Properties

Label 825.2.bx.h.49.4
Level $825$
Weight $2$
Character 825.49
Analytic conductor $6.588$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 825.bx (of order \(10\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.58765816676\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \( x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 165)
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 49.4
Root \(0.701538 - 0.227943i\) of defining polynomial
Character \(\chi\) \(=\) 825.49
Dual form 825.2.bx.h.724.4

$q$-expansion

\(f(q)\) \(=\) \(q+(2.33569 - 0.758911i) q^{2} +(0.587785 - 0.809017i) q^{3} +(3.26145 - 2.36959i) q^{4} +(0.758911 - 2.33569i) q^{6} +(1.93196 + 2.65911i) q^{7} +(2.93237 - 4.03606i) q^{8} +(-0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(2.33569 - 0.758911i) q^{2} +(0.587785 - 0.809017i) q^{3} +(3.26145 - 2.36959i) q^{4} +(0.758911 - 2.33569i) q^{6} +(1.93196 + 2.65911i) q^{7} +(2.93237 - 4.03606i) q^{8} +(-0.309017 - 0.951057i) q^{9} +(2.96813 + 1.47994i) q^{11} -4.03138i q^{12} +(0.297808 - 0.0967635i) q^{13} +(6.53048 + 4.74467i) q^{14} +(1.29455 - 3.98423i) q^{16} +(-4.75528 - 1.54508i) q^{17} +(-1.44353 - 1.98685i) q^{18} +(-6.03048 - 4.38140i) q^{19} +3.28684 q^{21} +(8.05576 + 1.20413i) q^{22} +1.07392i q^{23} +(-1.54164 - 4.74467i) q^{24} +(0.622150 - 0.452019i) q^{26} +(-0.951057 - 0.309017i) q^{27} +(12.6020 + 4.09463i) q^{28} +(-4.07459 + 2.96036i) q^{29} +(1.06580 + 3.28018i) q^{31} -0.310680i q^{32} +(2.94192 - 1.53138i) q^{33} -12.2794 q^{34} +(-3.26145 - 2.36959i) q^{36} +(1.54839 + 2.13118i) q^{37} +(-17.4104 - 5.65698i) q^{38} +(0.0967635 - 0.297808i) q^{39} +(-8.77557 - 6.37583i) q^{41} +(7.67703 - 2.49442i) q^{42} -5.51468i q^{43} +(13.1873 - 2.20648i) q^{44} +(0.815010 + 2.50834i) q^{46} +(7.05236 - 9.70674i) q^{47} +(-2.46239 - 3.38919i) q^{48} +(-1.17529 + 3.61718i) q^{49} +(-4.04508 + 2.93893i) q^{51} +(0.741996 - 1.02127i) q^{52} +(-4.69387 + 1.52513i) q^{53} -2.45589 q^{54} +16.3975 q^{56} +(-7.08925 + 2.30344i) q^{57} +(-7.27031 + 10.0067i) q^{58} +(-7.41391 + 5.38652i) q^{59} +(2.83811 - 8.73480i) q^{61} +(4.97873 + 6.85264i) q^{62} +(1.93196 - 2.65911i) q^{63} +(2.35333 + 7.24280i) q^{64} +(5.70922 - 5.80948i) q^{66} +15.2739i q^{67} +(-19.1704 + 6.22882i) q^{68} +(0.868820 + 0.631235i) q^{69} +(0.949335 - 2.92175i) q^{71} +(-4.74467 - 1.54164i) q^{72} +(5.08592 + 7.00018i) q^{73} +(5.23394 + 3.80268i) q^{74} -30.0502 q^{76} +(1.79898 + 10.7518i) q^{77} -0.769020i q^{78} +(-1.67316 - 5.14946i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-25.3357 - 8.23206i) q^{82} +(15.4503 + 5.02011i) q^{83} +(10.7199 - 7.78845i) q^{84} +(-4.18515 - 12.8806i) q^{86} +5.03647i q^{87} +(14.6768 - 7.63981i) q^{88} -1.62118 q^{89} +(0.832656 + 0.604960i) q^{91} +(2.54475 + 3.50254i) q^{92} +(3.28018 + 1.06580i) q^{93} +(9.10556 - 28.0240i) q^{94} +(-0.251345 - 0.182613i) q^{96} +(0.213115 - 0.0692451i) q^{97} +9.34054i q^{98} +(0.490303 - 3.28018i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16 q + 4 q^{4} + 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 16 q + 4 q^{4} + 4 q^{9} - 6 q^{11} + 20 q^{14} - 40 q^{16} - 12 q^{19} - 8 q^{21} + 40 q^{24} - 16 q^{26} + 6 q^{31} - 100 q^{34} - 4 q^{36} - 12 q^{39} - 50 q^{41} - 14 q^{44} - 12 q^{46} - 42 q^{49} - 20 q^{51} - 20 q^{54} + 40 q^{56} - 70 q^{59} + 42 q^{61} + 154 q^{64} + 50 q^{66} + 10 q^{69} + 50 q^{71} + 58 q^{74} - 28 q^{76} - 60 q^{79} - 4 q^{81} + 68 q^{84} - 68 q^{86} - 64 q^{89} + 74 q^{91} + 78 q^{94} + 20 q^{96} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.33569 0.758911i 1.65158 0.536631i 0.672499 0.740098i \(-0.265221\pi\)
0.979082 + 0.203468i \(0.0652211\pi\)
\(3\) 0.587785 0.809017i 0.339358 0.467086i
\(4\) 3.26145 2.36959i 1.63073 1.18479i
\(5\) 0 0
\(6\) 0.758911 2.33569i 0.309824 0.953540i
\(7\) 1.93196 + 2.65911i 0.730211 + 1.00505i 0.999122 + 0.0418845i \(0.0133361\pi\)
−0.268911 + 0.963165i \(0.586664\pi\)
\(8\) 2.93237 4.03606i 1.03675 1.42696i
\(9\) −0.309017 0.951057i −0.103006 0.317019i
\(10\) 0 0
\(11\) 2.96813 + 1.47994i 0.894924 + 0.446218i
\(12\) 4.03138i 1.16376i
\(13\) 0.297808 0.0967635i 0.0825970 0.0268374i −0.267427 0.963578i \(-0.586173\pi\)
0.350024 + 0.936741i \(0.386173\pi\)
\(14\) 6.53048 + 4.74467i 1.74534 + 1.26807i
\(15\) 0 0
\(16\) 1.29455 3.98423i 0.323638 0.996057i
\(17\) −4.75528 1.54508i −1.15333 0.374738i −0.330930 0.943655i \(-0.607363\pi\)
−0.822395 + 0.568917i \(0.807363\pi\)
\(18\) −1.44353 1.98685i −0.340244 0.468306i
\(19\) −6.03048 4.38140i −1.38349 1.00516i −0.996545 0.0830568i \(-0.973532\pi\)
−0.386941 0.922104i \(-0.626468\pi\)
\(20\) 0 0
\(21\) 3.28684 0.717248
\(22\) 8.05576 + 1.20413i 1.71749 + 0.256721i
\(23\) 1.07392i 0.223928i 0.993712 + 0.111964i \(0.0357141\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(24\) −1.54164 4.74467i −0.314685 0.968501i
\(25\) 0 0
\(26\) 0.622150 0.452019i 0.122014 0.0886482i
\(27\) −0.951057 0.309017i −0.183031 0.0594703i
\(28\) 12.6020 + 4.09463i 2.38155 + 0.773813i
\(29\) −4.07459 + 2.96036i −0.756632 + 0.549725i −0.897875 0.440250i \(-0.854890\pi\)
