −0.0967740 + 0.472911i
\(516\) −24.0000 −1.05654
\(517\) 5.49038 20.4904i 0.241467 0.901166i
\(518\) −5.07180 + 18.9282i −0.222842 + 0.831658i
\(519\) 13.8564 + 24.0000i 0.608229 + 1.05348i
\(520\) 8.00000 + 4.00000i 0.350823 + 0.175412i
\(521\) 13.0000 0.569540 0.284770 0.958596i \(-0.408083\pi\)
0.284770 + 0.958596i \(0.408083\pi\)
\(522\) 3.00000 + 3.00000i 0.131306 + 0.131306i
\(523\) −0.633975 + 2.36603i −0.0277218 + 0.103459i −0.978401 0.206718i \(-0.933722\pi\)
0.950679 + 0.310177i \(0.100388\pi\)
\(524\) 20.7846 + 36.0000i 0.907980 + 1.57267i
\(525\) −36.0000 48.0000i −1.57117 2.09489i
\(526\) 24.2487i 1.05729i
\(527\) 9.50962 + 35.4904i 0.414246 + 1.54599i
\(528\) −12.0000 + 12.0000i −0.522233 + 0.522233i
\(529\) −0.866025 0.500000i −0.0376533 0.0217391i
\(530\) −13.3923 + 0.803848i −0.581725 + 0.0349169i
\(531\) 5.19615i 0.225494i
\(532\) 15.7128 39.7128i 0.681237 1.72177i
\(533\) 8.00000 8.00000i 0.346518 0.346518i
\(534\) 1.73205 + 3.00000i 0.0749532 + 0.129823i
\(535\) 32.1962 + 6.58846i 1.39196 + 0.284844i
\(536\) −6.00000 + 3.46410i −0.259161 + 0.149626i
\(537\) 20.4904 5.49038i 0.884225 0.236927i
\(538\) 25.0000 25.0000i 1.07783 1.07783i
\(539\) −29.4449 −1.26828
\(540\) 0 0
\(541\) 10.5000 + 18.1865i 0.451430 + 0.781900i 0.998475 0.0552031i \(-0.0175806\pi\)
−0.547045 + 0.837103i \(0.684247\pi\)
\(542\) −15.5885 + 15.5885i −0.669582 + 0.669582i
\(543\) 20.7846 + 20.7846i 0.891953 + 0.891953i
\(544\) −20.7846 + 12.0000i −0.891133 + 0.514496i
\(545\) −0.401924 6.69615i −0.0172165 0.286832i
\(546\) −12.0000 20.7846i −0.513553 0.889499i
\(547\) −4.73205 1.26795i −0.202328 0.0542136i 0.156232 0.987720i \(-0.450065\pi\)
−0.358560 + 0.933507i \(0.616732\pi\)
\(548\) 20.0000 20.0000i 0.854358 0.854358i
\(549\) 7.79423 + 4.50000i 0.332650 + 0.192055i
\(550\) −7.56218 + 9.63397i −0.322452 + 0.410794i
\(551\) −0.500000 + 4.33013i −0.0213007 + 0.184470i
\(552\) 24.0000 + 24.0000i 1.02151 + 1.02151i
\(553\) 10.9808 + 40.9808i 0.466950 + 1.74268i
\(554\) 27.7128 16.0000i 1.17740 0.679775i
\(555\) −0.928203 15.4641i −0.0394000 0.656415i
\(556\) 20.7846i 0.881464i
\(557\) 8.78461 32.7846i 0.372216 1.38913i −0.485154 0.874428i \(-0.661237\pi\)
0.857370 0.514700i \(-0.172097\pi\)
\(558\) −35.4904 + 9.50962i −1.50243 + 0.402574i
\(559\) −6.92820 −0.293032
\(560\) 13.8564 + 41.5692i 0.585540 + 1.75662i
\(561\) 9.00000 + 15.5885i 0.379980 + 0.658145i
\(562\) 2.73205 0.732051i 0.115245 0.0308797i
\(563\) 15.5885 + 15.5885i 0.656975 + 0.656975i 0.954663 0.297688i \(-0.0962155\pi\)
−0.297688 + 0.954663i \(0.596216\pi\)
\(564\) 51.9615 + 30.0000i 2.18797 + 1.26323i
\(565\) −3.09808 0.633975i −0.130337 0.0266715i
\(566\) 31.1769i 1.31046i
\(567\) 11.4115 + 42.5885i 0.479240 + 1.78855i
