Properties

Label 380.2.v.b.7.1
Level $380$
Weight $2$
Character 380.7
Analytic conductor $3.034$
Analytic rank $0$
Dimension $4$
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 7.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 380.7
Dual form 380.2.v.b.163.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.36603 - 0.366025i) q^{2} +(-0.633975 + 2.36603i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.23205 + 0.133975i) q^{5} +3.46410i q^{6} +(-3.46410 + 3.46410i) q^{7} +(2.00000 - 2.00000i) q^{8} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(1.36603 - 0.366025i) q^{2} +(-0.633975 + 2.36603i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.23205 + 0.133975i) 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} +(1.26795 + 4.73205i) q^{12} +(-0.366025 - 1.36603i) q^{13} +(-3.46410 + 6.00000i) q^{14} +(1.09808 - 5.36603i) q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.09808 + 4.09808i) q^{17} +(-4.09808 - 1.09808i) q^{18} +(2.59808 + 3.50000i) q^{19} +(-3.73205 + 2.46410i) q^{20} +(-6.00000 - 10.3923i) q^{21} +(0.633975 + 2.36603i) q^{22} +(4.73205 - 1.26795i) q^{23} +(3.46410 + 6.00000i) q^{24} +(4.96410 - 0.598076i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-2.53590 + 9.46410i) q^{28} +(-0.866025 - 0.500000i) q^{29} +(-0.464102 - 7.73205i) q^{30} -8.66025i q^{31} +(1.46410 - 5.46410i) q^{32} +(-4.09808 - 1.09808i) q^{33} +6.00000i q^{34} +(7.26795 - 8.19615i) q^{35} -6.00000 q^{36} +(2.00000 + 2.00000i) q^{37} +(4.83013 + 3.83013i) q^{38} +3.46410 q^{39} +(-4.19615 + 4.73205i) q^{40} +(4.00000 + 6.92820i) q^{41} +(-12.0000 - 12.0000i) q^{42} +(-1.26795 + 4.73205i) q^{43} +(1.73205 + 3.00000i) q^{44} +(6.00000 + 3.00000i) q^{45} +(6.00000 - 3.46410i) q^{46} +(3.16987 + 11.8301i) q^{47} +(6.92820 + 6.92820i) q^{48} -17.0000i q^{49} +(6.56218 - 2.63397i) q^{50} +(-9.00000 - 5.19615i) q^{51} +(-2.00000 - 2.00000i) q^{52} +(-1.09808 - 4.09808i) q^{53} +(-0.232051 - 3.86603i) q^{55} +13.8564i q^{56} +(-9.92820 + 3.92820i) q^{57} +(-1.36603 - 0.366025i) q^{58} +(-0.866025 - 1.50000i) q^{59} +(-3.46410 - 10.3923i) q^{60} +(1.50000 - 2.59808i) q^{61} +(-3.16987 - 11.8301i) q^{62} +(14.1962 - 3.80385i) q^{63} -8.00000i q^{64} +(1.00000 + 3.00000i) q^{65} -6.00000 q^{66} +(-0.633975 - 2.36603i) q^{67} +(2.19615 + 8.19615i) q^{68} +12.0000i q^{69} +(6.92820 - 13.8564i) q^{70} +(1.50000 - 0.866025i) q^{71} +(-8.19615 + 2.19615i) q^{72} +(10.9282 + 2.92820i) 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} +(4.73205 - 1.26795i) 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} +(1.90192 - 9.29423i) q^{85} +6.92820i q^{86} +(1.73205 - 1.73205i) q^{87} +(3.46410 + 3.46410i) q^{88} +(0.866025 + 0.500000i) q^{89} +(9.29423 + 1.90192i) q^{90} +(6.00000 + 3.46410i) q^{91} +(6.92820 - 6.92820i) q^{92} +(20.4904 + 5.49038i) q^{93} +(8.66025 + 15.0000i) q^{94} +(-6.26795 - 7.46410i) q^{95} +(12.0000 + 6.92820i) q^{96} +(1.46410 - 5.46410i) q^{97} +(-6.22243 - 23.2224i) 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 \(\left(\mathbb{Z}/380\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.36603 0.366025i 0.965926 0.258819i
\(3\) −0.633975 + 2.36603i −0.366025 + 1.36603i 0.500000 + 0.866025i \(0.333333\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 1.73205 1.00000i 0.866025 0.500000i
\(5\) −2.23205 + 0.133975i −0.998203 + 0.0599153i
\(6\) 3.46410i 1.41421i
\(7\) −3.46410 + 3.46410i −1.30931 + 1.30931i −0.387392 + 0.921915i \(0.626624\pi\)
−0.921915 + 0.387392i \(0.873376\pi\)
\(8\) 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 \(0.0840907\pi\)
−0.965307 + 0.261116i \(0.915909\pi\)
\(12\) 1.26795 + 4.73205i 0.366025 + 1.36603i
\(13\) −0.366025 1.36603i −0.101517 0.378867i 0.896410 0.443227i \(-0.146166\pi\)
−0.997927 + 0.0643593i \(0.979500\pi\)
\(14\) −3.46410 + 6.00000i −0.925820 + 1.60357i
\(15\) 1.09808 5.36603i 0.283522 1.38550i
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −1.09808 + 4.09808i −0.266323 + 0.993929i 0.695113 + 0.718900i \(0.255354\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) −4.09808 1.09808i −0.965926 0.258819i
\(19\) 2.59808 + 3.50000i 0.596040 + 0.802955i
\(20\) −3.73205 + 2.46410i −0.834512 + 0.550990i
\(21\) −6.00000 10.3923i −1.30931 2.26779i
\(22\) 0.633975 + 2.36603i 0.135164 + 0.504438i
\(23\) 4.73205 1.26795i 0.986701 0.264386i 0.270837 0.962625i \(-0.412700\pi\)
0.715864 + 0.698240i \(0.246033\pi\)
\(24\) 3.46410 + 6.00000i 0.707107 + 1.22474i
\(25\) 4.96410 0.598076i 0.992820 0.119615i
\(26\) −1.00000 1.73205i −0.196116 0.339683i
\(27\) 0 0
\(28\) −2.53590 + 9.46410i −0.479240 + 1.78855i
\(29\) −0.866025 0.500000i −0.160817 0.0928477i 0.417432 0.908708i \(-0.362930\pi\)
−0.578249 + 0.815861i \(0.696264\pi\)
\(30\) −0.464102 7.73205i −0.0847330 1.41167i
\(31\) 8.66025i 1.55543i −0.628619 0.777714i \(-0.716379\pi\)
0.628619 0.777714i \(-0.283621\pi\)
\(32\) 1.46410 5.46410i 0.258819 0.965926i
\(33\) −4.09808 1.09808i −0.713384 0.191151i
\(34\) 6.00000i 1.02899i
\(35\) 7.26795 8.19615i 1.22851 1.38540i
\(36\) −6.00000 −1.00000
\(37\) 2.00000 + 2.00000i 0.328798 + 0.328798i 0.852129 0.523331i \(-0.175311\pi\)
