Properties

Label 637.2.u.e.361.2
Level $637$
Weight $2$
Character 637.361
Analytic conductor $5.086$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-7})\)
Defining polynomial: \( x^{4} - x^{3} - x^{2} - 2x + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 361.2
Root \(1.39564 - 0.228425i\) of defining polynomial
Character \(\chi\) \(=\) 637.361
Dual form 637.2.u.e.30.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.395644 + 0.228425i) q^{2} +2.79129 q^{3} +(-0.895644 - 1.55130i) q^{4} +(-0.395644 + 0.228425i) q^{5} +(1.10436 + 0.637600i) q^{6} -1.73205i q^{8} +4.79129 q^{9} +O(q^{10})\) \(q+(0.395644 + 0.228425i) q^{2} +2.79129 q^{3} +(-0.895644 - 1.55130i) q^{4} +(-0.395644 + 0.228425i) q^{5} +(1.10436 + 0.637600i) q^{6} -1.73205i q^{8} +4.79129 q^{9} -0.208712 q^{10} -3.92095i q^{11} +(-2.50000 - 4.33013i) q^{12} +(3.50000 + 0.866025i) q^{13} +(-1.10436 + 0.637600i) q^{15} +(-1.39564 + 2.41733i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(1.89564 + 1.09445i) q^{18} -1.37055i q^{19} +(0.708712 + 0.409175i) q^{20} +(0.895644 - 1.55130i) q^{22} +(0.791288 - 1.37055i) q^{23} -4.83465i q^{24} +(-2.39564 + 4.14938i) q^{25} +(1.18693 + 1.14213i) q^{26} +5.00000 q^{27} +(3.39564 + 5.88143i) q^{29} -0.582576 q^{30} +(7.50000 + 4.33013i) q^{31} +(-4.10436 + 2.36965i) q^{32} -10.9445i q^{33} -1.37055i q^{34} +(-4.29129 - 7.43273i) q^{36} +(-6.00000 - 3.46410i) q^{37} +(0.313068 - 0.542250i) q^{38} +(9.76951 + 2.41733i) q^{39} +(0.395644 + 0.685275i) q^{40} +(6.79129 - 3.92095i) q^{41} +(-4.68693 + 8.11800i) q^{43} +(-6.08258 + 3.51178i) q^{44} +(-1.89564 + 1.09445i) q^{45} +(0.626136 - 0.361500i) q^{46} +(8.29129 - 4.78698i) q^{47} +(-3.89564 + 6.74745i) q^{48} +(-1.89564 + 1.09445i) q^{50} +(-4.18693 - 7.25198i) q^{51} +(-1.79129 - 6.20520i) q^{52} +(-3.08258 + 5.33918i) q^{53} +(1.97822 + 1.14213i) q^{54} +(0.895644 + 1.55130i) q^{55} -3.82560i q^{57} +3.10260i q^{58} +(-10.6652 + 6.15753i) q^{59} +(1.97822 + 1.14213i) q^{60} -14.7477 q^{61} +(1.97822 + 3.42638i) q^{62} +3.41742 q^{64} +(-1.58258 + 0.456850i) q^{65} +(2.50000 - 4.33013i) q^{66} -4.47315i q^{67} +(-2.68693 + 4.65390i) q^{68} +(2.20871 - 3.82560i) q^{69} +(3.79129 + 2.18890i) q^{71} -8.29875i q^{72} +(-3.00000 - 1.73205i) q^{73} +(-1.58258 - 2.74110i) q^{74} +(-6.68693 + 11.5821i) q^{75} +(-2.12614 + 1.22753i) q^{76} +(3.31307 + 3.18800i) q^{78} +(3.00000 + 5.19615i) q^{79} -1.27520i q^{80} -0.417424 q^{81} +3.58258 q^{82} +7.02355i q^{83} +(1.18693 + 0.685275i) q^{85} +(-3.70871 + 2.14123i) q^{86} +(9.47822 + 16.4168i) q^{87} -6.79129 q^{88} +(13.9782 + 8.07033i) q^{89} -1.00000 q^{90} -2.83485 q^{92} +(20.9347 + 12.0866i) q^{93} +4.37386 q^{94} +(0.313068 + 0.542250i) q^{95} +(-11.4564 + 6.61438i) q^{96} +(-6.31307 - 3.64485i) q^{97} -18.7864i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + 9 q^{6} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 3 q^{2} + 2 q^{3} + q^{4} + 3 q^{5} + 9 q^{6} + 10 q^{9} - 10 q^{10} - 10 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} + 3 q^{18} + 12 q^{20} - q^{22} - 6 q^{23} - 5 q^{25} - 9 q^{26} + 20 q^{27} + 9 q^{29} + 16 q^{30} + 30 q^{31} - 21 q^{32} - 8 q^{36} - 24 q^{37} + 15 q^{38} + 7 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} - 6 q^{44} - 3 q^{45} + 30 q^{46} + 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} + 2 q^{52} + 6 q^{53} - 15 q^{54} - q^{55} - 6 q^{59} - 15 q^{60} - 4 q^{61} - 15 q^{62} + 32 q^{64} + 12 q^{65} + 10 q^{66} + 3 q^{68} + 18 q^{69} + 6 q^{71} - 12 q^{73} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} - 20 q^{81} - 4 q^{82} - 9 q^{85} - 24 q^{86} + 15 q^{87} - 18 q^{88} + 33 q^{89} - 4 q^{90} - 48 q^{92} + 15 q^{93} - 10 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.395644 + 0.228425i 0.279763 + 0.161521i 0.633316 0.773893i \(-0.281693\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 2.79129 1.61155 0.805775 0.592221i \(-0.201749\pi\)
0.805775 + 0.592221i \(0.201749\pi\)
\(4\) −0.895644 1.55130i −0.447822 0.775650i
\(5\) −0.395644 + 0.228425i −0.176937 + 0.102155i −0.585853 0.810417i \(-0.699240\pi\)
0.408916 + 0.912572i \(0.365907\pi\)
\(6\) 1.10436 + 0.637600i 0.450851 + 0.260299i
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) 4.79129 1.59710
\(10\) −0.208712 −0.0660006
\(11\) 3.92095i 1.18221i −0.806594 0.591106i \(-0.798692\pi\)
0.806594 0.591106i \(-0.201308\pi\)
\(12\) −2.50000 4.33013i −0.721688 1.25000i
\(13\) 3.50000 + 0.866025i 0.970725 + 0.240192i
\(14\) 0 0
\(15\) −1.10436 + 0.637600i −0.285144 + 0.164628i
\(16\) −1.39564 + 2.41733i −0.348911 + 0.604332i
\(17\) −1.50000 2.59808i −0.363803 0.630126i 0.624780 0.780801i \(-0.285189\pi\)
−0.988583 + 0.150675i \(0.951855\pi\)
\(18\) 1.89564 + 1.09445i 0.446808 + 0.257964i
\(19\) 1.37055i 0.314426i −0.987565 0.157213i \(-0.949749\pi\)
0.987565 0.157213i \(-0.0502509\pi\)
\(20\) 0.708712 + 0.409175i 0.158473 + 0.0914943i
\(21\) 0 0
\(22\) 0.895644 1.55130i 0.190952 0.330738i
\(23\) 0.791288 1.37055i 0.164995 0.285780i −0.771659 0.636037i \(-0.780573\pi\)
0.936653 + 0.350257i \(0.113906\pi\)
\(24\) 4.83465i 0.986869i
\(25\) −2.39564 + 4.14938i −0.479129 + 0.829875i
\(26\) 1.18693 + 1.14213i 0.232776 + 0.223989i
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 3.39564 + 5.88143i 0.630555 + 1.09215i 0.987438 + 0.158005i \(0.0505061\pi\)
