Properties

Label 637.2.q.e.589.1
Level $637$
Weight $2$
Character 637.589
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.q (of order \(6\), degree \(2\), 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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 589.1
Root \(1.39564 - 0.228425i\) of defining polynomial
Character \(\chi\) \(=\) 637.589
Dual form 637.2.q.e.491.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.395644 - 0.228425i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.895644 - 1.55130i) q^{4} +0.456850i q^{5} +(1.10436 - 0.637600i) q^{6} +1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})\) \(q+(-0.395644 - 0.228425i) q^{2} +(-1.39564 + 2.41733i) q^{3} +(-0.895644 - 1.55130i) q^{4} +0.456850i q^{5} +(1.10436 - 0.637600i) q^{6} +1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +(0.104356 - 0.180750i) q^{10} +(-3.39564 - 1.96048i) q^{11} +5.00000 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} +2.18890i q^{18} +(1.18693 - 0.685275i) q^{19} +(0.708712 - 0.409175i) q^{20} +(0.895644 + 1.55130i) q^{22} +(0.791288 - 1.37055i) q^{23} +(-4.18693 - 2.41733i) q^{24} +4.79129 q^{25} +(-1.58258 - 0.456850i) q^{26} +5.00000 q^{27} +(3.39564 - 5.88143i) q^{29} +(0.291288 + 0.504525i) q^{30} +8.66025i q^{31} +(4.10436 - 2.36965i) q^{32} +(9.47822 - 5.47225i) q^{33} +1.37055i q^{34} +(-4.29129 + 7.43273i) q^{36} +(6.00000 + 3.46410i) q^{37} -0.626136 q^{38} +(-2.79129 + 9.66930i) q^{39} -0.791288 q^{40} +(6.79129 + 3.92095i) q^{41} +(-4.68693 - 8.11800i) q^{43} +7.02355i q^{44} +(1.89564 - 1.09445i) q^{45} +(-0.626136 + 0.361500i) q^{46} -9.57395i q^{47} +(-3.89564 - 6.74745i) q^{48} +(-1.89564 - 1.09445i) q^{50} +8.37386 q^{51} +(-4.47822 - 4.65390i) q^{52} +6.16515 q^{53} +(-1.97822 - 1.14213i) q^{54} +(0.895644 - 1.55130i) q^{55} +3.82560i q^{57} +(-2.68693 + 1.55130i) q^{58} +(10.6652 - 6.15753i) q^{59} +2.28425i q^{60} +(7.37386 + 12.7719i) q^{61} +(1.97822 - 3.42638i) q^{62} +3.41742 q^{64} +(0.395644 + 1.59898i) q^{65} -5.00000 q^{66} +(-3.87386 - 2.23658i) q^{67} +(-2.68693 + 4.65390i) q^{68} +(2.20871 + 3.82560i) q^{69} +(3.79129 - 2.18890i) q^{71} +(7.18693 - 4.14938i) q^{72} -3.46410i 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} -6.00000 q^{79} +(-1.10436 - 0.637600i) q^{80} +(0.208712 - 0.361500i) q^{81} +(-1.79129 - 3.10260i) q^{82} -7.02355i q^{83} +(1.18693 - 0.685275i) q^{85} +4.28245i q^{86} +(9.47822 + 16.4168i) q^{87} +(3.39564 - 5.88143i) q^{88} +(-13.9782 - 8.07033i) q^{89} -1.00000 q^{90} -2.83485 q^{92} +(-20.9347 - 12.0866i) q^{93} +(-2.18693 + 3.78788i) q^{94} +(0.313068 + 0.542250i) q^{95} +13.2288i q^{96} +(-6.31307 + 3.64485i) q^{97} +18.7864i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} - q^{3} + q^{4} + 9 q^{6} - 5 q^{9} + 5 q^{10} - 9 q^{11} + 20 q^{12} + 14 q^{13} - 9 q^{15} - q^{16} - 6 q^{17} - 9 q^{19} + 12 q^{20} - q^{22} - 6 q^{23} - 3 q^{24} + 10 q^{25} + 12 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} + 21 q^{32} + 15 q^{33} - 8 q^{36} + 24 q^{37} - 30 q^{38} - 2 q^{39} + 6 q^{40} + 18 q^{41} - 5 q^{43} + 3 q^{45} - 30 q^{46} - 11 q^{48} - 3 q^{50} + 6 q^{51} + 5 q^{52} - 12 q^{53} + 15 q^{54} - q^{55} + 3 q^{58} + 6 q^{59} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 3 q^{65} - 20 q^{66} + 12 q^{67} + 3 q^{68} + 18 q^{69} + 6 q^{71} + 15 q^{72} + 12 q^{74} - 13 q^{75} - 36 q^{76} + 27 q^{78} - 24 q^{79} - 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 15 q^{87} + 9 q^{88} - 33 q^{89} - 4 q^{90} - 48 q^{92} - 15 q^{93} + 5 q^{94} + 15 q^{95} - 39 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.395644 0.228425i −0.279763 0.161521i 0.353553 0.935414i \(-0.384973\pi\)
−0.633316 + 0.773893i \(0.718307\pi\)
\(3\) −1.39564 + 2.41733i −0.805775 + 1.39564i 0.109991 + 0.993933i \(0.464918\pi\)
−0.915766 + 0.401711i \(0.868416\pi\)
\(4\) −0.895644 1.55130i −0.447822 0.775650i
\(5\) 0.456850i 0.204310i 0.994769 + 0.102155i \(0.0325737\pi\)
−0.994769 + 0.102155i \(0.967426\pi\)
\(6\) 1.10436 0.637600i 0.450851 0.260299i
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) −2.39564 4.14938i −0.798548 1.38313i
\(10\) 0.104356 0.180750i 0.0330003 0.0571582i
\(11\) −3.39564 1.96048i −1.02383 0.591106i −0.108616 0.994084i \(-0.534642\pi\)
−0.915210 + 0.402978i \(0.867975\pi\)
\(12\) 5.00000 1.44338
\(13\) 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 \(0.951855\pi\)
\(18\) 2.18890i 0.515929i
\(19\) 1.18693 0.685275i 0.272301 0.157213i −0.357632 0.933863i \(-0.616416\pi\)
0.629933 + 0.776650i \(0.283082\pi\)
\(20\) 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 \(0.113906\pi\)