\(568\) 4.73205 1.26795i 0.198552 0.0532020i
\(569\) 13.0000i 0.544988i 0.962157 + 0.272494i \(0.0878485\pi\)
−0.962157 + 0.272494i \(0.912151\pi\)
\(570\) −1.85641 + 33.7128i −0.0777563 + 1.41207i
\(571\) 8.66025i 0.362420i −0.983444 0.181210i \(-0.941999\pi\)
0.983444 0.181210i \(-0.0580014\pi\)
\(572\) −3.46410 + 3.46410i −0.144841 + 0.144841i
\(573\) 5.49038 + 20.4904i 0.229364 + 0.855998i
\(574\) 55.4256 2.31342
\(575\) 19.2679 + 15.1244i 0.803529 + 0.630729i
\(576\) −12.0000 20.7846i −0.500000 0.866025i
\(577\) −22.0000 22.0000i −0.915872 0.915872i 0.0808540 0.996726i \(-0.474235\pi\)
−0.996726 + 0.0808540i \(0.974235\pi\)
\(578\) 0.366025 + 1.36603i 0.0152246 + 0.0568192i
\(579\) 13.8564 + 24.0000i 0.575853 + 0.997406i
\(580\) −2.46410 3.73205i −0.102316 0.154965i
\(581\) 48.0000 1.99138
\(582\) 5.07180 + 18.9282i 0.210233 + 0.784599i
\(583\) 1.90192 7.09808i 0.0787696 0.293972i
\(584\) −27.7128 16.0000i −1.14676 0.662085i
\(585\) 7.09808 + 6.29423i 0.293469 + 0.260234i
\(586\) 4.00000 + 6.92820i 0.165238 + 0.286201i
\(587\) −8.87564 33.1244i −0.366337 1.36719i −0.865599 0.500737i \(-0.833062\pi\)
0.499262 0.866451i \(-0.333604\pi\)
\(588\) 21.5551 80.4449i 0.888919 3.31749i
\(589\) −30.3109 22.5000i −1.24894 0.927096i
\(590\) −1.09808 + 5.36603i −0.0452071 + 0.220916i
\(591\) −3.00000 1.73205i −0.123404 0.0712470i
\(592\) −2.92820 + 10.9282i −0.120348 + 0.449146i
\(593\) −10.9282 2.92820i −0.448768 0.120247i 0.0273551 0.999626i \(-0.491292\pi\)
−0.476123 + 0.879379i \(0.657958\pi\)
\(594\) 0 0
\(595\) 46.3923 2.78461i 1.90190 0.114158i
\(596\) −13.0000 22.5167i −0.532501 0.922318i
\(597\) 33.0000 + 33.0000i 1.35060 + 1.35060i
\(598\) 6.92820 + 6.92820i 0.283315 + 0.283315i
\(599\) 10.3923 + 18.0000i 0.424618 + 0.735460i 0.996385 0.0849563i \(-0.0270751\pi\)
−0.571767 + 0.820416i \(0.693742\pi\)
\(600\) −20.7846 27.7128i −0.848528 1.13137i
\(601\) 3.00000 0.122373 0.0611863 0.998126i \(-0.480512\pi\)
0.0611863 + 0.998126i \(0.480512\pi\)
\(602\) −24.0000 24.0000i −0.978167 0.978167i
\(603\) −7.09808 + 1.90192i −0.289056 + 0.0774523i
\(604\) 8.66025 15.0000i 0.352381 0.610341i
\(605\) 9.85641 + 14.9282i 0.400720 + 0.606918i
\(606\) 3.00000 1.73205i 0.121867 0.0703598i
\(607\) 8.66025 8.66025i 0.351509 0.351509i −0.509162 0.860671i \(-0.670045\pi\)
0.860671 + 0.509162i \(0.170045\pi\)
\(608\) 9.07180 22.9282i 0.367910 0.929861i
\(609\) 12.0000i 0.486265i
\(610\) −7.09808 6.29423i −0.287393 0.254846i
\(611\) 15.0000 + 8.66025i 0.606835 + 0.350356i
\(612\) −24.5885 + 6.58846i −0.993929 + 0.266323i
\(613\) −2.56218 9.56218i −0.103485 0.386213i 0.894684 0.446701i \(-0.147401\pi\)
−0.998169 + 0.0604878i \(0.980734\pi\)
\(614\) −3.46410 −0.139800
