Properties

Label 637.2.k.d.569.1
Level $637$
Weight $2$
Character 637.569
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.k (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 569.1
Root \(1.39564 - 0.228425i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.d.459.2

$q$-expansion

\(f(q)\) \(=\) \(q-0.456850i q^{2} +(-1.39564 + 2.41733i) q^{3} +1.79129 q^{4} +(0.395644 + 0.228425i) q^{5} +(1.10436 + 0.637600i) q^{6} -1.73205i q^{8} +(-2.39564 - 4.14938i) q^{9} +O(q^{10})\) \(q-0.456850i q^{2} +(-1.39564 + 2.41733i) q^{3} +1.79129 q^{4} +(0.395644 + 0.228425i) 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} +(-2.50000 + 4.33013i) q^{12} +(3.50000 + 0.866025i) q^{13} +(-1.10436 + 0.637600i) q^{15} +2.79129 q^{16} +3.00000 q^{17} +(-1.89564 + 1.09445i) q^{18} +(-1.18693 + 0.685275i) q^{19} +(0.708712 + 0.409175i) q^{20} +(0.895644 - 1.55130i) q^{22} -1.58258 q^{23} +(4.18693 + 2.41733i) q^{24} +(-2.39564 - 4.14938i) q^{25} +(0.395644 - 1.59898i) q^{26} +5.00000 q^{27} +(3.39564 + 5.88143i) q^{29} +(0.291288 + 0.504525i) q^{30} +(-7.50000 + 4.33013i) q^{31} -4.73930i q^{32} +(-9.47822 + 5.47225i) q^{33} -1.37055i q^{34} +(-4.29129 - 7.43273i) q^{36} +6.92820i q^{37} +(0.313068 + 0.542250i) q^{38} +(-6.97822 + 7.25198i) 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} -2.18890i q^{45} +0.723000i 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} +(6.26951 + 1.55130i) q^{52} +(-3.08258 - 5.33918i) q^{53} -2.28425i q^{54} +(0.895644 + 1.55130i) q^{55} -3.82560i q^{57} +(2.68693 - 1.55130i) q^{58} -12.3151i q^{59} +(-1.97822 + 1.14213i) q^{60} +(7.37386 + 12.7719i) q^{61} +(1.97822 + 3.42638i) q^{62} +3.41742 q^{64} +(1.18693 + 1.14213i) q^{65} +(2.50000 + 4.33013i) q^{66} +(3.87386 + 2.23658i) q^{67} +5.37386 q^{68} +(2.20871 - 3.82560i) q^{69} +(3.79129 + 2.18890i) q^{71} +(-7.18693 + 4.14938i) q^{72} +(3.00000 - 1.73205i) q^{73} +3.16515 q^{74} +13.3739 q^{75} +(-2.12614 + 1.22753i) q^{76} +(3.31307 + 3.18800i) q^{78} +(3.00000 - 5.19615i) 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} +(3.70871 + 2.14123i) q^{86} -18.9564 q^{87} +(3.39564 - 5.88143i) q^{88} -16.1407i q^{89} -1.00000 q^{90} -2.83485 q^{92} -24.1733i q^{93} +(-2.18693 + 3.78788i) q^{94} -0.626136 q^{95} +(11.4564 + 6.61438i) q^{96} +(-6.31307 - 3.64485i) q^{97} -18.7864i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{3} - 2 q^{4} - 3 q^{5} + 9 q^{6} - 5 q^{9} + 5 q^{10} + 9 q^{11} - 10 q^{12} + 14 q^{13} - 9 q^{15} + 2 q^{16} + 12 q^{17} - 3 q^{18} + 9 q^{19} + 12 q^{20} - q^{22} + 12 q^{23} + 3 q^{24} - 5 q^{25} - 3 q^{26} + 20 q^{27} + 9 q^{29} - 8 q^{30} - 30 q^{31} - 15 q^{33} - 8 q^{36} + 15 q^{38} - 5 q^{39} - 3 q^{40} + 18 q^{41} - 5 q^{43} + 6 q^{44} - 24 q^{47} - 11 q^{48} - 3 q^{50} - 3 q^{51} - 7 q^{52} + 6 q^{53} - q^{55} - 3 q^{58} + 15 q^{60} + 2 q^{61} - 15 q^{62} + 32 q^{64} - 9 q^{65} + 10 q^{66} - 12 q^{67} - 6 q^{68} + 18 q^{69} + 6 q^{71} - 15 q^{72} + 12 q^{73} - 24 q^{74} + 26 q^{75} - 36 q^{76} + 27 q^{78} + 12 q^{79} + 9 q^{80} + 10 q^{81} + 2 q^{82} - 9 q^{85} + 24 q^{86} - 30 q^{87} + 9 q^{88} - 4 q^{90} - 48 q^{92} + 5 q^{94} - 30 q^{95} - 39 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.456850i 0.323042i −0.986869 0.161521i \(-0.948360\pi\)
0.986869 0.161521i \(-0.0516399\pi\)
\(3\) −1.39564 + 2.41733i −0.805775 + 1.39564i 0.109991 + 0.993933i \(0.464918\pi\)
−0.915766 + 0.401711i \(0.868416\pi\)
\(4\) 1.79129 0.895644
\(5\) 0.395644 + 0.228425i 0.176937 + 0.102155i 0.585853 0.810417i \(-0.300760\pi\)
−0.408916 + 0.912572i \(0.634093\pi\)
\(6\) 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 0.915210 0.402978i \(-0.132025\pi\)
0.108616 + 0.994084i \(0.465358\pi\)
