Properties

Label 825.2.n.k.676.1
Level $825$
Weight $2$
Character 825.676
Analytic conductor $6.588$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.n (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.13140625.1
Defining polynomial: \(x^{8} - 3 x^{7} + 5 x^{6} - 3 x^{5} + 4 x^{4} + 3 x^{3} + 5 x^{2} + 3 x + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 676.1
Root \(0.418926 + 1.28932i\) of defining polynomial
Character \(\chi\) \(=\) 825.676
Dual form 825.2.n.k.526.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.758911 - 2.33569i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-3.26145 + 2.36959i) q^{4} +(0.758911 - 2.33569i) q^{6} +(2.65911 - 1.93196i) q^{7} +(4.03606 + 2.93237i) q^{8} +(0.309017 + 0.951057i) q^{9} +O(q^{10})\) \(q+(-0.758911 - 2.33569i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-3.26145 + 2.36959i) q^{4} +(0.758911 - 2.33569i) q^{6} +(2.65911 - 1.93196i) q^{7} +(4.03606 + 2.93237i) q^{8} +(0.309017 + 0.951057i) q^{9} +(2.96813 + 1.47994i) q^{11} -4.03138 q^{12} +(0.0967635 + 0.297808i) q^{13} +(-6.53048 - 4.74467i) q^{14} +(1.29455 - 3.98423i) q^{16} +(-1.54508 + 4.75528i) q^{17} +(1.98685 - 1.44353i) q^{18} +(6.03048 + 4.38140i) q^{19} +3.28684 q^{21} +(1.20413 - 8.05576i) q^{22} -1.07392 q^{23} +(1.54164 + 4.74467i) q^{24} +(0.622150 - 0.452019i) q^{26} +(-0.309017 + 0.951057i) q^{27} +(-4.09463 + 12.6020i) q^{28} +(4.07459 - 2.96036i) q^{29} +(1.06580 + 3.28018i) q^{31} -0.310680 q^{32} +(1.53138 + 2.94192i) q^{33} +12.2794 q^{34} +(-3.26145 - 2.36959i) q^{36} +(2.13118 - 1.54839i) q^{37} +(5.65698 - 17.4104i) q^{38} +(-0.0967635 + 0.297808i) q^{39} +(-8.77557 - 6.37583i) q^{41} +(-2.49442 - 7.67703i) q^{42} +5.51468 q^{43} +(-13.1873 + 2.20648i) q^{44} +(0.815010 + 2.50834i) q^{46} +(-9.70674 - 7.05236i) q^{47} +(3.38919 - 2.46239i) q^{48} +(1.17529 - 3.61718i) q^{49} +(-4.04508 + 2.93893i) q^{51} +(-1.02127 - 0.741996i) q^{52} +(-1.52513 - 4.69387i) q^{53} +2.45589 q^{54} +16.3975 q^{56} +(2.30344 + 7.08925i) q^{57} +(-10.0067 - 7.27031i) q^{58} +(7.41391 - 5.38652i) q^{59} +(2.83811 - 8.73480i) q^{61} +(6.85264 - 4.97873i) q^{62} +(2.65911 + 1.93196i) q^{63} +(-2.35333 - 7.24280i) q^{64} +(5.70922 - 5.80948i) q^{66} +15.2739 q^{67} +(-6.22882 - 19.1704i) q^{68} +(-0.868820 - 0.631235i) q^{69} +(0.949335 - 2.92175i) q^{71} +(-1.54164 + 4.74467i) q^{72} +(-7.00018 + 5.08592i) q^{73} +(-5.23394 - 3.80268i) q^{74} -30.0502 q^{76} +(10.7518 - 1.79898i) q^{77} +0.769020 q^{78} +(1.67316 + 5.14946i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-8.23206 + 25.3357i) q^{82} +(-5.02011 + 15.4503i) q^{83} +(-10.7199 + 7.78845i) q^{84} +(-4.18515 - 12.8806i) q^{86} +5.03647 q^{87} +(7.63981 + 14.6768i) q^{88} +1.62118 q^{89} +(0.832656 + 0.604960i) q^{91} +(3.50254 - 2.54475i) q^{92} +(-1.06580 + 3.28018i) q^{93} +(-9.10556 + 28.0240i) q^{94} +(-0.251345 - 0.182613i) q^{96} +(-0.0692451 - 0.213115i) q^{97} -9.34054 q^{98} +(-0.490303 + 3.28018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9} + O(q^{10}) \) \( 8 q + 2 q^{3} - 2 q^{4} - q^{7} - 5 q^{8} - 2 q^{9} - 3 q^{11} - 18 q^{12} - 6 q^{13} - 10 q^{14} - 20 q^{16} + 10 q^{17} + 5 q^{18} + 6 q^{19} - 4 q^{21} + 25 q^{22} + 10 q^{23} - 20 q^{24} - 8 q^{26} + 2 q^{27} - 31 q^{28} + 3 q^{31} - 60 q^{32} - 2 q^{33} + 50 q^{34} - 2 q^{36} + 19 q^{37} + 28 q^{38} + 6 q^{39} - 25 q^{41} - 15 q^{42} + 4 q^{43} + 7 q^{44} - 6 q^{46} - 15 q^{47} - 5 q^{48} + 21 q^{49} - 10 q^{51} - 6 q^{52} - 7 q^{53} + 10 q^{54} + 20 q^{56} + 9 q^{57} + 2 q^{58} + 35 q^{59} + 21 q^{61} + 19 q^{62} - q^{63} - 77 q^{64} + 25 q^{66} + 26 q^{67} + 35 q^{68} - 5 q^{69} + 25 q^{71} + 20 q^{72} - q^{73} - 29 q^{74} - 14 q^{76} + 61 q^{77} - 12 q^{78} + 30 q^{79} - 2 q^{81} - 57 q^{82} - 11 q^{83} - 34 q^{84} - 34 q^{86} - 10 q^{87} + 85 q^{88} + 32 q^{89} + 37 q^{91} + 10 q^{92} - 3 q^{93} - 39 q^{94} + 10 q^{96} - 5 q^{97} - 50 q^{98} - 3 q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).