−0.356883 + 0.934149i \(0.616161\pi\)
\(30\) −0.582576 −0.106363
\(31\) 7.50000 + 4.33013i 1.34704 + 0.777714i 0.987829 0.155543i \(-0.0497126\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −4.10436 + 2.36965i −0.725555 + 0.418899i
\(33\) 10.9445i 1.90519i
\(34\) 1.37055i 0.235048i
\(35\) 0 0
\(36\) −4.29129 7.43273i −0.715215 1.23879i
\(37\) −6.00000 3.46410i −0.986394 0.569495i −0.0821995 0.996616i \(-0.526194\pi\)
−0.904194 + 0.427121i \(0.859528\pi\)
\(38\) 0.313068 0.542250i 0.0507864 0.0879646i
\(39\) 9.76951 + 2.41733i 1.56437 + 0.387082i
\(40\) 0.395644 + 0.685275i 0.0625568 + 0.108352i
\(41\) 6.79129 3.92095i 1.06062 0.612350i 0.135017 0.990843i \(-0.456891\pi\)
0.925604 + 0.378493i \(0.123558\pi\)
\(42\) 0 0
\(43\) −4.68693 + 8.11800i −0.714750 + 1.23798i 0.248305 + 0.968682i \(0.420126\pi\)
−0.963056 + 0.269302i \(0.913207\pi\)
\(44\) −6.08258 + 3.51178i −0.916983 + 0.529420i
\(45\) −1.89564 + 1.09445i −0.282586 + 0.163151i
\(46\) 0.626136 0.361500i 0.0923188 0.0533003i
\(47\) 8.29129 4.78698i 1.20941 0.698252i 0.246778 0.969072i \(-0.420628\pi\)
0.962630 + 0.270820i \(0.0872947\pi\)
\(48\) −3.89564 + 6.74745i −0.562288 + 0.973911i
\(49\) 0 0
\(50\) −1.89564 + 1.09445i −0.268085 + 0.154779i
\(51\) −4.18693 7.25198i −0.586288 1.01548i
\(52\) −1.79129 6.20520i −0.248407 0.860507i
\(53\) −3.08258 + 5.33918i −0.423424 + 0.733392i −0.996272 0.0862695i \(-0.972505\pi\)
0.572848 + 0.819662i \(0.305839\pi\)
\(54\) 1.97822 + 1.14213i 0.269202 + 0.155424i
\(55\) 0.895644 + 1.55130i 0.120769 + 0.209177i
\(56\) 0 0
\(57\) 3.82560i 0.506713i
\(58\) 3.10260i 0.407392i
\(59\) −10.6652 + 6.15753i −1.38848 + 0.801642i −0.993145 0.116893i \(-0.962707\pi\)
−0.395340 + 0.918535i \(0.629373\pi\)
\(60\) 1.97822 + 1.14213i 0.255387 + 0.147448i
\(61\) −14.7477 −1.88825 −0.944126 0.329583i \(-0.893092\pi\)
−0.944126 + 0.329583i \(0.893092\pi\)
\(62\) 1.97822 + 3.42638i 0.251234 + 0.435150i
\(63\) 0 0
\(64\) 3.41742 0.427178
\(65\) −1.58258 + 0.456850i −0.196294 + 0.0566653i
\(66\) 2.50000 4.33013i 0.307729 0.533002i
\(67\) 4.47315i 0.546483i −0.961946 0.273241i \(-0.911904\pi\)
0.961946 0.273241i \(-0.0880957\pi\)
\(68\) −2.68693 + 4.65390i −0.325838 + 0.564369i
\(69\) 2.20871 3.82560i 0.265898 0.460548i
\(70\) 0 0
\(71\) 3.79129 + 2.18890i 0.449943 + 0.259775i 0.707806 0.706407i \(-0.249685\pi\)
−0.257863 + 0.966181i \(0.583018\pi\)
\(72\) 8.29875i 0.978018i
\(73\) −3.00000 1.73205i −0.351123 0.202721i 0.314057 0.949404i \(-0.398312\pi\)
−0.665180 + 0.746683i \(0.731645\pi\)
\(74\) −1.58258 2.74110i −0.183971 0.318647i
\(75\) −6.68693 + 11.5821i −0.772140 + 1.33739i
\(76\) −2.12614 + 1.22753i −0.243885 + 0.140807i
\(77\) 0 0
\(78\) 3.31307 + 3.18800i 0.375131 + 0.360970i
\(79\) 3.00000 + 5.19615i 0.337526 + 0.584613i 0.983967 0.178352i \(-0.0570765\pi\)
−0.646440 + 0.762964i \(0.723743\pi\)
\(80\) 1.27520i 0.142572i
\(81\) −0.417424 −0.0463805
\(82\) 3.58258 0.395629
\(83\) 7.02355i 0.770935i 0.922721 + 0.385468i \(0.125960\pi\)
−0.922721 + 0.385468i \(0.874040\pi\)
\(84\) 0 0
\(85\) 1.18693 + 0.685275i 0.128741 + 0.0743286i
\(86\) −3.70871 + 2.14123i −0.399921 + 0.230894i
\(87\) 9.47822 + 16.4168i 1.01617 + 1.76006i
\(88\) −6.79129 −0.723954
\(89\) 13.9782 + 8.07033i 1.48169 + 0.855453i 0.999784 0.0207708i \(-0.00661204\pi\)
0.481904 + 0.876224i \(0.339945\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −2.83485 −0.295553
\(93\) 20.9347 + 12.0866i 2.17082 + 1.25333i
\(94\) 4.37386 0.451130
\(95\) 0.313068 + 0.542250i 0.0321201 + 0.0556337i
\(96\) −11.4564 + 6.61438i −1.16927 + 0.675077i
\(97\) −6.31307 3.64485i −0.640995 0.370079i 0.144003 0.989577i \(-0.454003\pi\)
−0.784998 + 0.619499i \(0.787336\pi\)
\(98\) 0 0
\(99\) 18.7864i 1.88811i
\(100\) 8.58258 0.858258
\(101\) 5.20871 0.518286 0.259143 0.965839i \(-0.416560\pi\)
0.259143 + 0.965839i \(0.416560\pi\)
\(102\) 3.82560i 0.378791i
\(103\) −2.29129 3.96863i −0.225767 0.391040i 0.730782 0.682611i \(-0.239156\pi\)
−0.956549 + 0.291570i \(0.905822\pi\)
\(104\) 1.50000 6.06218i 0.147087 0.594445i
\(105\) 0 0
\(106\) −2.43920 + 1.40828i −0.236917 + 0.136784i
\(107\) 2.60436 4.51088i 0.251773 0.436083i −0.712241 0.701935i \(-0.752320\pi\)
0.964014 + 0.265852i \(0.0856532\pi\)
\(108\) −4.47822 7.75650i −0.430917 0.746370i
\(109\) −6.87386 3.96863i −0.658397 0.380126i 0.133269 0.991080i \(-0.457453\pi\)
−0.791666 + 0.610954i \(0.790786\pi\)
\(110\) 0.818350i 0.0780266i
\(111\) −16.7477 9.66930i −1.58962 0.917770i
\(112\) 0 0
\(113\) −5.29129 + 9.16478i −0.497762 + 0.862150i −0.999997 0.00258173i \(-0.999178\pi\)
0.502234 + 0.864732i \(0.332512\pi\)
\(114\) 0.873864 1.51358i 0.0818448 0.141759i
\(115\) 0.723000i 0.0674201i
\(116\) 6.08258 10.5353i 0.564753 0.978181i
\(117\) 16.7695 + 4.14938i 1.55034 + 0.383610i
\(118\) −5.62614 −0.517928
\(119\) 0 0
\(120\) 1.10436 + 1.91280i 0.100813 + 0.174614i
\(121\) −4.37386 −0.397624
\(122\) −5.83485 3.36875i −0.528262 0.304992i
\(123\) 18.9564 10.9445i 1.70924 0.986833i
\(124\) 15.5130i 1.39311i
\(125\) 4.47315i 0.400091i
\(126\) 0 0
\(127\) −3.47822 6.02445i −0.308642 0.534584i 0.669423 0.742881i \(-0.266541\pi\)
−0.978066 + 0.208297i \(0.933208\pi\)
\(128\) 9.56080 + 5.51993i 0.845063 + 0.487897i
\(129\) −13.0826 + 22.6597i −1.15186 + 1.99507i
\(130\) −0.730493 0.180750i −0.0640684 0.0158528i