\(24\) −4.18693 2.41733i −0.854654 0.493435i
\(25\) 4.79129 0.958258
\(26\) −1.58258 0.456850i −0.310369 0.0895957i
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) 3.39564 5.88143i 0.630555 1.09215i −0.356883 0.934149i \(-0.616161\pi\)
0.987438 0.158005i \(-0.0505061\pi\)
\(30\) 0.291288 + 0.504525i 0.0531816 + 0.0921133i
\(31\) 8.66025i 1.55543i 0.628619 + 0.777714i \(0.283621\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 4.10436 2.36965i 0.725555 0.418899i
\(33\) 9.47822 5.47225i 1.64995 0.952597i
\(34\) 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 0.904194 0.427121i \(-0.140472\pi\)
0.0821995 + 0.996616i \(0.473806\pi\)
\(38\) −0.626136 −0.101573
\(39\) −2.79129 + 9.66930i −0.446964 + 1.54833i
\(40\) −0.791288 −0.125114
\(41\) 6.79129 + 3.92095i 1.06062 + 0.612350i 0.925604 0.378493i \(-0.123558\pi\)
0.135017 + 0.990843i \(0.456891\pi\)
\(42\) 0 0
\(43\) −4.68693 8.11800i −0.714750 1.23798i −0.963056 0.269302i \(-0.913207\pi\)
0.248305 0.968682i \(-0.420126\pi\)
\(44\) 7.02355i 1.05884i
\(45\) 1.89564 1.09445i 0.282586 0.163151i
\(46\) −0.626136 + 0.361500i −0.0923188 + 0.0533003i
\(47\) 9.57395i 1.39650i −0.715852 0.698252i \(-0.753961\pi\)
0.715852 0.698252i \(-0.246039\pi\)
\(48\) −3.89564 6.74745i −0.562288 0.973911i
\(49\) 0 0
\(50\) −1.89564 1.09445i −0.268085 0.154779i
\(51\) 8.37386 1.17258
\(52\) −4.47822 4.65390i −0.621017 0.645380i
\(53\) 6.16515 0.846849 0.423424 0.905931i \(-0.360828\pi\)
0.423424 + 0.905931i \(0.360828\pi\)
\(54\) −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
\(58\) −2.68693 + 1.55130i −0.352811 + 0.203696i
\(59\) 10.6652 6.15753i 1.38848 0.801642i 0.395340 0.918535i \(-0.370627\pi\)
0.993145 + 0.116893i \(0.0372935\pi\)
\(60\) 2.28425i 0.294896i
\(61\) 7.37386 + 12.7719i 0.944126 + 1.63528i 0.757491 + 0.652846i \(0.226425\pi\)
0.186636 + 0.982429i \(0.440242\pi\)
\(62\) 1.97822 3.42638i 0.251234 0.435150i
\(63\) 0 0
\(64\) 3.41742 0.427178
\(65\) 0.395644 + 1.59898i 0.0490736 + 0.198329i
\(66\) −5.00000 −0.615457
\(67\) −3.87386 2.23658i −0.473268 0.273241i 0.244339 0.969690i \(-0.421429\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −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 −0.257863 0.966181i \(-0.583018\pi\)
0.707806 + 0.706407i \(0.249685\pi\)
\(72\) 7.18693 4.14938i 0.846988 0.489009i
\(73\) 3.46410i 0.405442i −0.979236 0.202721i \(-0.935021\pi\)
0.979236 0.202721i \(-0.0649785\pi\)
\(74\) −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
\(79\) −6.00000 −0.675053 −0.337526 0.941316i \(-0.609590\pi\)
−0.337526 + 0.941316i \(0.609590\pi\)
\(80\) −1.10436 0.637600i −0.123471 0.0712859i
\(81\) 0.208712 0.361500i 0.0231902 0.0401667i
\(82\) −1.79129 3.10260i −0.197815 0.342625i
\(83\) 7.02355i 0.770935i −0.922721 0.385468i \(-0.874040\pi\)
0.922721 0.385468i \(-0.125960\pi\)
\(84\) 0 0
\(85\) 1.18693 0.685275i 0.128741 0.0743286i
\(86\) 4.28245i 0.461789i
\(87\) 9.47822 + 16.4168i 1.01617 + 1.76006i
\(88\) 3.39564 5.88143i 0.361977 0.626962i
\(89\) −13.9782 8.07033i −1.48169 0.855453i −0.481904 0.876224i \(-0.660055\pi\)
−0.999784 + 0.0207708i \(0.993388\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −2.83485 −0.295553
\(93\) −20.9347 12.0866i −2.17082 1.25333i
\(94\) −2.18693 + 3.78788i −0.225565 + 0.390690i
\(95\) 0.313068 + 0.542250i 0.0321201 + 0.0556337i
\(96\) 13.2288i 1.35015i
\(97\) −6.31307 + 3.64485i −0.640995 + 0.370079i −0.784998 0.619499i \(-0.787336\pi\)
0.144003 + 0.989577i \(0.454003\pi\)
\(98\) 0 0
\(99\) 18.7864i 1.88811i
\(100\) −4.29129 7.43273i −0.429129 0.743273i
\(101\) −2.60436 + 4.51088i −0.259143 + 0.448849i −0.966013 0.258495i \(-0.916773\pi\)
0.706869 + 0.707344i \(0.250107\pi\)
\(102\) −3.31307 1.91280i −0.328043 0.189396i
\(103\) 4.58258 0.451535 0.225767 0.974181i \(-0.427511\pi\)
0.225767 + 0.974181i \(0.427511\pi\)
\(104\) 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
\(109\) 7.93725i 0.760251i −0.924935 0.380126i \(-0.875881\pi\)
0.924935 0.380126i \(-0.124119\pi\)
\(110\) −0.708712 + 0.409175i −0.0675731 + 0.0390133i
\(111\) −16.7477 + 9.66930i −1.58962 + 0.917770i
\(112\) 0 0
\(113\) −5.29129 9.16478i −0.497762 0.862150i 0.502234 0.864732i \(-0.332512\pi\)
−0.999997 + 0.00258173i \(0.999178\pi\)
\(114\) 0.873864 1.51358i 0.0818448 0.141759i
\(115\) 0.626136 + 0.361500i 0.0583875 + 0.0337101i
\(116\) −12.1652 −1.12951
\(117\) −11.9782 12.4481i −1.10739 1.15083i
\(118\) −5.62614 −0.517928
\(119\) 0 0
\(120\) 1.10436 1.91280i 0.100813 0.174614i
\(121\) 2.18693 + 3.78788i 0.198812 + 0.344352i
\(122\) 6.73750i 0.609985i
\(123\) −18.9564 + 10.9445i −1.70924 + 0.986833i
