Properties

Label 637.2.q.h.491.1
Level $637$
Weight $2$
Character 637.491
Analytic conductor $5.086$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.q (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.58891012706304.1
Defining polynomial: \(x^{12} - 5 x^{10} - 2 x^{9} + 15 x^{8} + 2 x^{7} - 30 x^{6} + 4 x^{5} + 60 x^{4} - 16 x^{3} - 80 x^{2} + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{4} \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 491.1
Root \(-1.12906 - 0.851598i\) of defining polynomial
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.h.589.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.34104 + 1.35160i) q^{2} +(-0.172975 - 0.299601i) q^{3} +(2.65363 - 4.59623i) q^{4} +3.25812i q^{5} +(0.809880 + 0.467584i) q^{6} +8.94020i q^{8} +(1.44016 - 2.49443i) q^{9} +O(q^{10})\) \(q+(-2.34104 + 1.35160i) q^{2} +(-0.172975 - 0.299601i) q^{3} +(2.65363 - 4.59623i) q^{4} +3.25812i q^{5} +(0.809880 + 0.467584i) q^{6} +8.94020i q^{8} +(1.44016 - 2.49443i) q^{9} +(-4.40367 - 7.62739i) q^{10} +(-1.59871 + 0.923014i) q^{11} -1.83605 q^{12} +(-3.60550 - 0.0186461i) q^{13} +(0.976136 - 0.563573i) q^{15} +(-6.77628 - 11.7369i) q^{16} +(-1.07657 + 1.86467i) q^{17} +7.78607i q^{18} +(2.07929 + 1.20048i) q^{19} +(14.9751 + 8.64587i) q^{20} +(2.49509 - 4.32162i) q^{22} +(0.906314 + 1.56978i) q^{23} +(2.67849 - 1.54643i) q^{24} -5.61537 q^{25} +(8.46582 - 4.82954i) q^{26} -2.03429 q^{27} +(1.36703 + 2.36777i) q^{29} +(-1.52345 + 2.63869i) q^{30} +1.74236i q^{31} +(16.2422 + 9.37743i) q^{32} +(0.553071 + 0.319316i) q^{33} -5.82036i q^{34} +(-7.64331 - 13.2386i) q^{36} +(-5.14042 + 2.96783i) q^{37} -6.49025 q^{38} +(0.618074 + 1.08344i) q^{39} -29.1283 q^{40} +(-3.65577 + 2.11066i) q^{41} +(-4.34111 + 7.51903i) q^{43} +9.79737i q^{44} +(8.12716 + 4.69222i) q^{45} +(-4.24343 - 2.44994i) q^{46} -5.87774i q^{47} +(-2.34425 + 4.06036i) q^{48} +(13.1458 - 7.58972i) q^{50} +0.744877 q^{51} +(-9.65339 + 16.5222i) q^{52} -9.30628 q^{53} +(4.76235 - 2.74954i) q^{54} +(-3.00729 - 5.20878i) q^{55} -0.830609i q^{57} +(-6.40054 - 3.69535i) q^{58} +(-9.31173 - 5.37613i) q^{59} -5.98206i q^{60} +(5.05504 - 8.75558i) q^{61} +(-2.35497 - 4.07893i) q^{62} -23.5929 q^{64} +(0.0607514 - 11.7472i) q^{65} -1.72635 q^{66} +(0.716130 - 0.413458i) q^{67} +(5.71365 + 9.89633i) q^{68} +(0.313538 - 0.543065i) q^{69} +(-2.03884 - 1.17712i) q^{71} +(22.3007 + 12.8753i) q^{72} -3.19482i q^{73} +(8.02261 - 13.8956i) q^{74} +(0.971316 + 1.68237i) q^{75} +(11.0353 - 6.37126i) q^{76} +(-2.91130 - 1.70098i) q^{78} +0.801911 q^{79} +(38.2402 - 22.0780i) q^{80} +(-3.96860 - 6.87381i) q^{81} +(5.70552 - 9.88225i) q^{82} +9.97031i q^{83} +(-6.07534 - 3.50760i) q^{85} -23.4698i q^{86} +(0.472923 - 0.819127i) q^{87} +(-8.25193 - 14.2928i) q^{88} +(-13.0886 + 7.55674i) q^{89} -25.3680 q^{90} +9.62010 q^{92} +(0.522012 - 0.301384i) q^{93} +(7.94435 + 13.7600i) q^{94} +(-3.91130 + 6.77458i) q^{95} -6.48823i q^{96} +(-7.99489 - 4.61585i) q^{97} +5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} + 18 q^{6} - 4 q^{9} - 12 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{13} + 6 q^{15} - 8 q^{16} + 4 q^{17} + 12 q^{20} + 6 q^{22} - 12 q^{23} - 12 q^{24} - 20 q^{25} + 42 q^{26} - 12 q^{27} + 8 q^{29} + 8 q^{30} + 36 q^{32} + 30 q^{33} - 10 q^{36} - 42 q^{37} - 4 q^{38} - 4 q^{39} - 92 q^{40} - 30 q^{41} + 2 q^{43} + 12 q^{46} + 2 q^{48} - 18 q^{50} + 52 q^{51} - 2 q^{52} - 44 q^{53} - 12 q^{54} + 6 q^{55} - 12 q^{58} - 18 q^{59} - 14 q^{61} + 4 q^{62} - 52 q^{64} + 60 q^{65} + 52 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 24 q^{71} + 60 q^{72} + 6 q^{74} - 46 q^{75} + 18 q^{76} - 10 q^{78} - 56 q^{79} + 72 q^{80} + 2 q^{81} - 14 q^{82} - 48 q^{85} + 2 q^{87} - 14 q^{88} + 12 q^{89} - 24 q^{90} + 24 q^{92} - 18 q^{93} - 4 q^{94} - 22 q^{95} - 6 q^{97} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.34104 + 1.35160i −1.65536 + 0.955724i −0.680549 + 0.732702i \(0.738259\pi\)
−0.974813 + 0.223022i \(0.928408\pi\)
\(3\) −0.172975 0.299601i −0.0998669 0.172975i 0.811763 0.583988i \(-0.198508\pi\)
−0.911629 + 0.411013i \(0.865175\pi\)
\(4\) 2.65363 4.59623i 1.32682 2.29811i
\(5\) 3.25812i 1.45708i 0.685005 + 0.728539i \(0.259800\pi\)
−0.685005 + 0.728539i \(0.740200\pi\)
\(6\) 0.809880 + 0.467584i 0.330632 + 0.190890i
\(7\) 0 0
\(8\) 8.94020i 3.16084i
\(9\) 1.44016 2.49443i 0.480053 0.831477i
\(10\) −4.40367 7.62739i −1.39256 2.41199i
\(11\) −1.59871 + 0.923014i −0.482028 + 0.278299i −0.721261 0.692663i \(-0.756437\pi\)
0.239233 + 0.970962i \(0.423104\pi\)
\(12\) −1.83605 −0.530021
\(13\) −3.60550 0.0186461i −0.999987 0.00517151i
\(14\) 0 0
\(15\) 0.976136 0.563573i 0.252037 0.145514i
\(16\) −6.77628 11.7369i −1.69407 2.93422i
\(17\) −1.07657 + 1.86467i −0.261107 + 0.452250i −0.966536 0.256530i \(-0.917421\pi\)
0.705430 + 0.708780i \(0.250754\pi\)
\(18\) 7.78607i 1.83519i
\(19\) 2.07929 + 1.20048i 0.477021 + 0.275408i 0.719174 0.694830i \(-0.244520\pi\)
−0.242153 + 0.970238i \(0.577854\pi\)
\(20\) 14.9751 + 8.64587i 3.34853 + 1.93328i
\(21\) 0 0
\(22\) 2.49509 4.32162i 0.531954 0.921372i
\(23\) 0.906314 + 1.56978i 0.188979 + 0.327322i 0.944910 0.327329i \(-0.106149\pi\)
−0.755931 + 0.654652i \(0.772815\pi\)
\(24\) 2.67849 1.54643i 0.546744 0.315663i
\(25\) −5.61537 −1.12307
\(26\) 8.46582 4.82954i 1.66028 0.947151i