0.141243 + 0.989975i \(0.454890\pi\)
\(30\) 0 0
\(31\) 1.06580 + 3.28018i 0.191423 + 0.589138i 1.00000 0.000748050i \(0.000238112\pi\)
−0.808577 + 0.588390i \(0.799762\pi\)
\(32\) 0.310680i 0.0549210i
\(33\) 2.94192 1.53138i 0.512122 0.266579i
\(34\) −12.2794 −2.10591
\(35\) 0 0
\(36\) −3.26145 2.36959i −0.543576 0.394931i
\(37\) 1.54839 + 2.13118i 0.254554 + 0.350364i 0.917100 0.398658i \(-0.130524\pi\)
−0.662546 + 0.749022i \(0.730524\pi\)
\(38\) −17.4104 5.65698i −2.82434 0.917683i
\(39\) 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 \(-0.621608\pi\)
\(42\) 7.67703 2.49442i 1.18459 0.384897i
\(43\) 5.51468i 0.840980i −0.907297 0.420490i \(-0.861858\pi\)
0.907297 0.420490i \(-0.138142\pi\)
\(44\) 13.1873 2.20648i 1.98805 0.332640i
\(45\) 0 0
\(46\) 0.815010 + 2.50834i 0.120167 + 0.369835i
\(47\) 7.05236 9.70674i 1.02869 1.41587i 0.122767 0.992435i \(-0.460823\pi\)
0.905925 0.423438i \(-0.139177\pi\)
\(48\) −2.46239 3.38919i −0.355415 0.489187i
\(49\) −1.17529 + 3.61718i −0.167899 + 0.516740i
\(50\) 0 0
\(51\) −4.04508 + 2.93893i −0.566425 + 0.411532i
\(52\) 0.741996 1.02127i 0.102896 0.141625i
\(53\) −4.69387 + 1.52513i −0.644753 + 0.209493i −0.613099 0.790006i \(-0.710077\pi\)
−0.0316539 + 0.999499i \(0.510077\pi\)
\(54\) −2.45589 −0.334204
\(55\) 0 0
\(56\) 16.3975 2.19121
\(57\) −7.08925 + 2.30344i −0.938994 + 0.305098i
\(58\) −7.27031 + 10.0067i −0.954639 + 1.31395i
\(59\) −7.41391 + 5.38652i −0.965208 + 0.701265i −0.954354 0.298676i \(-0.903455\pi\)
−0.0108537 + 0.999941i \(0.503455\pi\)
\(60\) 0 0
\(61\) 2.83811 8.73480i 0.363382 1.11838i −0.587605 0.809148i \(-0.699929\pi\)
0.950988 0.309229i \(-0.100071\pi\)
\(62\) 4.97873 + 6.85264i 0.632300 + 0.870286i
\(63\) 1.93196 2.65911i 0.243404 0.335016i
\(64\) 2.35333 + 7.24280i 0.294166 + 0.905350i
\(65\) 0 0
\(66\) 5.70922 5.80948i 0.702756 0.715097i
\(67\) 15.2739i 1.86600i 0.359876 + 0.933000i \(0.382819\pi\)
−0.359876 + 0.933000i \(0.617181\pi\)
\(68\) −19.1704 + 6.22882i −2.32475 + 0.755356i
\(69\) 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 \(0.0416470\pi\)
\(72\) −4.74467 1.54164i −0.559164 0.181684i
\(73\) 5.08592 + 7.00018i 0.595262 + 0.819309i 0.995264 0.0972058i \(-0.0309905\pi\)
−0.400002 + 0.916514i \(0.630991\pi\)
\(74\) 5.23394 + 3.80268i 0.608433 + 0.442052i
\(75\) 0 0
\(76\) −30.0502 −3.44700
\(77\) 1.79898 + 10.7518i 0.205012 + 1.22528i
\(78\) 0.769020i 0.0870744i
\(79\) −1.67316 5.14946i −0.188245 0.579360i 0.811744 0.584014i \(-0.198519\pi\)
−0.999989 + 0.00465401i \(0.998519\pi\)
\(80\) 0 0
\(81\) −0.809017 + 0.587785i −0.0898908 + 0.0653095i
\(82\) −25.3357 8.23206i −2.79786 0.909079i
\(83\) 15.4503 + 5.02011i 1.69589 + 0.551029i 0.987887 0.155178i \(-0.0495952\pi\)
0.708006 + 0.706207i \(0.249595\pi\)
\(84\) 10.7199 7.78845i 1.16964 0.849790i
\(85\) 0 0
\(86\) −4.18515 12.8806i −0.451296 1.38895i
\(87\) 5.03647i 0.539966i
\(88\) 14.6768 7.63981i 1.56455 0.814406i
\(89\) −1.62118 −0.171845 −0.0859223 0.996302i \(-0.527384\pi\)
−0.0859223 + 0.996302i \(0.527384\pi\)
\(90\) 0 0
\(91\) 0.832656 + 0.604960i 0.0872861 + 0.0634171i
\(92\) 2.54475 + 3.50254i 0.265308 + 0.365165i
\(93\) 3.28018 + 1.06580i 0.340139 + 0.110518i
\(94\) 9.10556 28.0240i 0.939166 2.89046i
\(95\) 0 0
\(96\) −0.251345 0.182613i −0.0256528 0.0186379i
\(97\) 0.213115 0.0692451i 0.0216385 0.00703078i −0.298178 0.954510i \(-0.596379\pi\)
0.319816 + 0.947480i \(0.396379\pi\)
\(98\) 9.34054i 0.943537i
\(99\) 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 \(0.908003\pi\)
\(102\) −7.21767 + 9.93427i −0.714656 + 0.983639i
\(103\) 3.76298 + 5.17930i 0.370778 + 0.510332i 0.953112 0.302618i \(-0.0978605\pi\)
−0.582334 + 0.812949i \(0.697861\pi\)
\(104\) 0.482738 1.48571i 0.0473363 0.145686i
\(105\) 0 0
\(106\) −9.80598 + 7.12446i −0.952441 + 0.691989i
\(107\) −1.22993 + 1.69286i −0.118902 + 0.163655i −0.864319 0.502943i \(-0.832250\pi\)
0.745417 + 0.666598i \(0.232250\pi\)
\(108\) −3.83407 + 1.24576i −0.368934 + 0.119874i
\(109\) 6.69278 0.641052 0.320526 0.947240i \(-0.396140\pi\)
0.320526 + 0.947240i \(0.396140\pi\)
\(110\) 0 0
\(111\) 2.63428 0.250035
\(112\) 13.0955 4.25499i 1.23741 0.402059i
\(113\) −6.34462 + 8.73262i −0.596852 + 0.821496i −0.995416 0.0956448i \(-0.969509\pi\)
0.398564 + 0.917141i \(0.369509\pi\)
\(114\) −14.8102 + 10.7602i −1.38710 + 1.00779i
\(115\) 0 0
\(116\) −6.27426 + 19.3102i −0.582550 + 1.79290i
\(117\) −0.184055 0.253330i −0.0170159 0.0234204i
\(118\) −13.2287 + 18.2077i −1.21780 + 1.67616i
\(119\) −5.07845 15.6299i −0.465541 1.43279i
\(120\) 0 0
\(121\) 6.61956 + 8.78529i 0.601779 + 0.798663i
\(122\) 22.5556i 2.04209i
\(123\) −10.3163 + 3.35197i −0.930190 + 0.302237i
\(124\) 11.2487 + 8.17267i 1.01017 + 0.733928i
\(125\) 0 0
\(126\) 2.49442 7.67703i 0.222221 0.683925i
\(127\) 16.1711 + 5.25430i 1.43495 + 0.466244i 0.920320 0.391167i \(-0.127929\pi\)
0.514632 + 0.857411i \(0.327929\pi\)
\(128\) 11.3585 + 15.6336i 1.00396 + 1.38183i
\(129\) −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 \(0.500599\pi\)