\(n\) \(376\) \(551\) \(727\)
\(\chi(n)\) \(e\left(\frac{2}{5}\right)\) \(1\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.758911 2.33569i −0.536631 1.65158i −0.740098 0.672499i \(-0.765221\pi\)
0.203468 0.979082i \(-0.434779\pi\)
\(3\) 0.809017 + 0.587785i 0.467086 + 0.339358i
\(4\) −3.26145 + 2.36959i −1.63073 + 1.18479i
\(5\) 0 0
\(6\) 0.758911 2.33569i 0.309824 0.953540i
\(7\) 2.65911 1.93196i 1.00505 0.730211i 0.0418845 0.999122i \(-0.486664\pi\)
0.963165 + 0.268911i \(0.0866639\pi\)
\(8\) 4.03606 + 2.93237i 1.42696 + 1.03675i
\(9\) 0.309017 + 0.951057i 0.103006 + 0.317019i
\(10\) 0 0
\(11\) 2.96813 + 1.47994i 0.894924 + 0.446218i
\(12\) −4.03138 −1.16376
\(13\) 0.0967635 + 0.297808i 0.0268374 + 0.0825970i 0.963578 0.267427i \(-0.0861734\pi\)
−0.936741 + 0.350024i \(0.886173\pi\)
\(14\) −6.53048 4.74467i −1.74534 1.26807i
\(15\) 0 0
\(16\) 1.29455 3.98423i 0.323638 0.996057i
\(17\) −1.54508 + 4.75528i −0.374738 + 1.15333i 0.568917 + 0.822395i \(0.307363\pi\)
−0.943655 + 0.330930i \(0.892637\pi\)
\(18\) 1.98685 1.44353i 0.468306 0.340244i
\(19\) 6.03048 + 4.38140i 1.38349 + 1.00516i 0.996545 + 0.0830568i \(0.0264683\pi\)
0.386941 + 0.922104i \(0.373532\pi\)
\(20\) 0 0
\(21\) 3.28684 0.717248
\(22\) 1.20413 8.05576i 0.256721 1.71749i
\(23\) −1.07392 −0.223928 −0.111964 0.993712i \(-0.535714\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(24\) 1.54164 + 4.74467i 0.314685 + 0.968501i
\(25\) 0 0
\(26\) 0.622150 0.452019i 0.122014 0.0886482i
\(27\) −0.309017 + 0.951057i −0.0594703 + 0.183031i
\(28\) −4.09463 + 12.6020i −0.773813 + 2.38155i
\(29\) 4.07459 2.96036i 0.756632 0.549725i −0.141243 0.989975i \(-0.545110\pi\)
0.897875 + 0.440250i \(0.145110\pi\)
\(30\) 0 0
\(31\) 1.06580 + 3.28018i 0.191423 + 0.589138i 1.00000 0.000748050i \(0.000238112\pi\)
−0.808577 + 0.588390i \(0.799762\pi\)
\(32\) −0.310680 −0.0549210
\(33\) 1.53138 + 2.94192i 0.266579 + 0.512122i
\(34\) 12.2794 2.10591
\(35\) 0 0
\(36\) −3.26145 2.36959i −0.543576 0.394931i
\(37\) 2.13118 1.54839i 0.350364 0.254554i −0.398658 0.917100i \(-0.630524\pi\)
0.749022 + 0.662546i \(0.230524\pi\)
\(38\) 5.65698 17.4104i 0.917683 2.82434i
\(39\) −0.0967635 + 0.297808i −0.0154946 + 0.0476874i
\(40\) 0 0
\(41\) −8.77557 6.37583i −1.37051 0.995737i −0.997697 0.0678321i \(-0.978392\pi\)
−0.372817 0.927905i \(-0.621608\pi\)
\(42\) −2.49442 7.67703i −0.384897 1.18459i
\(43\) 5.51468 0.840980 0.420490 0.907297i \(-0.361858\pi\)
0.420490 + 0.907297i \(0.361858\pi\)
\(44\) −13.1873 + 2.20648i −1.98805 + 0.332640i
\(45\) 0 0
\(46\) 0.815010 + 2.50834i 0.120167 + 0.369835i
\(47\) −9.70674 7.05236i −1.41587 1.02869i −0.992435 0.122767i \(-0.960823\pi\)
−0.423438 0.905925i \(-0.639177\pi\)
\(48\) 3.38919 2.46239i 0.489187 0.355415i
\(49\) 1.17529 3.61718i 0.167899 0.516740i
\(50\) 0 0
\(51\) −4.04508 + 2.93893i −0.566425 + 0.411532i
\(52\) −1.02127 0.741996i −0.141625 0.102896i
\(53\) −1.52513 4.69387i −0.209493 0.644753i −0.999499 0.0316539i \(-0.989923\pi\)
0.790006 0.613099i \(-0.210077\pi\)
\(54\) 2.45589 0.334204
\(55\) 0 0
\(56\) 16.3975 2.19121
\(57\) 2.30344 + 7.08925i 0.305098 + 0.938994i
\(58\) −10.0067 7.27031i −1.31395 0.954639i
\(59\) 7.41391 5.38652i 0.965208 0.701265i 0.0108537 0.999941i \(-0.496545\pi\)
0.954354 + 0.298676i \(0.0965451\pi\)
\(60\) 0 0
\(61\) 2.83811 8.73480i 0.363382 1.11838i −0.587605 0.809148i \(-0.699929\pi\)
0.950988 0.309229i \(-0.100071\pi\)
\(62\) 6.85264 4.97873i 0.870286 0.632300i
\(63\) 2.65911 + 1.93196i 0.335016 + 0.243404i
\(64\) −2.35333 7.24280i −0.294166 0.905350i
\(65\) 0 0
\(66\) 5.70922 5.80948i 0.702756 0.715097i
\(67\) 15.2739 1.86600 0.933000 0.359876i \(-0.117181\pi\)
0.933000 + 0.359876i \(0.117181\pi\)
\(68\) −6.22882 19.1704i −0.755356 2.32475i
\(69\) −0.868820 0.631235i −0.104594 0.0759917i
\(70\) 0 0
\(71\) 0.949335 2.92175i 0.112665 0.346748i −0.878788 0.477213i \(-0.841647\pi\)
0.991453 + 0.130465i \(0.0416470\pi\)
\(72\) −1.54164 + 4.74467i −0.181684 + 0.559164i
\(73\) −7.00018 + 5.08592i −0.819309 + 0.595262i −0.916514 0.400002i \(-0.869009\pi\)
0.0972058 + 0.995264i \(0.469009\pi\)
\(74\) −5.23394 3.80268i −0.608433 0.442052i
\(75\) 0 0
\(76\) −30.0502 −3.44700
\(77\) 10.7518 1.79898i 1.22528 0.205012i
\(78\) 0.769020 0.0870744
\(79\) 1.67316 + 5.14946i 0.188245 + 0.579360i 0.999989 0.00465401i \(-0.00148142\pi\)
−0.811744 + 0.584014i \(0.801481\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) −8.23206 + 25.3357i −0.909079 + 2.79786i
\(83\) −5.02011 + 15.4503i −0.551029 + 1.69589i 0.155178 + 0.987887i \(0.450405\pi\)
−0.706207 + 0.708006i \(0.749595\pi\)
\(84\) −10.7199 + 7.78845i −1.16964 + 0.849790i
\(85\) 0 0
\(86\) −4.18515 12.8806i −0.451296 1.38895i
\(87\) 5.03647 0.539966
\(88\) 7.63981 + 14.6768i 0.814406 + 1.56455i
\(89\) 1.62118 0.171845 0.0859223 0.996302i \(-0.472616\pi\)
0.0859223 + 0.996302i \(0.472616\pi\)
\(90\) 0 0
\(91\) 0.832656 + 0.604960i 0.0872861 + 0.0634171i
\(92\) 3.50254 2.54475i 0.365165 0.265308i
\(93\) −1.06580 + 3.28018i −0.110518 + 0.340139i
\(94\) −9.10556 + 28.0240i −0.939166 + 2.89046i
\(95\) 0 0
\(96\) −0.251345 0.182613i −0.0256528 0.0186379i
\(97\) −0.0692451 0.213115i −0.00703078 0.0216385i 0.947480 0.319816i \(-0.103621\pi\)
−0.954510 + 0.298178i \(0.903621\pi\)
\(98\) −9.34054 −0.943537
\(99\) −0.490303 + 3.28018i −0.0492773 + 0.329671i
\(100\) 0 0
\(101\) −0.156154 0.480593i −0.0155379 0.0478208i 0.942987 0.332830i \(-0.108003\pi\)
−0.958525 + 0.285009i \(0.908003\pi\)
\(102\) 9.93427 + 7.21767i 0.983639 + 0.714656i
\(103\) −5.17930 + 3.76298i −0.510332 + 0.370778i −0.812949 0.582334i \(-0.802139\pi\)
