Properties

Label 637.2.k.h.569.1
Level $637$
Weight $2$
Character 637.569
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.k (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: \( x^{12} - 5x^{10} - 2x^{9} + 15x^{8} + 2x^{7} - 30x^{6} + 4x^{5} + 60x^{4} - 16x^{3} - 80x^{2} + 64 \) Copy content Toggle raw display
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 569.1
Root \(-1.12906 - 0.851598i\) of defining polynomial
Character \(\chi\) \(=\) 637.569
Dual form 637.2.k.h.459.6

$q$-expansion

\(f(q)\) \(=\) \(q-2.70320i q^{2} +(0.172975 - 0.299601i) q^{3} -5.30727 q^{4} +(2.82162 + 1.62906i) q^{5} +(-0.809880 - 0.467584i) q^{6} +8.94020i q^{8} +(1.44016 + 2.49443i) q^{9} +O(q^{10})\) \(q-2.70320i q^{2} +(0.172975 - 0.299601i) q^{3} -5.30727 q^{4} +(2.82162 + 1.62906i) 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} +(-0.918023 + 1.59006i) q^{12} +(3.60550 + 0.0186461i) q^{13} +(0.976136 - 0.563573i) q^{15} +13.5526 q^{16} -2.15314 q^{17} +(6.74293 - 3.89303i) q^{18} +(2.07929 - 1.20048i) q^{19} +(-14.9751 - 8.64587i) q^{20} +(2.49509 - 4.32162i) q^{22} -1.81263 q^{23} +(2.67849 + 1.54643i) q^{24} +(2.80769 + 4.86305i) q^{25} +(0.0504042 - 9.74638i) q^{26} +2.03429 q^{27} +(1.36703 + 2.36777i) q^{29} +(-1.52345 - 2.63869i) q^{30} +(-1.50893 + 0.871180i) q^{31} -18.7549i q^{32} +(0.553071 - 0.319316i) q^{33} +5.82036i q^{34} +(-7.64331 - 13.2386i) q^{36} -5.93565i q^{37} +(-3.24513 - 5.62072i) q^{38} +(0.629247 - 1.07699i) 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} +9.38444i q^{45} +4.89989i 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} +(-19.1354 - 0.0989601i) q^{52} +(4.65314 + 8.05947i) q^{53} -5.49909i q^{54} +(3.00729 + 5.20878i) q^{55} -0.830609i q^{57} +(6.40054 - 3.69535i) q^{58} -10.7523i q^{59} +(-5.18062 + 2.99103i) q^{60} +(-5.05504 - 8.75558i) q^{61} +(2.35497 + 4.07893i) q^{62} -23.5929 q^{64} +(10.1430 + 5.92620i) q^{65} +(-0.863173 - 1.49506i) q^{66} +(-0.716130 - 0.413458i) q^{67} +11.4273 q^{68} +(-0.313538 + 0.543065i) q^{69} +(-2.03884 - 1.17712i) q^{71} +(-22.3007 + 12.8753i) q^{72} +(2.76680 - 1.59741i) q^{73} -16.0452 q^{74} +1.94263 q^{75} +(-11.0353 + 6.37126i) q^{76} +(-2.91130 - 1.70098i) q^{78} +(-0.400955 + 0.694475i) 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} +(20.3254 + 11.7349i) q^{86} +0.945847 q^{87} +(-8.25193 + 14.2928i) q^{88} +15.1135i q^{89} +25.3680 q^{90} +9.62010 q^{92} +0.602768i q^{93} +(-7.94435 + 13.7600i) q^{94} +7.82261 q^{95} +(-5.61897 - 3.24411i) q^{96} +(7.99489 + 4.61585i) q^{97} +5.31715i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 8 q^{4} + 6 q^{5} - 18 q^{6} - 4 q^{9} + 12 q^{10} - 6 q^{11} + 2 q^{12} + 4 q^{13} + 6 q^{15} + 16 q^{16} + 8 q^{17} + 12 q^{18} - 12 q^{20} + 6 q^{22} + 24 q^{23} - 12 q^{24} + 10 q^{25} + 18 q^{26} + 12 q^{27} + 8 q^{29} + 8 q^{30} - 18 q^{31} + 30 q^{33} - 10 q^{36} - 2 q^{38} + 14 q^{39} - 46 q^{40} + 30 q^{41} + 2 q^{43} - 24 q^{44} - 42 q^{47} - 2 q^{48} - 18 q^{50} - 26 q^{51} - 28 q^{52} + 22 q^{53} - 6 q^{55} + 12 q^{58} - 66 q^{60} + 14 q^{61} - 4 q^{62} - 52 q^{64} - 18 q^{65} + 26 q^{66} + 24 q^{67} + 16 q^{68} + 4 q^{69} - 24 q^{71} - 60 q^{72} - 30 q^{73} - 12 q^{74} - 92 q^{75} - 18 q^{76} - 10 q^{78} + 28 q^{79} + 72 q^{80} + 2 q^{81} + 14 q^{82} - 48 q^{85} + 60 q^{86} + 4 q^{87} - 14 q^{88} + 24 q^{90} + 24 q^{92} + 4 q^{94} + 44 q^{95} - 6 q^{96} + 6 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.70320i 1.91145i −0.294264 0.955724i \(-0.595075\pi\)
0.294264 0.955724i \(-0.404925\pi\)
\(3\) 0.172975 0.299601i 0.0998669 0.172975i −0.811763 0.583988i \(-0.801492\pi\)
0.911629 + 0.411013i \(0.134825\pi\)
\(4\) −5.30727 −2.65363
\(5\) 2.82162 + 1.62906i 1.26187 + 0.728539i 0.973435 0.228962i \(-0.0735332\pi\)
0.288431 + 0.957501i \(0.406867\pi\)
\(6\) −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 \(-0.243563\pi\)
−0.239233 + 0.970962i \(0.576896\pi\)
\(12\) −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
\(16\) 13.5526 3.38814
