Properties

Label 105.2.i.d.16.1
Level $105$
Weight $2$
Character 105.16
Analytic conductor $0.838$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [105,2,Mod(16,105)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(105, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("105.16");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 105 = 3 \cdot 5 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 105.i (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(0.838429221223\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
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: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 105.16
Dual form 105.2.i.d.46.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.366025 + 0.633975i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.732051 + 1.26795i) q^{4} +(-0.500000 + 0.866025i) q^{5} -0.732051 q^{6} +(-0.866025 - 2.50000i) q^{7} -2.53590 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.366025 + 0.633975i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.732051 + 1.26795i) q^{4} +(-0.500000 + 0.866025i) q^{5} -0.732051 q^{6} +(-0.866025 - 2.50000i) q^{7} -2.53590 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.366025 - 0.633975i) q^{10} +(1.36603 + 2.36603i) q^{11} +(-0.732051 + 1.26795i) q^{12} +5.73205 q^{13} +(1.90192 + 0.366025i) q^{14} -1.00000 q^{15} +(-0.535898 + 0.928203i) q^{16} +(-3.36603 - 5.83013i) q^{17} +(-0.366025 - 0.633975i) q^{18} +(1.23205 - 2.13397i) q^{19} -1.46410 q^{20} +(1.73205 - 2.00000i) q^{21} -2.00000 q^{22} +(0.633975 - 1.09808i) q^{23} +(-1.26795 - 2.19615i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.09808 + 3.63397i) q^{26} -1.00000 q^{27} +(2.53590 - 2.92820i) q^{28} +6.19615 q^{29} +(0.366025 - 0.633975i) q^{30} +(-3.23205 - 5.59808i) q^{31} +(-2.92820 - 5.07180i) q^{32} +(-1.36603 + 2.36603i) q^{33} +4.92820 q^{34} +(2.59808 + 0.500000i) q^{35} -1.46410 q^{36} +(-3.59808 + 6.23205i) q^{37} +(0.901924 + 1.56218i) q^{38} +(2.86603 + 4.96410i) q^{39} +(1.26795 - 2.19615i) q^{40} +2.73205 q^{41} +(0.633975 + 1.83013i) q^{42} -7.19615 q^{43} +(-2.00000 + 3.46410i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(0.464102 + 0.803848i) q^{46} +(-1.00000 + 1.73205i) q^{47} -1.07180 q^{48} +(-5.50000 + 4.33013i) q^{49} +0.732051 q^{50} +(3.36603 - 5.83013i) q^{51} +(4.19615 + 7.26795i) q^{52} +(4.19615 + 7.26795i) q^{53} +(0.366025 - 0.633975i) q^{54} -2.73205 q^{55} +(2.19615 + 6.33975i) q^{56} +2.46410 q^{57} +(-2.26795 + 3.92820i) q^{58} +(-5.09808 - 8.83013i) q^{59} +(-0.732051 - 1.26795i) q^{60} +(-2.00000 + 3.46410i) q^{61} +4.73205 q^{62} +(2.59808 + 0.500000i) q^{63} +2.14359 q^{64} +(-2.86603 + 4.96410i) q^{65} +(-1.00000 - 1.73205i) q^{66} +(-1.33013 - 2.30385i) q^{67} +(4.92820 - 8.53590i) q^{68} +1.26795 q^{69} +(-1.26795 + 1.46410i) q^{70} -4.19615 q^{71} +(1.26795 - 2.19615i) q^{72} +(2.33013 + 4.03590i) q^{73} +(-2.63397 - 4.56218i) q^{74} +(0.500000 - 0.866025i) q^{75} +3.60770 q^{76} +(4.73205 - 5.46410i) q^{77} -4.19615 q^{78} +(-6.69615 + 11.5981i) q^{79} +(-0.535898 - 0.928203i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} -9.12436 q^{83} +(3.80385 + 0.732051i) q^{84} +6.73205 q^{85} +(2.63397 - 4.56218i) q^{86} +(3.09808 + 5.36603i) q^{87} +(-3.46410 - 6.00000i) q^{88} +(4.56218 - 7.90192i) q^{89} +0.732051 q^{90} +(-4.96410 - 14.3301i) q^{91} +1.85641 q^{92} +(3.23205 - 5.59808i) q^{93} +(-0.732051 - 1.26795i) q^{94} +(1.23205 + 2.13397i) q^{95} +(2.92820 - 5.07180i) q^{96} +1.07180 q^{97} +(-0.732051 - 5.07180i) q^{98} -2.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 2 q^{5} + 4 q^{6} - 24 q^{8} - 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - 2 q^{5} + 4 q^{6} - 24 q^{8} - 2 q^{9} + 2 q^{10} + 2 q^{11} + 4 q^{12} + 16 q^{13} + 18 q^{14} - 4 q^{15} - 16 q^{16} - 10 q^{17} + 2 q^{18} - 2 q^{19} + 8 q^{20} - 8 q^{22} + 6 q^{23} - 12 q^{24} - 2 q^{25} + 2 q^{26} - 4 q^{27} + 24 q^{28} + 4 q^{29} - 2 q^{30} - 6 q^{31} + 16 q^{32} - 2 q^{33} - 8 q^{34} + 8 q^{36} - 4 q^{37} + 14 q^{38} + 8 q^{39} + 12 q^{40} + 4 q^{41} + 6 q^{42} - 8 q^{43} - 8 q^{44} - 2 q^{45} - 12 q^{46} - 4 q^{47} - 32 q^{48} - 22 q^{49} - 4 q^{50} + 10 q^{51} - 4 q^{52} - 4 q^{53} - 2 q^{54} - 4 q^{55} - 12 q^{56} - 4 q^{57} - 16 q^{58} - 10 q^{59} + 4 q^{60} - 8 q^{61} + 12 q^{62} + 64 q^{64} - 8 q^{65} - 4 q^{66} + 12 q^{67} - 8 q^{68} + 12 q^{69} - 12 q^{70} + 4 q^{71} + 12 q^{72} - 8 q^{73} - 14 q^{74} + 2 q^{75} + 56 q^{76} + 12 q^{77} + 4 q^{78} - 6 q^{79} - 16 q^{80} - 2 q^{81} - 4 q^{82} + 12 q^{83} + 36 q^{84} + 20 q^{85} + 14 q^{86} + 2 q^{87} - 6 q^{89} - 4 q^{90} - 6 q^{91} - 48 q^{92} + 6 q^{93} + 4 q^{94} - 2 q^{95} - 16 q^{96} + 32 q^{97} + 4 q^{98} - 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).