\(27\) −2.03429 −0.391500
\(28\) 0 0
\(29\) 1.36703 + 2.36777i 0.253851 + 0.439683i 0.964583 0.263780i \(-0.0849693\pi\)
−0.710732 + 0.703463i \(0.751636\pi\)
\(30\) −1.52345 + 2.63869i −0.278142 + 0.481756i
\(31\) 1.74236i 0.312937i 0.987683 + 0.156468i \(0.0500110\pi\)
−0.987683 + 0.156468i \(0.949989\pi\)
\(32\) 16.2422 + 9.37743i 2.87124 + 1.65771i
\(33\) 0.553071 + 0.319316i 0.0962774 + 0.0555858i
\(34\) 5.82036i 0.998183i
\(35\) 0 0
\(36\) −7.64331 13.2386i −1.27389 2.20643i
\(37\) −5.14042 + 2.96783i −0.845081 + 0.487908i −0.858988 0.511996i \(-0.828906\pi\)
0.0139073 + 0.999903i \(0.495573\pi\)
\(38\) −6.49025 −1.05286
\(39\) 0.618074 + 1.08344i 0.0989710 + 0.173489i
\(40\) −29.1283 −4.60558
\(41\) −3.65577 + 2.11066i −0.570935 + 0.329629i −0.757523 0.652809i \(-0.773590\pi\)
0.186588 + 0.982438i \(0.440257\pi\)
\(42\) 0 0
\(43\) −4.34111 + 7.51903i −0.662014 + 1.14664i 0.318072 + 0.948067i \(0.396965\pi\)
−0.980086 + 0.198575i \(0.936369\pi\)
\(44\) 9.79737i 1.47701i
\(45\) 8.12716 + 4.69222i 1.21153 + 0.699475i
\(46\) −4.24343 2.44994i −0.625659 0.361224i
\(47\) 5.87774i 0.857357i −0.903457 0.428678i \(-0.858979\pi\)
0.903457 0.428678i \(-0.141021\pi\)
\(48\) −2.34425 + 4.06036i −0.338363 + 0.586062i
\(49\) 0 0
\(50\) 13.1458 7.58972i 1.85910 1.07335i
\(51\) 0.744877 0.104304
\(52\) −9.65339 + 16.5222i −1.33868 + 2.29122i
\(53\) −9.30628 −1.27832 −0.639158 0.769076i \(-0.720717\pi\)
−0.639158 + 0.769076i \(0.720717\pi\)
\(54\) 4.76235 2.74954i 0.648074 0.374166i
\(55\) −3.00729 5.20878i −0.405503 0.702352i
\(56\) 0 0
\(57\) 0.830609i 0.110017i
\(58\) −6.40054 3.69535i −0.840432 0.485224i
\(59\) −9.31173 5.37613i −1.21228 0.699912i −0.249028 0.968496i \(-0.580111\pi\)
−0.963256 + 0.268584i \(0.913444\pi\)
\(60\) 5.98206i 0.772281i
\(61\) 5.05504 8.75558i 0.647231 1.12104i −0.336550 0.941665i \(-0.609260\pi\)
0.983781 0.179371i \(-0.0574064\pi\)
\(62\) −2.35497 4.07893i −0.299081 0.518024i
\(63\) 0 0
\(64\) −23.5929 −2.94911
\(65\) 0.0607514 11.7472i 0.00753529 1.45706i
\(66\) −1.72635 −0.212499
\(67\) 0.716130 0.413458i 0.0874892 0.0505119i −0.455617 0.890176i \(-0.650581\pi\)
0.543106 + 0.839664i \(0.317248\pi\)
\(68\) 5.71365 + 9.89633i 0.692881 + 1.20011i
\(69\) 0.313538 0.543065i 0.0377456 0.0653773i
\(70\) 0 0
\(71\) −2.03884 1.17712i −0.241965 0.139699i 0.374114 0.927383i \(-0.377947\pi\)
−0.616080 + 0.787684i \(0.711280\pi\)
\(72\) 22.3007 + 12.8753i 2.62816 + 1.51737i
\(73\) 3.19482i 0.373925i −0.982367 0.186963i \(-0.940136\pi\)
0.982367 0.186963i \(-0.0598644\pi\)
\(74\) 8.02261 13.8956i 0.932610 1.61533i
\(75\) 0.971316 + 1.68237i 0.112158 + 0.194263i
\(76\) 11.0353 6.37126i 1.26584 0.730833i
\(77\) 0 0
\(78\) −2.91130 1.70098i −0.329640 0.192598i
\(79\) 0.801911 0.0902220 0.0451110 0.998982i \(-0.485636\pi\)
0.0451110 + 0.998982i \(0.485636\pi\)
\(80\) 38.2402 22.0780i 4.27538 2.46839i
\(81\) −3.96860 6.87381i −0.440955 0.763757i
\(82\) 5.70552 9.88225i 0.630069 1.09131i
\(83\) 9.97031i 1.09438i 0.837007 + 0.547192i \(0.184303\pi\)
−0.837007 + 0.547192i \(0.815697\pi\)
\(84\) 0 0
\(85\) −6.07534 3.50760i −0.658963 0.380452i
\(86\) 23.4698i 2.53081i
\(87\) 0.472923 0.819127i 0.0507027 0.0878196i
\(88\) −8.25193 14.2928i −0.879658 1.52361i
\(89\) −13.0886 + 7.55674i −1.38739 + 0.801012i −0.993021 0.117938i \(-0.962372\pi\)
−0.394373 + 0.918950i \(0.629038\pi\)
\(90\) −25.3680 −2.67402
\(91\) 0 0
\(92\) 9.62010 1.00296
\(93\) 0.522012 0.301384i 0.0541301 0.0312520i
\(94\) 7.94435 + 13.7600i 0.819397 + 1.41924i
\(95\) −3.91130 + 6.77458i −0.401291 + 0.695057i
\(96\) 6.48823i 0.662202i
\(97\) −7.99489 4.61585i −0.811758 0.468669i 0.0358079 0.999359i \(-0.488600\pi\)
−0.847566 + 0.530690i \(0.821933\pi\)
\(98\) 0 0
\(99\) 5.31715i 0.534394i
\(100\) −14.9011 + 25.8095i −1.49011 + 2.58095i
\(101\) −7.41169 12.8374i −0.737491 1.27737i −0.953622 0.301007i \(-0.902677\pi\)
0.216131 0.976364i \(-0.430656\pi\)
\(102\) −1.74378 + 1.00677i −0.172660 + 0.0996855i
\(103\) −4.28286 −0.422003 −0.211001 0.977486i \(-0.567672\pi\)
−0.211001 + 0.977486i \(0.567672\pi\)
\(104\) 0.166700 32.2339i 0.0163463 3.16079i
\(105\) 0 0
\(106\) 21.7863 12.5783i 2.11608 1.22172i
\(107\) 9.56289 + 16.5634i 0.924479 + 1.60124i 0.792397 + 0.610006i \(0.208833\pi\)
0.132082 + 0.991239i \(0.457834\pi\)
\(108\) −5.39827 + 9.35007i −0.519448 + 0.899711i
\(109\) 4.27153i 0.409139i −0.978852 0.204569i \(-0.934421\pi\)
0.978852 0.204569i \(-0.0655794\pi\)
\(110\) 14.0804 + 8.12930i 1.34251 + 0.775099i
\(111\) 1.77833 + 1.02672i 0.168791 + 0.0974516i
\(112\) 0 0
\(113\) −1.37488 + 2.38137i −0.129338 + 0.224020i −0.923420 0.383790i \(-0.874619\pi\)
0.794082 + 0.607810i \(0.207952\pi\)
\(114\) 1.12265 + 1.94448i 0.105146 + 0.182118i
\(115\) −5.11454 + 2.95288i −0.476934 + 0.275358i
\(116\) 14.5104 1.34726
\(117\) −5.23901 + 8.96682i −0.484347 + 0.828983i
\(118\) 29.0655 2.67569
\(119\) 0 0
\(120\) 5.03845 + 8.72685i 0.459945 + 0.796649i
\(121\) −3.79609 + 6.57502i −0.345099 + 0.597729i
\(122\) 27.3295i 2.47430i
\(123\) 1.26471 + 0.730180i 0.114035 + 0.0658381i
\(124\) 8.00828 + 4.62358i 0.719165 + 0.415210i
\(125\) 2.00495i 0.179329i
\(126\) 0 0
\(127\) −4.86719 8.43022i −0.431893 0.748061i 0.565143 0.824993i \(-0.308821\pi\)
−0.997036 + 0.0769320i \(0.975488\pi\)
\(128\) 22.7475 13.1333i 2.01061 1.16083i