\(17\) −2.15314 −0.522213 −0.261107 0.965310i \(-0.584087\pi\)
−0.261107 + 0.965310i \(0.584087\pi\)
\(18\) 6.74293 3.89303i 1.58932 0.917597i
\(19\) 2.07929 1.20048i 0.477021 0.275408i −0.242153 0.970238i \(-0.577854\pi\)
0.719174 + 0.694830i \(0.244520\pi\)
\(20\) −14.9751 8.64587i −3.34853 1.93328i
\(21\) 0 0
\(22\) 2.49509 4.32162i 0.531954 0.921372i
\(23\) −1.81263 −0.377959 −0.188979 0.981981i \(-0.560518\pi\)
−0.188979 + 0.981981i \(0.560518\pi\)
\(24\) 2.67849 + 1.54643i 0.546744 + 0.315663i
\(25\) 2.80769 + 4.86305i 0.561537 + 0.972611i
\(26\) 0.0504042 9.74638i 0.00988507 1.91142i
\(27\) 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
\(31\) −1.50893 + 0.871180i −0.271011 + 0.156468i −0.629347 0.777124i \(-0.716678\pi\)
0.358336 + 0.933593i \(0.383344\pi\)
\(32\) 18.7549i 3.31542i
\(33\) 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
\(37\) 5.93565i 0.975815i −0.872895 0.487908i \(-0.837760\pi\)
0.872895 0.487908i \(-0.162240\pi\)
\(38\) −3.24513 5.62072i −0.526429 0.911802i
\(39\) 0.629247 1.07699i 0.100760 0.172456i
\(40\) −14.5641 + 25.2258i −2.30279 + 3.98855i
\(41\) 3.65577 2.11066i 0.570935 0.329629i −0.186588 0.982438i \(-0.559743\pi\)
0.757523 + 0.652809i \(0.226410\pi\)
\(42\) 0 0
\(43\) −4.34111 + 7.51903i −0.662014 + 1.14664i 0.318072 + 0.948067i \(0.396965\pi\)
−0.980086 + 0.198575i \(0.936369\pi\)
\(44\) −8.48477 4.89868i −1.27913 0.738504i
\(45\) 9.38444i 1.39895i
\(46\) 4.89989i 0.722449i
\(47\) −5.09027 2.93887i −0.742493 0.428678i 0.0804822 0.996756i \(-0.474354\pi\)
−0.822975 + 0.568078i \(0.807687\pi\)
\(48\) 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
\(52\) −19.1354 0.0989601i −2.65360 0.0137233i
\(53\) 4.65314 + 8.05947i 0.639158 + 1.10705i 0.985618 + 0.168989i \(0.0540503\pi\)
−0.346460 + 0.938065i \(0.612616\pi\)
\(54\) 5.49909i 0.748331i
\(55\) 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
\(59\) 10.7523i 1.39982i −0.714229 0.699912i \(-0.753222\pi\)
0.714229 0.699912i \(-0.246778\pi\)
\(60\) −5.18062 + 2.99103i −0.668815 + 0.386141i
\(61\) −5.05504 8.75558i −0.647231 1.12104i −0.983781 0.179371i \(-0.942594\pi\)
0.336550 0.941665i \(-0.390740\pi\)
\(62\) 2.35497 + 4.07893i 0.299081 + 0.518024i
\(63\) 0 0
\(64\) −23.5929 −2.94911
\(65\) 10.1430 + 5.92620i 1.25808 + 0.735055i
\(66\) −0.863173 1.49506i −0.106249 0.184029i
\(67\) −0.716130 0.413458i −0.0874892 0.0505119i 0.455617 0.890176i \(-0.349419\pi\)
−0.543106 + 0.839664i \(0.682752\pi\)
\(68\) 11.4273 1.38576
\(69\) −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
\(73\) 2.76680 1.59741i 0.323829 0.186963i −0.329269 0.944236i \(-0.606802\pi\)
0.653098 + 0.757273i \(0.273469\pi\)
\(74\) −16.0452 −1.86522
\(75\) 1.94263 0.224316
\(76\) −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 \(0.181031\pi\)
\(80\) 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 \(-0.815697\pi\)
0.837007 0.547192i \(-0.184303\pi\)
\(84\) 0 0
\(85\) −6.07534 3.50760i −0.658963 0.380452i
\(86\) 20.3254 + 11.7349i 2.19175 + 1.26541i
\(87\) 0.945847 0.101405
\(88\) −8.25193 + 14.2928i −0.879658 + 1.52361i
\(89\) 15.1135i 1.60202i 0.598648 + 0.801012i \(0.295705\pi\)
−0.598648 + 0.801012i \(0.704295\pi\)
\(90\) 25.3680 2.67402
\(91\) 0 0
\(92\) 9.62010 1.00296
\(93\) 0.602768i 0.0625041i
\(94\) −7.94435 + 13.7600i −0.819397 + 1.41924i
\(95\) 7.82261 0.802583
\(96\) −5.61897 3.24411i −0.573484 0.331101i
\(97\) 7.99489 + 4.61585i 0.811758 + 0.468669i 0.847566 0.530690i \(-0.178067\pi\)
−0.0358079 + 0.999359i \(0.511400\pi\)
\(98\) 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 −0.216131 0.976364i \(-0.569344\pi\)
0.953622 0.301007i \(-0.0973228\pi\)
\(102\) 1.74378 + 1.00677i 0.172660 + 0.0996855i
\(103\) −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
\(107\) −19.1258 −1.84896 −0.924479 0.381233i \(-0.875500\pi\)
−0.924479 + 0.381233i \(0.875500\pi\)
\(108\) −10.7965 −1.03890
\(109\) −3.69925 + 2.13577i −0.354324 + 0.204569i −0.666588 0.745426i \(-0.732246\pi\)
0.312264 + 0.949995i \(0.398913\pi\)
