Properties

Label 165.2.c.b.34.2
Level $165$
Weight $2$
Character 165.34
Analytic conductor $1.318$
Analytic rank $0$
Dimension $6$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [165,2,Mod(34,165)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(165, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("165.34");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 165 = 3 \cdot 5 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 165.c (of order \(2\), degree \(1\), 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: \(1.31753163335\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.0.350464.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 34.2
Root \(0.403032 - 0.403032i\) of defining polynomial
Character \(\chi\) \(=\) 165.34
Dual form 165.2.c.b.34.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.48119i q^{2} -1.00000i q^{3} -0.193937 q^{4} +(-1.48119 - 1.67513i) q^{5} -1.48119 q^{6} +1.19394i q^{7} -2.67513i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q-1.48119i q^{2} -1.00000i q^{3} -0.193937 q^{4} +(-1.48119 - 1.67513i) q^{5} -1.48119 q^{6} +1.19394i q^{7} -2.67513i q^{8} -1.00000 q^{9} +(-2.48119 + 2.19394i) q^{10} +1.00000 q^{11} +0.193937i q^{12} -0.806063i q^{13} +1.76845 q^{14} +(-1.67513 + 1.48119i) q^{15} -4.35026 q^{16} +3.76845i q^{17} +1.48119i q^{18} +5.35026 q^{19} +(0.287258 + 0.324869i) q^{20} +1.19394 q^{21} -1.48119i q^{22} -4.00000i q^{23} -2.67513 q^{24} +(-0.612127 + 4.96239i) q^{25} -1.19394 q^{26} +1.00000i q^{27} -0.231548i q^{28} +4.31265 q^{29} +(2.19394 + 2.48119i) q^{30} +0.962389 q^{31} +1.09332i q^{32} -1.00000i q^{33} +5.58181 q^{34} +(2.00000 - 1.76845i) q^{35} +0.193937 q^{36} +1.61213i q^{37} -7.92478i q^{38} -0.806063 q^{39} +(-4.48119 + 3.96239i) q^{40} +9.08840 q^{41} -1.76845i q^{42} -4.41819i q^{43} -0.193937 q^{44} +(1.48119 + 1.67513i) q^{45} -5.92478 q^{46} +12.3127i q^{47} +4.35026i q^{48} +5.57452 q^{49} +(7.35026 + 0.906679i) q^{50} +3.76845 q^{51} +0.156325i q^{52} -1.42548i q^{53} +1.48119 q^{54} +(-1.48119 - 1.67513i) q^{55} +3.19394 q^{56} -5.35026i q^{57} -6.38787i q^{58} -13.2750 q^{59} +(0.324869 - 0.287258i) q^{60} -0.0752228 q^{61} -1.42548i q^{62} -1.19394i q^{63} -7.08110 q^{64} +(-1.35026 + 1.19394i) q^{65} -1.48119 q^{66} -2.70052i q^{67} -0.730841i q^{68} -4.00000 q^{69} +(-2.61942 - 2.96239i) q^{70} -14.0508 q^{71} +2.67513i q^{72} +10.7308i q^{73} +2.38787 q^{74} +(4.96239 + 0.612127i) q^{75} -1.03761 q^{76} +1.19394i q^{77} +1.19394i q^{78} -13.9756 q^{79} +(6.44358 + 7.28726i) q^{80} +1.00000 q^{81} -13.4617i q^{82} +9.89446i q^{83} -0.231548 q^{84} +(6.31265 - 5.58181i) q^{85} -6.54420 q^{86} -4.31265i q^{87} -2.67513i q^{88} -16.8872 q^{89} +(2.48119 - 2.19394i) q^{90} +0.962389 q^{91} +0.775746i q^{92} -0.962389i q^{93} +18.2374 q^{94} +(-7.92478 - 8.96239i) q^{95} +1.09332 q^{96} +11.4763i q^{97} -8.25694i q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 6 q - 2 q^{4} + 2 q^{5} + 2 q^{6} - 6 q^{9} - 4 q^{10} + 6 q^{11} - 12 q^{14} - 6 q^{16} + 12 q^{19} - 10 q^{20} + 8 q^{21} - 6 q^{24} - 2 q^{25} - 8 q^{26} - 16 q^{29} + 14 q^{30} - 16 q^{31} + 36 q^{34} + 12 q^{35} + 2 q^{36} - 4 q^{39} - 16 q^{40} + 16 q^{41} - 2 q^{44} - 2 q^{45} + 8 q^{46} + 10 q^{49} + 24 q^{50} - 2 q^{54} + 2 q^{55} + 20 q^{56} - 16 q^{59} + 12 q^{60} - 44 q^{61} + 22 q^{64} + 12 q^{65} + 2 q^{66} - 24 q^{69} - 40 q^{70} - 24 q^{71} + 16 q^{74} + 8 q^{75} - 28 q^{76} + 20 q^{79} + 6 q^{80} + 6 q^{81} - 24 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} + 4 q^{90} - 16 q^{91} + 24 q^{94} - 4 q^{95} - 6 q^{96} - 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/165\mathbb{Z}\right)^\times\).

\(n\) \(46\) \(56\) \(67\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.48119i 1.04736i −0.851914 0.523681i \(-0.824558\pi\)
0.851914 0.523681i \(-0.175442\pi\)
\(3\) 1.00000i 0.577350i
\(4\) −0.193937 −0.0969683
\(5\) −1.48119 1.67513i −0.662410 0.749141i
\(6\) −1.48119 −0.604695
\(7\) 1.19394i 0.451266i 0.974212 + 0.225633i \(0.0724450\pi\)
−0.974212 + 0.225633i \(0.927555\pi\)
\(8\) 2.67513i 0.945802i
\(9\) −1.00000 −0.333333
\(10\) −2.48119 + 2.19394i −0.784623 + 0.693784i
\(11\) 1.00000 0.301511
\(12\) 0.193937i 0.0559847i
\(13\) 0.806063i 0.223562i −0.993733 0.111781i \(-0.964345\pi\)
0.993733 0.111781i \(-0.0356555\pi\)
\(14\) 1.76845 0.472639
\(15\) −1.67513 + 1.48119i −0.432517 + 0.382443i
\(16\) −4.35026 −1.08757
\(17\) 3.76845i 0.913984i 0.889471 + 0.456992i \(0.151073\pi\)
−0.889471 + 0.456992i \(0.848927\pi\)
\(18\) 1.48119i 0.349121i
\(19\) 5.35026 1.22743 0.613717 0.789526i \(-0.289674\pi\)
0.613717 + 0.789526i \(0.289674\pi\)
\(20\) 0.287258 + 0.324869i 0.0642328 + 0.0726429i
\(21\) 1.19394 0.260538
\(22\) 1.48119i 0.315792i