\(129\) 3.00361 0.264453
\(130\) 15.7352 + 27.5827i 1.38007 + 2.41916i
\(131\) 18.6615 1.63046 0.815230 0.579138i \(-0.196611\pi\)
0.815230 + 0.579138i \(0.196611\pi\)
\(132\) 2.93530 1.69470i 0.255485 0.147504i
\(133\) 0 0
\(134\) −1.11766 + 1.93584i −0.0965509 + 0.167231i
\(135\) 6.62797i 0.570445i
\(136\) −16.6706 9.62475i −1.42949 0.825315i
\(137\) −7.29328 4.21078i −0.623107 0.359751i 0.154971 0.987919i \(-0.450472\pi\)
−0.778078 + 0.628168i \(0.783805\pi\)
\(138\) 1.69511i 0.144298i
\(139\) −8.81809 + 15.2734i −0.747941 + 1.29547i 0.200867 + 0.979619i \(0.435624\pi\)
−0.948808 + 0.315853i \(0.897709\pi\)
\(140\) 0 0
\(141\) −1.76098 + 1.01670i −0.148301 + 0.0856216i
\(142\) 6.36399 0.534054
\(143\) 5.78135 3.29812i 0.483461 0.275803i
\(144\) −39.0357 −3.25298
\(145\) −7.71448 + 4.45396i −0.640653 + 0.369881i
\(146\) 4.31811 + 7.47919i 0.357370 + 0.618982i
\(147\) 0 0
\(148\) 31.5021i 2.58946i
\(149\) −3.48232 2.01052i −0.285283 0.164708i 0.350530 0.936552i \(-0.386002\pi\)
−0.635813 + 0.771843i \(0.719335\pi\)
\(150\) −4.54777 2.62566i −0.371324 0.214384i
\(151\) 18.9010i 1.53814i 0.639165 + 0.769069i \(0.279280\pi\)
−0.639165 + 0.769069i \(0.720720\pi\)
\(152\) −10.7325 + 18.5892i −0.870521 + 1.50779i
\(153\) 3.10086 + 5.37086i 0.250690 + 0.434208i
\(154\) 0 0
\(155\) −5.67682 −0.455973
\(156\) 6.61987 + 0.0342352i 0.530014 + 0.00274101i
\(157\) 11.5735 0.923670 0.461835 0.886966i \(-0.347191\pi\)
0.461835 + 0.886966i \(0.347191\pi\)
\(158\) −1.87730 + 1.08386i −0.149350 + 0.0862273i
\(159\) 1.60975 + 2.78817i 0.127661 + 0.221116i
\(160\) −30.5528 + 52.9190i −2.41541 + 4.18362i
\(161\) 0 0
\(162\) 18.5813 + 10.7279i 1.45988 + 0.842863i
\(163\) −3.81520 2.20271i −0.298830 0.172529i 0.343087 0.939304i \(-0.388527\pi\)
−0.641917 + 0.766774i \(0.721861\pi\)
\(164\) 22.4037i 1.74943i
\(165\) −1.04037 + 1.80197i −0.0809927 + 0.140284i
\(166\) −13.4759 23.3409i −1.04593 1.81160i
\(167\) 7.81076 4.50954i 0.604415 0.348959i −0.166362 0.986065i \(-0.553202\pi\)
0.770776 + 0.637106i \(0.219869\pi\)
\(168\) 0 0
\(169\) 12.9993 + 0.134457i 0.999947 + 0.0103429i
\(170\) 18.9635 1.45443
\(171\) 5.98901 3.45776i 0.457991 0.264421i
\(172\) 23.0395 + 39.9055i 1.75674 + 3.04277i
\(173\) −3.04600 + 5.27583i −0.231583 + 0.401114i −0.958274 0.285851i \(-0.907724\pi\)
0.726691 + 0.686964i \(0.241057\pi\)
\(174\) 2.55681i 0.193831i
\(175\) 0 0
\(176\) 21.6666 + 12.5092i 1.63318 + 0.942917i
\(177\) 3.71974i 0.279592i
\(178\) 20.4273 35.3812i 1.53109 2.65193i
\(179\) 1.93982 + 3.35987i 0.144989 + 0.251128i 0.929369 0.369152i \(-0.120352\pi\)
−0.784380 + 0.620281i \(0.787019\pi\)
\(180\) 43.1330 24.9029i 3.21495 1.85615i
\(181\) 6.58392 0.489379 0.244690 0.969601i \(-0.421314\pi\)
0.244690 + 0.969601i \(0.421314\pi\)
\(182\) 0 0
\(183\) −3.49757 −0.258548
\(184\) −14.0342 + 8.10262i −1.03461 + 0.597333i
\(185\) −9.66954 16.7481i −0.710919 1.23135i
\(186\) −0.814700 + 1.41110i −0.0597367 + 0.103467i
\(187\) 3.97476i 0.290663i
\(188\) −27.0155 15.5974i −1.97030 1.13756i
\(189\) 0 0
\(190\) 21.1460i 1.53410i
\(191\) 6.87168 11.9021i 0.497218 0.861206i −0.502777 0.864416i \(-0.667688\pi\)
0.999995 + 0.00320983i \(0.00102172\pi\)
\(192\) 4.08097 + 7.06845i 0.294519 + 0.510122i
\(193\) 19.7047 11.3765i 1.41838 0.818899i 0.422219 0.906494i \(-0.361251\pi\)
0.996156 + 0.0875946i \(0.0279180\pi\)
\(194\) 24.9551 1.79167
\(195\) −3.52997 + 2.01376i −0.252786 + 0.144208i
\(196\) 0 0
\(197\) −12.5809 + 7.26358i −0.896352 + 0.517509i −0.876015 0.482284i \(-0.839807\pi\)
−0.0203371 + 0.999793i \(0.506474\pi\)
\(198\) −7.18665 12.4476i −0.510733 0.884615i
\(199\) −11.9202 + 20.6464i −0.845001 + 1.46358i 0.0406192 + 0.999175i \(0.487067\pi\)
−0.885620 + 0.464410i \(0.846266\pi\)
\(200\) 50.2025i 3.54985i
\(201\) −0.247745 0.143035i −0.0174746 0.0100889i
\(202\) 34.7021 + 20.0353i 2.44163 + 1.40968i
\(203\) 0 0
\(204\) 1.97663 3.42363i 0.138392 0.239702i
\(205\) −6.87678 11.9109i −0.480295 0.831896i
\(206\) 10.0263 5.78871i 0.698568 0.403318i
\(207\) 5.22095 0.362881
\(208\) 24.2131 + 42.4437i 1.67887 + 2.94294i
\(209\) −4.43223 −0.306584
\(210\) 0 0
\(211\) −2.15764 3.73714i −0.148538 0.257275i 0.782149 0.623091i \(-0.214123\pi\)
−0.930687 + 0.365816i \(0.880790\pi\)
\(212\) −24.6955 + 42.7738i −1.69609 + 2.93772i
\(213\) 0.814450i 0.0558052i
\(214\) −44.7741 25.8504i −3.06070 1.76709i
\(215\) −24.4979 14.1439i −1.67075 0.964605i
\(216\) 18.1870i 1.23747i
\(217\) 0 0
\(218\) 5.77339 + 9.99981i 0.391024 + 0.677273i
\(219\) −0.957171 + 0.552623i −0.0646796 + 0.0373428i
\(220\) −31.9210 −2.15212
\(221\) 3.91635 6.70301i 0.263442 0.450893i
\(222\) −5.55083 −0.372548
\(223\) 20.2604 11.6973i 1.35674 0.783312i 0.367553 0.930003i \(-0.380196\pi\)
0.989182 + 0.146691i \(0.0468623\pi\)
\(224\) 0 0
\(225\) −8.08703 + 14.0071i −0.539135 + 0.933810i
\(226\) 7.43315i 0.494446i
\(227\) 23.1427 + 13.3614i 1.53603 + 0.886829i 0.999065 + 0.0432270i \(0.0137639\pi\)
0.536968 + 0.843602i \(0.319569\pi\)
\(228\) −3.81767 2.20413i −0.252831 0.145972i
\(229\) 3.00670i 0.198688i 0.995053 + 0.0993442i \(0.0316745\pi\)
−0.995053 + 0.0993442i \(0.968326\pi\)
\(230\) 7.98222 13.8256i 0.526332 0.911634i
\(231\) 0 0
\(232\) −21.1683 + 12.2215i −1.38977 + 0.802383i
\(233\) 11.7148 0.767462 0.383731 0.923445i \(-0.374639\pi\)
