Properties

Label 450.2.h.e.181.2
Level $450$
Weight $2$
Character 450.181
Analytic conductor $3.593$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 450.h (of order \(5\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.59326809096\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{5})\)
Coefficient field: 8.0.58140625.2
Defining polynomial: \(x^{8} - 3 x^{7} + 4 x^{6} - 7 x^{5} + 11 x^{4} + 5 x^{3} - 10 x^{2} - 25 x + 25\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 5 \)
Twist minimal: no (minimal twist has level 50)
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 181.2
Root \(-0.983224 - 0.644389i\) of defining polynomial
Character \(\chi\) \(=\) 450.181
Dual form 450.2.h.e.271.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(2.15743 + 0.587785i) q^{5} -0.833366 q^{7} +(0.809017 + 0.587785i) q^{8} +O(q^{10})\) \(q+(-0.309017 - 0.951057i) q^{2} +(-0.809017 + 0.587785i) q^{4} +(2.15743 + 0.587785i) q^{5} -0.833366 q^{7} +(0.809017 + 0.587785i) q^{8} +(-0.107666 - 2.23347i) q^{10} +(-0.257524 - 0.792578i) q^{11} +(1.41027 - 4.34038i) q^{13} +(0.257524 + 0.792578i) q^{14} +(0.309017 - 0.951057i) q^{16} +(4.41027 + 3.20425i) q^{17} +(7.00116 + 5.08664i) q^{19} +(-2.09089 + 0.792578i) q^{20} +(-0.674207 + 0.489840i) q^{22} +(-1.09089 - 3.35741i) q^{23} +(4.30902 + 2.53621i) q^{25} -4.56375 q^{26} +(0.674207 - 0.489840i) q^{28} +(2.64518 - 1.92183i) q^{29} +(-4.85599 - 3.52808i) q^{31} -1.00000 q^{32} +(1.68458 - 5.18459i) q^{34} +(-1.79793 - 0.489840i) q^{35} +(2.26042 - 6.95685i) q^{37} +(2.67421 - 8.23036i) q^{38} +(1.39991 + 1.74363i) q^{40} +(-0.576909 + 1.77554i) q^{41} -1.63877 q^{43} +(0.674207 + 0.489840i) q^{44} +(-2.85599 + 2.07500i) q^{46} +(-0.674207 + 0.489840i) q^{47} -6.30550 q^{49} +(1.08052 - 4.88185i) q^{50} +(1.41027 + 4.34038i) q^{52} +(5.19972 - 3.77782i) q^{53} +(-0.0897250 - 1.86130i) q^{55} +(-0.674207 - 0.489840i) q^{56} +(-2.64518 - 1.92183i) q^{58} +(-4.18178 + 12.8702i) q^{59} +(1.81832 + 5.59621i) q^{61} +(-1.85482 + 5.70855i) q^{62} +(0.309017 + 0.951057i) q^{64} +(5.59378 - 8.53513i) q^{65} +(-1.21345 - 0.881621i) q^{67} -5.45140 q^{68} +(0.0897250 + 1.86130i) q^{70} +(-1.91027 + 1.38790i) q^{71} +(-1.02903 - 3.16703i) q^{73} -7.31486 q^{74} -8.65392 q^{76} +(0.214612 + 0.660507i) q^{77} +(-4.18178 + 3.03824i) q^{79} +(1.22570 - 1.87020i) q^{80} +1.86692 q^{82} +(-9.97971 - 7.25068i) q^{83} +(7.63145 + 9.50525i) q^{85} +(0.506408 + 1.55856i) q^{86} +(0.257524 - 0.792578i) q^{88} +(2.16491 + 6.66290i) q^{89} +(-1.17527 + 3.61712i) q^{91} +(2.85599 + 2.07500i) q^{92} +(0.674207 + 0.489840i) q^{94} +(12.1147 + 