−0.523331 + 0.852129i \(0.675311\pi\)
\(38\) 4.83013 + 3.83013i 0.783550 + 0.621329i
\(39\) 3.46410 0.554700
\(40\) −4.19615 + 4.73205i −0.663470 + 0.748203i
\(41\) 4.00000 + 6.92820i 0.624695 + 1.08200i 0.988600 + 0.150567i \(0.0481100\pi\)
−0.363905 + 0.931436i \(0.618557\pi\)
\(42\) −12.0000 12.0000i −1.85164 1.85164i
\(43\) −1.26795 + 4.73205i −0.193360 + 0.721631i 0.799325 + 0.600899i \(0.205191\pi\)
−0.992685 + 0.120732i \(0.961476\pi\)
\(44\) 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
\(47\) 3.16987 + 11.8301i 0.462373 + 1.72560i 0.665454 + 0.746439i \(0.268238\pi\)
−0.203080 + 0.979162i \(0.565095\pi\)
\(48\) 6.92820 + 6.92820i 1.00000 + 1.00000i
\(49\) 17.0000i 2.42857i
\(50\) 6.56218 2.63397i 0.928032 0.372500i
\(51\) −9.00000 5.19615i −1.26025 0.727607i
\(52\) −2.00000 2.00000i −0.277350 0.277350i
\(53\) −1.09808 4.09808i −0.150832 0.562914i −0.999426 0.0338693i \(-0.989217\pi\)
0.848594 0.529045i \(-0.177450\pi\)
\(54\) 0 0
\(55\) −0.232051 3.86603i −0.0312897 0.521295i
\(56\) 13.8564i 1.85164i
\(57\) −9.92820 + 3.92820i −1.31502 + 0.520303i
\(58\) −1.36603 0.366025i −0.179368 0.0480615i
\(59\) −0.866025 1.50000i −0.112747 0.195283i 0.804130 0.594454i \(-0.202632\pi\)
−0.916877 + 0.399170i \(0.869298\pi\)
\(60\) −3.46410 10.3923i −0.447214 1.34164i
\(61\) 1.50000 2.59808i 0.192055 0.332650i −0.753876 0.657017i \(-0.771818\pi\)
0.945931 + 0.324367i \(0.105151\pi\)
\(62\) −3.16987 11.8301i −0.402574 1.50243i
\(63\) 14.1962 3.80385i 1.78855 0.479240i
\(64\) 8.00000i 1.00000i
\(65\) 1.00000 + 3.00000i 0.124035 + 0.372104i
\(66\) −6.00000 −0.738549
\(67\) −0.633975 2.36603i −0.0774523 0.289056i 0.916326 0.400433i \(-0.131140\pi\)
−0.993778 + 0.111377i \(0.964474\pi\)
\(68\) 2.19615 + 8.19615i 0.266323 + 0.993929i
\(69\) 12.0000i 1.44463i
\(70\) 6.92820 13.8564i 0.828079 1.65616i
\(71\) 1.50000 0.866025i 0.178017 0.102778i −0.408344 0.912828i \(-0.633893\pi\)
0.586361 + 0.810050i \(0.300560\pi\)
\(72\) −8.19615 + 2.19615i −0.965926 + 0.258819i
\(73\) 10.9282 + 2.92820i 1.27905 + 0.342720i 0.833491 0.552533i \(-0.186339\pi\)
0.445558 + 0.895253i \(0.353005\pi\)
\(74\) 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
\(78\) 4.73205 1.26795i 0.535799 0.143567i
\(79\) 4.33013 + 7.50000i 0.487177 + 0.843816i 0.999891 0.0147436i \(-0.00469319\pi\)
−0.512714 + 0.858559i \(0.671360\pi\)
\(80\) −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 0.215938 0.976407i \(-0.430719\pi\)
−0.976407 + 0.215938i \(0.930719\pi\)
\(84\) −20.7846 12.0000i −2.26779 1.30931i
\(85\) 1.90192 9.29423i 0.206293 1.00810i
\(86\) 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 \(-0.316455\pi\)
−0.453398 + 0.891308i \(0.649788\pi\)
\(90\) 9.29423 + 1.90192i 0.979698 + 0.200480i
\(91\) 6.00000 + 3.46410i 0.628971 + 0.363137i
\(92\) 6.92820 6.92820i 0.722315 0.722315i
\(93\) 20.4904 + 5.49038i 2.12475 + 0.569326i
\(94\) 8.66025 + 15.0000i 0.893237 + 1.54713i
\(95\) −6.26795 7.46410i −0.643078 0.765801i
\(96\) 12.0000 + 6.92820i 1.22474 + 0.707107i
\(97\) 1.46410 5.46410i 0.148657 0.554795i −0.850908 0.525314i \(-0.823948\pi\)
0.999565 0.0294813i \(-0.00938554\pi\)
\(98\) −6.22243 23.2224i −0.628561 2.34582i
\(99\) 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 −0.840077 0.542467i \(-0.817490\pi\)
0.889829 + 0.456294i \(0.150824\pi\)
\(102\) −14.1962 3.80385i −1.40563 0.376637i
\(103\) −3.46410 3.46410i −0.341328 0.341328i 0.515538 0.856866i \(-0.327592\pi\)
−0.856866 + 0.515538i \(0.827592\pi\)
\(104\) −3.46410 2.00000i −0.339683 0.196116i
\(105\) 14.7846 + 22.3923i 1.44283 + 2.18527i
\(106\) −3.00000 5.19615i −0.291386 0.504695i
\(107\) −10.3923 + 10.3923i −1.00466 + 1.00466i −0.00467295 + 0.999989i \(0.501487\pi\)
−0.999989 + 0.00467295i \(0.998513\pi\)
\(108\) 0 0
\(109\) 2.59808 1.50000i 0.248851 0.143674i −0.370387 0.928877i \(-0.620775\pi\)
0.619238 + 0.785203i \(0.287442\pi\)
\(110\) −1.73205 5.19615i −0.165145 0.495434i
\(111\) −6.00000 + 3.46410i −0.569495 + 0.328798i
\(112\) 5.07180 + 18.9282i 0.479240 + 1.78855i
\(113\) −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
\(117\) −1.09808 + 4.09808i −0.101517 + 0.378867i
\(118\) −1.73205 1.73205i −0.159448 0.159448i
\(119\) −10.3923 18.0000i −0.952661 1.65006i
\(120\) −8.53590 12.9282i −0.779217 1.18018i
\(121\) 8.00000 0.727273
\(122\) 1.09808 4.09808i 0.0994151 0.371022i
\(123\) −18.9282 + 5.07180i −1.70670 + 0.457309i
\(124\) −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
\(127\) −4.43782 16.5622i −0.393793 1.46966i −0.823826 0.566843i \(-0.808165\pi\)
0.430033 0.902813i \(-0.358502\pi\)
\(128\) −2.92820 10.9282i −0.258819 0.965926i
\(129\) −10.3923 6.00000i −0.914991 0.528271i
\(130\) 2.46410 + 3.73205i 0.216116 + 0.327323i
\(131\) −18.0000 + 10.3923i −1.57267 + 0.907980i −0.576827 + 0.816866i \(0.695709\pi\)
−0.995841 + 0.0911134i \(0.970957\pi\)
\(132\) −8.19615 + 2.19615i −0.713384 + 0.191151i
\(133\) −21.1244 3.12436i −1.83171 0.270916i
\(134\) −1.73205 3.00000i −0.149626 0.259161i
\(135\) 0 0
\(136\) 6.00000 + 10.3923i 0.514496 + 0.891133i
\(137\) 13.6603 3.66025i 1.16707 0.312717i 0.377286 0.926097i \(-0.376857\pi\)