\(131\) 8.68693 + 15.0462i 0.758981 + 1.31459i 0.943371 + 0.331740i \(0.107636\pi\)
−0.184390 + 0.982853i \(0.559031\pi\)
\(132\) −16.9782 + 9.80238i −1.47776 + 0.853188i
\(133\) 0 0
\(134\) 1.02178 1.76978i 0.0882684 0.152885i
\(135\) −1.97822 + 1.14213i −0.170258 + 0.0982985i
\(136\) −4.50000 + 2.59808i −0.385872 + 0.222783i
\(137\) −10.3521 + 5.97678i −0.884438 + 0.510631i −0.872119 0.489294i \(-0.837255\pi\)
−0.0123190 + 0.999924i \(0.503921\pi\)
\(138\) 1.74773 1.00905i 0.148776 0.0858961i
\(139\) −1.89564 + 3.28335i −0.160786 + 0.278490i −0.935151 0.354249i \(-0.884736\pi\)
0.774365 + 0.632740i \(0.218070\pi\)
\(140\) 0 0
\(141\) 23.1434 13.3618i 1.94902 1.12527i
\(142\) 1.00000 + 1.73205i 0.0839181 + 0.145350i
\(143\) 3.39564 13.7233i 0.283958 1.14760i
\(144\) −6.68693 + 11.5821i −0.557244 + 0.965175i
\(145\) −2.68693 1.55130i −0.223138 0.128829i
\(146\) −0.791288 1.37055i −0.0654874 0.113428i
\(147\) 0 0
\(148\) 12.4104i 1.02013i
\(149\) 0.456850i 0.0374266i 0.999825 + 0.0187133i \(0.00595698\pi\)
−0.999825 + 0.0187133i \(0.994043\pi\)
\(150\) −5.29129 + 3.05493i −0.432032 + 0.249434i
\(151\) −10.5000 6.06218i −0.854478 0.493333i 0.00768132 0.999970i \(-0.497555\pi\)
−0.862159 + 0.506637i \(0.830888\pi\)
\(152\) −2.37386 −0.192546
\(153\) −7.18693 12.4481i −0.581029 1.00637i
\(154\) 0 0
\(155\) −3.95644 −0.317789
\(156\) −5.00000 17.3205i −0.400320 1.38675i
\(157\) 0.478220 0.828301i 0.0381661 0.0661056i −0.846311 0.532689i \(-0.821182\pi\)
0.884477 + 0.466583i \(0.154515\pi\)
\(158\) 2.74110i 0.218070i
\(159\) −8.60436 + 14.9032i −0.682370 + 1.18190i
\(160\) 1.08258 1.87508i 0.0855851 0.148238i
\(161\) 0 0
\(162\) −0.165151 0.0953502i −0.0129755 0.00749142i
\(163\) 6.92820i 0.542659i −0.962487 0.271329i \(-0.912537\pi\)
0.962487 0.271329i \(-0.0874633\pi\)
\(164\) −12.1652 7.02355i −0.949939 0.548447i
\(165\) 2.50000 + 4.33013i 0.194625 + 0.337100i
\(166\) −1.60436 + 2.77883i −0.124522 + 0.215679i
\(167\) 12.7087 7.33738i 0.983430 0.567783i 0.0801258 0.996785i \(-0.474468\pi\)
0.903304 + 0.429001i \(0.141134\pi\)
\(168\) 0 0
\(169\) 11.5000 + 6.06218i 0.884615 + 0.466321i
\(170\) 0.313068 + 0.542250i 0.0240112 + 0.0415887i
\(171\) 6.56670i 0.502168i
\(172\) 16.7913 1.28032
\(173\) 19.7477 1.50139 0.750696 0.660648i \(-0.229718\pi\)
0.750696 + 0.660648i \(0.229718\pi\)
\(174\) 8.66025i 0.656532i
\(175\) 0 0
\(176\) 9.47822 + 5.47225i 0.714448 + 0.412487i
\(177\) −29.7695 + 17.1874i −2.23761 + 1.29189i
\(178\) 3.68693 + 6.38595i 0.276347 + 0.478647i
\(179\) −9.00000 −0.672692 −0.336346 0.941739i \(-0.609191\pi\)
−0.336346 + 0.941739i \(0.609191\pi\)
\(180\) 3.39564 + 1.96048i 0.253096 + 0.146125i
\(181\) −9.16515 −0.681240 −0.340620 0.940201i \(-0.610637\pi\)
−0.340620 + 0.940201i \(0.610637\pi\)
\(182\) 0 0
\(183\) −41.1652 −3.04302
\(184\) −2.37386 1.37055i −0.175004 0.101038i
\(185\) 3.16515 0.232707
\(186\) 5.52178 + 9.56400i 0.404877 + 0.701267i
\(187\) −10.1869 + 5.88143i −0.744942 + 0.430093i
\(188\) −14.8521 8.57485i −1.08320 0.625386i
\(189\) 0 0
\(190\) 0.286051i 0.0207523i
\(191\) −14.3739 −1.04006 −0.520028 0.854149i \(-0.674079\pi\)
−0.520028 + 0.854149i \(0.674079\pi\)
\(192\) 9.53901 0.688419
\(193\) 19.3386i 1.39202i 0.718030 + 0.696012i \(0.245044\pi\)
−0.718030 + 0.696012i \(0.754956\pi\)
\(194\) −1.66515 2.88413i −0.119551 0.207068i
\(195\) −4.41742 + 1.27520i −0.316338 + 0.0913190i
\(196\) 0 0
\(197\) 1.97822 1.14213i 0.140942 0.0813731i −0.427871 0.903840i \(-0.640736\pi\)
0.568813 + 0.822467i \(0.307403\pi\)
\(198\) 4.29129 7.43273i 0.304969 0.528221i
\(199\) 5.50000 + 9.52628i 0.389885 + 0.675300i 0.992434 0.122782i \(-0.0391815\pi\)
−0.602549 + 0.798082i \(0.705848\pi\)
\(200\) 7.18693 + 4.14938i 0.508193 + 0.293405i
\(201\) 12.4859i 0.880684i
\(202\) 2.06080 + 1.18980i 0.144997 + 0.0837141i
\(203\) 0 0
\(204\) −7.50000 + 12.9904i −0.525105 + 0.909509i
\(205\) −1.79129 + 3.10260i −0.125109 + 0.216695i
\(206\) 2.09355i 0.145865i
\(207\) 3.79129 6.56670i 0.263513 0.456417i
\(208\) −6.97822 + 7.25198i −0.483852 + 0.502834i
\(209\) −5.37386 −0.371718
\(210\) 0 0
\(211\) −5.29129 9.16478i −0.364267 0.630929i 0.624391 0.781112i \(-0.285347\pi\)
−0.988658 + 0.150183i \(0.952014\pi\)
\(212\) 11.0436 0.758475
\(213\) 10.5826 + 6.10985i 0.725106 + 0.418640i
\(214\) 2.06080 1.18980i 0.140873 0.0813331i
\(215\) 4.28245i 0.292061i
\(216\) 8.66025i 0.589256i
\(217\) 0 0
\(218\) −1.81307 3.14033i −0.122796 0.212690i
\(219\) −8.37386 4.83465i −0.565853 0.326696i
\(220\) 1.60436 2.77883i 0.108166 0.187348i
\(221\) −3.00000 10.3923i −0.201802 0.699062i
\(222\) −4.41742 7.65120i −0.296478 0.513515i
\(223\) 16.4347 9.48855i 1.10055 0.635401i 0.164182 0.986430i \(-0.447502\pi\)
0.936364 + 0.351029i \(0.114168\pi\)
\(224\) 0 0
\(225\) −11.4782 + 19.8809i −0.765215 + 1.32539i
\(226\) −4.18693 + 2.41733i −0.278511 + 0.160798i
\(227\) 7.66515 4.42548i 0.508754 0.293729i −0.223567 0.974688i \(-0.571770\pi\)
0.732321 + 0.680959i \(0.238437\pi\)
\(228\) −5.93466 + 3.42638i −0.393032 + 0.226917i
\(229\) 6.00000 3.46410i 0.396491 0.228914i −0.288478 0.957487i \(-0.593149\pi\)
0.684969 + 0.728572i \(0.259816\pi\)
\(230\) −0.165151 + 0.286051i −0.0108898 + 0.0188616i
\(231\) 0 0
\(232\) 10.1869 5.88143i 0.668805 0.386135i
\(233\) −7.97822 13.8187i −0.522671 0.905292i −0.999652 0.0263786i \(-0.991602\pi\)