15.0893i) q^{95} +(-8.97214 + 6.51864i) q^{97} +(1.94851 + 5.99689i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} + O(q^{10}) \) \( 8q + 2q^{2} - 2q^{4} + 4q^{7} + 2q^{8} - q^{11} - 13q^{13} + q^{14} - 2q^{16} + 11q^{17} + 20q^{19} - 5q^{20} + q^{22} + 3q^{23} + 30q^{25} - 22q^{26} - q^{28} + 15q^{29} - 9q^{31} - 8q^{32} - q^{34} + 15q^{35} - 6q^{37} + 15q^{38} - 5q^{40} + 9q^{41} + 12q^{43} - q^{44} + 7q^{46} + q^{47} - 4q^{49} + 5q^{50} - 13q^{52} - 7q^{53} - 25q^{55} + q^{56} - 15q^{58} - 10q^{59} + 6q^{61} - 21q^{62} - 2q^{64} + 10q^{65} - 11q^{67} - 24q^{68} + 25q^{70} + 9q^{71} - 8q^{73} - 24q^{74} - 10q^{76} - 33q^{77} - 10q^{79} + 26q^{82} - 27q^{83} + 5q^{85} + 23q^{86} + q^{88} + 15q^{89} + q^{91} - 7q^{92} - q^{94} + 30q^{95} - 36q^{97} + 19q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.309017 0.951057i −0.218508 0.672499i
\(3\) 0 0
\(4\) −0.809017 + 0.587785i −0.404508 + 0.293893i
\(5\) 2.15743 + 0.587785i 0.964832 + 0.262866i
\(6\) 0 0
\(7\) −0.833366 −0.314983 −0.157491 0.987520i \(-0.550341\pi\)
−0.157491 + 0.987520i \(0.550341\pi\)
\(8\) 0.809017 + 0.587785i 0.286031 + 0.207813i
\(9\) 0 0
\(10\) −0.107666 2.23347i −0.0340469 0.706287i
\(11\) −0.257524 0.792578i −0.0776465 0.238971i 0.904698 0.426054i \(-0.140097\pi\)
−0.982344 + 0.187083i \(0.940097\pi\)
\(12\) 0 0
\(13\) 1.41027 4.34038i 0.391140 1.20380i −0.540787 0.841159i \(-0.681874\pi\)
0.931927 0.362645i \(-0.118126\pi\)
\(14\) 0.257524 + 0.792578i 0.0688262 + 0.211825i
\(15\) 0 0
\(16\) 0.309017 0.951057i 0.0772542 0.237764i
\(17\) 4.41027 + 3.20425i 1.06965 + 0.777145i 0.975849 0.218446i \(-0.0700987\pi\)
0.0937997 + 0.995591i \(0.470099\pi\)
\(18\) 0 0
\(19\) 7.00116 + 5.08664i 1.60618 + 1.16696i 0.874116 + 0.485718i \(0.161442\pi\)
0.732062 + 0.681238i \(0.238558\pi\)
\(20\) −2.09089 + 0.792578i −0.467537 + 0.177226i
\(21\) 0 0
\(22\) −0.674207 + 0.489840i −0.143741 + 0.104434i
\(23\) −1.09089 3.35741i −0.227466 0.700069i −0.998032 0.0627085i \(-0.980026\pi\)
0.770566 0.637361i \(-0.219974\pi\)
\(24\) 0 0
\(25\) 4.30902 + 2.53621i 0.861803 + 0.507242i
\(26\) −4.56375 −0.895024
\(27\) 0 0
\(28\) 0.674207 0.489840i 0.127413 0.0925711i
\(29\) 2.64518 1.92183i 0.491197 0.356876i −0.314447 0.949275i \(-0.601819\pi\)
0.805645 + 0.592399i \(0.201819\pi\)
\(30\) 0 0
\(31\) −4.85599 3.52808i −0.872161 0.633662i 0.0590050 0.998258i \(-0.481207\pi\)
−0.931166 + 0.364596i \(0.881207\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) 1.68458 5.18459i 0.288902 0.889150i
\(35\) −1.79793 0.489840i −0.303905 0.0827981i
\(36\) 0 0
\(37\) 2.26042 6.95685i 0.371610 1.14370i −0.574127 0.818766i \(-0.694658\pi\)