\(615\) −41.5692 + 13.8564i −1.67623 + 0.558744i
\(616\) −24.0000 −0.966988
\(617\) −10.9808 + 40.9808i −0.442069 + 1.64982i 0.281493 + 0.959563i \(0.409171\pi\)
−0.723561 + 0.690260i \(0.757496\pi\)
\(618\) 12.0000 12.0000i 0.482711 0.482711i
\(619\) 34.6410 1.39234 0.696170 0.717877i \(-0.254886\pi\)
0.696170 + 0.717877i \(0.254886\pi\)
\(620\) 38.6603 2.32051i 1.55263 0.0931938i
\(621\) 0 0
\(622\) −18.9282 5.07180i −0.758952 0.203361i
\(623\) −1.26795 + 4.73205i −0.0507993 + 0.189586i
\(624\) −6.92820 12.0000i −0.277350 0.480384i
\(625\) −17.2846 18.0622i −0.691384 0.722487i
\(626\) 5.00000 8.66025i 0.199840 0.346133i
\(627\) −17.1962 6.80385i −0.686748 0.271719i
\(628\) −13.6603 3.66025i −0.545103 0.146060i
\(629\) 10.3923 + 6.00000i 0.414368 + 0.239236i
\(630\) 2.78461 + 46.3923i 0.110942 + 1.84831i
\(631\) −7.50000 + 4.33013i −0.298570 + 0.172380i −0.641800 0.766872i \(-0.721812\pi\)
0.343230 + 0.939251i \(0.388479\pi\)
\(632\) 6.33975 + 23.6603i 0.252182 + 0.941154i
\(633\) −36.8827 9.88269i −1.46596 0.392801i
\(634\) 20.7846 + 12.0000i 0.825462 + 0.476581i
\(635\) −12.1244 36.3731i −0.481140 1.44342i
\(636\) 18.0000 + 10.3923i 0.713746 + 0.412082i
\(637\) 6.22243 23.2224i 0.246542 0.920106i
\(638\) 2.36603 0.633975i 0.0936718 0.0250993i
\(639\) 5.19615 0.205557
\(640\) 8.00000 + 24.0000i 0.316228 + 0.948683i
\(641\) 14.5000 25.1147i 0.572716 0.991972i −0.423570 0.905863i \(-0.639223\pi\)
0.996286 0.0861092i \(-0.0274434\pi\)
\(642\) −36.0000 36.0000i −1.42081 1.42081i
\(643\) −2.36603 + 0.633975i −0.0933069 + 0.0250015i −0.305170 0.952298i \(-0.598713\pi\)
0.211864 + 0.977299i \(0.432047\pi\)
\(644\) 48.0000i 1.89146i
\(645\) 24.0000 + 12.0000i 0.944999 + 0.472500i
\(646\) −21.0000 15.5885i −0.826234 0.613320i
\(647\) 15.5885 15.5885i 0.612845 0.612845i −0.330841 0.943687i \(-0.607332\pi\)
0.943687 + 0.330841i \(0.107332\pi\)
\(648\) 6.58846 + 24.5885i 0.258819 + 0.965926i
\(649\) −2.59808 1.50000i −0.101983 0.0588802i
\(650\) −6.00000 8.00000i −0.235339 0.313786i
\(651\) −90.0000 51.9615i −3.52738 2.03653i
\(652\) 6.33975 + 23.6603i 0.248284 + 0.926607i
\(653\) −24.0000 + 24.0000i −0.939193 + 0.939193i −0.998254 0.0590618i \(-0.981189\pi\)
0.0590618 + 0.998254i \(0.481189\pi\)
\(654\) −5.19615 + 9.00000i −0.203186 + 0.351928i
\(655\) −2.78461 46.3923i −0.108804 1.81270i
\(656\) 32.0000 1.24939
\(657\) −24.0000 24.0000i −0.936329 0.936329i
\(658\) 21.9615 + 81.9615i 0.856149 + 3.19519i
\(659\) −24.2487 42.0000i −0.944596 1.63609i −0.756559 0.653926i \(-0.773121\pi\)
−0.188037 0.982162i \(-0.560212\pi\)
\(660\) 18.0000 6.00000i 0.700649 0.233550i
\(661\) −22.5000 38.9711i −0.875149 1.51580i −0.856604 0.515974i \(-0.827430\pi\)
−0.0185442 0.999828i \(-0.505903\pi\)