\(124\) 13.4347 7.75650i 1.20647 0.696555i
\(125\) 4.47315i 0.400091i
\(126\) 0 0
\(127\) −3.47822 + 6.02445i −0.308642 + 0.534584i −0.978066 0.208297i \(-0.933208\pi\)
0.669423 + 0.742881i \(0.266541\pi\)
\(128\) −9.56080 5.51993i −0.845063 0.487897i
\(129\) 26.1652 2.30371
\(130\) 0.208712 0.723000i 0.0183053 0.0634113i
\(131\) −17.3739 −1.51796 −0.758981 0.651113i \(-0.774302\pi\)
−0.758981 + 0.651113i \(0.774302\pi\)
\(132\) −16.9782 9.80238i −1.47776 0.853188i
\(133\) 0 0
\(134\) 1.02178 + 1.76978i 0.0882684 + 0.152885i
\(135\) 2.28425i 0.196597i
\(136\) 4.50000 2.59808i 0.385872 0.222783i
\(137\) 10.3521 5.97678i 0.884438 0.510631i 0.0123190 0.999924i \(-0.496079\pi\)
0.872119 + 0.489294i \(0.162745\pi\)
\(138\) 2.01810i 0.171792i
\(139\) −1.89564 3.28335i −0.160786 0.278490i 0.774365 0.632740i \(-0.218070\pi\)
−0.935151 + 0.354249i \(0.884736\pi\)
\(140\) 0 0
\(141\) 23.1434 + 13.3618i 1.94902 + 1.12527i
\(142\) −2.00000 −0.167836
\(143\) −13.5826 3.92095i −1.13583 0.327886i
\(144\) 13.3739 1.11449
\(145\) 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
\(149\) −0.395644 + 0.228425i −0.0324124 + 0.0187133i −0.516119 0.856517i \(-0.672624\pi\)
0.483706 + 0.875230i \(0.339290\pi\)
\(150\) 5.29129 3.05493i 0.432032 0.249434i
\(151\) 12.1244i 0.986666i −0.869841 0.493333i \(-0.835778\pi\)
0.869841 0.493333i \(-0.164222\pi\)
\(152\) 1.18693 + 2.05583i 0.0962729 + 0.166750i
\(153\) −7.18693 + 12.4481i −0.581029 + 1.00637i
\(154\) 0 0
\(155\) −3.95644 −0.317789
\(156\) 17.5000 4.33013i 1.40112 0.346688i
\(157\) −0.956439 −0.0763322 −0.0381661 0.999271i \(-0.512152\pi\)
−0.0381661 + 0.999271i \(0.512152\pi\)
\(158\) 2.37386 + 1.37055i 0.188854 + 0.109035i
\(159\) −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
\(163\) 6.00000 3.46410i 0.469956 0.271329i −0.246265 0.969202i \(-0.579203\pi\)
0.716221 + 0.697873i \(0.245870\pi\)
\(164\) 14.0471i 1.09689i
\(165\) 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 0.903304 0.429001i \(-0.141134\pi\)
0.0801258 + 0.996785i \(0.474468\pi\)
\(168\) 0 0
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) −0.626136 −0.0480225
\(171\) −5.68693 3.28335i −0.434891 0.251084i
\(172\) −8.39564 + 14.5417i −0.640162 + 1.10879i
\(173\) −9.87386 17.1020i −0.750696 1.30024i −0.947486 0.319798i \(-0.896385\pi\)
0.196790 0.980446i \(-0.436948\pi\)
\(174\) 8.66025i 0.656532i
\(175\) 0 0
\(176\) 9.47822 5.47225i 0.714448 0.412487i
\(177\) 34.3749i 2.58377i
\(178\) 3.68693 + 6.38595i 0.276347 + 0.478647i
\(179\) 4.50000 7.79423i 0.336346 0.582568i −0.647397 0.762153i \(-0.724142\pi\)
0.983742 + 0.179585i \(0.0574756\pi\)
\(180\) −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
\(185\) −1.58258 + 2.74110i −0.116353 + 0.201530i
\(186\) 5.52178 + 9.56400i 0.404877 + 0.701267i
\(187\) 11.7629i 0.860185i
\(188\) −14.8521 + 8.57485i −1.08320 + 0.625386i
\(189\) 0 0
\(190\) 0.286051i 0.0207523i
\(191\) 7.18693 + 12.4481i 0.520028 + 0.900715i 0.999729 + 0.0232830i \(0.00741188\pi\)
−0.479701 + 0.877432i \(0.659255\pi\)
\(192\) −4.76951 + 8.26103i −0.344210 + 0.596188i
\(193\) 16.7477 + 9.66930i 1.20553 + 0.696012i 0.961779 0.273827i \(-0.0882895\pi\)
0.243749 + 0.969838i \(0.421623\pi\)
\(194\) 3.33030 0.239102
\(195\) −4.41742 1.27520i −0.316338 0.0913190i
\(196\) 0 0
\(197\) 1.97822 + 1.14213i 0.140942 + 0.0813731i 0.568813 0.822467i \(-0.307403\pi\)
−0.427871 + 0.903840i \(0.640736\pi\)
\(198\) 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 \(0.705848\pi\)
\(200\) 8.29875i 0.586811i
\(201\) 10.8131 6.24293i 0.762695 0.440342i
\(202\) 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
\(206\) −1.81307 1.04678i −0.126322 0.0729323i
\(207\) −7.58258 −0.527025
\(208\) −2.79129 + 9.66930i −0.193541 + 0.670446i
\(209\) −5.37386 −0.371718
\(210\) 0 0
\(211\) −5.29129 + 9.16478i −0.364267 + 0.630929i −0.988658 0.150183i \(-0.952014\pi\)
0.624391 + 0.781112i \(0.285347\pi\)
\(212\) −5.52178 9.56400i −0.379237 0.656859i
\(213\) 12.2197i 0.837280i
\(214\) −2.06080 + 1.18980i −0.140873 + 0.0813331i
\(215\) 3.70871 2.14123i 0.252932 0.146030i
\(216\) 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
\(220\) −3.20871 −0.216331
\(221\) −7.50000 7.79423i −0.504505 0.524297i
\(222\) 8.83485 0.592956
\(223\) 16.4347 + 9.48855i 1.10055 + 0.635401i 0.936364 0.351029i \(-0.114168\pi\)
0.164182 + 0.986430i \(0.447502\pi\)
\(224\) 0 0
\(225\) −11.4782 19.8809i −0.765215 1.32539i
\(226\) 4.83465i 0.321596i
\(227\) −7.66515 + 4.42548i −0.508754 + 0.293729i −0.732321 0.680959i \(-0.761563\pi\)
0.223567 + 0.974688i \(0.428230\pi\)
\(228\) 5.93466 3.42638i 0.393032 0.226917i