0.476981 0.878913i \(-0.341731\pi\)
\(234\) 5.68693 + 5.47225i 0.371766 + 0.357732i
\(235\) −2.18693 + 3.78788i −0.142660 + 0.247094i
\(236\) 19.1044 + 11.0299i 1.24359 + 0.717986i
\(237\) 8.37386 + 14.5040i 0.543941 + 0.942133i
\(238\) 0 0
\(239\) 13.2288i 0.855697i −0.903850 0.427849i \(-0.859272\pi\)
0.903850 0.427849i \(-0.140728\pi\)
\(240\) 3.55945i 0.229762i
\(241\) −17.0608 + 9.85005i −1.09898 + 0.634498i −0.935954 0.352123i \(-0.885460\pi\)
−0.163029 + 0.986621i \(0.552126\pi\)
\(242\) −1.73049 0.999100i −0.111240 0.0642246i
\(243\) −16.1652 −1.03699
\(244\) 13.2087 + 22.8782i 0.845601 + 1.46462i
\(245\) 0 0
\(246\) 10.0000 0.637577
\(247\) 1.18693 4.79693i 0.0755227 0.305221i
\(248\) 7.50000 12.9904i 0.476250 0.824890i
\(249\) 19.6048i 1.24240i
\(250\) 1.02178 1.76978i 0.0646231 0.111930i
\(251\) −1.41742 + 2.45505i −0.0894670 + 0.154961i −0.907286 0.420514i \(-0.861850\pi\)
0.817819 + 0.575476i \(0.195183\pi\)
\(252\) 0 0
\(253\) −5.37386 3.10260i −0.337852 0.195059i
\(254\) 3.17805i 0.199409i
\(255\) 3.31307 + 1.91280i 0.207472 + 0.119784i
\(256\) −0.895644 1.55130i −0.0559777 0.0969563i
\(257\) 2.52178 4.36785i 0.157304 0.272459i −0.776591 0.630005i \(-0.783053\pi\)
0.933896 + 0.357546i \(0.116386\pi\)
\(258\) −10.3521 + 5.97678i −0.644493 + 0.372098i
\(259\) 0 0
\(260\) 2.12614 + 2.04588i 0.131857 + 0.126880i
\(261\) 16.2695 + 28.1796i 1.00706 + 1.74427i
\(262\) 7.93725i 0.490365i
\(263\) 9.33030 0.575331 0.287666 0.957731i \(-0.407121\pi\)
0.287666 + 0.957731i \(0.407121\pi\)
\(264\) −18.9564 −1.16669
\(265\) 2.81655i 0.173019i
\(266\) 0 0
\(267\) 39.0172 + 22.5266i 2.38782 + 1.37861i
\(268\) −6.93920 + 4.00635i −0.423879 + 0.244727i
\(269\) −7.89564 13.6757i −0.481406 0.833819i 0.518366 0.855159i \(-0.326540\pi\)
−0.999772 + 0.0213391i \(0.993207\pi\)
\(270\) −1.04356 −0.0635091
\(271\) −11.1261 6.42368i −0.675865 0.390211i 0.122430 0.992477i \(-0.460931\pi\)
−0.798295 + 0.602266i \(0.794264\pi\)
\(272\) 8.37386 0.507740
\(273\) 0 0
\(274\) −5.46099 −0.329910
\(275\) 16.2695 + 9.39320i 0.981088 + 0.566432i
\(276\) −7.91288 −0.476299
\(277\) −5.87386 10.1738i −0.352926 0.611286i 0.633835 0.773469i \(-0.281480\pi\)
−0.986761 + 0.162182i \(0.948147\pi\)
\(278\) −1.50000 + 0.866025i −0.0899640 + 0.0519408i
\(279\) 35.9347 + 20.7469i 2.15135 + 1.24208i
\(280\) 0 0
\(281\) 30.6446i 1.82810i −0.405597 0.914052i \(-0.632936\pi\)
0.405597 0.914052i \(-0.367064\pi\)
\(282\) 12.2087 0.727018
\(283\) −2.74773 −0.163335 −0.0816677 0.996660i \(-0.526025\pi\)
−0.0816677 + 0.996660i \(0.526025\pi\)
\(284\) 7.84190i 0.465331i
\(285\) 0.873864 + 1.51358i 0.0517632 + 0.0896565i
\(286\) 4.47822 4.65390i 0.264803 0.275191i
\(287\) 0 0
\(288\) −19.6652 + 11.3537i −1.15878 + 0.669022i
\(289\) 4.00000 6.92820i 0.235294 0.407541i
\(290\) −0.708712 1.22753i −0.0416170 0.0720828i
\(291\) −17.6216 10.1738i −1.03300 0.596400i
\(292\) 6.20520i 0.363132i
\(293\) −2.20871 1.27520i −0.129034 0.0744980i 0.434093 0.900868i \(-0.357069\pi\)
−0.563128 + 0.826370i \(0.690402\pi\)
\(294\) 0 0
\(295\) 2.81307 4.87238i 0.163783 0.283681i
\(296\) −6.00000 + 10.3923i −0.348743 + 0.604040i
\(297\) 19.6048i 1.13758i
\(298\) −0.104356 + 0.180750i −0.00604519 + 0.0104706i
\(299\) 3.95644 4.11165i 0.228807 0.237783i
\(300\) 23.9564 1.38313
\(301\) 0 0
\(302\) −2.76951 4.79693i −0.159367 0.276032i
\(303\) 14.5390 0.835245
\(304\) 3.31307 + 1.91280i 0.190017 + 0.109707i
\(305\) 5.83485 3.36875i 0.334102 0.192894i
\(306\) 6.56670i 0.375393i
\(307\) 15.5130i 0.885374i 0.896676 + 0.442687i \(0.145975\pi\)
−0.896676 + 0.442687i \(0.854025\pi\)
\(308\) 0 0
\(309\) −6.39564 11.0776i −0.363835 0.630182i
\(310\) −1.56534 0.903750i −0.0889054 0.0513296i
\(311\) 13.2695 22.9835i 0.752445 1.30327i −0.194190 0.980964i \(-0.562208\pi\)
0.946635 0.322309i \(-0.104459\pi\)
\(312\) 4.18693 16.9213i 0.237038 0.957979i
\(313\) −3.37386 5.84370i −0.190702 0.330306i 0.754781 0.655977i \(-0.227743\pi\)
−0.945483 + 0.325671i \(0.894410\pi\)
\(314\) 0.378409 0.218475i 0.0213549 0.0123292i
\(315\) 0 0
\(316\) 5.37386 9.30780i 0.302303 0.523605i
\(317\) 16.0390 9.26013i 0.900841 0.520101i 0.0233679 0.999727i \(-0.492561\pi\)
0.877473 + 0.479626i \(0.159228\pi\)
\(318\) −6.80852 + 3.93090i −0.381803 + 0.220434i
\(319\) 23.0608 13.3142i 1.29116 0.745450i
\(320\) −1.35208 + 0.780626i −0.0755837 + 0.0436383i
\(321\) 7.26951 12.5912i 0.405744 0.702770i
\(322\) 0 0
\(323\) −3.56080 + 2.05583i −0.198128 + 0.114389i
\(324\) 0.373864 + 0.647551i 0.0207702 + 0.0359750i
\(325\) −11.9782 + 12.4481i −0.664432 + 0.690498i
\(326\) 1.58258 2.74110i 0.0876508 0.151816i
\(327\) −19.1869 11.0776i −1.06104 0.612592i
\(328\) −6.79129 11.7629i −0.374986 0.649495i
\(329\) 0 0
\(330\) 2.28425i 0.125744i
\(331\) 24.8963i 1.36842i −0.729284 0.684211i \(-0.760147\pi\)
0.729284 0.684211i \(-0.239853\pi\)
\(332\) 10.8956 6.29060i 0.597976 0.345242i
\(333\) −28.7477 16.5975i −1.57537 0.909538i
\(334\) 6.70417 0.366836
\(335\) 1.02178 + 1.76978i 0.0558258 + 0.0966932i
\(336\) 0 0
\(337\) 9.95644 0.542362 0.271181 0.962528i \(-0.412586\pi\)
0.271181 + 0.962528i \(0.412586\pi\)
\(338\) 3.16515 + 5.02535i 0.172162 + 0.273343i
\(339\) −14.7695 + 25.5815i −0.802170 + 1.38940i
\(340\) 2.45505i 0.133144i
\(341\) 16.9782 29.4071i 0.919422 1.59249i