0.945737 0.324932i \(-0.105342\pi\)
\(38\) 2.67421 8.23036i 0.433814 1.33514i
\(39\) 0 0
\(40\) 1.39991 + 1.74363i 0.221345 + 0.275693i
\(41\) −0.576909 + 1.77554i −0.0900981 + 0.277293i −0.985945 0.167069i \(-0.946570\pi\)
0.895847 + 0.444362i \(0.146570\pi\)
\(42\) 0 0
\(43\) −1.63877 −0.249910 −0.124955 0.992162i \(-0.539879\pi\)
−0.124955 + 0.992162i \(0.539879\pi\)
\(44\) 0.674207 + 0.489840i 0.101641 + 0.0738462i
\(45\) 0 0
\(46\) −2.85599 + 2.07500i −0.421092 + 0.305941i
\(47\) −0.674207 + 0.489840i −0.0983432 + 0.0714505i −0.635870 0.771796i \(-0.719359\pi\)
0.537527 + 0.843247i \(0.319359\pi\)
\(48\) 0 0
\(49\) −6.30550 −0.900786
\(50\) 1.08052 4.88185i 0.152809 0.690398i
\(51\) 0 0
\(52\) 1.41027 + 4.34038i 0.195570 + 0.601902i
\(53\) 5.19972 3.77782i 0.714237 0.518923i −0.170301 0.985392i \(-0.554474\pi\)
0.884538 + 0.466469i \(0.154474\pi\)
\(54\) 0 0
\(55\) −0.0897250 1.86130i −0.0120985 0.250978i
\(56\) −0.674207 0.489840i −0.0900947 0.0654576i
\(57\) 0 0
\(58\) −2.64518 1.92183i −0.347329 0.252349i
\(59\) −4.18178 + 12.8702i −0.544421 + 1.67556i 0.177940 + 0.984041i \(0.443057\pi\)
−0.722362 + 0.691515i \(0.756943\pi\)
\(60\) 0 0
\(61\) 1.81832 + 5.59621i 0.232812 + 0.716521i 0.997404 + 0.0720066i \(0.0229403\pi\)
−0.764592 + 0.644514i \(0.777060\pi\)
\(62\) −1.85482 + 5.70855i −0.235563 + 0.724987i
\(63\) 0 0
\(64\) 0.309017 + 0.951057i 0.0386271 + 0.118882i
\(65\) 5.59378 8.53513i 0.693823 1.05865i
\(66\) 0 0
\(67\) −1.21345 0.881621i −0.148246 0.107707i 0.511190 0.859468i \(-0.329205\pi\)
−0.659436 + 0.751761i \(0.729205\pi\)
\(68\) −5.45140 −0.661079
\(69\) 0 0
\(70\) 0.0897250 + 1.86130i 0.0107242 + 0.222468i
\(71\) −1.91027 + 1.38790i −0.226708 + 0.164713i −0.695341 0.718680i \(-0.744747\pi\)
0.468633 + 0.883393i \(0.344747\pi\)
\(72\) 0 0
\(73\) −1.02903 3.16703i −0.120439 0.370672i 0.872604 0.488429i \(-0.162430\pi\)
−0.993043 + 0.117756i \(0.962430\pi\)
\(74\) −7.31486 −0.850335
\(75\) 0 0
\(76\) −8.65392 −0.992672
\(77\) 0.214612 + 0.660507i 0.0244573 + 0.0752718i
\(78\) 0 0
\(79\) −4.18178 + 3.03824i −0.470487 + 0.341829i −0.797631 0.603146i \(-0.793914\pi\)
0.327144 + 0.944974i \(0.393914\pi\)
\(80\) 1.22570 1.87020i 0.137037 0.209095i
\(81\) 0 0
\(82\) 1.86692 0.206167
\(83\) −9.97971 7.25068i −1.09542 0.795866i −0.115110 0.993353i \(-0.536722\pi\)
−0.980306 + 0.197487i \(0.936722\pi\)
\(84\) 0 0
\(85\) 7.63145 + 9.50525i 0.827747 + 1.03099i
\(86\) 0.506408 + 1.55856i 0.0546074 + 0.168064i
\(87\) 0 0
\(88\) 0.257524 0.792578i 0.0274522 0.0844891i
\(89\) 2.16491 + 6.66290i 0.229480 + 0.706266i 0.997806 + 0.0662073i \(0.0210899\pi\)
