Properties

Label 637.2.u.h.30.6
Level $637$
Weight $2$
Character 637.30
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.u (of order \(6\), degree \(2\), not 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: \(\Z[a_1, a_2, a_3]\)
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 30.6
Root \(-1.12906 - 0.851598i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.h.361.6

$q$-expansion

\(f(q)\) \(=\) \(q+(2.34104 - 1.35160i) q^{2} -0.345949 q^{3} +(2.65363 - 4.59623i) q^{4} +(-2.82162 - 1.62906i) q^{5} +(-0.809880 + 0.467584i) q^{6} -8.94020i q^{8} -2.88032 q^{9} +O(q^{10})\) \(q+(2.34104 - 1.35160i) q^{2} -0.345949 q^{3} +(2.65363 - 4.59623i) q^{4} +(-2.82162 - 1.62906i) q^{5} +(-0.809880 + 0.467584i) q^{6} -8.94020i q^{8} -2.88032 q^{9} -8.80735 q^{10} +1.84603i q^{11} +(-0.918023 + 1.59006i) 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} +(-6.74293 + 3.89303i) q^{18} -2.40096i q^{19} +(-14.9751 + 8.64587i) q^{20} +(2.49509 + 4.32162i) q^{22} +(0.906314 + 1.56978i) q^{23} +3.09285i q^{24} +(2.80769 + 4.86305i) q^{25} +(8.41541 - 4.91684i) q^{26} +2.03429 q^{27} +(1.36703 - 2.36777i) q^{29} +3.04689 q^{30} +(1.50893 - 0.871180i) q^{31} +(-16.2422 - 9.37743i) q^{32} -0.638632i q^{33} -5.82036i q^{34} +(-7.64331 + 13.2386i) q^{36} +(5.14042 - 2.96783i) q^{37} +(-3.24513 - 5.62072i) q^{38} +(-1.24732 + 0.00645062i) q^{39} +(-14.5641 + 25.2258i) q^{40} +(3.65577 + 2.11066i) q^{41} +(-4.34111 - 7.51903i) q^{43} +(8.48477 + 4.89868i) q^{44} +(8.12716 + 4.69222i) q^{45} +(4.24343 + 2.44994i) q^{46} +(5.09027 + 2.93887i) q^{47} +(2.34425 + 4.06036i) q^{48} +(13.1458 + 7.58972i) q^{50} +(-0.372438 + 0.645082i) q^{51} +(9.48199 - 16.6212i) q^{52} +(4.65314 + 8.05947i) q^{53} +(4.76235 - 2.74954i) q^{54} +(3.00729 - 5.20878i) q^{55} +0.830609i q^{57} -7.39071i q^{58} +(-9.31173 - 5.37613i) q^{59} +(5.18062 - 2.99103i) q^{60} +10.1101 q^{61} +(2.35497 - 4.07893i) q^{62} -23.5929 q^{64} +(-10.2037 - 5.82098i) q^{65} +(-0.863173 - 1.49506i) q^{66} -0.826916i q^{67} +(-5.71365 - 9.89633i) q^{68} +(-0.313538 - 0.543065i) q^{69} +(-2.03884 + 1.17712i) q^{71} +25.7506i q^{72} +(-2.76680 + 1.59741i) 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} +(-0.400955 + 0.694475i) q^{79} +44.1559i q^{80} +7.93720 q^{81} +11.4110 q^{82} +9.97031i q^{83} +(-6.07534 + 3.50760i) q^{85} +(-20.3254 - 11.7349i) q^{86} +(-0.472923 + 0.819127i) q^{87} +16.5039 q^{88} +(-13.0886 + 7.55674i) q^{89} +25.3680 q^{90} +9.62010 q^{92} +(-0.522012 + 0.301384i) q^{93} +15.8887 q^{94} +(-3.91130 + 6.77458i) q^{95} +(5.61897 + 3.24411i) q^{96} +(7.99489 - 4.61585i) q^{97} -5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} + O(q^{10}) \) \( 12 q + 4 q^{4} - 6 q^{5} - 18 q^{6} + 8 q^{9} - 24 q^{10} + 2 q^{12} + 4 q^{13} + 6 q^{15} - 8 q^{16} - 4 q^{17} - 12 q^{18} - 12 q^{20} + 6 q^{22} - 12 q^{23} + 10 q^{25} + 24 q^{26} + 12 q^{27} + 8 q^{29} - 16 q^{30} + 18 q^{31} - 36 q^{32} - 10 q^{36} + 42 q^{37} - 2 q^{38} - 10 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} + 24 q^{44} - 12 q^{46} + 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} + 26 q^{52} + 22 q^{53} - 12 q^{54} - 6 q^{55} - 18 q^{59} + 66 q^{60} - 28 q^{61} - 4 q^{62} - 52 q^{64} - 42 q^{65} + 26 q^{66} - 8 q^{68} + 4 q^{69} - 24 q^{71} + 30 q^{73} + 6 q^{74} + 46 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} - 4 q^{81} - 28 q^{82} - 48 q^{85} - 60 q^{86} - 2 q^{87} + 28 q^{88} + 12 q^{89} + 24 q^{90} + 24 q^{92} + 18 q^{93} - 8 q^{94} - 22 q^{95} + 6 q^{96} + 6 q^{97} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.34104 1.35160i 1.65536 0.955724i 0.680549 0.732702i \(-0.261741\pi\)
0.974813 0.223022i \(-0.0715921\pi\)
\(3\) −0.345949 −0.199734 −0.0998669 0.995001i \(-0.531842\pi\)
−0.0998669 + 0.995001i \(0.531842\pi\)
\(4\) 2.65363 4.59623i 1.32682 2.29811i
\(5\) −2.82162 1.62906i −1.26187 0.728539i −0.288431 0.957501i \(-0.593133\pi\)
−0.973435 + 0.228962i \(0.926467\pi\)
\(6\) −0.809880 + 0.467584i −0.330632 + 0.190890i
\(7\) 0 0
\(8\) 8.94020i 3.16084i
\(9\) −2.88032 −0.960106
\(10\) −8.80735 −2.78513
\(11\) 1.84603i 0.556598i 0.960494 + 0.278299i \(0.0897707\pi\)
−0.960494 + 0.278299i \(0.910229\pi\)
\(12\) −0.918023 + 1.59006i −0.265010 + 0.459011i
\(13\) 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 −0.705430 0.708780i \(-0.749246\pi\)
0.966536 + 0.256530i \(0.0825793\pi\)
\(18\) −6.74293 + 3.89303i −1.58932 + 0.917597i
\(19\) 2.40096i 0.550817i −0.961327 0.275408i \(-0.911187\pi\)
0.961327 0.275408i \(-0.0888131\pi\)
\(20\) −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 \(0.772815\pi\)