\(110\) 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 \(0.207952\pi\)
\(114\) −2.24530 −0.210291
\(115\) −5.11454 2.95288i −0.476934 0.275358i
\(116\) −7.25520 12.5664i −0.673629 1.16676i
\(117\) 5.14599 + 9.02053i 0.475747 + 0.833948i
\(118\) −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
\(122\) −23.6680 + 13.6648i −2.14280 + 1.23715i
\(123\) 1.46036i 0.131676i
\(124\) 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 \(0.975488\pi\)
\(128\) 26.2666i 2.32166i
\(129\) 1.50181 + 2.60120i 0.132227 + 0.229023i
\(130\) 16.0197 27.4185i 1.40502 2.40476i
\(131\) 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
\(136\) 19.2495i 1.65063i
\(137\) 8.42156i 0.719502i 0.933048 + 0.359751i \(0.117138\pi\)
−0.933048 + 0.359751i \(0.882862\pi\)
\(138\) 1.46801 + 0.847556i 0.124965 + 0.0721488i
\(139\) 8.81809 15.2734i 0.747941 1.29547i −0.200867 0.979619i \(-0.564376\pi\)
0.948808 0.315853i \(-0.102291\pi\)
\(140\) 0 0
\(141\) −1.76098 + 1.01670i −0.148301 + 0.0856216i
\(142\) −3.18199 + 5.51138i −0.267027 + 0.462504i
\(143\) 5.74693 + 3.35774i 0.480583 + 0.280788i
\(144\) 19.5179 + 33.8059i 1.62649 + 2.81716i
\(145\) 8.90791i 0.739762i
\(146\) −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 \(-0.613998\pi\)
0.635813 + 0.771843i \(0.280665\pi\)
\(150\) 5.25132i 0.428768i
\(151\) 16.3687 9.45048i 1.33207 0.769069i 0.346451 0.938068i \(-0.387387\pi\)
0.985616 + 0.168999i \(0.0540534\pi\)
\(152\) 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
\(156\) −3.33958 + 5.71586i −0.267381 + 0.457635i
\(157\) 5.78677 + 10.0230i 0.461835 + 0.799922i 0.999052 0.0435222i \(-0.0138579\pi\)
−0.537218 + 0.843444i \(0.680525\pi\)
\(158\) 1.87730 + 1.08386i 0.149350 + 0.0862273i
\(159\) 3.21950 0.255323
\(160\) 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 \(-0.611473\pi\)
0.641917 + 0.766774i \(0.278139\pi\)
\(164\) −19.4021 + 11.2018i −1.51505 + 0.874716i
\(165\) 2.08074 0.161985
\(166\) −26.9517 −2.09186
\(167\) −7.81076 + 4.50954i −0.604415 + 0.348959i −0.770776 0.637106i \(-0.780131\pi\)
0.166362 + 0.986065i \(0.446798\pi\)
\(168\) 0 0
\(169\) 12.9993 + 0.134457i 0.999947 + 0.0103429i
\(170\) −9.48173 + 16.4228i −0.727215 + 1.25957i
\(171\) 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 \(-0.0922761\pi\)
−0.726691 + 0.686964i \(0.758943\pi\)
\(174\) 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
\(178\) 40.8547 3.06219
\(179\) 1.93982 3.35987i 0.144989 0.251128i −0.784380 0.620281i \(-0.787019\pi\)
0.929369 + 0.369152i \(0.120352\pi\)
\(180\) 49.8057i 3.71230i
\(181\) −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
\(184\) 16.2052i 1.19467i
\(185\) 9.66954 16.7481i 0.710919 1.23135i
\(186\) 1.62940 0.119473
\(187\) −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
\(191\) 6.87168 + 11.9021i 0.497218 + 0.861206i 0.999995 0.00320983i \(-0.00102172\pi\)
−0.502777 + 0.864416i \(0.667688\pi\)
\(192\) −4.08097 + 7.06845i −0.294519 + 0.510122i
\(193\) −19.7047 11.3765i −1.41838 0.818899i −0.422219 0.906494i \(-0.638749\pi\)
−0.996156 + 0.0875946i \(0.972082\pi\)
\(194\) 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 −0.876015 0.482284i \(-0.839807\pi\)
−0.0203371 + 0.999793i \(0.506474\pi\)
\(198\) 14.3733 1.02147
\(199\) −23.8404 −1.69000 −0.845001 0.534765i \(-0.820400\pi\)
−0.845001 + 0.534765i \(0.820400\pi\)
\(200\) −43.4767 + 25.1013i −3.07426 + 1.77493i
\(201\) −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
\(205\) 13.7536 0.960591
\(206\) 10.0263 + 5.78871i 0.698568 + 0.403318i
\(207\) −2.61047 4.52147i −0.181440 0.314264i
\(208\) 48.8638 + 0.252703i 3.38810 + 0.0175218i
\(209\) 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
\(213\) −0.705334 + 0.407225i −0.0483287 + 0.0279026i
\(214\) 51.7007i 3.53419i
\(215\) −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
\(219\) 1.10525i 0.0746856i
\(220\) −15.9605 27.6444i −1.07606 1.86379i
\(221\) −7.76315 0.0401478i −0.522206 0.00270063i
\(222\) −2.77542 + 4.80716i −0.186274 + 0.322636i