\(342\) 1.50000 2.59808i 0.0811107 0.140488i
\(343\) 0 0
\(344\) 14.0608 + 8.11800i 0.758107 + 0.437693i
\(345\) 2.01810i 0.108651i
\(346\) 7.81307 + 4.51088i 0.420033 + 0.242506i
\(347\) 6.79129 + 11.7629i 0.364575 + 0.631463i 0.988708 0.149855i \(-0.0478808\pi\)
−0.624132 + 0.781319i \(0.714547\pi\)
\(348\) 16.9782 29.4071i 0.910128 1.57639i
\(349\) 18.2477 10.5353i 0.976778 0.563943i 0.0754825 0.997147i \(-0.475950\pi\)
0.901296 + 0.433204i \(0.142617\pi\)
\(350\) 0 0
\(351\) 17.5000 + 4.33013i 0.934081 + 0.231125i
\(352\) 9.29129 + 16.0930i 0.495227 + 0.857759i
\(353\) 18.1588i 0.966493i −0.875484 0.483247i \(-0.839457\pi\)
0.875484 0.483247i \(-0.160543\pi\)
\(354\) −15.7042 −0.834667
\(355\) −2.00000 −0.106149
\(356\) 28.9126i 1.53236i
\(357\) 0 0
\(358\) −3.56080 2.05583i −0.188194 0.108654i
\(359\) 0.478220 0.276100i 0.0252395 0.0145720i −0.487327 0.873219i \(-0.662028\pi\)
0.512567 + 0.858647i \(0.328695\pi\)
\(360\) 1.89564 + 3.28335i 0.0999092 + 0.173048i
\(361\) 17.1216 0.901136
\(362\) −3.62614 2.09355i −0.190586 0.110035i
\(363\) −12.2087 −0.640791
\(364\) 0 0
\(365\) 1.58258 0.0828358
\(366\) −16.2867 9.40315i −0.851322 0.491511i
\(367\) 18.0000 0.939592 0.469796 0.882775i \(-0.344327\pi\)
0.469796 + 0.882775i \(0.344327\pi\)
\(368\) 2.20871 + 3.82560i 0.115137 + 0.199423i
\(369\) 32.5390 18.7864i 1.69391 0.977981i
\(370\) 1.25227 + 0.723000i 0.0651026 + 0.0375870i
\(371\) 0 0
\(372\) 43.3013i 2.24507i
\(373\) 32.2087 1.66770 0.833852 0.551988i \(-0.186131\pi\)
0.833852 + 0.551988i \(0.186131\pi\)
\(374\) −5.37386 −0.277876
\(375\) 12.4859i 0.644767i
\(376\) −8.29129 14.3609i −0.427591 0.740609i
\(377\) 6.79129 + 23.5257i 0.349769 + 1.21164i
\(378\) 0 0
\(379\) −24.5608 + 14.1802i −1.26160 + 0.728387i −0.973385 0.229178i \(-0.926396\pi\)
−0.288219 + 0.957565i \(0.593063\pi\)
\(380\) 0.560795 0.971326i 0.0287682 0.0498280i
\(381\) −9.70871 16.8160i −0.497392 0.861509i
\(382\) −5.68693 3.28335i −0.290969 0.167991i
\(383\) 1.27520i 0.0651597i 0.999469 + 0.0325799i \(0.0103723\pi\)
−0.999469 + 0.0325799i \(0.989628\pi\)
\(384\) 26.6869 + 15.4077i 1.36186 + 0.786271i
\(385\) 0 0
\(386\) −4.41742 + 7.65120i −0.224841 + 0.389436i
\(387\) −22.4564 + 38.8957i −1.14152 + 1.97718i
\(388\) 13.0580i 0.662917i
\(389\) 0.165151 0.286051i 0.00837351 0.0145033i −0.861808 0.507234i \(-0.830668\pi\)
0.870182 + 0.492731i \(0.164001\pi\)
\(390\) −2.03901 0.504525i −0.103250 0.0255476i
\(391\) −4.74773 −0.240103
\(392\) 0 0
\(393\) 24.2477 + 41.9983i 1.22314 + 2.11853i
\(394\) 1.04356 0.0525738
\(395\) −2.37386 1.37055i −0.119442 0.0689599i
\(396\) −29.1434 + 16.8259i −1.46451 + 0.845535i
\(397\) 32.4720i 1.62972i 0.579655 + 0.814862i \(0.303187\pi\)
−0.579655 + 0.814862i \(0.696813\pi\)
\(398\) 5.02535i 0.251898i
\(399\) 0 0
\(400\) −6.68693 11.5821i −0.334347 0.579105i
\(401\) −27.0998 15.6461i −1.35330 0.781328i −0.364590 0.931168i \(-0.618791\pi\)
−0.988710 + 0.149840i \(0.952124\pi\)
\(402\) 2.85208 4.93995i 0.142249 0.246382i
\(403\) 22.5000 + 21.6506i 1.12080 + 1.07849i
\(404\) −4.66515 8.08028i −0.232100 0.402009i
\(405\) 0.165151 0.0953502i 0.00820644 0.00473799i
\(406\) 0 0
\(407\) −13.5826 + 23.5257i −0.673263 + 1.16613i
\(408\) −12.5608 + 7.25198i −0.621852 + 0.359026i
\(409\) 7.18693 4.14938i 0.355371 0.205173i −0.311677 0.950188i \(-0.600891\pi\)
0.667048 + 0.745015i \(0.267557\pi\)
\(410\) −1.41742 + 0.818350i −0.0700016 + 0.0404154i
\(411\) −28.8956 + 16.6829i −1.42532 + 0.822907i
\(412\) −4.10436 + 7.10895i −0.202207 + 0.350233i
\(413\) 0 0
\(414\) 3.00000 1.73205i 0.147442 0.0851257i
\(415\) −1.60436 2.77883i −0.0787547 0.136407i
\(416\) −16.4174 + 4.73930i −0.804930 + 0.232363i
\(417\) −5.29129 + 9.16478i −0.259115 + 0.448801i
\(418\) −2.12614 1.22753i −0.103993 0.0600402i
\(419\) −0.873864 1.51358i −0.0426910 0.0739430i 0.843890 0.536516i \(-0.180260\pi\)
−0.886581 + 0.462573i \(0.846926\pi\)
\(420\) 0 0
\(421\) 4.18710i 0.204067i −0.994781 0.102033i \(-0.967465\pi\)
0.994781 0.102033i \(-0.0325349\pi\)
\(422\) 4.83465i 0.235347i
\(423\) 39.7259 22.9358i 1.93154 1.11518i
\(424\) 9.24773 + 5.33918i 0.449109 + 0.259293i
\(425\) 14.3739 0.697235
\(426\) 2.79129 + 4.83465i 0.135238 + 0.234240i
\(427\) 0 0
\(428\) −9.33030 −0.450997
\(429\) 9.47822 38.3058i 0.457613 1.84942i
\(430\) 0.978220 1.69433i 0.0471739 0.0817077i
\(431\) 34.6609i 1.66956i 0.550585 + 0.834779i \(0.314405\pi\)
−0.550585 + 0.834779i \(0.685595\pi\)
\(432\) −6.97822 + 12.0866i −0.335740 + 0.581518i
\(433\) −16.2477 + 28.1419i −0.780816 + 1.35241i 0.150651 + 0.988587i \(0.451863\pi\)
−0.931467 + 0.363826i \(0.881470\pi\)
\(434\) 0 0
\(435\) −7.50000 4.33013i −0.359597 0.207614i
\(436\) 14.2179i 0.680914i
\(437\) −1.87841 1.08450i −0.0898565 0.0518787i
\(438\) −2.20871 3.82560i −0.105536 0.182794i
\(439\) −10.2695 + 17.7873i −0.490137 + 0.848942i −0.999936 0.0113518i \(-0.996387\pi\)
0.509799 + 0.860294i \(0.329720\pi\)
\(440\) 2.68693 1.55130i 0.128094 0.0739554i
\(441\) 0 0
\(442\) 1.18693 4.79693i 0.0564566 0.228167i
\(443\) 7.58258 + 13.1334i 0.360259 + 0.623987i 0.988003 0.154433i \(-0.0493550\pi\)
−0.627744 + 0.778420i \(0.716022\pi\)
\(444\) 34.6410i 1.64399i
\(445\) −7.37386 −0.349555
\(446\) 8.66970 0.410522
\(447\) 1.27520i 0.0603149i
\(448\) 0 0
\(449\) −21.7913 12.5812i −1.02839 0.593744i −0.111870 0.993723i \(-0.535684\pi\)