\(n\) \(22\) \(31\) \(71\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{3}\right)\) \(1\)

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 + 0.633975i −0.258819 + 0.448288i −0.965926 0.258819i \(-0.916667\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.732051 + 1.26795i 0.366025 + 0.633975i
\(5\) −0.500000 + 0.866025i −0.223607 + 0.387298i
\(6\) −0.732051 −0.298858
\(7\) −0.866025 2.50000i −0.327327 0.944911i
\(8\) −2.53590 −0.896575
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −0.366025 0.633975i −0.115747 0.200480i
\(11\) 1.36603 + 2.36603i 0.411872 + 0.713384i 0.995094 0.0989291i \(-0.0315417\pi\)
−0.583222 + 0.812313i \(0.698208\pi\)
\(12\) −0.732051 + 1.26795i −0.211325 + 0.366025i
\(13\) 5.73205 1.58978 0.794892 0.606750i \(-0.207527\pi\)
0.794892 + 0.606750i \(0.207527\pi\)
\(14\) 1.90192 + 0.366025i 0.508311 + 0.0978244i
\(15\) −1.00000 −0.258199
\(16\) −0.535898 + 0.928203i −0.133975 + 0.232051i
\(17\) −3.36603 5.83013i −0.816381 1.41401i −0.908332 0.418250i \(-0.862644\pi\)
0.0919509 0.995764i \(-0.470690\pi\)
\(18\) −0.366025 0.633975i −0.0862730 0.149429i
\(19\) 1.23205 2.13397i 0.282652 0.489567i −0.689385 0.724395i \(-0.742119\pi\)
0.972037 + 0.234828i \(0.0754526\pi\)
\(20\) −1.46410 −0.327383
\(21\) 1.73205 2.00000i 0.377964 0.436436i
\(22\) −2.00000 −0.426401
\(23\) 0.633975 1.09808i 0.132193 0.228965i −0.792329 0.610094i \(-0.791132\pi\)
0.924522 + 0.381130i \(0.124465\pi\)
\(24\) −1.26795 2.19615i −0.258819 0.448288i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) −2.09808 + 3.63397i −0.411467 + 0.712681i
\(27\) −1.00000 −0.192450
\(28\) 2.53590 2.92820i 0.479240 0.553378i
\(29\) 6.19615 1.15060 0.575298 0.817944i \(-0.304886\pi\)
0.575298 + 0.817944i \(0.304886\pi\)
\(30\) 0.366025 0.633975i 0.0668268 0.115747i
\(31\) −3.23205 5.59808i −0.580493 1.00544i −0.995421 0.0955896i \(-0.969526\pi\)
0.414927 0.909855i \(-0.363807\pi\)
\(32\) −2.92820 5.07180i −0.517638 0.896575i
\(33\) −1.36603 + 2.36603i −0.237795 + 0.411872i
\(34\) 4.92820 0.845180
\(35\) 2.59808 + 0.500000i 0.439155 + 0.0845154i
\(36\) −1.46410 −0.244017
\(37\) −3.59808 + 6.23205i −0.591520 + 1.02454i 0.402508 + 0.915417i \(0.368139\pi\)
−0.994028 + 0.109126i \(0.965195\pi\)
\(38\) 0.901924 + 1.56218i 0.146311 + 0.253419i
\(39\) 2.86603 + 4.96410i 0.458931 + 0.794892i
\(40\) 1.26795 2.19615i 0.200480 0.347242i
\(41\) 2.73205 0.426675 0.213337 0.976979i \(-0.431567\pi\)
0.213337 + 0.976979i \(0.431567\pi\)
\(42\) 0.633975 + 1.83013i 0.0978244 + 0.282395i
\(43\) −7.19615 −1.09740 −0.548701 0.836018i \(-0.684878\pi\)
−0.548701 + 0.836018i \(0.684878\pi\)
\(44\) −2.00000 + 3.46410i −0.301511 + 0.522233i
\(45\) −0.500000 0.866025i −0.0745356 0.129099i
\(46\) 0.464102 + 0.803848i 0.0684280 + 0.118521i
\(47\) −1.00000 + 1.73205i −0.145865 + 0.252646i −0.929695 0.368329i \(-0.879930\pi\)
0.783830 + 0.620975i \(0.213263\pi\)
\(48\) −1.07180 −0.154701
\(49\) −5.50000 + 4.33013i −0.785714 + 0.618590i
\(50\) 0.732051 0.103528
\(51\) 3.36603 5.83013i 0.471338 0.816381i
\(52\) 4.19615 + 7.26795i 0.581902 + 1.00788i
\(53\) 4.19615 + 7.26795i 0.576386 + 0.998330i 0.995890 + 0.0905760i \(0.0288708\pi\)
−0.419504 + 0.907754i \(0.637796\pi\)
\(54\) 0.366025 0.633975i 0.0498097 0.0862730i
\(55\) −2.73205 −0.368390
\(56\) 2.19615 + 6.33975i 0.293473 + 0.847184i
\(57\) 2.46410 0.326378
\(58\) −2.26795 + 3.92820i −0.297796 + 0.515798i
\(59\) −5.09808 8.83013i −0.663713 1.14958i −0.979633 0.200799i \(-0.935646\pi\)
0.315920 0.948786i \(-0.397687\pi\)
\(60\) −0.732051 1.26795i −0.0945074 0.163692i
\(61\) −2.00000 + 3.46410i −0.256074 + 0.443533i −0.965187 0.261562i \(-0.915762\pi\)
0.709113 + 0.705095i \(0.249096\pi\)
\(62\) 4.73205 0.600971
\(63\) 2.59808 + 0.500000i 0.327327 + 0.0629941i
\(64\) 2.14359 0.267949
\(65\) −2.86603 + 4.96410i −0.355487 + 0.615721i
\(66\) −1.00000 1.73205i −0.123091 0.213201i
\(67\) −1.33013 2.30385i −0.162501 0.281460i 0.773264 0.634084i \(-0.218623\pi\)
−0.935765 + 0.352624i \(0.885289\pi\)
\(68\) 4.92820 8.53590i 0.597632 1.03513i
\(69\) 1.26795 0.152643
\(70\) −1.26795 + 1.46410i −0.151549 + 0.174994i
\(71\) −4.19615 −0.497992 −0.248996 0.968505i \(-0.580101\pi\)
−0.248996 + 0.968505i \(0.580101\pi\)
\(72\) 1.26795 2.19615i 0.149429 0.258819i
\(73\) 2.33013 + 4.03590i 0.272721 + 0.472366i 0.969558 0.244864i \(-0.0787432\pi\)
−0.696837 + 0.717230i \(0.745410\pi\)
\(74\) −2.63397 4.56218i −0.306193 0.530342i
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 3.60770 0.413831
\(77\) 4.73205 5.46410i 0.539267 0.622692i
\(78\) −4.19615 −0.475121
\(79\) −6.69615 + 11.5981i −0.753376 + 1.30489i 0.192802 + 0.981238i \(0.438243\pi\)
−0.946178 + 0.323648i \(0.895091\pi\)
\(80\) −0.535898 0.928203i −0.0599153 0.103776i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −1.00000 + 1.73205i −0.110432 + 0.191273i
\(83\) −9.12436 −1.00153 −0.500764 0.865584i \(-0.666948\pi\)
−0.500764 + 0.865584i \(0.666948\pi\)
\(84\) 3.80385 + 0.732051i 0.415034 + 0.0798733i
\(85\) 6.73205 0.730193
\(86\) 2.63397 4.56218i 0.284029 0.491952i
\(87\) 3.09808 + 5.36603i 0.332149 + 0.575298i
\(88\) −3.46410 6.00000i −0.369274 0.639602i
\(89\) 4.56218 7.90192i 0.483590 0.837602i −0.516233 0.856448i \(-0.672666\pi\)
0.999822 + 0.0188462i \(0.00599930\pi\)
\(90\) 0.732051 0.0771649
\(91\) −4.96410 14.3301i −0.520379 1.50221i
\(92\) 1.85641 0.193544
\(93\) 3.23205 5.59808i 0.335148 0.580493i
\(94\) −0.732051 1.26795i −0.0755053 0.130779i
\(95\) 1.23205 + 2.13397i 0.126406 + 0.218941i
\(96\) 2.92820 5.07180i 0.298858 0.517638i
\(97\) 1.07180 0.108824 0.0544122 0.998519i \(-0.482671\pi\)
0.0544122 + 0.998519i \(0.482671\pi\)
\(98\) −0.732051 5.07180i −0.0739483 0.512329i
\(99\) −2.73205 −0.274581
\(100\) 0.732051 1.26795i 0.0732051 0.126795i
\(101\) 5.36603 + 9.29423i 0.533939 + 0.924810i 0.999214 + 0.0396438i \(0.0126223\pi\)
−0.465274 + 0.885167i \(0.654044\pi\)
\(102\) 2.46410 + 4.26795i 0.243982 + 0.422590i