\(229\) 6.92820i 0.457829i −0.973447 0.228914i \(-0.926482\pi\)
0.973447 0.228914i \(-0.0735176\pi\)
\(230\) −0.165151 0.286051i −0.0108898 0.0188616i
\(231\) 0 0
\(232\) 10.1869 + 5.88143i 0.668805 + 0.386135i
\(233\) 15.9564 1.04534 0.522671 0.852535i \(-0.324936\pi\)
0.522671 + 0.852535i \(0.324936\pi\)
\(234\) 1.89564 + 7.66115i 0.123922 + 0.500825i
\(235\) 4.37386 0.285319
\(236\) −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 \(0.140728\pi\)
−0.903850 + 0.427849i \(0.859272\pi\)
\(240\) 3.08258 1.77973i 0.198979 0.114881i
\(241\) 17.0608 9.85005i 1.09898 0.634498i 0.163029 0.986621i \(-0.447874\pi\)
0.935954 + 0.352123i \(0.114540\pi\)
\(242\) 1.99820i 0.128449i
\(243\) 8.08258 + 13.9994i 0.518497 + 0.898064i
\(244\) 13.2087 22.8782i 0.845601 1.46462i
\(245\) 0 0
\(246\) 10.0000 0.637577
\(247\) 3.56080 3.42638i 0.226568 0.218015i
\(248\) −15.0000 −0.952501
\(249\) 16.9782 + 9.80238i 1.07595 + 0.621201i
\(250\) 1.02178 1.76978i 0.0646231 0.111930i
\(251\) −1.41742 2.45505i −0.0894670 0.154961i 0.817819 0.575476i \(-0.195183\pi\)
−0.907286 + 0.420514i \(0.861850\pi\)
\(252\) 0 0
\(253\) −5.37386 + 3.10260i −0.337852 + 0.195059i
\(254\) 2.75227 1.58903i 0.172693 0.0997043i
\(255\) 3.82560i 0.239568i
\(256\) −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
\(261\) −32.5390 −2.01411
\(262\) 6.87386 + 3.96863i 0.424669 + 0.245183i
\(263\) −4.66515 + 8.08028i −0.287666 + 0.498251i −0.973252 0.229740i \(-0.926212\pi\)
0.685587 + 0.727991i \(0.259546\pi\)
\(264\) 9.47822 + 16.4168i 0.583344 + 1.01038i
\(265\) 2.81655i 0.173019i
\(266\) 0 0
\(267\) 39.0172 22.5266i 2.38782 1.37861i
\(268\) 8.01270i 0.489454i
\(269\) −7.89564 13.6757i −0.481406 0.833819i 0.518366 0.855159i \(-0.326540\pi\)
−0.999772 + 0.0213391i \(0.993207\pi\)
\(270\) 0.521780 0.903750i 0.0317545 0.0550005i
\(271\) 11.1261 + 6.42368i 0.675865 + 0.390211i 0.798295 0.602266i \(-0.205736\pi\)
−0.122430 + 0.992477i \(0.539069\pi\)
\(272\) 8.37386 0.507740
\(273\) 0 0
\(274\) −5.46099 −0.329910
\(275\) −16.2695 9.39320i −0.981088 0.566432i
\(276\) 3.95644 6.85275i 0.238150 0.412487i
\(277\) −5.87386 10.1738i −0.352926 0.611286i 0.633835 0.773469i \(-0.281480\pi\)
−0.986761 + 0.162182i \(0.948147\pi\)
\(278\) 1.73205i 0.103882i
\(279\) 35.9347 20.7469i 2.15135 1.24208i
\(280\) 0 0
\(281\) 30.6446i 1.82810i 0.405597 + 0.914052i \(0.367064\pi\)
−0.405597 + 0.914052i \(0.632936\pi\)
\(282\) −6.10436 10.5731i −0.363509 0.629616i
\(283\) 1.37386 2.37960i 0.0816677 0.141453i −0.822299 0.569056i \(-0.807309\pi\)
0.903966 + 0.427603i \(0.140642\pi\)
\(284\) −6.79129 3.92095i −0.402989 0.232666i
\(285\) −1.74773 −0.103526
\(286\) 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
\(291\) 20.3477i 1.19280i
\(292\) −5.37386 + 3.10260i −0.314482 + 0.181566i
\(293\) −2.20871 + 1.27520i −0.129034 + 0.0744980i −0.563128 0.826370i \(-0.690402\pi\)
0.434093 + 0.900868i \(0.357069\pi\)
\(294\) 0 0
\(295\) 2.81307 + 4.87238i 0.163783 + 0.283681i
\(296\) −6.00000 + 10.3923i −0.348743 + 0.604040i
\(297\) −16.9782 9.80238i −0.985176 0.568792i
\(298\) 0.208712 0.0120904
\(299\) 1.58258 5.48220i 0.0915227 0.317044i
\(300\) 23.9564 1.38313
\(301\) 0 0
\(302\) −2.76951 + 4.79693i −0.159367 + 0.276032i
\(303\) −7.26951 12.5912i −0.417622 0.723343i
\(304\) 3.82560i 0.219413i
\(305\) −5.83485 + 3.36875i −0.334102 + 0.192894i
\(306\) 5.68693 3.28335i 0.325100 0.187697i
\(307\) 15.5130i 0.885374i −0.896676 0.442687i \(-0.854025\pi\)
0.896676 0.442687i \(-0.145975\pi\)
\(308\) 0 0
\(309\) −6.39564 + 11.0776i −0.363835 + 0.630182i
\(310\) 1.56534 + 0.903750i 0.0889054 + 0.0513296i
\(311\) −26.5390 −1.50489 −0.752445 0.658655i \(-0.771126\pi\)
−0.752445 + 0.658655i \(0.771126\pi\)
\(312\) −16.7477 4.83465i −0.948153 0.273708i
\(313\) 6.74773 0.381404 0.190702 0.981648i \(-0.438924\pi\)
0.190702 + 0.981648i \(0.438924\pi\)
\(314\) 0.378409 + 0.218475i 0.0213549 + 0.0123292i
\(315\) 0 0
\(316\) 5.37386 + 9.30780i 0.302303 + 0.523605i
\(317\) 18.5203i 1.04020i −0.854105 0.520101i \(-0.825894\pi\)
0.854105 0.520101i \(-0.174106\pi\)
\(318\) 6.80852 3.93090i 0.381803 0.220434i
\(319\) −23.0608 + 13.3142i −1.29116 + 0.745450i
\(320\) 1.56125i 0.0872766i
\(321\) 7.26951 + 12.5912i 0.405744 + 0.702770i
\(322\) 0 0
\(323\) −3.56080 2.05583i −0.198128 0.114389i
\(324\) −0.747727 −0.0415404
\(325\) 16.7695 4.14938i 0.930205 0.230166i
\(326\) −3.16515 −0.175302
\(327\) 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
\(331\) 21.5608 12.4481i 1.18509 0.684211i 0.227902 0.973684i \(-0.426813\pi\)
0.957186 + 0.289473i \(0.0934800\pi\)
\(332\) −10.8956 + 6.29060i −0.597976 + 0.345242i