0.302618 + 0.953112i \(0.402139\pi\)
\(104\) −0.482738 + 1.48571i −0.0473363 + 0.145686i
\(105\) 0 0
\(106\) −9.80598 + 7.12446i −0.952441 + 0.691989i
\(107\) 1.69286 + 1.22993i 0.163655 + 0.118902i 0.666598 0.745417i \(-0.267750\pi\)
−0.502943 + 0.864319i \(0.667750\pi\)
\(108\) −1.24576 3.83407i −0.119874 0.368934i
\(109\) −6.69278 −0.641052 −0.320526 0.947240i \(-0.603860\pi\)
−0.320526 + 0.947240i \(0.603860\pi\)
\(110\) 0 0
\(111\) 2.63428 0.250035
\(112\) −4.25499 13.0955i −0.402059 1.23741i
\(113\) −8.73262 6.34462i −0.821496 0.596852i 0.0956448 0.995416i \(-0.469509\pi\)
−0.917141 + 0.398564i \(0.869509\pi\)
\(114\) 14.8102 10.7602i 1.38710 1.00779i
\(115\) 0 0
\(116\) −6.27426 + 19.3102i −0.582550 + 1.79290i
\(117\) −0.253330 + 0.184055i −0.0234204 + 0.0170159i
\(118\) −18.2077 13.2287i −1.67616 1.21780i
\(119\) 5.07845 + 15.6299i 0.465541 + 1.43279i
\(120\) 0 0
\(121\) 6.61956 + 8.78529i 0.601779 + 0.798663i
\(122\) −22.5556 −2.04209
\(123\) −3.35197 10.3163i −0.302237 0.930190i
\(124\) −11.2487 8.17267i −1.01017 0.733928i
\(125\) 0 0
\(126\) 2.49442 7.67703i 0.222221 0.683925i
\(127\) 5.25430 16.1711i 0.466244 1.43495i −0.391167 0.920320i \(-0.627929\pi\)
0.857411 0.514632i \(-0.172071\pi\)
\(128\) −15.6336 + 11.3585i −1.38183 + 1.00396i
\(129\) 4.46147 + 3.24145i 0.392810 + 0.285393i
\(130\) 0 0
\(131\) −0.0430508 −0.00376136 −0.00188068 0.999998i \(-0.500599\pi\)
−0.00188068 + 0.999998i \(0.500599\pi\)
\(132\) −11.9657 5.96619i −1.04148 0.519291i
\(133\) 24.5004 2.12445
\(134\) −11.5915 35.6750i −1.00135 3.08185i
\(135\) 0 0
\(136\) −20.1803 + 14.6618i −1.73044 + 1.25724i
\(137\) −2.27516 + 7.00222i −0.194380 + 0.598240i 0.805603 + 0.592455i \(0.201841\pi\)
−0.999983 + 0.00578480i \(0.998159\pi\)
\(138\) −0.815010 + 2.50834i −0.0693783 + 0.213524i
\(139\) −10.7109 + 7.78189i −0.908483 + 0.660052i −0.940631 0.339432i \(-0.889765\pi\)
0.0321478 + 0.999483i \(0.489765\pi\)
\(140\) 0 0
\(141\) −3.70764 11.4110i −0.312240 0.960976i
\(142\) −7.54476 −0.633142
\(143\) −0.153530 + 1.02713i −0.0128388 + 0.0858933i
\(144\) 4.18926 0.349105
\(145\) 0 0
\(146\) 17.1916 + 12.4905i 1.42279 + 1.03372i
\(147\) 3.07696 2.23554i 0.253783 0.184384i
\(148\) −3.28170 + 10.1000i −0.269754 + 0.830217i
\(149\) −1.81658 + 5.59087i −0.148820 + 0.458022i −0.997482 0.0709136i \(-0.977409\pi\)
0.848662 + 0.528935i \(0.177409\pi\)
\(150\) 0 0
\(151\) −6.17135 4.48375i −0.502217 0.364882i 0.307646 0.951501i \(-0.400459\pi\)
−0.809863 + 0.586619i \(0.800459\pi\)
\(152\) 11.4915 + 35.3671i 0.932082 + 2.86865i
\(153\) −5.00000 −0.404226
\(154\) −12.3615 23.7475i −0.996116 1.91363i
\(155\) 0 0
\(156\) −0.390091 1.20058i −0.0312322 0.0961230i
\(157\) −8.19795 5.95616i −0.654267 0.475353i 0.210455 0.977604i \(-0.432506\pi\)
−0.864722 + 0.502250i \(0.832506\pi\)
\(158\) 10.7578 7.81596i 0.855841 0.621805i
\(159\) 1.52513 4.69387i 0.120951 0.372248i
\(160\) 0 0
\(161\) −2.85567 + 2.07477i −0.225059 + 0.163515i
\(162\) 1.98685 + 1.44353i 0.156102 + 0.113415i
\(163\) 1.55407 + 4.78292i 0.121724 + 0.374627i 0.993290 0.115651i \(-0.0368953\pi\)
−0.871566 + 0.490278i \(0.836895\pi\)
\(164\) 43.7292 3.41468
\(165\) 0 0
\(166\) 39.8969 3.09660
\(167\) −1.78953 5.50761i −0.138478 0.426192i 0.857637 0.514256i \(-0.171932\pi\)
−0.996115 + 0.0880642i \(0.971932\pi\)
\(168\) 13.2659 + 9.63822i 1.02348 + 0.743605i
\(169\) 10.4379 7.58357i 0.802915 0.583352i
\(170\) 0 0
\(171\) −2.30344 + 7.08925i −0.176148 + 0.542128i
\(172\) −17.9859 + 13.0675i −1.37141 + 0.996387i
\(173\) 12.9970 + 9.44290i 0.988146 + 0.717930i 0.959514 0.281660i \(-0.0908850\pi\)
0.0286316 + 0.999590i \(0.490885\pi\)
\(174\) −3.82223 11.7636i −0.289762 0.891797i
\(175\) 0 0
\(176\) 9.73881 9.90983i 0.734090 0.746982i
\(177\) 9.16409 0.688815
\(178\) −1.23033 3.78657i −0.0922171 0.283815i
\(179\) 6.71734 + 4.88043i 0.502078 + 0.364781i 0.809810 0.586692i \(-0.199570\pi\)
−0.307732 + 0.951473i \(0.599570\pi\)
\(180\) 0 0
\(181\) −1.99756 + 6.14787i −0.148478 + 0.456968i −0.997442 0.0714830i \(-0.977227\pi\)
0.848964 + 0.528451i \(0.177227\pi\)
\(182\) 0.781086 2.40394i 0.0578980 0.178192i
\(183\) 7.43026 5.39840i 0.549261 0.399061i
\(184\) −4.33440 3.14913i −0.319536 0.232157i
\(185\) 0 0
\(186\) 8.47033 0.621074
\(187\) −11.6235 + 11.8277i −0.849997 + 0.864924i
\(188\) 48.3693 3.52769
\(189\) 1.01569 + 3.12597i 0.0738806 + 0.227381i
\(190\) 0 0
\(191\) −12.4340 + 9.03384i −0.899694 + 0.653666i −0.938387 0.345585i \(-0.887680\pi\)
0.0386935 + 0.999251i \(0.487680\pi\)
\(192\) 2.35333 7.24280i 0.169837 0.522704i
\(193\) −4.86757 + 14.9808i −0.350375 + 1.07834i 0.608267 + 0.793732i \(0.291865\pi\)
−0.958643 + 0.284612i \(0.908135\pi\)
\(194\) −0.445218 + 0.323470i −0.0319648 + 0.0232238i
\(195\) 0 0
\(196\) 4.73805 + 14.5822i 0.338432 + 1.04159i
\(197\) −16.3940 −1.16802 −0.584010 0.811746i \(-0.698517\pi\)
−0.584010 + 0.811746i \(0.698517\pi\)
\(198\) 8.03358 1.34417i 0.570922 0.0955261i
\(199\) 6.96500 0.493736 0.246868 0.969049i \(-0.420599\pi\)
0.246868 + 0.969049i \(0.420599\pi\)
\(200\) 0 0
\(201\) 12.3568 + 8.97776i 0.871583 + 0.633242i
\(202\) −1.00401 + 0.729455i −0.0706418 + 0.0513242i
\(203\) 5.11549 15.7439i 0.359037 1.10500i
\(204\) 6.22882 19.1704i 0.436105 1.34219i
\(205\) 0 0
\(206\) 12.7198 + 9.24146i 0.886229 + 0.643883i
\(207\) −0.331860 1.02136i −0.0230658 0.0709894i
\(208\) 1.31180 0.0909569
\(209\) 11.4150 + 21.9293i 0.789594 + 1.51688i
\(210\) 0 0
\(211\) −6.16585 18.9765i −0.424475 1.30640i −0.903496 0.428596i \(-0.859008\pi\)
0.479022 0.877803i \(-0.340992\pi\)
\(212\) 16.0967 + 11.6949i 1.10552 + 0.803211i