\(24\) 3.09285i 0.631326i
\(25\) 2.80769 + 4.86305i 0.561537 + 0.972611i
\(26\) 8.41541 4.91684i 1.65040 0.964272i
\(27\) 2.03429 0.391500
\(28\) 0 0
\(29\) 1.36703 2.36777i 0.253851 0.439683i −0.710732 0.703463i \(-0.751636\pi\)
0.964583 + 0.263780i \(0.0849693\pi\)
\(30\) 3.04689 0.556284
\(31\) 1.50893 0.871180i 0.271011 0.156468i −0.358336 0.933593i \(-0.616656\pi\)
0.629347 + 0.777124i \(0.283322\pi\)
\(32\) −16.2422 9.37743i −2.87124 1.65771i
\(33\) 0.638632i 0.111172i
\(34\) 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 −0.0139073 0.999903i \(-0.504427\pi\)
0.858988 + 0.511996i \(0.171094\pi\)
\(38\) −3.24513 5.62072i −0.526429 0.911802i
\(39\) −1.24732 + 0.00645062i −0.199731 + 0.00103293i
\(40\) −14.5641 + 25.2258i −2.30279 + 3.98855i
\(41\) 3.65577 + 2.11066i 0.570935 + 0.329629i 0.757523 0.652809i \(-0.226410\pi\)
−0.186588 + 0.982438i \(0.559743\pi\)
\(42\) 0 0
\(43\) −4.34111 7.51903i −0.662014 1.14664i −0.980086 0.198575i \(-0.936369\pi\)
0.318072 0.948067i \(-0.396965\pi\)
\(44\) 8.48477 + 4.89868i 1.27913 + 0.738504i
\(45\) 8.12716 + 4.69222i 1.21153 + 0.699475i
\(46\) 4.24343 + 2.44994i 0.625659 + 0.361224i
\(47\) 5.09027 + 2.93887i 0.742493 + 0.428678i 0.822975 0.568078i \(-0.192313\pi\)
−0.0804822 + 0.996756i \(0.525646\pi\)
\(48\) 2.34425 + 4.06036i 0.338363 + 0.586062i
\(49\) 0 0
\(50\) 13.1458 + 7.58972i 1.85910 + 1.07335i
\(51\) −0.372438 + 0.645082i −0.0521518 + 0.0903296i
\(52\) 9.48199 16.6212i 1.31491 2.30495i
\(53\) 4.65314 + 8.05947i 0.639158 + 1.10705i 0.985618 + 0.168989i \(0.0540503\pi\)
−0.346460 + 0.938065i \(0.612616\pi\)
\(54\) 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
\(58\) 7.39071i 0.970447i
\(59\) −9.31173 5.37613i −1.21228 0.699912i −0.249028 0.968496i \(-0.580111\pi\)
−0.963256 + 0.268584i \(0.913444\pi\)
\(60\) 5.18062 2.99103i 0.668815 0.386141i
\(61\) 10.1101 1.29446 0.647231 0.762294i \(-0.275927\pi\)
0.647231 + 0.762294i \(0.275927\pi\)
\(62\) 2.35497 4.07893i 0.299081 0.518024i
\(63\) 0 0
\(64\) −23.5929 −2.94911
\(65\) −10.2037 5.82098i −1.26562 0.722003i
\(66\) −0.863173 1.49506i −0.106249 0.184029i
\(67\) 0.826916i 0.101024i −0.998723 0.0505119i \(-0.983915\pi\)
0.998723 0.0505119i \(-0.0160853\pi\)
\(68\) −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 −0.616080 0.787684i \(-0.711280\pi\)
0.374114 + 0.927383i \(0.377947\pi\)
\(72\) 25.7506i 3.03474i
\(73\) −2.76680 + 1.59741i −0.323829 + 0.186963i −0.653098 0.757273i \(-0.726531\pi\)
0.329269 + 0.944236i \(0.393198\pi\)
\(74\) 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
\(79\) −0.400955 + 0.694475i −0.0451110 + 0.0781345i −0.887699 0.460424i \(-0.847697\pi\)
0.842588 + 0.538558i \(0.181031\pi\)
\(80\) 44.1559i 4.93678i
\(81\) 7.93720 0.881911
\(82\) 11.4110 1.26014
\(83\) 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
\(86\) −20.3254 11.7349i −2.19175 1.26541i
\(87\) −0.472923 + 0.819127i −0.0507027 + 0.0878196i
\(88\) 16.5039 1.75932
\(89\) −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
\(94\) 15.8887 1.63879
\(95\) −3.91130 + 6.77458i −0.401291 + 0.695057i
\(96\) 5.61897 + 3.24411i 0.573484 + 0.331101i
\(97\) 7.99489 4.61585i 0.811758 0.468669i −0.0358079 0.999359i \(-0.511400\pi\)
0.847566 + 0.530690i \(0.178067\pi\)
\(98\) 0 0
\(99\) 5.31715i 0.534394i
\(100\) 29.8023 2.98023
\(101\) −14.8234 −1.47498 −0.737491 0.675357i \(-0.763989\pi\)
−0.737491 + 0.675357i \(0.763989\pi\)
\(102\) 2.01355i 0.199371i
\(103\) −2.14143 + 3.70907i −0.211001 + 0.365465i −0.952028 0.306010i \(-0.901006\pi\)
0.741027 + 0.671475i \(0.234339\pi\)
\(104\) −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
\(109\) 3.69925 2.13577i 0.354324 0.204569i −0.312264 0.949995i \(-0.601087\pi\)
0.666588 + 0.745426i \(0.267754\pi\)
\(110\) 16.2586i 1.55020i
\(111\) −1.77833 + 1.02672i −0.168791 + 0.0974516i
\(112\) 0 0
\(113\) −1.37488 2.38137i −0.129338 0.224020i 0.794082 0.607810i \(-0.207952\pi\)
−0.923420 + 0.383790i \(0.874619\pi\)
\(114\) 1.12265 + 1.94448i 0.105146 + 0.182118i
\(115\) 5.90576i 0.550715i
\(116\) −7.25520 12.5664i −0.673629 1.16676i
\(117\) −10.3850 + 0.0537068i −0.960094 + 0.00496520i
\(118\) −29.0655 −2.67569
\(119\) 0 0
\(120\) 5.03845 8.72685i 0.459945 0.796649i
\(121\) 7.59218 0.690198
\(122\) 23.6680 13.6648i 2.14280 1.23715i
\(123\) −1.26471 0.730180i −0.114035 0.0658381i
\(124\) 9.24717i 0.830420i
\(125\) 2.00495i 0.179329i
\(126\) 0 0
\(127\) −4.86719 + 8.43022i −0.431893 + 0.748061i −0.997036 0.0769320i \(-0.975488\pi\)
0.565143 + 0.824993i \(0.308821\pi\)
\(128\) −22.7475 + 13.1333i −2.01061 + 1.16083i
\(129\) 1.50181 + 2.60120i 0.132227 + 0.229023i