−0.916524 + 0.399979i \(0.869017\pi\)
\(450\) −9.08258 + 5.24383i −0.428157 + 0.247196i
\(451\) −15.3739 26.6283i −0.723927 1.25388i
\(452\) 18.9564 0.891636
\(453\) −29.3085 16.9213i −1.37703 0.795031i
\(454\) 4.04356 0.189774
\(455\) 0 0
\(456\) −6.62614 −0.310297
\(457\) −19.7477 11.4014i −0.923760 0.533333i −0.0389271 0.999242i \(-0.512394\pi\)
−0.884833 + 0.465909i \(0.845727\pi\)
\(458\) 3.16515 0.147898
\(459\) −7.50000 12.9904i −0.350070 0.606339i
\(460\) 1.12159 0.647551i 0.0522944 0.0301922i
\(461\) −4.02178 2.32198i −0.187313 0.108145i 0.403411 0.915019i \(-0.367824\pi\)
−0.590724 + 0.806874i \(0.701158\pi\)
\(462\) 0 0
\(463\) 7.93725i 0.368875i −0.982844 0.184438i \(-0.940954\pi\)
0.982844 0.184438i \(-0.0590464\pi\)
\(464\) −18.9564 −0.880031
\(465\) −11.0436 −0.512133
\(466\) 7.28970i 0.337689i
\(467\) 15.0826 + 26.1238i 0.697938 + 1.20886i 0.969180 + 0.246353i \(0.0792324\pi\)
−0.271242 + 0.962511i \(0.587434\pi\)
\(468\) −8.58258 29.7309i −0.396730 1.37431i
\(469\) 0 0
\(470\) −1.73049 + 0.999100i −0.0798217 + 0.0460851i
\(471\) 1.33485 2.31203i 0.0615066 0.106533i
\(472\) 10.6652 + 18.4726i 0.490903 + 0.850270i
\(473\) 31.8303 + 18.3772i 1.46356 + 0.844986i
\(474\) 7.65120i 0.351431i
\(475\) 5.68693 + 3.28335i 0.260934 + 0.150651i
\(476\) 0 0
\(477\) −14.7695 + 25.5815i −0.676249 + 1.17130i
\(478\) 3.02178 5.23388i 0.138213 0.239392i
\(479\) 18.8818i 0.862730i 0.902178 + 0.431365i \(0.141968\pi\)
−0.902178 + 0.431365i \(0.858032\pi\)
\(480\) 3.02178 5.23388i 0.137925 0.238893i
\(481\) −18.0000 17.3205i −0.820729 0.789747i
\(482\) −9.00000 −0.409939
\(483\) 0 0
\(484\) 3.91742 + 6.78518i 0.178065 + 0.308417i
\(485\) 3.33030 0.151221
\(486\) −6.39564 3.69253i −0.290112 0.167496i
\(487\) −25.4347 + 14.6847i −1.15255 + 0.665428i −0.949508 0.313742i \(-0.898417\pi\)
−0.203046 + 0.979169i \(0.565084\pi\)
\(488\) 25.5438i 1.15631i
\(489\) 19.3386i 0.874522i
\(490\) 0 0
\(491\) 2.06080 + 3.56940i 0.0930024 + 0.161085i 0.908773 0.417291i \(-0.137020\pi\)
−0.815771 + 0.578375i \(0.803687\pi\)
\(492\) −33.9564 19.6048i −1.53087 0.883851i
\(493\) 10.1869 17.6443i 0.458796 0.794659i
\(494\) 1.56534 1.62675i 0.0704280 0.0731910i
\(495\) 4.29129 + 7.43273i 0.192879 + 0.334076i
\(496\) −20.9347 + 12.0866i −0.939994 + 0.542706i
\(497\) 0 0
\(498\) −4.47822 + 7.75650i −0.200674 + 0.347577i
\(499\) −15.9392 + 9.20250i −0.713537 + 0.411961i −0.812369 0.583143i \(-0.801823\pi\)
0.0988324 + 0.995104i \(0.468489\pi\)
\(500\) −6.93920 + 4.00635i −0.310331 + 0.179169i
\(501\) 35.4737 20.4807i 1.58485 0.915012i
\(502\) −1.12159 + 0.647551i −0.0500590 + 0.0289016i
\(503\) 9.56080 16.5598i 0.426295 0.738364i −0.570246 0.821474i \(-0.693152\pi\)
0.996540 + 0.0831100i \(0.0264853\pi\)
\(504\) 0 0
\(505\) −2.06080 + 1.18980i −0.0917042 + 0.0529454i
\(506\) −1.41742 2.45505i −0.0630122 0.109140i
\(507\) 32.0998 + 16.9213i 1.42560 + 0.751501i
\(508\) −6.23049 + 10.7915i −0.276433 + 0.478797i
\(509\) −13.0390 7.52808i −0.577944 0.333676i 0.182372 0.983230i \(-0.441623\pi\)
−0.760316 + 0.649553i \(0.774956\pi\)
\(510\) 0.873864 + 1.51358i 0.0386953 + 0.0670223i
\(511\) 0 0
\(512\) 22.8981i 1.01196i
\(513\) 6.85275i 0.302556i
\(514\) 1.99545 1.15208i 0.0880157 0.0508159i
\(515\) 1.81307 + 1.04678i 0.0798933 + 0.0461264i
\(516\) 46.8693 2.06331
\(517\) −18.7695 32.5097i −0.825482 1.42978i
\(518\) 0 0
\(519\) 55.1216 2.41957
\(520\) 0.791288 + 2.74110i 0.0347003 + 0.120205i
\(521\) 8.20871 14.2179i 0.359630 0.622898i −0.628269 0.777996i \(-0.716236\pi\)
0.987899 + 0.155099i \(0.0495695\pi\)
\(522\) 14.8655i 0.650643i
\(523\) 12.1652 21.0707i 0.531945 0.921356i −0.467360 0.884067i \(-0.654795\pi\)
0.999305 0.0372883i \(-0.0118720\pi\)
\(524\) 15.5608 26.9521i 0.679776 1.17741i
\(525\) 0 0
\(526\) 3.69148 + 2.13128i 0.160956 + 0.0929280i
\(527\) 25.9808i 1.13174i
\(528\) 26.4564 + 15.2746i 1.15137 + 0.664743i
\(529\) 10.2477 + 17.7496i 0.445553 + 0.771721i
\(530\) 0.643371 1.11435i 0.0279463 0.0484043i
\(531\) −51.0998 + 29.5025i −2.21754 + 1.28030i
\(532\) 0 0
\(533\) 27.1652 7.84190i 1.17665 0.339671i
\(534\) 10.2913 + 17.8250i 0.445348 + 0.771365i
\(535\) 2.37960i 0.102879i
\(536\) −7.74773 −0.334651
\(537\) −25.1216 −1.08408
\(538\) 7.21425i 0.311029i
\(539\) 0 0
\(540\) 3.54356 + 2.04588i 0.152491 + 0.0880405i
\(541\) −5.43920 + 3.14033i −0.233850 + 0.135013i −0.612347 0.790589i \(-0.709774\pi\)
0.378497 + 0.925602i \(0.376441\pi\)
\(542\) −2.93466 5.08298i −0.126054 0.218333i
\(543\) −25.5826 −1.09785
\(544\) 12.3131 + 7.10895i 0.527918 + 0.304794i
\(545\) 3.62614 0.155327
\(546\) 0 0
\(547\) −11.7477 −0.502297 −0.251148 0.967949i \(-0.580808\pi\)
−0.251148 + 0.967949i \(0.580808\pi\)
\(548\) 18.5436 + 10.7061i 0.792142 + 0.457343i
\(549\) −70.6606 −3.01572
\(550\) 4.29129 + 7.43273i 0.182981 + 0.316933i
\(551\) 8.06080 4.65390i 0.343401 0.198263i
\(552\) −6.62614 3.82560i −0.282027 0.162828i
\(553\) 0 0
\(554\) 5.36695i 0.228020i
\(555\) 8.83485 0.375018
\(556\) 6.79129 0.288015
\(557\) 33.0242i 1.39928i −0.714495 0.699640i \(-0.753344\pi\)
0.714495 0.699640i \(-0.246656\pi\)
\(558\) 9.47822 + 16.4168i 0.401245 + 0.694977i
\(559\) −23.4347 + 24.3540i −0.991180 + 1.03006i
\(560\) 0 0
\(561\) −28.4347 + 16.4168i −1.20051 + 0.693116i
\(562\) 7.00000 12.1244i 0.295277 0.511435i