\(333\) 33.1950i 1.81908i
\(334\) −3.35208 5.80598i −0.183418 0.317689i
\(335\) 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 \(0.412586\pi\)
\(338\) −5.93466 0.228425i −0.322803 0.0124247i
\(339\) 29.5390 1.60434
\(340\) −2.12614 1.22753i −0.115306 0.0665719i
\(341\) 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
\(345\) −1.74773 + 1.00905i −0.0940945 + 0.0543255i
\(346\) 9.02175i 0.485013i
\(347\) 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 0.901296 0.433204i \(-0.142617\pi\)
0.0754825 + 0.997147i \(0.475950\pi\)
\(350\) 0 0
\(351\) 17.5000 4.33013i 0.934081 0.231125i
\(352\) −18.5826 −0.990455
\(353\) −15.7259 9.07938i −0.837008 0.483247i 0.0192383 0.999815i \(-0.493876\pi\)
−0.856246 + 0.516568i \(0.827209\pi\)
\(354\) 7.85208 13.6002i 0.417334 0.722843i
\(355\) 1.00000 + 1.73205i 0.0530745 + 0.0919277i
\(356\) 28.9126i 1.53236i
\(357\) 0 0
\(358\) −3.56080 + 2.05583i −0.188194 + 0.108654i
\(359\) 0.552200i 0.0291440i −0.999894 0.0145720i \(-0.995361\pi\)
0.999894 0.0145720i \(-0.00463858\pi\)
\(360\) 1.89564 + 3.28335i 0.0999092 + 0.173048i
\(361\) −8.56080 + 14.8277i −0.450568 + 0.780407i
\(362\) 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
\(367\) −9.00000 + 15.5885i −0.469796 + 0.813711i −0.999404 0.0345320i \(-0.989006\pi\)
0.529607 + 0.848243i \(0.322339\pi\)
\(368\) 2.20871 + 3.82560i 0.115137 + 0.199423i
\(369\) 37.5728i 1.95596i
\(370\) 1.25227 0.723000i 0.0651026 0.0375870i
\(371\) 0 0
\(372\) 43.3013i 2.24507i
\(373\) −16.1044 27.8936i −0.833852 1.44427i −0.894962 0.446143i \(-0.852797\pi\)
0.0611098 0.998131i \(-0.480536\pi\)
\(374\) 2.68693 4.65390i 0.138938 0.240648i
\(375\) −10.8131 6.24293i −0.558384 0.322383i
\(376\) 16.5826 0.855181
\(377\) 6.79129 23.5257i 0.349769 1.21164i
\(378\) 0 0
\(379\) −24.5608 14.1802i −1.26160 0.728387i −0.288219 0.957565i \(-0.593063\pi\)
−0.973385 + 0.229178i \(0.926396\pi\)
\(380\) 0.560795 0.971326i 0.0287682 0.0498280i
\(381\) −9.70871 16.8160i −0.497392 0.861509i
\(382\) 6.56670i 0.335982i
\(383\) −1.10436 + 0.637600i −0.0564300 + 0.0325799i −0.527950 0.849276i \(-0.677039\pi\)
0.471520 + 0.881856i \(0.343706\pi\)
\(384\) 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
\(388\) 11.3085 + 6.52898i 0.574103 + 0.331459i
\(389\) −0.330303 −0.0167470 −0.00837351 0.999965i \(-0.502665\pi\)
−0.00837351 + 0.999965i \(0.502665\pi\)
\(390\) 1.45644 + 1.51358i 0.0737497 + 0.0766429i
\(391\) −4.74773 −0.240103
\(392\) 0 0
\(393\) 24.2477 41.9983i 1.22314 2.11853i
\(394\) −0.521780 0.903750i −0.0262869 0.0455303i
\(395\) 2.74110i 0.137920i
\(396\) 29.1434 16.8259i 1.46451 0.845535i
\(397\) −28.1216 + 16.2360i −1.41138 + 0.814862i −0.995519 0.0945652i \(-0.969854\pi\)
−0.415864 + 0.909427i \(0.636521\pi\)
\(398\) 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 0.988710 0.149840i \(-0.0478759\pi\)
0.364590 + 0.931168i \(0.381209\pi\)
\(402\) −5.70417 −0.284498
\(403\) 7.50000 + 30.3109i 0.373602 + 1.50989i
\(404\) 9.33030 0.464200
\(405\) 0.165151 + 0.0953502i 0.00820644 + 0.00473799i
\(406\) 0 0
\(407\) −13.5826 23.5257i −0.673263 1.16613i
\(408\) 14.5040i 0.718053i
\(409\) −7.18693 + 4.14938i −0.355371 + 0.205173i −0.667048 0.745015i \(-0.732443\pi\)
0.311677 + 0.950188i \(0.399109\pi\)
\(410\) 1.41742 0.818350i 0.0700016 0.0404154i
\(411\) 33.3658i 1.64581i
\(412\) −4.10436 7.10895i −0.202207 0.350233i
\(413\) 0 0
\(414\) 3.00000 + 1.73205i 0.147442 + 0.0851257i
\(415\) 3.20871 0.157509
\(416\) 12.3131 11.8483i 0.603698 0.580909i
\(417\) 10.5826 0.518231
\(418\) 2.12614 + 1.22753i 0.103993 + 0.0600402i
\(419\) −0.873864 + 1.51358i −0.0426910 + 0.0739430i −0.886581 0.462573i \(-0.846926\pi\)
0.843890 + 0.536516i \(0.180260\pi\)
\(420\) 0 0
\(421\) 4.18710i 0.204067i 0.994781 + 0.102033i \(0.0325349\pi\)
−0.994781 + 0.102033i \(0.967465\pi\)
\(422\) 4.18693 2.41733i 0.203817 0.117674i
\(423\) −39.7259 + 22.9358i −1.93154 + 1.11518i
\(424\) 10.6784i 0.518587i
\(425\) −7.18693 12.4481i −0.348617 0.603823i
\(426\) 2.79129 4.83465i 0.135238 0.234240i
\(427\) 0 0
\(428\) −9.33030 −0.450997
\(429\) 28.4347 27.3613i 1.37284 1.32101i
\(430\) −1.95644 −0.0943479
\(431\) 30.0172 + 17.3305i 1.44588 + 0.834779i 0.998232 0.0594316i \(-0.0189288\pi\)
0.447647 + 0.894210i \(0.352262\pi\)
\(432\) −6.97822 + 12.0866i −0.335740 + 0.581518i
\(433\) −16.2477 28.1419i −0.780816 1.35241i −0.931467 0.363826i \(-0.881470\pi\)
0.150651 0.988587i \(-0.451863\pi\)
\(434\) 0 0
\(435\) −7.50000 + 4.33013i −0.359597 + 0.207614i
\(436\) −12.3131 + 7.10895i −0.589689 + 0.340457i
\(437\) 2.16900i 0.103757i