\(12\) −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
\(16\) 2.79129 0.697822
\(17\) 3.00000 0.727607 0.363803 0.931476i \(-0.381478\pi\)
0.363803 + 0.931476i \(0.381478\pi\)
\(18\) −1.89564 + 1.09445i −0.446808 + 0.257964i
\(19\) −1.18693 + 0.685275i −0.272301 + 0.157213i −0.629933 0.776650i \(-0.716918\pi\)
0.357632 + 0.933863i \(0.383584\pi\)
\(20\) 0.708712 + 0.409175i 0.158473 + 0.0914943i
\(21\) 0 0
\(22\) 0.895644 1.55130i 0.190952 0.330738i
\(23\) −1.58258 −0.329990 −0.164995 0.986294i \(-0.552761\pi\)
−0.164995 + 0.986294i \(0.552761\pi\)
\(24\) 4.18693 + 2.41733i 0.854654 + 0.493435i
\(25\) −2.39564 4.14938i −0.479129 0.829875i
\(26\) 0.395644 1.59898i 0.0775922 0.313585i
\(27\) 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 \(0.616161\pi\)
\(30\) 0.291288 + 0.504525i 0.0531816 + 0.0921133i
\(31\) −7.50000 + 4.33013i −1.34704 + 0.777714i −0.987829 0.155543i \(-0.950287\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 4.73930i 0.837798i
\(33\) −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
\(37\) 6.92820i 1.13899i 0.821995 + 0.569495i \(0.192861\pi\)
−0.821995 + 0.569495i \(0.807139\pi\)
\(38\) 0.313068 + 0.542250i 0.0507864 + 0.0879646i
\(39\) −6.97822 + 7.25198i −1.11741 + 1.16125i
\(40\) 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
\(45\) 2.18890i 0.326302i
\(46\) 0.723000i 0.106601i
\(47\) −8.29129 4.78698i −1.20941 0.698252i −0.246778 0.969072i \(-0.579372\pi\)
−0.962630 + 0.270820i \(0.912705\pi\)
\(48\) −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
\(52\) 6.26951 + 1.55130i 0.869424 + 0.215127i
\(53\) −3.08258 5.33918i −0.423424 0.733392i 0.572848 0.819662i \(-0.305839\pi\)
−0.996272 + 0.0862695i \(0.972505\pi\)
\(54\) 2.28425i 0.310847i
\(55\) 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
\(59\) 12.3151i 1.60328i −0.597805 0.801642i \(-0.703960\pi\)
0.597805 0.801642i \(-0.296040\pi\)
\(60\) −1.97822 + 1.14213i −0.255387 + 0.147448i
\(61\) 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
\(65\) 1.18693 + 1.14213i 0.147221 + 0.141663i
\(66\) 2.50000 + 4.33013i 0.307729 + 0.533002i
\(67\) 3.87386 + 2.23658i 0.473268 + 0.273241i 0.717607 0.696449i \(-0.245238\pi\)
−0.244339 + 0.969690i \(0.578571\pi\)
\(68\) 5.37386 0.651677
\(69\) 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 \(0.583018\pi\)
\(72\) −7.18693 + 4.14938i −0.846988 + 0.489009i
\(73\) 3.00000 1.73205i 0.351123 0.202721i −0.314057 0.949404i \(-0.601688\pi\)
0.665180 + 0.746683i \(0.268355\pi\)
\(74\) 3.16515 0.367941
\(75\) 13.3739 1.54428
\(76\) −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 −0.646440 0.762964i \(-0.723743\pi\)
0.983967 + 0.178352i \(0.0570765\pi\)
\(80\) 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 \(0.125960\pi\)
−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
\(87\) −18.9564 −2.03234
\(88\) 3.39564 5.88143i 0.361977 0.626962i
\(89\) 16.1407i 1.71091i −0.517880 0.855453i \(-0.673279\pi\)
0.517880 0.855453i \(-0.326721\pi\)
\(90\) −1.00000 −0.105409
\(91\) 0 0
\(92\) −2.83485 −0.295553
\(93\) 24.1733i 2.50665i
\(94\) −2.18693 + 3.78788i −0.225565 + 0.390690i
\(95\) −0.626136 −0.0642402
\(96\) 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
\(100\) −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
\(103\) −2.29129 + 3.96863i −0.225767 + 0.391040i −0.956549 0.291570i \(-0.905822\pi\)
0.730782 + 0.682611i \(0.239156\pi\)
\(104\) 1.50000 6.06218i 0.147087 0.594445i
\(105\) 0 0
\(106\) −2.43920 + 1.40828i −0.236917 + 0.136784i
\(107\) −5.20871 −0.503545 −0.251773 0.967786i \(-0.581014\pi\)
−0.251773 + 0.967786i \(0.581014\pi\)
\(108\) 8.95644 0.861834
\(109\) 6.87386 3.96863i 0.658397 0.380126i −0.133269 0.991080i \(-0.542547\pi\)