0.789788 + 0.613380i \(0.210191\pi\)
\(138\) 4.39230 + 16.3923i 0.373898 + 1.39541i
\(139\) −5.19615 + 9.00000i −0.440732 + 0.763370i −0.997744 0.0671344i \(-0.978614\pi\)
0.557012 + 0.830504i \(0.311948\pi\)
\(140\) 4.39230 21.4641i 0.371218 1.81405i
\(141\) −30.0000 −2.52646
\(142\) 1.73205 1.73205i 0.145350 0.145350i
\(143\) 2.36603 0.633975i 0.197857 0.0530156i
\(144\) −10.3923 + 6.00000i −0.866025 + 0.500000i
\(145\) 2.00000 + 1.00000i 0.166091 + 0.0830455i
\(146\) 16.0000 1.32417
\(147\) 40.2224 + 10.7776i 3.31749 + 0.888919i
\(148\) 5.46410 + 1.46410i 0.449146 + 0.120348i
\(149\) −11.2583 + 6.50000i −0.922318 + 0.532501i −0.884374 0.466779i \(-0.845414\pi\)
−0.0379444 + 0.999280i \(0.512081\pi\)
\(150\) 2.07180 + 17.1962i 0.169161 + 1.40406i
\(151\) 8.66025i 0.704761i −0.935857 0.352381i \(-0.885372\pi\)
0.935857 0.352381i \(-0.114628\pi\)
\(152\) 12.1962 + 1.80385i 0.989239 + 0.146311i
\(153\) 9.00000 9.00000i 0.727607 0.727607i
\(154\) −10.3923 6.00000i −0.837436 0.483494i
\(155\) 1.16025 + 19.3301i 0.0931938 + 1.55263i
\(156\) 6.00000 3.46410i 0.480384 0.277350i
\(157\) −1.83013 + 6.83013i −0.146060 + 0.545103i 0.853646 + 0.520854i \(0.174386\pi\)
−0.999706 + 0.0242497i \(0.992280\pi\)
\(158\) 8.66025 + 8.66025i 0.688973 + 0.688973i
\(159\) 10.3923 0.824163
\(160\) −2.53590 + 12.3923i −0.200480 + 0.979698i
\(161\) −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 0.959621 0.281297i \(-0.0907647\pi\)
−0.281297 + 0.959621i \(0.590765\pi\)
\(164\) 13.8564 + 8.00000i 1.08200 + 0.624695i
\(165\) 9.29423 + 1.90192i 0.723555 + 0.148065i
\(166\) −12.0000 6.92820i −0.931381 0.537733i
\(167\) 0 0 0.965926 0.258819i \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(168\) −32.7846 8.78461i −2.52939 0.677747i
\(169\) 9.52628 5.50000i 0.732791 0.423077i
\(170\) −0.803848 13.3923i −0.0616523 1.02714i
\(171\) −1.50000 12.9904i −0.114708 0.993399i
\(172\) 2.53590 + 9.46410i 0.193360 + 0.721631i
\(173\) 10.9282 + 2.92820i 0.830856 + 0.222627i 0.649087 0.760714i \(-0.275151\pi\)
0.181769 + 0.983341i \(0.441818\pi\)
\(174\) 1.73205 3.00000i 0.131306 0.227429i
\(175\) −15.1244 + 19.2679i −1.14329 + 1.45652i
\(176\) 6.00000 + 3.46410i 0.452267 + 0.261116i
\(177\) 4.09808 1.09808i 0.308030 0.0825365i
\(178\) 1.36603 + 0.366025i 0.102388 + 0.0274348i
\(179\) 8.66025 0.647298 0.323649 0.946177i \(-0.395090\pi\)
0.323649 + 0.946177i \(0.395090\pi\)
\(180\) 13.3923 0.803848i 0.998203 0.0599153i
\(181\) −6.00000 + 10.3923i −0.445976 + 0.772454i −0.998120 0.0612954i \(-0.980477\pi\)
0.552143 + 0.833749i \(0.313810\pi\)
\(182\) 9.46410 + 2.53590i 0.701526 + 0.187973i
\(183\) 5.19615 + 5.19615i 0.384111 + 0.384111i
\(184\) 6.92820 12.0000i 0.510754 0.884652i
\(185\) −4.73205 4.19615i −0.347907 0.308507i
\(186\) 30.0000 2.19971
\(187\) −7.09808 1.90192i −0.519063 0.139082i
\(188\) 17.3205 + 17.3205i 1.26323 + 1.26323i
\(189\) 0 0
\(190\) −11.2942 7.90192i −0.819369 0.573266i
\(191\) 8.66025i 0.626634i 0.949649 + 0.313317i \(0.101440\pi\)
−0.949649 + 0.313317i \(0.898560\pi\)
\(192\) 18.9282 + 5.07180i 1.36603 + 0.366025i
\(193\) 10.9282 + 2.92820i 0.786629 + 0.210777i 0.629705 0.776834i \(-0.283176\pi\)
0.156924 + 0.987611i \(0.449842\pi\)
\(194\) 8.00000i 0.574367i
\(195\) −7.73205 + 0.464102i −0.553704 + 0.0332350i
\(196\) −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 \(0.733957\pi\)
\(198\) 1.90192 7.09808i 0.135164 0.504438i
\(199\) 9.52628 16.5000i 0.675300 1.16965i −0.301081 0.953599i \(-0.597347\pi\)
0.976381 0.216055i \(-0.0693192\pi\)
\(200\) 8.73205 11.1244i 0.617449 0.786611i
\(201\) 6.00000 0.423207
\(202\) 0.366025 1.36603i 0.0257535 0.0961132i
\(203\) 4.73205 1.26795i 0.332125 0.0889926i
\(204\) −20.7846 −1.45521
\(205\) −9.85641 14.9282i −0.688401 1.04263i
\(206\) −6.00000 3.46410i −0.418040 0.241355i
\(207\) −14.1962 3.80385i −0.986701 0.264386i
\(208\) −5.46410 1.46410i −0.378867 0.101517i
\(209\) −6.06218 + 4.50000i −0.419330 + 0.311272i
\(210\) 28.3923 + 25.1769i 1.95926 + 1.73737i
\(211\) 13.5000 7.79423i 0.929378 0.536577i 0.0427634 0.999085i \(-0.486384\pi\)
0.886615 + 0.462508i \(0.153050\pi\)
\(212\) −6.00000 6.00000i −0.412082 0.412082i
\(213\) 1.09808 + 4.09808i 0.0752389 + 0.280796i
\(214\) −10.3923 + 18.0000i −0.710403 + 1.23045i
\(215\) 2.19615 10.7321i 0.149776 0.731920i
\(216\) 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
\(220\) −4.26795 6.46410i −0.287745 0.435810i
\(221\) 6.00000 0.403604
\(222\) −6.92820 + 6.92820i −0.464991 + 0.464991i
\(223\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(224\) 13.8564 + 24.0000i 0.925820 + 1.60357i
\(225\) −13.7942 5.89230i −0.919615 0.392820i
\(226\) −1.00000 + 1.73205i −0.0665190 + 0.115214i
\(227\) 3.46410 3.46410i 0.229920 0.229920i −0.582739 0.812659i \(-0.698019\pi\)
0.812659 + 0.582739i \(0.198019\pi\)
\(228\) −13.2679 + 16.7321i −0.878691 + 1.10811i
\(229\) 1.00000i 0.0660819i 0.999454 + 0.0330409i \(0.0105192\pi\)
−0.999454 + 0.0330409i \(0.989481\pi\)
\(230\) −12.9282 + 8.53590i −0.852460 + 0.562840i
\(231\) 18.0000 10.3923i 1.18431 0.683763i