−0.768326 + 0.640058i \(0.778910\pi\)
\(90\) 0 0
\(91\) −1.17527 + 3.61712i −0.123202 + 0.379178i
\(92\) 2.85599 + 2.07500i 0.297757 + 0.216333i
\(93\) 0 0
\(94\) 0.674207 + 0.489840i 0.0695391 + 0.0505231i
\(95\) 12.1147 + 15.0893i 1.24294 + 1.54813i
\(96\) 0 0
\(97\) −8.97214 + 6.51864i −0.910982 + 0.661867i −0.941263 0.337674i \(-0.890360\pi\)
0.0302807 + 0.999541i \(0.490360\pi\)
\(98\) 1.94851 + 5.99689i 0.196829 + 0.605777i
\(99\) 0 0
\(100\) −4.97682 + 0.480938i −0.497682 + 0.0480938i
\(101\) −12.7085 −1.26454 −0.632272 0.774746i \(-0.717878\pi\)
−0.632272 + 0.774746i \(0.717878\pi\)
\(102\) 0 0
\(103\) −5.67537 + 4.12340i −0.559211 + 0.406291i −0.831170 0.556018i \(-0.812328\pi\)
0.271959 + 0.962309i \(0.412328\pi\)
\(104\) 3.69215 2.68250i 0.362045 0.263041i
\(105\) 0 0
\(106\) −5.19972 3.77782i −0.505042 0.366934i
\(107\) 10.7700 1.04118 0.520589 0.853807i \(-0.325712\pi\)
0.520589 + 0.853807i \(0.325712\pi\)
\(108\) 0 0
\(109\) −3.28655 + 10.1150i −0.314795 + 0.968838i 0.661044 + 0.750347i \(0.270114\pi\)
−0.975839 + 0.218491i \(0.929886\pi\)
\(110\) −1.74248 + 0.660507i −0.166139 + 0.0629769i
\(111\) 0 0
\(112\) −0.257524 + 0.792578i −0.0243337 + 0.0748916i
\(113\) −0.538232 + 1.65651i −0.0506326 + 0.155831i −0.973176 0.230063i \(-0.926107\pi\)
0.922543 + 0.385894i \(0.126107\pi\)
\(114\) 0 0
\(115\) −0.380081 7.88460i −0.0354428 0.735242i
\(116\) −1.01037 + 3.10959i −0.0938103 + 0.288718i
\(117\) 0 0
\(118\) 13.5325 1.24577
\(119\) −3.67537 2.67031i −0.336921 0.244787i
\(120\) 0 0
\(121\) 8.33733 6.05742i 0.757939 0.550675i
\(122\) 4.76042 3.45865i 0.430988 0.313131i
\(123\) 0 0
\(124\) 6.00233 0.539025
\(125\) 7.80566 + 8.00448i 0.698159 + 0.715942i
\(126\) 0 0
\(127\) 1.75112 + 5.38938i 0.155386 + 0.478230i 0.998200 0.0599756i \(-0.0191023\pi\)
−0.842813 + 0.538206i \(0.819102\pi\)
\(128\) 0.809017 0.587785i 0.0715077 0.0519534i
\(129\) 0 0
\(130\) −9.84597 2.68250i −0.863548 0.235271i
\(131\) −13.3281 9.68345i −1.16448 0.846047i −0.174145 0.984720i \(-0.555716\pi\)
−0.990338 + 0.138673i \(0.955716\pi\)
\(132\) 0 0
\(133\) −5.83453 4.23903i −0.505918 0.367571i
\(134\) −0.463496 + 1.42649i −0.0400399 + 0.123230i
\(135\) 0 0
\(136\) 1.68458 + 5.18459i 0.144451 + 0.444575i
\(137\) 0.894062 2.75164i 0.0763849 0.235088i −0.905572 0.424192i \(-0.860558\pi\)
0.981957 + 0.189104i \(0.0605582\pi\)
\(138\) 0 0
\(139\) 1.54184 + 4.74531i 0.130778 + 0.402492i 0.994909 0.100774i \(-0.0321318\pi\)
−0.864132 + 0.503266i \(0.832132\pi\)
\(140\) 1.74248 0.660507i 0.147266 0.0558230i
\(141\) 0 0
\(142\) 1.91027 + 1.38790i 0.160307 + 0.116470i
\(143\) −3.80327 −0.318045
\(144\) 0 0