\(130\) −31.7549 + 0.164223i −2.78509 + 0.0144033i
\(131\) 9.33073 16.1613i 0.815230 1.41202i −0.0939330 0.995579i \(-0.529944\pi\)
0.909163 0.416441i \(-0.136723\pi\)
\(132\) −2.93530 1.69470i −0.255485 0.147504i
\(133\) 0 0
\(134\) −1.11766 1.93584i −0.0965509 0.167231i
\(135\) −5.73999 3.31399i −0.494020 0.285223i
\(136\) −16.6706 9.62475i −1.42949 0.825315i
\(137\) 7.29328 + 4.21078i 0.623107 + 0.359751i 0.778078 0.628168i \(-0.216195\pi\)
−0.154971 + 0.987919i \(0.549528\pi\)
\(138\) −1.46801 0.847556i −0.124965 0.0721488i
\(139\) 8.81809 + 15.2734i 0.747941 + 1.29547i 0.948808 + 0.315853i \(0.102291\pi\)
−0.200867 + 0.979619i \(0.564376\pi\)
\(140\) 0 0
\(141\) −1.76098 1.01670i −0.148301 0.0856216i
\(142\) −3.18199 + 5.51138i −0.267027 + 0.462504i
\(143\) 0.0344213 + 6.65586i 0.00287845 + 0.556591i
\(144\) 19.5179 + 33.8059i 1.62649 + 2.81716i
\(145\) −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
\(149\) 4.02104i 0.329416i −0.986342 0.164708i \(-0.947332\pi\)
0.986342 0.164708i \(-0.0526683\pi\)
\(150\) −4.54777 2.62566i −0.371324 0.214384i
\(151\) −16.3687 + 9.45048i −1.33207 + 0.769069i −0.985616 0.168999i \(-0.945947\pi\)
−0.346451 + 0.938068i \(0.612613\pi\)
\(152\) −21.4650 −1.74104
\(153\) −3.10086 + 5.37086i −0.250690 + 0.434208i
\(154\) 0 0
\(155\) −5.67682 −0.455973
\(156\) −3.28029 + 5.75009i −0.262633 + 0.460376i
\(157\) 5.78677 + 10.0230i 0.461835 + 0.799922i 0.999052 0.0435222i \(-0.0138579\pi\)
−0.537218 + 0.843444i \(0.680525\pi\)
\(158\) 2.16772i 0.172455i
\(159\) −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
\(163\) 4.40542i 0.345059i −0.985004 0.172529i \(-0.944806\pi\)
0.985004 0.172529i \(-0.0551940\pi\)
\(164\) 19.4021 11.2018i 1.51505 0.874716i
\(165\) −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 \(-0.446798\pi\)
−0.770776 + 0.637106i \(0.780131\pi\)
\(168\) 0 0
\(169\) 12.9993 0.134457i 0.999947 0.0103429i
\(170\) −9.48173 + 16.4228i −0.727215 + 1.25957i
\(171\) 6.91552i 0.528843i
\(172\) −46.0789 −3.51349
\(173\) −6.09200 −0.463166 −0.231583 0.972815i \(-0.574391\pi\)
−0.231583 + 0.972815i \(0.574391\pi\)
\(174\) 2.55681i 0.193831i
\(175\) 0 0
\(176\) 21.6666 12.5092i 1.63318 0.942917i
\(177\) 3.22139 + 1.85987i 0.242134 + 0.139796i
\(178\) −20.4273 + 35.3812i −1.53109 + 2.65193i
\(179\) −3.87964 −0.289978 −0.144989 0.989433i \(-0.546315\pi\)
−0.144989 + 0.989433i \(0.546315\pi\)
\(180\) 43.1330 24.9029i 3.21495 1.85615i
\(181\) −6.58392 −0.489379 −0.244690 0.969601i \(-0.578686\pi\)
−0.244690 + 0.969601i \(0.578686\pi\)
\(182\) 0 0
\(183\) −3.49757 −0.258548
\(184\) 14.0342 8.10262i 1.03461 0.597333i
\(185\) −19.3391 −1.42184
\(186\) −0.814700 + 1.41110i −0.0597367 + 0.103467i
\(187\) 3.44224 + 1.98738i 0.251721 + 0.145331i
\(188\) 27.0155 15.5974i 1.97030 1.13756i
\(189\) 0 0
\(190\) 21.1460i 1.53410i
\(191\) −13.7434 −0.994435 −0.497218 0.867626i \(-0.665645\pi\)
−0.497218 + 0.867626i \(0.665645\pi\)
\(192\) 8.16195 0.589038
\(193\) 22.7530i 1.63780i −0.573937 0.818899i \(-0.694585\pi\)
0.573937 0.818899i \(-0.305415\pi\)
\(194\) 12.4776 21.6118i 0.895836 1.55163i
\(195\) 3.52997 + 2.01376i 0.252786 + 0.144208i
\(196\) 0 0
\(197\) −12.5809 7.26358i −0.896352 0.517509i −0.0203371 0.999793i \(-0.506474\pi\)
−0.876015 + 0.482284i \(0.839807\pi\)
\(198\) −7.18665 12.4476i −0.510733 0.884615i
\(199\) 11.9202 20.6464i 0.845001 1.46358i −0.0406192 0.999175i \(-0.512933\pi\)
0.885620 0.464410i \(-0.153734\pi\)
\(200\) 43.4767 25.1013i 3.07426 1.77493i
\(201\) 0.286071i 0.0201779i
\(202\) −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
\(206\) 11.5774i 0.806637i
\(207\) −2.61047 4.52147i −0.181440 0.314264i
\(208\) −24.6508 42.1910i −1.70922 2.92542i
\(209\) 4.43223 0.306584
\(210\) 0 0
\(211\) −2.15764 + 3.73714i −0.148538 + 0.257275i −0.930687 0.365816i \(-0.880790\pi\)
0.782149 + 0.623091i \(0.214123\pi\)
\(212\) 49.3909 3.39218
\(213\) 0.705334 0.407225i 0.0483287 0.0279026i
\(214\) 44.7741 + 25.8504i 3.06070 + 1.76709i
\(215\) 28.2878i 1.92921i
\(216\) 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
\(220\) −15.9605 27.6444i −1.07606 1.86379i
\(221\) 3.84681 6.74316i 0.258764 0.453594i
\(222\) −2.77542 + 4.80716i −0.186274 + 0.322636i
\(223\) −20.2604 11.6973i −1.35674 0.783312i −0.367553 0.930003i \(-0.619804\pi\)
−0.989182 + 0.146691i \(0.953138\pi\)
\(224\) 0 0
\(225\) −8.08703 14.0071i −0.539135 0.933810i
\(226\) −6.43730 3.71658i −0.428203 0.247223i
\(227\) 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
\(229\) −2.60388 1.50335i −0.172069 0.0993442i 0.411492 0.911413i \(-0.365008\pi\)