\(232\) −2.73205 + 0.732051i −0.179368 + 0.0480615i
\(233\) −20.4904 5.49038i −1.34237 0.359687i −0.485057 0.874483i \(-0.661201\pi\)
−0.857313 + 0.514796i \(0.827868\pi\)
\(234\) 6.00000i 0.392232i
\(235\) −8.66025 25.9808i −0.564933 1.69480i
\(236\) −3.00000 1.73205i −0.195283 0.112747i
\(237\) −20.4904 + 5.49038i −1.33099 + 0.356639i
\(238\) −20.7846 20.7846i −1.34727 1.34727i
\(239\) −1.73205 −0.112037 −0.0560185 0.998430i \(-0.517841\pi\)
−0.0560185 + 0.998430i \(0.517841\pi\)
\(240\) −16.3923 14.5359i −1.05812 0.938288i
\(241\) −9.50000 + 16.4545i −0.611949 + 1.05993i 0.378963 + 0.925412i \(0.376281\pi\)
−0.990912 + 0.134515i \(0.957053\pi\)
\(242\) 10.9282 2.92820i 0.702492 0.188232i
\(243\) 21.2942 5.70577i 1.36603 0.366025i
\(244\) 6.00000i 0.384111i
\(245\) 2.27757 + 37.9449i 0.145508 + 2.42421i
\(246\) −24.0000 + 13.8564i −1.53018 + 0.883452i
\(247\) 3.83013 4.83013i 0.243705 0.307334i
\(248\) −17.3205 17.3205i −1.09985 1.09985i
\(249\) 20.7846 12.0000i 1.31717 0.760469i
\(250\) −14.2942 + 6.75833i −0.904046 + 0.427434i
\(251\) −4.50000 2.59808i −0.284037 0.163989i 0.351212 0.936296i \(-0.385770\pi\)
−0.635250 + 0.772307i \(0.719103\pi\)
\(252\) 20.7846 20.7846i 1.30931 1.30931i
\(253\) 2.19615 + 8.19615i 0.138071 + 0.515288i
\(254\) −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
\(257\) 15.0263 4.02628i 0.937314 0.251152i 0.242343 0.970191i \(-0.422084\pi\)
0.694971 + 0.719038i \(0.255417\pi\)
\(258\) −16.3923 4.39230i −1.02054 0.273453i
\(259\) −13.8564 −0.860995
\(260\) 4.73205 + 4.19615i 0.293469 + 0.260234i
\(261\) 1.50000 + 2.59808i 0.0928477 + 0.160817i
\(262\) −20.7846 + 20.7846i −1.28408 + 1.28408i
\(263\) −4.43782 + 16.5622i −0.273648 + 1.02127i 0.683094 + 0.730330i \(0.260634\pi\)
−0.956742 + 0.290937i \(0.906033\pi\)
\(264\) −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 \(-0.390816\pi\)
0.983738 + 0.179608i \(0.0574829\pi\)
\(270\) 0 0
\(271\) 13.5000 7.79423i 0.820067 0.473466i −0.0303728 0.999539i \(-0.509669\pi\)
0.850439 + 0.526073i \(0.176336\pi\)
\(272\) 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
\(275\) 1.03590 + 8.59808i 0.0624670 + 0.518484i
\(276\) 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 \(0.987923\pi\)
\(278\) −3.80385 + 14.1962i −0.228140 + 0.851429i
\(279\) −12.9904 + 22.5000i −0.777714 + 1.34704i
\(280\) −1.85641 30.9282i −0.110942 1.84831i
\(281\) −1.00000 + 1.73205i −0.0596550 + 0.103325i −0.894311 0.447447i \(-0.852333\pi\)
0.834656 + 0.550772i \(0.185667\pi\)
\(282\) −40.9808 + 10.9808i −2.44037 + 0.653895i
\(283\) 5.70577 21.2942i 0.339173 1.26581i −0.560101 0.828424i \(-0.689238\pi\)
0.899274 0.437386i \(-0.144096\pi\)
\(284\) 1.73205 3.00000i 0.102778 0.178017i
\(285\) 21.6340 10.0981i 1.28149 0.598158i
\(286\) 3.00000 1.73205i 0.177394 0.102418i
\(287\) −37.8564 10.1436i −2.23459 0.598757i
\(288\) −12.0000 + 12.0000i −0.707107 + 0.707107i
\(289\) −0.866025 0.500000i −0.0509427 0.0294118i
\(290\) 3.09808 + 0.633975i 0.181925 + 0.0372283i
\(291\) 12.0000 + 6.92820i 0.703452 + 0.406138i
\(292\) 21.8564 5.85641i 1.27905 0.342720i
\(293\) 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
\(295\) 2.13397 + 3.23205i 0.124245 + 0.188177i
\(296\) 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
\(300\) 9.12436 + 22.7321i 0.526795 + 1.31244i
\(301\) −12.0000 20.7846i −0.691669 1.19800i
\(302\) −3.16987 11.8301i −0.182406 0.680747i
\(303\) 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
\(307\) 2.36603 + 0.633975i 0.135036 + 0.0361828i 0.325704 0.945472i \(-0.394399\pi\)
−0.190668 + 0.981655i \(0.561065\pi\)
\(308\) −16.3923 4.39230i −0.934038 0.250275i
\(309\) 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 \(-0.871485\pi\)
0.919597 0.392862i \(-0.128515\pi\)
\(312\) 6.92820 6.92820i 0.392232 0.392232i
\(313\) 1.83013 + 6.83013i 0.103445 + 0.386062i 0.998164 0.0605675i \(-0.0192910\pi\)
−0.894719 + 0.446629i \(0.852624\pi\)
\(314\) 10.0000i 0.564333i
\(315\) −31.1769 + 10.3923i −1.75662 + 0.585540i
\(316\) 15.0000 + 8.66025i 0.843816 + 0.487177i
\(317\) −16.3923 + 4.39230i −0.920684 + 0.246696i −0.687878 0.725827i \(-0.741457\pi\)
−0.232806 + 0.972523i \(0.574791\pi\)
\(318\) 14.1962 3.80385i 0.796081 0.213309i
\(319\) 0.866025 1.50000i 0.0484881 0.0839839i
\(320\) 1.07180 + 17.8564i 0.0599153 + 0.998203i
\(321\) −18.0000 31.1769i −1.00466 1.74013i
\(322\) −8.78461 + 32.7846i −0.489547 + 1.82701i
\(323\) −17.1962 + 6.80385i −0.956820 + 0.378576i
\(324\) −15.5885 9.00000i −0.866025 0.500000i
\(325\) −2.63397 6.56218i −0.146107 0.364004i
\(326\) 15.0000 + 8.66025i 0.830773 + 0.479647i
\(327\) 1.90192 + 7.09808i 0.105177 + 0.392525i
\(328\) 21.8564 + 5.85641i 1.20682 + 0.323366i
\(329\) −51.9615 30.0000i −2.86473 1.65395i
\(330\) 13.3923 0.803848i 0.737222 0.0442504i
\(331\) 20.7846i 1.14243i −0.820802 0.571213i \(-0.806473\pi\)
0.820802 0.571213i \(-0.193527\pi\)
\(332\) −18.9282 5.07180i −1.03882 0.278351i
\(333\) −2.19615 8.19615i −0.120348 0.449146i
\(334\) 0 0
\(335\) 1.73205 + 5.19615i 0.0946320 + 0.283896i
\(336\) −48.0000 −2.61861
\(337\) 5.12436 19.1244i 0.279141 1.04177i −0.673874 0.738847i \(-0.735371\pi\)