\(145\) 6.83642 2.59143i 0.567733 0.215206i
\(146\) −2.69403 + 1.95733i −0.222960 + 0.161990i
\(147\) 0 0
\(148\) 2.26042 + 6.95685i 0.185805 + 0.571849i
\(149\) −2.00579 −0.164320 −0.0821602 0.996619i \(-0.526182\pi\)
−0.0821602 + 0.996619i \(0.526182\pi\)
\(150\) 0 0
\(151\) −1.96971 −0.160293 −0.0801463 0.996783i \(-0.525539\pi\)
−0.0801463 + 0.996783i \(0.525539\pi\)
\(152\) 2.67421 + 8.23036i 0.216907 + 0.667571i
\(153\) 0 0
\(154\) 0.561861 0.408216i 0.0452760 0.0328950i
\(155\) −8.40270 10.4659i −0.674921 0.840639i
\(156\) 0 0
\(157\) 7.78467 0.621284 0.310642 0.950527i \(-0.399456\pi\)
0.310642 + 0.950527i \(0.399456\pi\)
\(158\) 4.18178 + 3.03824i 0.332685 + 0.241709i
\(159\) 0 0
\(160\) −2.15743 0.587785i −0.170560 0.0464685i
\(161\) 0.909110 + 2.79795i 0.0716479 + 0.220510i
\(162\) 0 0
\(163\) 4.35589 13.4060i 0.341180 1.05004i −0.622418 0.782685i \(-0.713849\pi\)
0.963597 0.267358i \(-0.0861505\pi\)
\(164\) −0.576909 1.77554i −0.0450490 0.138647i
\(165\) 0 0
\(166\) −3.81191 + 11.7319i −0.295862 + 0.910568i
\(167\) −6.59846 4.79406i −0.510604 0.370976i 0.302448 0.953166i \(-0.402196\pi\)
−0.813053 + 0.582190i \(0.802196\pi\)
\(168\) 0 0
\(169\) −6.33280 4.60105i −0.487139 0.353927i
\(170\) 6.68178 10.1952i 0.512469 0.781938i
\(171\) 0 0
\(172\) 1.32579 0.963245i 0.101091 0.0734467i
\(173\) 0.773580 + 2.38084i 0.0588142 + 0.181012i 0.976147 0.217109i \(-0.0696626\pi\)
−0.917333 + 0.398120i \(0.869663\pi\)
\(174\) 0 0
\(175\) −3.59099 2.11359i −0.271453 0.159773i
\(176\) −0.833366 −0.0628173
\(177\) 0 0
\(178\) 5.66780 4.11790i 0.424820 0.308649i
\(179\) −16.2067 + 11.7749i −1.21135 + 0.880096i −0.995352 0.0962986i \(-0.969300\pi\)
−0.215995 + 0.976394i \(0.569300\pi\)
\(180\) 0 0
\(181\) −6.37367 4.63074i −0.473751 0.344201i 0.325150 0.945662i \(-0.394585\pi\)
−0.798902 + 0.601462i \(0.794585\pi\)
\(182\) 3.80327 0.281917
\(183\) 0 0
\(184\) 1.09089 3.35741i 0.0804215 0.247512i
\(185\) 8.96583 13.6803i 0.659181 1.00579i
\(186\) 0 0
\(187\) 1.40387 4.32066i 0.102661 0.315958i
\(188\) 0.257524 0.792578i 0.0187819 0.0578047i
\(189\) 0 0
\(190\) 10.6071 16.1846i 0.769520 1.17415i
\(191\) 1.63013 5.01702i 0.117952 0.363019i −0.874599 0.484847i \(-0.838875\pi\)
0.992551 + 0.121827i \(0.0388755\pi\)
\(192\) 0 0
\(193\) −13.4461 −0.967873 −0.483937 0.875103i \(-0.660793\pi\)
−0.483937 + 0.875103i \(0.660793\pi\)
\(194\) 8.97214 + 6.51864i 0.644162 + 0.468011i
\(195\) 0 0
\(196\) 5.10126 3.70628i 0.364376 0.264734i
\(197\) −4.39991 + 3.19672i −0.313480 + 0.227757i −0.733388 0.679810i \(-0.762062\pi\)
0.419908 + 0.907567i \(0.362062\pi\)
\(198\) 0 0