\(213\) 2.48539 1.80574i 0.170296 0.123727i
\(214\) 1.58801 4.88740i 0.108554 0.334096i
\(215\) 0 0
\(216\) −4.03606 + 2.93237i −0.274619 + 0.199522i
\(217\) 9.17124 + 6.66330i 0.622585 + 0.452334i
\(218\) 5.07922 + 15.6322i 0.344008 + 1.05875i
\(219\) −8.65269 −0.584695
\(220\) 0 0
\(221\) −1.56567 −0.105318
\(222\) −1.99919 6.15286i −0.134177 0.412953i
\(223\) −16.2990 11.8419i −1.09146 0.792992i −0.111815 0.993729i \(-0.535666\pi\)
−0.979645 + 0.200737i \(0.935666\pi\)
\(224\) −0.826133 + 0.600220i −0.0551983 + 0.0401039i
\(225\) 0 0
\(226\) −8.19177 + 25.2117i −0.544908 + 1.67706i
\(227\) 0.431964 0.313840i 0.0286705 0.0208303i −0.573358 0.819305i \(-0.694359\pi\)
0.602028 + 0.798475i \(0.294359\pi\)
\(228\) −24.3111 17.6631i −1.61004 1.16977i
\(229\) −6.85803 21.1068i −0.453191 1.39478i −0.873245 0.487281i \(-0.837989\pi\)
0.420054 0.907499i \(-0.362011\pi\)
\(230\) 0 0
\(231\) 9.75577 + 4.86432i 0.641882 + 0.320049i
\(232\) 25.1261 1.64961
\(233\) 1.41087 + 4.34221i 0.0924291 + 0.284467i 0.986575 0.163308i \(-0.0522164\pi\)
−0.894146 + 0.447775i \(0.852216\pi\)
\(234\) 0.622150 + 0.452019i 0.0406712 + 0.0295494i
\(235\) 0 0
\(236\) −11.4163 + 35.1358i −0.743138 + 2.28714i
\(237\) −1.67316 + 5.14946i −0.108684 + 0.334493i
\(238\) 32.6524 23.7233i 2.11654 1.53776i
\(239\) 4.74126 + 3.44473i 0.306687 + 0.222821i 0.730474 0.682941i \(-0.239299\pi\)
−0.423787 + 0.905762i \(0.639299\pi\)
\(240\) 0 0
\(241\) 9.96074 0.641628 0.320814 0.947142i \(-0.396044\pi\)
0.320814 + 0.947142i \(0.396044\pi\)
\(242\) 15.4960 22.1285i 0.996123 1.42247i
\(243\) −1.00000 −0.0641500
\(244\) 11.4415 + 35.2133i 0.732466 + 2.25430i
\(245\) 0 0
\(246\) −21.5518 + 15.6583i −1.37409 + 0.998337i
\(247\) −0.721283 + 2.21988i −0.0458941 + 0.141248i
\(248\) −5.31709 + 16.3643i −0.337635 + 1.03913i
\(249\) −13.1428 + 9.54882i −0.832892 + 0.605132i
\(250\) 0 0
\(251\) −5.21584 16.0527i −0.329221 1.01324i −0.969499 0.245094i \(-0.921181\pi\)
0.640279 0.768143i \(-0.278819\pi\)
\(252\) −13.2505 −0.834704
\(253\) −3.18753 1.58934i −0.200399 0.0999207i
\(254\) −41.7581 −2.62014
\(255\) 0 0
\(256\) 26.0723 + 18.9426i 1.62952 + 1.18391i
\(257\) 9.01534 6.55003i 0.562362 0.408580i −0.269961 0.962871i \(-0.587011\pi\)
0.832323 + 0.554292i \(0.187011\pi\)
\(258\) 4.18515 12.8806i 0.260556 0.801909i
\(259\) 2.67561 8.23470i 0.166255 0.511679i
\(260\) 0 0
\(261\) 4.07459 + 2.96036i 0.252211 + 0.183242i
\(262\) 0.0326717 + 0.100553i 0.00201846 + 0.00621220i
\(263\) 26.8726 1.65704 0.828519 0.559961i \(-0.189184\pi\)
0.828519 + 0.559961i \(0.189184\pi\)
\(264\) −2.44604 + 16.3643i −0.150544 + 1.00715i
\(265\) 0 0
\(266\) −18.5936 57.2252i −1.14005 3.50870i
\(267\) 1.31156 + 0.952905i 0.0802662 + 0.0583168i
\(268\) −49.8150 + 36.1927i −3.04294 + 2.21082i
\(269\) −3.10961 + 9.57038i −0.189596 + 0.583516i −0.999997 0.00235886i \(-0.999249\pi\)
0.810401 + 0.585875i \(0.199249\pi\)
\(270\) 0 0
\(271\) −8.53037 + 6.19767i −0.518183 + 0.376482i −0.815919 0.578166i \(-0.803768\pi\)
0.297736 + 0.954648i \(0.403768\pi\)
\(272\) 16.9459 + 12.3119i 1.02750 + 0.746521i
\(273\) 0.318046 + 0.978846i 0.0192490 + 0.0592425i
\(274\) 18.0816 1.09235
\(275\) 0 0
\(276\) 4.32938 0.260598
\(277\) 5.54302 + 17.0597i 0.333048 + 1.02502i 0.967676 + 0.252198i \(0.0811534\pi\)
−0.634628 + 0.772818i \(0.718847\pi\)
\(278\) 26.3047 + 19.1114i 1.57765 + 1.14623i
\(279\) −2.79029 + 2.02726i −0.167050 + 0.121369i
\(280\) 0 0
\(281\) 2.29013 7.04830i 0.136618 0.420467i −0.859220 0.511606i \(-0.829051\pi\)
0.995838 + 0.0911392i \(0.0290508\pi\)
\(282\) −23.8387 + 17.3198i −1.41957 + 1.03138i
\(283\) 4.35804 + 3.16630i 0.259059 + 0.188217i 0.709732 0.704472i \(-0.248816\pi\)
−0.450673 + 0.892689i \(0.648816\pi\)
\(284\) 3.82713 + 11.7787i 0.227098 + 0.698937i
\(285\) 0 0
\(286\) 2.51558 0.420905i 0.148749 0.0248886i
\(287\) −35.6530 −2.10453
\(288\) −0.0960054 0.295474i −0.00565717 0.0174110i
\(289\) −6.47214 4.70228i −0.380714 0.276605i
\(290\) 0 0
\(291\) 0.0692451 0.213115i 0.00405922 0.0124930i
\(292\) 10.7792 33.1750i 0.630806 1.94142i
\(293\) −1.40774 + 1.02278i −0.0822409 + 0.0597515i −0.628146 0.778096i \(-0.716186\pi\)
0.545905 + 0.837847i \(0.316186\pi\)
\(294\) −7.55666 5.49023i −0.440713 0.320197i
\(295\) 0 0
\(296\) 13.1420 0.763864
\(297\) −2.32471 + 2.36553i −0.134893 + 0.137262i
\(298\) 14.4371 0.836321
\(299\) −0.103916 0.319822i −0.00600964 0.0184958i
\(300\) 0 0
\(301\) 14.6641 10.6541i 0.845227 0.614093i
\(302\) −5.78913 + 17.8171i −0.333127 + 1.02526i
\(303\) 0.156154 0.480593i 0.00897082 0.0276094i
\(304\) 25.2633 18.3548i 1.44895 1.05272i
\(305\) 0 0
\(306\) 3.79455 + 11.6784i 0.216920 + 0.667612i
\(307\) −21.3566 −1.21889 −0.609444 0.792829i \(-0.708607\pi\)
−0.609444 + 0.792829i \(0.708607\pi\)
\(308\) −30.8035 + 31.3445i −1.75519 + 1.78602i
\(309\) −6.40197 −0.364195
\(310\) 0 0
\(311\) −26.5435 19.2850i −1.50514 1.09355i −0.968275 0.249886i \(-0.919607\pi\)
−0.536870 0.843665i \(-0.680393\pi\)
\(312\) −1.26382 + 0.918222i −0.0715499 + 0.0519841i
\(313\) 1.06874 3.28925i 0.0604089 0.185919i −0.916298 0.400497i \(-0.868837\pi\)
0.976707 + 0.214578i \(0.0688375\pi\)
\(314\) −7.69021 + 23.6680i −0.433984 + 1.33566i
\(315\) 0 0
\(316\) −17.6590 12.8300i −0.993398 0.721746i
\(317\) 0.888626 + 2.73491i 0.0499102 + 0.153608i 0.972905 0.231204i \(-0.0742664\pi\)
−0.922995 + 0.384812i \(0.874266\pi\)
\(318\) −12.1209 −0.679704
\(319\) 16.4751 2.75659i 0.922426 0.154340i
\(320\) 0 0
\(321\) 0.646615 + 1.99008i 0.0360905 + 0.111075i
\(322\) 7.01321 + 5.09540i 0.390831 + 0.283955i