\(23\) 4.00000i 0.834058i −0.908893 0.417029i \(-0.863071\pi\)
0.908893 0.417029i \(-0.136929\pi\)
\(24\) −2.67513 −0.546059
\(25\) −0.612127 + 4.96239i −0.122425 + 0.992478i
\(26\) −1.19394 −0.234150
\(27\) 1.00000i 0.192450i
\(28\) 0.231548i 0.0437585i
\(29\) 4.31265 0.800839 0.400420 0.916332i \(-0.368864\pi\)
0.400420 + 0.916332i \(0.368864\pi\)
\(30\) 2.19394 + 2.48119i 0.400556 + 0.453002i
\(31\) 0.962389 0.172850 0.0864250 0.996258i \(-0.472456\pi\)
0.0864250 + 0.996258i \(0.472456\pi\)
\(32\) 1.09332i 0.193274i
\(33\) 1.00000i 0.174078i
\(34\) 5.58181 0.957272
\(35\) 2.00000 1.76845i 0.338062 0.298923i
\(36\) 0.193937 0.0323228
\(37\) 1.61213i 0.265032i 0.991181 + 0.132516i \(0.0423056\pi\)
−0.991181 + 0.132516i \(0.957694\pi\)
\(38\) 7.92478i 1.28557i
\(39\) −0.806063 −0.129073
\(40\) −4.48119 + 3.96239i −0.708539 + 0.626509i
\(41\) 9.08840 1.41937 0.709685 0.704520i \(-0.248837\pi\)
0.709685 + 0.704520i \(0.248837\pi\)
\(42\) 1.76845i 0.272878i
\(43\) 4.41819i 0.673768i −0.941546 0.336884i \(-0.890627\pi\)
0.941546 0.336884i \(-0.109373\pi\)
\(44\) −0.193937 −0.0292370
\(45\) 1.48119 + 1.67513i 0.220803 + 0.249714i
\(46\) −5.92478 −0.873561
\(47\) 12.3127i 1.79598i 0.440011 + 0.897992i \(0.354974\pi\)
−0.440011 + 0.897992i \(0.645026\pi\)
\(48\) 4.35026i 0.627906i
\(49\) 5.57452 0.796359
\(50\) 7.35026 + 0.906679i 1.03948 + 0.128224i
\(51\) 3.76845 0.527689
\(52\) 0.156325i 0.0216784i
\(53\) 1.42548i 0.195805i −0.995196 0.0979027i \(-0.968787\pi\)
0.995196 0.0979027i \(-0.0312134\pi\)
\(54\) 1.48119 0.201565
\(55\) −1.48119 1.67513i −0.199724 0.225875i
\(56\) 3.19394 0.426808
\(57\) 5.35026i 0.708659i
\(58\) 6.38787i 0.838769i
\(59\) −13.2750 −1.72826 −0.864131 0.503266i \(-0.832132\pi\)
−0.864131 + 0.503266i \(0.832132\pi\)
\(60\) 0.324869 0.287258i 0.0419404 0.0370848i
\(61\) −0.0752228 −0.00963129 −0.00481565 0.999988i \(-0.501533\pi\)
−0.00481565 + 0.999988i \(0.501533\pi\)
\(62\) 1.42548i 0.181037i
\(63\) 1.19394i 0.150422i
\(64\) −7.08110 −0.885138
\(65\) −1.35026 + 1.19394i −0.167479 + 0.148090i
\(66\) −1.48119 −0.182322
\(67\) 2.70052i 0.329921i −0.986300 0.164961i \(-0.947250\pi\)
0.986300 0.164961i \(-0.0527497\pi\)
\(68\) 0.730841i 0.0886274i
\(69\) −4.00000 −0.481543
\(70\) −2.61942 2.96239i −0.313081 0.354073i
\(71\) −14.0508 −1.66752 −0.833761 0.552126i \(-0.813817\pi\)
−0.833761 + 0.552126i \(0.813817\pi\)
\(72\) 2.67513i 0.315267i
\(73\) 10.7308i 1.25595i 0.778234 + 0.627975i \(0.216116\pi\)
−0.778234 + 0.627975i \(0.783884\pi\)
\(74\) 2.38787 0.277585
\(75\) 4.96239 + 0.612127i 0.573007 + 0.0706823i
\(76\) −1.03761 −0.119022
\(77\) 1.19394i 0.136062i
\(78\) 1.19394i 0.135187i
\(79\) −13.9756 −1.57237 −0.786187 0.617989i \(-0.787948\pi\)
−0.786187 + 0.617989i \(0.787948\pi\)
\(80\) 6.44358 + 7.28726i 0.720414 + 0.814740i
\(81\) 1.00000 0.111111
\(82\) 13.4617i 1.48659i
\(83\) 9.89446i 1.08606i 0.839714 + 0.543029i \(0.182723\pi\)
−0.839714 + 0.543029i \(0.817277\pi\)
\(84\) −0.231548 −0.0252640
\(85\) 6.31265 5.58181i 0.684703 0.605432i
\(86\) −6.54420 −0.705679
\(87\) 4.31265i 0.462365i
\(88\) 2.67513i 0.285170i
\(89\) −16.8872 −1.79004 −0.895018 0.446030i \(-0.852837\pi\)
−0.895018 + 0.446030i \(0.852837\pi\)
\(90\) 2.48119 2.19394i 0.261541 0.231261i
\(91\) 0.962389 0.100886
\(92\) 0.775746i 0.0808771i
\(93\) 0.962389i 0.0997950i
\(94\) 18.2374 1.88105
\(95\) −7.92478 8.96239i −0.813065 0.919522i
\(96\) 1.09332 0.111587
\(97\) 11.4763i 1.16524i 0.812745 + 0.582619i \(0.197972\pi\)
−0.812745 + 0.582619i \(0.802028\pi\)
\(98\) 8.25694i 0.834077i
\(99\) −1.00000 −0.100504
\(100\) 0.118714 0.962389i 0.0118714 0.0962389i
\(101\) 10.7612 1.07078 0.535388 0.844606i \(-0.320166\pi\)
0.535388 + 0.844606i \(0.320166\pi\)
\(102\) 5.58181i 0.552682i
\(103\) 16.9380i 1.66895i −0.551049 0.834473i \(-0.685772\pi\)
0.551049 0.834473i \(-0.314228\pi\)
\(104\) −2.15633 −0.211445
\(105\) −1.76845 2.00000i −0.172583 0.195180i
\(106\) −2.11142 −0.205079
\(107\) 8.28233i 0.800683i 0.916366 + 0.400342i \(0.131109\pi\)
−0.916366 + 0.400342i \(0.868891\pi\)
\(108\) 0.193937i 0.0186616i
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) −2.48119 + 2.19394i −0.236573 + 0.209184i
\(111\) 1.61213 0.153016
\(112\) 5.19394i 0.490781i
\(113\) 2.26187i 0.212778i −0.994325 0.106389i \(-0.966071\pi\)
0.994325 0.106389i \(-0.0339289\pi\)
\(114\) −7.92478 −0.742223
\(115\) −6.70052 + 5.92478i −0.624827 + 0.552488i
\(116\) −0.836381 −0.0776560
\(117\) 0.806063i 0.0745206i
\(118\) 19.6629i 1.81012i
\(119\) −4.49929 −0.412449
\(120\) 3.96239 + 4.48119i 0.361715 + 0.409075i
\(121\) 1.00000 0.0909091
\(122\) 0.111420i 0.0100875i
\(123\) 9.08840i 0.819473i
\(124\) −0.186642 −0.0167610
\(125\) 9.21933 6.32487i 0.824602 0.565713i