−0.583561 + 0.812069i \(0.698341\pi\)
\(230\) −7.98222 13.8256i −0.526332 0.911634i
\(231\) 0 0
\(232\) −21.1683 12.2215i −1.38977 0.802383i
\(233\) −5.85740 + 10.1453i −0.383731 + 0.664641i −0.991592 0.129402i \(-0.958694\pi\)
0.607861 + 0.794043i \(0.292028\pi\)
\(234\) −24.2391 + 14.1621i −1.58456 + 0.925804i
\(235\) −9.57521 16.5847i −0.624618 1.08187i
\(236\) −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 \(-0.985294\pi\)
0.998933 0.0461838i \(-0.0147060\pi\)
\(240\) 15.2757i 0.986043i
\(241\) 2.32068 + 1.33984i 0.149488 + 0.0863069i 0.572878 0.819640i \(-0.305827\pi\)
−0.423390 + 0.905947i \(0.639160\pi\)
\(242\) 17.7736 10.2616i 1.14253 0.659639i
\(243\) −8.84874 −0.567647
\(244\) 26.8284 46.4682i 1.71751 2.97482i
\(245\) 0 0
\(246\) −3.94764 −0.251692
\(247\) −0.0447686 8.65665i −0.00284856 0.550810i
\(248\) −7.78852 13.4901i −0.494571 0.856623i
\(249\) 3.44922i 0.218586i
\(250\) −2.70989 4.69367i −0.171389 0.296854i
\(251\) 5.46696 + 9.46906i 0.345072 + 0.597681i 0.985367 0.170447i \(-0.0545213\pi\)
−0.640295 + 0.768129i \(0.721188\pi\)
\(252\) 0 0
\(253\) −2.89786 + 1.67308i −0.182187 + 0.105186i
\(254\) 26.3139i 1.65108i
\(255\) 2.10176 1.21345i 0.131617 0.0759892i
\(256\) −11.9089 + 20.6268i −0.744307 + 1.28918i
\(257\) 2.07569 + 3.59520i 0.129478 + 0.224262i 0.923474 0.383660i \(-0.125337\pi\)
−0.793996 + 0.607922i \(0.792003\pi\)
\(258\) 7.03156 + 4.05967i 0.437766 + 0.252744i
\(259\) 0 0
\(260\) −53.8315 + 31.4519i −3.33849 + 1.95057i
\(261\) −3.93749 + 6.81993i −0.243724 + 0.422143i
\(262\) 50.4456i 3.11654i
\(263\) 4.05360 0.249955 0.124978 0.992160i \(-0.460114\pi\)
0.124978 + 0.992160i \(0.460114\pi\)
\(264\) −5.70949 −0.351395
\(265\) 30.3210i 1.86260i
\(266\) 0 0
\(267\) 4.52801 2.61425i 0.277110 0.159989i
\(268\) −3.80069 2.19433i −0.232164 0.134040i
\(269\) −2.00011 + 3.46430i −0.121949 + 0.211222i −0.920536 0.390657i \(-0.872248\pi\)
0.798587 + 0.601879i \(0.205581\pi\)
\(270\) −17.9167 −1.09038
\(271\) 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
\(276\) −3.32807 −0.200326
\(277\) 8.34618 14.4560i 0.501474 0.868578i −0.498525 0.866875i \(-0.666125\pi\)
0.999999 0.00170243i \(-0.000541901\pi\)
\(278\) 41.2870 + 23.8370i 2.47623 + 1.42965i
\(279\) −4.34619 + 2.50928i −0.260200 + 0.150226i
\(280\) 0 0
\(281\) 13.3731i 0.797774i −0.917000 0.398887i \(-0.869397\pi\)
0.917000 0.398887i \(-0.130603\pi\)
\(282\) −5.49668 −0.327322
\(283\) 18.8862 1.12267 0.561335 0.827589i \(-0.310288\pi\)
0.561335 + 0.827589i \(0.310288\pi\)
\(284\) 12.4946i 0.741419i
\(285\) 1.35311 2.34366i 0.0801515 0.138826i
\(286\) 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
\(291\) −2.76583 + 1.59685i −0.162136 + 0.0936090i
\(292\) 16.9558i 0.992262i
\(293\) −2.95999 + 1.70895i −0.172925 + 0.0998380i −0.583964 0.811779i \(-0.698499\pi\)
0.411040 + 0.911617i \(0.365166\pi\)
\(294\) 0 0
\(295\) 17.5161 + 30.3388i 1.01983 + 1.76639i
\(296\) −26.5329 45.9564i −1.54220 2.67116i
\(297\) 3.75536i 0.217908i
\(298\) −5.43483 9.41340i −0.314831 0.545304i
\(299\) 3.29699 + 5.64295i 0.190670 + 0.326340i
\(300\) −10.3101 −0.595252
\(301\) 0 0
\(302\) −25.5465 + 44.2479i −1.47004 + 2.54618i
\(303\) 5.12814 0.294604
\(304\) −28.1797 + 16.2696i −1.61622 + 0.933123i
\(305\) −28.5268 16.4699i −1.63344 0.943066i
\(306\) 16.7645i 0.958362i
\(307\) 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
\(311\) 11.8489 + 20.5230i 0.671891 + 1.16375i 0.977367 + 0.211550i \(0.0678511\pi\)
−0.305476 + 0.952200i \(0.598816\pi\)
\(312\) 0.0576698 + 11.1513i 0.00326491 + 0.631318i
\(313\) 2.59013 4.48623i 0.146403 0.253577i −0.783493 0.621401i \(-0.786564\pi\)
0.929895 + 0.367824i \(0.119897\pi\)
\(314\) 27.0941 + 15.6428i 1.52901 + 0.882774i
\(315\) 0 0
\(316\) 2.12798 + 3.68577i 0.119708 + 0.207341i
\(317\) −5.25276 3.03268i −0.295024 0.170332i 0.345181 0.938536i \(-0.387817\pi\)
−0.640206 + 0.768204i \(0.721151\pi\)
\(318\) −7.53697 4.35147i −0.422652 0.244018i
\(319\) 4.37096 + 2.52358i 0.244727 + 0.141293i
\(320\) 66.5702 + 38.4343i 3.72139 + 2.14854i
\(321\) −3.30827 5.73010i −0.184650 0.319823i
\(322\) 0 0
\(323\) −4.47700 2.58480i −0.249107 0.143822i
\(324\) 21.0624 36.4812i 1.17013 2.02673i
\(325\) 10.2138 + 17.4814i 0.566559 + 0.969694i
\(326\) −5.95435 10.3132i −0.329781 0.571198i
\(327\) −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
\(331\) 17.2749i 0.949512i 0.880118 + 0.474756i \(0.157464\pi\)
−0.880118 + 0.474756i \(0.842536\pi\)
\(332\) 45.8258 + 26.4576i 2.51502 + 1.45205i
\(333\) −14.8061 + 8.54829i −0.811367 + 0.468443i
\(334\) −24.3804 −1.33403