\(223\) −20.2604 + 11.6973i −1.35674 + 0.783312i −0.989182 0.146691i \(-0.953138\pi\)
−0.367553 + 0.930003i \(0.619804\pi\)
\(224\) 0 0
\(225\) −8.08703 + 14.0071i −0.539135 + 0.933810i
\(226\) 6.43730 + 3.71658i 0.428203 + 0.247223i
\(227\) 26.7229i 1.77366i 0.462097 + 0.886829i \(0.347097\pi\)
−0.462097 + 0.886829i \(0.652903\pi\)
\(228\) 4.40826i 0.291944i
\(229\) 2.60388 + 1.50335i 0.172069 + 0.0993442i 0.583561 0.812069i \(-0.301659\pi\)
−0.411492 + 0.911413i \(0.634992\pi\)
\(230\) −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 \(0.292028\pi\)
\(234\) 24.3843 13.9106i 1.59405 0.909365i
\(235\) −9.57521 16.5847i −0.624618 1.08187i
\(236\) 57.0651i 3.71462i
\(237\) 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
\(241\) 2.67969i 0.172614i 0.996269 + 0.0863069i \(0.0275065\pi\)
−0.996269 + 0.0863069i \(0.972493\pi\)
\(242\) −17.7736 + 10.2616i −1.14253 + 0.659639i
\(243\) 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
\(247\) 7.51926 4.28956i 0.478439 0.272938i
\(248\) −7.78852 13.4901i −0.494571 0.856623i
\(249\) −2.98711 1.72461i −0.189301 0.109293i
\(250\) 5.41978 0.342777
\(251\) 5.46696 9.46906i 0.345072 0.597681i −0.640295 0.768129i \(-0.721188\pi\)
0.985367 + 0.170447i \(0.0545213\pi\)
\(252\) 0 0
\(253\) −2.89786 1.67308i −0.182187 0.105186i
\(254\) −22.7885 + 13.1570i −1.42988 + 0.825541i
\(255\) −2.10176 + 1.21345i −0.131617 + 0.0759892i
\(256\) 23.8178 1.48861
\(257\) −4.15138 −0.258956 −0.129478 0.991582i \(-0.541330\pi\)
−0.129478 + 0.991582i \(0.541330\pi\)
\(258\) 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
\(262\) −43.6872 25.2228i −2.69900 1.55827i
\(263\) −2.02680 + 3.51052i −0.124978 + 0.216468i −0.921724 0.387846i \(-0.873219\pi\)
0.796747 + 0.604314i \(0.206553\pi\)
\(264\) 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
\(268\) 3.80069 + 2.19433i 0.232164 + 0.134040i
\(269\) 4.00022 0.243898 0.121949 0.992536i \(-0.461086\pi\)
0.121949 + 0.992536i \(0.461086\pi\)
\(270\) 8.95836 15.5163i 0.545188 0.944294i
\(271\) 2.78502i 0.169178i −0.996416 0.0845888i \(-0.973042\pi\)
0.996416 0.0845888i \(-0.0269577\pi\)
\(272\) −29.1806 −1.76933
\(273\) 0 0
\(274\) 22.7651 1.37529
\(275\) 10.3661i 0.625101i
\(276\) 1.66403 2.88219i 0.100163 0.173487i
\(277\) −16.6924 −1.00295 −0.501474 0.865173i \(-0.667209\pi\)
−0.501474 + 0.865173i \(0.667209\pi\)
\(278\) −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 \(0.130603\pi\)
−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 0.436045 + 0.899925i \(0.356379\pi\)
−0.997380 + 0.0723362i \(0.976955\pi\)
\(284\) 10.8207 + 6.24731i 0.642088 + 0.370710i
\(285\) 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
\(289\) −12.3640 −0.727293
\(290\) 24.0798 1.41402
\(291\) 2.76583 1.59685i 0.162136 0.0936090i
\(292\) −14.6841 + 8.47789i −0.859324 + 0.496131i
\(293\) −2.95999 1.70895i −0.172925 0.0998380i 0.411040 0.911617i \(-0.365166\pi\)
−0.583964 + 0.811779i \(0.698499\pi\)
\(294\) 0 0
\(295\) 17.5161 30.3388i 1.01983 1.76639i
\(296\) 53.0659 3.08439
\(297\) 3.25224 + 1.87768i 0.188714 + 0.108954i
\(298\) −5.43483 9.41340i −0.314831 0.545304i
\(299\) −6.53543 0.0337985i −0.377954 0.00195462i
\(300\) −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
\(304\) 28.1797 16.2696i 1.61622 0.933123i
\(305\) 32.9399i 1.88613i
\(306\) −14.5185 + 8.38225i −0.829966 + 0.479181i
\(307\) 16.3679i 0.934165i −0.884214 0.467083i \(-0.845305\pi\)
0.884214 0.467083i \(-0.154695\pi\)
\(308\) 0 0
\(309\) 0.740826 + 1.28315i 0.0421441 + 0.0729958i
\(310\) 15.3456i 0.871569i
\(311\) 11.8489 + 20.5230i 0.671891 + 1.16375i 0.977367 + 0.211550i \(0.0678511\pi\)
−0.305476 + 0.952200i \(0.598816\pi\)
\(312\) 9.62847 + 5.62559i 0.545105 + 0.318486i
\(313\) 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 0.640206 0.768204i \(-0.278849\pi\)
−0.345181 + 0.938536i \(0.612183\pi\)
\(318\) 8.70294i 0.488037i
\(319\) 5.04715i 0.282586i
\(320\) −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
\(325\) 10.0324 + 17.5861i 0.556500 + 0.975502i