\(103\) −0.598076 + 1.03590i −0.0589302 + 0.102070i −0.893985 0.448096i \(-0.852102\pi\)
0.835055 + 0.550166i \(0.185436\pi\)
\(104\) −14.5359 −1.42536
\(105\) 0.866025 + 2.50000i 0.0845154 + 0.243975i
\(106\) −6.14359 −0.596719
\(107\) 4.09808 7.09808i 0.396176 0.686197i −0.597075 0.802186i \(-0.703670\pi\)
0.993251 + 0.115989i \(0.0370037\pi\)
\(108\) −0.732051 1.26795i −0.0704416 0.122008i
\(109\) −5.50000 9.52628i −0.526804 0.912452i −0.999512 0.0312328i \(-0.990057\pi\)
0.472708 0.881219i \(-0.343277\pi\)
\(110\) 1.00000 1.73205i 0.0953463 0.165145i
\(111\) −7.19615 −0.683029
\(112\) 2.78461 + 0.535898i 0.263121 + 0.0506376i
\(113\) −4.92820 −0.463606 −0.231803 0.972763i \(-0.574463\pi\)
−0.231803 + 0.972763i \(0.574463\pi\)
\(114\) −0.901924 + 1.56218i −0.0844729 + 0.146311i
\(115\) 0.633975 + 1.09808i 0.0591184 + 0.102396i
\(116\) 4.53590 + 7.85641i 0.421148 + 0.729449i
\(117\) −2.86603 + 4.96410i −0.264964 + 0.458931i
\(118\) 7.46410 0.687126
\(119\) −11.6603 + 13.4641i −1.06889 + 1.23425i
\(120\) 2.53590 0.231495
\(121\) 1.76795 3.06218i 0.160723 0.278380i
\(122\) −1.46410 2.53590i −0.132554 0.229589i
\(123\) 1.36603 + 2.36603i 0.123170 + 0.213337i
\(124\) 4.73205 8.19615i 0.424951 0.736036i
\(125\) 1.00000 0.0894427
\(126\) −1.26795 + 1.46410i −0.112958 + 0.130433i
\(127\) 15.1962 1.34844 0.674220 0.738530i \(-0.264480\pi\)
0.674220 + 0.738530i \(0.264480\pi\)
\(128\) 5.07180 8.78461i 0.448288 0.776457i
\(129\) −3.59808 6.23205i −0.316793 0.548701i
\(130\) −2.09808 3.63397i −0.184013 0.318721i
\(131\) −4.26795 + 7.39230i −0.372892 + 0.645869i −0.990009 0.141003i \(-0.954967\pi\)
0.617117 + 0.786872i \(0.288301\pi\)
\(132\) −4.00000 −0.348155
\(133\) −6.40192 1.23205i −0.555117 0.106832i
\(134\) 1.94744 0.168233
\(135\) 0.500000 0.866025i 0.0430331 0.0745356i
\(136\) 8.53590 + 14.7846i 0.731947 + 1.26777i
\(137\) 4.09808 + 7.09808i 0.350122 + 0.606430i 0.986271 0.165137i \(-0.0528067\pi\)
−0.636148 + 0.771567i \(0.719473\pi\)
\(138\) −0.464102 + 0.803848i −0.0395070 + 0.0684280i
\(139\) −7.92820 −0.672461 −0.336231 0.941780i \(-0.609152\pi\)
−0.336231 + 0.941780i \(0.609152\pi\)
\(140\) 1.26795 + 3.66025i 0.107161 + 0.309348i
\(141\) −2.00000 −0.168430
\(142\) 1.53590 2.66025i 0.128890 0.223244i
\(143\) 7.83013 + 13.5622i 0.654788 + 1.13413i
\(144\) −0.535898 0.928203i −0.0446582 0.0773503i
\(145\) −3.09808 + 5.36603i −0.257281 + 0.445624i
\(146\) −3.41154 −0.282341
\(147\) −6.50000 2.59808i −0.536111 0.214286i
\(148\) −10.5359 −0.866046
\(149\) 10.9282 18.9282i 0.895273 1.55066i 0.0618073 0.998088i \(-0.480314\pi\)
0.833466 0.552571i \(-0.186353\pi\)
\(150\) 0.366025 + 0.633975i 0.0298858 + 0.0517638i
\(151\) −2.46410 4.26795i −0.200526 0.347321i 0.748172 0.663505i \(-0.230932\pi\)
−0.948698 + 0.316184i \(0.897598\pi\)
\(152\) −3.12436 + 5.41154i −0.253419 + 0.438934i
\(153\) 6.73205 0.544254
\(154\) 1.73205 + 5.00000i 0.139573 + 0.402911i
\(155\) 6.46410 0.519209
\(156\) −4.19615 + 7.26795i −0.335961 + 0.581902i
\(157\) 7.19615 + 12.4641i 0.574315 + 0.994744i 0.996116 + 0.0880548i \(0.0280651\pi\)
−0.421800 + 0.906689i \(0.638602\pi\)
\(158\) −4.90192 8.49038i −0.389976 0.675458i
\(159\) −4.19615 + 7.26795i −0.332777 + 0.576386i
\(160\) 5.85641 0.462990
\(161\) −3.29423 0.633975i −0.259622 0.0499642i
\(162\) 0.732051 0.0575153
\(163\) 2.92820 5.07180i 0.229355 0.397254i −0.728262 0.685298i \(-0.759672\pi\)
0.957617 + 0.288045i \(0.0930051\pi\)
\(164\) 2.00000 + 3.46410i 0.156174 + 0.270501i
\(165\) −1.36603 2.36603i −0.106345 0.184195i
\(166\) 3.33975 5.78461i 0.259215 0.448973i
\(167\) −0.339746 −0.0262903 −0.0131452 0.999914i \(-0.504184\pi\)
−0.0131452 + 0.999914i \(0.504184\pi\)
\(168\) −4.39230 + 5.07180i −0.338874 + 0.391298i
\(169\) 19.8564 1.52742
\(170\) −2.46410 + 4.26795i −0.188988 + 0.327337i
\(171\) 1.23205 + 2.13397i 0.0942173 + 0.163189i
\(172\) −5.26795 9.12436i −0.401677 0.695726i
\(173\) −10.7321 + 18.5885i −0.815943 + 1.41325i 0.0927063 + 0.995693i \(0.470448\pi\)
−0.908649 + 0.417561i \(0.862885\pi\)
\(174\) −4.53590 −0.343866
\(175\) −1.73205 + 2.00000i −0.130931 + 0.151186i
\(176\) −2.92820 −0.220722
\(177\) 5.09808 8.83013i 0.383195 0.663713i
\(178\) 3.33975 + 5.78461i 0.250325 + 0.433575i
\(179\) 5.00000 + 8.66025i 0.373718 + 0.647298i 0.990134 0.140122i \(-0.0447496\pi\)
−0.616417 + 0.787420i \(0.711416\pi\)
\(180\) 0.732051 1.26795i 0.0545638 0.0945074i
\(181\) 10.3205 0.767117 0.383559 0.923517i \(-0.374698\pi\)
0.383559 + 0.923517i \(0.374698\pi\)
\(182\) 10.9019 + 2.09808i 0.808104 + 0.155520i
\(183\) −4.00000 −0.295689
\(184\) −1.60770 + 2.78461i −0.118521 + 0.205284i
\(185\) −3.59808 6.23205i −0.264536 0.458189i
\(186\) 2.36603 + 4.09808i 0.173485 + 0.300486i
\(187\) 9.19615 15.9282i 0.672489 1.16479i
\(188\) −2.92820 −0.213561
\(189\) 0.866025 + 2.50000i 0.0629941 + 0.181848i
\(190\) −1.80385 −0.130865
\(191\) −2.46410 + 4.26795i −0.178296 + 0.308818i −0.941297 0.337579i \(-0.890392\pi\)
0.763001 + 0.646397i \(0.223725\pi\)
\(192\) 1.07180 + 1.85641i 0.0773503 + 0.133975i
\(193\) 4.59808 + 7.96410i 0.330977 + 0.573269i 0.982704 0.185185i \(-0.0592885\pi\)
−0.651727 + 0.758454i \(0.725955\pi\)
\(194\) −0.392305 + 0.679492i −0.0281658 + 0.0487847i
\(195\) −5.73205 −0.410481
\(196\) −9.51666 3.80385i −0.679761 0.271703i
\(197\) −17.6603 −1.25824 −0.629121 0.777308i \(-0.716585\pi\)
−0.629121 + 0.777308i \(0.716585\pi\)
\(198\) 1.00000 1.73205i 0.0710669 0.123091i
\(199\) −11.0000 19.0526i −0.779769 1.35060i −0.932075 0.362267i \(-0.882003\pi\)
0.152305 0.988334i \(-0.451330\pi\)
\(200\) 1.26795 + 2.19615i 0.0896575 + 0.155291i
\(201\) 1.33013 2.30385i 0.0938199 0.162501i
\(202\) −7.85641 −0.552775
\(203\) −5.36603 15.4904i −0.376621 1.08721i
\(204\) 9.85641 0.690086
\(205\) −1.36603 + 2.36603i −0.0954074 + 0.165250i
\(206\) −0.437822 0.758330i −0.0305045 0.0528354i
\(207\) 0.633975 + 1.09808i 0.0440643 + 0.0763216i
\(208\) −3.07180 + 5.32051i −0.212991 + 0.368911i
\(209\) 6.73205 0.465666
\(210\) −1.90192 0.366025i −0.131245 0.0252582i