0.791666 + 0.610954i \(0.209214\pi\)
\(110\) 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 −0.999997 0.00258173i \(-0.999178\pi\)
0.502234 + 0.864732i \(0.332512\pi\)
\(114\) −1.74773 −0.163690
\(115\) −0.626136 0.361500i −0.0583875 0.0337101i
\(116\) 6.08258 + 10.5353i 0.564753 + 0.978181i
\(117\) −4.79129 16.5975i −0.442955 1.53444i
\(118\) −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
\(122\) 5.83485 3.36875i 0.528262 0.304992i
\(123\) 21.8890i 1.97367i
\(124\) −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 0.669423 0.742881i \(-0.266541\pi\)
−0.978066 + 0.208297i \(0.933208\pi\)
\(128\) 11.0399i 0.975795i
\(129\) −13.0826 22.6597i −1.15186 1.99507i
\(130\) 0.521780 0.542250i 0.0457632 0.0475585i
\(131\) 8.68693 15.0462i 0.758981 1.31459i −0.184390 0.982853i \(-0.559031\pi\)
0.943371 0.331740i \(-0.107636\pi\)
\(132\) −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
\(136\) 5.19615i 0.445566i
\(137\) 11.9536i 1.02126i −0.859800 0.510631i \(-0.829412\pi\)
0.859800 0.510631i \(-0.170588\pi\)
\(138\) −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
\(143\) 10.1869 + 9.80238i 0.851874 + 0.819716i
\(144\) −6.68693 11.5821i −0.557244 0.965175i
\(145\) 3.10260i 0.257657i
\(146\) −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 −0.483706 0.875230i \(-0.660710\pi\)
0.516119 + 0.856517i \(0.327376\pi\)
\(150\) 6.10985i 0.498867i
\(151\) 10.5000 6.06218i 0.854478 0.493333i −0.00768132 0.999970i \(-0.502445\pi\)
0.862159 + 0.506637i \(0.169112\pi\)
\(152\) 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
\(156\) −12.5000 + 12.9904i −1.00080 + 1.04006i
\(157\) 0.478220 + 0.828301i 0.0381661 + 0.0661056i 0.884477 0.466583i \(-0.154515\pi\)
−0.846311 + 0.532689i \(0.821182\pi\)
\(158\) −2.37386 1.37055i −0.188854 0.109035i
\(159\) 17.2087 1.36474
\(160\) 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 −0.716221 0.697873i \(-0.754130\pi\)
0.246265 + 0.969202i \(0.420797\pi\)
\(164\) 12.1652 7.02355i 0.949939 0.548447i
\(165\) −5.00000 −0.389249
\(166\) 3.20871 0.249044
\(167\) 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
\(171\) 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
\(177\) 29.7695 + 17.1874i 2.23761 + 1.29189i
\(178\) −7.37386 −0.552694
\(179\) 4.50000 7.79423i 0.336346 0.582568i −0.647397 0.762153i \(-0.724142\pi\)
0.983742 + 0.179585i \(0.0574756\pi\)
\(180\) 3.92095i 0.292250i
\(181\) −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
\(184\) 2.74110i 0.202077i
\(185\) −1.58258 + 2.74110i −0.116353 + 0.201530i
\(186\) −11.0436 −0.809753
\(187\) 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
\(191\) 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 −0.243749 0.969838i \(-0.578377\pi\)
−0.961779 + 0.273827i \(0.911711\pi\)
\(194\) −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 \(0.307403\pi\)
\(198\) −8.58258 −0.609937
\(199\) −11.0000 −0.779769 −0.389885 0.920864i \(-0.627485\pi\)
−0.389885 + 0.920864i \(0.627485\pi\)
\(200\) −7.18693 + 4.14938i −0.508193 + 0.293405i
\(201\) −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
\(205\) 3.58258 0.250218
\(206\) 1.81307 + 1.04678i 0.126322 + 0.0729323i
\(207\) 3.79129 + 6.56670i 0.263513 + 0.456417i
\(208\) 9.76951 + 2.41733i 0.677393 + 0.167611i
\(209\) −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 \(0.952014\pi\)
\(212\) −5.52178 9.56400i −0.379237 0.656859i
\(213\) −10.5826 + 6.10985i −0.725106 + 0.418640i
\(214\) 2.37960i 0.162666i
\(215\) −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
\(219\) 9.66930i 0.653391i
\(220\) 1.60436 + 2.77883i 0.108166 + 0.187348i
\(221\) 10.5000 + 2.59808i 0.706306 + 0.174766i