\(132\) 5.96619 11.9657i 0.519291 1.04148i
\(133\) 24.5004i 2.12445i
\(134\) 11.5915 + 35.6750i 1.00135 + 3.08185i
\(135\) 0 0
\(136\) −20.1803 + 14.6618i −1.73044 + 1.25724i
\(137\) −7.00222 2.27516i −0.598240 0.194380i −0.00578480 0.999983i \(-0.501841\pi\)
−0.592455 + 0.805603i \(0.701841\pi\)
\(138\) 2.50834 + 0.815010i 0.213524 + 0.0693783i
\(139\) 10.7109 7.78189i 0.908483 0.660052i −0.0321478 0.999483i \(-0.510235\pi\)
0.940631 + 0.339432i \(0.110235\pi\)
\(140\) 0 0
\(141\) −3.70764 11.4110i −0.312240 0.960976i
\(142\) 7.54476i 0.633142i
\(143\) 1.02713 + 0.153530i 0.0858933 + 0.0128388i
\(144\) −4.18926 −0.349105
\(145\) 0 0
\(146\) 17.1916 + 12.4905i 1.42279 + 1.03372i
\(147\) 2.23554 + 3.07696i 0.184384 + 0.253783i
\(148\) 10.1000 + 3.28170i 0.830217 + 0.269754i
\(149\) 1.81658 5.59087i 0.148820 0.458022i −0.848662 0.528935i \(-0.822591\pi\)
0.997482 + 0.0709136i \(0.0225915\pi\)
\(150\) 0 0
\(151\) −6.17135 4.48375i −0.502217 0.364882i 0.307646 0.951501i \(-0.400459\pi\)
−0.809863 + 0.586619i \(0.800459\pi\)
\(152\) −35.3671 + 11.4915i −2.86865 + 0.932082i
\(153\) 5.00000i 0.404226i
\(154\) 12.3615 + 23.7475i 0.996116 + 1.91363i
\(155\) 0 0
\(156\) −0.390091 1.20058i −0.0312322 0.0961230i
\(157\) 5.95616 8.19795i 0.475353 0.654267i −0.502250 0.864722i \(-0.667494\pi\)
0.977604 + 0.210455i \(0.0674945\pi\)
\(158\) −7.81596 10.7578i −0.621805 0.855841i
\(159\) −1.52513 + 4.69387i −0.120951 + 0.372248i
\(160\) 0 0
\(161\) −2.85567 + 2.07477i −0.225059 + 0.163515i
\(162\) −1.44353 + 1.98685i −0.113415 + 0.156102i
\(163\) 4.78292 1.55407i 0.374627 0.121724i −0.115651 0.993290i \(-0.536895\pi\)
0.490278 + 0.871566i \(0.336895\pi\)
\(164\) −43.7292 −3.41468
\(165\) 0 0
\(166\) 39.8969 3.09660
\(167\) 5.50761 1.78953i 0.426192 0.138478i −0.0880642 0.996115i \(-0.528068\pi\)
0.514256 + 0.857637i \(0.328068\pi\)
\(168\) 9.63822 13.2659i 0.743605 1.02348i
\(169\) −10.4379 + 7.58357i −0.802915 + 0.583352i
\(170\) 0 0
\(171\) −2.30344 + 7.08925i −0.176148 + 0.542128i
\(172\) −13.0675 17.9859i −0.996387 1.37141i
\(173\) 9.44290 12.9970i 0.717930 0.988146i −0.281660 0.959514i \(-0.590885\pi\)
0.999590 0.0286316i \(-0.00911498\pi\)
\(174\) 3.82223 + 11.7636i 0.289762 + 0.891797i
\(175\) 0 0
\(176\) 9.73881 9.90983i 0.734090 0.746982i
\(177\) 9.16409i 0.688815i
\(178\) −3.78657 + 1.23033i −0.283815 + 0.0922171i
\(179\) −6.71734 4.88043i −0.502078 0.364781i 0.307732 0.951473i \(-0.400430\pi\)
−0.809810 + 0.586692i \(0.800430\pi\)
\(180\) 0 0
\(181\) −1.99756 + 6.14787i −0.148478 + 0.456968i −0.997442 0.0714830i \(-0.977227\pi\)
0.848964 + 0.528451i \(0.177227\pi\)
\(182\) 2.40394 + 0.781086i 0.178192 + 0.0578980i
\(183\) −5.39840 7.43026i −0.399061 0.549261i
\(184\) 4.33440 + 3.14913i 0.319536 + 0.232157i
\(185\) 0 0
\(186\) 8.47033 0.621074
\(187\) −11.8277 11.6235i −0.864924 0.849997i
\(188\) 48.3693i 3.52769i
\(189\) −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 \(0.487680\pi\)
\(192\) 7.24280 + 2.35333i 0.522704 + 0.169837i
\(193\) 14.9808 + 4.86757i 1.07834 + 0.350375i 0.793732 0.608267i \(-0.208135\pi\)
0.284612 + 0.958643i \(0.408135\pi\)
\(194\) 0.445218 0.323470i 0.0319648 0.0232238i
\(195\) 0 0
\(196\) 4.73805 + 14.5822i 0.338432 + 1.04159i
\(197\) 16.3940i 1.16802i −0.811746 0.584010i \(-0.801483\pi\)
0.811746 0.584010i \(-0.198517\pi\)
\(198\) −1.34417 8.03358i −0.0955261 0.570922i
\(199\) −6.96500 −0.493736 −0.246868 0.969049i \(-0.579401\pi\)
−0.246868 + 0.969049i \(0.579401\pi\)
\(200\) 0 0
\(201\) 12.3568 + 8.97776i 0.871583 + 0.633242i
\(202\) −0.729455 1.00401i −0.0513242 0.0706418i
\(203\) −15.7439 5.11549i −1.10500 0.359037i
\(204\) −6.22882 + 19.1704i −0.436105 + 1.34219i
\(205\) 0 0
\(206\) 12.7198 + 9.24146i 0.886229 + 0.643883i
\(207\) 1.02136 0.331860i 0.0709894 0.0230658i
\(208\) 1.31180i 0.0909569i
\(209\) −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 \(-0.340992\pi\)
\(212\) −11.6949 + 16.0967i −0.803211 + 1.10552i
\(213\) −1.80574 2.48539i −0.123727 0.170296i
\(214\) −1.58801 + 4.88740i −0.108554 + 0.334096i
\(215\) 0 0
\(216\) −4.03606 + 2.93237i −0.274619 + 0.199522i
\(217\) −6.66330 + 9.17124i −0.452334 + 0.622585i
\(218\) 15.6322 5.07922i 1.05875 0.344008i
\(219\) 8.65269 0.584695
\(220\) 0 0
\(221\) −1.56567 −0.105318
\(222\) 6.15286 1.99919i 0.412953 0.134177i
\(223\) −11.8419 + 16.2990i −0.792992 + 1.09146i 0.200737 + 0.979645i \(0.435666\pi\)
−0.993729 + 0.111815i \(0.964334\pi\)
\(224\) 0.826133 0.600220i 0.0551983 0.0401039i
\(225\) 0 0
\(226\) −8.19177 + 25.2117i −0.544908 + 1.67706i
\(227\) 0.313840 + 0.431964i 0.0208303 + 0.0286705i 0.819305 0.573358i \(-0.194359\pi\)
−0.798475 + 0.602028i \(0.794359\pi\)
\(228\) −17.6631 + 24.3111i −1.16977 + 1.61004i
\(229\) 6.85803 + 21.1068i 0.453191 + 1.39478i 0.873245 + 0.487281i \(0.162011\pi\)
−0.420054 + 0.907499i \(0.637989\pi\)
\(230\) 0 0
\(231\) 9.75577 + 4.86432i 0.641882 + 0.320049i
\(232\) 25.1261i 1.64961i
\(233\) 4.34221 1.41087i 0.284467 0.0924291i −0.163308 0.986575i \(-0.552216\pi\)
0.447775 + 0.894146i \(0.352216\pi\)
\(234\) −0.622150 0.452019i −0.0406712 0.0295494i