\(199\) −17.4090 −1.23409 −0.617045 0.786927i \(-0.711671\pi\)
−0.617045 + 0.786927i \(0.711671\pi\)
\(200\) 1.99532 + 4.58462i 0.141090 + 0.324181i
\(201\) 0 0
\(202\) 3.92715 + 12.0865i 0.276313 + 0.850404i
\(203\) −2.20440 + 1.60159i −0.154719 + 0.112410i
\(204\) 0 0
\(205\) −2.28828 + 3.49152i −0.159820 + 0.243858i
\(206\) 5.67537 + 4.12340i 0.395422 + 0.287291i
\(207\) 0 0
\(208\) −3.69215 2.68250i −0.256004 0.185998i
\(209\) 2.22859 6.85890i 0.154155 0.474440i
\(210\) 0 0
\(211\) −0.0834142 0.256723i −0.00574247 0.0176735i 0.948144 0.317840i \(-0.102958\pi\)
−0.953887 + 0.300167i \(0.902958\pi\)
\(212\) −1.98612 + 6.11264i −0.136407 + 0.419818i
\(213\) 0 0
\(214\) −3.32812 10.2429i −0.227506 0.700191i
\(215\) −3.53553 0.963245i −0.241121 0.0656928i
\(216\) 0 0
\(217\) 4.04681 + 2.94018i 0.274716 + 0.199593i
\(218\) 10.6355 0.720328
\(219\) 0 0
\(220\) 1.16663 + 1.45309i 0.0786545 + 0.0979670i
\(221\) 20.1274 14.6234i 1.35391 0.983676i
\(222\) 0 0
\(223\) 7.16032 + 22.0372i 0.479491 + 1.47572i 0.839804 + 0.542889i \(0.182670\pi\)
−0.360313 + 0.932831i \(0.617330\pi\)
\(224\) 0.833366 0.0556816
\(225\) 0 0
\(226\) 1.74176 0.115860
\(227\) 0.0780741 + 0.240287i 0.00518196 + 0.0159484i 0.953614 0.301032i \(-0.0973311\pi\)
−0.948432 + 0.316980i \(0.897331\pi\)
\(228\) 0 0
\(229\) 17.0625 12.3966i 1.12752 0.819191i 0.142187 0.989840i \(-0.454586\pi\)
0.985332 + 0.170649i \(0.0545864\pi\)
\(230\) −7.38125 + 2.79795i −0.486705 + 0.184492i
\(231\) 0 0
\(232\) 3.26962 0.214661
\(233\) −11.8178 8.58610i −0.774207 0.562494i 0.129028 0.991641i \(-0.458814\pi\)
−0.903235 + 0.429147i \(0.858814\pi\)
\(234\) 0 0
\(235\) −1.74248 + 0.660507i −0.113667 + 0.0430867i
\(236\) −4.18178 12.8702i −0.272211 0.837778i
\(237\) 0 0
\(238\) −1.40387 + 4.32066i −0.0909992 + 0.280067i
\(239\) −1.79793 5.53346i −0.116298 0.357930i 0.875917 0.482461i \(-0.160257\pi\)
−0.992216 + 0.124532i \(0.960257\pi\)
\(240\) 0 0
\(241\) 4.24254 13.0572i 0.273286 0.841087i −0.716382 0.697708i \(-0.754203\pi\)
0.989668 0.143379i \(-0.0457968\pi\)
\(242\) −8.33733 6.05742i −0.535944 0.389386i
\(243\) 0 0
\(244\) −4.76042 3.45865i −0.304754 0.221417i
\(245\) −13.6037 3.70628i −0.869108 0.236786i
\(246\) 0 0
\(247\) 31.9515 23.2141i 2.03303 1.47708i
\(248\) −1.85482 5.70855i −0.117781 0.362494i
\(249\) 0 0
\(250\) 5.20063 9.89714i 0.328917 0.625950i
\(251\) 15.8938 1.00320 0.501602 0.865098i \(-0.332744\pi\)
0.501602 + 0.865098i \(0.332744\pi\)
\(252\) 0 0
\(253\) −2.38008 + 1.72923i −0.149634 + 0.108716i
\(254\) 4.58448 3.33082i 0.287656 0.208994i
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.0505636 0.0367366i