\(335\) −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 \(0.573073\pi\)
\(338\) 30.2501 17.8846i 1.64539 0.972794i
\(339\) 0.475639 + 0.823832i 0.0258332 + 0.0447444i
\(340\) 37.2315i 2.01916i
\(341\) 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
\(345\) 2.04309i 0.109997i
\(346\) −14.2616 + 8.23394i −0.766708 + 0.442659i
\(347\) −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 \(-0.434913\pi\)
−0.746457 + 0.665434i \(0.768247\pi\)
\(350\) 0 0
\(351\) 7.33464 0.0379317i 0.391494 0.00202464i
\(352\) 17.3110 29.9835i 0.922679 1.59813i
\(353\) 17.8362i 0.949326i −0.880168 0.474663i \(-0.842570\pi\)
0.880168 0.474663i \(-0.157430\pi\)
\(354\) 10.0552 0.534426
\(355\) 7.67043 0.407104
\(356\) 80.2113i 4.25119i
\(357\) 0 0
\(358\) −9.08239 + 5.24372i −0.480019 + 0.277139i
\(359\) −4.92042 2.84081i −0.259690 0.149932i 0.364503 0.931202i \(-0.381239\pi\)
−0.624193 + 0.781270i \(0.714572\pi\)
\(360\) 41.9494 72.6584i 2.21093 3.82943i
\(361\) 13.2354 0.696601
\(362\) −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
\(367\) −19.6316 −1.02476 −0.512381 0.858758i \(-0.671236\pi\)
−0.512381 + 0.858758i \(0.671236\pi\)
\(368\) 12.2829 21.2746i 0.640289 1.10901i
\(369\) −10.5298 6.07937i −0.548158 0.316479i
\(370\) −45.2735 + 26.1387i −2.35366 + 1.35888i
\(371\) 0 0
\(372\) 3.19905i 0.165863i
\(373\) 32.0645 1.66024 0.830119 0.557586i \(-0.188272\pi\)
0.830119 + 0.557586i \(0.188272\pi\)
\(374\) 10.7445 0.555587
\(375\) 0.693612i 0.0358180i
\(376\) 26.2741 45.5081i 1.35498 2.34690i
\(377\) 4.88468 8.56248i 0.251574 0.440990i
\(378\) 0 0
\(379\) −16.4745 9.51154i −0.846237 0.488575i 0.0131425 0.999914i \(-0.495816\pi\)
−0.859379 + 0.511339i \(0.829150\pi\)
\(380\) 20.7583 + 35.9545i 1.06488 + 1.84443i
\(381\) 1.68380 2.91643i 0.0862637 0.149413i
\(382\) −32.1737 + 18.5755i −1.64615 + 0.950406i
\(383\) 0.699829i 0.0357596i 0.999840 + 0.0178798i \(0.00569162\pi\)
−0.999840 + 0.0178798i \(0.994308\pi\)
\(384\) 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
\(388\) 48.9951i 2.48735i
\(389\) −10.0274 17.3679i −0.508407 0.880587i −0.999953 0.00973506i \(-0.996901\pi\)
0.491545 0.870852i \(-0.336432\pi\)
\(390\) 10.9856 0.0568128i 0.556277 0.00287683i
\(391\) 3.90284 0.197375
\(392\) 0 0
\(393\) −3.22796 + 5.59099i −0.162829 + 0.282028i
\(394\) −39.2698 −1.97838
\(395\) 2.26269 1.30636i 0.113848 0.0657302i
\(396\) −24.4388 14.1098i −1.22810 0.709043i
\(397\) 22.2803i 1.11822i −0.829095 0.559108i \(-0.811144\pi\)
0.829095 0.559108i \(-0.188856\pi\)
\(398\) 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 −0.392429 0.919782i \(-0.628365\pi\)
0.600340 + 0.799745i \(0.295032\pi\)
\(402\) 0.386653 + 0.669702i 0.0192845 + 0.0334017i
\(403\) 5.42420 3.16918i 0.270199 0.157868i
\(404\) −39.3358 + 68.1317i −1.95703 + 3.38968i
\(405\) −22.3957 12.9302i −1.11285 0.642506i
\(406\) 0 0
\(407\) 5.47869 + 9.48937i 0.271568 + 0.470370i
\(408\) 5.76716 + 3.32967i 0.285517 + 0.164843i
\(409\) −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
\(411\) −2.52310 1.45672i −0.124456 0.0718545i
\(412\) 11.3651 + 19.6850i 0.559921 + 0.969811i
\(413\) 0 0
\(414\) −12.2224 7.05662i −0.600699 0.346814i
\(415\) 16.2423 28.1324i 0.797301 1.38097i
\(416\) −58.7361 33.5075i −2.87977 1.64284i
\(417\) −3.05061 5.28382i −0.149389 0.258750i
\(418\) 10.3760 5.99059i 0.507507 0.293009i
\(419\) −14.6334 + 25.3457i −0.714887 + 1.23822i 0.248116 + 0.968730i \(0.420188\pi\)
−0.963003 + 0.269490i \(0.913145\pi\)
\(420\) 0 0
\(421\) 7.53862i 0.367410i 0.982981 + 0.183705i \(0.0588091\pi\)
−0.982981 + 0.183705i \(0.941191\pi\)
\(422\) 11.6650i 0.567845i
\(423\) −14.6616 8.46489i −0.712872 0.411577i
\(424\) 72.0533 41.6000i 3.49922 2.02027i
\(425\) 12.0907 0.586484
\(426\) 1.10081 1.90666i 0.0533343 0.0923778i
\(427\) 0 0
\(428\) 101.506 4.90646
\(429\) −0.0119080 2.30259i −0.000574925 0.111170i
\(430\) 38.2337 + 66.2227i 1.84379 + 3.19354i
\(431\) 31.2261i 1.50411i 0.659101 + 0.752055i \(0.270937\pi\)
−0.659101 + 0.752055i \(0.729063\pi\)
\(432\) −13.7849 23.8762i −0.663228 1.14874i
\(433\) 2.94202 + 5.09573i 0.141384 + 0.244885i 0.928018 0.372535i \(-0.121511\pi\)
−0.786634 + 0.617420i \(0.788178\pi\)
\(434\) 0 0
\(435\) 2.66882 1.54084i 0.127960 0.0738777i
\(436\) 22.6702i 1.08570i
\(437\) 3.76898 2.17602i 0.180295 0.104093i
\(438\) 1.49385 2.58742i 0.0713788 0.123632i
\(439\) −4.97821 8.62251i −0.237597 0.411530i 0.722427 0.691447i \(-0.243026\pi\)
−0.960024 + 0.279917i \(0.909693\pi\)
\(440\) −46.5676 26.8858i −2.22002 1.28173i
\(441\) 0 0
\(442\) −0.108527 20.9853i −0.00516212 0.998170i
\(443\) 17.9406 31.0741i 0.852385 1.47637i −0.0266653 0.999644i \(-0.508489\pi\)