\(235\) 0 0
\(236\) −11.4163 + 35.1358i −0.743138 + 2.28714i
\(237\) −5.14946 1.67316i −0.334493 0.108684i
\(238\) −23.7233 32.6524i −1.53776 2.11654i
\(239\) −4.74126 3.44473i −0.306687 0.222821i 0.423787 0.905762i \(-0.360701\pi\)
−0.730474 + 0.682941i \(0.760701\pi\)
\(240\) 0 0
\(241\) 9.96074 0.641628 0.320814 0.947142i \(-0.396044\pi\)
0.320814 + 0.947142i \(0.396044\pi\)
\(242\) 22.1285 + 15.4960i 1.42247 + 0.996123i
\(243\) 1.00000i 0.0641500i
\(244\) −11.4415 35.2133i −0.732466 2.25430i
\(245\) 0 0
\(246\) −21.5518 + 15.6583i −1.37409 + 0.998337i
\(247\) −2.21988 0.721283i −0.141248 0.0458941i
\(248\) 16.3643 + 5.31709i 1.03913 + 0.337635i
\(249\) 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 \(-0.278819\pi\)
\(252\) 13.2505i 0.834704i
\(253\) −1.58934 + 3.18753i −0.0999207 + 0.200399i
\(254\) 41.7581 2.62014
\(255\) 0 0
\(256\) 26.0723 + 18.9426i 1.62952 + 1.18391i
\(257\) 6.55003 + 9.01534i 0.408580 + 0.562362i 0.962871 0.269961i \(-0.0870108\pi\)
−0.554292 + 0.832323i \(0.687011\pi\)
\(258\) −12.8806 4.18515i −0.801909 0.260556i
\(259\) −2.67561 + 8.23470i −0.166255 + 0.511679i
\(260\) 0 0
\(261\) 4.07459 + 2.96036i 0.252211 + 0.183242i
\(262\) −0.100553 + 0.0326717i −0.00621220 + 0.00201846i
\(263\) 26.8726i 1.65704i −0.559961 0.828519i \(-0.689184\pi\)
0.559961 0.828519i \(-0.310816\pi\)
\(264\) 2.44604 16.3643i 0.150544 1.00715i
\(265\) 0 0
\(266\) −18.5936 57.2252i −1.14005 3.50870i
\(267\) −0.952905 + 1.31156i −0.0583168 + 0.0802662i
\(268\) 36.1927 + 49.8150i 2.21082 + 3.04294i
\(269\) 3.10961 9.57038i 0.189596 0.583516i −0.810401 0.585875i \(-0.800751\pi\)
0.999997 + 0.00235886i \(0.000750850\pi\)
\(270\) 0 0
\(271\) −8.53037 + 6.19767i −0.518183 + 0.376482i −0.815919 0.578166i \(-0.803768\pi\)
0.297736 + 0.954648i \(0.403768\pi\)
\(272\) −12.3119 + 16.9459i −0.746521 + 1.02750i
\(273\) 0.978846 0.318046i 0.0592425 0.0192490i
\(274\) −18.0816 −1.09235
\(275\) 0 0
\(276\) 4.32938 0.260598
\(277\) −17.0597 + 5.54302i −1.02502 + 0.333048i −0.772818 0.634628i \(-0.781153\pi\)
−0.252198 + 0.967676i \(0.581153\pi\)
\(278\) 19.1114 26.3047i 1.14623 1.57765i
\(279\) 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 \(0.0290508\pi\)
\(282\) −17.3198 23.8387i −1.03138 1.41957i
\(283\) 3.16630 4.35804i 0.188217 0.259059i −0.704472 0.709732i \(-0.748816\pi\)
0.892689 + 0.450673i \(0.148816\pi\)
\(284\) −3.82713 11.7787i −0.227098 0.698937i
\(285\) 0 0
\(286\) 2.51558 0.420905i 0.148749 0.0248886i
\(287\) 35.6530i 2.10453i
\(288\) −0.295474 + 0.0960054i −0.0174110 + 0.00565717i
\(289\) 6.47214 + 4.70228i 0.380714 + 0.276605i
\(290\) 0 0
\(291\) 0.0692451 0.213115i 0.00405922 0.0124930i
\(292\) 33.1750 + 10.7792i 1.94142 + 0.630806i
\(293\) 1.02278 + 1.40774i 0.0597515 + 0.0822409i 0.837847 0.545905i \(-0.183814\pi\)
−0.778096 + 0.628146i \(0.783814\pi\)
\(294\) 7.55666 + 5.49023i 0.440713 + 0.320197i
\(295\) 0 0
\(296\) 13.1420 0.763864
\(297\) −2.36553 2.32471i −0.137262 0.134893i
\(298\) 14.4371i 0.836321i
\(299\) 0.103916 + 0.319822i 0.00600964 + 0.0184958i
\(300\) 0 0
\(301\) 14.6641 10.6541i 0.845227 0.614093i
\(302\) −17.8171 5.78913i −1.02526 0.333127i
\(303\) −0.480593 0.156154i −0.0276094 0.00897082i
\(304\) −25.2633 + 18.3548i −1.44895 + 1.05272i
\(305\) 0 0
\(306\) 3.79455 + 11.6784i 0.216920 + 0.667612i
\(307\) 21.3566i 1.21889i −0.792829 0.609444i \(-0.791393\pi\)
0.792829 0.609444i \(-0.208607\pi\)
\(308\) 31.3445 + 30.8035i 1.78602 + 1.75519i
\(309\) 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 \(-0.680393\pi\)
\(312\) −0.918222 1.26382i −0.0519841 0.0715499i
\(313\) −3.28925 1.06874i −0.185919 0.0604089i 0.214578 0.976707i \(-0.431163\pi\)
−0.400497 + 0.916298i \(0.631163\pi\)
\(314\) 7.69021 23.6680i 0.433984 1.33566i
\(315\) 0 0
\(316\) −17.6590 12.8300i −0.993398 0.721746i
\(317\) −2.73491 + 0.888626i −0.153608 + 0.0499102i −0.384812 0.922995i \(-0.625734\pi\)
0.231204 + 0.972905i \(0.425734\pi\)
\(318\) 12.1209i 0.679704i
\(319\) −16.4751 + 2.75659i −0.922426 + 0.154340i
\(320\) 0 0
\(321\) 0.646615 + 1.99008i 0.0360905 + 0.111075i
\(322\) −5.09540 + 7.01321i −0.283955 + 0.390831i
\(323\) 21.9070 + 30.1524i 1.21894 + 1.67772i
\(324\) −1.24576 + 3.83407i −0.0692092 + 0.213004i
\(325\) 0 0
\(326\) 9.99201 7.25962i 0.553406 0.402073i
\(327\) 3.93392 5.41457i 0.217546 0.299427i
\(328\) −51.4664 + 16.7224i −2.84176 + 0.923342i
\(329\) 39.4362 2.17419
\(330\) 0 0
\(331\) −14.1221 −0.776219 −0.388109 0.921613i \(-0.626872\pi\)
−0.388109 + 0.921613i \(0.626872\pi\)
\(332\) 62.2861 20.2380i 3.41839 1.11070i
\(333\) 1.54839 2.13118i 0.0848514 0.116788i
\(334\) 11.5060 8.35958i 0.629579 0.457416i
\(335\) 0 0
\(336\) 4.25499 13.0955i 0.232129 0.714419i
\(337\) 9.37457 + 12.9030i 0.510665 + 0.702870i 0.984031 0.177995i \(-0.0569612\pi\)
−0.473366 + 0.880866i \(0.656961\pi\)
\(338\) −18.6244 + 25.6343i −1.01303 + 1.39432i
\(339\) 3.33556 + 10.2658i 0.181163 + 0.557562i
\(340\) 0 0
\(341\) −1.69105 + 11.3133i −0.0915755 + 0.612650i
\(342\) 18.3064i 0.989895i
\(343\) 9.99271 3.24683i 0.539555 0.175312i