0.953015 0.302923i \(-0.0979626\pi\)
\(338\) 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
\(342\) −6.80385 17.1962i −0.367910 0.929861i
\(343\) 34.6410 + 34.6410i 1.87044 + 1.87044i
\(344\) 6.92820 + 12.0000i 0.373544 + 0.646997i
\(345\) −1.60770 26.7846i −0.0865554 1.44203i
\(346\) 16.0000 0.860165
\(347\) −18.9282 5.07180i −1.01612 0.272268i −0.287935 0.957650i \(-0.592969\pi\)
−0.728184 + 0.685382i \(0.759635\pi\)
\(348\) 1.26795 4.73205i 0.0679692 0.253665i
\(349\) 24.0000i 1.28469i 0.766415 + 0.642345i \(0.222038\pi\)
−0.766415 + 0.642345i \(0.777962\pi\)
\(350\) −13.6077 + 31.8564i −0.727362 + 1.70280i
\(351\) 0 0
\(352\) 9.46410 + 2.53590i 0.504438 + 0.135164i
\(353\) 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
\(355\) −3.23205 + 2.13397i −0.171539 + 0.113260i
\(356\) 2.00000 0.106000
\(357\) 49.1769 13.1769i 2.60272 0.697396i
\(358\) 11.8301 3.16987i 0.625242 0.167533i
\(359\) 3.46410 + 6.00000i 0.182828 + 0.316668i 0.942843 0.333238i \(-0.108141\pi\)
−0.760014 + 0.649906i \(0.774808\pi\)
\(360\) 18.0000 6.00000i 0.948683 0.316228i
\(361\) −5.50000 + 18.1865i −0.289474 + 0.957186i
\(362\) −4.39230 + 16.3923i −0.230854 + 0.861560i
\(363\) −5.07180 + 18.9282i −0.266200 + 0.993473i
\(364\) 13.8564 0.726273
\(365\) −24.7846 5.07180i −1.29729 0.265470i
\(366\) 9.00000 + 5.19615i 0.470438 + 0.271607i
\(367\) −2.53590 9.46410i −0.132373 0.494022i 0.867622 0.497224i \(-0.165647\pi\)
−0.999995 + 0.00320218i \(0.998981\pi\)
\(368\) 5.07180 18.9282i 0.264386 0.986701i
\(369\) 24.0000i 1.24939i
\(370\) −8.00000 4.00000i −0.415900 0.207950i
\(371\) 18.0000 + 10.3923i 0.934513 + 0.539542i
\(372\) 40.9808 10.9808i 2.12475 0.569326i
\(373\) 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
\(375\) 2.24167 27.2942i 0.115759 1.40947i
\(376\) 30.0000 + 17.3205i 1.54713 + 0.893237i
\(377\) −0.366025 + 1.36603i −0.0188513 + 0.0703539i
\(378\) 0 0
\(379\) 36.3731 1.86836 0.934179 0.356803i \(-0.116133\pi\)
0.934179 + 0.356803i \(0.116133\pi\)
\(380\) −18.3205 6.66025i −0.939822 0.341664i
\(381\) 42.0000 2.15173
\(382\) 3.16987 + 11.8301i 0.162185 + 0.605282i
\(383\) 1.90192 7.09808i 0.0971838 0.362695i −0.900158 0.435564i \(-0.856549\pi\)
0.997341 + 0.0728693i \(0.0232156\pi\)
\(384\) 27.7128 1.41421
\(385\) 14.1962 + 12.5885i 0.723503 + 0.641567i
\(386\) 16.0000 0.814379
\(387\) 10.3923 10.3923i 0.528271 0.528271i
\(388\) −2.92820 10.9282i −0.148657 0.554795i
\(389\) 4.33013 + 2.50000i 0.219546 + 0.126755i 0.605740 0.795663i \(-0.292877\pi\)
−0.386194 + 0.922418i \(0.626210\pi\)
\(390\) −10.3923 + 3.46410i −0.526235 + 0.175412i
\(391\) 20.7846i 1.05112i
\(392\) −34.0000 34.0000i −1.71726 1.71726i
\(393\) −13.1769 49.1769i −0.664687 2.48065i
\(394\) 1.73205 + 1.00000i 0.0872595 + 0.0503793i
\(395\) −10.6699 16.1603i −0.536860 0.813111i
\(396\) 10.3923i 0.522233i
\(397\) 8.05256 30.0526i 0.404146 1.50829i −0.401478 0.915868i \(-0.631504\pi\)
0.805625 0.592426i \(-0.201830\pi\)
\(398\) 6.97372 26.0263i 0.349561 1.30458i
\(399\) 20.7846 48.0000i 1.04053 2.40301i
\(400\) 7.85641 18.3923i 0.392820 0.919615i
\(401\) −5.50000 9.52628i −0.274657 0.475720i 0.695392 0.718631i \(-0.255231\pi\)
−0.970049 + 0.242911i \(0.921898\pi\)
\(402\) 8.19615 2.19615i 0.408787 0.109534i
\(403\) −11.8301 + 3.16987i −0.589301 + 0.157903i
\(404\) 2.00000i 0.0995037i
\(405\) 11.0885 + 16.7942i 0.550990 + 0.834512i
\(406\) 6.00000 3.46410i 0.297775 0.171920i
\(407\) −3.46410 + 3.46410i −0.171709 + 0.171709i
\(408\) −28.3923 + 7.60770i −1.40563 + 0.376637i
\(409\) 7.79423 + 4.50000i 0.385400 + 0.222511i 0.680165 0.733059i \(-0.261908\pi\)
−0.294765 + 0.955570i \(0.595241\pi\)
\(410\) −18.9282 16.7846i −0.934797 0.828933i
\(411\) 34.6410i 1.70872i
\(412\) −9.46410 2.53590i −0.466263 0.124935i
\(413\) 8.19615 + 2.19615i 0.403306 + 0.108066i
\(414\) −20.7846 −1.02151
\(415\) 16.3923 + 14.5359i 0.804667 + 0.713539i
\(416\) −8.00000 −0.392232
\(417\) −18.0000 18.0000i −0.881464 0.881464i
\(418\) −6.63397 + 8.36603i −0.324478 + 0.409196i
\(419\) 5.19615 0.253849 0.126924 0.991912i \(-0.459489\pi\)
0.126924 + 0.991912i \(0.459489\pi\)
\(420\) 48.0000 + 24.0000i 2.34216 + 1.17108i
\(421\) −11.5000 19.9186i −0.560476 0.970772i −0.997455 0.0713008i \(-0.977285\pi\)
0.436979 0.899472i \(-0.356048\pi\)
\(422\) 15.5885 15.5885i 0.758834 0.758834i
\(423\) 9.50962 35.4904i 0.462373 1.72560i
\(424\) −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
\(427\) 3.80385 + 14.1962i 0.184081 + 0.687000i
\(428\) −7.60770 + 28.3923i −0.367732 + 1.37239i
\(429\) 6.00000i 0.289683i
\(430\) −0.928203 15.4641i −0.0447619 0.745745i
\(431\) 10.5000 + 6.06218i 0.505767 + 0.292005i 0.731092 0.682279i \(-0.239011\pi\)
−0.225325 + 0.974284i \(0.572344\pi\)
\(432\) 0 0
\(433\) −8.05256 30.0526i −0.386981 1.44423i −0.835020 0.550220i \(-0.814544\pi\)
0.448039 0.894014i \(-0.352123\pi\)
\(434\) 51.9615 + 30.0000i 2.49423 + 1.44005i
\(435\) −3.63397 + 4.09808i −0.174236 + 0.196488i
\(436\) 3.00000 5.19615i 0.143674 0.248851i
\(437\) 16.7321 + 13.2679i 0.800403 + 0.634692i
\(438\) −10.1436 + 37.8564i −0.484680 + 1.80885i