\(563\) 18.1652 + 31.4630i 0.765570 + 1.32601i 0.939945 + 0.341327i \(0.110876\pi\)
−0.174375 + 0.984679i \(0.555790\pi\)
\(564\) −41.4564 23.9349i −1.74563 1.00784i
\(565\) 4.83465i 0.203395i
\(566\) −1.08712 0.627650i −0.0456951 0.0263821i
\(567\) 0 0
\(568\) 3.79129 6.56670i 0.159079 0.275533i
\(569\) −8.37386 + 14.5040i −0.351051 + 0.608038i −0.986434 0.164159i \(-0.947509\pi\)
0.635383 + 0.772197i \(0.280842\pi\)
\(570\) 0.798450i 0.0334434i
\(571\) 1.02178 1.76978i 0.0427602 0.0740628i −0.843853 0.536574i \(-0.819718\pi\)
0.886613 + 0.462511i \(0.153052\pi\)
\(572\) −24.3303 + 7.02355i −1.01730 + 0.293670i
\(573\) −40.1216 −1.67610
\(574\) 0 0
\(575\) 3.79129 + 6.56670i 0.158108 + 0.273850i
\(576\) 16.3739 0.682244
\(577\) −30.8739 17.8250i −1.28530 0.742066i −0.307484 0.951553i \(-0.599487\pi\)
−0.977811 + 0.209487i \(0.932821\pi\)
\(578\) 3.16515 1.82740i 0.131653 0.0760099i
\(579\) 53.9796i 2.24332i
\(580\) 5.55765i 0.230769i
\(581\) 0 0
\(582\) −4.64792 8.05043i −0.192662 0.333701i
\(583\) 20.9347 + 12.0866i 0.867025 + 0.500577i
\(584\) −3.00000 + 5.19615i −0.124141 + 0.215018i
\(585\) −7.58258 + 2.18890i −0.313501 + 0.0904999i
\(586\) −0.582576 1.00905i −0.0240660 0.0416835i
\(587\) 8.22595 4.74925i 0.339521 0.196023i −0.320539 0.947235i \(-0.603864\pi\)
0.660060 + 0.751213i \(0.270531\pi\)
\(588\) 0 0
\(589\) 5.93466 10.2791i 0.244533 0.423544i
\(590\) 2.22595 1.28515i 0.0916408 0.0529088i
\(591\) 5.52178 3.18800i 0.227136 0.131137i
\(592\) 16.7477 9.66930i 0.688327 0.397406i
\(593\) 5.52178 3.18800i 0.226752 0.130916i −0.382321 0.924030i \(-0.624875\pi\)
0.609073 + 0.793114i \(0.291542\pi\)
\(594\) 4.47822 7.75650i 0.183744 0.318253i
\(595\) 0 0
\(596\) 0.708712 0.409175i 0.0290300 0.0167605i
\(597\) 15.3521 + 26.5906i 0.628319 + 1.08828i
\(598\) 2.50455 0.723000i 0.102418 0.0295657i
\(599\) 3.31307 5.73840i 0.135368 0.234465i −0.790370 0.612630i \(-0.790112\pi\)
0.925738 + 0.378165i \(0.123445\pi\)
\(600\) 20.0608 + 11.5821i 0.818979 + 0.472837i
\(601\) −6.18693 10.7161i −0.252370 0.437118i 0.711808 0.702374i \(-0.247877\pi\)
−0.964178 + 0.265256i \(0.914543\pi\)
\(602\) 0 0
\(603\) 21.4322i 0.872785i
\(604\) 21.7182i 0.883701i
\(605\) 1.73049 0.999100i 0.0703545 0.0406192i
\(606\) 5.75227 + 3.32108i 0.233670 + 0.134910i
\(607\) 19.7477 0.801536 0.400768 0.916180i \(-0.368743\pi\)
0.400768 + 0.916180i \(0.368743\pi\)
\(608\) 3.24773 + 5.62523i 0.131713 + 0.228133i
\(609\) 0 0
\(610\) 3.07803 0.124626
\(611\) 33.1652 9.57395i 1.34172 0.387321i
\(612\) −12.8739 + 22.2982i −0.520395 + 0.901351i
\(613\) 18.2541i 0.737277i −0.929573 0.368638i \(-0.879824\pi\)
0.929573 0.368638i \(-0.120176\pi\)
\(614\) −3.54356 + 6.13763i −0.143006 + 0.247694i
\(615\) −5.00000 + 8.66025i −0.201619 + 0.349215i
\(616\) 0 0
\(617\) −14.9174 8.61258i −0.600553 0.346729i 0.168706 0.985666i \(-0.446041\pi\)
−0.769259 + 0.638937i \(0.779374\pi\)
\(618\) 5.84370i 0.235068i
\(619\) −16.7477 9.66930i −0.673148 0.388642i 0.124120 0.992267i \(-0.460389\pi\)
−0.797268 + 0.603625i \(0.793722\pi\)
\(620\) 3.54356 + 6.13763i 0.142313 + 0.246493i
\(621\) 3.95644 6.85275i 0.158766 0.274992i
\(622\) 10.5000 6.06218i 0.421012 0.243071i
\(623\) 0 0
\(624\) −19.4782 + 20.2424i −0.779753 + 0.810343i
\(625\) −10.9564 18.9771i −0.438258 0.759084i
\(626\) 3.08270i 0.123210i
\(627\) −15.0000 −0.599042
\(628\) −1.71326 −0.0683664
\(629\) 20.7846i 0.828737i
\(630\) 0 0
\(631\) 23.9347 + 13.8187i 0.952824 + 0.550113i 0.893957 0.448153i \(-0.147918\pi\)
0.0588668 + 0.998266i \(0.481251\pi\)
\(632\) 9.00000 5.19615i 0.358001 0.206692i
\(633\) −14.7695 25.5815i −0.587035 1.01677i
\(634\) 8.46099 0.336029
\(635\) 2.75227 + 1.58903i 0.109221 + 0.0630586i
\(636\) 30.8258 1.22232
\(637\) 0 0
\(638\) 12.1652 0.481623
\(639\) 18.1652 + 10.4877i 0.718602 + 0.414885i
\(640\) −5.04356 −0.199364
\(641\) −14.6869 25.4385i −0.580099 1.00476i −0.995467 0.0951074i \(-0.969681\pi\)
0.415368 0.909653i \(-0.363653\pi\)
\(642\) 5.75227 3.32108i 0.227024 0.131072i
\(643\) −39.2477 22.6597i −1.54778 0.893611i −0.998311 0.0580962i \(-0.981497\pi\)
−0.549468 0.835515i \(-0.685170\pi\)
\(644\) 0 0
\(645\) 11.9536i 0.470671i
\(646\) −1.87841 −0.0739050
\(647\) −35.0780 −1.37906 −0.689530 0.724257i \(-0.742183\pi\)
−0.689530 + 0.724257i \(0.742183\pi\)
\(648\) 0.723000i 0.0284021i
\(649\) 24.1434 + 41.8175i 0.947710 + 1.64148i
\(650\) −7.58258 + 2.18890i −0.297413 + 0.0858558i
\(651\) 0 0
\(652\) −10.7477 + 6.20520i −0.420913 + 0.243015i
\(653\) −7.89564 + 13.6757i −0.308980 + 0.535170i −0.978140 0.207949i \(-0.933321\pi\)
0.669159 + 0.743119i \(0.266654\pi\)
\(654\) −5.06080 8.76555i −0.197893 0.342760i
\(655\) −6.87386 3.96863i −0.268584 0.155067i
\(656\) 21.8890i 0.854622i
\(657\) −14.3739 8.29875i −0.560778 0.323765i
\(658\) 0 0
\(659\) −3.00000 + 5.19615i −0.116863 + 0.202413i −0.918523 0.395367i \(-0.870617\pi\)
0.801660 + 0.597781i \(0.203951\pi\)
\(660\) 4.47822 7.75650i 0.174314 0.301922i
\(661\) 50.5155i 1.96483i 0.186720 + 0.982413i \(0.440214\pi\)
−0.186720 + 0.982413i \(0.559786\pi\)
\(662\) 5.68693 9.85005i 0.221029 0.382833i
\(663\) −8.37386 29.0079i −0.325214 1.12657i
\(664\) 12.1652 0.472099
\(665\) 0 0
\(666\) −7.58258 13.1334i −0.293819 0.508909i
\(667\) 10.7477 0.416154
\(668\) −22.7650 13.1434i −0.880803 0.508532i