\(344\) −22.2575 16.1711i −1.20005 0.871885i
\(345\) 0 0
\(346\) 12.1921 37.5233i 0.655449 2.01727i
\(347\) −28.2275 9.17166i −1.51533 0.492360i −0.570884 0.821030i \(-0.693400\pi\)
−0.944445 + 0.328670i \(0.893400\pi\)
\(348\) 11.9343 + 16.4262i 0.639748 + 0.880537i
\(349\) 25.6408 + 18.6291i 1.37252 + 0.997194i 0.997536 + 0.0701620i \(0.0223516\pi\)
0.374984 + 0.927031i \(0.377648\pi\)
\(350\) 0 0
\(351\) −0.313133 −0.0167138
\(352\) 0.459787 0.922138i 0.0245067 0.0491501i
\(353\) 1.20189i 0.0639703i 0.999488 + 0.0319852i \(0.0101829\pi\)
−0.999488 + 0.0319852i \(0.989817\pi\)
\(354\) 6.95473 + 21.4044i 0.369640 + 1.13763i
\(355\) 0 0
\(356\) −5.28740 + 3.84152i −0.280232 + 0.203600i
\(357\) −15.6299 5.07845i −0.827220 0.268780i
\(358\) −19.3934 6.30130i −1.02497 0.333034i
\(359\) −9.43239 + 6.85304i −0.497823 + 0.361689i −0.808185 0.588929i \(-0.799550\pi\)
0.310362 + 0.950618i \(0.399550\pi\)
\(360\) 0 0
\(361\) 11.2987 + 34.7737i 0.594667 + 1.83020i
\(362\) 15.8755i 0.834396i
\(363\) 10.9983 0.191475i 0.577263 0.0100498i
\(364\) 4.14918 0.217476
\(365\) 0 0
\(366\) −18.2479 13.2579i −0.953832 0.693000i
\(367\) 9.39636 + 12.9330i 0.490486 + 0.675096i 0.980478 0.196631i \(-0.0630001\pi\)
−0.489991 + 0.871727i \(0.663000\pi\)
\(368\) 4.27874 + 1.39025i 0.223045 + 0.0724717i
\(369\) −3.35197 + 10.3163i −0.174497 + 0.537045i
\(370\) 0 0
\(371\) −13.1239 9.53504i −0.681357 0.495035i
\(372\) 13.2237 4.29663i 0.685615 0.222770i
\(373\) 0.321975i 0.0166712i 0.999965 + 0.00833561i \(0.00265334\pi\)
−0.999965 + 0.00833561i \(0.997347\pi\)
\(374\) −36.4469 18.1728i −1.88463 0.939693i
\(375\) 0 0
\(376\) −18.4968 56.9274i −0.953902 2.93581i
\(377\) −0.926988 + 1.27589i −0.0477423 + 0.0657117i
\(378\) −4.74467 6.53048i −0.244039 0.335891i
\(379\) −3.52819 + 10.8586i −0.181231 + 0.557771i −0.999863 0.0165471i \(-0.994733\pi\)
0.818632 + 0.574318i \(0.194733\pi\)
\(380\) 0 0
\(381\) 13.7559 9.99428i 0.704738 0.512022i
\(382\) −22.1861 + 30.5365i −1.13514 + 1.56239i
\(383\) −26.9789 + 8.76597i −1.37856 + 0.447920i −0.902195 0.431329i \(-0.858045\pi\)
−0.476362 + 0.879249i \(0.658045\pi\)
\(384\) 19.3242 0.986136
\(385\) 0 0
\(386\) 38.6846 1.96899
\(387\) −5.24477 + 1.70413i −0.266607 + 0.0866257i
\(388\) 0.530981 0.730833i 0.0269565 0.0371024i
\(389\) 12.2810 8.92269i 0.622673 0.452398i −0.231181 0.972911i \(-0.574259\pi\)
0.853854 + 0.520513i \(0.174259\pi\)
\(390\) 0 0
\(391\) 1.65930 5.10680i 0.0839143 0.258262i
\(392\) 11.1528 + 15.3504i 0.563299 + 0.775315i
\(393\) −0.0253046 + 0.0348288i −0.00127645 + 0.00175688i
\(394\) −12.4415 38.2911i −0.626796 1.92908i
\(395\) 0 0
\(396\) −6.17357 11.8600i −0.310234 0.595987i
\(397\) 5.22461i 0.262216i −0.991368 0.131108i \(-0.958147\pi\)
0.991368 0.131108i \(-0.0418534\pi\)
\(398\) −16.2681 + 5.28581i −0.815444 + 0.264954i
\(399\) −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 \(-0.0136757\pi\)
\(402\) 35.6750 + 11.5915i 1.77931 + 0.578132i
\(403\) 0.634804 + 0.873733i 0.0316219 + 0.0435238i
\(404\) −1.64810 1.19741i −0.0819959 0.0595735i
\(405\) 0 0
\(406\) −40.6549 −2.01767
\(407\) 1.44181 + 8.61714i 0.0714680 + 0.427136i
\(408\) 24.9442i 1.23492i
\(409\) −10.2937 31.6809i −0.508993 1.56652i −0.793953 0.607979i \(-0.791980\pi\)
0.284960 0.958539i \(-0.408020\pi\)
\(410\) 0 0
\(411\) −5.95645 + 4.32761i −0.293810 + 0.213465i
\(412\) 24.5456 + 7.97535i 1.20927 + 0.392917i
\(413\) −28.6467 9.30787i −1.40961 0.458011i
\(414\) 2.13372 1.55024i 0.104867 0.0761902i
\(415\) 0 0
\(416\) −0.0300625 0.0925229i −0.00147394 0.00453631i
\(417\) 13.2393i 0.648334i
\(418\) −43.3043 42.5569i −2.11808 2.08153i
\(419\) 5.28460 0.258170 0.129085 0.991634i \(-0.458796\pi\)
0.129085 + 0.991634i \(0.458796\pi\)
\(420\) 0 0
\(421\) 24.9023 + 18.0926i 1.21367 + 0.881780i 0.995558 0.0941452i \(-0.0300118\pi\)
0.218107 + 0.975925i \(0.430012\pi\)
\(422\) −28.8030 39.6439i −1.40211 1.92984i
\(423\) −11.4110 3.70764i −0.554820 0.180272i
\(424\) −7.60864 + 23.4170i −0.369508 + 1.13723i
\(425\) 0 0
\(426\) −6.10384 4.43470i −0.295732 0.214862i
\(427\) 28.7099 9.32841i 1.38937 0.451433i
\(428\) 8.43562i 0.407751i
\(429\) 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 \(0.803862\pi\)
\(432\) −2.46239 + 3.38919i −0.118472 + 0.163062i
\(433\) −0.830465 1.14304i −0.0399096 0.0549308i 0.788596 0.614912i \(-0.210808\pi\)
−0.828505 + 0.559981i \(0.810808\pi\)
\(434\) −8.60323 + 26.4780i −0.412968 + 1.27098i
\(435\) 0 0
\(436\) 21.8282 15.8591i 1.04538 0.759514i
\(437\) 4.70527 6.47625i 0.225084 0.309801i
\(438\) 20.2100 6.56662i 0.965670 0.313765i
\(439\) 7.58532 0.362028 0.181014 0.983481i \(-0.442062\pi\)
0.181014 + 0.983481i \(0.442062\pi\)
\(440\) 0 0
\(441\) 3.80333 0.181111
\(442\) −3.65691 + 1.18820i −0.173941 + 0.0565170i
\(443\) 6.50455 8.95274i 0.309040 0.425358i −0.626041 0.779790i \(-0.715326\pi\)
0.935082 + 0.354432i \(0.115326\pi\)
\(444\) 8.59160 6.24216i 0.407739 0.296240i
\(445\) 0 0
\(446\) −15.2895 + 47.0562i −0.723979 + 2.22818i
\(447\) −3.45534 4.75587i −0.163432 0.224945i
\(448\) −14.7129 + 20.2505i −0.695118 + 0.956748i