\(326\) −5.95435 10.3132i −0.329781 0.571198i
\(327\) 1.47773i 0.0817188i
\(328\) 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 \(-0.824130\pi\)
0.0289082 + 0.999582i \(0.490797\pi\)
\(332\) 52.9151i 2.90410i
\(333\) 14.8061 8.54829i 0.811367 0.468443i
\(334\) 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 \(0.573073\pi\)
\(338\) 0.363465 35.1397i 0.0197699 1.91135i
\(339\) 0.475639 + 0.823832i 0.0258332 + 0.0447444i
\(340\) 32.2435 + 18.6158i 1.74865 + 1.00958i
\(341\) −3.21644 −0.174180
\(342\) 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
\(346\) 14.2616 8.23394i 0.766708 0.442659i
\(347\) 28.8220 1.54725 0.773623 0.633646i \(-0.218443\pi\)
0.773623 + 0.633646i \(0.218443\pi\)
\(348\) −5.01986 −0.269093
\(349\) −10.1516 + 5.86103i −0.543403 + 0.313734i −0.746457 0.665434i \(-0.768247\pi\)
0.203054 + 0.979167i \(0.434913\pi\)
\(350\) 0 0
\(351\) 7.33464 + 0.0379317i 0.391494 + 0.00202464i
\(352\) 17.3110 29.9835i 0.922679 1.59813i
\(353\) −15.4466 8.91811i −0.822141 0.474663i 0.0290134 0.999579i \(-0.490763\pi\)
−0.851154 + 0.524916i \(0.824097\pi\)
\(354\) −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
\(359\) 4.92042 + 2.84081i 0.259690 + 0.149932i 0.624193 0.781270i \(-0.285428\pi\)
−0.364503 + 0.931202i \(0.618761\pi\)
\(360\) −83.8987 −4.42185
\(361\) −6.61771 + 11.4622i −0.348300 + 0.603274i
\(362\) 17.7976i 0.935423i
\(363\) −2.62651 −0.137856
\(364\) 0 0
\(365\) 10.4091 0.544838
\(366\) 9.45462i 0.494201i
\(367\) 9.81580 17.0015i 0.512381 0.887469i −0.487516 0.873114i \(-0.662097\pi\)
0.999897 0.0143554i \(-0.00456964\pi\)
\(368\) −24.5658 −1.28058
\(369\) 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
\(373\) −16.0323 27.7687i −0.830119 1.43781i −0.897943 0.440111i \(-0.854939\pi\)
0.0678240 0.997697i \(-0.478394\pi\)
\(374\) −5.37227 + 9.30505i −0.277794 + 0.481153i
\(375\) 0.600686 + 0.346806i 0.0310193 + 0.0179090i
\(376\) 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 −0.859379 0.511339i \(-0.829150\pi\)
0.0131425 + 0.999914i \(0.495816\pi\)
\(380\) −41.5167 −2.12976
\(381\) −3.36760 −0.172527
\(382\) 32.1737 18.5755i 1.64615 0.950406i
\(383\) −0.606070 + 0.349915i −0.0309687 + 0.0178798i −0.515404 0.856947i \(-0.672358\pi\)
0.484436 + 0.874827i \(0.339025\pi\)
\(384\) 7.86948 + 4.54345i 0.401588 + 0.231857i
\(385\) 0 0
\(386\) −30.7529 + 53.2657i −1.56528 + 2.71115i
\(387\) −25.0076 −1.27121
\(388\) −42.4310 24.4976i −2.15411 1.24368i
\(389\) −10.0274 17.3679i −0.508407 0.880587i −0.999953 0.00973506i \(-0.996901\pi\)
0.491545 0.870852i \(-0.336432\pi\)
\(390\) −5.44359 9.54220i −0.275647 0.483188i
\(391\) 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
\(395\) −2.26269 + 1.30636i −0.113848 + 0.0657302i
\(396\) 28.2195i 1.41809i
\(397\) 19.2953 11.1401i 0.968403 0.559108i 0.0696541 0.997571i \(-0.477810\pi\)
0.898749 + 0.438463i \(0.144477\pi\)
\(398\) 64.4453i 3.23035i
\(399\) 0 0
\(400\) 38.0513 + 65.9069i 1.90257 + 3.29534i
\(401\) 4.80749i 0.240074i −0.992769 0.120037i \(-0.961699\pi\)
0.992769 0.120037i \(-0.0383014\pi\)
\(402\) 0.386653 + 0.669702i 0.0192845 + 0.0334017i
\(403\) −5.45669 + 3.11290i −0.271817 + 0.155065i
\(404\) −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
\(409\) 36.8035i 1.81981i −0.414811 0.909907i \(-0.636152\pi\)
0.414811 0.909907i \(-0.363848\pi\)
\(410\) 37.1786i 1.83612i
\(411\) 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
\(416\) 0.349706 67.6207i 0.0171457 3.31538i
\(417\) −3.05061 5.28382i −0.149389 0.258750i
\(418\) 11.9812i 0.586019i
\(419\) −14.6334 25.3457i −0.714887 1.23822i −0.963003 0.269490i \(-0.913145\pi\)
0.248116 0.968730i \(-0.420188\pi\)
\(420\) 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
\(423\) 16.9298i 0.823154i
\(424\) −72.0533 + 41.6000i −3.49922 + 2.02027i
\(425\) −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
\(429\) 2.00005 1.14098i 0.0965635 0.0550871i
\(430\) 38.2337 + 66.2227i 1.84379 + 3.19354i
\(431\) 27.0426 + 15.6131i 1.30260 + 0.752055i 0.980849 0.194771i \(-0.0623963\pi\)