\(211\) 20.9282 1.44076 0.720378 0.693581i \(-0.243968\pi\)
0.720378 + 0.693581i \(0.243968\pi\)
\(212\) −6.14359 + 10.6410i −0.421944 + 0.730828i
\(213\) −2.09808 3.63397i −0.143758 0.248996i
\(214\) 3.00000 + 5.19615i 0.205076 + 0.355202i
\(215\) 3.59808 6.23205i 0.245387 0.425022i
\(216\) 2.53590 0.172546
\(217\) −11.1962 + 12.9282i −0.760044 + 0.877624i
\(218\) 8.05256 0.545388
\(219\) −2.33013 + 4.03590i −0.157455 + 0.272721i
\(220\) −2.00000 3.46410i −0.134840 0.233550i
\(221\) −19.2942 33.4186i −1.29787 2.24798i
\(222\) 2.63397 4.56218i 0.176781 0.306193i
\(223\) 0.392305 0.0262707 0.0131353 0.999914i \(-0.495819\pi\)
0.0131353 + 0.999914i \(0.495819\pi\)
\(224\) −10.1436 + 11.7128i −0.677747 + 0.782595i
\(225\) 1.00000 0.0666667
\(226\) 1.80385 3.12436i 0.119990 0.207829i
\(227\) −7.83013 13.5622i −0.519704 0.900153i −0.999738 0.0229034i \(-0.992709\pi\)
0.480034 0.877250i \(-0.340624\pi\)
\(228\) 1.80385 + 3.12436i 0.119463 + 0.206916i
\(229\) 1.50000 2.59808i 0.0991228 0.171686i −0.812199 0.583380i \(-0.801730\pi\)
0.911322 + 0.411695i \(0.135063\pi\)
\(230\) −0.928203 −0.0612039
\(231\) 7.09808 + 1.36603i 0.467019 + 0.0898779i
\(232\) −15.7128 −1.03160
\(233\) 8.66025 15.0000i 0.567352 0.982683i −0.429474 0.903079i \(-0.641301\pi\)
0.996827 0.0796037i \(-0.0253655\pi\)
\(234\) −2.09808 3.63397i −0.137156 0.237560i
\(235\) −1.00000 1.73205i −0.0652328 0.112987i
\(236\) 7.46410 12.9282i 0.485872 0.841554i
\(237\) −13.3923 −0.869924
\(238\) −4.26795 12.3205i −0.276650 0.798620i
\(239\) 20.9282 1.35373 0.676866 0.736106i \(-0.263337\pi\)
0.676866 + 0.736106i \(0.263337\pi\)
\(240\) 0.535898 0.928203i 0.0345921 0.0599153i
\(241\) −3.26795 5.66025i −0.210507 0.364609i 0.741366 0.671101i \(-0.234178\pi\)
−0.951873 + 0.306492i \(0.900845\pi\)
\(242\) 1.29423 + 2.24167i 0.0831962 + 0.144100i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) −5.85641 −0.374918
\(245\) −1.00000 6.92820i −0.0638877 0.442627i
\(246\) −2.00000 −0.127515
\(247\) 7.06218 12.2321i 0.449356 0.778307i
\(248\) 8.19615 + 14.1962i 0.520456 + 0.901457i
\(249\) −4.56218 7.90192i −0.289116 0.500764i
\(250\) −0.366025 + 0.633975i −0.0231495 + 0.0400961i
\(251\) 6.58846 0.415860 0.207930 0.978144i \(-0.433327\pi\)
0.207930 + 0.978144i \(0.433327\pi\)
\(252\) 1.26795 + 3.66025i 0.0798733 + 0.230574i
\(253\) 3.46410 0.217786
\(254\) −5.56218 + 9.63397i −0.349002 + 0.604489i
\(255\) 3.36603 + 5.83013i 0.210789 + 0.365097i
\(256\) 5.85641 + 10.1436i 0.366025 + 0.633975i
\(257\) −5.83013 + 10.0981i −0.363673 + 0.629901i −0.988562 0.150813i \(-0.951811\pi\)
0.624889 + 0.780714i \(0.285144\pi\)
\(258\) 5.26795 0.327968
\(259\) 18.6962 + 3.59808i 1.16172 + 0.223574i
\(260\) −8.39230 −0.520469
\(261\) −3.09808 + 5.36603i −0.191766 + 0.332149i
\(262\) −3.12436 5.41154i −0.193023 0.334326i
\(263\) 6.19615 + 10.7321i 0.382071 + 0.661767i 0.991358 0.131183i \(-0.0418776\pi\)
−0.609287 + 0.792950i \(0.708544\pi\)
\(264\) 3.46410 6.00000i 0.213201 0.369274i
\(265\) −8.39230 −0.515535
\(266\) 3.12436 3.60770i 0.191567 0.221202i
\(267\) 9.12436 0.558401
\(268\) 1.94744 3.37307i 0.118959 0.206043i
\(269\) 9.73205 + 16.8564i 0.593374 + 1.02775i 0.993774 + 0.111413i \(0.0355377\pi\)
−0.400401 + 0.916340i \(0.631129\pi\)
\(270\) 0.366025 + 0.633975i 0.0222756 + 0.0385825i
\(271\) −8.46410 + 14.6603i −0.514158 + 0.890547i 0.485708 + 0.874121i \(0.338562\pi\)
−0.999865 + 0.0164256i \(0.994771\pi\)
\(272\) 7.21539 0.437497
\(273\) 9.92820 11.4641i 0.600882 0.693839i
\(274\) −6.00000 −0.362473
\(275\) 1.36603 2.36603i 0.0823744 0.142677i
\(276\) 0.928203 + 1.60770i 0.0558713 + 0.0967719i
\(277\) −1.33013 2.30385i −0.0799196 0.138425i 0.823295 0.567613i \(-0.192133\pi\)
−0.903215 + 0.429188i \(0.858800\pi\)
\(278\) 2.90192 5.02628i 0.174046 0.301456i
\(279\) 6.46410 0.386996
\(280\) −6.58846 1.26795i −0.393736 0.0757745i
\(281\) −13.8564 −0.826604 −0.413302 0.910594i \(-0.635625\pi\)
−0.413302 + 0.910594i \(0.635625\pi\)
\(282\) 0.732051 1.26795i 0.0435930 0.0755053i
\(283\) −0.0621778 0.107695i −0.00369609 0.00640181i 0.864171 0.503197i \(-0.167843\pi\)
−0.867868 + 0.496796i \(0.834510\pi\)
\(284\) −3.07180 5.32051i −0.182278 0.315714i
\(285\) −1.23205 + 2.13397i −0.0729804 + 0.126406i
\(286\) −11.4641 −0.677887
\(287\) −2.36603 6.83013i −0.139662 0.403170i
\(288\) 5.85641 0.345092
\(289\) −14.1603 + 24.5263i −0.832956 + 1.44272i
\(290\) −2.26795 3.92820i −0.133179 0.230672i
\(291\) 0.535898 + 0.928203i 0.0314149 + 0.0544122i
\(292\) −3.41154 + 5.90897i −0.199645 + 0.345796i
\(293\) 5.07180 0.296298 0.148149 0.988965i \(-0.452669\pi\)
0.148149 + 0.988965i \(0.452669\pi\)
\(294\) 4.02628 3.16987i 0.234817 0.184871i
\(295\) 10.1962 0.593643
\(296\) 9.12436 15.8038i 0.530342 0.918580i
\(297\) −1.36603 2.36603i −0.0792648 0.137291i
\(298\) 8.00000 + 13.8564i 0.463428 + 0.802680i
\(299\) 3.63397 6.29423i 0.210158 0.364005i
\(300\) 1.46410 0.0845299
\(301\) 6.23205 + 17.9904i 0.359209 + 1.03695i
\(302\) 3.60770 0.207600
\(303\) −5.36603 + 9.29423i −0.308270 + 0.533939i
\(304\) 1.32051 + 2.28719i 0.0757363 + 0.131179i
\(305\) −2.00000 3.46410i −0.114520 0.198354i
\(306\) −2.46410 + 4.26795i −0.140863 + 0.243982i
\(307\) −7.87564 −0.449487 −0.224743 0.974418i \(-0.572154\pi\)
−0.224743 + 0.974418i \(0.572154\pi\)
\(308\) 10.3923 + 2.00000i 0.592157 + 0.113961i
\(309\) −1.19615 −0.0680467
\(310\) −2.36603 + 4.09808i −0.134381 + 0.232755i
\(311\) 7.56218 + 13.0981i 0.428812 + 0.742724i 0.996768 0.0803351i \(-0.0255990\pi\)
−0.567956 + 0.823059i \(0.692266\pi\)
\(312\) −7.26795 12.5885i −0.411467 0.712681i
\(313\) −2.33013 + 4.03590i −0.131707 + 0.228122i −0.924335 0.381583i \(-0.875379\pi\)
0.792628 + 0.609706i \(0.208712\pi\)
\(314\) −10.5359 −0.594575
\(315\) −1.73205 + 2.00000i −0.0975900 + 0.112687i
\(316\) −19.6077 −1.10302
\(317\) −15.2224 + 26.3660i −0.854977 + 1.48086i 0.0216894 + 0.999765i \(0.493095\pi\)
−0.876666 + 0.481099i \(0.840238\pi\)