\(126\) −1.76845 −0.157546
\(127\) 13.8192i 1.22626i −0.789982 0.613130i \(-0.789910\pi\)
0.789982 0.613130i \(-0.210090\pi\)
\(128\) 12.6751i 1.12033i
\(129\) −4.41819 −0.389000
\(130\) 1.76845 + 2.00000i 0.155104 + 0.175412i
\(131\) −5.92478 −0.517650 −0.258825 0.965924i \(-0.583335\pi\)
−0.258825 + 0.965924i \(0.583335\pi\)
\(132\) 0.193937i 0.0168800i
\(133\) 6.38787i 0.553899i
\(134\) −4.00000 −0.345547
\(135\) 1.67513 1.48119i 0.144172 0.127481i
\(136\) 10.0811 0.864447
\(137\) 3.35026i 0.286232i 0.989706 + 0.143116i \(0.0457122\pi\)
−0.989706 + 0.143116i \(0.954288\pi\)
\(138\) 5.92478i 0.504351i
\(139\) 21.1998 1.79814 0.899072 0.437800i \(-0.144242\pi\)
0.899072 + 0.437800i \(0.144242\pi\)
\(140\) −0.387873 + 0.342968i −0.0327813 + 0.0289860i
\(141\) 12.3127 1.03691
\(142\) 20.8119i 1.74650i
\(143\) 0.806063i 0.0674064i
\(144\) 4.35026 0.362522
\(145\) −6.38787 7.22425i −0.530484 0.599942i
\(146\) 15.8945 1.31543
\(147\) 5.57452i 0.459778i
\(148\) 0.312650i 0.0256997i
\(149\) −6.38787 −0.523315 −0.261657 0.965161i \(-0.584269\pi\)
−0.261657 + 0.965161i \(0.584269\pi\)
\(150\) 0.906679 7.35026i 0.0740300 0.600146i
\(151\) −2.64974 −0.215633 −0.107816 0.994171i \(-0.534386\pi\)
−0.107816 + 0.994171i \(0.534386\pi\)
\(152\) 14.3127i 1.16091i
\(153\) 3.76845i 0.304661i
\(154\) 1.76845 0.142506
\(155\) −1.42548 1.61213i −0.114498 0.129489i
\(156\) 0.156325 0.0125160
\(157\) 1.61213i 0.128662i 0.997929 + 0.0643309i \(0.0204913\pi\)
−0.997929 + 0.0643309i \(0.979509\pi\)
\(158\) 20.7005i 1.64685i
\(159\) −1.42548 −0.113048
\(160\) 1.83146 1.61942i 0.144789 0.128026i
\(161\) 4.77575 0.376382
\(162\) 1.48119i 0.116374i
\(163\) 0.312650i 0.0244887i 0.999925 + 0.0122443i \(0.00389759\pi\)
−0.999925 + 0.0122443i \(0.996102\pi\)
\(164\) −1.76257 −0.137634
\(165\) −1.67513 + 1.48119i −0.130409 + 0.115311i
\(166\) 14.6556 1.13750
\(167\) 0.493413i 0.0381815i 0.999818 + 0.0190907i \(0.00607714\pi\)
−0.999818 + 0.0190907i \(0.993923\pi\)
\(168\) 3.19394i 0.246418i
\(169\) 12.3503 0.950020
\(170\) −8.26774 9.35026i −0.634107 0.717132i
\(171\) −5.35026 −0.409145
\(172\) 0.856849i 0.0653341i
\(173\) 23.3054i 1.77187i 0.463806 + 0.885937i \(0.346483\pi\)
−0.463806 + 0.885937i \(0.653517\pi\)
\(174\) −6.38787 −0.484263
\(175\) −5.92478 0.730841i −0.447871 0.0552464i
\(176\) −4.35026 −0.327913
\(177\) 13.2750i 0.997813i
\(178\) 25.0132i 1.87482i
\(179\) 10.7005 0.799795 0.399897 0.916560i \(-0.369046\pi\)
0.399897 + 0.916560i \(0.369046\pi\)
\(180\) −0.287258 0.324869i −0.0214109 0.0242143i
\(181\) −7.79877 −0.579678 −0.289839 0.957075i \(-0.593602\pi\)
−0.289839 + 0.957075i \(0.593602\pi\)
\(182\) 1.42548i 0.105664i
\(183\) 0.0752228i 0.00556063i
\(184\) −10.7005 −0.788853
\(185\) 2.70052 2.38787i 0.198546 0.175560i
\(186\) −1.42548 −0.104522
\(187\) 3.76845i 0.275577i
\(188\) 2.38787i 0.174154i
\(189\) −1.19394 −0.0868461
\(190\) −13.2750 + 11.7381i −0.963073 + 0.851574i
\(191\) 1.29948 0.0940268 0.0470134 0.998894i \(-0.485030\pi\)
0.0470134 + 0.998894i \(0.485030\pi\)
\(192\) 7.08110i 0.511035i
\(193\) 8.59498i 0.618680i −0.950951 0.309340i \(-0.899892\pi\)
0.950951 0.309340i \(-0.100108\pi\)
\(194\) 16.9986 1.22043
\(195\) 1.19394 + 1.35026i 0.0854996 + 0.0966943i
\(196\) −1.08110 −0.0772216
\(197\) 20.7064i 1.47527i −0.675200 0.737635i \(-0.735943\pi\)
0.675200 0.737635i \(-0.264057\pi\)
\(198\) 1.48119i 0.105264i
\(199\) −5.55149 −0.393535 −0.196767 0.980450i \(-0.563044\pi\)
−0.196767 + 0.980450i \(0.563044\pi\)
\(200\) 13.2750 + 1.63752i 0.938687 + 0.115790i
\(201\) −2.70052 −0.190480
\(202\) 15.9394i 1.12149i
\(203\) 5.14903i 0.361391i
\(204\) −0.730841 −0.0511691
\(205\) −13.4617 15.2243i −0.940205 1.06331i
\(206\) −25.0884 −1.74799
\(207\) 4.00000i 0.278019i
\(208\) 3.50659i 0.243138i
\(209\) 5.35026 0.370085
\(210\) −2.96239 + 2.61942i −0.204424 + 0.180757i
\(211\) −18.4993 −1.27354 −0.636772 0.771052i \(-0.719731\pi\)
−0.636772 + 0.771052i \(0.719731\pi\)
\(212\) 0.276454i 0.0189869i
\(213\) 14.0508i 0.962744i
\(214\) 12.2677 0.838606
\(215\) −7.40105 + 6.54420i −0.504747 + 0.446311i
\(216\) 2.67513 0.182020
\(217\) 1.14903i 0.0780013i
\(218\) 14.8119i 1.00319i
\(219\) 10.7308 0.725123
\(220\) 0.287258 + 0.324869i 0.0193669 + 0.0219027i
\(221\) 3.03761 0.204332
\(222\) 2.38787i 0.160264i
\(223\) 17.6121i 1.17940i −0.807624 0.589698i \(-0.799247\pi\)
0.807624 0.589698i \(-0.200753\pi\)
\(224\) −1.30536 −0.0872178
\(225\) 0.612127 4.96239i 0.0408085 0.330826i
\(226\) −3.35026 −0.222856
\(227\) 17.4314i 1.15696i −0.815696 0.578480i \(-0.803646\pi\)
0.815696 0.578480i \(-0.196354\pi\)
\(228\) 1.03761i 0.0687175i
\(229\) −13.0738 −0.863942 −0.431971 0.901888i \(-0.642182\pi\)
−0.431971 + 0.901888i \(0.642182\pi\)