\(439\) −16.4545 28.5000i −0.785330 1.36023i −0.928802 0.370576i \(-0.879160\pi\)
0.143472 0.989654i \(-0.454173\pi\)
\(440\) −8.19615 7.26795i −0.390736 0.346486i
\(441\) −25.5000 + 44.1673i −1.21429 + 2.10320i
\(442\) 8.19615 2.19615i 0.389851 0.104460i
\(443\) −14.1962 + 3.80385i −0.674480 + 0.180726i −0.579772 0.814779i \(-0.696858\pi\)
−0.0947077 + 0.995505i \(0.530192\pi\)
\(444\) −6.92820 + 12.0000i −0.328798 + 0.569495i
\(445\) −2.00000 1.00000i −0.0948091 0.0474045i
\(446\) 0 0
\(447\) −8.24167 30.7583i −0.389818 1.45482i
\(448\) 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
\(452\) −0.732051 + 2.73205i −0.0344328 + 0.128505i
\(453\) 20.4904 + 5.49038i 0.962722 + 0.257961i
\(454\) 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 \(0.608513\pi\)
\(458\) 0.366025 + 1.36603i 0.0171032 + 0.0638302i
\(459\) 0 0
\(460\) −14.5359 + 16.3923i −0.677740 + 0.764295i
\(461\) −0.500000 0.866025i −0.0232873 0.0403348i 0.854147 0.520032i \(-0.174080\pi\)
−0.877434 + 0.479697i \(0.840747\pi\)
\(462\) 20.7846 20.7846i 0.966988 0.966988i
\(463\) 6.92820 + 6.92820i 0.321981 + 0.321981i 0.849527 0.527546i \(-0.176888\pi\)
−0.527546 + 0.849527i \(0.676888\pi\)
\(464\) −3.46410 + 2.00000i −0.160817 + 0.0928477i
\(465\) −46.4711 9.50962i −2.15505 0.440998i
\(466\) −30.0000 −1.38972
\(467\) 17.3205 17.3205i 0.801498 0.801498i −0.181832 0.983330i \(-0.558203\pi\)
0.983330 + 0.181832i \(0.0582027\pi\)
\(468\) 2.19615 + 8.19615i 0.101517 + 0.378867i
\(469\) 10.3923 + 6.00000i 0.479872 + 0.277054i
\(470\) −21.3397 32.3205i −0.984329 1.49083i
\(471\) −15.0000 8.66025i −0.691164 0.399043i
\(472\) −4.73205 1.26795i −0.217810 0.0583621i
\(473\) −8.19615 2.19615i −0.376859 0.100979i
\(474\) −25.9808 + 15.0000i −1.19334 + 0.688973i
\(475\) 14.9904 + 15.8205i 0.687806 + 0.725895i
\(476\) −36.0000 20.7846i −1.65006 0.952661i
\(477\) −3.29423 + 12.2942i −0.150832 + 0.562914i
\(478\) −2.36603 + 0.633975i −0.108219 + 0.0289973i
\(479\) −6.06218 + 10.5000i −0.276988 + 0.479757i −0.970635 0.240558i \(-0.922670\pi\)
0.693647 + 0.720315i \(0.256003\pi\)
\(480\) −27.7128 13.8564i −1.26491 0.632456i
\(481\) 2.00000 3.46410i 0.0911922 0.157949i
\(482\) −6.95448 + 25.9545i −0.316768 + 1.18219i
\(483\) −41.5692 41.5692i −1.89146 1.89146i
\(484\) 13.8564 8.00000i 0.629837 0.363636i
\(485\) −2.53590 + 12.3923i −0.115149 + 0.562706i
\(486\) 27.0000 15.5885i 1.22474 0.707107i
\(487\) −5.19615 + 5.19615i −0.235460 + 0.235460i −0.814967 0.579507i \(-0.803245\pi\)
0.579507 + 0.814967i \(0.303245\pi\)
\(488\) −2.19615 8.19615i −0.0994151 0.371022i
\(489\) −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 0.308215 0.951317i \(-0.400268\pi\)
0.977972 + 0.208736i \(0.0669350\pi\)
\(492\) −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
\(497\) −2.19615 + 8.19615i −0.0985109 + 0.367648i
\(498\) 24.0000 24.0000i 1.07547 1.07547i
\(499\) 13.8564 + 24.0000i 0.620298 + 1.07439i 0.989430 + 0.145011i \(0.0463216\pi\)
−0.369132 + 0.929377i \(0.620345\pi\)
\(500\) −17.0526 + 14.4641i −0.762614 + 0.646854i
\(501\) 0 0
\(502\) −7.09808 1.90192i −0.316803 0.0848870i
\(503\) 2.36603 0.633975i 0.105496 0.0282675i −0.205685 0.978618i \(-0.565942\pi\)
0.311181 + 0.950351i \(0.399276\pi\)
\(504\) 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
\(507\) 6.97372 + 26.0263i 0.309714 + 1.15587i
\(508\) −24.2487 24.2487i −1.07586 1.07586i
\(509\) 34.6410 + 20.0000i 1.53544 + 0.886484i 0.999097 + 0.0424816i \(0.0135264\pi\)
0.536339 + 0.844003i \(0.319807\pi\)
\(510\) 32.1962 + 6.58846i 1.42567 + 0.291742i
\(511\) −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
\(515\) 8.19615 + 7.26795i 0.361166 + 0.320264i
\(516\) −24.0000 −1.05654
\(517\) −20.4904 + 5.49038i −0.901166 + 0.241467i
\(518\) −18.9282 + 5.07180i −0.831658 + 0.222842i
\(519\) −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
\(523\) −2.36603 + 0.633975i −0.103459 + 0.0277218i −0.310177 0.950679i \(-0.600388\pi\)
0.206718 + 0.978401i \(0.433722\pi\)
\(524\) −20.7846 + 36.0000i −0.907980 + 1.57267i
\(525\) −36.0000 48.0000i −1.57117 2.09489i
\(526\) 24.2487i 1.05729i
\(527\) 35.4904 + 9.50962i 1.54599 + 0.414246i
\(528\) −12.0000 + 12.0000i −0.522233 + 0.522233i
\(529\) 0.866025 0.500000i 0.0376533 0.0217391i
\(530\) 7.39230 + 11.1962i 0.321101 + 0.486330i
\(531\) 5.19615i 0.225494i
\(532\) −39.7128 + 15.7128i −1.72177 + 0.681237i
\(533\) 8.00000 8.00000i 0.346518 0.346518i
\(534\) −1.73205 + 3.00000i −0.0749532 + 0.129823i
\(535\) 21.8038 24.5885i 0.942663 1.06305i
\(536\) −6.00000 3.46410i −0.259161 0.149626i
\(537\) −5.49038 + 20.4904i −0.236927 + 0.884225i
\(538\) 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 −0.547045 0.837103i \(-0.684247\pi\)
0.998475 + 0.0552031i \(0.0175806\pi\)
\(542\) 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
\(545\) −5.59808 + 3.69615i −0.239795 + 0.158326i
\(546\) −12.0000 + 20.7846i −0.513553 + 0.889499i
\(547\) −1.26795 4.73205i −0.0542136 0.202328i 0.933507 0.358560i \(-0.116732\pi\)
−0.987720 + 0.156232i \(0.950065\pi\)
\(548\) 20.0000 20.0000i 0.854358 0.854358i
\(549\) −7.79423 + 4.50000i −0.332650 + 0.192055i
\(550\) 4.56218 + 11.3660i 0.194532 + 0.484649i