0.383731 + 0.923445i \(0.374639\pi\)
\(234\) 0.145180 28.0727i 0.00949072 1.83517i
\(235\) 19.1504 1.24924
\(236\) −49.4199 + 28.5326i −3.21696 + 1.85731i
\(237\) −0.138710 0.240253i −0.00901019 0.0156061i
\(238\) 0 0
\(239\) 1.42797i 0.0923677i 0.998933 + 0.0461838i \(0.0147060\pi\)
−0.998933 + 0.0461838i \(0.985294\pi\)
\(240\) −13.2292 7.63786i −0.853938 0.493021i
\(241\) 2.32068 + 1.33984i 0.149488 + 0.0863069i 0.572878 0.819640i \(-0.305827\pi\)
−0.423390 + 0.905947i \(0.639160\pi\)
\(242\) 20.5232i 1.31928i
\(243\) −4.42437 + 7.66323i −0.283824 + 0.491597i
\(244\) −26.8284 46.4682i −1.71751 2.97482i
\(245\) 0 0
\(246\) −3.94764 −0.251692
\(247\) −7.47450 4.36710i −0.475591 0.277872i
\(248\) −15.5770 −0.989143
\(249\) 2.98711 1.72461i 0.189301 0.109293i
\(250\) 2.70989 + 4.69367i 0.171389 + 0.296854i
\(251\) −5.46696 + 9.46906i −0.345072 + 0.597681i −0.985367 0.170447i \(-0.945479\pi\)
0.640295 + 0.768129i \(0.278812\pi\)
\(252\) 0 0
\(253\) −2.89786 1.67308i −0.182187 0.105186i
\(254\) 22.7885 + 13.1570i 1.42988 + 0.825541i
\(255\) 2.42690i 0.151978i
\(256\) −11.9089 + 20.6268i −0.744307 + 1.28918i
\(257\) −2.07569 3.59520i −0.129478 0.224262i 0.793996 0.607922i \(-0.207997\pi\)
−0.923474 + 0.383660i \(0.874663\pi\)
\(258\) −7.03156 + 4.05967i −0.437766 + 0.252744i
\(259\) 0 0
\(260\) −53.8315 31.4519i −3.33849 1.95057i
\(261\) 7.87497 0.487448
\(262\) −43.6872 + 25.2228i −2.69900 + 1.55827i
\(263\) −2.02680 3.51052i −0.124978 0.216468i 0.796747 0.604314i \(-0.206553\pi\)
−0.921724 + 0.387846i \(0.873219\pi\)
\(264\) −2.85475 + 4.94457i −0.175698 + 0.304317i
\(265\) 30.3210i 1.86260i
\(266\) 0 0
\(267\) 4.52801 + 2.61425i 0.277110 + 0.159989i
\(268\) 4.38866i 0.268080i
\(269\) 2.00011 3.46430i 0.121949 0.211222i −0.798587 0.601879i \(-0.794419\pi\)
0.920536 + 0.390657i \(0.127752\pi\)
\(270\) 8.95836 + 15.5163i 0.545188 + 0.944294i
\(271\) 2.41189 1.39251i 0.146512 0.0845888i −0.424952 0.905216i \(-0.639709\pi\)
0.571464 + 0.820627i \(0.306376\pi\)
\(272\) 29.1806 1.76933
\(273\) 0 0
\(274\) 22.7651 1.37529
\(275\) 8.97733 5.18306i 0.541353 0.312551i
\(276\) −1.66403 2.88219i −0.100163 0.173487i
\(277\) 8.34618 14.4560i 0.501474 0.868578i −0.498525 0.866875i \(-0.666125\pi\)
0.999999 0.00170243i \(-0.000541901\pi\)
\(278\) 47.6741i 2.85930i
\(279\) 4.34619 + 2.50928i 0.260200 + 0.150226i
\(280\) 0 0
\(281\) 13.3731i 0.797774i 0.917000 + 0.398887i \(0.130603\pi\)
−0.917000 + 0.398887i \(0.869397\pi\)
\(282\) 2.74834 4.76026i 0.163661 0.283470i
\(283\) 9.44312 + 16.3560i 0.561335 + 0.972261i 0.997380 + 0.0723362i \(0.0230455\pi\)
−0.436045 + 0.899925i \(0.643621\pi\)
\(284\) −10.8207 + 6.24731i −0.642088 + 0.370710i
\(285\) 2.70623 0.160303
\(286\) −9.07663 + 15.5351i −0.536712 + 0.918609i
\(287\) 0 0
\(288\) 46.7827 27.0100i 2.75669 1.59158i
\(289\) 6.18199 + 10.7075i 0.363647 + 0.629855i
\(290\) 12.0399 20.8537i 0.707008 1.22457i
\(291\) 3.19370i 0.187218i
\(292\) −14.6841 8.47789i −0.859324 0.496131i
\(293\) 2.95999 + 1.70895i 0.172925 + 0.0998380i 0.583964 0.811779i \(-0.301501\pi\)
−0.411040 + 0.911617i \(0.634834\pi\)
\(294\) 0 0
\(295\) 17.5161 30.3388i 1.01983 1.76639i
\(296\) −26.5329 45.9564i −1.54220 2.67116i
\(297\) 3.25224 1.87768i 0.188714 0.108954i
\(298\) 10.8697 0.629663
\(299\) −3.23845 5.67675i −0.187284 0.328295i
\(300\) 10.3101 0.595252
\(301\) 0 0
\(302\) −25.5465 44.2479i −1.47004 2.54618i
\(303\) −2.56407 + 4.44110i −0.147302 + 0.255134i
\(304\) 32.5391i 1.86625i
\(305\) 28.5268 + 16.4699i 1.63344 + 0.943066i
\(306\) −14.5185 8.38225i −0.829966 0.479181i
\(307\) 16.3679i 0.934165i 0.884214 + 0.467083i \(0.154695\pi\)
−0.884214 + 0.467083i \(0.845305\pi\)
\(308\) 0 0
\(309\) 0.740826 + 1.28315i 0.0421441 + 0.0729958i
\(310\) 13.2896 7.67278i 0.754801 0.435785i
\(311\) 23.6979 1.34378 0.671891 0.740650i \(-0.265482\pi\)
0.671891 + 0.740650i \(0.265482\pi\)
\(312\) −9.68614 + 5.52570i −0.548370 + 0.312831i
\(313\) 5.18025 0.292805 0.146403 0.989225i \(-0.453231\pi\)
0.146403 + 0.989225i \(0.453231\pi\)
\(314\) −27.0941 + 15.6428i −1.52901 + 0.882774i
\(315\) 0 0
\(316\) 2.12798 3.68577i 0.119708 0.207341i
\(317\) 6.06537i 0.340665i −0.985387 0.170332i \(-0.945516\pi\)
0.985387 0.170332i \(-0.0544842\pi\)
\(318\) −7.53697 4.35147i −0.422652 0.244018i
\(319\) −4.37096 2.52358i −0.244727 0.141293i
\(320\) 76.8686i 4.29709i
\(321\) 3.30827 5.73010i 0.184650 0.319823i
\(322\) 0 0
\(323\) −4.47700 + 2.58480i −0.249107 + 0.143822i
\(324\) −42.1248 −2.34027
\(325\) 20.2462 + 0.104705i 1.12306 + 0.00580799i
\(326\) 11.9087 0.659562
\(327\) −1.27975 + 0.738866i −0.0707706 + 0.0408594i
\(328\) −18.8697 32.6833i −1.04190 1.80463i
\(329\) 0 0
\(330\) 5.62465i 0.309627i
\(331\) 14.9605 + 8.63743i 0.822301 + 0.474756i 0.851209 0.524826i \(-0.175870\pi\)
−0.0289082 + 0.999582i \(0.509203\pi\)
\(332\) 45.8258 + 26.4576i 2.51502 + 1.45205i
\(333\) 17.0966i 0.936886i
\(334\) −12.1902 + 21.1140i −0.667017 + 1.15531i
\(335\) 1.34710 + 2.33324i 0.0735998 + 0.127479i
\(336\) 0 0
\(337\) −8.35464 −0.455106 −0.227553 0.973766i \(-0.573073\pi\)
−0.227553 + 0.973766i \(0.573073\pi\)
\(338\) −30.6136 + 17.2551i −1.66516 + 0.938552i
\(339\) 0.951279 0.0516664
\(340\) −32.2435 + 18.6158i −1.74865 + 1.00958i
\(341\) −1.60822 2.78552i −0.0870901 0.150844i
\(342\) −9.34700 + 16.1895i −0.505428 + 0.875427i