\(662\) −28.3923 7.60770i −1.10350 0.295681i
\(663\) −14.1962 + 3.80385i −0.551333 + 0.147729i
\(664\) 27.7128 1.07547
\(665\) −35.5692 + 31.8564i −1.37932 + 1.23534i
\(666\) −6.00000 + 10.3923i −0.232495 + 0.402694i
\(667\) −1.26795 4.73205i −0.0490952 0.183226i
\(668\) 0 0
\(669\) 0 0
\(670\) 7.73205 0.464102i 0.298715 0.0179298i
\(671\) 4.50000 2.59808i 0.173721 0.100298i
\(672\) 17.5692 65.5692i 0.677747 2.52939i
\(673\) −26.0000 + 26.0000i −1.00223 + 1.00223i −0.00222883 + 0.999998i \(0.500709\pi\)
−0.999998 + 0.00222883i \(0.999291\pi\)
\(674\) 28.0000i 1.07852i
\(675\) 0 0
\(676\) 11.0000 + 19.0526i 0.423077 + 0.732791i
\(677\) −18.0000 18.0000i −0.691796 0.691796i 0.270831 0.962627i \(-0.412702\pi\)
−0.962627 + 0.270831i \(0.912702\pi\)
\(678\) 3.46410 + 3.46410i 0.133038 + 0.133038i
\(679\) −13.8564 + 24.0000i −0.531760 + 0.921035i
\(680\) 26.7846 1.60770i 1.02714 0.0616523i
\(681\) 6.00000 10.3923i 0.229920 0.398234i
\(682\) −5.49038 + 20.4904i −0.210238 + 0.784617i
\(683\) −12.1244 12.1244i −0.463926 0.463926i 0.436014 0.899940i \(-0.356390\pi\)
−0.899940 + 0.436014i \(0.856390\pi\)
\(684\) 15.5885 21.0000i 0.596040 0.802955i
\(685\) −30.0000 + 10.0000i −1.14624 + 0.382080i
\(686\) 60.0000 34.6410i 2.29081 1.32260i
\(687\) −0.633975 2.36603i −0.0241876 0.0902695i
\(688\) −13.8564 13.8564i −0.528271 0.528271i
\(689\) 5.19615 + 3.00000i 0.197958 + 0.114291i
\(690\) −12.0000 36.0000i −0.456832 1.37050i
\(691\) 39.8372i 1.51548i 0.652558 + 0.757739i \(0.273696\pi\)
−0.652558 + 0.757739i \(0.726304\pi\)
\(692\) −5.85641 + 21.8564i −0.222627 + 0.830856i
\(693\) −24.5885 6.58846i −0.934038 0.250275i
\(694\) 27.7128 1.05196
\(695\) −10.3923 + 20.7846i −0.394203 + 0.788405i
\(696\) 6.92820i 0.262613i
\(697\) 8.78461 32.7846i 0.332741 1.24181i
\(698\) −32.7846 8.78461i −1.24092 0.332502i
\(699\) −25.9808 45.0000i −0.982683 1.70206i
\(700\) 6.92820 48.4974i 0.261861 1.83303i
\(701\) −8.00000 + 13.8564i −0.302156 + 0.523349i −0.976624 0.214955i \(-0.931040\pi\)
0.674468 + 0.738304i \(0.264373\pi\)
\(702\) 0 0
\(703\) −12.1962 + 1.80385i −0.459987 + 0.0680334i
\(704\) −13.8564 −0.522233
\(705\) −36.9615 55.9808i −1.39205 2.10836i
\(706\) 6.00000 + 10.3923i 0.225813 + 0.391120i
\(707\) 4.73205 + 1.26795i 0.177967 + 0.0476861i
\(708\) 6.00000 6.00000i 0.225494 0.225494i
\(709\) −11.2583 + 6.50000i −0.422815 + 0.244113i −0.696281 0.717769i \(-0.745163\pi\)
0.273466 + 0.961882i \(0.411830\pi\)
\(710\) −5.36603 1.09808i −0.201383 0.0412101i
\(711\) 25.9808i 0.974355i
\(712\) −0.732051 + 2.73205i −0.0274348 + 0.102388i
\(713\) 40.9808 + 10.9808i 1.53474 + 0.411233i
\(714\) −62.3538 36.0000i −2.33353 1.34727i
\(715\) 5.19615 1.73205i 0.194325 0.0647750i
\(716\) 15.0000 + 8.66025i 0.560576 + 0.323649i