\(222\) −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
\(227\) 8.85095i 0.587458i 0.955889 + 0.293729i \(0.0948964\pi\)
−0.955889 + 0.293729i \(0.905104\pi\)
\(228\) 6.85275i 0.453835i
\(229\) −6.00000 3.46410i −0.396491 0.228914i 0.288478 0.957487i \(-0.406851\pi\)
−0.684969 + 0.728572i \(0.740184\pi\)
\(230\) −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 0.476981 + 0.878913i \(0.341731\pi\)
−0.999652 + 0.0263786i \(0.991602\pi\)
\(234\) −7.58258 + 2.18890i −0.495688 + 0.143093i
\(235\) −2.18693 3.78788i −0.142660 0.247094i
\(236\) 22.0598i 1.43597i
\(237\) 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 \(-0.140728\pi\)
\(240\) −3.08258 + 1.77973i −0.198979 + 0.114881i
\(241\) 19.7001i 1.26900i −0.772925 0.634498i \(-0.781207\pi\)
0.772925 0.634498i \(-0.218793\pi\)
\(242\) 1.73049 0.999100i 0.111240 0.0642246i
\(243\) 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
\(247\) −4.74773 + 1.37055i −0.302091 + 0.0872061i
\(248\) 7.50000 + 12.9904i 0.476250 + 0.824890i
\(249\) −16.9782 9.80238i −1.07595 0.621201i
\(250\) −2.04356 −0.129246
\(251\) −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
\(254\) −2.75227 + 1.58903i −0.172693 + 0.0997043i
\(255\) −3.31307 + 1.91280i −0.207472 + 0.119784i
\(256\) 1.79129 0.111955
\(257\) −5.04356 −0.314609 −0.157304 0.987550i \(-0.550280\pi\)
−0.157304 + 0.987550i \(0.550280\pi\)
\(258\) −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
\(262\) −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
\(268\) 6.93920 + 4.00635i 0.423879 + 0.244727i
\(269\) 15.7913 0.962812 0.481406 0.876498i \(-0.340126\pi\)
0.481406 + 0.876498i \(0.340126\pi\)
\(270\) 0.521780 0.903750i 0.0317545 0.0550005i
\(271\) 12.8474i 0.780421i 0.920726 + 0.390211i \(0.127598\pi\)
−0.920726 + 0.390211i \(0.872402\pi\)
\(272\) 8.37386 0.507740
\(273\) 0 0
\(274\) −5.46099 −0.329910
\(275\) 18.7864i 1.13286i
\(276\) 3.95644 6.85275i 0.238150 0.412487i
\(277\) 11.7477 0.705853 0.352926 0.935651i \(-0.385187\pi\)
0.352926 + 0.935651i \(0.385187\pi\)
\(278\) 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 \(-0.367064\pi\)
\(282\) −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
\(285\) 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
\(289\) −8.00000 −0.470588
\(290\) 1.41742 0.0832340
\(291\) 17.6216 10.1738i 1.03300 0.596400i
\(292\) 5.37386 3.10260i 0.314482 0.181566i
\(293\) −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
\(296\) 12.0000 0.697486
\(297\) 16.9782 + 9.80238i 0.985176 + 0.568792i
\(298\) −0.104356 0.180750i −0.00604519 0.0104706i
\(299\) −5.53901 1.37055i −0.320330 0.0792610i
\(300\) 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
\(304\) −3.31307 + 1.91280i −0.190017 + 0.109707i
\(305\) 6.73750i 0.385788i
\(306\) −5.68693 + 3.28335i −0.325100 + 0.187697i
\(307\) 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
\(310\) 1.80750i 0.102659i
\(311\) 13.2695 + 22.9835i 0.752445 + 1.30327i 0.946635 + 0.322309i \(0.104459\pi\)
−0.194190 + 0.980964i \(0.562208\pi\)
\(312\) 12.5608 + 12.0866i 0.711115 + 0.684271i
\(313\) −3.37386 + 5.84370i −0.190702 + 0.330306i −0.945483 0.325671i \(-0.894410\pi\)
0.754781 + 0.655977i \(0.227743\pi\)
\(314\) 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 \(-0.507439\pi\)
−0.877473 + 0.479626i \(0.840772\pi\)
\(318\) 7.86180i 0.440868i
\(319\) 26.6283i 1.49090i
\(320\) 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
\(325\) −4.79129 16.5975i −0.265773 0.920664i
\(326\) 1.58258 + 2.74110i 0.0876508 + 0.151816i
\(327\) 22.1552i 1.22518i
\(328\) −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 −0.957186 0.289473i \(-0.906520\pi\)
−0.227902 + 0.973684i \(0.573187\pi\)