\(343\) 0 0
\(344\) −67.2216 38.8104i −3.62435 2.09252i
\(345\) 1.76937 + 1.02155i 0.0952598 + 0.0549983i
\(346\) 16.4679i 0.885318i
\(347\) −14.4110 + 24.9606i −0.773623 + 1.33995i 0.161942 + 0.986800i \(0.448224\pi\)
−0.935565 + 0.353154i \(0.885109\pi\)
\(348\) −2.50993 4.34733i −0.134546 0.233041i
\(349\) 10.1516 5.86103i 0.543403 0.313734i −0.203054 0.979167i \(-0.565087\pi\)
0.746457 + 0.665434i \(0.231753\pi\)
\(350\) 0 0
\(351\) 7.33464 + 0.0379317i 0.391494 + 0.00202464i
\(352\) −34.6220 −1.84536
\(353\) −15.4466 + 8.91811i −0.822141 + 0.474663i −0.851154 0.524916i \(-0.824097\pi\)
0.0290134 + 0.999579i \(0.490763\pi\)
\(354\) −5.02759 8.70804i −0.267213 0.462827i
\(355\) 3.83521 6.64278i 0.203552 0.352562i
\(356\) 80.2113i 4.25119i
\(357\) 0 0
\(358\) −9.08239 5.24372i −0.480019 0.277139i
\(359\) 5.68162i 0.299864i −0.988696 0.149932i \(-0.952094\pi\)
0.988696 0.149932i \(-0.0479055\pi\)
\(360\) −41.9494 + 72.6584i −2.21093 + 3.82943i
\(361\) −6.61771 11.4622i −0.348300 0.603274i
\(362\) −15.4132 + 8.89882i −0.810100 + 0.467712i
\(363\) 2.62651 0.137856
\(364\) 0 0
\(365\) 10.4091 0.544838
\(366\) 8.18794 4.72731i 0.427991 0.247100i
\(367\) −9.81580 17.0015i −0.512381 0.887469i −0.999897 0.0143554i \(-0.995430\pi\)
0.487516 0.873114i \(-0.337903\pi\)
\(368\) 12.2829 21.2746i 0.640289 1.10901i
\(369\) 12.1587i 0.632958i
\(370\) 45.2735 + 26.1387i 2.35366 + 1.35888i
\(371\) 0 0
\(372\) 3.19905i 0.165863i
\(373\) −16.0323 + 27.7687i −0.830119 + 1.43781i 0.0678240 + 0.997697i \(0.478394\pi\)
−0.897943 + 0.440111i \(0.854939\pi\)
\(374\) 5.37227 + 9.30505i 0.277794 + 0.481153i
\(375\) −0.600686 + 0.346806i −0.0310193 + 0.0179090i
\(376\) 52.5482 2.70997
\(377\) −4.88468 8.56248i −0.251574 0.440990i
\(378\) 0 0
\(379\) −16.4745 + 9.51154i −0.846237 + 0.488575i −0.859379 0.511339i \(-0.829150\pi\)
0.0131425 + 0.999914i \(0.495816\pi\)
\(380\) 20.7583 + 35.9545i 1.06488 + 1.84443i
\(381\) −1.68380 + 2.91643i −0.0862637 + 0.149413i
\(382\) 37.1510i 1.90081i
\(383\) −0.606070 0.349915i −0.0309687 0.0178798i 0.484436 0.874827i \(-0.339025\pi\)
−0.515404 + 0.856947i \(0.672358\pi\)
\(384\) −7.86948 4.54345i −0.401588 0.231857i
\(385\) 0 0
\(386\) −30.7529 + 53.2657i −1.56528 + 2.71115i
\(387\) 12.5038 + 21.6572i 0.635604 + 1.10090i
\(388\) −42.4310 + 24.4976i −2.15411 + 1.24368i
\(389\) 20.0547 1.01681 0.508407 0.861117i \(-0.330235\pi\)
0.508407 + 0.861117i \(0.330235\pi\)
\(390\) 5.54200 9.48539i 0.280630 0.480311i
\(391\) −3.90284 −0.197375
\(392\) 0 0
\(393\) −3.22796 5.59099i −0.162829 0.282028i
\(394\) 19.6349 34.0086i 0.989192 1.71333i
\(395\) 2.61272i 0.131460i
\(396\) 24.4388 + 14.1098i 1.22810 + 0.709043i
\(397\) 19.2953 + 11.1401i 0.968403 + 0.559108i 0.898749 0.438463i \(-0.144477\pi\)
0.0696541 + 0.997571i \(0.477810\pi\)
\(398\) 64.4453i 3.23035i
\(399\) 0 0
\(400\) 38.0513 + 65.9069i 1.90257 + 3.29534i
\(401\) −4.16341 + 2.40374i −0.207911 + 0.120037i −0.600340 0.799745i \(-0.704968\pi\)
0.392429 + 0.919782i \(0.371635\pi\)
\(402\) 0.773306 0.0385690
\(403\) 0.0324883 6.28208i 0.00161836 0.312933i
\(404\) −78.6717 −3.91406
\(405\) 22.3957 12.9302i 1.11285 0.642506i
\(406\) 0 0
\(407\) 5.47869 9.48937i 0.271568 0.470370i
\(408\) 6.65935i 0.329687i
\(409\) −31.8727 18.4017i −1.57601 0.909907i −0.995409 0.0957164i \(-0.969486\pi\)
−0.580597 0.814191i \(-0.697181\pi\)
\(410\) 32.1976 + 18.5893i 1.59013 + 0.918060i
\(411\) 2.91343i 0.143709i
\(412\) −11.3651 + 19.6850i −0.559921 + 0.969811i
\(413\) 0 0
\(414\) −12.2224 + 7.05662i −0.600699 + 0.346814i
\(415\) −32.4845 −1.59460
\(416\) −58.3864 34.1132i −2.86263 1.67254i
\(417\) 6.10122 0.298778
\(418\) 10.3760 5.99059i 0.507507 0.293009i
\(419\) 14.6334 + 25.3457i 0.714887 + 1.23822i 0.963003 + 0.269490i \(0.0868552\pi\)
−0.248116 + 0.968730i \(0.579812\pi\)
\(420\) 0 0
\(421\) 7.53862i 0.367410i −0.982981 0.183705i \(-0.941191\pi\)
0.982981 0.183705i \(-0.0588091\pi\)
\(422\) 10.1022 + 5.83251i 0.491768 + 0.283922i
\(423\) −14.6616 8.46489i −0.712872 0.411577i
\(424\) 83.2000i 4.04055i
\(425\) 6.04534 10.4708i 0.293242 0.507910i
\(426\) −1.10081 1.90666i −0.0533343 0.0923778i
\(427\) 0 0
\(428\) 101.506 4.90646
\(429\) −1.98815 1.16161i −0.0959886 0.0560829i
\(430\) 76.4674 3.68759
\(431\) −27.0426 + 15.6131i −1.30260 + 0.752055i −0.980849 0.194771i \(-0.937604\pi\)
−0.321748 + 0.946825i \(0.604270\pi\)
\(432\) 13.7849 + 23.8762i 0.663228 + 1.14874i
\(433\) −2.94202 + 5.09573i −0.141384 + 0.244885i −0.928018 0.372535i \(-0.878489\pi\)
0.786634 + 0.617420i \(0.211822\pi\)
\(434\) 0 0
\(435\) 2.66882 + 1.54084i 0.127960 + 0.0738777i
\(436\) −19.6329 11.3351i −0.940247 0.542852i
\(437\) 4.35204i 0.208186i
\(438\) 1.49385 2.58742i 0.0713788 0.123632i
\(439\) 4.97821 + 8.62251i 0.237597 + 0.411530i 0.960024 0.279917i \(-0.0903069\pi\)
−0.722427 + 0.691447i \(0.756974\pi\)
\(440\) 46.5676 26.8858i 2.22002 1.28173i
\(441\) 0 0
\(442\) −0.108527 + 20.9853i −0.00516212 + 0.998170i
\(443\) −35.8813 −1.70477 −0.852385 0.522915i \(-0.824845\pi\)
−0.852385 + 0.522915i \(0.824845\pi\)
\(444\) 9.43805 5.44906i 0.447910 0.258601i
\(445\) −24.6208 42.6444i −1.16714 2.02154i
\(446\) −31.6202 + 54.7678i −1.49726 + 2.59333i
\(447\) 1.39108i 0.0657956i
\(448\) 0 0
\(449\) 3.46001 + 1.99764i 0.163288 + 0.0942744i 0.579417 0.815031i \(-0.303280\pi\)