0.879050 0.476729i \(-0.158178\pi\)
\(444\) 10.8981i 0.517202i
\(445\) 49.2416 2.33427
\(446\) −63.2404 −2.99452
\(447\) 1.39108i 0.0657956i
\(448\) 0 0
\(449\) 3.46001 1.99764i 0.163288 0.0942744i −0.416129 0.909306i \(-0.636614\pi\)
0.579417 + 0.815031i \(0.303280\pi\)
\(450\) −37.8641 21.8608i −1.78493 1.03053i
\(451\) −3.89633 + 6.74864i −0.183471 + 0.317781i
\(452\) −14.5937 −0.686432
\(453\) 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 \(0.747840\pi\)
−0.967660 + 0.252257i \(0.918827\pi\)
\(458\) −8.12770 −0.379783
\(459\) 2.19006 3.79329i 0.102223 0.177056i
\(460\) −27.1443 15.6717i −1.26561 0.730699i
\(461\) 21.4139 12.3633i 0.997343 0.575816i 0.0898818 0.995952i \(-0.471351\pi\)
0.907461 + 0.420136i \(0.138018\pi\)
\(462\) 0 0
\(463\) 24.4057i 1.13423i 0.823639 + 0.567115i \(0.191940\pi\)
−0.823639 + 0.567115i \(0.808060\pi\)
\(464\) −37.0536 −1.72017
\(465\) 1.96389 0.0910733
\(466\) 31.6674i 1.46696i
\(467\) −2.22430 + 3.85260i −0.102928 + 0.178277i −0.912890 0.408206i \(-0.866155\pi\)
0.809962 + 0.586483i \(0.199488\pi\)
\(468\) −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
\(473\) 13.8803 8.01382i 0.638219 0.368476i
\(474\) 0.749922i 0.0344450i
\(475\) 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
\(479\) 31.6766i 1.44734i 0.690145 + 0.723671i \(0.257547\pi\)
−0.690145 + 0.723671i \(0.742453\pi\)
\(480\) −10.5697 18.3073i −0.482440 0.835610i
\(481\) 18.4785 10.7964i 0.842546 0.492271i
\(482\) 7.24372 0.329942
\(483\) 0 0
\(484\) 20.1469 34.8954i 0.915767 1.58616i
\(485\) −30.0780 −1.36577
\(486\) −20.7152 + 11.9599i −0.939662 + 0.542514i
\(487\) −23.3096 13.4578i −1.05626 0.609832i −0.131864 0.991268i \(-0.542096\pi\)
−0.924395 + 0.381436i \(0.875430\pi\)
\(488\) 90.3860i 4.09158i
\(489\) 1.52405i 0.0689200i
\(490\) 0 0
\(491\) 4.86358 8.42396i 0.219490 0.380168i −0.735162 0.677891i \(-0.762894\pi\)
0.954652 + 0.297723i \(0.0962273\pi\)
\(492\) −6.71215 + 3.87526i −0.302607 + 0.174710i
\(493\) −2.94341 5.09813i −0.132564 0.229608i
\(494\) −11.8051 20.2050i −0.531137 0.909067i
\(495\) −8.66196 + 15.0030i −0.389326 + 0.674333i
\(496\) −20.4498 11.8067i −0.918225 0.530137i
\(497\) 0 0
\(498\) −4.66196 8.07475i −0.208907 0.361838i
\(499\) 6.82017 + 3.93763i 0.305313 + 0.176272i 0.644827 0.764329i \(-0.276929\pi\)
−0.339514 + 0.940601i \(0.610263\pi\)
\(500\) −9.21523 5.32042i −0.412118 0.237936i
\(501\) 2.70213 + 1.56007i 0.120722 + 0.0696989i
\(502\) 25.5967 + 14.7783i 1.14244 + 0.659586i
\(503\) 4.87603 + 8.44553i 0.217411 + 0.376568i 0.954016 0.299756i \(-0.0969053\pi\)
−0.736604 + 0.676324i \(0.763572\pi\)
\(504\) 0 0
\(505\) 41.8259 + 24.1482i 1.86123 + 1.07458i
\(506\) −4.52266 + 7.83348i −0.201057 + 0.348241i
\(507\) −4.49710 + 0.0465154i −0.199723 + 0.00206582i
\(508\) 25.8315 + 44.7414i 1.14609 + 1.98508i
\(509\) 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
\(513\) 4.88424i 0.215645i
\(514\) 9.71853 + 5.61100i 0.428666 + 0.247490i
\(515\) 12.0846 6.97705i 0.532511 0.307445i
\(516\) 15.9410 0.701762
\(517\) −5.42524 + 9.39679i −0.238602 + 0.413270i
\(518\) 0 0
\(519\) 2.10752 0.0925100
\(520\) −52.0407 + 91.2233i −2.28213 + 4.00041i
\(521\) −0.243241 0.421305i −0.0106566 0.0184577i 0.860648 0.509200i \(-0.170059\pi\)
−0.871305 + 0.490743i \(0.836725\pi\)
\(522\) 21.2876i 0.931733i
\(523\) 17.3135 + 29.9878i 0.757065 + 1.31128i 0.944341 + 0.328968i \(0.106701\pi\)
−0.187275 + 0.982307i \(0.559966\pi\)
\(524\) −49.5207 85.7724i −2.16332 3.74698i
\(525\) 0 0
\(526\) 9.48962 5.47883i 0.413767 0.238888i
\(527\) 3.75154i 0.163420i
\(528\) −7.49554 + 4.32755i −0.326201 + 0.188332i
\(529\) 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
\(534\) 7.06682 12.2401i 0.305811 0.529681i
\(535\) 62.3141i 2.69408i
\(536\) −7.39279 −0.319320
\(537\) 1.34216 0.0579185
\(538\) 10.8134i 0.466198i
\(539\) 0 0
\(540\) −30.4637 + 17.5882i −1.31095 + 0.756876i
\(541\) 19.5188 + 11.2692i 0.839181 + 0.484501i 0.856986 0.515340i \(-0.172334\pi\)
−0.0178050 + 0.999841i \(0.505668\pi\)
\(542\) 3.76422 6.51982i 0.161687 0.280050i
\(543\) 2.27770 0.0977456
\(544\) −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
\(549\) −29.1202 −1.24282
\(550\) −14.0108 + 24.2675i −0.597424 + 1.03477i
\(551\) −5.68490 3.28218i −0.242185 0.139826i
\(552\) −4.85510 + 2.80310i −0.206647 + 0.119308i
\(553\) 0 0
\(554\) 45.1227i 1.91708i
\(555\) 6.69034 0.283989
\(556\) 93.6000 3.96952
\(557\) 0.726975i 0.0308029i −0.999881 0.0154015i \(-0.995097\pi\)
0.999881 0.0154015i \(-0.00490263\pi\)
\(558\) −6.78306 + 11.7486i −0.287150 + 0.497358i