\(332\) 12.5812i 0.690483i
\(333\) 28.7477 16.5975i 1.57537 0.909538i
\(334\) −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 \(0.412586\pi\)
\(338\) 2.76951 5.25378i 0.150641 0.285768i
\(339\) −14.7695 25.5815i −0.802170 1.38940i
\(340\) 2.12614 + 1.22753i 0.115306 + 0.0665719i
\(341\) −33.9564 −1.83884
\(342\) 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
\(346\) −7.81307 + 4.51088i −0.420033 + 0.242506i
\(347\) −13.5826 −0.729151 −0.364575 0.931174i \(-0.618786\pi\)
−0.364575 + 0.931174i \(0.618786\pi\)
\(348\) −33.9564 −1.82026
\(349\) 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
\(353\) 15.7259 + 9.07938i 0.837008 + 0.483247i 0.856246 0.516568i \(-0.172791\pi\)
−0.0192383 + 0.999815i \(0.506124\pi\)
\(354\) 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
\(359\) −0.478220 0.276100i −0.0252395 0.0145720i 0.487327 0.873219i \(-0.337972\pi\)
−0.512567 + 0.858647i \(0.671305\pi\)
\(360\) −3.79129 −0.199818
\(361\) −8.56080 + 14.8277i −0.450568 + 0.780407i
\(362\) 4.18710i 0.220069i
\(363\) −12.2087 −0.640791
\(364\) 0 0
\(365\) 1.58258 0.0828358
\(366\) 18.8063i 0.983022i
\(367\) −9.00000 + 15.5885i −0.469796 + 0.813711i −0.999404 0.0345320i \(-0.989006\pi\)
0.529607 + 0.848243i \(0.322339\pi\)
\(368\) −4.41742 −0.230274
\(369\) −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
\(373\) −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
\(376\) −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 \(0.593063\pi\)
\(380\) −1.12159 −0.0575364
\(381\) 19.4174 0.994785
\(382\) 5.68693 3.28335i 0.290969 0.167991i
\(383\) 1.10436 0.637600i 0.0564300 0.0325799i −0.471520 0.881856i \(-0.656294\pi\)
0.527950 + 0.849276i \(0.322961\pi\)
\(384\) 26.6869 + 15.4077i 1.36186 + 0.786271i
\(385\) 0 0
\(386\) −4.41742 + 7.65120i −0.224841 + 0.389436i
\(387\) 44.9129 2.28305
\(388\) −11.3085 6.52898i −0.574103 0.331459i
\(389\) 0.165151 + 0.286051i 0.00837351 + 0.0145033i 0.870182 0.492731i \(-0.164001\pi\)
−0.861808 + 0.507234i \(0.830668\pi\)
\(390\) 0.582576 + 2.01810i 0.0294999 + 0.102191i
\(391\) −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
\(395\) 2.37386 1.37055i 0.119442 0.0689599i
\(396\) 33.6519i 1.69107i
\(397\) 28.1216 16.2360i 1.41138 0.814862i 0.415864 0.909427i \(-0.363479\pi\)
0.995519 + 0.0945652i \(0.0301461\pi\)
\(398\) 5.02535i 0.251898i
\(399\) 0 0
\(400\) −6.68693 11.5821i −0.334347 0.579105i
\(401\) 31.2922i 1.56266i 0.624121 + 0.781328i \(0.285457\pi\)
−0.624121 + 0.781328i \(0.714543\pi\)
\(402\) 2.85208 + 4.93995i 0.142249 + 0.246382i
\(403\) −30.0000 + 8.66025i −1.49441 + 0.431398i
\(404\) −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
\(409\) 8.29875i 0.410347i 0.978726 + 0.205173i \(0.0657759\pi\)
−0.978726 + 0.205173i \(0.934224\pi\)
\(410\) 1.63670i 0.0808309i
\(411\) 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
\(416\) 4.10436 16.5876i 0.201233 0.813272i
\(417\) −5.29129 9.16478i −0.259115 0.448801i
\(418\) 2.45505i 0.120080i
\(419\) −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 \(-0.0325349\pi\)
\(422\) −4.18693 + 2.41733i −0.203817 + 0.117674i
\(423\) 45.8716i 2.23035i
\(424\) −9.24773 + 5.33918i −0.449109 + 0.259293i
\(425\) −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
\(429\) −37.9129 + 10.9445i −1.83045 + 0.528406i
\(430\) 0.978220 + 1.69433i 0.0471739 + 0.0817077i
\(431\) −30.0172 17.3305i −1.44588 0.834779i −0.447647 0.894210i \(-0.647738\pi\)
−0.998232 + 0.0594316i \(0.981071\pi\)
\(432\) 13.9564 0.671479
\(433\) −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
\(436\) 12.3131 7.10895i 0.589689 0.340457i
\(437\) 1.87841 1.08450i 0.0898565 0.0518787i
\(438\) 4.41742 0.211073