−0.416129 + 0.909306i \(0.636614\pi\)
\(450\) 43.7217i 2.06106i
\(451\) 3.89633 6.74864i 0.183471 0.317781i
\(452\) 7.29687 + 12.6386i 0.343216 + 0.594467i
\(453\) 5.66274 3.26939i 0.266059 0.153609i
\(454\) −72.2371 −3.39026
\(455\) 0 0
\(456\) 7.42580 0.347745
\(457\) 35.6995 20.6111i 1.66995 0.964147i 0.702291 0.711890i \(-0.252160\pi\)
0.967660 0.252257i \(-0.0811729\pi\)
\(458\) −4.06385 7.03880i −0.189891 0.328901i
\(459\) 2.19006 3.79329i 0.102223 0.177056i
\(460\) 31.3435i 1.46140i
\(461\) −21.4139 12.3633i −0.997343 0.575816i −0.0898818 0.995952i \(-0.528649\pi\)
−0.907461 + 0.420136i \(0.861982\pi\)
\(462\) 0 0
\(463\) 24.4057i 1.13423i −0.823639 0.567115i \(-0.808060\pi\)
0.823639 0.567115i \(-0.191940\pi\)
\(464\) 18.5268 32.0893i 0.860084 1.48971i
\(465\) 0.981946 + 1.70078i 0.0455366 + 0.0788718i
\(466\) −27.4248 + 15.8337i −1.27043 + 0.733482i
\(467\) −4.44860 −0.205857 −0.102928 0.994689i \(-0.532821\pi\)
−0.102928 + 0.994689i \(0.532821\pi\)
\(468\) 27.3111 + 47.8744i 1.26246 + 2.21299i
\(469\) 0 0
\(470\) −44.8318 + 25.8837i −2.06794 + 1.19392i
\(471\) −2.00193 3.46744i −0.0922441 0.159771i
\(472\) 48.0637 83.2487i 2.21231 3.83183i
\(473\) 16.0276i 0.736951i
\(474\) 0.649451 + 0.374961i 0.0298303 + 0.0172225i
\(475\) −11.6760 6.74113i −0.535730 0.309304i
\(476\) 0 0
\(477\) −13.4025 + 23.2139i −0.613660 + 1.06289i
\(478\) −1.93004 3.34293i −0.0882780 0.152902i
\(479\) 27.4328 15.8383i 1.25343 0.723671i 0.281645 0.959519i \(-0.409120\pi\)
0.971790 + 0.235848i \(0.0757868\pi\)
\(480\) 21.1394 0.964879
\(481\) 18.5892 10.6047i 0.847593 0.483531i
\(482\) −7.24372 −0.329942
\(483\) 0 0
\(484\) 20.1469 + 34.8954i 0.915767 + 1.58616i
\(485\) 15.0390 26.0483i 0.682887 1.18279i
\(486\) 23.9199i 1.08503i
\(487\) 23.3096 + 13.4578i 1.05626 + 0.609832i 0.924395 0.381436i \(-0.124570\pi\)
0.131864 + 0.991268i \(0.457904\pi\)
\(488\) 78.2766 + 45.1930i 3.54341 + 2.04579i
\(489\) 1.52405i 0.0689200i
\(490\) 0 0
\(491\) 4.86358 + 8.42396i 0.219490 + 0.380168i 0.954652 0.297723i \(-0.0962273\pi\)
−0.735162 + 0.677891i \(0.762894\pi\)
\(492\) 6.71215 3.87526i 0.302607 0.174710i
\(493\) −5.88682 −0.265129
\(494\) 23.4006 + 0.121018i 1.05284 + 0.00544487i
\(495\) −17.3239 −0.778653
\(496\) 20.4498 11.8067i 0.918225 0.530137i
\(497\) 0 0
\(498\) −4.66196 + 8.07475i −0.208907 + 0.361838i
\(499\) 7.87525i 0.352545i 0.984341 + 0.176272i \(0.0564039\pi\)
−0.984341 + 0.176272i \(0.943596\pi\)
\(500\) −9.21523 5.32042i −0.412118 0.237936i
\(501\) −2.70213 1.56007i −0.120722 0.0696989i
\(502\) 29.5565i 1.31917i
\(503\) −4.87603 + 8.44553i −0.217411 + 0.376568i −0.954016 0.299756i \(-0.903095\pi\)
0.736604 + 0.676324i \(0.236428\pi\)
\(504\) 0 0
\(505\) 41.8259 24.1482i 1.86123 1.07458i
\(506\) 9.04533 0.402114
\(507\) −2.20827 3.91786i −0.0980725 0.173998i
\(508\) −51.6630 −2.29217
\(509\) 19.9407 11.5128i 0.883857 0.510295i 0.0119288 0.999929i \(-0.496203\pi\)
0.871928 + 0.489634i \(0.162870\pi\)
\(510\) −3.28019 5.68146i −0.145249 0.251579i
\(511\) 0 0
\(512\) 11.8512i 0.523752i
\(513\) −4.22988 2.44212i −0.186754 0.107822i
\(514\) 9.71853 + 5.61100i 0.428666 + 0.247490i
\(515\) 13.9541i 0.614891i
\(516\) 7.97048 13.8053i 0.350881 0.607744i
\(517\) 5.42524 + 9.39679i 0.238602 + 0.413270i
\(518\) 0 0
\(519\) 2.10752 0.0925100
\(520\) 105.022 + 0.543130i 4.60552 + 0.0238178i
\(521\) −0.486481 −0.0213131 −0.0106566 0.999943i \(-0.503392\pi\)
−0.0106566 + 0.999943i \(0.503392\pi\)
\(522\) −18.4356 + 10.6438i −0.806904 + 0.465866i
\(523\) −17.3135 29.9878i −0.757065 1.31128i −0.944341 0.328968i \(-0.893299\pi\)
0.187275 0.982307i \(-0.440034\pi\)
\(524\) 49.5207 85.7724i 2.16332 3.74698i
\(525\) 0 0
\(526\) 9.48962 + 5.47883i 0.413767 + 0.238888i
\(527\) −3.24893 1.87577i −0.141526 0.0817099i
\(528\) 8.65510i 0.376665i
\(529\) 9.85719 17.0732i 0.428574 0.742311i
\(530\) 40.9818 + 70.9826i 1.78014 + 3.08329i
\(531\) −26.8208 + 15.4850i −1.16392 + 0.671990i
\(532\) 0 0
\(533\) 13.2202 7.54182i 0.572632 0.326672i
\(534\) −14.1336 −0.611622
\(535\) −53.9656 + 31.1571i −2.33314 + 1.34704i
\(536\) 3.69639 + 6.40234i 0.159660 + 0.276539i
\(537\) 0.671080 1.16234i 0.0289592 0.0501589i
\(538\) 10.8134i 0.466198i
\(539\) 0 0
\(540\) −30.4637 17.5882i −1.31095 0.756876i
\(541\) 22.5384i 0.969002i 0.874791 + 0.484501i \(0.160999\pi\)
−0.874791 + 0.484501i \(0.839001\pi\)
\(542\) −3.76422 + 6.51982i −0.161687 + 0.280050i
\(543\) −1.13885 1.97255i −0.0488728 0.0846502i
\(544\) −34.9717 + 20.1909i −1.49940 + 0.865678i
\(545\) 13.9172 0.596146
\(546\) 0 0
\(547\) 39.3716 1.68341 0.841704 0.539940i \(-0.181553\pi\)
0.841704 + 0.539940i \(0.181553\pi\)
\(548\) −38.7074 + 22.3477i −1.65350 + 0.954648i
\(549\) −14.5601 25.2189i −0.621411 1.07631i
\(550\) −14.0108 + 24.2675i −0.597424 + 1.03477i
\(551\) 6.56436i 0.279651i
\(552\) 4.85510 + 2.80310i 0.206647 + 0.119308i
\(553\) 0 0
\(554\) 45.1227i 1.91708i
\(555\) −3.34517 + 5.79401i −0.141995 + 0.245942i
\(556\) 46.8000 + 81.0600i 1.98476 + 3.43771i
\(557\) 0.629579 0.363487i 0.0266761 0.0154015i −0.486603 0.873623i \(-0.661764\pi\)
0.513279 + 0.858222i \(0.328431\pi\)
\(558\) −13.5661 −0.574300
\(559\) 15.7921 27.0289i 0.667935 1.14320i
\(560\) 0 0
\(561\) −1.19084 + 0.687532i −0.0502773 + 0.0290276i
\(562\) −18.0751 31.3070i −0.762452 1.32061i