\(230\) 8.77575 + 9.92478i 0.578656 + 0.654420i
\(231\) 1.19394 0.0785553
\(232\) 11.5369i 0.757435i
\(233\) 13.8437i 0.906929i 0.891274 + 0.453465i \(0.149812\pi\)
−0.891274 + 0.453465i \(0.850188\pi\)
\(234\) 1.19394 0.0780501
\(235\) 20.6253 18.2374i 1.34545 1.18968i
\(236\) 2.57452 0.167587
\(237\) 13.9756i 0.907810i
\(238\) 6.66433i 0.431984i
\(239\) 12.3733 0.800361 0.400181 0.916436i \(-0.368947\pi\)
0.400181 + 0.916436i \(0.368947\pi\)
\(240\) 7.28726 6.44358i 0.470390 0.415931i
\(241\) −24.5501 −1.58141 −0.790705 0.612198i \(-0.790286\pi\)
−0.790705 + 0.612198i \(0.790286\pi\)
\(242\) 1.48119i 0.0952148i
\(243\) 1.00000i 0.0641500i
\(244\) 0.0145884 0.000933930
\(245\) −8.25694 9.33804i −0.527517 0.596586i
\(246\) −13.4617 −0.858285
\(247\) 4.31265i 0.274407i
\(248\) 2.57452i 0.163482i
\(249\) 9.89446 0.627036
\(250\) −9.36836 13.6556i −0.592507 0.863657i
\(251\) 13.9003 0.877382 0.438691 0.898638i \(-0.355442\pi\)
0.438691 + 0.898638i \(0.355442\pi\)
\(252\) 0.231548i 0.0145862i
\(253\) 4.00000i 0.251478i
\(254\) −20.4690 −1.28434
\(255\) −5.58181 6.31265i −0.349546 0.395313i
\(256\) 4.61213 0.288258
\(257\) 18.8872i 1.17815i −0.808079 0.589075i \(-0.799492\pi\)
0.808079 0.589075i \(-0.200508\pi\)
\(258\) 6.54420i 0.407424i
\(259\) −1.92478 −0.119600
\(260\) 0.261865 0.231548i 0.0162402 0.0143600i
\(261\) −4.31265 −0.266946
\(262\) 8.77575i 0.542167i
\(263\) 20.8061i 1.28296i −0.767141 0.641478i \(-0.778321\pi\)
0.767141 0.641478i \(-0.221679\pi\)
\(264\) −2.67513 −0.164643
\(265\) −2.38787 + 2.11142i −0.146686 + 0.129703i
\(266\) 9.46168 0.580133
\(267\) 16.8872i 1.03348i
\(268\) 0.523730i 0.0319919i
\(269\) 32.3996 1.97544 0.987720 0.156233i \(-0.0499351\pi\)
0.987720 + 0.156233i \(0.0499351\pi\)
\(270\) −2.19394 2.48119i −0.133519 0.151001i
\(271\) −16.8265 −1.02214 −0.511069 0.859539i \(-0.670751\pi\)
−0.511069 + 0.859539i \(0.670751\pi\)
\(272\) 16.3938i 0.994017i
\(273\) 0.962389i 0.0582464i
\(274\) 4.96239 0.299789
\(275\) −0.612127 + 4.96239i −0.0369126 + 0.299243i
\(276\) 0.775746 0.0466944
\(277\) 16.9076i 1.01588i 0.861392 + 0.507941i \(0.169593\pi\)
−0.861392 + 0.507941i \(0.830407\pi\)
\(278\) 31.4010i 1.88331i
\(279\) −0.962389 −0.0576167
\(280\) −4.73084 5.35026i −0.282722 0.319739i
\(281\) 5.61213 0.334791 0.167396 0.985890i \(-0.446464\pi\)
0.167396 + 0.985890i \(0.446464\pi\)
\(282\) 18.2374i 1.08602i
\(283\) 5.81924i 0.345918i −0.984929 0.172959i \(-0.944667\pi\)
0.984929 0.172959i \(-0.0553328\pi\)
\(284\) 2.72496 0.161697
\(285\) −8.96239 + 7.92478i −0.530886 + 0.469423i
\(286\) −1.19394 −0.0705989
\(287\) 10.8510i 0.640512i
\(288\) 1.09332i 0.0644246i
\(289\) 2.79877 0.164633
\(290\) −10.7005 + 9.46168i −0.628356 + 0.555609i
\(291\) 11.4763 0.672751
\(292\) 2.08110i 0.121787i
\(293\) 8.29218i 0.484434i 0.970222 + 0.242217i \(0.0778747\pi\)
−0.970222 + 0.242217i \(0.922125\pi\)
\(294\) −8.25694 −0.481555
\(295\) 19.6629 + 22.2374i 1.14482 + 1.29471i
\(296\) 4.31265 0.250668
\(297\) 1.00000i 0.0580259i
\(298\) 9.46168i 0.548100i
\(299\) −3.22425 −0.186463
\(300\) −0.962389 0.118714i −0.0555635 0.00685394i
\(301\) 5.27504 0.304048
\(302\) 3.92478i 0.225846i
\(303\) 10.7612i 0.618212i
\(304\) −23.2750 −1.33492
\(305\) 0.111420 + 0.126008i 0.00637987 + 0.00721520i
\(306\) −5.58181 −0.319091
\(307\) 25.6688i 1.46500i 0.680770 + 0.732498i \(0.261646\pi\)
−0.680770 + 0.732498i \(0.738354\pi\)
\(308\) 0.231548i 0.0131937i
\(309\) −16.9380 −0.963566
\(310\) −2.38787 + 2.11142i −0.135622 + 0.119921i
\(311\) −15.7235 −0.891601 −0.445800 0.895132i \(-0.647081\pi\)
−0.445800 + 0.895132i \(0.647081\pi\)
\(312\) 2.15633i 0.122078i
\(313\) 26.8627i 1.51837i 0.650874 + 0.759186i \(0.274403\pi\)
−0.650874 + 0.759186i \(0.725597\pi\)
\(314\) 2.38787 0.134755
\(315\) −2.00000 + 1.76845i −0.112687 + 0.0996410i
\(316\) 2.71037 0.152470
\(317\) 0.710373i 0.0398985i 0.999801 + 0.0199492i \(0.00635046\pi\)
−0.999801 + 0.0199492i \(0.993650\pi\)
\(318\) 2.11142i 0.118403i
\(319\) 4.31265 0.241462
\(320\) 10.4885 + 11.8618i 0.586324 + 0.663093i
\(321\) 8.28233 0.462275
\(322\) 7.07381i 0.394208i
\(323\) 20.1622i 1.12186i
\(324\) −0.193937 −0.0107743
\(325\) 4.00000 + 0.493413i 0.221880 + 0.0273696i
\(326\) 0.463096 0.0256485
\(327\) 10.0000i 0.553001i
\(328\) 24.3127i 1.34244i
\(329\) −14.7005 −0.810466
\(330\) 2.19394 + 2.48119i 0.120772 + 0.136585i
\(331\) 0.962389 0.0528977 0.0264488 0.999650i \(-0.491580\pi\)
0.0264488 + 0.999650i \(0.491580\pi\)
\(332\) 1.91890i 0.105313i
\(333\) 1.61213i 0.0883440i
\(334\) 0.730841 0.0399898
\(335\) −4.52373 + 4.00000i −0.247158 + 0.218543i
\(336\) −5.19394 −0.283352
\(337\) 19.8192i 1.07962i 0.841786 + 0.539811i \(0.181504\pi\)
−0.841786 + 0.539811i \(0.818496\pi\)
\(338\) 18.2931i 0.995015i