\(257\) 2.31253 0.144252 0.0721259 0.997396i \(-0.477022\pi\)
0.0721259 + 0.997396i \(0.477022\pi\)
\(258\) 0 0
\(259\) −1.88375 + 5.79760i −0.117051 + 0.360245i
\(260\) 0.491360 + 10.1930i 0.0304728 + 0.632144i
\(261\) 0 0
\(262\) −5.09089 + 15.6681i −0.314516 + 0.967981i
\(263\) 6.63129 20.4090i 0.408903 1.25847i −0.508689 0.860951i \(-0.669870\pi\)
0.917592 0.397524i \(-0.130130\pi\)
\(264\) 0 0
\(265\) 13.4386 5.09406i 0.825526 0.312926i
\(266\) −2.22859 + 6.85890i −0.136644 + 0.420546i
\(267\) 0 0
\(268\) 1.49990 0.0916212
\(269\) 17.3020 + 12.5706i 1.05492 + 0.766445i 0.973142 0.230206i \(-0.0739399\pi\)
0.0817787 + 0.996651i \(0.473940\pi\)
\(270\) 0 0
\(271\) 21.1400 15.3591i 1.28417 0.933001i 0.284495 0.958677i \(-0.408174\pi\)
0.999670 + 0.0256766i \(0.00817402\pi\)
\(272\) 4.41027 3.20425i 0.267412 0.194286i
\(273\) 0 0
\(274\) −2.89324 −0.174787
\(275\) 0.900470 4.06837i 0.0543004 0.245332i
\(276\) 0 0
\(277\) −5.76220 17.7342i −0.346217 1.06555i −0.960929 0.276795i \(-0.910728\pi\)
0.614712 0.788752i \(-0.289272\pi\)
\(278\) 4.03660 2.93276i 0.242099 0.175895i
\(279\) 0 0
\(280\) −1.16663 1.45309i −0.0697197 0.0868384i
\(281\) 11.9886 + 8.71023i 0.715180 + 0.519609i 0.884841 0.465894i \(-0.154267\pi\)
−0.169661 + 0.985503i \(0.554267\pi\)
\(282\) 0 0
\(283\) −12.7663 9.27523i −0.758875 0.551355i 0.139690 0.990195i \(-0.455389\pi\)
−0.898565 + 0.438840i \(0.855389\pi\)
\(284\) 0.729660 2.24566i 0.0432974 0.133256i
\(285\) 0 0
\(286\) 1.17527 + 3.61712i 0.0694955 + 0.213885i
\(287\) 0.480776 1.47968i 0.0283793 0.0873426i
\(288\) 0 0
\(289\) 3.93000 + 12.0953i 0.231177 + 0.711489i
\(290\) −4.57716 5.70102i −0.268780 0.334776i
\(291\) 0 0
\(292\) 2.69403 + 1.95733i 0.157656 + 0.114544i
\(293\) −18.4003 −1.07496 −0.537479 0.843277i \(-0.680623\pi\)
−0.537479 + 0.843277i \(0.680623\pi\)
\(294\) 0 0
\(295\) −16.5868 + 25.3086i −0.965722 + 1.47352i
\(296\) 5.91785 4.29957i 0.343968 0.249907i
\(297\) 0 0
\(298\) 0.619822 + 1.90761i 0.0359053 + 0.110505i
\(299\) −16.1109 −0.931718
\(300\) 0 0
\(301\) 1.36569 0.0787173
\(302\) 0.608674 + 1.87330i 0.0350252 + 0.107797i
\(303\) 0 0
\(304\) 7.00116 5.08664i 0.401544 0.291739i
\(305\) 0.633527 + 13.1422i 0.0362757 + 0.752521i
\(306\) 0 0
\(307\) −34.1179 −1.94721 −0.973606 0.228237i \(-0.926704\pi\)
−0.973606 + 0.228237i \(0.926704\pi\)
\(308\) −0.561861 0.408216i −0.0320150 0.0232603i
\(309\) 0 0
\(310\) −7.35705 + 11.2256i −0.417853 + 0.637570i
\(311\) 4.02893 + 12.3998i 0.228460 + 0.703127i 0.997922 + 0.0644345i \(0.0205243\pi\)
−0.769462 + 0.638692i \(0.779476\pi\)
\(312\) 0 0
\(313\) 1.07619 3.31217i 0.0608298 0.187215i −0.916024 0.401124i \(-0.868620\pi\)