\(323\) −30.1524 + 21.9070i −1.67772 + 1.21894i
\(324\) 1.24576 3.83407i 0.0692092 0.213004i
\(325\) 0 0
\(326\) 9.99201 7.25962i 0.553406 0.402073i
\(327\) −5.41457 3.93392i −0.299427 0.217546i
\(328\) −16.7224 51.4664i −0.923342 2.84176i
\(329\) −39.4362 −2.17419
\(330\) 0 0
\(331\) −14.1221 −0.776219 −0.388109 0.921613i \(-0.626872\pi\)
−0.388109 + 0.921613i \(0.626872\pi\)
\(332\) −20.2380 62.2861i −1.11070 3.41839i
\(333\) 2.13118 + 1.54839i 0.116788 + 0.0848514i
\(334\) −11.5060 + 8.35958i −0.629579 + 0.457416i
\(335\) 0 0
\(336\) 4.25499 13.0955i 0.232129 0.714419i
\(337\) 12.9030 9.37457i 0.702870 0.510665i −0.177995 0.984031i \(-0.556961\pi\)
0.880866 + 0.473366i \(0.156961\pi\)
\(338\) −25.6343 18.6244i −1.39432 1.01303i
\(339\) −3.33556 10.2658i −0.181163 0.557562i
\(340\) 0 0
\(341\) −1.69105 + 11.3133i −0.0915755 + 0.612650i
\(342\) 18.3064 0.989895
\(343\) 3.24683 + 9.99271i 0.175312 + 0.539555i
\(344\) 22.2575 + 16.1711i 1.20005 + 0.871885i
\(345\) 0 0
\(346\) 12.1921 37.5233i 0.655449 2.01727i
\(347\) −9.17166 + 28.2275i −0.492360 + 1.51533i 0.328670 + 0.944445i \(0.393400\pi\)
−0.821030 + 0.570884i \(0.806600\pi\)
\(348\) −16.4262 + 11.9343i −0.880537 + 0.639748i
\(349\) −25.6408 18.6291i −1.37252 0.997194i −0.997536 0.0701620i \(-0.977648\pi\)
−0.374984 0.927031i \(-0.622352\pi\)
\(350\) 0 0
\(351\) −0.313133 −0.0167138
\(352\) −0.922138 0.459787i −0.0491501 0.0245067i
\(353\) −1.20189 −0.0639703 −0.0319852 0.999488i \(-0.510183\pi\)
−0.0319852 + 0.999488i \(0.510183\pi\)
\(354\) −6.95473 21.4044i −0.369640 1.13763i
\(355\) 0 0
\(356\) −5.28740 + 3.84152i −0.280232 + 0.203600i
\(357\) −5.07845 + 15.6299i −0.268780 + 0.827220i
\(358\) 6.30130 19.3934i 0.333034 1.02497i
\(359\) 9.43239 6.85304i 0.497823 0.361689i −0.310362 0.950618i \(-0.600450\pi\)
0.808185 + 0.588929i \(0.200450\pi\)
\(360\) 0 0
\(361\) 11.2987 + 34.7737i 0.594667 + 1.83020i
\(362\) 15.8755 0.834396
\(363\) 0.191475 + 10.9983i 0.0100498 + 0.577263i
\(364\) −4.14918 −0.217476
\(365\) 0 0
\(366\) −18.2479 13.2579i −0.953832 0.693000i
\(367\) 12.9330 9.39636i 0.675096 0.490486i −0.196631 0.980478i \(-0.563000\pi\)
0.871727 + 0.489991i \(0.163000\pi\)
\(368\) −1.39025 + 4.27874i −0.0724717 + 0.223045i
\(369\) 3.35197 10.3163i 0.174497 0.537045i
\(370\) 0 0
\(371\) −13.1239 9.53504i −0.681357 0.495035i
\(372\) −4.29663 13.2237i −0.222770 0.685615i
\(373\) −0.321975 −0.0166712 −0.00833561 0.999965i \(-0.502653\pi\)
−0.00833561 + 0.999965i \(0.502653\pi\)
\(374\) 36.4469 + 18.1728i 1.88463 + 0.939693i
\(375\) 0 0
\(376\) −18.4968 56.9274i −0.953902 2.93581i
\(377\) 1.27589 + 0.926988i 0.0657117 + 0.0477423i
\(378\) 6.53048 4.74467i 0.335891 0.244039i
\(379\) 3.52819 10.8586i 0.181231 0.557771i −0.818632 0.574318i \(-0.805267\pi\)
0.999863 + 0.0165471i \(0.00526734\pi\)
\(380\) 0 0
\(381\) 13.7559 9.99428i 0.704738 0.512022i
\(382\) 30.5365 + 22.1861i 1.56239 + 1.13514i
\(383\) −8.76597 26.9789i −0.447920 1.37856i −0.879249 0.476362i \(-0.841955\pi\)
0.431329 0.902195i \(-0.358045\pi\)
\(384\) −19.3242 −0.986136
\(385\) 0 0
\(386\) 38.6846 1.96899
\(387\) 1.70413 + 5.24477i 0.0866257 + 0.266607i
\(388\) 0.730833 + 0.530981i 0.0371024 + 0.0269565i
\(389\) −12.2810 + 8.92269i −0.622673 + 0.452398i −0.853854 0.520513i \(-0.825741\pi\)
0.231181 + 0.972911i \(0.425741\pi\)
\(390\) 0 0
\(391\) 1.65930 5.10680i 0.0839143 0.258262i
\(392\) 15.3504 11.1528i 0.775315 0.563299i
\(393\) −0.0348288 0.0253046i −0.00175688 0.00127645i
\(394\) 12.4415 + 38.2911i 0.626796 + 1.92908i
\(395\) 0 0
\(396\) −6.17357 11.8600i −0.310234 0.595987i
\(397\) −5.22461 −0.262216 −0.131108 0.991368i \(-0.541853\pi\)
−0.131108 + 0.991368i \(0.541853\pi\)
\(398\) −5.28581 16.2681i −0.264954 0.815444i
\(399\) 19.8212 + 14.4010i 0.992302 + 0.720950i
\(400\) 0 0
\(401\) 4.32644 13.3154i 0.216052 0.664941i −0.783025 0.621990i \(-0.786324\pi\)
0.999077 0.0429502i \(-0.0136757\pi\)
\(402\) 11.5915 35.6750i 0.578132 1.77931i
\(403\) −0.873733 + 0.634804i −0.0435238 + 0.0316219i
\(404\) 1.64810 + 1.19741i 0.0819959 + 0.0595735i
\(405\) 0 0
\(406\) −40.6549 −2.01767
\(407\) 8.61714 1.44181i 0.427136 0.0714680i
\(408\) −24.9442 −1.23492
\(409\) 10.2937 + 31.6809i 0.508993 + 1.56652i 0.793953 + 0.607979i \(0.208020\pi\)
−0.284960 + 0.958539i \(0.591980\pi\)
\(410\) 0 0
\(411\) −5.95645 + 4.32761i −0.293810 + 0.213465i
\(412\) 7.97535 24.5456i 0.392917 1.20927i
\(413\) 9.30787 28.6467i 0.458011 1.40961i
\(414\) −2.13372 + 1.55024i −0.104867 + 0.0761902i
\(415\) 0 0
\(416\) −0.0300625 0.0925229i −0.00147394 0.00453631i
\(417\) −13.2393 −0.648334
\(418\) 42.5569 43.3043i 2.08153 2.11808i
\(419\) −5.28460 −0.258170 −0.129085 0.991634i \(-0.541204\pi\)
−0.129085 + 0.991634i \(0.541204\pi\)
\(420\) 0 0
\(421\) 24.9023 + 18.0926i 1.21367 + 0.881780i 0.995558 0.0941452i \(-0.0300118\pi\)
0.218107 + 0.975925i \(0.430012\pi\)
\(422\) −39.6439 + 28.8030i −1.92984 + 1.40211i
\(423\) 3.70764 11.4110i 0.180272 0.554820i
\(424\) 7.60864 23.4170i 0.369508 1.13723i
\(425\) 0 0
\(426\) −6.10384 4.43470i −0.295732 0.214862i
\(427\) −9.32841 28.7099i −0.451433 1.38937i
\(428\) −8.43562 −0.407751
\(429\) −0.727943 + 0.740727i −0.0351454 + 0.0357626i
\(430\) 0 0
\(431\) 3.81656 + 11.7462i 0.183837 + 0.565793i 0.999926 0.0121333i \(-0.00386225\pi\)
−0.816089 + 0.577926i \(0.803862\pi\)
\(432\) 3.38919 + 2.46239i 0.163062 + 0.118472i
\(433\) 1.14304 0.830465i 0.0549308 0.0399096i −0.559981 0.828505i \(-0.689192\pi\)
0.614912 + 0.788596i \(0.289192\pi\)
\(434\) 8.60323 26.4780i 0.412968 1.27098i
\(435\) 0 0
\(436\) 21.8282 15.8591i 1.04538 0.759514i