\(559\) −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 \(-0.493022\pi\)
0.854857 0.518863i \(-0.173645\pi\)
\(564\) −9.34597 + 5.39590i −0.393537 + 0.227208i
\(565\) 8.95907i 0.376911i
\(566\) 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 \(-0.345292\pi\)
\(570\) 7.31546i 0.306411i
\(571\) 8.49958 + 14.7217i 0.355697 + 0.616084i 0.987237 0.159259i \(-0.0509103\pi\)
−0.631540 + 0.775343i \(0.717577\pi\)
\(572\) 30.6832 + 17.5040i 1.28293 + 0.731879i
\(573\) 4.75451 0.198622
\(574\) 0 0
\(575\) −5.08929 + 8.81490i −0.212238 + 0.367607i
\(576\) 67.9551 2.83146
\(577\) 13.8355 7.98794i 0.575980 0.332542i −0.183554 0.983010i \(-0.558760\pi\)
0.759534 + 0.650467i \(0.225427\pi\)
\(578\) 28.9445 + 16.7111i 1.20393 + 0.695092i
\(579\) 7.87139i 0.327124i
\(580\) 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
\(584\) 14.2812 + 24.7357i 0.590959 + 1.02357i
\(585\) 29.3900 + 16.7663i 1.21513 + 0.693200i
\(586\) −4.61963 + 8.00144i −0.190835 + 0.330536i
\(587\) −13.8404 7.99075i −0.571254 0.329814i 0.186396 0.982475i \(-0.440319\pi\)
−0.757650 + 0.652661i \(0.773653\pi\)
\(588\) 0 0
\(589\) −2.09166 3.62287i −0.0861855 0.149278i
\(590\) 82.0116 + 47.3494i 3.37637 + 1.94935i
\(591\) 4.35235 + 2.51283i 0.179032 + 0.103364i
\(592\) −69.6660 40.2217i −2.86325 1.65310i
\(593\) −25.1608 14.5266i −1.03323 0.596536i −0.115322 0.993328i \(-0.536790\pi\)
−0.917908 + 0.396792i \(0.870123\pi\)
\(594\) 5.07574 + 8.79143i 0.208260 + 0.360717i
\(595\) 0 0
\(596\) −18.4816 10.6704i −0.757037 0.437075i
\(597\) −4.12379 + 7.14261i −0.168775 + 0.292327i
\(598\) 15.3454 + 8.75416i 0.627519 + 0.357984i
\(599\) −1.72777 2.99259i −0.0705948 0.122274i 0.828567 0.559889i \(-0.189156\pi\)
−0.899162 + 0.437616i \(0.855823\pi\)
\(600\) −15.0407 + 8.68376i −0.614035 + 0.354513i
\(601\) −7.76518 + 13.4497i −0.316748 + 0.548624i −0.979808 0.199943i \(-0.935924\pi\)
0.663059 + 0.748567i \(0.269258\pi\)
\(602\) 0 0
\(603\) 2.38178i 0.0969936i
\(604\) 100.313i 4.08166i
\(605\) −21.4222 12.3681i −0.870938 0.502836i
\(606\) 12.0052 6.93118i 0.487676 0.281560i
\(607\) 15.4784 0.628250 0.314125 0.949382i \(-0.398289\pi\)
0.314125 + 0.949382i \(0.398289\pi\)
\(608\) −22.5148 + 38.9967i −0.913095 + 1.58153i
\(609\) 0 0
\(610\) −89.0429 −3.60524
\(611\) 18.4078 + 10.5012i 0.744700 + 0.424833i
\(612\) 16.4571 + 28.5046i 0.665240 + 1.15223i
\(613\) 7.13223i 0.288068i 0.989573 + 0.144034i \(0.0460075\pi\)
−0.989573 + 0.144034i \(0.953993\pi\)
\(614\) 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 −0.584079 0.811697i \(-0.698544\pi\)
0.410911 + 0.911676i \(0.365211\pi\)
\(618\) 4.00520i 0.161113i
\(619\) 36.6822 21.1785i 1.47438 0.851235i 0.474799 0.880094i \(-0.342521\pi\)
0.999583 + 0.0288589i \(0.00918734\pi\)
\(620\) −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
\(625\) 10.7722 18.6581i 0.430889 0.746322i
\(626\) 14.0032i 0.559682i
\(627\) −1.53333 −0.0612352
\(628\) 61.4239 2.45108
\(629\) 12.7803i 0.509583i
\(630\) 0 0
\(631\) −5.42803 + 3.13387i −0.216086 + 0.124758i −0.604137 0.796881i \(-0.706482\pi\)
0.388050 + 0.921638i \(0.373149\pi\)
\(632\) 6.20874 + 3.58462i 0.246971 + 0.142589i
\(633\) 0.746432 1.29286i 0.0296680 0.0513865i
\(634\) −16.3959 −0.651163
\(635\) 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
\(640\) 85.5797 3.38283
\(641\) −15.7818 + 27.3350i −0.623345 + 1.07967i 0.365513 + 0.930806i \(0.380894\pi\)
−0.988858 + 0.148860i \(0.952440\pi\)
\(642\) −15.4896 8.94291i −0.611325 0.352949i
\(643\) 15.8053 9.12520i 0.623300 0.359863i −0.154852 0.987938i \(-0.549490\pi\)
0.778153 + 0.628075i \(0.216157\pi\)
\(644\) 0 0
\(645\) 9.78613i 0.385329i
\(646\) −13.9744 −0.549816
\(647\) −23.0273 −0.905298 −0.452649 0.891689i \(-0.649521\pi\)
−0.452649 + 0.891689i \(0.649521\pi\)
\(648\) 70.9601i 2.78758i
\(649\) 9.92448 17.1897i 0.389570 0.674755i
\(650\) 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
\(655\) −52.6555 + 30.4007i −2.05742 + 1.18785i
\(656\) 57.2096i 2.23366i
\(657\) 7.96926 4.60105i 0.310910 0.179504i
\(658\) 0 0
\(659\) 15.6114 + 27.0397i 0.608134 + 1.05332i 0.991548 + 0.129742i \(0.0414149\pi\)
−0.383414 + 0.923577i \(0.625252\pi\)
\(660\) 5.52153 + 9.56356i 0.214925 + 0.372261i
\(661\) 26.5582i 1.03299i 0.856289 + 0.516496i \(0.172764\pi\)
−0.856289 + 0.516496i \(0.827236\pi\)
\(662\) 23.3487 + 40.4411i 0.907471 + 1.57179i
\(663\) −1.33080 + 2.33279i −0.0516840 + 0.0905981i
\(664\) 89.1366 3.45917
\(665\) 0 0
\(666\) −23.1077 + 40.0237i −0.895405 + 1.55089i
\(667\) 4.95584 0.191891
\(668\) −41.4538 + 23.9334i −1.60390 + 0.926010i
\(669\) 7.00906 + 4.04668i 0.270986 + 0.156454i