\(438\) −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
\(443\) −15.1652 −0.720518 −0.360259 0.932852i \(-0.617312\pi\)
−0.360259 + 0.932852i \(0.617312\pi\)
\(444\) 30.0000 + 17.3205i 1.42374 + 0.821995i
\(445\) 3.68693 6.38595i 0.174777 0.302723i
\(446\) −4.33485 7.50818i −0.205261 0.355523i
\(447\) 1.27520i 0.0603149i
\(448\) 0 0
\(449\) −21.7913 + 12.5812i −1.02839 + 0.593744i −0.916524 0.399979i \(-0.869017\pi\)
−0.111870 + 0.993723i \(0.535684\pi\)
\(450\) 10.4877i 0.494393i
\(451\) −15.3739 26.6283i −0.723927 1.25388i
\(452\) −9.47822 + 16.4168i −0.445818 + 0.772179i
\(453\) 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 0.884833 0.465909i \(-0.154273\pi\)
0.0389271 + 0.999242i \(0.487606\pi\)
\(458\) −1.58258 + 2.74110i −0.0739489 + 0.128083i
\(459\) −7.50000 12.9904i −0.350070 0.606339i
\(460\) 1.29510i 0.0603844i
\(461\) −4.02178 + 2.32198i −0.187313 + 0.108145i −0.590724 0.806874i \(-0.701158\pi\)
0.403411 + 0.915019i \(0.367824\pi\)
\(462\) 0 0
\(463\) 7.93725i 0.368875i 0.982844 + 0.184438i \(0.0590464\pi\)
−0.982844 + 0.184438i \(0.940954\pi\)
\(464\) 9.47822 + 16.4168i 0.440015 + 0.762129i
\(465\) 5.52178 9.56400i 0.256066 0.443520i
\(466\) −6.31307 3.64485i −0.292447 0.168844i
\(467\) −30.1652 −1.39588 −0.697938 0.716158i \(-0.745899\pi\)
−0.697938 + 0.716158i \(0.745899\pi\)
\(468\) −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
\(473\) 36.7545i 1.68997i
\(474\) −6.62614 + 3.82560i −0.304349 + 0.175716i
\(475\) 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
\(479\) 16.3521 + 9.44088i 0.747146 + 0.431365i 0.824662 0.565626i \(-0.191366\pi\)
−0.0775159 + 0.996991i \(0.524699\pi\)
\(480\) −6.04356 −0.275850
\(481\) 24.0000 + 6.92820i 1.09431 + 0.315899i
\(482\) −9.00000 −0.409939
\(483\) 0 0
\(484\) 3.91742 6.78518i 0.178065 0.308417i
\(485\) −1.66515 2.88413i −0.0756106 0.130961i
\(486\) 7.38505i 0.334993i
\(487\) 25.4347 14.6847i 1.15255 0.665428i 0.203046 0.979169i \(-0.434916\pi\)
0.949508 + 0.313742i \(0.101583\pi\)
\(488\) −22.1216 + 12.7719i −1.00140 + 0.578157i
\(489\) 19.3386i 0.874522i
\(490\) 0 0
\(491\) 2.06080 3.56940i 0.0930024 0.161085i −0.815771 0.578375i \(-0.803687\pi\)
0.908773 + 0.417291i \(0.137020\pi\)
\(492\) 33.9564 + 19.6048i 1.53087 + 0.883851i
\(493\) −20.3739 −0.917593
\(494\) −2.19148 + 0.542250i −0.0985992 + 0.0243970i
\(495\) −8.58258 −0.385758
\(496\) −20.9347 12.0866i −0.939994 0.542706i
\(497\) 0 0
\(498\) −4.47822 7.75650i −0.200674 0.347577i
\(499\) 18.4050i 0.823921i 0.911202 + 0.411961i \(0.135156\pi\)
−0.911202 + 0.411961i \(0.864844\pi\)
\(500\) 6.93920 4.00635i 0.310331 0.179169i
\(501\) −35.4737 + 20.4807i −1.58485 + 0.915012i
\(502\) 1.29510i 0.0578032i
\(503\) 9.56080 + 16.5598i 0.426295 + 0.738364i 0.996540 0.0831100i \(-0.0264853\pi\)
−0.570246 + 0.821474i \(0.693152\pi\)
\(504\) 0 0
\(505\) −2.06080 1.18980i −0.0917042 0.0529454i
\(506\) 2.83485 0.126024
\(507\) −1.39564 + 36.2599i −0.0619827 + 1.61036i
\(508\) 12.4610 0.552867
\(509\) 13.0390 + 7.52808i 0.577944 + 0.333676i 0.760316 0.649553i \(-0.225044\pi\)
−0.182372 + 0.983230i \(0.558377\pi\)
\(510\) 0.873864 1.51358i 0.0386953 0.0670223i
\(511\) 0 0
\(512\) 22.8981i 1.01196i
\(513\) 5.93466 3.42638i 0.262022 0.151278i
\(514\) −1.99545 + 1.15208i −0.0880157 + 0.0508159i
\(515\) 2.09355i 0.0922529i
\(516\) −23.4347 40.5900i −1.03165 1.78688i
\(517\) −18.7695 + 32.5097i −0.825482 + 1.42978i
\(518\) 0 0
\(519\) 55.1216 2.41957
\(520\) −2.76951 + 0.685275i −0.121451 + 0.0300513i
\(521\) −16.4174 −0.719260 −0.359630 0.933095i \(-0.617097\pi\)
−0.359630 + 0.933095i \(0.617097\pi\)
\(522\) 12.8739 + 7.43273i 0.563474 + 0.325322i
\(523\) 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
\(527\) 22.5000 12.9904i 0.980115 0.565870i
\(528\) 30.5493i 1.32949i
\(529\) 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
\(534\) −20.5826 −0.890695
\(535\) 2.06080 + 1.18980i 0.0890960 + 0.0514396i
\(536\) 3.87386 6.70973i 0.167325 0.289816i
\(537\) 12.5608 + 21.7559i 0.542038 + 0.938838i
\(538\) 7.21425i 0.311029i
\(539\) 0 0
\(540\) 3.54356 2.04588i 0.152491 0.0880405i
\(541\) 6.28065i 0.270026i 0.990844 + 0.135013i \(0.0431077\pi\)
−0.990844 + 0.135013i \(0.956892\pi\)
\(542\) −2.93466 5.08298i −0.126054 0.218333i
\(543\) 12.7913 22.1552i 0.548927 0.950769i
\(544\) −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
\(549\) 35.3303 61.1939i 1.50786 2.61169i
\(550\) 4.29129 + 7.43273i 0.182981 + 0.316933i
\(551\) 9.30780i 0.396526i
\(552\) −6.62614 + 3.82560i −0.282027 + 0.162828i
\(553\) 0 0
\(554\) 5.36695i 0.228020i
\(555\) −4.41742 7.65120i −0.187509 0.324775i
\(556\) −3.39564 + 5.88143i −0.144007 + 0.249428i