\(437\) −6.47625 4.70527i −0.309801 0.225084i
\(438\) 6.56662 + 20.2100i 0.313765 + 0.965670i
\(439\) −7.58532 −0.362028 −0.181014 0.983481i \(-0.557938\pi\)
−0.181014 + 0.983481i \(0.557938\pi\)
\(440\) 0 0
\(441\) 3.80333 0.181111
\(442\) 1.18820 + 3.65691i 0.0565170 + 0.173941i
\(443\) 8.95274 + 6.50455i 0.425358 + 0.309040i 0.779790 0.626041i \(-0.215326\pi\)
−0.354432 + 0.935082i \(0.615326\pi\)
\(444\) −8.59160 + 6.24216i −0.407739 + 0.296240i
\(445\) 0 0
\(446\) −15.2895 + 47.0562i −0.723979 + 2.22818i
\(447\) −4.75587 + 3.45534i −0.224945 + 0.163432i
\(448\) −20.2505 14.7129i −0.956748 0.695118i
\(449\) 1.95563 + 6.01882i 0.0922920 + 0.284045i 0.986538 0.163529i \(-0.0522878\pi\)
−0.894247 + 0.447575i \(0.852288\pi\)
\(450\) 0 0
\(451\) −16.6112 31.9116i −0.782190 1.50266i
\(452\) 43.5152 2.04678
\(453\) −2.35725 7.25486i −0.110753 0.340863i
\(454\) −1.06085 0.770756i −0.0497884 0.0361734i
\(455\) 0 0
\(456\) −11.4915 + 35.3671i −0.538138 + 1.65622i
\(457\) 0.0585832 0.180300i 0.00274040 0.00843410i −0.949677 0.313231i \(-0.898589\pi\)
0.952417 + 0.304797i \(0.0985886\pi\)
\(458\) −44.0944 + 32.0364i −2.06039 + 1.49696i
\(459\) −4.04508 2.93893i −0.188808 0.137177i
\(460\) 0 0
\(461\) −26.6198 −1.23981 −0.619904 0.784678i \(-0.712828\pi\)
−0.619904 + 0.784678i \(0.712828\pi\)
\(462\) 3.95778 26.4780i 0.184133 1.23187i
\(463\) −20.9935 −0.975652 −0.487826 0.872941i \(-0.662210\pi\)
−0.487826 + 0.872941i \(0.662210\pi\)
\(464\) −6.51998 20.0664i −0.302682 0.931561i
\(465\) 0 0
\(466\) 9.07131 6.59070i 0.420221 0.305308i
\(467\) −2.44120 + 7.51324i −0.112965 + 0.347671i −0.991517 0.129976i \(-0.958510\pi\)
0.878552 + 0.477647i \(0.158510\pi\)
\(468\) 0.390091 1.20058i 0.0180319 0.0554966i
\(469\) 40.6149 29.5085i 1.87542 1.36257i
\(470\) 0 0
\(471\) −3.13134 9.63727i −0.144284 0.444062i
\(472\) 45.7182 2.10435
\(473\) 16.3683 + 8.16138i 0.752614 + 0.375261i
\(474\) 13.2973 0.610766
\(475\) 0 0
\(476\) −53.5994 38.9423i −2.45673 1.78492i
\(477\) 3.99285 2.90097i 0.182820 0.132826i
\(478\) 4.44762 13.6884i 0.203429 0.626091i
\(479\) 12.3523 38.0164i 0.564389 1.73701i −0.105369 0.994433i \(-0.533602\pi\)
0.669758 0.742579i \(-0.266398\pi\)
\(480\) 0 0
\(481\) 0.667344 + 0.484854i 0.0304282 + 0.0221074i
\(482\) −7.55931 23.2652i −0.344317 1.05970i
\(483\) −3.52981 −0.160612
\(484\) −42.4069 12.9672i −1.92759 0.589419i
\(485\) 0 0
\(486\) 0.758911 + 2.33569i 0.0344249 + 0.105949i
\(487\) −8.03804 5.83998i −0.364238 0.264635i 0.390579 0.920569i \(-0.372275\pi\)
−0.754818 + 0.655935i \(0.772275\pi\)
\(488\) 37.0684 26.9318i 1.67801 1.21914i
\(489\) −1.55407 + 4.78292i −0.0702773 + 0.216291i
\(490\) 0 0
\(491\) −4.02364 + 2.92335i −0.181584 + 0.131929i −0.674864 0.737942i \(-0.735798\pi\)
0.493280 + 0.869871i \(0.335798\pi\)
\(492\) 35.3777 + 25.7034i 1.59495 + 1.15880i
\(493\) 7.78177 + 23.9498i 0.350473 + 1.07865i
\(494\) 5.73234 0.257910
\(495\) 0 0
\(496\) 14.4487 0.648767
\(497\) −3.12031 9.60333i −0.139965 0.430768i
\(498\) 32.2773 + 23.4508i 1.44638 + 1.05086i
\(499\) −35.4153 + 25.7307i −1.58541 + 1.15186i −0.675256 + 0.737584i \(0.735967\pi\)
−0.910149 + 0.414281i \(0.864033\pi\)
\(500\) 0 0
\(501\) 1.78953 5.50761i 0.0799504 0.246062i
\(502\) −33.5357 + 24.3651i −1.49677 + 1.08747i
\(503\) 5.08254 + 3.69268i 0.226619 + 0.164648i 0.695301 0.718718i \(-0.255271\pi\)
−0.468682 + 0.883367i \(0.655271\pi\)
\(504\) 5.06711 + 15.5950i 0.225707 + 0.694655i
\(505\) 0 0
\(506\) −1.29314 + 8.65125i −0.0574870 + 0.384595i
\(507\) 12.9019 0.572996
\(508\) 21.1821 + 65.1918i 0.939803 + 2.89242i
\(509\) −20.0945 14.5995i −0.890671 0.647111i 0.0453816 0.998970i \(-0.485550\pi\)
−0.936053 + 0.351859i \(0.885550\pi\)
\(510\) 0 0
\(511\) −8.78845 + 27.0481i −0.388778 + 1.19654i
\(512\) 12.5144 38.5155i 0.553066 1.70216i
\(513\) −6.03048 + 4.38140i −0.266252 + 0.193443i
\(514\) −22.1407 16.0861i −0.976583 0.709529i
\(515\) 0 0
\(516\) −22.2318 −0.978699
\(517\) −18.3738 35.2977i −0.808078 1.55239i
\(518\) −21.2642 −0.934296
\(519\) 4.96442 + 15.2789i 0.217914 + 0.670670i
\(520\) 0 0
\(521\) 5.62161 4.08434i 0.246287 0.178938i −0.457792 0.889059i \(-0.651360\pi\)
0.704080 + 0.710121i \(0.251360\pi\)
\(522\) 3.82223 11.7636i 0.167294 0.514879i
\(523\) 8.26650 25.4417i 0.361469 1.11249i −0.590694 0.806896i \(-0.701146\pi\)
0.952163 0.305591i \(-0.0988541\pi\)
\(524\) 0.140408 0.102013i 0.00613376 0.00445644i
\(525\) 0 0
\(526\) −20.3939 62.7661i −0.889218 2.73673i
\(527\) −17.2449 −0.751202
\(528\) 13.7037 2.29290i 0.596378 0.0997854i
\(529\) −21.8467 −0.949856
\(530\) 0 0
\(531\) 7.41391 + 5.38652i 0.321736 + 0.233755i
\(532\) −79.9069 + 58.0557i −3.46440 + 2.51704i
\(533\) 1.04961 3.23038i 0.0454638 0.139923i
\(534\) 1.23033 3.78657i 0.0532416 0.163861i
\(535\) 0 0
\(536\) 61.6462 + 44.7886i 2.66271 + 1.93457i
\(537\) 2.56580 + 7.89671i 0.110722 + 0.340768i
\(538\) 24.7133 1.06547
\(539\) 8.84162 8.99689i 0.380836 0.387524i
\(540\) 0 0
\(541\) 4.48336 + 13.7984i 0.192755 + 0.593237i 0.999995 + 0.00301536i \(0.000959822\pi\)
−0.807241 + 0.590222i \(0.799040\pi\)
\(542\) 20.9496 + 15.2208i 0.899863 + 0.653789i
\(543\) −5.22969 + 3.79959i −0.224428 + 0.163056i
\(544\) 0.480027 1.47737i 0.0205810 0.0633418i
\(545\) 0 0
\(546\) 2.04491 1.48571i 0.0875141 0.0635827i
\(547\) −21.6287 15.7142i −0.924777 0.671890i 0.0199316 0.999801i \(-0.493655\pi\)
−0.944708 + 0.327912i \(0.893655\pi\)
\(548\) −9.17203 28.2286i −0.391810 1.20587i
\(549\) 9.18431 0.391977
\(550\) 0 0
\(551\) 37.5422 1.59935
\(552\) −1.65559 5.09540i −0.0704668 0.216875i
\(553\) 14.3977 + 10.4605i 0.612251 + 0.444826i