\(439\) 20.5390 0.980274 0.490137 0.871645i \(-0.336947\pi\)
0.490137 + 0.871645i \(0.336947\pi\)
\(440\) 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 −0.627744 0.778420i \(-0.716022\pi\)
0.988003 + 0.154433i \(0.0493550\pi\)
\(444\) −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 −0.111870 0.993723i \(-0.535684\pi\)
−0.916524 + 0.399979i \(0.869017\pi\)
\(450\) 9.08258 + 5.24383i 0.428157 + 0.247196i
\(451\) 30.7477 1.44785
\(452\) −9.47822 + 16.4168i −0.445818 + 0.772179i
\(453\) 33.8426i 1.59006i
\(454\) 4.04356 0.189774
\(455\) 0 0
\(456\) −6.62614 −0.310297
\(457\) 22.8027i 1.06667i 0.845905 + 0.533333i \(0.179061\pi\)
−0.845905 + 0.533333i \(0.820939\pi\)
\(458\) −1.58258 + 2.74110i −0.0739489 + 0.128083i
\(459\) 15.0000 0.700140
\(460\) −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 \(-0.0590464\pi\)
\(464\) 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
\(467\) 15.0826 26.1238i 0.697938 1.20886i −0.271242 0.962511i \(-0.587434\pi\)
0.969180 0.246353i \(-0.0792324\pi\)
\(468\) −8.58258 29.7309i −0.396730 1.37431i
\(469\) 0 0
\(470\) −1.73049 + 0.999100i −0.0798217 + 0.0460851i
\(471\) −2.66970 −0.123013
\(472\) −21.3303 −0.981807
\(473\) −31.8303 + 18.3772i −1.46356 + 0.844986i
\(474\) 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
\(478\) −6.04356 −0.276426
\(479\) −16.3521 9.44088i −0.747146 0.431365i 0.0775159 0.996991i \(-0.475301\pi\)
−0.824662 + 0.565626i \(0.808634\pi\)
\(480\) 3.02178 + 5.23388i 0.137925 + 0.238893i
\(481\) −6.00000 + 24.2487i −0.273576 + 1.10565i
\(482\) −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
\(486\) 6.39564 3.69253i 0.290112 0.167496i
\(487\) 29.3694i 1.33086i −0.746462 0.665428i \(-0.768249\pi\)
0.746462 0.665428i \(-0.231751\pi\)
\(488\) 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 0.908773 0.417291i \(-0.137020\pi\)
−0.815771 + 0.578375i \(0.803687\pi\)
\(492\) 39.2095i 1.76770i
\(493\) 10.1869 + 17.6443i 0.458796 + 0.794659i
\(494\) 0.626136 + 2.16900i 0.0281712 + 0.0975879i
\(495\) 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 \(-0.198177\pi\)
−0.0988324 + 0.995104i \(0.531511\pi\)
\(500\) 8.01270i 0.358339i
\(501\) 40.9615i 1.83002i
\(502\) 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
\(507\) −30.7042 + 19.3386i −1.36362 + 0.858858i
\(508\) −6.23049 10.7915i −0.276433 0.478797i
\(509\) 15.0562i 0.667352i 0.942688 + 0.333676i \(0.108289\pi\)
−0.942688 + 0.333676i \(0.891711\pi\)
\(510\) 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
\(514\) 2.30415i 0.101632i
\(515\) −1.81307 + 1.04678i −0.0798933 + 0.0461264i
\(516\) −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
\(520\) 1.97822 2.05583i 0.0867507 0.0901539i
\(521\) 8.20871 + 14.2179i 0.359630 + 0.622898i 0.987899 0.155099i \(-0.0495695\pi\)
−0.628269 + 0.777996i \(0.716236\pi\)
\(522\) −12.8739 7.43273i −0.563474 0.325322i
\(523\) −24.3303 −1.06389 −0.531945 0.846779i \(-0.678539\pi\)
−0.531945 + 0.846779i \(0.678539\pi\)
\(524\) 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
\(528\) −26.4564 + 15.2746i −1.15137 + 0.664743i
\(529\) −20.4955 −0.891107
\(530\) −1.28674 −0.0558925
\(531\) −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
\(535\) −2.06080 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
\(541\) 5.43920 + 3.14033i 0.233850 + 0.135013i 0.612347 0.790589i \(-0.290226\pi\)
−0.378497 + 0.925602i \(0.623559\pi\)
\(542\) 5.86932 0.252109
\(543\) 12.7913 22.1552i 0.548927 0.950769i
\(544\) 14.2179i 0.609588i
\(545\) 3.62614 0.155327
\(546\) 0 0
\(547\) −11.7477 −0.502297 −0.251148 0.967949i \(-0.580808\pi\)
−0.251148 + 0.967949i \(0.580808\pi\)
\(548\) 21.4123i 0.914686i
\(549\) 35.3303 61.1939i 1.50786 2.61169i