\(339\) −2.26187 −0.122848
\(340\) −1.22425 + 1.08252i −0.0663945 + 0.0587077i
\(341\) 0.962389 0.0521163
\(342\) 7.92478i 0.428523i
\(343\) 15.0132i 0.810635i
\(344\) −11.8192 −0.637251
\(345\) 5.92478 + 6.70052i 0.318979 + 0.360744i
\(346\) 34.5198 1.85579
\(347\) 6.20711i 0.333215i 0.986023 + 0.166608i \(0.0532813\pi\)
−0.986023 + 0.166608i \(0.946719\pi\)
\(348\) 0.836381i 0.0448347i
\(349\) −4.44851 −0.238123 −0.119062 0.992887i \(-0.537989\pi\)
−0.119062 + 0.992887i \(0.537989\pi\)
\(350\) −1.08252 + 8.77575i −0.0578630 + 0.469083i
\(351\) 0.806063 0.0430245
\(352\) 1.09332i 0.0582742i
\(353\) 6.57452i 0.349926i −0.984575 0.174963i \(-0.944019\pi\)
0.984575 0.174963i \(-0.0559806\pi\)
\(354\) 19.6629 1.04507
\(355\) 20.8119 + 23.5369i 1.10458 + 1.24921i
\(356\) 3.27504 0.173577
\(357\) 4.49929i 0.238128i
\(358\) 15.8496i 0.837675i
\(359\) −8.62530 −0.455226 −0.227613 0.973752i \(-0.573092\pi\)
−0.227613 + 0.973752i \(0.573092\pi\)
\(360\) 4.48119 3.96239i 0.236180 0.208836i
\(361\) 9.62530 0.506595
\(362\) 11.5515i 0.607133i
\(363\) 1.00000i 0.0524864i
\(364\) −0.186642 −0.00978272
\(365\) 17.9756 15.8945i 0.940884 0.831954i
\(366\) 0.111420 0.00582399
\(367\) 23.0132i 1.20128i 0.799520 + 0.600639i \(0.205087\pi\)
−0.799520 + 0.600639i \(0.794913\pi\)
\(368\) 17.4010i 0.907092i
\(369\) −9.08840 −0.473123
\(370\) −3.53690 4.00000i −0.183875 0.207950i
\(371\) 1.70194 0.0883602
\(372\) 0.186642i 0.00967695i
\(373\) 28.1925i 1.45975i −0.683579 0.729877i \(-0.739577\pi\)
0.683579 0.729877i \(-0.260423\pi\)
\(374\) 5.58181 0.288629
\(375\) −6.32487 9.21933i −0.326615 0.476084i
\(376\) 32.9380 1.69865
\(377\) 3.47627i 0.179037i
\(378\) 1.76845i 0.0909594i
\(379\) −3.74798 −0.192521 −0.0962605 0.995356i \(-0.530688\pi\)
−0.0962605 + 0.995356i \(0.530688\pi\)
\(380\) 1.53690 + 1.73813i 0.0788415 + 0.0891644i
\(381\) −13.8192 −0.707981
\(382\) 1.92478i 0.0984802i
\(383\) 1.76257i 0.0900632i −0.998986 0.0450316i \(-0.985661\pi\)
0.998986 0.0450316i \(-0.0143389\pi\)
\(384\) 12.6751 0.646825
\(385\) 2.00000 1.76845i 0.101929 0.0901287i
\(386\) −12.7308 −0.647983
\(387\) 4.41819i 0.224589i
\(388\) 2.22567i 0.112991i
\(389\) −6.52373 −0.330766 −0.165383 0.986229i \(-0.552886\pi\)
−0.165383 + 0.986229i \(0.552886\pi\)
\(390\) 2.00000 1.76845i 0.101274 0.0895491i
\(391\) 15.0738 0.762315
\(392\) 14.9126i 0.753198i
\(393\) 5.92478i 0.298865i
\(394\) −30.6702 −1.54514
\(395\) 20.7005 + 23.4109i 1.04156 + 1.17793i
\(396\) 0.193937 0.00974568
\(397\) 23.6991i 1.18942i −0.803939 0.594712i \(-0.797266\pi\)
0.803939 0.594712i \(-0.202734\pi\)
\(398\) 8.22284i 0.412174i
\(399\) 6.38787 0.319794
\(400\) 2.66291 21.5877i 0.133146 1.07938i
\(401\) 8.88717 0.443804 0.221902 0.975069i \(-0.428774\pi\)
0.221902 + 0.975069i \(0.428774\pi\)
\(402\) 4.00000i 0.199502i
\(403\) 0.775746i 0.0386427i
\(404\) −2.08698 −0.103831
\(405\) −1.48119 1.67513i −0.0736011 0.0832379i
\(406\) 7.62672 0.378508
\(407\) 1.61213i 0.0799102i
\(408\) 10.0811i 0.499089i
\(409\) 4.85097 0.239865 0.119932 0.992782i \(-0.461732\pi\)
0.119932 + 0.992782i \(0.461732\pi\)
\(410\) −22.5501 + 19.9394i −1.11367 + 0.984735i
\(411\) 3.35026 0.165256
\(412\) 3.28489i 0.161835i
\(413\) 15.8496i 0.779906i
\(414\) 5.92478 0.291187
\(415\) 16.5745 14.6556i 0.813611 0.719416i
\(416\) 0.881286 0.0432086
\(417\) 21.1998i 1.03816i
\(418\) 7.92478i 0.387614i
\(419\) 10.7005 0.522755 0.261377 0.965237i \(-0.415823\pi\)
0.261377 + 0.965237i \(0.415823\pi\)
\(420\) 0.342968 + 0.387873i 0.0167351 + 0.0189263i
\(421\) −30.6009 −1.49139 −0.745697 0.666285i \(-0.767884\pi\)
−0.745697 + 0.666285i \(0.767884\pi\)
\(422\) 27.4010i 1.33386i
\(423\) 12.3127i 0.598662i
\(424\) −3.81336 −0.185193
\(425\) −18.7005 2.30677i −0.907109 0.111895i
\(426\) 20.8119 1.00834
\(427\) 0.0898112i 0.00434627i
\(428\) 1.60625i 0.0776409i
\(429\) −0.806063 −0.0389171
\(430\) 9.69323 + 10.9624i 0.467449 + 0.528653i
\(431\) −5.92478 −0.285386 −0.142693 0.989767i \(-0.545576\pi\)
−0.142693 + 0.989767i \(0.545576\pi\)
\(432\) 4.35026i 0.209302i
\(433\) 16.0000i 0.768911i 0.923144 + 0.384455i \(0.125611\pi\)
−0.923144 + 0.384455i \(0.874389\pi\)
\(434\) 1.70194 0.0816956
\(435\) −7.22425 + 6.38787i −0.346376 + 0.306275i
\(436\) −1.93937 −0.0928788
\(437\) 21.4010i 1.02375i
\(438\) 15.8945i 0.759467i
\(439\) −5.35026 −0.255354 −0.127677 0.991816i \(-0.540752\pi\)
−0.127677 + 0.991816i \(0.540752\pi\)
\(440\) −4.48119 + 3.96239i −0.213633 + 0.188899i
\(441\) −5.57452 −0.265453
\(442\) 4.49929i 0.214010i
\(443\) 19.6873i 0.935374i −0.883894 0.467687i \(-0.845087\pi\)
0.883894 0.467687i \(-0.154913\pi\)
\(444\) −0.312650 −0.0148377
\(445\) 25.0132 + 28.2882i 1.18574 + 1.34099i
\(446\) −26.0870 −1.23525
\(447\) 6.38787i 0.302136i
\(448\) 8.45439i 0.399432i