0.321748 + 0.946825i \(0.395730\pi\)
\(432\) 27.5699 1.32646
\(433\) 2.94202 5.09573i 0.141384 0.244885i −0.786634 0.617420i \(-0.788178\pi\)
0.928018 + 0.372535i \(0.121511\pi\)
\(434\) 0 0
\(435\) 2.66882 + 1.54084i 0.127960 + 0.0738777i
\(436\) 19.6329 11.3351i 0.940247 0.542852i
\(437\) −3.76898 + 2.17602i −0.180295 + 0.104093i
\(438\) −2.98770 −0.142758
\(439\) 9.95642 0.475194 0.237597 0.971364i \(-0.423640\pi\)
0.237597 + 0.971364i \(0.423640\pi\)
\(440\) −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 \(-0.158178\pi\)
\(444\) 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 \(0.636614\pi\)
\(450\) 37.8641 + 21.8608i 1.78493 + 1.03053i
\(451\) 7.79266 0.366942
\(452\) 7.29687 12.6386i 0.343216 0.594467i
\(453\) 6.53877i 0.307218i
\(454\) 72.2371 3.39026
\(455\) 0 0
\(456\) 7.42580 0.347745
\(457\) 41.2222i 1.92829i 0.265369 + 0.964147i \(0.414506\pi\)
−0.265369 + 0.964147i \(0.585494\pi\)
\(458\) 4.06385 7.03880i 0.189891 0.328901i
\(459\) −4.38011 −0.204446
\(460\) 27.1443 + 15.6717i 1.26561 + 0.730699i
\(461\) 21.4139 + 12.3633i 0.997343 + 0.575816i 0.907461 0.420136i \(-0.138018\pi\)
0.0898818 + 0.995952i \(0.471351\pi\)
\(462\) 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
\(467\) −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
\(471\) 4.00386 0.184488
\(472\) 96.1273 4.42462
\(473\) −13.8803 + 8.01382i −0.638219 + 0.368476i
\(474\) 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
\(478\) 3.86008 0.176556
\(479\) 27.4328 + 15.8383i 1.25343 + 0.723671i 0.971790 0.235848i \(-0.0757868\pi\)
0.281645 + 0.959519i \(0.409120\pi\)
\(480\) −10.5697 18.3073i −0.482440 0.835610i
\(481\) 0.110677 21.4010i 0.00504644 0.975802i
\(482\) 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
\(486\) 20.7152 11.9599i 0.939662 0.542514i
\(487\) 26.9156i 1.21966i −0.792531 0.609832i \(-0.791237\pi\)
0.792531 0.609832i \(-0.208763\pi\)
\(488\) 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 \(0.762894\pi\)
\(492\) 7.75052i 0.349421i
\(493\) −2.94341 5.09813i −0.132564 0.229608i
\(494\) −11.5955 20.3260i −0.521707 0.914512i
\(495\) −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 0.339514 0.940601i \(-0.389737\pi\)
−0.644827 + 0.764329i \(0.723071\pi\)
\(500\) 10.6408i 0.475872i
\(501\) 3.12015i 0.139398i
\(502\) −25.5967 14.7783i −1.14244 0.659586i
\(503\) 4.87603 8.44553i 0.217411 0.376568i −0.736604 0.676324i \(-0.763572\pi\)
0.954016 + 0.299756i \(0.0969053\pi\)
\(504\) 0 0
\(505\) 41.8259 24.1482i 1.86123 1.07458i
\(506\) −4.52266 + 7.83348i −0.201057 + 0.348241i
\(507\) 2.28883 3.87134i 0.101651 0.171932i
\(508\) 25.8315 + 44.7414i 1.14609 + 1.98508i
\(509\) 23.0256i 1.02059i −0.859999 0.510295i \(-0.829536\pi\)
0.859999 0.510295i \(-0.170464\pi\)
\(510\) 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
\(514\) 11.2220i 0.494981i
\(515\) −12.0846 + 6.97705i −0.532511 + 0.307445i
\(516\) −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
\(520\) −52.9814 + 90.6802i −2.32339 + 3.97659i
\(521\) −0.243241 0.421305i −0.0106566 0.0184577i 0.860648 0.509200i \(-0.170059\pi\)
−0.871305 + 0.490743i \(0.836725\pi\)
\(522\) 18.4356 + 10.6438i 0.806904 + 0.465866i
\(523\) −34.6270 −1.51413 −0.757065 0.653339i \(-0.773368\pi\)
−0.757065 + 0.653339i \(0.773368\pi\)
\(524\) −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
\(528\) 7.49554 4.32755i 0.326201 0.188332i
\(529\) −19.7144 −0.857147
\(530\) 81.9636 3.56027
\(531\) 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
\(535\) −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
\(541\) −19.5188 11.2692i −0.839181 0.484501i 0.0178050 0.999841i \(-0.494332\pi\)
−0.856986 + 0.515340i \(0.827666\pi\)
\(542\) −7.52844 −0.323374
\(543\) −1.13885 + 1.97255i −0.0488728 + 0.0846502i
\(544\) 40.3818i 1.73136i
\(545\) −13.9172 −0.596146
\(546\) 0 0
\(547\) 39.3716 1.68341 0.841704 0.539940i \(-0.181553\pi\)
0.841704 + 0.539940i \(0.181553\pi\)
\(548\) 44.6955i 1.90930i