\(449\) −1.95563 6.01882i −0.0922920 0.284045i 0.894247 0.447575i \(-0.147712\pi\)
−0.986538 + 0.163529i \(0.947712\pi\)
\(450\) 0 0
\(451\) −16.6112 31.9116i −0.782190 1.50266i
\(452\) 43.5152i 2.04678i
\(453\) −7.25486 + 2.35725i −0.340863 + 0.110753i
\(454\) 1.06085 + 0.770756i 0.0497884 + 0.0361734i
\(455\) 0 0
\(456\) −11.4915 + 35.3671i −0.538138 + 1.65622i
\(457\) 0.180300 + 0.0585832i 0.00843410 + 0.00274040i 0.313231 0.949677i \(-0.398589\pi\)
−0.304797 + 0.952417i \(0.598589\pi\)
\(458\) 32.0364 + 44.0944i 1.49696 + 2.06039i
\(459\) 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 \(0.712828\pi\)
\(462\) 26.4780 + 3.95778i 1.23187 + 0.184133i
\(463\) 20.9935i 0.975652i 0.872941 + 0.487826i \(0.162210\pi\)
−0.872941 + 0.487826i \(0.837790\pi\)
\(464\) 6.51998 + 20.0664i 0.302682 + 0.931561i
\(465\) 0 0
\(466\) 9.07131 6.59070i 0.420221 0.305308i
\(467\) −7.51324 2.44120i −0.347671 0.112965i 0.129976 0.991517i \(-0.458510\pi\)
−0.477647 + 0.878552i \(0.658510\pi\)
\(468\) −1.20058 0.390091i −0.0554966 0.0180319i
\(469\) −40.6149 + 29.5085i −1.87542 + 1.36257i
\(470\) 0 0
\(471\) −3.13134 9.63727i −0.144284 0.444062i
\(472\) 45.7182i 2.10435i
\(473\) 8.16138 16.3683i 0.375261 0.752614i
\(474\) −13.2973 −0.610766
\(475\) 0 0
\(476\) −53.5994 38.9423i −2.45673 1.78492i
\(477\) 2.90097 + 3.99285i 0.132826 + 0.182820i
\(478\) −13.6884 4.44762i −0.626091 0.203429i
\(479\) −12.3523 + 38.0164i −0.564389 + 1.73701i 0.105369 + 0.994433i \(0.466398\pi\)
−0.669758 + 0.742579i \(0.733602\pi\)
\(480\) 0 0
\(481\) 0.667344 + 0.484854i 0.0304282 + 0.0221074i
\(482\) 23.2652 7.55931i 1.05970 0.344317i
\(483\) 3.52981i 0.160612i
\(484\) 42.4069 + 12.9672i 1.92759 + 0.589419i
\(485\) 0 0
\(486\) 0.758911 + 2.33569i 0.0344249 + 0.105949i
\(487\) 5.83998 8.03804i 0.264635 0.364238i −0.655935 0.754818i \(-0.727725\pi\)
0.920569 + 0.390579i \(0.127725\pi\)
\(488\) −26.9318 37.0684i −1.21914 1.67801i
\(489\) 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 \(0.335798\pi\)
\(492\) −25.7034 + 35.3777i −1.15880 + 1.59495i
\(493\) 23.9498 7.78177i 1.07865 0.350473i
\(494\) −5.73234 −0.257910
\(495\) 0 0
\(496\) 14.4487 0.648767
\(497\) 9.60333 3.12031i 0.430768 0.139965i
\(498\) 23.4508 32.2773i 1.05086 1.44638i
\(499\) 35.4153 25.7307i 1.58541 1.15186i 0.675256 0.737584i \(-0.264033\pi\)
0.910149 0.414281i \(-0.135967\pi\)
\(500\) 0 0
\(501\) 1.78953 5.50761i 0.0799504 0.246062i
\(502\) −24.3651 33.5357i −1.08747 1.49677i
\(503\) 3.69268 5.08254i 0.164648 0.226619i −0.718718 0.695301i \(-0.755271\pi\)
0.883367 + 0.468682i \(0.155271\pi\)
\(504\) −5.06711 15.5950i −0.225707 0.694655i
\(505\) 0 0
\(506\) −1.29314 + 8.65125i −0.0574870 + 0.384595i
\(507\) 12.9019i 0.572996i
\(508\) 65.1918 21.1821i 2.89242 0.939803i
\(509\) 20.0945 + 14.5995i 0.890671 + 0.647111i 0.936053 0.351859i \(-0.114450\pi\)
−0.0453816 + 0.998970i \(0.514450\pi\)
\(510\) 0 0
\(511\) −8.78845 + 27.0481i −0.388778 + 1.19654i
\(512\) 38.5155 + 12.5144i 1.70216 + 0.553066i
\(513\) 4.38140 + 6.03048i 0.193443 + 0.266252i
\(514\) 22.1407 + 16.0861i 0.976583 + 0.709529i
\(515\) 0 0
\(516\) −22.2318 −0.978699
\(517\) 35.2977 18.3738i 1.55239 0.808078i
\(518\) 21.2642i 0.934296i
\(519\) −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 \(0.251360\pi\)
\(522\) 11.7636 + 3.82223i 0.514879 + 0.167294i
\(523\) −25.4417 8.26650i −1.11249 0.361469i −0.305591 0.952163i \(-0.598854\pi\)
−0.806896 + 0.590694i \(0.798854\pi\)
\(524\) −0.140408 + 0.102013i −0.00613376 + 0.00445644i
\(525\) 0 0
\(526\) −20.3939 62.7661i −0.889218 2.73673i
\(527\) 17.2449i 0.751202i
\(528\) −2.29290 13.7037i −0.0997854 0.596378i
\(529\) 21.8467 0.949856
\(530\) 0 0
\(531\) 7.41391 + 5.38652i 0.321736 + 0.233755i
\(532\) −58.0557 79.9069i −2.51704 3.46440i
\(533\) −3.23038 1.04961i −0.139923 0.0454638i
\(534\) −1.23033 + 3.78657i −0.0532416 + 0.163861i
\(535\) 0 0
\(536\) 61.6462 + 44.7886i 2.66271 + 1.93457i
\(537\) −7.89671 + 2.56580i −0.340768 + 0.110722i
\(538\) 24.7133i 1.06547i
\(539\) −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 \(0.799040\pi\)
\(542\) −15.2208 + 20.9496i −0.653789 + 0.899863i
\(543\) 3.79959 + 5.22969i 0.163056 + 0.224428i
\(544\) −0.480027 + 1.47737i −0.0205810 + 0.0633418i
\(545\) 0 0
\(546\) 2.04491 1.48571i 0.0875141 0.0635827i
\(547\) 15.7142 21.6287i 0.671890 0.924777i −0.327912 0.944708i \(-0.606345\pi\)
0.999801 + 0.0199316i \(0.00634485\pi\)
\(548\) −28.2286 + 9.17203i −1.20587 + 0.391810i
\(549\) −9.18431 −0.391977
\(550\) 0 0
\(551\) 37.5422 1.59935
\(552\) 5.09540 1.65559i 0.216875 0.0704668i
\(553\) 10.4605 14.3977i 0.444826 0.612251i
\(554\) −35.6394 + 25.8935i −1.51417 + 1.10011i
\(555\) 0 0
\(556\) 16.4931 50.7606i 0.699464 2.15273i
\(557\) 10.1360 + 13.9510i 0.429477 + 0.591125i 0.967833 0.251593i \(-0.0809544\pi\)
−0.538356 + 0.842718i \(0.680954\pi\)
\(558\) 4.97873 6.85264i 0.210767 0.290095i
\(559\) −0.533620 1.64231i −0.0225697 0.0694624i
\(560\) 0 0
\(561\) −16.3558 + 2.73663i −0.690541 + 0.115541i
\(562\) 18.2006i 0.767748i