\(449\) 31.3357 1.47882 0.739411 0.673254i \(-0.235104\pi\)
0.739411 + 0.673254i \(0.235104\pi\)
\(450\) −7.35026 0.906679i −0.346495 0.0427412i
\(451\) 9.08840 0.427956
\(452\) 0.438658i 0.0206328i
\(453\) 2.64974i 0.124496i
\(454\) −25.8192 −1.21176
\(455\) −1.42548 1.61213i −0.0668277 0.0755777i
\(456\) −14.3127 −0.670251
\(457\) 37.5936i 1.75855i −0.476312 0.879276i \(-0.658027\pi\)
0.476312 0.879276i \(-0.341973\pi\)
\(458\) 19.3649i 0.904860i
\(459\) −3.76845 −0.175896
\(460\) 1.29948 1.14903i 0.0605884 0.0535738i
\(461\) 17.9854 0.837664 0.418832 0.908064i \(-0.362440\pi\)
0.418832 + 0.908064i \(0.362440\pi\)
\(462\) 1.76845i 0.0822758i
\(463\) 39.0132i 1.81310i −0.422103 0.906548i \(-0.638708\pi\)
0.422103 0.906548i \(-0.361292\pi\)
\(464\) −18.7612 −0.870965
\(465\) −1.61213 + 1.42548i −0.0747606 + 0.0661053i
\(466\) 20.5052 0.949884
\(467\) 14.5501i 0.673297i 0.941630 + 0.336649i \(0.109293\pi\)
−0.941630 + 0.336649i \(0.890707\pi\)
\(468\) 0.156325i 0.00722613i
\(469\) 3.22425 0.148882
\(470\) −27.0132 30.5501i −1.24602 1.40917i
\(471\) 1.61213 0.0742829
\(472\) 35.5125i 1.63459i
\(473\) 4.41819i 0.203149i
\(474\) 20.7005 0.950807
\(475\) −3.27504 + 26.5501i −0.150269 + 1.21820i
\(476\) 0.872577 0.0399945
\(477\) 1.42548i 0.0652685i
\(478\) 18.3272i 0.838268i
\(479\) −28.6253 −1.30792 −0.653962 0.756528i \(-0.726894\pi\)
−0.653962 + 0.756528i \(0.726894\pi\)
\(480\) −1.61942 1.83146i −0.0739161 0.0835941i
\(481\) 1.29948 0.0592510
\(482\) 36.3634i 1.65631i
\(483\) 4.77575i 0.217304i
\(484\) −0.193937 −0.00881530
\(485\) 19.2243 16.9986i 0.872928 0.771866i
\(486\) −1.48119 −0.0671883
\(487\) 1.44992i 0.0657022i 0.999460 + 0.0328511i \(0.0104587\pi\)
−0.999460 + 0.0328511i \(0.989541\pi\)
\(488\) 0.201231i 0.00910929i
\(489\) 0.312650 0.0141385
\(490\) −13.8315 + 12.2301i −0.624841 + 0.552501i
\(491\) −8.00000 −0.361035 −0.180517 0.983572i \(-0.557777\pi\)
−0.180517 + 0.983572i \(0.557777\pi\)
\(492\) 1.76257i 0.0794629i
\(493\) 16.2520i 0.731954i
\(494\) −6.38787 −0.287404
\(495\) 1.48119 + 1.67513i 0.0665747 + 0.0752915i
\(496\) −4.18664 −0.187986
\(497\) 16.7757i 0.752495i
\(498\) 14.6556i 0.656734i
\(499\) −30.7005 −1.37434 −0.687172 0.726495i \(-0.741148\pi\)
−0.687172 + 0.726495i \(0.741148\pi\)
\(500\) −1.78797 + 1.22662i −0.0799602 + 0.0548563i
\(501\) 0.493413 0.0220441
\(502\) 20.5891i 0.918937i
\(503\) 19.7586i 0.880993i 0.897754 + 0.440496i \(0.145198\pi\)
−0.897754 + 0.440496i \(0.854802\pi\)
\(504\) −3.19394 −0.142269
\(505\) −15.9394 18.0263i −0.709292 0.802162i
\(506\) −5.92478 −0.263388
\(507\) 12.3503i 0.548494i
\(508\) 2.68006i 0.118908i
\(509\) −22.1016 −0.979635 −0.489817 0.871825i \(-0.662937\pi\)
−0.489817 + 0.871825i \(0.662937\pi\)
\(510\) −9.35026 + 8.26774i −0.414037 + 0.366102i
\(511\) −12.8119 −0.566767
\(512\) 18.5188i 0.818423i
\(513\) 5.35026i 0.236220i
\(514\) −27.9756 −1.23395
\(515\) −28.3733 + 25.0884i −1.25028 + 1.10553i
\(516\) 0.856849 0.0377207
\(517\) 12.3127i 0.541510i
\(518\) 2.85097i 0.125264i
\(519\) 23.3054 1.02299
\(520\) 3.19394 + 3.61213i 0.140063 + 0.158402i
\(521\) −22.8119 −0.999409 −0.499705 0.866196i \(-0.666558\pi\)
−0.499705 + 0.866196i \(0.666558\pi\)
\(522\) 6.38787i 0.279590i
\(523\) 12.2677i 0.536431i 0.963359 + 0.268216i \(0.0864339\pi\)
−0.963359 + 0.268216i \(0.913566\pi\)
\(524\) 1.14903 0.0501957
\(525\) −0.730841 + 5.92478i −0.0318965 + 0.258578i
\(526\) −30.8178 −1.34372
\(527\) 3.62672i 0.157982i
\(528\) 4.35026i 0.189321i
\(529\) 7.00000 0.304348
\(530\) 3.12742 + 3.53690i 0.135847 + 0.153633i
\(531\) 13.2750 0.576088
\(532\) 1.23884i 0.0537106i
\(533\) 7.32582i 0.317317i
\(534\) 25.0132 1.08243
\(535\) 13.8740 12.2677i 0.599825 0.530381i
\(536\) −7.22425 −0.312040
\(537\) 10.7005i 0.461762i
\(538\) 47.9902i 2.06900i
\(539\) 5.57452 0.240111
\(540\) −0.324869 + 0.287258i −0.0139801 + 0.0123616i
\(541\) −5.22425 −0.224608 −0.112304 0.993674i \(-0.535823\pi\)
−0.112304 + 0.993674i \(0.535823\pi\)
\(542\) 24.9234i 1.07055i
\(543\) 7.79877i 0.334677i
\(544\) −4.12013 −0.176649
\(545\) −14.8119 16.7513i −0.634474 0.717547i
\(546\) −1.42548 −0.0610051
\(547\) 17.9697i 0.768328i −0.923265 0.384164i \(-0.874490\pi\)
0.923265 0.384164i \(-0.125510\pi\)
\(548\) 0.649738i 0.0277554i
\(549\) 0.0752228 0.00321043
\(550\) 7.35026 + 0.906679i 0.313416 + 0.0386609i
\(551\) 23.0738 0.982977
\(552\) 10.7005i 0.455445i
\(553\) 16.6859i 0.709558i
\(554\) 25.0435 1.06400
\(555\) −2.38787 2.70052i −0.101360 0.114631i
\(556\) −4.11142 −0.174363
\(557\) 15.8700i 0.672434i 0.941784 + 0.336217i \(0.109148\pi\)
−0.941784 + 0.336217i \(0.890852\pi\)
\(558\) 1.42548i 0.0603456i
\(559\) −3.56134 −0.150629
\(560\) −8.70052 + 7.69323i −0.367664 + 0.325098i
\(561\) 3.76845 0.159104