\(557\) −28.5998 16.5121i −1.21181 0.699640i −0.248659 0.968591i \(-0.579990\pi\)
−0.963154 + 0.268951i \(0.913323\pi\)
\(558\) −18.9564 −0.802490
\(559\) −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 \(0.555790\pi\)
\(564\) 47.8698i 2.01568i
\(565\) 4.18693 2.41733i 0.176146 0.101698i
\(566\) −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 \(0.280842\pi\)
\(570\) 0.691478 + 0.399225i 0.0289628 + 0.0167217i
\(571\) −2.04356 −0.0855204 −0.0427602 0.999085i \(-0.513615\pi\)
−0.0427602 + 0.999085i \(0.513615\pi\)
\(572\) 6.08258 + 24.5824i 0.254325 + 1.02784i
\(573\) −40.1216 −1.67610
\(574\) 0 0
\(575\) 3.79129 6.56670i 0.158108 0.273850i
\(576\) −8.18693 14.1802i −0.341122 0.590841i
\(577\) 35.6501i 1.48413i −0.670327 0.742066i \(-0.733846\pi\)
0.670327 0.742066i \(-0.266154\pi\)
\(578\) −3.16515 + 1.82740i −0.131653 + 0.0760099i
\(579\) −46.7477 + 26.9898i −1.94277 + 1.12166i
\(580\) 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
\(584\) 6.00000 0.248282
\(585\) 5.68693 5.47225i 0.235126 0.226250i
\(586\) 1.16515 0.0481320
\(587\) 8.22595 + 4.74925i 0.339521 + 0.196023i 0.660060 0.751213i \(-0.270531\pi\)
−0.320539 + 0.947235i \(0.603864\pi\)
\(588\) 0 0
\(589\) 5.93466 + 10.2791i 0.244533 + 0.423544i
\(590\) 2.57030i 0.105818i
\(591\) −5.52178 + 3.18800i −0.227136 + 0.131137i
\(592\) −16.7477 + 9.66930i −0.688327 + 0.397406i
\(593\) 6.37600i 0.261831i −0.991394 0.130916i \(-0.958208\pi\)
0.991394 0.130916i \(-0.0417917\pi\)
\(594\) 4.47822 + 7.75650i 0.183744 + 0.318253i
\(595\) 0 0
\(596\) 0.708712 + 0.409175i 0.0290300 + 0.0167605i
\(597\) −30.7042 −1.25664
\(598\) −1.87841 + 1.80750i −0.0768139 + 0.0739142i
\(599\) −6.62614 −0.270737 −0.135368 0.990795i \(-0.543222\pi\)
−0.135368 + 0.990795i \(0.543222\pi\)
\(600\) −20.0608 11.5821i −0.818979 0.472837i
\(601\) −6.18693 + 10.7161i −0.252370 + 0.437118i −0.964178 0.265256i \(-0.914543\pi\)
0.711808 + 0.702374i \(0.247877\pi\)
\(602\) 0 0
\(603\) 21.4322i 0.872785i
\(604\) −18.8085 + 10.8591i −0.765308 + 0.441851i
\(605\) −1.73049 + 0.999100i −0.0703545 + 0.0406192i
\(606\) 6.64215i 0.269819i
\(607\) −9.87386 17.1020i −0.400768 0.694150i 0.593051 0.805165i \(-0.297923\pi\)
−0.993819 + 0.111015i \(0.964590\pi\)
\(608\) 3.24773 5.62523i 0.131713 0.228133i
\(609\) 0 0
\(610\) 3.07803 0.124626
\(611\) −8.29129 33.5088i −0.335430 1.35562i
\(612\) 25.7477 1.04079
\(613\) −15.8085 9.12705i −0.638500 0.368638i 0.145536 0.989353i \(-0.453509\pi\)
−0.784037 + 0.620715i \(0.786843\pi\)
\(614\) −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 −0.769259 0.638937i \(-0.779374\pi\)
0.168706 + 0.985666i \(0.446041\pi\)
\(618\) 5.06080 2.92185i 0.203575 0.117534i
\(619\) 19.3386i 0.777284i −0.921389 0.388642i \(-0.872944\pi\)
0.921389 0.388642i \(-0.127056\pi\)
\(620\) 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
\(625\) 21.9129 0.876515
\(626\) −2.66970 1.54135i −0.106703 0.0616048i
\(627\) 7.50000 12.9904i 0.299521 0.518786i
\(628\) 0.856629 + 1.48372i 0.0341832 + 0.0592071i
\(629\) 20.7846i 0.828737i
\(630\) 0 0
\(631\) 23.9347 13.8187i 0.952824 0.550113i 0.0588668 0.998266i \(-0.481251\pi\)
0.893957 + 0.448153i \(0.147918\pi\)
\(632\) 10.3923i 0.413384i
\(633\) −14.7695 25.5815i −0.587035 1.01677i
\(634\) −4.23049 + 7.32743i −0.168014 + 0.291009i
\(635\) −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
\(640\) 2.52178 4.36785i 0.0996821 0.172654i
\(641\) −14.6869 25.4385i −0.580099 1.00476i −0.995467 0.0951074i \(-0.969681\pi\)
0.415368 0.909653i \(-0.363653\pi\)
\(642\) 6.64215i 0.262145i
\(643\) −39.2477 + 22.6597i −1.54778 + 0.893611i −0.549468 + 0.835515i \(0.685170\pi\)
−0.998311 + 0.0580962i \(0.981497\pi\)
\(644\) 0 0
\(645\) 11.9536i 0.470671i
\(646\) 0.939205 + 1.62675i 0.0369525 + 0.0640036i
\(647\) 17.5390 30.3785i 0.689530 1.19430i −0.282460 0.959279i \(-0.591151\pi\)
0.971990 0.235022i \(-0.0755161\pi\)
\(648\) 0.626136 + 0.361500i 0.0245970 + 0.0142011i
\(649\) −48.2867 −1.89542
\(650\) −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
\(655\) 7.93725i 0.310134i
\(656\) −18.9564 + 10.9445i −0.740125 + 0.427311i
\(657\) −14.3739 + 8.29875i −0.560778 + 0.323765i
\(658\) 0 0
\(659\) −3.00000 5.19615i −0.116863 0.202413i 0.801660 0.597781i \(-0.203951\pi\)
−0.918523 + 0.395367i \(0.870617\pi\)
\(660\) 4.47822 7.75650i 0.174314 0.301922i
\(661\) 43.7477 + 25.2578i 1.70159 + 0.982413i 0.944155 + 0.329502i \(0.106881\pi\)
0.757434 + 0.652911i \(0.226453\pi\)
\(662\) −11.3739 −0.442058
\(663\) 29.3085 7.25198i 1.13825 0.281644i
\(664\) 12.1652 0.472099
\(665\) 0 0