\(554\) 35.6394 25.8935i 1.51417 1.10011i
\(555\) 0 0
\(556\) 16.4931 50.7606i 0.699464 2.15273i
\(557\) 13.9510 10.1360i 0.591125 0.429477i −0.251593 0.967833i \(-0.580954\pi\)
0.842718 + 0.538356i \(0.180954\pi\)
\(558\) 6.85264 + 4.97873i 0.290095 + 0.210767i
\(559\) 0.533620 + 1.64231i 0.0225697 + 0.0694624i
\(560\) 0 0
\(561\) −16.3558 + 2.73663i −0.690541 + 0.115541i
\(562\) −18.2006 −0.767748
\(563\) 0.257075 + 0.791197i 0.0108344 + 0.0333450i 0.956328 0.292297i \(-0.0944196\pi\)
−0.945493 + 0.325642i \(0.894420\pi\)
\(564\) 39.1316 + 28.4307i 1.64774 + 1.19715i
\(565\) 0 0
\(566\) 4.08813 12.5820i 0.171837 0.528860i
\(567\) −1.01569 + 3.12597i −0.0426550 + 0.131278i
\(568\) 12.3992 9.00855i 0.520259 0.377991i
\(569\) −9.38141 6.81599i −0.393289 0.285741i 0.373513 0.927625i \(-0.378153\pi\)
−0.766802 + 0.641884i \(0.778153\pi\)
\(570\) 0 0
\(571\) 21.8414 0.914034 0.457017 0.889458i \(-0.348918\pi\)
0.457017 + 0.889458i \(0.348918\pi\)
\(572\) −1.93315 3.71376i −0.0808292 0.155280i
\(573\) −15.3693 −0.642061
\(574\) 27.0575 + 83.2744i 1.12936 + 3.47580i
\(575\) 0 0
\(576\) 6.16110 4.47630i 0.256712 0.186512i
\(577\) −3.01164 + 9.26888i −0.125376 + 0.385868i −0.993969 0.109657i \(-0.965025\pi\)
0.868593 + 0.495526i \(0.165025\pi\)
\(578\) −6.07129 + 18.6855i −0.252532 + 0.777214i
\(579\) −12.7435 + 9.25867i −0.529600 + 0.384777i
\(580\) 0 0
\(581\) 16.5003 + 50.7827i 0.684548 + 2.10682i
\(582\) −0.550320 −0.0228115
\(583\) 2.41986 16.1891i 0.100220 0.670485i
\(584\) −43.1669 −1.78626
\(585\) 0 0
\(586\) 3.45724 + 2.51183i 0.142817 + 0.103763i
\(587\) 18.5622 13.4862i 0.766143 0.556635i −0.134645 0.990894i \(-0.542990\pi\)
0.900788 + 0.434258i \(0.142990\pi\)
\(588\) −4.73805 + 14.5822i −0.195394 + 0.601361i
\(589\) −7.94453 + 24.4507i −0.327349 + 1.00748i
\(590\) 0 0
\(591\) −13.2630 9.63612i −0.545566 0.396377i
\(592\) −3.41022 10.4956i −0.140159 0.431366i
\(593\) −28.7819 −1.18193 −0.590965 0.806697i \(-0.701253\pi\)
−0.590965 + 0.806697i \(0.701253\pi\)
\(594\) 7.28939 + 3.63456i 0.299087 + 0.149128i
\(595\) 0 0
\(596\) −7.32333 22.5389i −0.299975 0.923229i
\(597\) 5.63480 + 4.09392i 0.230617 + 0.167553i
\(598\) −0.668140 + 0.485432i −0.0273223 + 0.0198508i
\(599\) −9.02179 + 27.7662i −0.368620 + 1.13450i 0.579062 + 0.815283i \(0.303419\pi\)
−0.947683 + 0.319214i \(0.896581\pi\)
\(600\) 0 0
\(601\) 5.40494 3.92692i 0.220472 0.160182i −0.472067 0.881563i \(-0.656492\pi\)
0.692539 + 0.721380i \(0.256492\pi\)
\(602\) −36.0135 26.1653i −1.46780 1.06642i
\(603\) 4.71989 + 14.5263i 0.192209 + 0.591557i
\(604\) 30.7522 1.25129
\(605\) 0 0
\(606\) −1.24102 −0.0504131
\(607\) 13.1674 + 40.5252i 0.534450 + 1.64487i 0.744834 + 0.667250i \(0.232529\pi\)
−0.210384 + 0.977619i \(0.567471\pi\)
\(608\) −1.87355 1.36121i −0.0759824 0.0552044i
\(609\) 13.3925 9.73024i 0.542693 0.394289i
\(610\) 0 0
\(611\) 1.16099 3.57315i 0.0469685 0.144554i
\(612\) 16.3073 11.8479i 0.659182 0.478924i
\(613\) −4.71783 3.42771i −0.190552 0.138444i 0.488419 0.872609i \(-0.337574\pi\)
−0.678971 + 0.734165i \(0.737574\pi\)
\(614\) 16.2078 + 49.8824i 0.654093 + 2.01309i
\(615\) 0 0
\(616\) 48.6699 + 24.2673i 1.96097 + 0.977758i
\(617\) 33.6386 1.35424 0.677119 0.735874i \(-0.263228\pi\)
0.677119 + 0.735874i \(0.263228\pi\)
\(618\) 4.85852 + 14.9530i 0.195438 + 0.601498i
\(619\) −34.4331 25.0171i −1.38398 1.00552i −0.996495 0.0836477i \(-0.973343\pi\)
−0.387488 0.921875i \(-0.626657\pi\)
\(620\) 0 0
\(621\) 0.331860 1.02136i 0.0133171 0.0409857i
\(622\) −24.8996 + 76.6329i −0.998381 + 3.07270i
\(623\) 4.31089 3.13205i 0.172712 0.125483i
\(624\) 1.06127 + 0.771056i 0.0424847 + 0.0308669i
\(625\) 0 0
\(626\) −8.49374 −0.339478
\(627\) −3.65476 + 24.4507i −0.145957 + 0.976468i
\(628\) 40.8509 1.63013
\(629\) 4.07019 + 12.5268i 0.162289 + 0.499475i
\(630\) 0 0
\(631\) 7.20016 5.23122i 0.286634 0.208252i −0.435172 0.900347i \(-0.643312\pi\)
0.721806 + 0.692096i \(0.243312\pi\)
\(632\) −8.34713 + 25.6898i −0.332031 + 1.02189i
\(633\) 6.16585 18.9765i 0.245071 0.754250i
\(634\) 5.71351 4.15111i 0.226912 0.164862i
\(635\) 0 0
\(636\) 6.14839 + 18.9228i 0.243799 + 0.750337i
\(637\) 1.19095 0.0471871
\(638\) −18.9416 36.3886i −0.749906 1.44064i
\(639\) 3.07211 0.121531
\(640\) 0 0
\(641\) 4.99007 + 3.62549i 0.197096 + 0.143198i 0.681956 0.731393i \(-0.261130\pi\)
−0.484860 + 0.874592i \(0.661130\pi\)
\(642\) 4.15747 3.02058i 0.164082 0.119213i
\(643\) −1.34526 + 4.14029i −0.0530519 + 0.163277i −0.974072 0.226238i \(-0.927357\pi\)
0.921020 + 0.389515i \(0.127357\pi\)
\(644\) 4.39731 13.5335i 0.173278 0.533296i
\(645\) 0 0
\(646\) 74.0508 + 53.8011i 2.91349 + 2.11677i
\(647\) −4.16967 12.8329i −0.163927 0.504514i 0.835029 0.550206i \(-0.185451\pi\)
−0.998956 + 0.0456916i \(0.985451\pi\)
\(648\) −4.98884 −0.195980
\(649\) 29.9771 5.01575i 1.17671 0.196885i
\(650\) 0 0
\(651\) 3.50310 + 10.7814i 0.137297 + 0.422558i
\(652\) −16.4021 11.9168i −0.642354 0.466697i
\(653\) 22.2060 16.1336i 0.868988 0.631357i −0.0613270 0.998118i \(-0.519533\pi\)
0.930315 + 0.366761i \(0.119533\pi\)
\(654\) −5.07922 + 15.6322i −0.198613 + 0.611269i
\(655\) 0 0
\(656\) −36.7632 + 26.7100i −1.43536 + 1.04285i
\(657\) −7.00018 5.08592i −0.273103 0.198421i
\(658\) 29.9285 + 92.1105i 1.16674 + 3.59084i
\(659\) −18.7768 −0.731441 −0.365721 0.930725i \(-0.619177\pi\)
−0.365721 + 0.930725i \(0.619177\pi\)
\(660\) 0 0
\(661\) −21.6525 −0.842184 −0.421092 0.907018i \(-0.638353\pi\)
−0.421092 + 0.907018i \(0.638353\pi\)
\(662\) 10.7174 + 32.9847i 0.416543 + 1.28199i
\(663\) −1.26665 0.920276i −0.0491927 0.0357406i
\(664\) −65.5674 + 47.6375i −2.54451 + 1.84869i