\(563\) −20.8038 + 36.0333i −0.876777 + 1.51862i −0.0219200 + 0.999760i \(0.506978\pi\)
−0.854857 + 0.518863i \(0.826355\pi\)
\(564\) 10.7918i 0.454417i
\(565\) −7.75879 4.47954i −0.326415 0.188456i
\(566\) −44.2134 25.5266i −1.85843 1.07296i
\(567\) 0 0
\(568\) 10.5237 18.2276i 0.441565 0.764813i
\(569\) −12.6944 21.9873i −0.532177 0.921757i −0.999294 0.0375618i \(-0.988041\pi\)
0.467118 0.884195i \(-0.345292\pi\)
\(570\) −6.33537 + 3.65773i −0.265360 + 0.153205i
\(571\) −16.9992 −0.711393 −0.355697 0.934602i \(-0.615756\pi\)
−0.355697 + 0.934602i \(0.615756\pi\)
\(572\) 0.182683 35.3244i 0.00763836 1.47699i
\(573\) −4.75451 −0.198622
\(574\) 0 0
\(575\) −5.08929 8.81490i −0.212238 0.367607i
\(576\) −33.9776 + 58.8508i −1.41573 + 2.45212i
\(577\) 15.9759i 0.665084i 0.943088 + 0.332542i \(0.107906\pi\)
−0.943088 + 0.332542i \(0.892094\pi\)
\(578\) −28.9445 16.7111i −1.20393 0.695092i
\(579\) −6.81682 3.93570i −0.283298 0.163562i
\(580\) 47.2767i 1.96306i
\(581\) 0 0
\(582\) −4.31660 7.47657i −0.178929 0.309914i
\(583\) 14.8780 8.58982i 0.616184 0.355754i
\(584\) 28.5623 1.18192
\(585\) −29.2150 17.0693i −1.20789 0.705731i
\(586\) −9.23926 −0.381670
\(587\) 13.8404 7.99075i 0.571254 0.329814i −0.186396 0.982475i \(-0.559681\pi\)
0.757650 + 0.652661i \(0.226347\pi\)
\(588\) 0 0
\(589\) −2.09166 + 3.62287i −0.0861855 + 0.149278i
\(590\) 94.6989i 3.89869i
\(591\) 4.35235 + 2.51283i 0.179032 + 0.103364i
\(592\) 69.6660 + 40.2217i 2.86325 + 1.65310i
\(593\) 29.0532i 1.19307i 0.802586 + 0.596536i \(0.203457\pi\)
−0.802586 + 0.596536i \(0.796543\pi\)
\(594\) −5.07574 + 8.79143i −0.208260 + 0.360717i
\(595\) 0 0
\(596\) −18.4816 + 10.6704i −0.757037 + 0.437075i
\(597\) 8.24757 0.337551
\(598\) 15.2540 + 8.91240i 0.623783 + 0.364455i
\(599\) 3.45554 0.141190 0.0705948 0.997505i \(-0.477510\pi\)
0.0705948 + 0.997505i \(0.477510\pi\)
\(600\) −15.0407 + 8.68376i −0.614035 + 0.354513i
\(601\) 7.76518 + 13.4497i 0.316748 + 0.548624i 0.979808 0.199943i \(-0.0640756\pi\)
−0.663059 + 0.748567i \(0.730742\pi\)
\(602\) 0 0
\(603\) 2.38178i 0.0969936i
\(604\) 86.8732 + 50.1563i 3.53482 + 2.04083i
\(605\) −21.4222 12.3681i −0.870938 0.502836i
\(606\) 13.8624i 0.563120i
\(607\) 7.73922 13.4047i 0.314125 0.544081i −0.665126 0.746731i \(-0.731622\pi\)
0.979251 + 0.202650i \(0.0649555\pi\)
\(608\) 22.5148 + 38.9967i 0.913095 + 1.58153i
\(609\) 0 0
\(610\) −89.0429 −3.60524
\(611\) −0.109597 + 21.1922i −0.00443383 + 0.857345i
\(612\) 32.9142 1.33048
\(613\) −6.17669 + 3.56611i −0.249474 + 0.144034i −0.619523 0.784978i \(-0.712674\pi\)
0.370049 + 0.929012i \(0.379341\pi\)
\(614\) −22.1228 38.3178i −0.892804 1.54638i
\(615\) −2.37902 + 4.12058i −0.0959312 + 0.166158i
\(616\) 0 0
\(617\) −4.30142 2.48342i −0.173168 0.0999789i 0.410911 0.911676i \(-0.365211\pi\)
−0.584079 + 0.811697i \(0.698544\pi\)
\(618\) −3.46860 2.00260i −0.139528 0.0805563i
\(619\) 42.3570i 1.70247i 0.524784 + 0.851235i \(0.324146\pi\)
−0.524784 + 0.851235i \(0.675854\pi\)
\(620\) −15.0642 + 26.0920i −0.604993 + 1.04788i
\(621\) −1.84371 3.19339i −0.0739854 0.128146i
\(622\) −55.4776 + 32.0300i −2.22445 + 1.28429i
\(623\) 0 0
\(624\) 8.52791 14.5959i 0.341390 0.584305i
\(625\) −21.5445 −0.861779
\(626\) −12.1272 + 7.00162i −0.484699 + 0.279841i
\(627\) 0.766663 + 1.32790i 0.0306176 + 0.0530312i
\(628\) 30.7120 53.1947i 1.22554 2.12270i
\(629\) 12.7803i 0.509583i
\(630\) 0 0
\(631\) −5.42803 3.13387i −0.216086 0.124758i 0.388050 0.921638i \(-0.373149\pi\)
−0.604137 + 0.796881i \(0.706482\pi\)
\(632\) 7.16924i 0.285177i
\(633\) −0.746432 + 1.29286i −0.0296680 + 0.0513865i
\(634\) 8.19794 + 14.1992i 0.325582 + 0.563924i
\(635\) 27.4667 15.8579i 1.08998 0.629302i
\(636\) 17.0868 0.677534
\(637\) 0 0
\(638\) 13.6434 0.540149
\(639\) −5.87250 + 3.39049i −0.232313 + 0.134126i
\(640\) 42.7898 + 74.1142i 1.69142 + 2.92962i
\(641\) −15.7818 + 27.3350i −0.623345 + 1.07967i 0.365513 + 0.930806i \(0.380894\pi\)
−0.988858 + 0.148860i \(0.952440\pi\)
\(642\) 17.8858i 0.705897i
\(643\) −15.8053 9.12520i −0.623300 0.359863i 0.154852 0.987938i \(-0.450510\pi\)
−0.778153 + 0.628075i \(0.783843\pi\)
\(644\) 0 0
\(645\) 9.78613i 0.385329i
\(646\) 6.98721 12.1022i 0.274908 0.476155i
\(647\) −11.5137 19.9423i −0.452649 0.784011i 0.545901 0.837850i \(-0.316188\pi\)
−0.998550 + 0.0538387i \(0.982854\pi\)
\(648\) 61.4532 35.4800i 2.41411 1.39379i
\(649\) 19.8490 0.779140
\(650\) −47.5387 + 27.1197i −1.86462 + 1.06372i
\(651\) 0 0
\(652\) −20.2483 + 11.6904i −0.792985 + 0.457830i
\(653\) −14.4062 24.9523i −0.563759 0.976459i −0.997164 0.0752597i \(-0.976021\pi\)
0.433405 0.901199i \(-0.357312\pi\)
\(654\) 1.99730 3.45943i 0.0781006 0.135274i
\(655\) 60.8014i 2.37571i
\(656\) 49.5450 + 28.6048i 1.93441 + 1.11683i
\(657\) −7.96926 4.60105i −0.310910 0.179504i
\(658\) 0 0
\(659\) 15.6114 27.0397i 0.608134 1.05332i −0.383414 0.923577i \(-0.625252\pi\)
0.991548 0.129742i \(-0.0414149\pi\)
\(660\) 5.52153 + 9.56356i 0.214925 + 0.372261i
\(661\) 23.0000 13.2791i 0.894598 0.516496i 0.0191541 0.999817i \(-0.493903\pi\)
0.875444 + 0.483320i \(0.160569\pi\)
\(662\) −46.6973 −1.81494
\(663\) −2.68566 0.0138891i −0.104302 0.000539407i
\(664\) −89.1366 −3.45917
\(665\) 0 0
\(666\) −23.1077 40.0237i −0.895405 1.55089i
\(667\) −2.47792 + 4.29188i −0.0959454 + 0.166182i
\(668\) 47.8667i 1.85202i