\(318\) −3.07180 5.32051i −0.172258 0.298359i
\(319\) 8.46410 + 14.6603i 0.473899 + 0.820817i
\(320\) −1.07180 + 1.85641i −0.0599153 + 0.103776i
\(321\) 8.19615 0.457465
\(322\) 1.60770 1.85641i 0.0895933 0.103453i
\(323\) −16.5885 −0.923006
\(324\) 0.732051 1.26795i 0.0406695 0.0704416i
\(325\) −2.86603 4.96410i −0.158978 0.275359i
\(326\) 2.14359 + 3.71281i 0.118723 + 0.205634i
\(327\) 5.50000 9.52628i 0.304151 0.526804i
\(328\) −6.92820 −0.382546
\(329\) 5.19615 + 1.00000i 0.286473 + 0.0551318i
\(330\) 2.00000 0.110096
\(331\) −10.9641 + 18.9904i −0.602642 + 1.04381i 0.389778 + 0.920909i \(0.372552\pi\)
−0.992419 + 0.122897i \(0.960782\pi\)
\(332\) −6.67949 11.5692i −0.366585 0.634943i
\(333\) −3.59808 6.23205i −0.197173 0.341514i
\(334\) 0.124356 0.215390i 0.00680444 0.0117856i
\(335\) 2.66025 0.145345
\(336\) 0.928203 + 2.67949i 0.0506376 + 0.146178i
\(337\) −33.9808 −1.85105 −0.925525 0.378686i \(-0.876376\pi\)
−0.925525 + 0.378686i \(0.876376\pi\)
\(338\) −7.26795 + 12.5885i −0.395324 + 0.684722i
\(339\) −2.46410 4.26795i −0.133832 0.231803i
\(340\) 4.92820 + 8.53590i 0.267269 + 0.462924i
\(341\) 8.83013 15.2942i 0.478178 0.828229i
\(342\) −1.80385 −0.0975409
\(343\) 15.5885 + 10.0000i 0.841698 + 0.539949i
\(344\) 18.2487 0.983905
\(345\) −0.633975 + 1.09808i −0.0341320 + 0.0591184i
\(346\) −7.85641 13.6077i −0.422363 0.731554i
\(347\) 17.4641 + 30.2487i 0.937522 + 1.62384i 0.770074 + 0.637955i \(0.220219\pi\)
0.167449 + 0.985881i \(0.446447\pi\)
\(348\) −4.53590 + 7.85641i −0.243150 + 0.421148i
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) −0.633975 1.83013i −0.0338874 0.0978244i
\(351\) −5.73205 −0.305954
\(352\) 8.00000 13.8564i 0.426401 0.738549i
\(353\) −10.5622 18.2942i −0.562168 0.973704i −0.997307 0.0733402i \(-0.976634\pi\)
0.435139 0.900363i \(-0.356699\pi\)
\(354\) 3.73205 + 6.46410i 0.198356 + 0.343563i
\(355\) 2.09808 3.63397i 0.111354 0.192871i
\(356\) 13.3590 0.708025
\(357\) −17.4904 3.36603i −0.925689 0.178149i
\(358\) −7.32051 −0.386901
\(359\) 2.36603 4.09808i 0.124874 0.216288i −0.796810 0.604230i \(-0.793481\pi\)
0.921684 + 0.387942i \(0.126814\pi\)
\(360\) 1.26795 + 2.19615i 0.0668268 + 0.115747i
\(361\) 6.46410 + 11.1962i 0.340216 + 0.589271i
\(362\) −3.77757 + 6.54294i −0.198545 + 0.343889i
\(363\) 3.53590 0.185587
\(364\) 14.5359 16.7846i 0.761888 0.879753i
\(365\) −4.66025 −0.243929
\(366\) 1.46410 2.53590i 0.0765298 0.132554i
\(367\) −0.401924 0.696152i −0.0209803 0.0363389i 0.855345 0.518059i \(-0.173345\pi\)
−0.876325 + 0.481721i \(0.840012\pi\)
\(368\) 0.679492 + 1.17691i 0.0354210 + 0.0613509i
\(369\) −1.36603 + 2.36603i −0.0711124 + 0.123170i
\(370\) 5.26795 0.273868
\(371\) 14.5359 16.7846i 0.754666 0.871414i
\(372\) 9.46410 0.490691
\(373\) 9.25833 16.0359i 0.479378 0.830307i −0.520342 0.853958i \(-0.674196\pi\)
0.999720 + 0.0236505i \(0.00752890\pi\)
\(374\) 6.73205 + 11.6603i 0.348106 + 0.602937i
\(375\) 0.500000 + 0.866025i 0.0258199 + 0.0447214i
\(376\) 2.53590 4.39230i 0.130779 0.226516i
\(377\) 35.5167 1.82920
\(378\) −1.90192 0.366025i −0.0978244 0.0188263i
\(379\) −28.3205 −1.45473 −0.727363 0.686253i \(-0.759255\pi\)
−0.727363 + 0.686253i \(0.759255\pi\)
\(380\) −1.80385 + 3.12436i −0.0925354 + 0.160276i
\(381\) 7.59808 + 13.1603i 0.389261 + 0.674220i
\(382\) −1.80385 3.12436i −0.0922929 0.159856i
\(383\) −5.66025 + 9.80385i −0.289225 + 0.500953i −0.973625 0.228154i \(-0.926731\pi\)
0.684400 + 0.729107i \(0.260064\pi\)
\(384\) 10.1436 0.517638
\(385\) 2.36603 + 6.83013i 0.120584 + 0.348096i
\(386\) −6.73205 −0.342652
\(387\) 3.59808 6.23205i 0.182900 0.316793i
\(388\) 0.784610 + 1.35898i 0.0398325 + 0.0689920i
\(389\) −18.2942 31.6865i −0.927554 1.60657i −0.787401 0.616441i \(-0.788574\pi\)
−0.140153 0.990130i \(-0.544760\pi\)
\(390\) 2.09808 3.63397i 0.106240 0.184013i
\(391\) −8.53590 −0.431679
\(392\) 13.9474 10.9808i 0.704452 0.554612i
\(393\) −8.53590 −0.430579
\(394\) 6.46410 11.1962i 0.325657 0.564054i
\(395\) −6.69615 11.5981i −0.336920 0.583563i
\(396\) −2.00000 3.46410i −0.100504 0.174078i
\(397\) 10.4019 18.0167i 0.522058 0.904230i −0.477613 0.878570i \(-0.658498\pi\)
0.999671 0.0256600i \(-0.00816873\pi\)
\(398\) 16.1051 0.807277
\(399\) −2.13397 6.16025i −0.106832 0.308398i
\(400\) 1.07180 0.0535898
\(401\) −2.19615 + 3.80385i −0.109671 + 0.189955i −0.915637 0.402006i \(-0.868313\pi\)
0.805966 + 0.591962i \(0.201646\pi\)
\(402\) 0.973721 + 1.68653i 0.0485648 + 0.0841166i
\(403\) −18.5263 32.0885i −0.922860 1.59844i
\(404\) −7.85641 + 13.6077i −0.390871 + 0.677008i
\(405\) 1.00000 0.0496904
\(406\) 11.7846 + 2.26795i 0.584860 + 0.112556i
\(407\) −19.6603 −0.974523
\(408\) −8.53590 + 14.7846i −0.422590 + 0.731947i
\(409\) −15.4282 26.7224i −0.762876 1.32134i −0.941362 0.337397i \(-0.890454\pi\)
0.178487 0.983942i \(-0.442880\pi\)
\(410\) −1.00000 1.73205i −0.0493865 0.0855399i
\(411\) −4.09808 + 7.09808i −0.202143 + 0.350122i
\(412\) −1.75129 −0.0862798
\(413\) −17.6603 + 20.3923i −0.869004 + 1.00344i
\(414\) −0.928203 −0.0456187
\(415\) 4.56218 7.90192i 0.223949 0.387890i
\(416\) −16.7846 29.0718i −0.822933 1.42536i
\(417\) −3.96410 6.86603i −0.194123 0.336231i
\(418\) −2.46410 + 4.26795i −0.120523 + 0.208752i
\(419\) −28.5359 −1.39407 −0.697035 0.717037i \(-0.745498\pi\)
−0.697035 + 0.717037i \(0.745498\pi\)
\(420\) −2.53590 + 2.92820i −0.123739 + 0.142882i
\(421\) 13.9282 0.678819 0.339410 0.940639i \(-0.389773\pi\)
0.339410 + 0.940639i \(0.389773\pi\)
\(422\) −7.66025 + 13.2679i −0.372895 + 0.645874i
\(423\) −1.00000 1.73205i −0.0486217 0.0842152i
\(424\) −10.6410 18.4308i −0.516773 0.895078i
\(425\) −3.36603 + 5.83013i −0.163276 + 0.282803i
\(426\) 3.07180 0.148829
\(427\) 10.3923 + 2.00000i 0.502919 + 0.0967868i
\(428\) 12.0000 0.580042
\(429\) −7.83013 + 13.5622i −0.378042 + 0.654788i
\(430\) 2.63397 + 4.56218i 0.127022 + 0.220008i
\(431\) 8.66025 + 15.0000i 0.417150 + 0.722525i 0.995651 0.0931566i \(-0.0296957\pi\)
−0.578502 + 0.815681i \(0.696362\pi\)