\(717\) −4.09808 + 1.09808i −0.153045 + 0.0410084i
\(718\) −6.92820 6.92820i −0.258558 0.258558i
\(719\) 16.4545 28.5000i 0.613649 1.06287i −0.376971 0.926225i \(-0.623034\pi\)
0.990620 0.136646i \(-0.0436322\pi\)
\(720\) 1.60770 + 26.7846i 0.0599153 + 0.998203i
\(721\) 24.0000 0.893807
\(722\) 26.8564 0.856406i 0.999492 0.0318721i
\(723\) 32.9090 + 32.9090i 1.22390 + 1.22390i
\(724\) 24.0000i 0.891953i
\(725\) 0.598076 + 4.96410i 0.0222120 + 0.184362i
\(726\) 27.7128i 1.02852i
\(727\) 6.97372 + 26.0263i 0.258641 + 0.965261i 0.966029 + 0.258435i \(0.0832069\pi\)
−0.707388 + 0.706826i \(0.750126\pi\)
\(728\) 5.07180 18.9282i 0.187973 0.701526i
\(729\) 27.0000i 1.00000i
\(730\) 19.7128 + 29.8564i 0.729604 + 1.10504i
\(731\) −18.0000 + 10.3923i −0.665754 + 0.384373i
\(732\) 3.80385 + 14.1962i 0.140594 + 0.524705i
\(733\) −28.0000 + 28.0000i −1.03420 + 1.03420i −0.0348096 + 0.999394i \(0.511082\pi\)
−0.999394 + 0.0348096i \(0.988918\pi\)
\(734\) 6.92820 12.0000i 0.255725 0.442928i
\(735\) −61.7776 + 69.6673i −2.27870 + 2.56972i
\(736\) 27.7128i 1.02151i
\(737\) −1.09808 + 4.09808i −0.0404482 + 0.150955i
\(738\) 32.7846 + 8.78461i 1.20682 + 0.323366i
\(739\) −7.79423 + 13.5000i −0.286715 + 0.496606i −0.973024 0.230705i \(-0.925897\pi\)
0.686308 + 0.727311i \(0.259230\pi\)
\(740\) 8.39230 9.46410i 0.308507 0.347907i
\(741\) 9.00000 12.1244i 0.330623 0.445399i
\(742\) 7.60770 + 28.3923i 0.279287 + 1.04231i
\(743\) −9.46410 + 2.53590i −0.347204 + 0.0930331i −0.428207 0.903681i \(-0.640854\pi\)
0.0810025 + 0.996714i \(0.474188\pi\)
\(744\) −51.9615 30.0000i −1.90500 1.09985i
\(745\) 1.74167 + 29.0167i 0.0638098 + 1.06309i
\(746\) 10.0000 + 17.3205i 0.366126 + 0.634149i
\(747\) 28.3923 + 7.60770i 1.03882 + 0.278351i
\(748\) −3.80385 + 14.1962i −0.139082 + 0.519063i
\(749\) 72.0000i 2.63082i
\(750\) 6.92820 + 38.1051i 0.252982 + 1.39140i
\(751\) −16.5000 + 9.52628i −0.602094 + 0.347619i −0.769865 0.638207i \(-0.779676\pi\)
0.167771 + 0.985826i \(0.446343\pi\)
\(752\) 12.6795 + 47.3205i 0.462373 + 1.72560i
\(753\) 9.00000 9.00000i 0.327978 0.327978i
\(754\) 2.00000i 0.0728357i
\(755\) −16.1603 + 10.6699i −0.588132 + 0.388316i
\(756\) 0 0
\(757\) 6.83013 1.83013i 0.248245 0.0665171i −0.132551 0.991176i \(-0.542317\pi\)
0.380796 + 0.924659i \(0.375650\pi\)
\(758\) 13.3135 49.6865i 0.483567 1.80470i
\(759\) 20.7846 0.754434
\(760\) −20.5359 + 18.3923i −0.744915 + 0.667159i
\(761\) −20.0000 −0.724999 −0.362500 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(762\) −15.3731 + 57.3731i −0.556907 + 2.07841i
\(763\) −14.1962 + 3.80385i −0.513935 + 0.137709i
\(764\) −8.66025 + 15.0000i −0.313317 + 0.542681i
\(765\) 27.8827 + 5.70577i 1.00810 + 0.206293i
\(766\)