\(549\) 14.5601 25.2189i 0.621411 1.07631i
\(550\) 28.0217 1.19485
\(551\) 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
\(555\) −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 \(-0.338236\pi\)
−0.513279 + 0.858222i \(0.671569\pi\)
\(558\) −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
\(562\) 36.1502 1.52490
\(563\) −41.6077 −1.75355 −0.876777 0.480897i \(-0.840311\pi\)
−0.876777 + 0.480897i \(0.840311\pi\)
\(564\) 9.34597 5.39590i 0.393537 0.227208i
\(565\) −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
\(569\) 25.3888 1.06435 0.532177 0.846633i \(-0.321374\pi\)
0.532177 + 0.846633i \(0.321374\pi\)
\(570\) −6.33537 3.65773i −0.265360 0.153205i
\(571\) 8.49958 + 14.7217i 0.355697 + 0.616084i 0.987237 0.159259i \(-0.0509103\pi\)
−0.631540 + 0.775343i \(0.717577\pi\)
\(572\) −30.5005 17.8204i −1.27529 0.745109i
\(573\) 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
\(577\) −13.8355 + 7.98794i −0.575980 + 0.332542i −0.759534 0.650467i \(-0.774573\pi\)
0.183554 + 0.983010i \(0.441240\pi\)
\(578\) 33.4223i 1.39018i
\(579\) −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
\(583\) 17.1796i 0.711508i
\(584\) 14.2812 + 24.7357i 0.590959 + 1.02357i
\(585\) −0.174984 + 33.8356i −0.00723468 + 1.39893i
\(586\) −4.61963 + 8.00144i −0.190835 + 0.330536i
\(587\) −13.8404 + 7.99075i −0.571254 + 0.329814i −0.757650 0.652661i \(-0.773653\pi\)
0.186396 + 0.982475i \(0.440319\pi\)
\(588\) 0 0
\(589\) −2.09166 + 3.62287i −0.0861855 + 0.149278i
\(590\) −82.0116 47.3494i −3.37637 1.94935i
\(591\) 5.02566i 0.206728i
\(592\) 80.4433i 3.30620i
\(593\) 25.1608 + 14.5266i 1.03323 + 0.596536i 0.917908 0.396792i \(-0.129877\pi\)
0.115322 + 0.993328i \(0.463210\pi\)
\(594\) 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
\(598\) −0.0913640 + 17.6666i −0.00373615 + 0.722439i
\(599\) −1.72777 2.99259i −0.0705948 0.122274i 0.828567 0.559889i \(-0.189156\pi\)
−0.899162 + 0.437616i \(0.855823\pi\)
\(600\) 17.3675i 0.709026i
\(601\) −7.76518 13.4497i −0.316748 0.548624i 0.663059 0.748567i \(-0.269258\pi\)
−0.979808 + 0.199943i \(0.935924\pi\)
\(602\) 0 0
\(603\) 2.38178i 0.0969936i
\(604\) −86.8732 + 50.1563i −3.53482 + 2.04083i
\(605\) 24.7363i 1.00567i
\(606\) −12.0052 + 6.93118i −0.487676 + 0.281560i
\(607\) −7.73922 13.4047i −0.314125 0.544081i 0.665126 0.746731i \(-0.268378\pi\)
−0.979251 + 0.202650i \(0.935044\pi\)
\(608\) −22.5148 38.9967i −0.913095 1.58153i
\(609\) 0 0
\(610\) −89.0429 −3.60524
\(611\) −18.2982 10.6910i −0.740266 0.432513i
\(612\) 16.4571 + 28.5046i 0.665240 + 1.15223i
\(613\) 6.17669 + 3.56611i 0.249474 + 0.144034i 0.619523 0.784978i \(-0.287326\pi\)
−0.370049 + 0.929012i \(0.620659\pi\)
\(614\) −44.2456 −1.78561
\(615\) 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
\(619\) −36.6822 + 21.1785i −1.47438 + 0.851235i −0.999583 0.0288589i \(-0.990813\pi\)
−0.474799 + 0.880094i \(0.657479\pi\)
\(620\) 30.1284 1.20999
\(621\) −3.68741 −0.147971
\(622\) 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
\(626\) −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 \(0.706482\pi\)
\(632\) −6.20874 3.58462i −0.246971 0.142589i
\(633\) −1.49286 −0.0593361
\(634\) 8.19794 14.1992i 0.325582 0.563924i
\(635\) 31.7158i 1.25860i
\(636\) −17.0868 −0.677534
\(637\) 0 0
\(638\) 13.6434 0.540149
\(639\) 6.78098i 0.268251i
\(640\) −42.7898 + 74.1142i −1.69142 + 2.92962i
\(641\) 31.5637 1.24669 0.623345 0.781947i \(-0.285773\pi\)
0.623345 + 0.781947i \(0.285773\pi\)
\(642\) 15.4896 + 8.94291i 0.611325 + 0.352949i
\(643\) 15.8053 + 9.12520i 0.623300 + 0.359863i 0.778153 0.628075i \(-0.216157\pi\)
−0.154852 + 0.987938i \(0.549490\pi\)
\(644\) 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 \(-0.683812\pi\)
0.998550 + 0.0538387i \(0.0171457\pi\)
\(648\) −61.4532 35.4800i −2.41411 1.39379i
\(649\) 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
\(653\) 28.8124 1.12752 0.563759 0.825939i \(-0.309355\pi\)
0.563759 + 0.825939i \(0.309355\pi\)
\(654\) 3.99460 0.156201