\(563\) 0.791197 0.257075i 0.0333450 0.0108344i −0.292297 0.956328i \(-0.594420\pi\)
0.325642 + 0.945493i \(0.394420\pi\)
\(564\) −39.1316 28.4307i −1.64774 1.19715i
\(565\) 0 0
\(566\) 4.08813 12.5820i 0.171837 0.528860i
\(567\) −3.12597 1.01569i −0.131278 0.0426550i
\(568\) −9.00855 12.3992i −0.377991 0.520259i
\(569\) 9.38141 + 6.81599i 0.393289 + 0.285741i 0.766802 0.641884i \(-0.221847\pi\)
−0.373513 + 0.927625i \(0.621847\pi\)
\(570\) 0 0
\(571\) 21.8414 0.914034 0.457017 0.889458i \(-0.348918\pi\)
0.457017 + 0.889458i \(0.348918\pi\)
\(572\) 3.71376 1.93315i 0.155280 0.0808292i
\(573\) 15.3693i 0.642061i
\(574\) −27.0575 83.2744i −1.12936 3.47580i
\(575\) 0 0
\(576\) 6.16110 4.47630i 0.256712 0.186512i
\(577\) −9.26888 3.01164i −0.385868 0.125376i 0.109657 0.993969i \(-0.465025\pi\)
−0.495526 + 0.868593i \(0.665025\pi\)
\(578\) 18.6855 + 6.07129i 0.777214 + 0.252532i
\(579\) 12.7435 9.25867i 0.529600 0.384777i
\(580\) 0 0
\(581\) 16.5003 + 50.7827i 0.684548 + 2.10682i
\(582\) 0.550320i 0.0228115i
\(583\) −16.1891 2.41986i −0.670485 0.100220i
\(584\) 43.1669 1.78626
\(585\) 0 0
\(586\) 3.45724 + 2.51183i 0.142817 + 0.103763i
\(587\) 13.4862 + 18.5622i 0.556635 + 0.766143i 0.990894 0.134645i \(-0.0429895\pi\)
−0.434258 + 0.900788i \(0.642990\pi\)
\(588\) 14.5822 + 4.73805i 0.601361 + 0.195394i
\(589\) 7.94453 24.4507i 0.327349 1.00748i
\(590\) 0 0
\(591\) −13.2630 9.63612i −0.545566 0.396377i
\(592\) 10.4956 3.41022i 0.431366 0.140159i
\(593\) 28.7819i 1.18193i 0.806697 + 0.590965i \(0.201253\pi\)
−0.806697 + 0.590965i \(0.798747\pi\)
\(594\) −7.28939 3.63456i −0.299087 0.149128i
\(595\) 0 0
\(596\) −7.32333 22.5389i −0.299975 0.923229i
\(597\) −4.09392 + 5.63480i −0.167553 + 0.230617i
\(598\) 0.485432 + 0.668140i 0.0198508 + 0.0273223i
\(599\) 9.02179 27.7662i 0.368620 1.13450i −0.579062 0.815283i \(-0.696581\pi\)
0.947683 0.319214i \(-0.103419\pi\)
\(600\) 0 0
\(601\) 5.40494 3.92692i 0.220472 0.160182i −0.472067 0.881563i \(-0.656492\pi\)
0.692539 + 0.721380i \(0.256492\pi\)
\(602\) 26.1653 36.0135i 1.06642 1.46780i
\(603\) 14.5263 4.71989i 0.591557 0.192209i
\(604\) −30.7522 −1.25129
\(605\) 0 0
\(606\) −1.24102 −0.0504131
\(607\) −40.5252 + 13.1674i −1.64487 + 0.534450i −0.977619 0.210384i \(-0.932529\pi\)
−0.667250 + 0.744834i \(0.732529\pi\)
\(608\) −1.36121 + 1.87355i −0.0552044 + 0.0759824i
\(609\) −13.3925 + 9.73024i −0.542693 + 0.394289i
\(610\) 0 0
\(611\) 1.16099 3.57315i 0.0469685 0.144554i
\(612\) 11.8479 + 16.3073i 0.478924 + 0.659182i
\(613\) −3.42771 + 4.71783i −0.138444 + 0.190552i −0.872609 0.488419i \(-0.837574\pi\)
0.734165 + 0.678971i \(0.237574\pi\)
\(614\) −16.2078 49.8824i −0.654093 2.01309i
\(615\) 0 0
\(616\) 48.6699 + 24.2673i 1.96097 + 0.977758i
\(617\) 33.6386i 1.35424i 0.735874 + 0.677119i \(0.236772\pi\)
−0.735874 + 0.677119i \(0.763228\pi\)
\(618\) 14.9530 4.85852i 0.601498 0.195438i
\(619\) 34.4331 + 25.0171i 1.38398 + 1.00552i 0.996495 + 0.0836477i \(0.0266570\pi\)
0.387488 + 0.921875i \(0.373343\pi\)
\(620\) 0 0
\(621\) 0.331860 1.02136i 0.0133171 0.0409857i
\(622\) −76.6329 24.8996i −3.07270 0.998381i
\(623\) −3.13205 4.31089i −0.125483 0.172712i
\(624\) −1.06127 0.771056i −0.0424847 0.0308669i
\(625\) 0 0
\(626\) −8.49374 −0.339478
\(627\) −24.4507 3.65476i −0.976468 0.145957i
\(628\) 40.8509i 1.63013i
\(629\) −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 \(0.243312\pi\)
\(632\) −25.6898 8.34713i −1.02189 0.332031i
\(633\) −18.9765 6.16585i −0.754250 0.245071i
\(634\) −5.71351 + 4.15111i −0.226912 + 0.164862i
\(635\) 0 0
\(636\) 6.14839 + 18.9228i 0.243799 + 0.750337i
\(637\) 1.19095i 0.0471871i
\(638\) −36.3886 + 18.9416i −1.44064 + 0.749906i
\(639\) −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 \(0.661130\pi\)
\(642\) 3.02058 + 4.15747i 0.119213 + 0.164082i
\(643\) 4.14029 + 1.34526i 0.163277 + 0.0530519i 0.389515 0.921020i \(-0.372643\pi\)
−0.226238 + 0.974072i \(0.572643\pi\)
\(644\) −4.39731 + 13.5335i −0.173278 + 0.533296i
\(645\) 0 0
\(646\) 74.0508 + 53.8011i 2.91349 + 2.11677i
\(647\) 12.8329 4.16967i 0.504514 0.163927i −0.0456916 0.998956i \(-0.514549\pi\)
0.550206 + 0.835029i \(0.314549\pi\)
\(648\) 4.98884i 0.195980i
\(649\) −29.9771 + 5.01575i −1.17671 + 0.196885i
\(650\) 0 0
\(651\) 3.50310 + 10.7814i 0.137297 + 0.422558i
\(652\) 11.9168 16.4021i 0.466697 0.642354i
\(653\) −16.1336 22.2060i −0.631357 0.868988i 0.366761 0.930315i \(-0.380467\pi\)
−0.998118 + 0.0613270i \(0.980467\pi\)
\(654\) 5.07922 15.6322i 0.198613 0.611269i
\(655\) 0 0
\(656\) −36.7632 + 26.7100i −1.43536 + 1.04285i
\(657\) 5.08592 7.00018i 0.198421 0.273103i
\(658\) 92.1105 29.9285i 3.59084 1.16674i
\(659\) 18.7768 0.731441 0.365721 0.930725i \(-0.380823\pi\)
0.365721 + 0.930725i \(0.380823\pi\)
\(660\) 0 0
\(661\) −21.6525 −0.842184 −0.421092 0.907018i \(-0.638353\pi\)
−0.421092 + 0.907018i \(0.638353\pi\)
\(662\) −32.9847 + 10.7174i −1.28199 + 0.416543i
\(663\) −0.920276 + 1.26665i −0.0357406 + 0.0491927i
\(664\) 65.5674 47.6375i 2.54451 1.84869i
\(665\) 0 0
\(666\) 1.99919 6.15286i 0.0774669 0.238419i