\(432\) 0.535898 0.928203i 0.0257834 0.0446582i
\(433\) 4.80385 0.230858 0.115429 0.993316i \(-0.463176\pi\)
0.115429 + 0.993316i \(0.463176\pi\)
\(434\) −4.09808 11.8301i −0.196714 0.567864i
\(435\) −6.19615 −0.297083
\(436\) 8.05256 13.9474i 0.385648 0.667961i
\(437\) −1.56218 2.70577i −0.0747291 0.129435i
\(438\) −1.70577 2.95448i −0.0815049 0.141171i
\(439\) −3.73205 + 6.46410i −0.178121 + 0.308515i −0.941237 0.337747i \(-0.890335\pi\)
0.763116 + 0.646262i \(0.223669\pi\)
\(440\) 6.92820 0.330289
\(441\) −1.00000 6.92820i −0.0476190 0.329914i
\(442\) 28.2487 1.34365
\(443\) −1.26795 + 2.19615i −0.0602421 + 0.104342i −0.894574 0.446921i \(-0.852521\pi\)
0.834331 + 0.551263i \(0.185854\pi\)
\(444\) −5.26795 9.12436i −0.250006 0.433023i
\(445\) 4.56218 + 7.90192i 0.216268 + 0.374587i
\(446\) −0.143594 + 0.248711i −0.00679935 + 0.0117768i
\(447\) 21.8564 1.03377
\(448\) −1.85641 5.35898i −0.0877070 0.253188i
\(449\) −8.14359 −0.384320 −0.192160 0.981364i \(-0.561549\pi\)
−0.192160 + 0.981364i \(0.561549\pi\)
\(450\) −0.366025 + 0.633975i −0.0172546 + 0.0298858i
\(451\) 3.73205 + 6.46410i 0.175735 + 0.304383i
\(452\) −3.60770 6.24871i −0.169692 0.293915i
\(453\) 2.46410 4.26795i 0.115774 0.200526i
\(454\) 11.4641 0.538037
\(455\) 14.8923 + 2.86603i 0.698162 + 0.134361i
\(456\) −6.24871 −0.292623
\(457\) −0.330127 + 0.571797i −0.0154427 + 0.0267475i −0.873643 0.486567i \(-0.838249\pi\)
0.858201 + 0.513314i \(0.171582\pi\)
\(458\) 1.09808 + 1.90192i 0.0513097 + 0.0888711i
\(459\) 3.36603 + 5.83013i 0.157113 + 0.272127i
\(460\) −0.928203 + 1.60770i −0.0432777 + 0.0749592i
\(461\) −34.9808 −1.62922 −0.814608 0.580012i \(-0.803048\pi\)
−0.814608 + 0.580012i \(0.803048\pi\)
\(462\) −3.46410 + 4.00000i −0.161165 + 0.186097i
\(463\) 22.2679 1.03488 0.517440 0.855720i \(-0.326885\pi\)
0.517440 + 0.855720i \(0.326885\pi\)
\(464\) −3.32051 + 5.75129i −0.154151 + 0.266997i
\(465\) 3.23205 + 5.59808i 0.149883 + 0.259605i
\(466\) 6.33975 + 10.9808i 0.293683 + 0.508674i
\(467\) 13.9282 24.1244i 0.644520 1.11634i −0.339892 0.940465i \(-0.610390\pi\)
0.984412 0.175877i \(-0.0562762\pi\)
\(468\) −8.39230 −0.387934
\(469\) −4.60770 + 5.32051i −0.212764 + 0.245678i
\(470\) 1.46410 0.0675340
\(471\) −7.19615 + 12.4641i −0.331581 + 0.574315i
\(472\) 12.9282 + 22.3923i 0.595069 + 1.03069i
\(473\) −9.83013 17.0263i −0.451990 0.782869i
\(474\) 4.90192 8.49038i 0.225153 0.389976i
\(475\) −2.46410 −0.113061
\(476\) −25.6077 4.92820i −1.17373 0.225884i
\(477\) −8.39230 −0.384257
\(478\) −7.66025 + 13.2679i −0.350372 + 0.606862i
\(479\) 16.3923 + 28.3923i 0.748984 + 1.29728i 0.948310 + 0.317344i \(0.102791\pi\)
−0.199327 + 0.979933i \(0.563876\pi\)
\(480\) 2.92820 + 5.07180i 0.133654 + 0.231495i
\(481\) −20.6244 + 35.7224i −0.940390 + 1.62880i
\(482\) 4.78461 0.217933
\(483\) −1.09808 3.16987i −0.0499642 0.144234i
\(484\) 5.17691 0.235314
\(485\) −0.535898 + 0.928203i −0.0243339 + 0.0421475i
\(486\) 0.366025 + 0.633975i 0.0166032 + 0.0287577i
\(487\) 15.7942 + 27.3564i 0.715705 + 1.23964i 0.962687 + 0.270617i \(0.0872277\pi\)
−0.246982 + 0.969020i \(0.579439\pi\)
\(488\) 5.07180 8.78461i 0.229589 0.397661i
\(489\) 5.85641 0.264836
\(490\) 4.75833 + 1.90192i 0.214959 + 0.0859202i
\(491\) 10.2487 0.462518 0.231259 0.972892i \(-0.425716\pi\)
0.231259 + 0.972892i \(0.425716\pi\)
\(492\) −2.00000 + 3.46410i −0.0901670 + 0.156174i
\(493\) −20.8564 36.1244i −0.939325 1.62696i
\(494\) 5.16987 + 8.95448i 0.232604 + 0.402881i
\(495\) 1.36603 2.36603i 0.0613983 0.106345i
\(496\) 6.92820 0.311086
\(497\) 3.63397 + 10.4904i 0.163006 + 0.470558i
\(498\) 6.67949 0.299315
\(499\) 10.2321 17.7224i 0.458050 0.793365i −0.540808 0.841146i \(-0.681882\pi\)
0.998858 + 0.0477808i \(0.0152149\pi\)
\(500\) 0.732051 + 1.26795i 0.0327383 + 0.0567044i
\(501\) −0.169873 0.294229i −0.00758937 0.0131452i
\(502\) −2.41154 + 4.17691i −0.107632 + 0.186425i
\(503\) −6.39230 −0.285019 −0.142509 0.989793i \(-0.545517\pi\)
−0.142509 + 0.989793i \(0.545517\pi\)
\(504\) −6.58846 1.26795i −0.293473 0.0564789i
\(505\) −10.7321 −0.477570
\(506\) −1.26795 + 2.19615i −0.0563672 + 0.0976309i
\(507\) 9.92820 + 17.1962i 0.440927 + 0.763708i
\(508\) 11.1244 + 19.2679i 0.493563 + 0.854877i
\(509\) −5.73205 + 9.92820i −0.254069 + 0.440060i −0.964642 0.263563i \(-0.915102\pi\)
0.710573 + 0.703623i \(0.248436\pi\)
\(510\) −4.92820 −0.218225
\(511\) 8.07180 9.32051i 0.357075 0.412315i
\(512\) 11.7128 0.517638
\(513\) −1.23205 + 2.13397i −0.0543964 + 0.0942173i
\(514\) −4.26795 7.39230i −0.188251 0.326061i
\(515\) −0.598076 1.03590i −0.0263544 0.0456471i
\(516\) 5.26795 9.12436i 0.231909 0.401677i
\(517\) −5.46410 −0.240311
\(518\) −9.12436 + 10.5359i −0.400901 + 0.462921i
\(519\) −21.4641 −0.942169
\(520\) 7.26795 12.5885i 0.318721 0.552040i
\(521\) −0.732051 1.26795i −0.0320717 0.0555499i 0.849544 0.527518i \(-0.176877\pi\)
−0.881616 + 0.471968i \(0.843544\pi\)
\(522\) −2.26795 3.92820i −0.0992654 0.171933i
\(523\) 12.1340 21.0167i 0.530582 0.918994i −0.468782 0.883314i \(-0.655307\pi\)
0.999363 0.0356803i \(-0.0113598\pi\)
\(524\) −12.4974 −0.545952
\(525\) −2.59808 0.500000i −0.113389 0.0218218i
\(526\) −9.07180 −0.395549
\(527\) −21.7583 + 37.6865i −0.947808 + 1.64165i
\(528\) −1.46410 2.53590i −0.0637168 0.110361i
\(529\) 10.6962 + 18.5263i 0.465050 + 0.805490i
\(530\) 3.07180 5.32051i 0.133430 0.231108i
\(531\) 10.1962 0.442475
\(532\) −3.12436 9.01924i −0.135458 0.391034i
\(533\) 15.6603 0.678321
\(534\) −3.33975 + 5.78461i −0.144525 + 0.250325i
\(535\) 4.09808 + 7.09808i 0.177175 + 0.306877i
\(536\) 3.37307 + 5.84232i 0.145694 + 0.252350i
\(537\) −5.00000 + 8.66025i −0.215766 + 0.373718i
\(538\) −14.2487 −0.614306
\(539\) −17.7583 7.09808i −0.764905 0.305736i
\(540\) 1.46410 0.0630049
\(541\) 17.8923 30.9904i 0.769250 1.33238i −0.168720 0.985664i \(-0.553963\pi\)
0.937970 0.346716i \(-0.112703\pi\)
\(542\) −6.19615 10.7321i −0.266148 0.460981i
\(543\) 5.16025 + 8.93782i 0.221448 + 0.383559i
\(544\) −19.7128 + 34.1436i −0.845180 + 1.46389i