\(551\) −0.500000 4.33013i −0.0213007 0.184470i
\(552\) 24.0000 + 24.0000i 1.02151 + 1.02151i
\(553\) −40.9808 10.9808i −1.74268 0.466950i
\(554\) −27.7128 16.0000i −1.17740 0.679775i
\(555\) 12.9282 8.53590i 0.548772 0.362329i
\(556\) 20.7846i 0.881464i
\(557\) −32.7846 + 8.78461i −1.38913 + 0.372216i −0.874428 0.485154i \(-0.838763\pi\)
−0.514700 + 0.857370i \(0.672097\pi\)
\(558\) −9.50962 + 35.4904i −0.402574 + 1.50243i
\(559\) 6.92820 0.293032
\(560\) −13.8564 41.5692i −0.585540 1.75662i
\(561\) 9.00000 15.5885i 0.379980 0.658145i
\(562\) −0.732051 + 2.73205i −0.0308797 + 0.115245i
\(563\) −15.5885 15.5885i −0.656975 0.656975i 0.297688 0.954663i \(-0.403784\pi\)
−0.954663 + 0.297688i \(0.903784\pi\)
\(564\) −51.9615 + 30.0000i −2.18797 + 1.26323i
\(565\) 2.09808 2.36603i 0.0882667 0.0995394i
\(566\) 31.1769i 1.31046i
\(567\) 42.5885 + 11.4115i 1.78855 + 0.479240i
\(568\) 1.26795 4.73205i 0.0532020 0.198552i
\(569\) 13.0000i 0.544988i 0.962157 + 0.272494i \(0.0878485\pi\)
−0.962157 + 0.272494i \(0.912151\pi\)
\(570\) 25.8564 21.7128i 1.08301 0.909450i
\(571\) 8.66025i 0.362420i 0.983444 + 0.181210i \(0.0580014\pi\)
−0.983444 + 0.181210i \(0.941999\pi\)
\(572\) 3.46410 3.46410i 0.144841 0.144841i
\(573\) −20.4904 5.49038i −0.855998 0.229364i
\(574\) −55.4256 −2.31342
\(575\) 22.7321 9.12436i 0.947992 0.380512i
\(576\) −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 \(0.974235\pi\)
\(578\) −1.36603 0.366025i −0.0568192 0.0152246i
\(579\) −13.8564 + 24.0000i −0.575853 + 0.997406i
\(580\) 4.46410 0.267949i 0.185362 0.0111260i
\(581\) 48.0000 1.99138
\(582\) 18.9282 + 5.07180i 0.784599 + 0.210233i
\(583\) 7.09808 1.90192i 0.293972 0.0787696i
\(584\) 27.7128 16.0000i 1.14676 0.662085i
\(585\) 1.90192 9.29423i 0.0786349 0.384269i
\(586\) 4.00000 6.92820i 0.165238 0.286201i
\(587\) −33.1244 8.87564i −1.36719 0.366337i −0.500737 0.865599i \(-0.666938\pi\)
−0.866451 + 0.499262i \(0.833604\pi\)
\(588\) 80.4449 21.5551i 3.31749 0.888919i
\(589\) 30.3109 22.5000i 1.24894 0.927096i
\(590\) 4.09808 + 3.63397i 0.168715 + 0.149608i
\(591\) −3.00000 + 1.73205i −0.123404 + 0.0712470i
\(592\) 10.9282 2.92820i 0.449146 0.120348i
\(593\) 2.92820 + 10.9282i 0.120247 + 0.448768i 0.999626 0.0273551i \(-0.00870850\pi\)
−0.879379 + 0.476123i \(0.842042\pi\)
\(594\) 0 0
\(595\) 25.6077 + 38.7846i 1.04981 + 1.59001i
\(596\) −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 \(-0.972925\pi\)
0.571767 + 0.820416i \(0.306258\pi\)
\(600\) 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
\(603\) −1.90192 + 7.09808i −0.0774523 + 0.289056i
\(604\) −8.66025 15.0000i −0.352381 0.610341i
\(605\) −17.8564 + 1.07180i −0.725966 + 0.0435747i
\(606\) 3.00000 + 1.73205i 0.121867 + 0.0703598i
\(607\) −8.66025 + 8.66025i −0.351509 + 0.351509i −0.860671 0.509162i \(-0.829955\pi\)
0.509162 + 0.860671i \(0.329955\pi\)
\(608\) 22.9282 9.07180i 0.929861 0.367910i
\(609\) 12.0000i 0.486265i
\(610\) −1.90192 + 9.29423i −0.0770066 + 0.376312i
\(611\) 15.0000 8.66025i 0.606835 0.350356i
\(612\) 6.58846 24.5885i 0.266323 0.993929i
\(613\) 9.56218 + 2.56218i 0.386213 + 0.103485i 0.446701 0.894684i \(-0.352599\pi\)
−0.0604878 + 0.998169i \(0.519266\pi\)
\(614\) 3.46410 0.139800
\(615\) 41.5692 13.8564i 1.67623 0.558744i
\(616\) −24.0000 −0.966988
\(617\) 40.9808 10.9808i 1.64982 0.442069i 0.690260 0.723561i \(-0.257496\pi\)
0.959563 + 0.281493i \(0.0908295\pi\)
\(618\) 12.0000 12.0000i 0.482711 0.482711i
\(619\) −34.6410 −1.39234 −0.696170 0.717877i \(-0.745114\pi\)
−0.696170 + 0.717877i \(0.745114\pi\)
\(620\) 21.3397 + 32.3205i 0.857025 + 1.29802i
\(621\) 0 0
\(622\) −5.07180 18.9282i −0.203361 0.758952i
\(623\) −4.73205 + 1.26795i −0.189586 + 0.0507993i
\(624\) 6.92820 12.0000i 0.277350 0.480384i
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) 5.00000 + 8.66025i 0.199840 + 0.346133i
\(627\) −6.80385 17.1962i −0.271719 0.686748i
\(628\) 3.66025 + 13.6603i 0.146060 + 0.545103i
\(629\) −10.3923 + 6.00000i −0.414368 + 0.239236i
\(630\) −38.7846 + 25.6077i −1.54522 + 1.02023i
\(631\) −7.50000 4.33013i −0.298570 0.172380i 0.343230 0.939251i \(-0.388479\pi\)
−0.641800 + 0.766872i \(0.721812\pi\)
\(632\) 23.6603 + 6.33975i 0.941154 + 0.252182i
\(633\) 9.88269 + 36.8827i 0.392801 + 1.46596i
\(634\) −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
\(637\) −23.2224 + 6.22243i −0.920106 + 0.246542i
\(638\) 0.633975 2.36603i 0.0250993 0.0936718i
\(639\) −5.19615 −0.205557
\(640\) 8.00000 + 24.0000i 0.316228 + 0.948683i
\(641\) 14.5000 + 25.1147i 0.572716 + 0.991972i 0.996286 + 0.0861092i \(0.0274434\pi\)
−0.423570 + 0.905863i \(0.639223\pi\)
\(642\) −36.0000 36.0000i −1.42081 1.42081i
\(643\) −0.633975 + 2.36603i −0.0250015 + 0.0933069i −0.977299 0.211864i \(-0.932047\pi\)
0.952298 + 0.305170i \(0.0987134\pi\)
\(644\) 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 −0.943687 0.330841i \(-0.892668\pi\)
0.330841 + 0.943687i \(0.392668\pi\)
\(648\) −24.5885 6.58846i −0.965926 0.258819i
\(649\) 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
\(652\) 23.6603 + 6.33975i 0.926607 + 0.248284i