\(669\) 45.8739 26.4853i 1.77359 1.02398i
\(670\) 0.933601i 0.0360682i
\(671\) 57.8251i 2.23231i
\(672\) 0 0
\(673\) −13.2477 22.9457i −0.510662 0.884493i −0.999924 0.0123559i \(-0.996067\pi\)
0.489261 0.872137i \(-0.337266\pi\)
\(674\) 3.93920 + 2.27430i 0.151732 + 0.0876028i
\(675\) −11.9782 + 20.7469i −0.461042 + 0.798548i
\(676\) −0.895644 23.2695i −0.0344478 0.894981i
\(677\) −14.6044 25.2955i −0.561291 0.972185i −0.997384 0.0722830i \(-0.976972\pi\)
0.436093 0.899902i \(-0.356362\pi\)
\(678\) −11.6869 + 6.74745i −0.448834 + 0.259134i
\(679\) 0 0
\(680\) 1.18693 2.05583i 0.0455168 0.0788373i
\(681\) 21.3956 12.3528i 0.819883 0.473360i
\(682\) 13.4347 7.75650i 0.514440 0.297012i
\(683\) −26.2913 + 15.1793i −1.00601 + 0.580819i −0.910020 0.414563i \(-0.863934\pi\)
−0.0959878 + 0.995383i \(0.530601\pi\)
\(684\) −10.1869 + 5.88143i −0.389507 + 0.224882i
\(685\) 2.73049 4.72935i 0.104327 0.180699i
\(686\) 0 0
\(687\) 16.7477 9.66930i 0.638966 0.368907i
\(688\) −13.0826 22.6597i −0.498769 0.863892i
\(689\) −15.4129 + 16.0175i −0.587184 + 0.610219i
\(690\) −0.460985 + 0.798450i −0.0175494 + 0.0303965i
\(691\) −8.93466 5.15843i −0.339890 0.196236i 0.320333 0.947305i \(-0.396205\pi\)
−0.660224 + 0.751069i \(0.729538\pi\)
\(692\) −17.6869 30.6347i −0.672356 1.16456i
\(693\) 0 0
\(694\) 6.20520i 0.235546i
\(695\) 1.73205i 0.0657004i
\(696\) 28.4347 16.4168i 1.07781 0.622276i
\(697\) −20.3739 11.7629i −0.771715 0.445550i
\(698\) 9.62614 0.364355
\(699\) −22.2695 38.5719i −0.842310 1.45892i
\(700\) 0 0
\(701\) −13.9129 −0.525482 −0.262741 0.964866i \(-0.584627\pi\)
−0.262741 + 0.964866i \(0.584627\pi\)
\(702\) 5.93466 + 5.71063i 0.223989 + 0.215534i
\(703\) −4.74773 + 8.22330i −0.179064 + 0.310148i
\(704\) 13.3996i 0.505015i
\(705\) −6.10436 + 10.5731i −0.229903 + 0.398204i
\(706\) 4.14792 7.18440i 0.156109 0.270389i
\(707\) 0 0
\(708\) 53.3258 + 30.7876i 2.00410 + 1.15707i
\(709\) 15.2270i 0.571860i 0.958250 + 0.285930i \(0.0923025\pi\)
−0.958250 + 0.285930i \(0.907697\pi\)
\(710\) −0.791288 0.456850i −0.0296965 0.0171453i
\(711\) 14.3739 + 24.8963i 0.539062 + 0.933683i
\(712\) 13.9782 24.2110i 0.523856 0.907345i
\(713\) 11.8693 6.85275i 0.444509 0.256638i
\(714\) 0 0
\(715\) 1.79129 + 6.20520i 0.0669904 + 0.232061i
\(716\) 8.06080 + 13.9617i 0.301246 + 0.521773i
\(717\) 36.9253i 1.37900i
\(718\) 0.252273 0.00941474
\(719\) −24.1652 −0.901208 −0.450604 0.892724i \(-0.648791\pi\)
−0.450604 + 0.892724i \(0.648791\pi\)
\(720\) 6.10985i 0.227701i
\(721\) 0 0
\(722\) 6.77405 + 3.91100i 0.252104 + 0.145552i
\(723\) −47.6216 + 27.4943i −1.77107 + 1.02253i
\(724\) 8.20871 + 14.2179i 0.305074 + 0.528404i
\(725\) −32.5390 −1.20847
\(726\) −4.83030 2.78878i −0.179269 0.103501i
\(727\) 0.252273 0.00935628 0.00467814 0.999989i \(-0.498511\pi\)
0.00467814 + 0.999989i \(0.498511\pi\)
\(728\) 0 0
\(729\) −43.8693 −1.62479
\(730\) 0.626136 + 0.361500i 0.0231744 + 0.0133797i
\(731\) 28.1216 1.04011
\(732\) 36.8693 + 63.8595i 1.36273 + 2.36032i
\(733\) 14.6869 8.47950i 0.542474 0.313198i −0.203607 0.979053i \(-0.565266\pi\)
0.746081 + 0.665855i \(0.231933\pi\)
\(734\) 7.12159 + 4.11165i 0.262863 + 0.151764i
\(735\) 0 0
\(736\) 7.50030i 0.276465i
\(737\) −17.5390 −0.646058
\(738\) 17.1652 0.631858
\(739\) 19.3386i 0.711382i 0.934604 + 0.355691i \(0.115754\pi\)
−0.934604 + 0.355691i \(0.884246\pi\)
\(740\) −2.83485 4.91010i −0.104211 0.180499i
\(741\) 3.31307 13.3896i 0.121709 0.491879i
\(742\) 0 0
\(743\) 29.8521 17.2351i 1.09517 0.632295i 0.160219 0.987081i \(-0.448780\pi\)
0.934947 + 0.354787i \(0.115446\pi\)
\(744\) 20.9347 36.2599i 0.767502 1.32935i
\(745\) −0.104356 0.180750i −0.00382331 0.00662217i
\(746\) 12.7432 + 7.35728i 0.466561 + 0.269369i
\(747\) 33.6519i 1.23126i
\(748\) 18.2477 + 10.5353i 0.667203 + 0.385210i
\(749\) 0 0
\(750\) 2.85208 4.93995i 0.104143 0.180382i
\(751\) −11.8739 + 20.5661i −0.433283 + 0.750469i −0.997154 0.0753944i \(-0.975978\pi\)
0.563870 + 0.825863i \(0.309312\pi\)
\(752\) 26.7237i 0.974512i
\(753\) −3.95644 + 6.85275i −0.144181 + 0.249728i
\(754\) −2.68693 + 10.8591i −0.0978523 + 0.395465i
\(755\) 5.53901 0.201585
\(756\) 0 0
\(757\) −3.00000 5.19615i −0.109037 0.188857i 0.806343 0.591448i \(-0.201443\pi\)
−0.915380 + 0.402590i \(0.868110\pi\)
\(758\) −12.9564 −0.470599
\(759\) −15.0000 8.66025i −0.544466 0.314347i
\(760\) 0.939205 0.542250i 0.0340685 0.0196695i
\(761\) 12.9626i 0.469894i 0.972008 + 0.234947i \(0.0754917\pi\)
−0.972008 + 0.234947i \(0.924508\pi\)
\(762\) 8.87086i 0.321357i
\(763\) 0 0
\(764\) 12.8739 + 22.2982i 0.465760 + 0.806720i
\(765\) 5.68693 + 3.28335i 0.205611 + 0.118710i
\(766\) −0.291288 + 0.504525i −0.0105247 + 0.0182292i
\(767\) −42.6606 + 12.3151i −1.54039 + 0.444671i
\(768\) −2.50000 4.33013i −0.0902110 0.156250i
\(769\) 8.12614 4.69163i 0.293036 0.169184i −0.346274 0.938133i \(-0.612553\pi\)
0.639310 + 0.768949i \(0.279220\pi\)
\(770\) 0 0
\(771\) 7.03901 12.1919i 0.253504 0.439082i
\(772\) 30.0000 17.3205i 1.07972 0.623379i
\(773\) 16.8303 9.71698i 0.605344 0.349495i −0.165797 0.986160i \(-0.553020\pi\)
0.771141 + 0.636664i \(0.219686\pi\)
\(774\) −17.7695 + 10.2592i −0.638712 + 0.368760i
\(775\) −35.9347 + 20.7469i −1.29081 + 0.745250i
\(776\) −6.31307 + 10.9346i −0.226626 + 0.392528i
\(777\) 0 0
\(778\) 0.130682 0.0754495i 0.00468519