\(669\) −7.00906 4.04668i −0.270986 0.156454i
\(670\) −6.30721 3.64147i −0.243669 0.140682i
\(671\) 18.6635i 0.720495i
\(672\) 0 0
\(673\) −9.86930 17.0941i −0.380434 0.658930i 0.610691 0.791869i \(-0.290892\pi\)
−0.991124 + 0.132939i \(0.957559\pi\)
\(674\) 19.5585 11.2921i 0.753366 0.434956i
\(675\) 11.4233 0.439683
\(676\) 35.1134 59.3910i 1.35052 2.28427i
\(677\) 13.1440 0.505163 0.252582 0.967576i \(-0.418720\pi\)
0.252582 + 0.967576i \(0.418720\pi\)
\(678\) −2.22698 + 1.28575i −0.0855266 + 0.0493788i
\(679\) 0 0
\(680\) 31.3586 54.3147i 1.20255 2.08287i
\(681\) 9.24475i 0.354260i
\(682\) 7.52981 + 4.34734i 0.288331 + 0.166468i
\(683\) −5.85654 3.38128i −0.224094 0.129381i 0.383750 0.923437i \(-0.374632\pi\)
−0.607845 + 0.794056i \(0.707966\pi\)
\(684\) 36.7025i 1.40336i
\(685\) 13.7192 23.7624i 0.524185 0.907915i
\(686\) 0 0
\(687\) 0.900810 0.520083i 0.0343681 0.0198424i
\(688\) 117.666 4.48599
\(689\) 33.5538 + 0.173526i 1.27830 + 0.00661082i
\(690\) −5.52288 −0.210253
\(691\) −7.94223 + 4.58545i −0.302137 + 0.174439i −0.643402 0.765528i \(-0.722478\pi\)
0.341266 + 0.939967i \(0.389144\pi\)
\(692\) 16.1659 + 28.0002i 0.614537 + 1.06441i
\(693\) 0 0
\(694\) 77.9115i 2.95748i
\(695\) −49.7626 28.7304i −1.88760 1.08981i
\(696\) 7.32316 + 4.22803i 0.277584 + 0.160263i
\(697\) 9.08908i 0.344273i
\(698\) −15.8435 + 27.4418i −0.599686 + 1.03869i
\(699\) −2.02636 3.50976i −0.0766440 0.132751i
\(700\) 0 0
\(701\) 47.4700 1.79292 0.896459 0.443127i \(-0.146131\pi\)
0.896459 + 0.443127i \(0.146131\pi\)
\(702\) −17.2219 + 9.82469i −0.650000 + 0.370809i
\(703\) −14.2512 −0.537495
\(704\) 37.7181 21.7766i 1.42156 0.820736i
\(705\) −3.31253 5.73748i −0.124757 0.216086i
\(706\) 24.1074 41.7552i 0.907294 1.57148i
\(707\) 0 0
\(708\) 17.0968 + 9.87082i 0.642535 + 0.370968i
\(709\) 30.2866 + 17.4860i 1.13744 + 0.656699i 0.945795 0.324766i \(-0.105285\pi\)
0.191642 + 0.981465i \(0.438619\pi\)
\(710\) 20.7347i 0.778158i
\(711\) 1.15488 2.00031i 0.0433114 0.0750175i
\(712\) −67.5587 117.015i −2.53187 4.38533i
\(713\) −2.73512 + 1.57912i −0.102431 + 0.0591387i
\(714\) 0 0
\(715\) 10.7457 + 18.8364i 0.401866 + 0.704440i
\(716\) 20.5903 0.769496
\(717\) 0.427821 0.247002i 0.0159773 0.00922448i
\(718\) 7.67926 + 13.3009i 0.286588 + 0.496384i
\(719\) 4.18051 7.24085i 0.155907 0.270038i −0.777482 0.628905i \(-0.783503\pi\)
0.933389 + 0.358867i \(0.116837\pi\)
\(720\) 127.183i 4.73984i
\(721\) 0 0
\(722\) 30.9846 + 17.8890i 1.15313 + 0.665758i
\(723\) 0.927035i 0.0344768i
\(724\) 17.4713 30.2612i 0.649317 1.12465i
\(725\) −7.67639 13.2959i −0.285094 0.493797i
\(726\) −6.14875 + 3.54998i −0.228202 + 0.131752i
\(727\) 27.4014 1.01626 0.508131 0.861280i \(-0.330337\pi\)
0.508131 + 0.861280i \(0.330337\pi\)
\(728\) 0 0
\(729\) −20.7504 −0.768532
\(730\) −24.3681 + 14.0689i −0.901905 + 0.520715i
\(731\) −9.34703 16.1895i −0.345712 0.598791i
\(732\) −9.28127 + 16.0756i −0.343046 + 0.594173i
\(733\) 12.1569i 0.449026i 0.974471 + 0.224513i \(0.0720792\pi\)
−0.974471 + 0.224513i \(0.927921\pi\)
\(734\) 45.9583 + 26.5340i 1.69635 + 0.979389i
\(735\) 0 0
\(736\) 33.9956i 1.25309i
\(737\) −0.763255 + 1.32200i −0.0281148 + 0.0486963i
\(738\) −16.4337 28.4640i −0.604934 1.04778i
\(739\) −41.9537 + 24.2220i −1.54329 + 0.891019i −0.544662 + 0.838656i \(0.683342\pi\)
−0.998628 + 0.0523634i \(0.983325\pi\)
\(740\) −102.638 −3.77304
\(741\) −0.0154876 + 2.99476i −0.000568953 + 0.110015i
\(742\) 0 0
\(743\) −14.7143 + 8.49532i −0.539816 + 0.311663i −0.745004 0.667060i \(-0.767553\pi\)
0.205188 + 0.978722i \(0.434219\pi\)
\(744\) 2.69443 + 4.66689i 0.0987826 + 0.171097i
\(745\) 6.55052 11.3458i 0.239993 0.415679i
\(746\) 86.6767i 3.17346i
\(747\) 24.8702 + 14.3588i 0.909955 + 0.525363i
\(748\) −18.2689 10.5475i −0.667977 0.385657i
\(749\) 0 0
\(750\) 0.937485 1.62377i 0.0342321 0.0592917i
\(751\) 21.5162 + 37.2671i 0.785136 + 1.35990i 0.928918 + 0.370287i \(0.120741\pi\)
−0.143781 + 0.989610i \(0.545926\pi\)
\(752\) −68.9863 + 39.8292i −2.51567 + 1.45242i
\(753\) 3.78258 0.137845
\(754\) 23.0083 + 13.4430i 0.837911 + 0.489563i
\(755\) −61.5817 −2.24119
\(756\) 0 0
\(757\) −14.5892 25.2693i −0.530255 0.918428i −0.999377 0.0352949i \(-0.988763\pi\)
0.469122 0.883133i \(-0.344570\pi\)
\(758\) 25.7116 44.5337i 0.933886 1.61754i
\(759\) 1.15760i 0.0420183i
\(760\) −60.5661 34.9678i −2.19696 1.26842i
\(761\) 25.4829 + 14.7126i 0.923754 + 0.533330i 0.884831 0.465912i \(-0.154274\pi\)
0.0389234 + 0.999242i \(0.487607\pi\)
\(762\) 9.10328i 0.329777i
\(763\) 0 0
\(764\) −36.4699 63.1677i −1.31943 2.28533i
\(765\) −17.4989 + 10.1030i −0.632675 + 0.365275i
\(766\) 1.89178 0.0683526
\(767\) 33.4732 + 19.5573i 1.20865 + 0.706172i
\(768\) 8.23976 0.297327
\(769\) −14.8839 + 8.59322i −0.536727 + 0.309879i −0.743751 0.668456i \(-0.766955\pi\)
0.207024 + 0.978336i \(0.433622\pi\)
\(770\) 0 0
\(771\) −0.718083 + 1.24376i −0.0258611 + 0.0447928i
\(772\) 120.756i 4.34612i
\(773\) −19.0180 10.9801i −0.684031 0.394926i 0.117341 0.993092i \(-0.462563\pi\)
−0.801372 + 0.598166i \(0.795896\pi\)
\(774\) −58.5437 33.8002i −2.10431 1.21492i
\(775\) 9.78399i 0.351451i
\(776\) 41.2666 71.4759i 1.48139 2.56584i
\(777\) 0 0
\(778\) −46.9488 + 27.1059i −1.68320 + 0.971794i
\(779\) −10.1352 −0.363131
\(780\) −0.111542 + 21.5683i −0.00399386 + 0.772271i
\(781\) 4.34600