\(653\) −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
\(655\) 38.7846 25.6077i 1.51544 1.00058i
\(656\) 32.0000 1.24939
\(657\) −24.0000 24.0000i −0.936329 0.936329i
\(658\) −81.9615 21.9615i −3.19519 0.856149i
\(659\) 24.2487 42.0000i 0.944596 1.63609i 0.188037 0.982162i \(-0.439788\pi\)
0.756559 0.653926i \(-0.226879\pi\)
\(660\) 18.0000 6.00000i 0.700649 0.233550i
\(661\) −22.5000 + 38.9711i −0.875149 + 1.51580i −0.0185442 + 0.999828i \(0.505903\pi\)
−0.856604 + 0.515974i \(0.827430\pi\)
\(662\) −7.60770 28.3923i −0.295681 1.10350i
\(663\) −3.80385 + 14.1962i −0.147729 + 0.551333i
\(664\) −27.7128 −1.07547
\(665\) 47.5692 + 4.14359i 1.84466 + 0.160682i
\(666\) −6.00000 10.3923i −0.232495 0.402694i
\(667\) −4.73205 1.26795i −0.183226 0.0490952i
\(668\) 0 0
\(669\) 0 0
\(670\) 4.26795 + 6.46410i 0.164885 + 0.249730i
\(671\) 4.50000 + 2.59808i 0.173721 + 0.100298i
\(672\) −65.5692 + 17.5692i −2.52939 + 0.677747i
\(673\) −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
\(680\) −14.7846 22.3923i −0.566964 0.858706i
\(681\) 6.00000 + 10.3923i 0.229920 + 0.398234i
\(682\) 20.4904 5.49038i 0.784617 0.210238i
\(683\) 12.1244 + 12.1244i 0.463926 + 0.463926i 0.899940 0.436014i \(-0.143610\pi\)
−0.436014 + 0.899940i \(0.643610\pi\)
\(684\) −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
\(687\) −2.36603 0.633975i −0.0902695 0.0241876i
\(688\) 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 \(-0.726304\pi\)
0.652558 0.757739i \(-0.273696\pi\)
\(692\) 21.8564 5.85641i 0.830856 0.222627i
\(693\) 6.58846 + 24.5885i 0.250275 + 0.934038i
\(694\) −27.7128 −1.05196
\(695\) 10.3923 20.7846i 0.394203 0.788405i
\(696\) 6.92820i 0.262613i
\(697\) −32.7846 + 8.78461i −1.24181 + 0.332741i
\(698\) 8.78461 + 32.7846i 0.332502 + 1.24092i
\(699\) 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 0.674468 0.738304i \(-0.264373\pi\)
−0.976624 + 0.214955i \(0.931040\pi\)
\(702\) 0 0
\(703\) −1.80385 + 12.1962i −0.0680334 + 0.459987i
\(704\) 13.8564 0.522233
\(705\) 66.9615 4.01924i 2.52192 0.151373i
\(706\) 6.00000 10.3923i 0.225813 0.391120i
\(707\) 1.26795 + 4.73205i 0.0476861 + 0.177967i
\(708\) 6.00000 6.00000i 0.225494 0.225494i
\(709\) 11.2583 + 6.50000i 0.422815 + 0.244113i 0.696281 0.717769i \(-0.254837\pi\)
−0.273466 + 0.961882i \(0.588170\pi\)
\(710\) −3.63397 + 4.09808i −0.136381 + 0.153798i
\(711\) 25.9808i 0.974355i
\(712\) 2.73205 0.732051i 0.102388 0.0274348i
\(713\) −10.9808 40.9808i −0.411233 1.53474i
\(714\) 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
\(717\) 1.09808 4.09808i 0.0410084 0.153045i
\(718\) 6.92820 + 6.92820i 0.258558 + 0.258558i
\(719\) −16.4545 28.5000i −0.613649 1.06287i −0.990620 0.136646i \(-0.956368\pi\)
0.376971 0.926225i \(-0.376966\pi\)
\(720\) 22.3923 14.7846i 0.834512 0.550990i
\(721\) 24.0000 0.893807
\(722\) −0.856406 + 26.8564i −0.0318721 + 0.999492i
\(723\) −32.9090 32.9090i −1.22390 1.22390i
\(724\) 24.0000i 0.891953i
\(725\) −4.59808 1.96410i −0.170768 0.0729449i
\(726\) 27.7128i 1.02852i
\(727\) 26.0263 + 6.97372i 0.965261 + 0.258641i 0.706826 0.707388i \(-0.250126\pi\)
0.258435 + 0.966029i \(0.416793\pi\)
\(728\) 18.9282 5.07180i 0.701526 0.187973i
\(729\) 27.0000i 1.00000i
\(730\) −35.7128 + 2.14359i −1.32179 + 0.0793380i
\(731\) −18.0000 10.3923i −0.665754 0.384373i
\(732\) 14.1962 + 3.80385i 0.524705 + 0.140594i
\(733\) −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
\(735\) −91.2224 18.6673i −3.36479 0.688554i
\(736\) 27.7128i 1.02151i
\(737\) 4.09808 1.09808i 0.150955 0.0404482i
\(738\) −8.78461 32.7846i −0.323366 1.20682i
\(739\) 7.79423 + 13.5000i 0.286715 + 0.496606i 0.973024 0.230705i \(-0.0741033\pi\)
−0.686308 + 0.727311i \(0.740770\pi\)
\(740\) −12.3923 2.53590i −0.455550 0.0932215i
\(741\) 9.00000 + 12.1244i 0.330623 + 0.445399i
\(742\) 28.3923 + 7.60770i 1.04231 + 0.279287i
\(743\) −2.53590 + 9.46410i −0.0930331 + 0.347204i −0.996714 0.0810025i \(-0.974188\pi\)
0.903681 + 0.428207i \(0.140854\pi\)
\(744\) 51.9615 30.0000i 1.90500 1.09985i
\(745\) 24.2583 16.0167i 0.888756 0.586805i
\(746\) 10.0000 17.3205i 0.366126 0.634149i
\(747\) 7.60770 + 28.3923i 0.278351 + 1.03882i
\(748\) −14.1962 + 3.80385i −0.519063 + 0.139082i
\(749\) 72.0000i 2.63082i
\(750\) −6.92820 38.1051i −0.252982 1.39140i
\(751\) −16.5000 9.52628i −0.602094 0.347619i 0.167771 0.985826i \(-0.446343\pi\)
−0.769865 + 0.638207i \(0.779676\pi\)
\(752\) 47.3205 + 12.6795i 1.72560 + 0.462373i
\(753\) 9.00000 9.00000i 0.327978 0.327978i
\(754\) 2.00000i 0.0728357i
\(755\) 1.16025 + 19.3301i 0.0422260 + 0.703495i
\(756\) 0 0
\(757\) −1.83013 + 6.83013i −0.0665171 + 0.248245i −0.991176 0.132551i \(-0.957683\pi\)
0.924659 + 0.380796i \(0.124350\pi\)
\(758\) 49.6865 13.3135i 1.80470 0.483567i
\(759\) −20.7846 −0.754434
\(760\) −27.4641 2.39230i −0.996228 0.0867780i
\(761\) −20.0000 −0.724999 −0.362500 0.931984i \(-0.618077\pi\)
−0.362500 + 0.931984i \(0.618077\pi\)
\(762\) 57.3731 15.3731i 2.07841 0.556907i
\(763\) −3.80385 + 14.1962i −0.137709 + 0.513935i
\(764\) 8.66025 + 15.0000i 0.313317 + 0.542681i
\(765\) −18.8827 + 21.2942i −0.682705 + 0.769894i
\(766\)