\(665\) 0 0
\(666\) 1.99919 6.15286i 0.0774669 0.238419i
\(667\) −4.37578 + 3.17919i −0.169431 + 0.123099i
\(668\) 18.8872 + 13.7224i 0.730769 + 0.530935i
\(669\) −6.22565 19.1606i −0.240698 0.740791i
\(670\) 0 0
\(671\) 21.3508 21.7258i 0.824240 0.838714i
\(672\) −1.02116 −0.0393919
\(673\) −7.20076 22.1617i −0.277569 0.854269i −0.988528 0.151036i \(-0.951739\pi\)
0.710959 0.703233i \(-0.248261\pi\)
\(674\) −31.6883 23.0229i −1.22059 0.886808i
\(675\) 0 0
\(676\) −16.0728 + 49.4670i −0.618184 + 1.90258i
\(677\) −10.2843 + 31.6519i −0.395259 + 1.21648i 0.533501 + 0.845800i \(0.320876\pi\)
−0.928760 + 0.370683i \(0.879124\pi\)
\(678\) −21.4463 + 15.5817i −0.823641 + 0.598410i
\(679\) −0.595859 0.432917i −0.0228670 0.0166138i
\(680\) 0 0
\(681\) 0.533937 0.0204605
\(682\) 27.7077 4.63603i 1.06098 0.177523i
\(683\) −16.9244 −0.647593 −0.323796 0.946127i \(-0.604959\pi\)
−0.323796 + 0.946127i \(0.604959\pi\)
\(684\) −9.28603 28.5795i −0.355060 1.09276i
\(685\) 0 0
\(686\) 20.8758 15.1671i 0.797041 0.579084i
\(687\) 6.85803 21.1068i 0.261650 0.805276i
\(688\) 7.13905 21.9717i 0.272174 0.837664i
\(689\) 1.25029 0.908392i 0.0476324 0.0346070i
\(690\) 0 0
\(691\) −14.9668 46.0630i −0.569363 1.75232i −0.654617 0.755961i \(-0.727170\pi\)
0.0852532 0.996359i \(-0.472830\pi\)
\(692\) −64.7650 −2.46200
\(693\) 5.03340 + 9.66962i 0.191203 + 0.367318i
\(694\) 72.8910 2.76690
\(695\) 0 0
\(696\) 20.3275 + 14.7688i 0.770511 + 0.559809i
\(697\) 43.8779 31.8791i 1.66199 1.20751i
\(698\) −24.0527 + 74.0267i −0.910409 + 2.80195i
\(699\) −1.41087 + 4.34221i −0.0533640 + 0.164237i
\(700\) 0 0
\(701\) 36.7424 + 26.6949i 1.38774 + 1.00825i 0.996109 + 0.0881330i \(0.0280900\pi\)
0.391634 + 0.920121i \(0.371910\pi\)
\(702\) 0.237640 + 0.731382i 0.00896916 + 0.0276042i
\(703\) 19.6361 0.740591
\(704\) 3.73392 24.9803i 0.140727 0.941482i
\(705\) 0 0
\(706\) 0.912130 + 2.80725i 0.0343285 + 0.105652i
\(707\) −1.34372 0.976267i −0.0505357 0.0367163i
\(708\) −29.8883 + 21.7151i −1.12327 + 0.816103i
\(709\) −0.545405 + 1.67858i −0.0204831 + 0.0630406i −0.960776 0.277327i \(-0.910551\pi\)
0.940292 + 0.340368i \(0.110551\pi\)
\(710\) 0 0
\(711\) −4.38039 + 3.18254i −0.164278 + 0.119355i
\(712\) 6.54317 + 4.75389i 0.245216 + 0.178160i
\(713\) −1.14458 3.52266i −0.0428649 0.131925i
\(714\) 40.3606 1.51046
\(715\) 0 0
\(716\) −33.4729 −1.25094
\(717\) 1.81100 + 5.57369i 0.0676331 + 0.208153i
\(718\) −23.1649 16.8303i −0.864506 0.628100i
\(719\) 2.66974 1.93968i 0.0995645 0.0723379i −0.536889 0.843653i \(-0.680401\pi\)
0.636454 + 0.771315i \(0.280401\pi\)
\(720\) 0 0
\(721\) −6.50241 + 20.0124i −0.242163 + 0.745300i
\(722\) 72.6459 52.7803i 2.70360 1.96428i
\(723\) 8.05841 + 5.85477i 0.299695 + 0.217741i
\(724\) −8.05294 24.7844i −0.299285 0.921105i
\(725\) 0 0
\(726\) 25.5434 8.79398i 0.948003 0.326375i
\(727\) −11.7838 −0.437037 −0.218519 0.975833i \(-0.570122\pi\)
−0.218519 + 0.975833i \(0.570122\pi\)
\(728\) 1.58668 + 4.88331i 0.0588064 + 0.180987i
\(729\) −0.809017 0.587785i −0.0299636 0.0217698i
\(730\) 0 0
\(731\) −8.52064 + 26.2238i −0.315147 + 0.969924i
\(732\) −11.4415 + 35.2133i −0.422890 + 1.30152i
\(733\) 4.63654 3.36865i 0.171255 0.124424i −0.498856 0.866685i \(-0.666246\pi\)
0.670111 + 0.742261i \(0.266246\pi\)
\(734\) −31.7619 23.0764i −1.17235 0.851765i
\(735\) 0 0
\(736\) 0.333646 0.0122983
\(737\) 45.3348 + 22.6044i 1.66993 + 0.832643i
\(738\) −26.6395 −0.980614
\(739\) −6.50638 20.0246i −0.239341 0.736616i −0.996516 0.0834038i \(-0.973421\pi\)
0.757175 0.653212i \(-0.226579\pi\)
\(740\) 0 0
\(741\) −1.88834 + 1.37196i −0.0693700 + 0.0504003i
\(742\) −12.3110 + 37.8895i −0.451952 + 1.39097i
\(743\) −4.05686 + 12.4857i −0.148832 + 0.458058i −0.997484 0.0708942i \(-0.977415\pi\)
0.848652 + 0.528952i \(0.177415\pi\)
\(744\) −13.9203 + 10.1137i −0.510343 + 0.370786i
\(745\) 0 0
\(746\) 0.244350 + 0.752032i 0.00894629 + 0.0275339i
\(747\) −16.2454 −0.594389
\(748\) 9.88299 66.1183i 0.361358 2.41753i
\(749\) 6.87768 0.251305
\(750\) 0 0
\(751\) −20.7311 15.0621i −0.756490 0.549622i 0.141342 0.989961i \(-0.454858\pi\)
−0.897832 + 0.440339i \(0.854858\pi\)
\(752\) −40.6641 + 29.5442i −1.48287 + 1.07737i
\(753\) 5.21584 16.0527i 0.190076 0.584993i
\(754\) 1.19687 3.68358i 0.0435874 0.134148i
\(755\) 0 0
\(756\) −10.7199 7.78845i −0.389878 0.283263i
\(757\) −9.64039 29.6701i −0.350386 1.07838i −0.958637 0.284632i \(-0.908129\pi\)
0.608251 0.793745i \(-0.291871\pi\)
\(758\) −28.0400 −1.01846
\(759\) −1.64458 3.15939i −0.0596945 0.114678i
\(760\) 0 0
\(761\) 3.51539 + 10.8193i 0.127433 + 0.392198i 0.994336 0.106278i \(-0.0338932\pi\)
−0.866904 + 0.498476i \(0.833893\pi\)
\(762\) −33.7830 24.5448i −1.22383 0.889165i
\(763\) −17.7968 + 12.9302i −0.644289 + 0.468103i
\(764\) 19.1465 58.9269i 0.692697 2.13190i
\(765\) 0 0
\(766\) −56.3617 + 40.9491i −2.03643 + 1.47955i
\(767\) 2.32154 + 1.68670i 0.0838260 + 0.0609032i
\(768\) 9.95872 + 30.6498i 0.359354 + 1.10598i
\(769\) 10.3938 0.374811 0.187405 0.982283i \(-0.439992\pi\)
0.187405 + 0.982283i \(0.439992\pi\)
\(770\) 0 0
\(771\) 11.1436 0.401326
\(772\) −19.6230 60.3935i −0.706248 2.17361i
\(773\) 11.3544 + 8.24944i 0.408389 + 0.296712i 0.772949 0.634468i \(-0.218781\pi\)
−0.364560 + 0.931180i \(0.618781\pi\)
\(774\) 10.9569 7.96062i 0.393836 0.286139i
\(775\) 0 0
\(776\) 0.345453 1.06319i 0.0124010 0.0381665i
\(777\) 7.00485 5.08932i 0.251298 0.182578i
\(778\) 30.1608 + 21.9131i 1.08132 + 0.785623i
\(779\) −24.9858 76.8985i −0.895211 2.75518i
\(780\) 0 0
\(781\) 7.14176 7.26717i 0.255552 0.260040i
\(782\) −13.1871 −0.471571