\(670\) 7.28293i 0.281364i
\(671\) 18.6635i 0.720495i
\(672\) 0 0
\(673\) −9.86930 + 17.0941i −0.380434 + 0.658930i −0.991124 0.132939i \(-0.957559\pi\)
0.610691 + 0.791869i \(0.290892\pi\)
\(674\) −19.5585 + 11.2921i −0.753366 + 0.434956i
\(675\) 5.71165 + 9.89287i 0.219842 + 0.380777i
\(676\) 33.8774 60.1046i 1.30298 2.31172i
\(677\) 6.57198 11.3830i 0.252582 0.437484i −0.711654 0.702530i \(-0.752054\pi\)
0.964236 + 0.265046i \(0.0853871\pi\)
\(678\) 2.22698 + 1.28575i 0.0855266 + 0.0493788i
\(679\) 0 0
\(680\) 31.3586 + 54.3147i 1.20255 + 2.08287i
\(681\) −8.00619 4.62238i −0.306798 0.177130i
\(682\) 7.52981 + 4.34734i 0.288331 + 0.166468i
\(683\) 5.85654 + 3.38128i 0.224094 + 0.129381i 0.607845 0.794056i \(-0.292034\pi\)
−0.383750 + 0.923437i \(0.625368\pi\)
\(684\) 31.7853 + 18.3513i 1.21534 + 0.701678i
\(685\) −13.7192 23.7624i −0.524185 0.907915i
\(686\) 0 0
\(687\) 0.900810 + 0.520083i 0.0343681 + 0.0198424i
\(688\) −58.8332 + 101.902i −2.24300 + 3.88498i
\(689\) 16.9272 + 28.9717i 0.644874 + 1.10373i
\(690\) 2.76144 + 4.78296i 0.105126 + 0.182084i
\(691\) −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
\(695\) 57.4609i 2.17962i
\(696\) 7.32316 + 4.22803i 0.277584 + 0.160263i
\(697\) 7.87137 4.54454i 0.298150 0.172137i
\(698\) −31.6870 −1.19937
\(699\) 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 \(0.146131\pi\)
\(702\) 17.1194 10.0023i 0.646130 0.377512i
\(703\) −7.12562 12.3419i −0.268748 0.465485i
\(704\) 43.5532i 1.64147i
\(705\) 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
\(709\) 34.9719i 1.31340i 0.754153 + 0.656699i \(0.228048\pi\)
−0.754153 + 0.656699i \(0.771952\pi\)
\(710\) 17.9567 10.3673i 0.673905 0.389079i
\(711\) 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
\(716\) −10.2952 + 17.8317i −0.384748 + 0.666403i
\(717\) 0.494005i 0.0184490i
\(718\) −15.3585 −0.573175
\(719\) 8.36101 0.311813 0.155907 0.987772i \(-0.450170\pi\)
0.155907 + 0.987772i \(0.450170\pi\)
\(720\) 127.183i 4.73984i
\(721\) 0 0
\(722\) 30.9846 17.8890i 1.15313 0.665758i
\(723\) −0.802836 0.463517i −0.0298578 0.0172384i
\(724\) −17.4713 + 30.2612i −0.649317 + 1.12465i
\(725\) 15.3528 0.570188
\(726\) −6.14875 + 3.54998i −0.228202 + 0.131752i
\(727\) −27.4014 −1.01626 −0.508131 0.861280i \(-0.669663\pi\)
−0.508131 + 0.861280i \(0.669663\pi\)
\(728\) 0 0
\(729\) −20.7504 −0.768532
\(730\) 24.3681 14.0689i 0.901905 0.520715i
\(731\) −18.6941 −0.691425
\(732\) −9.28127 + 16.0756i −0.343046 + 0.594173i
\(733\) −10.5282 6.07846i −0.388868 0.224513i 0.292802 0.956173i \(-0.405412\pi\)
−0.681670 + 0.731660i \(0.738746\pi\)
\(734\) −45.9583 + 26.5340i −1.69635 + 0.979389i
\(735\) 0 0
\(736\) 33.9956i 1.25309i
\(737\) 1.52651 0.0562297
\(738\) −32.8674 −1.20987
\(739\) 48.4439i 1.78204i 0.453966 + 0.891019i \(0.350009\pi\)
−0.453966 + 0.891019i \(0.649991\pi\)
\(740\) −51.3189 + 88.8869i −1.88652 + 3.26755i
\(741\) 0.0154876 + 2.99476i 0.000568953 + 0.110015i
\(742\) 0 0
\(743\) −14.7143 8.49532i −0.539816 0.311663i 0.205188 0.978722i \(-0.434219\pi\)
−0.745004 + 0.667060i \(0.767553\pi\)
\(744\) 2.69443 + 4.66689i 0.0987826 + 0.171097i
\(745\) −6.55052 + 11.3458i −0.239993 + 0.415679i
\(746\) 75.0642 43.3384i 2.74830 1.58673i
\(747\) 28.7177i 1.05073i
\(748\) 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 \(0.545926\pi\)
\(752\) 79.6585i 2.90485i
\(753\) −1.89129 3.27581i −0.0689225 0.119377i
\(754\) −0.137808 26.6472i −0.00501868 0.970434i
\(755\) 61.5817 2.24119
\(756\) 0 0
\(757\) −14.5892 + 25.2693i −0.530255 + 0.918428i 0.469122 + 0.883133i \(0.344570\pi\)
−0.999377 + 0.0352949i \(0.988763\pi\)
\(758\) −51.4231 −1.86777
\(759\) 1.00251 0.578801i 0.0363889 0.0210091i
\(760\) 60.5661 + 34.9678i 2.19696 + 1.26842i
\(761\) 29.4251i 1.06666i −0.845907 0.533330i \(-0.820941\pi\)
0.845907 0.533330i \(-0.179059\pi\)
\(762\) 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
\(766\) 0.945888 + 1.63833i 0.0341763 + 0.0591951i
\(767\) −33.6737 19.2100i −1.21589 0.693634i
\(768\) 4.11988 7.13584i 0.148663 0.257492i
\(769\) 14.8839 + 8.59322i 0.536727 + 0.309879i 0.743751 0.668456i \(-0.233045\pi\)
−0.207024 + 0.978336i \(0.566378\pi\)
\(770\) 0 0
\(771\) −0.718083 1.24376i −0.0258611 0.0447928i
\(772\) −104.578 60.3782i −3.76385 2.17306i
\(773\) −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
\(775\) 8.47319 + 4.89200i 0.304366 + 0.175726i
\(776\) −41.2666 71.4759i −1.48139 2.56584i
\(777\) 0 0
\(778\) −46.9488 27.1059i −1.68320 0.971794i
\(779\) 5.06759 8.77733i 0.181565 0.314480i
\(780\) 18.6230 10.8808i 0.666809 0.389594i
\(781\) −2.17300 3.76375i