\(562\) 8.31265i 0.350648i
\(563\) 31.6688i 1.33468i −0.744753 0.667340i \(-0.767433\pi\)
0.744753 0.667340i \(-0.232567\pi\)
\(564\) −2.38787 −0.100548
\(565\) −3.78892 + 3.35026i −0.159401 + 0.140947i
\(566\) −8.61942 −0.362301
\(567\) 1.19394i 0.0501406i
\(568\) 37.5877i 1.57714i
\(569\) 24.3127 1.01924 0.509620 0.860400i \(-0.329786\pi\)
0.509620 + 0.860400i \(0.329786\pi\)
\(570\) 11.7381 + 13.2750i 0.491656 + 0.556030i
\(571\) 8.05079 0.336915 0.168457 0.985709i \(-0.446121\pi\)
0.168457 + 0.985709i \(0.446121\pi\)
\(572\) 0.156325i 0.00653628i
\(573\) 1.29948i 0.0542864i
\(574\) 16.0724 0.670849
\(575\) 19.8496 + 2.44851i 0.827784 + 0.102110i
\(576\) 7.08110 0.295046
\(577\) 44.5355i 1.85404i −0.375016 0.927018i \(-0.622363\pi\)
0.375016 0.927018i \(-0.377637\pi\)
\(578\) 4.14552i 0.172431i
\(579\) −8.59498 −0.357195
\(580\) 1.23884 + 1.40105i 0.0514401 + 0.0581753i
\(581\) −11.8134 −0.490101
\(582\) 16.9986i 0.704614i
\(583\) 1.42548i 0.0590375i
\(584\) 28.7064 1.18788
\(585\) 1.35026 1.19394i 0.0558265 0.0493632i
\(586\) 12.2823 0.507379
\(587\) 15.4763i 0.638774i −0.947624 0.319387i \(-0.896523\pi\)
0.947624 0.319387i \(-0.103477\pi\)
\(588\) 1.08110i 0.0445839i
\(589\) 5.14903 0.212162
\(590\) 32.9380 29.1246i 1.35603 1.19904i
\(591\) −20.7064 −0.851748
\(592\) 7.01317i 0.288240i
\(593\) 9.53102i 0.391392i 0.980665 + 0.195696i \(0.0626966\pi\)
−0.980665 + 0.195696i \(0.937303\pi\)
\(594\) 1.48119 0.0607741
\(595\) 6.66433 + 7.53690i 0.273211 + 0.308983i
\(596\) 1.23884 0.0507450
\(597\) 5.55149i 0.227207i
\(598\) 4.77575i 0.195295i
\(599\) 25.5515 1.04401 0.522003 0.852944i \(-0.325185\pi\)
0.522003 + 0.852944i \(0.325185\pi\)
\(600\) 1.63752 13.2750i 0.0668515 0.541951i
\(601\) 12.0263 0.490565 0.245282 0.969452i \(-0.421119\pi\)
0.245282 + 0.969452i \(0.421119\pi\)
\(602\) 7.81336i 0.318449i
\(603\) 2.70052i 0.109974i
\(604\) 0.513881 0.0209095
\(605\) −1.48119 1.67513i −0.0602191 0.0681038i
\(606\) −15.9394 −0.647492
\(607\) 6.86670i 0.278711i −0.990242 0.139355i \(-0.955497\pi\)
0.990242 0.139355i \(-0.0445030\pi\)
\(608\) 5.84955i 0.237231i
\(609\) 5.14903 0.208649
\(610\) 0.186642 0.165034i 0.00755693 0.00668203i
\(611\) 9.92478 0.401514
\(612\) 0.730841i 0.0295425i
\(613\) 7.25457i 0.293009i 0.989210 + 0.146505i \(0.0468023\pi\)
−0.989210 + 0.146505i \(0.953198\pi\)
\(614\) 38.0205 1.53438
\(615\) −15.2243 + 13.4617i −0.613901 + 0.542827i
\(616\) 3.19394 0.128687
\(617\) 38.3634i 1.54445i 0.635347 + 0.772227i \(0.280857\pi\)
−0.635347 + 0.772227i \(0.719143\pi\)
\(618\) 25.0884i 1.00920i
\(619\) 29.6893 1.19331 0.596656 0.802497i \(-0.296496\pi\)
0.596656 + 0.802497i \(0.296496\pi\)
\(620\) 0.276454 + 0.312650i 0.0111026 + 0.0125563i
\(621\) 4.00000 0.160514
\(622\) 23.2896i 0.933829i
\(623\) 20.1622i 0.807782i
\(624\) 3.50659 0.140376
\(625\) −24.2506 6.07522i −0.970024 0.243009i
\(626\) 39.7889 1.59029
\(627\) 5.35026i 0.213669i
\(628\) 0.312650i 0.0124761i
\(629\) −6.07522 −0.242235
\(630\) 2.61942 + 2.96239i 0.104360 + 0.118024i
\(631\) −19.6991 −0.784209 −0.392105 0.919921i \(-0.628253\pi\)
−0.392105 + 0.919921i \(0.628253\pi\)
\(632\) 37.3865i 1.48715i
\(633\) 18.4993i 0.735281i
\(634\) 1.05220 0.0417882
\(635\) −23.1490 + 20.4690i −0.918641 + 0.812287i
\(636\) 0.276454 0.0109621
\(637\) 4.49341i 0.178036i
\(638\) 6.38787i 0.252898i
\(639\) 14.0508 0.555840
\(640\) 21.2325 18.7743i 0.839288 0.742121i
\(641\) −31.4372 −1.24170 −0.620848 0.783931i \(-0.713212\pi\)
−0.620848 + 0.783931i \(0.713212\pi\)
\(642\) 12.2677i 0.484169i
\(643\) 34.4894i 1.36013i 0.733151 + 0.680065i \(0.238049\pi\)
−0.733151 + 0.680065i \(0.761951\pi\)
\(644\) −0.926192 −0.0364971
\(645\) 6.54420 + 7.40105i 0.257678 + 0.291416i
\(646\) 29.8641 1.17499
\(647\) 5.61213i 0.220635i −0.993896 0.110318i \(-0.964813\pi\)
0.993896 0.110318i \(-0.0351868\pi\)
\(648\) 2.67513i 0.105089i
\(649\) −13.2750 −0.521091
\(650\) 0.730841 5.92478i 0.0286659 0.232389i
\(651\) 1.14903 0.0450341
\(652\) 0.0606343i 0.00237462i
\(653\) 4.06537i 0.159090i −0.996831 0.0795452i \(-0.974653\pi\)
0.996831 0.0795452i \(-0.0253468\pi\)
\(654\) −14.8119 −0.579193
\(655\) 8.77575 + 9.92478i 0.342897 + 0.387793i
\(656\) −39.5369 −1.54366
\(657\) 10.7308i 0.418650i
\(658\) 21.7743i 0.848852i
\(659\) −11.3747 −0.443095 −0.221548 0.975150i \(-0.571111\pi\)
−0.221548 + 0.975150i \(0.571111\pi\)
\(660\) 0.324869 0.287258i 0.0126455 0.0111815i
\(661\) −42.4749 −1.65208 −0.826040 0.563611i \(-0.809412\pi\)
−0.826040 + 0.563611i \(0.809412\pi\)
\(662\) 1.42548i 0.0554030i
\(663\) 3.03761i 0.117971i
\(664\) 26.4690 1.02720
\(665\) 10.7005 9.46168i 0.414949 0.366908i
\(666\) −2.38787 −0.0925282
\(667\) 17.2506i 0.667946i
\(668\) 0.0956908i 0.00370239i