\(655\) 52.6555 30.4007i 2.05742 1.18785i
\(656\) 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 \(-0.0414149\pi\)
\(660\) −11.0431 −0.429850
\(661\) 23.0000 + 13.2791i 0.894598 + 0.516496i 0.875444 0.483320i \(-0.160569\pi\)
0.0191541 + 0.999817i \(0.493903\pi\)
\(662\) 23.3487 + 40.4411i 0.907471 + 1.57179i
\(663\) −1.35486 + 2.31890i −0.0526183 + 0.0900587i
\(664\) 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
\(668\) 41.4538 23.9334i 1.60390 0.926010i
\(669\) 8.09337i 0.312908i
\(670\) −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 \(0.957559\pi\)
\(674\) 22.5842i 0.869912i
\(675\) 5.71165 + 9.89287i 0.219842 + 0.380777i
\(676\) −68.9908 0.713602i −2.65349 0.0274462i
\(677\) 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
\(682\) 8.69468i 0.332936i
\(683\) 6.76255i 0.258762i 0.991595 + 0.129381i \(0.0412990\pi\)
−0.991595 + 0.129381i \(0.958701\pi\)
\(684\) −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
\(689\) 16.6266 + 29.1452i 0.633424 + 1.11034i
\(690\) 2.76144 + 4.78296i 0.105126 + 0.182084i
\(691\) 9.17090i 0.348877i 0.984668 + 0.174439i \(0.0558111\pi\)
−0.984668 + 0.174439i \(0.944189\pi\)
\(692\) −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
\(696\) 8.45605i 0.320526i
\(697\) −7.87137 + 4.54454i −0.298150 + 0.172137i
\(698\) 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 \(0.146131\pi\)
\(702\) 0.102537 19.8270i 0.00387000 0.748321i
\(703\) −7.12562 12.3419i −0.268748 0.465485i
\(704\) −37.7181 21.7766i −1.42156 0.820736i
\(705\) −6.62507 −0.249515
\(706\) −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 \(-0.894715\pi\)
−0.191642 + 0.981465i \(0.561381\pi\)
\(710\) −17.9567 + 10.3673i −0.673905 + 0.389079i
\(711\) −2.30976 −0.0866227
\(712\) −135.117 −5.06374
\(713\) 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
\(717\) 0.427821 + 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 \(-0.216497\pi\)
−0.933389 + 0.358867i \(0.883163\pi\)
\(720\) 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
\(724\) 34.9427 1.29863
\(725\) −7.67639 + 13.2959i −0.285094 + 0.493797i
\(726\) 7.09997i 0.263505i
\(727\) −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
\(730\) 28.1379i 1.04143i
\(731\) 9.34703 16.1895i 0.345712 0.598791i
\(732\) 18.5625 0.686092
\(733\) 10.5282 + 6.07846i 0.388868 + 0.224513i 0.681670 0.731660i \(-0.261254\pi\)
−0.292802 + 0.956173i \(0.594588\pi\)
\(734\) −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 0.998628 + 0.0523634i \(0.0166754\pi\)
0.544662 + 0.838656i \(0.316658\pi\)
\(740\) −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 −0.745004 0.667060i \(-0.767553\pi\)
0.205188 + 0.978722i \(0.434219\pi\)
\(744\) −5.38886 −0.197565
\(745\) 13.1010 0.479985
\(746\) −75.0642 + 43.3384i −2.74830 + 1.58673i
\(747\) 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
\(751\) −43.0323 −1.57027 −0.785136 0.619323i \(-0.787407\pi\)
−0.785136 + 0.619323i \(0.787407\pi\)
\(752\) −68.9863 39.8292i −2.51567 1.45242i
\(753\) −1.89129 3.27581i −0.0689225 0.119377i
\(754\) 23.1461 13.2043i 0.842930 0.480871i
\(755\) 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
\(759\) −1.00251 + 0.578801i −0.0363889 + 0.0210091i
\(760\) 69.9357i 2.53683i
\(761\) 25.4829 14.7126i 0.923754 0.533330i 0.0389234 0.999242i \(-0.487607\pi\)
0.884831 + 0.465912i \(0.154274\pi\)
\(762\) 9.10328i 0.329777i
\(763\) 0 0
\(764\) −36.4699 63.1677i −1.31943 2.28533i
\(765\) 20.2060i 0.730550i
\(766\) 0.945888 + 1.63833i 0.0341763 + 0.0591951i
\(767\) 0.200488 38.7673i 0.00723921 1.39981i
\(768\) 4.11988 7.13584i 0.148663 0.257492i
\(769\) 14.8839 8.59322i 0.536727 0.309879i −0.207024 0.978336i \(-0.566378\pi\)
0.743751 + 0.668456i \(0.233045\pi\)
\(770\) 0 0
\(771\) −0.718083 + 1.24376i −0.0258611 + 0.0447928i
\(772\) 104.578 + 60.3782i 3.76385 + 2.17306i
\(773\) 21.9601i 0.789851i −0.918713 0.394926i \(-0.870770\pi\)
0.918713 0.394926i \(-0.129230\pi\)
\(774\) 67.6004i 2.42985i
\(775\) −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