\(550\) −8.58258 −0.365962
\(551\) −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
\(555\) −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 0.963154 0.268951i \(-0.0866769\pi\)
0.248659 + 0.968591i \(0.420010\pi\)
\(558\) 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
\(562\) −14.0000 −0.590554
\(563\) −36.3303 −1.53114 −0.765570 0.643353i \(-0.777543\pi\)
−0.765570 + 0.643353i \(0.777543\pi\)
\(564\) 41.4564 23.9349i 1.74563 1.00784i
\(565\) −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
\(569\) 16.7477 0.702101 0.351051 0.936356i \(-0.385825\pi\)
0.351051 + 0.936356i \(0.385825\pi\)
\(570\) −0.691478 0.399225i −0.0289628 0.0167217i
\(571\) 1.02178 + 1.76978i 0.0427602 + 0.0740628i 0.886613 0.462511i \(-0.153052\pi\)
−0.843853 + 0.536574i \(0.819718\pi\)
\(572\) 18.2477 + 17.5589i 0.762976 + 0.734174i
\(573\) −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
\(577\) 30.8739 17.8250i 1.28530 0.742066i 0.307484 0.951553i \(-0.400513\pi\)
0.977811 + 0.209487i \(0.0671795\pi\)
\(578\) 3.65480i 0.152020i
\(579\) 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
\(583\) 24.1733i 1.00115i
\(584\) −3.00000 5.19615i −0.124141 0.215018i
\(585\) 1.89564 7.66115i 0.0783752 0.316750i
\(586\) −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
\(591\) 6.37600i 0.262274i
\(592\) 19.3386i 0.794812i
\(593\) −5.52178 3.18800i −0.226752 0.130916i 0.382321 0.924030i \(-0.375125\pi\)
−0.609073 + 0.793114i \(0.708458\pi\)
\(594\) 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
\(598\) −0.626136 + 2.53050i −0.0256046 + 0.103480i
\(599\) 3.31307 + 5.73840i 0.135368 + 0.234465i 0.925738 0.378165i \(-0.123445\pi\)
−0.790370 + 0.612630i \(0.790112\pi\)
\(600\) 23.1642i 0.945675i
\(601\) −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
\(604\) 18.8085 10.8591i 0.765308 0.441851i
\(605\) 1.99820i 0.0812384i
\(606\) −5.75227 + 3.32108i −0.233670 + 0.134910i
\(607\) −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
\(611\) −24.8739 23.9349i −1.00629 0.968302i
\(612\) −12.8739 22.2982i −0.520395 0.901351i
\(613\) 15.8085 + 9.12705i 0.638500 + 0.368638i 0.784037 0.620715i \(-0.213157\pi\)
−0.145536 + 0.989353i \(0.546491\pi\)
\(614\) 7.08712 0.286013
\(615\) −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 \(0.779374\pi\)
\(618\) −5.06080 + 2.92185i −0.203575 + 0.117534i
\(619\) 16.7477 9.66930i 0.673148 0.388642i −0.124120 0.992267i \(-0.539611\pi\)
0.797268 + 0.603625i \(0.206278\pi\)
\(620\) −7.08712 −0.284626
\(621\) −7.91288 −0.317533
\(622\) 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
\(626\) 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 0.893957 0.448153i \(-0.147918\pi\)
0.0588668 + 0.998266i \(0.481251\pi\)
\(632\) −9.00000 5.19615i −0.358001 0.206692i
\(633\) 29.5390 1.17407
\(634\) −4.23049 + 7.32743i −0.168014 + 0.291009i
\(635\) 3.17805i 0.126117i
\(636\) 30.8258 1.22232
\(637\) 0 0
\(638\) 12.1652 0.481623
\(639\) 20.9753i 0.829770i
\(640\) 2.52178 4.36785i 0.0996821 0.172654i
\(641\) 29.3739 1.16020 0.580099 0.814546i \(-0.303014\pi\)
0.580099 + 0.814546i \(0.303014\pi\)
\(642\) −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
\(646\) 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
\(649\) 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
\(653\) 15.7913 0.617961 0.308980 0.951068i \(-0.400012\pi\)
0.308980 + 0.951068i \(0.400012\pi\)
\(654\) 10.1216 0.395786
\(655\) 6.87386 3.96863i 0.268584 0.155067i
\(656\) 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 −0.918523 0.395367i \(-0.870617\pi\)
0.801660 + 0.597781i \(0.203951\pi\)
\(660\) −8.95644 −0.348629
\(661\) −43.7477 25.2578i −1.70159 0.982413i −0.944155 0.329502i \(-0.893119\pi\)