\(669\) −17.6121 −0.680924
\(670\) 5.92478 + 6.70052i 0.228894 + 0.258864i
\(671\) −0.0752228 −0.00290394
\(672\) 1.30536i 0.0503552i
\(673\) 14.8813i 0.573631i 0.957986 + 0.286816i \(0.0925967\pi\)
−0.957986 + 0.286816i \(0.907403\pi\)
\(674\) 29.3561 1.13076
\(675\) −4.96239 0.612127i −0.191002 0.0235608i
\(676\) −2.39517 −0.0921218
\(677\) 27.7685i 1.06723i −0.845728 0.533614i \(-0.820833\pi\)
0.845728 0.533614i \(-0.179167\pi\)
\(678\) 3.35026i 0.128666i
\(679\) −13.7019 −0.525832
\(680\) −14.9321 16.8872i −0.572619 0.647593i
\(681\) −17.4314 −0.667971
\(682\) 1.42548i 0.0545846i
\(683\) 25.4617i 0.974264i 0.873328 + 0.487132i \(0.161957\pi\)
−0.873328 + 0.487132i \(0.838043\pi\)
\(684\) 1.03761 0.0396741
\(685\) 5.61213 4.96239i 0.214428 0.189603i
\(686\) 22.2374 0.849029
\(687\) 13.0738i 0.498797i
\(688\) 19.2203i 0.732766i
\(689\) −1.14903 −0.0437746
\(690\) 9.92478 8.77575i 0.377830 0.334087i
\(691\) 43.6991 1.66239 0.831196 0.555979i \(-0.187657\pi\)
0.831196 + 0.555979i \(0.187657\pi\)
\(692\) 4.51976i 0.171816i
\(693\) 1.19394i 0.0453539i
\(694\) 9.19394 0.348997
\(695\) −31.4010 35.5125i −1.19111 1.34706i
\(696\) −11.5369 −0.437305
\(697\) 34.2492i 1.29728i
\(698\) 6.58910i 0.249401i
\(699\) 13.8437 0.523616
\(700\) 1.14903 + 0.141737i 0.0434293 + 0.00535714i
\(701\) 7.01317 0.264884 0.132442 0.991191i \(-0.457718\pi\)
0.132442 + 0.991191i \(0.457718\pi\)
\(702\) 1.19394i 0.0450622i
\(703\) 8.62530i 0.325309i
\(704\) −7.08110 −0.266879
\(705\) −18.2374 20.6253i −0.686861 0.776794i
\(706\) −9.73813 −0.366500
\(707\) 12.8481i 0.483204i
\(708\) 2.57452i 0.0967562i
\(709\) −45.6747 −1.71535 −0.857674 0.514194i \(-0.828091\pi\)
−0.857674 + 0.514194i \(0.828091\pi\)
\(710\) 34.8627 30.8265i 1.30837 1.15690i
\(711\) 13.9756 0.524125
\(712\) 45.1754i 1.69302i
\(713\) 3.84955i 0.144167i
\(714\) 6.66433 0.249406
\(715\) −1.35026 + 1.19394i −0.0504969 + 0.0446507i
\(716\) −2.07522 −0.0775547
\(717\) 12.3733i 0.462089i
\(718\) 12.7757i 0.476787i
\(719\) −16.2520 −0.606098 −0.303049 0.952975i \(-0.598005\pi\)
−0.303049 + 0.952975i \(0.598005\pi\)
\(720\) −6.44358 7.28726i −0.240138 0.271580i
\(721\) 20.2228 0.753138
\(722\) 14.2569i 0.530588i
\(723\) 24.5501i 0.913027i
\(724\) 1.51247 0.0562104
\(725\) −2.63989 + 21.4010i −0.0980430 + 0.794815i
\(726\) −1.48119 −0.0549723
\(727\) 15.2243i 0.564636i 0.959321 + 0.282318i \(0.0911034\pi\)
−0.959321 + 0.282318i \(0.908897\pi\)
\(728\) 2.57452i 0.0954179i
\(729\) −1.00000 −0.0370370
\(730\) −23.5428 26.6253i −0.871358 0.985447i
\(731\) 16.6497 0.615813
\(732\) 0.0145884i 0.000539205i
\(733\) 43.5066i 1.60695i 0.595337 + 0.803476i \(0.297019\pi\)
−0.595337 + 0.803476i \(0.702981\pi\)
\(734\) 34.0870 1.25817
\(735\) −9.33804 + 8.25694i −0.344439 + 0.304562i
\(736\) 4.37328 0.161201
\(737\) 2.70052i 0.0994751i
\(738\) 13.4617i 0.495531i
\(739\) 7.02302 0.258346 0.129173 0.991622i \(-0.458768\pi\)
0.129173 + 0.991622i \(0.458768\pi\)
\(740\) −0.523730 + 0.463096i −0.0192527 + 0.0170237i
\(741\) −4.31265 −0.158429
\(742\) 2.52090i 0.0925452i
\(743\) 2.94192i 0.107929i 0.998543 + 0.0539643i \(0.0171857\pi\)
−0.998543 + 0.0539643i \(0.982814\pi\)
\(744\) −2.57452 −0.0943863
\(745\) 9.46168 + 10.7005i 0.346649 + 0.392037i
\(746\) −41.7586 −1.52889
\(747\) 9.89446i 0.362019i
\(748\) 0.730841i 0.0267222i
\(749\) −9.88858 −0.361321
\(750\) −13.6556 + 9.36836i −0.498633 + 0.342084i
\(751\) 24.1016 0.879479 0.439739 0.898125i \(-0.355071\pi\)
0.439739 + 0.898125i \(0.355071\pi\)
\(752\) 53.5633i 1.95325i
\(753\) 13.9003i 0.506557i
\(754\) −5.14903 −0.187517
\(755\) 3.92478 + 4.43866i 0.142837 + 0.161539i
\(756\) 0.231548 0.00842132
\(757\) 16.3127i 0.592893i −0.955049 0.296447i \(-0.904198\pi\)
0.955049 0.296447i \(-0.0958017\pi\)
\(758\) 5.55149i 0.201639i
\(759\) −4.00000 −0.145191
\(760\) −23.9756 + 21.1998i −0.869685 + 0.768998i
\(761\) −5.08840 −0.184454 −0.0922271 0.995738i \(-0.529399\pi\)
−0.0922271 + 0.995738i \(0.529399\pi\)
\(762\) 20.4690i 0.741513i
\(763\) 11.9394i 0.432234i
\(764\) −0.252016 −0.00911762
\(765\) −6.31265 + 5.58181i −0.228234 + 0.201811i
\(766\) −2.61071 −0.0943289
\(767\) 10.7005i 0.386374i
\(768\) 4.61213i 0.166426i
\(769\) −2.10157 −0.0757846 −0.0378923 0.999282i \(-0.512064\pi\)
−0.0378923 + 0.999282i \(0.512064\pi\)
\(770\) −2.61942 2.96239i −0.0943974 0.106757i
\(771\) −18.8872 −0.680205
\(772\) 1.66688i 0.0599924i
\(773\) 46.0625i 1.65675i −0.560171 0.828377i \(-0.689264\pi\)
0.560171 0.828377i \(-0.310736\pi\)
\(774\) 6.54420 0.235226
\(775\) −0.589104 + 4.77575i −0.0211612 + 0.171550i
\(776\) 30.7005 1.10208
\(777\) 1.92478i 0.0690510i
\(778\) 9.66291i 0.346432i
\(779\) 48.6253 1.74218
\(780\) −0.231548 0.261865i −0.00829075 0.00937628i
\(781\) −14.0508 −0.502777
\(782\)