\(545\) 11.0000 0.471188
\(546\) 3.63397 + 10.4904i 0.155520 + 0.448947i
\(547\) 22.2487 0.951286 0.475643 0.879638i \(-0.342215\pi\)
0.475643 + 0.879638i \(0.342215\pi\)
\(548\) −6.00000 + 10.3923i −0.256307 + 0.443937i
\(549\) −2.00000 3.46410i −0.0853579 0.147844i
\(550\) 1.00000 + 1.73205i 0.0426401 + 0.0738549i
\(551\) 7.63397 13.2224i 0.325218 0.563295i
\(552\) −3.21539 −0.136856
\(553\) 34.7942 + 6.69615i 1.47960 + 0.284749i
\(554\) 1.94744 0.0827388
\(555\) 3.59808 6.23205i 0.152730 0.264536i
\(556\) −5.80385 10.0526i −0.246138 0.426323i
\(557\) 13.3923 + 23.1962i 0.567450 + 0.982853i 0.996817 + 0.0797224i \(0.0254034\pi\)
−0.429367 + 0.903130i \(0.641263\pi\)
\(558\) −2.36603 + 4.09808i −0.100162 + 0.173485i
\(559\) −41.2487 −1.74463
\(560\) −1.85641 + 2.14359i −0.0784475 + 0.0905834i
\(561\) 18.3923 0.776524
\(562\) 5.07180 8.78461i 0.213941 0.370556i
\(563\) 9.00000 + 15.5885i 0.379305 + 0.656975i 0.990961 0.134148i \(-0.0428299\pi\)
−0.611656 + 0.791123i \(0.709497\pi\)
\(564\) −1.46410 2.53590i −0.0616498 0.106781i
\(565\) 2.46410 4.26795i 0.103666 0.179554i
\(566\) 0.0910347 0.00382647
\(567\) −1.73205 + 2.00000i −0.0727393 + 0.0839921i
\(568\) 10.6410 0.446487
\(569\) 13.2224 22.9019i 0.554313 0.960099i −0.443643 0.896203i \(-0.646314\pi\)
0.997957 0.0638952i \(-0.0203523\pi\)
\(570\) −0.901924 1.56218i −0.0377774 0.0654324i
\(571\) −19.6962 34.1147i −0.824258 1.42766i −0.902485 0.430722i \(-0.858259\pi\)
0.0782265 0.996936i \(-0.475074\pi\)
\(572\) −11.4641 + 19.8564i −0.479338 + 0.830238i
\(573\) −4.92820 −0.205879
\(574\) 5.19615 + 1.00000i 0.216883 + 0.0417392i
\(575\) −1.26795 −0.0528771
\(576\) −1.07180 + 1.85641i −0.0446582 + 0.0773503i
\(577\) −5.66987 9.82051i −0.236040 0.408833i 0.723534 0.690288i \(-0.242516\pi\)
−0.959574 + 0.281455i \(0.909183\pi\)
\(578\) −10.3660 17.9545i −0.431170 0.746808i
\(579\) −4.59808 + 7.96410i −0.191090 + 0.330977i
\(580\) −9.07180 −0.376686
\(581\) 7.90192 + 22.8109i 0.327827 + 0.946355i
\(582\) −0.784610 −0.0325231
\(583\) −11.4641 + 19.8564i −0.474795 + 0.822368i
\(584\) −5.90897 10.2346i −0.244515 0.423512i
\(585\) −2.86603 4.96410i −0.118496 0.205240i
\(586\) −1.85641 + 3.21539i −0.0766874 + 0.132827i
\(587\) 37.2679 1.53821 0.769106 0.639121i \(-0.220702\pi\)
0.769106 + 0.639121i \(0.220702\pi\)
\(588\) −1.46410 10.1436i −0.0603785 0.418315i
\(589\) −15.9282 −0.656310
\(590\) −3.73205 + 6.46410i −0.153646 + 0.266123i
\(591\) −8.83013 15.2942i −0.363223 0.629121i
\(592\) −3.85641 6.67949i −0.158497 0.274525i
\(593\) 18.9545 32.8301i 0.778367 1.34817i −0.154515 0.987990i \(-0.549381\pi\)
0.932882 0.360181i \(-0.117285\pi\)
\(594\) 2.00000 0.0820610
\(595\) −5.83013 16.8301i −0.239012 0.689968i
\(596\) 32.0000 1.31077
\(597\) 11.0000 19.0526i 0.450200 0.779769i
\(598\) 2.66025 + 4.60770i 0.108786 + 0.188423i
\(599\) −5.12436 8.87564i −0.209375 0.362649i 0.742142 0.670242i \(-0.233810\pi\)
−0.951518 + 0.307593i \(0.900476\pi\)
\(600\) −1.26795 + 2.19615i −0.0517638 + 0.0896575i
\(601\) −13.9282 −0.568143 −0.284072 0.958803i \(-0.591685\pi\)
−0.284072 + 0.958803i \(0.591685\pi\)
\(602\) −13.6865 2.63397i −0.557821 0.107353i
\(603\) 2.66025 0.108334
\(604\) 3.60770 6.24871i 0.146795 0.254256i
\(605\) 1.76795 + 3.06218i 0.0718774 + 0.124495i
\(606\) −3.92820 6.80385i −0.159572 0.276387i
\(607\) 3.59808 6.23205i 0.146041 0.252951i −0.783720 0.621115i \(-0.786680\pi\)
0.929761 + 0.368164i \(0.120013\pi\)
\(608\) −14.4308 −0.585245
\(609\) 10.7321 12.3923i 0.434885 0.502162i
\(610\) 2.92820 0.118559
\(611\) −5.73205 + 9.92820i −0.231894 + 0.401652i
\(612\) 4.92820 + 8.53590i 0.199211 + 0.345043i
\(613\) 6.53590 + 11.3205i 0.263982 + 0.457231i 0.967297 0.253648i \(-0.0816306\pi\)
−0.703314 + 0.710879i \(0.748297\pi\)
\(614\) 2.88269 4.99296i 0.116336 0.201499i
\(615\) −2.73205 −0.110167
\(616\) −12.0000 + 13.8564i −0.483494 + 0.558291i
\(617\) 12.2487 0.493115 0.246557 0.969128i \(-0.420701\pi\)
0.246557 + 0.969128i \(0.420701\pi\)
\(618\) 0.437822 0.758330i 0.0176118 0.0305045i
\(619\) 21.9641 + 38.0429i 0.882812 + 1.52907i 0.848201 + 0.529674i \(0.177686\pi\)
0.0346105 + 0.999401i \(0.488981\pi\)
\(620\) 4.73205 + 8.19615i 0.190044 + 0.329165i
\(621\) −0.633975 + 1.09808i −0.0254405 + 0.0440643i
\(622\) −11.0718 −0.443939
\(623\) −23.7058 4.56218i −0.949752 0.182780i
\(624\) −6.14359 −0.245941
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −1.70577 2.95448i −0.0681763 0.118085i
\(627\) 3.36603 + 5.83013i 0.134426 + 0.232833i
\(628\) −10.5359 + 18.2487i −0.420428 + 0.728203i
\(629\) 48.4449 1.93162
\(630\) −0.633975 1.83013i −0.0252582 0.0729140i
\(631\) 7.21539 0.287240 0.143620 0.989633i \(-0.454126\pi\)
0.143620 + 0.989633i \(0.454126\pi\)
\(632\) 16.9808 29.4115i 0.675458 1.16993i
\(633\) 10.4641 + 18.1244i 0.415911 + 0.720378i
\(634\) −11.1436 19.3013i −0.442569 0.766551i
\(635\) −7.59808 + 13.1603i −0.301520 + 0.522249i
\(636\) −12.2872 −0.487219
\(637\) −31.5263 + 24.8205i −1.24912 + 0.983424i
\(638\) −12.3923 −0.490616
\(639\) 2.09808 3.63397i 0.0829986 0.143758i
\(640\) 5.07180 + 8.78461i 0.200480 + 0.347242i
\(641\) −7.09808 12.2942i −0.280357 0.485593i 0.691116 0.722744i \(-0.257120\pi\)
−0.971473 + 0.237151i \(0.923786\pi\)
\(642\) −3.00000 + 5.19615i −0.118401 + 0.205076i
\(643\) −40.5167 −1.59782 −0.798911 0.601450i \(-0.794590\pi\)
−0.798911 + 0.601450i \(0.794590\pi\)
\(644\) −1.60770 4.64102i −0.0633521 0.182882i
\(645\) 7.19615 0.283348
\(646\) 6.07180 10.5167i 0.238892 0.413772i
\(647\) −18.9545 32.8301i −0.745178 1.29069i −0.950112 0.311910i \(-0.899031\pi\)
0.204934 0.978776i \(-0.434302\pi\)
\(648\) 1.26795 + 2.19615i 0.0498097 + 0.0862730i
\(649\) 13.9282 24.1244i 0.546730 0.946964i
\(650\) 4.19615 0.164587
\(651\) −16.7942 3.23205i −0.658218 0.126674i
\(652\) 8.57437 0.335798
\(653\) 6.70577 11.6147i 0.262417 0.454520i −0.704467 0.709737i \(-0.748814\pi\)
0.966884 + 0.255217i \(0.0821470\pi\)
\(654\) 4.02628 + 6.97372i 0.157440 + 0.272694i