\(667\) −3.17919 4.37578i −0.123099 0.169431i
\(668\) 13.7224 18.8872i 0.530935 0.730769i
\(669\) 6.22565 + 19.1606i 0.240698 + 0.740791i
\(670\) 0 0
\(671\) 21.3508 21.7258i 0.824240 0.838714i
\(672\) 1.02116i 0.0393919i
\(673\) −22.1617 + 7.20076i −0.854269 + 0.277569i −0.703233 0.710959i \(-0.748261\pi\)
−0.151036 + 0.988528i \(0.548261\pi\)
\(674\) 31.6883 + 23.0229i 1.22059 + 0.886808i
\(675\) 0 0
\(676\) −16.0728 + 49.4670i −0.618184 + 1.90258i
\(677\) −31.6519 10.2843i −1.21648 0.395259i −0.370683 0.928760i \(-0.620876\pi\)
−0.845800 + 0.533501i \(0.820876\pi\)
\(678\) 15.5817 + 21.4463i 0.598410 + 0.823641i
\(679\) 0.595859 + 0.432917i 0.0228670 + 0.0166138i
\(680\) 0 0
\(681\) 0.533937 0.0204605
\(682\) 4.63603 + 27.7077i 0.177523 + 1.06098i
\(683\) 16.9244i 0.647593i 0.946127 + 0.323796i \(0.104959\pi\)
−0.946127 + 0.323796i \(0.895041\pi\)
\(684\) 9.28603 + 28.5795i 0.355060 + 1.09276i
\(685\) 0 0
\(686\) 20.8758 15.1671i 0.797041 0.579084i
\(687\) 21.1068 + 6.85803i 0.805276 + 0.261650i
\(688\) −21.9717 7.13905i −0.837664 0.272174i
\(689\) −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 \(-0.472830\pi\)
\(692\) 64.7650i 2.46200i
\(693\) 9.66962 5.03340i 0.367318 0.191203i
\(694\) −72.8910 −2.76690
\(695\) 0 0
\(696\) 20.3275 + 14.7688i 0.770511 + 0.559809i
\(697\) 31.8791 + 43.8779i 1.20751 + 1.66199i
\(698\) 74.0267 + 24.0527i 2.80195 + 0.910409i
\(699\) 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 \(0.371910\pi\)
\(702\) −0.731382 + 0.237640i −0.0276042 + 0.00896916i
\(703\) 19.6361i 0.740591i
\(704\) −3.73392 + 24.9803i −0.140727 + 0.941482i
\(705\) 0 0
\(706\) 0.912130 + 2.80725i 0.0343285 + 0.105652i
\(707\) 0.976267 1.34372i 0.0367163 0.0505357i
\(708\) 21.7151 + 29.8883i 0.816103 + 1.12327i
\(709\) 0.545405 1.67858i 0.0204831 0.0630406i −0.940292 0.340368i \(-0.889449\pi\)
0.960776 + 0.277327i \(0.0894485\pi\)
\(710\) 0 0
\(711\) −4.38039 + 3.18254i −0.164278 + 0.119355i
\(712\) −4.75389 + 6.54317i −0.178160 + 0.245216i
\(713\) −3.52266 + 1.14458i −0.131925 + 0.0428649i
\(714\) −40.3606 −1.51046
\(715\) 0 0
\(716\) −33.4729 −1.25094
\(717\) −5.57369 + 1.81100i −0.208153 + 0.0676331i
\(718\) −16.8303 + 23.1649i −0.628100 + 0.864506i
\(719\) −2.66974 + 1.93968i −0.0995645 + 0.0723379i −0.636454 0.771315i \(-0.719599\pi\)
0.536889 + 0.843653i \(0.319599\pi\)
\(720\) 0 0
\(721\) −6.50241 + 20.0124i −0.242163 + 0.745300i
\(722\) 52.7803 + 72.6459i 1.96428 + 2.70360i
\(723\) 5.85477 8.05841i 0.217741 0.299695i
\(724\) 8.05294 + 24.7844i 0.299285 + 0.921105i
\(725\) 0 0
\(726\) 25.5434 8.79398i 0.948003 0.326375i
\(727\) 11.7838i 0.437037i −0.975833 0.218519i \(-0.929878\pi\)
0.975833 0.218519i \(-0.0701225\pi\)
\(728\) 4.88331 1.58668i 0.180987 0.0588064i
\(729\) 0.809017 + 0.587785i 0.0299636 + 0.0217698i
\(730\) 0 0
\(731\) −8.52064 + 26.2238i −0.315147 + 0.969924i
\(732\) −35.2133 11.4415i −1.30152 0.422890i
\(733\) −3.36865 4.63654i −0.124424 0.171255i 0.742261 0.670111i \(-0.233754\pi\)
−0.866685 + 0.498856i \(0.833754\pi\)
\(734\) 31.7619 + 23.0764i 1.17235 + 0.851765i
\(735\) 0 0
\(736\) 0.333646 0.0122983
\(737\) −22.6044 + 45.3348i −0.832643 + 1.66993i
\(738\) 26.6395i 0.980614i
\(739\) 6.50638 + 20.0246i 0.239341 + 0.736616i 0.996516 + 0.0834038i \(0.0265791\pi\)
−0.757175 + 0.653212i \(0.773421\pi\)
\(740\) 0 0
\(741\) −1.88834 + 1.37196i −0.0693700 + 0.0504003i
\(742\) −37.8895 12.3110i −1.39097 0.451952i
\(743\) 12.4857 + 4.05686i 0.458058 + 0.148832i 0.528952 0.848652i \(-0.322585\pi\)
−0.0708942 + 0.997484i \(0.522585\pi\)
\(744\) 13.9203 10.1137i 0.510343 0.370786i
\(745\) 0 0
\(746\) 0.244350 + 0.752032i 0.00894629 + 0.0275339i
\(747\) 16.2454i 0.594389i
\(748\) −66.1183 9.88299i −2.41753 0.361358i
\(749\) −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 \(0.854858\pi\)
\(752\) −29.5442 40.6641i −1.07737 1.48287i
\(753\) −16.0527 5.21584i −0.584993 0.190076i
\(754\) −1.19687 + 3.68358i −0.0435874 + 0.134148i
\(755\) 0 0
\(756\) −10.7199 7.78845i −0.389878 0.283263i
\(757\) 29.6701 9.64039i 1.07838 0.350386i 0.284632 0.958637i \(-0.408129\pi\)
0.793745 + 0.608251i \(0.208129\pi\)
\(758\) 28.0400i 1.01846i
\(759\) 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 \(0.833893\pi\)
\(762\) 24.5448 33.7830i 0.889165 1.22383i
\(763\) 12.9302 + 17.7968i 0.468103 + 0.644289i
\(764\) −19.1465 + 58.9269i −0.692697 + 2.13190i
\(765\) 0 0
\(766\) −56.3617 + 40.9491i −2.03643 + 1.47955i
\(767\) −1.68670 + 2.32154i −0.0609032 + 0.0838260i
\(768\) 30.6498 9.95872i 1.10598 0.359354i
\(769\) −10.3938 −0.374811 −0.187405 0.982283i \(-0.560008\pi\)
−0.187405 + 0.982283i \(0.560008\pi\)
\(770\) 0 0
\(771\) 11.1436 0.401326
\(772\) 60.3935 19.6230i 2.17361 0.706248i
\(773\) 8.24944 11.3544i 0.296712 0.408389i −0.634468 0.772949i \(-0.718781\pi\)
0.931180 + 0.364560i \(0.118781\pi\)
\(774\) −10.9569 + 7.96062i −0.393836 + 0.286139i
\(775\) 0 0
\(776\) 0.345453 1.06319i 0.0124010 0.0381665i
\(777\) 5.08932 + 7.00485i 0.182578 + 0.251298i
\(778\) 21.9131 30.1608i 0.785623 1.08132i
\(779\) 24.9858 + 76.8985i 0.895211 + 2.75518i