\(666\) −7.58258 + 13.1334i −0.293819 + 0.508909i
\(667\) −5.37386 9.30780i −0.208077 0.360400i
\(668\) 26.2867i 1.01706i
\(669\) −45.8739 + 26.4853i −1.77359 + 1.02398i
\(670\) −0.808522 + 0.466801i −0.0312359 + 0.0180341i
\(671\) 57.8251i 2.23231i
\(672\) 0 0
\(673\) −13.2477 + 22.9457i −0.510662 + 0.884493i 0.489261 + 0.872137i \(0.337266\pi\)
−0.999924 + 0.0123559i \(0.996067\pi\)
\(674\) −3.93920 2.27430i −0.151732 0.0876028i
\(675\) 23.9564 0.922084
\(676\) −19.7042 12.4104i −0.757853 0.477323i
\(677\) 29.2087 1.12258 0.561291 0.827619i \(-0.310305\pi\)
0.561291 + 0.827619i \(0.310305\pi\)
\(678\) −11.6869 6.74745i −0.448834 0.259134i
\(679\) 0 0
\(680\) 1.18693 + 2.05583i 0.0455168 + 0.0788373i
\(681\) 24.7056i 0.946719i
\(682\) −13.4347 + 7.75650i −0.514440 + 0.297012i
\(683\) 26.2913 15.1793i 1.00601 0.580819i 0.0959878 0.995383i \(-0.469399\pi\)
0.910020 + 0.414563i \(0.136066\pi\)
\(684\) 11.7629i 0.449764i
\(685\) 2.73049 + 4.72935i 0.104327 + 0.180699i
\(686\) 0 0
\(687\) 16.7477 + 9.66930i 0.638966 + 0.368907i
\(688\) 26.1652 0.997537
\(689\) 21.5780 5.33918i 0.822057 0.203406i
\(690\) 0.921970 0.0350988
\(691\) 8.93466 + 5.15843i 0.339890 + 0.196236i 0.660224 0.751069i \(-0.270462\pi\)
−0.320333 + 0.947305i \(0.603795\pi\)
\(692\) −17.6869 + 30.6347i −0.672356 + 1.16456i
\(693\) 0 0
\(694\) 6.20520i 0.235546i
\(695\) 1.50000 0.866025i 0.0568982 0.0328502i
\(696\) −28.4347 + 16.4168i −1.07781 + 0.622276i
\(697\) 23.5257i 0.891100i
\(698\) −4.81307 8.33648i −0.182177 0.315540i
\(699\) −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 \(0.584627\pi\)
\(702\) −7.91288 2.28425i −0.298652 0.0862135i
\(703\) 9.49545 0.358128
\(704\) −11.6044 6.69978i −0.437356 0.252507i
\(705\) −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
\(709\) −13.1869 + 7.61348i −0.495246 + 0.285930i −0.726748 0.686904i \(-0.758969\pi\)
0.231502 + 0.972834i \(0.425636\pi\)
\(710\) 0.913701i 0.0342906i
\(711\) 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
\(716\) −16.1216 −0.602492
\(717\) −31.9782 18.4626i −1.19425 0.689500i
\(718\) −0.126136 + 0.218475i −0.00470737 + 0.00815341i
\(719\) 12.0826 + 20.9276i 0.450604 + 0.780469i 0.998424 0.0561274i \(-0.0178753\pi\)
−0.547820 + 0.836597i \(0.684542\pi\)
\(720\) 6.10985i 0.227701i
\(721\) 0 0
\(722\) 6.77405 3.91100i 0.252104 0.145552i
\(723\) 54.9887i 2.04505i
\(724\) 8.20871 + 14.2179i 0.305074 + 0.528404i
\(725\) 16.2695 28.1796i 0.604234 1.04656i
\(726\) 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
\(731\) −14.0608 + 24.3540i −0.520057 + 0.900766i
\(732\) 36.8693 + 63.8595i 1.36273 + 2.36032i
\(733\) 16.9590i 0.626395i −0.949688 0.313198i \(-0.898600\pi\)
0.949688 0.313198i \(-0.101400\pi\)
\(734\) 7.12159 4.11165i 0.262863 0.151764i
\(735\) 0 0
\(736\) 7.50030i 0.276465i
\(737\) 8.76951 + 15.1892i 0.323029 + 0.559503i
\(738\) −8.58258 + 14.8655i −0.315929 + 0.547205i
\(739\) 16.7477 + 9.66930i 0.616075 + 0.355691i 0.775339 0.631545i \(-0.217579\pi\)
−0.159264 + 0.987236i \(0.550912\pi\)
\(740\) 5.66970 0.208422
\(741\) 3.31307 + 13.3896i 0.121709 + 0.491879i
\(742\) 0 0
\(743\) 29.8521 + 17.2351i 1.09517 + 0.632295i 0.934947 0.354787i \(-0.115446\pi\)
0.160219 + 0.987081i \(0.448780\pi\)
\(744\) 20.9347 36.2599i 0.767502 1.32935i
\(745\) −0.104356 0.180750i −0.00382331 0.00662217i
\(746\) 14.7146i 0.538738i
\(747\) −29.1434 + 16.8259i −1.06630 + 0.615629i
\(748\) 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 \(0.309312\pi\)
\(752\) 23.1434 + 13.3618i 0.843952 + 0.487256i
\(753\) 7.91288 0.288361
\(754\) −8.06080 + 7.75650i −0.293557 + 0.282475i
\(755\) 5.53901 0.201585
\(756\) 0 0
\(757\) −3.00000 + 5.19615i −0.109037 + 0.188857i −0.915380 0.402590i \(-0.868110\pi\)
0.806343 + 0.591448i \(0.201443\pi\)
\(758\) 6.47822 + 11.2206i 0.235300 + 0.407551i
\(759\) 17.3205i 0.628695i
\(760\) −0.939205 + 0.542250i −0.0340685 + 0.0196695i
\(761\) −11.2259 + 6.48130i −0.406940 + 0.234947i −0.689474 0.724310i \(-0.742158\pi\)
0.282534 + 0.959257i \(0.408825\pi\)
\(762\) 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
\(766\) 0.582576 0.0210493
\(767\) 31.9955 30.7876i 1.15529 1.11168i
\(768\) 5.00000 0.180422
\(769\) 8.12614 + 4.69163i 0.293036 + 0.169184i 0.639310 0.768949i \(-0.279220\pi\)
−0.346274 + 0.938133i \(0.612553\pi\)
\(770\) 0 0
\(771\) 7.03901 + 12.1919i 0.253504 + 0.439082i
\(772\) 34.6410i 1.24676i
\(773\) −16.8303 + 9.71698i −0.605344 + 0.349495i −0.771141 0.636664i \(-0.780314\pi\)
0.165797 + 0.986160i \(0.446980\pi\)
\(774\) 17.7695 10.2592i 0.638712 0.368760i
\(775\) 41.4938i 1.49050i
\(776\) −6.31307 10.9346i −0.226626 0.392528i
\(777\) 0 0