\(655\) −4.26795 7.39230i −0.166763 0.288841i
\(656\) −1.46410 + 2.53590i −0.0571636 + 0.0990102i
\(657\) −4.66025 −0.181814
\(658\) −2.53590 + 2.92820i −0.0988596 + 0.114153i
\(659\) −10.9282 −0.425702 −0.212851 0.977085i \(-0.568275\pi\)
−0.212851 + 0.977085i \(0.568275\pi\)
\(660\) 2.00000 3.46410i 0.0778499 0.134840i
\(661\) −1.76795 3.06218i −0.0687653 0.119105i 0.829593 0.558369i \(-0.188573\pi\)
−0.898358 + 0.439264i \(0.855239\pi\)
\(662\) −8.02628 13.9019i −0.311950 0.540314i
\(663\) 19.2942 33.4186i 0.749326 1.29787i
\(664\) 23.1384 0.897946
\(665\) 4.26795 4.92820i 0.165504 0.191108i
\(666\) 5.26795 0.204129
\(667\) 3.92820 6.80385i 0.152101 0.263446i
\(668\) −0.248711 0.430781i −0.00962293 0.0166674i
\(669\) 0.196152 + 0.339746i 0.00758369 + 0.0131353i
\(670\) −0.973721 + 1.68653i −0.0376181 + 0.0651565i
\(671\) −10.9282 −0.421879
\(672\) −15.2154 2.92820i −0.586946 0.112958i
\(673\) −44.6603 −1.72153 −0.860763 0.509006i \(-0.830013\pi\)
−0.860763 + 0.509006i \(0.830013\pi\)
\(674\) 12.4378 21.5429i 0.479087 0.829803i
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 14.5359 + 25.1769i 0.559073 + 0.968343i
\(677\) 4.43782 7.68653i 0.170559 0.295417i −0.768056 0.640382i \(-0.778776\pi\)
0.938616 + 0.344965i \(0.112109\pi\)
\(678\) 3.60770 0.138553
\(679\) −0.928203 2.67949i −0.0356212 0.102829i
\(680\) −17.0718 −0.654674
\(681\) 7.83013 13.5622i 0.300051 0.519704i
\(682\) 6.46410 + 11.1962i 0.247523 + 0.428723i
\(683\) −5.02628 8.70577i −0.192325 0.333117i 0.753695 0.657224i \(-0.228270\pi\)
−0.946020 + 0.324107i \(0.894936\pi\)
\(684\) −1.80385 + 3.12436i −0.0689718 + 0.119463i
\(685\) −8.19615 −0.313159
\(686\) −12.0455 + 6.22243i −0.459900 + 0.237574i
\(687\) 3.00000 0.114457
\(688\) 3.85641 6.67949i 0.147024 0.254653i
\(689\) 24.0526 + 41.6603i 0.916330 + 1.58713i
\(690\) −0.464102 0.803848i −0.0176680 0.0306020i
\(691\) 9.42820 16.3301i 0.358666 0.621227i −0.629072 0.777347i \(-0.716565\pi\)
0.987738 + 0.156119i \(0.0498985\pi\)
\(692\) −31.4256 −1.19462
\(693\) 2.36603 + 6.83013i 0.0898779 + 0.259455i
\(694\) −25.5692 −0.970594
\(695\) 3.96410 6.86603i 0.150367 0.260443i
\(696\) −7.85641 13.6077i −0.297796 0.515798i
\(697\) −9.19615 15.9282i −0.348329 0.603324i
\(698\) −8.05256 + 13.9474i −0.304794 + 0.527918i
\(699\) 17.3205 0.655122
\(700\) −3.80385 0.732051i −0.143772 0.0276689i
\(701\) 22.5885 0.853154 0.426577 0.904451i \(-0.359719\pi\)
0.426577 + 0.904451i \(0.359719\pi\)
\(702\) 2.09808 3.63397i 0.0791868 0.137156i
\(703\) 8.86603 + 15.3564i 0.334388 + 0.579178i
\(704\) 2.92820 + 5.07180i 0.110361 + 0.191151i
\(705\) 1.00000 1.73205i 0.0376622 0.0652328i
\(706\) 15.4641 0.581999
\(707\) 18.5885 21.4641i 0.699091 0.807241i
\(708\) 14.9282 0.561036
\(709\) 7.46410 12.9282i 0.280320 0.485529i −0.691143 0.722718i \(-0.742893\pi\)
0.971464 + 0.237189i \(0.0762260\pi\)
\(710\) 1.53590 + 2.66025i 0.0576412 + 0.0998376i
\(711\) −6.69615 11.5981i −0.251125 0.434962i
\(712\) −11.5692 + 20.0385i −0.433575 + 0.750974i
\(713\) −8.19615 −0.306948
\(714\) 8.53590 9.85641i 0.319448 0.368867i
\(715\) −15.6603 −0.585660
\(716\) −7.32051 + 12.6795i −0.273580 + 0.473855i
\(717\) 10.4641 + 18.1244i 0.390789 + 0.676866i
\(718\) 1.73205 + 3.00000i 0.0646396 + 0.111959i
\(719\) 13.7321 23.7846i 0.512119 0.887016i −0.487782 0.872965i \(-0.662194\pi\)
0.999901 0.0140509i \(-0.00447269\pi\)
\(720\) 1.07180 0.0399435
\(721\) 3.10770 + 0.598076i 0.115737 + 0.0222735i
\(722\) −9.46410 −0.352217
\(723\) 3.26795 5.66025i 0.121536 0.210507i
\(724\) 7.55514 + 13.0859i 0.280784 + 0.486333i
\(725\) −3.09808 5.36603i −0.115060 0.199289i
\(726\) −1.29423 + 2.24167i −0.0480333 + 0.0831962i
\(727\) −30.6603 −1.13713 −0.568563 0.822640i \(-0.692500\pi\)
−0.568563 + 0.822640i \(0.692500\pi\)
\(728\) 12.5885 + 36.3397i 0.466559 + 1.34684i
\(729\) 1.00000 0.0370370
\(730\) 1.70577 2.95448i 0.0631334 0.109350i
\(731\) 24.2224 + 41.9545i 0.895899 + 1.55174i
\(732\) −2.92820 5.07180i −0.108230 0.187459i
\(733\) 9.33013 16.1603i 0.344616 0.596893i −0.640668 0.767818i \(-0.721342\pi\)
0.985284 + 0.170926i \(0.0546758\pi\)
\(734\) 0.588457 0.0217204
\(735\) 5.50000 4.33013i 0.202871 0.159719i
\(736\) −7.42563 −0.273712
\(737\) 3.63397 6.29423i 0.133859 0.231851i
\(738\) −1.00000 1.73205i −0.0368105 0.0637577i
\(739\) 6.89230 + 11.9378i 0.253538 + 0.439140i 0.964497 0.264093i \(-0.0850725\pi\)
−0.710960 + 0.703233i \(0.751739\pi\)
\(740\) 5.26795 9.12436i 0.193654 0.335418i
\(741\) 14.1244 0.518871
\(742\) 5.32051 + 15.3590i 0.195322 + 0.563846i
\(743\) 49.9090 1.83098 0.915491 0.402338i \(-0.131802\pi\)
0.915491 + 0.402338i \(0.131802\pi\)
\(744\) −8.19615 + 14.1962i −0.300486 + 0.520456i
\(745\) 10.9282 + 18.9282i 0.400378 + 0.693476i
\(746\) 6.77757 + 11.7391i 0.248144 + 0.429799i
\(747\) 4.56218 7.90192i 0.166921 0.289116i
\(748\) 26.9282 0.984593
\(749\) −21.2942 4.09808i −0.778074 0.149740i
\(750\) −0.732051 −0.0267307
\(751\) −15.9641 + 27.6506i −0.582538 + 1.00899i 0.412639 + 0.910895i \(0.364607\pi\)
−0.995177 + 0.0980914i \(0.968726\pi\)
\(752\) −1.07180 1.85641i −0.0390844 0.0676962i
\(753\) 3.29423 + 5.70577i 0.120048 + 0.207930i
\(754\) −13.0000 + 22.5167i −0.473432 + 0.820008i
\(755\) 4.92820 0.179356
\(756\) −2.53590 + 2.92820i −0.0922297 + 0.106498i
\(757\) −0.143594 −0.00521900 −0.00260950 0.999997i \(-0.500831\pi\)
−0.00260950 + 0.999997i \(0.500831\pi\)
\(758\) 10.3660 17.9545i 0.376511 0.652136i
\(759\) 1.73205 + 3.00000i 0.0628695 + 0.108893i
\(760\) −3.12436 5.41154i −0.113332 0.196297i
\(761\) −21.6340 + 37.4711i −0.784231 + 1.35833i 0.145226 + 0.989398i \(0.453609\pi\)
−0.929457 + 0.368929i \(0.879724\pi\)
\(762\) −11.1244 −0.402993
\(763\) −19.0526 + 22.0000i −0.689749 + 0.796453i
\(764\) −7.21539 −0.261044
\(765\) −3.36603 + 5.83013i −0.121699 + 0.210789i
\(766\) −4.14359 7.17691i −0.149714 0.259312i
\(767\) −29.2224 50.6147i −1.05516 1.82759i
\(768\) −5.85641 + 10.1436i −0.211325 + 0.366025i
\(769\) 17.6795 0.637539