−0.757434 0.652911i \(-0.773547\pi\)
\(662\) 5.68693 + 9.85005i 0.221029 + 0.382833i
\(663\) −20.9347 + 21.7559i −0.813035 + 0.844931i
\(664\) 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
\(668\) 22.7650 13.1434i 0.880803 0.508532i
\(669\) 52.9706i 2.04796i
\(670\) 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 −0.999924 0.0123559i \(-0.996067\pi\)
0.489261 0.872137i \(-0.337266\pi\)
\(674\) 4.54860i 0.175206i
\(675\) −11.9782 20.7469i −0.461042 0.798548i
\(676\) 20.5998 + 10.8591i 0.792300 + 0.417658i
\(677\) −14.6044 + 25.2955i −0.561291 + 0.972185i 0.436093 + 0.899902i \(0.356362\pi\)
−0.997384 + 0.0722830i \(0.976972\pi\)
\(678\) −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
\(682\) 15.5130i 0.594024i
\(683\) 30.3586i 1.16164i −0.814033 0.580819i \(-0.802732\pi\)
0.814033 0.580819i \(-0.197268\pi\)
\(684\) 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
\(689\) −6.16515 21.3567i −0.234874 0.813626i
\(690\) −0.460985 0.798450i −0.0175494 0.0303965i
\(691\) 10.3169i 0.392472i 0.980557 + 0.196236i \(0.0628718\pi\)
−0.980557 + 0.196236i \(0.937128\pi\)
\(692\) −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
\(696\) 32.8335i 1.24455i
\(697\) 20.3739 11.7629i 0.771715 0.445550i
\(698\) −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 \(0.584627\pi\)
\(702\) 1.97822 7.99488i 0.0746631 0.301747i
\(703\) −4.74773 8.22330i −0.179064 0.310148i
\(704\) 11.6044 + 6.69978i 0.437356 + 0.252507i
\(705\) 12.2087 0.459807
\(706\) 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 −0.231502 0.972834i \(-0.574364\pi\)
0.726748 + 0.686904i \(0.241031\pi\)
\(710\) 0.791288 0.456850i 0.0296965 0.0171453i
\(711\) −28.7477 −1.07812
\(712\) −27.9564 −1.04771
\(713\) 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
\(717\) 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
\(723\) 47.6216 + 27.4943i 1.77107 + 1.02253i
\(724\) −16.4174 −0.610149
\(725\) 16.2695 28.1796i 0.604234 1.04656i
\(726\) 5.57755i 0.207002i
\(727\) 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
\(730\) 0.723000i 0.0267594i
\(731\) −14.0608 + 24.3540i −0.520057 + 0.900766i
\(732\) −73.7386 −2.72546
\(733\) −14.6869 8.47950i −0.542474 0.313198i 0.203607 0.979053i \(-0.434734\pi\)
−0.746081 + 0.665855i \(0.768067\pi\)
\(734\) 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 0.159264 0.987236i \(-0.449088\pi\)
−0.775339 + 0.631545i \(0.782421\pi\)
\(740\) −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 \(0.115446\pi\)
\(744\) −41.8693 −1.53500
\(745\) 0.208712 0.00764662
\(746\) −12.7432 + 7.35728i −0.466561 + 0.269369i
\(747\) 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
\(751\) 23.7477 0.866567 0.433283 0.901258i \(-0.357355\pi\)
0.433283 + 0.901258i \(0.357355\pi\)
\(752\) −23.1434 13.3618i −0.843952 0.487256i
\(753\) −3.95644 6.85275i −0.144181 0.249728i
\(754\) 10.7477 3.10260i 0.391409 0.112990i
\(755\) 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 \(0.868110\pi\)
\(758\) 6.47822 + 11.2206i 0.235300 + 0.407551i
\(759\) 15.0000 8.66025i 0.544466 0.314347i
\(760\) 1.08450i 0.0393390i
\(761\) 11.2259 6.48130i 0.406940 0.234947i −0.282534 0.959257i \(-0.591175\pi\)
0.689474 + 0.724310i \(0.257842\pi\)
\(762\) 8.87086i 0.321357i
\(763\) 0 0
\(764\) 12.8739 + 22.2982i 0.465760 + 0.806720i
\(765\) 6.56670i 0.237420i
\(766\) −0.291288 0.504525i −0.0105247 0.0182292i
\(767\) 10.6652 43.1027i 0.385096 1.55635i
\(768\) −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
\(773\) 19.4340i 0.698991i 0.936938 + 0.349495i \(0.113647\pi\)
−0.936938 + 0.349495i \(0.886353\pi\)
\(774\) 20.5185i 0.737521i
\(775\) 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