0.976854 + 0.213909i \(0.0686196\pi\)
\(314\) −2.40559 7.40366i −0.135756 0.417813i
\(315\) 0 0
\(316\) 1.59730 4.91598i 0.0898550 0.276545i
\(317\) 3.89975 + 2.83333i 0.219032 + 0.159136i 0.691891 0.722002i \(-0.256778\pi\)
−0.472859 + 0.881138i \(0.656778\pi\)
\(318\) 0 0
\(319\) −2.20440 1.60159i −0.123423 0.0896719i
\(320\) 0.107666 + 2.23347i 0.00601870 + 0.124855i
\(321\) 0 0
\(322\) 2.38008 1.72923i 0.132637 0.0963662i
\(323\) 14.5782 + 44.8670i 0.811151 + 2.49647i
\(324\) 0 0
\(325\) 17.0850 15.1260i 0.947707 0.839040i
\(326\) −14.0960 −0.780703
\(327\) 0 0
\(328\) −1.51037 + 1.09735i −0.0833961 + 0.0605908i
\(329\) 0.561861 0.408216i 0.0309764 0.0225057i
\(330\) 0 0
\(331\) −6.92796 5.03346i −0.380795 0.276664i 0.380878 0.924625i \(-0.375622\pi\)
−0.761673 + 0.647961i \(0.775622\pi\)
\(332\) 12.3356 0.677004
\(333\) 0 0
\(334\) −2.52039 + 7.75696i −0.137910 + 0.424442i
\(335\) −2.09972 2.61528i −0.114720 0.142888i
\(336\) 0 0
\(337\) −4.53365 + 13.9531i −0.246964 + 0.760076i 0.748344 + 0.663311i \(0.230849\pi\)
−0.995307 + 0.0967646i \(0.969151\pi\)
\(338\) −2.41892 + 7.44466i −0.131572 + 0.404936i
\(339\) 0 0
\(340\) −11.7610 3.20425i −0.637831 0.173775i
\(341\) −1.54574 + 4.75731i −0.0837068 + 0.257623i
\(342\) 0 0
\(343\) 11.0883 0.598715
\(344\) −1.32579 0.963245i −0.0714820 0.0519347i
\(345\) 0 0
\(346\) 2.02526 1.47144i 0.108879 0.0791049i
\(347\) −18.5970 + 13.5115i −0.998340 + 0.725337i −0.961732 0.273993i \(-0.911656\pi\)
−0.0366088 + 0.999330i \(0.511656\pi\)
\(348\) 0 0
\(349\) 3.55023 0.190040 0.0950198 0.995475i \(-0.469709\pi\)
0.0950198 + 0.995475i \(0.469709\pi\)
\(350\) −0.900470 + 4.06837i −0.0481321 + 0.217463i
\(351\) 0 0
\(352\) 0.257524 + 0.792578i 0.0137261 + 0.0422445i
\(353\) −4.56375 + 3.31576i −0.242904 + 0.176480i −0.702576 0.711609i \(-0.747967\pi\)
0.459672 + 0.888089i \(0.347967\pi\)
\(354\) 0 0
\(355\) −4.93707 + 1.87146i −0.262033 + 0.0993267i
\(356\) −5.66780 4.11790i −0.300393 0.218248i
\(357\) 0 0
\(358\) 16.2067 + 11.7749i 0.856552 + 0.622322i
\(359\) 5.22442 16.0791i 0.275734 0.848623i −0.713290 0.700869i \(-0.752796\pi\)
0.989024 0.147754i \(-0.0472043\pi\)
\(360\) 0 0
\(361\) 17.2710 + 53.1548i 0.909002 + 2.79762i
\(362\) −2.43453 + 7.49270i −0.127956 + 0.393808i
\(363\) 0 0
\(364\) −1.17527 3.61712i −0.0616011 0.189589i
\(365\) −0.358528 7.43749i −0.0187662 0.389296i
\(366\) 0 0
\(367\) 10.2044 + 7.41393i 0.532665 + 0.387004i 0.821354 0.570419i \(-0.193219\pi\)
−0.288688 + 0.957423i \(0.593219\pi\)
\(368\) −3.53019 −0.184024
\(369\) 0 0
\(370\) −15.7813 4.29957i −0.820431 0.223524i
\(371\) −4.33327 + 3.14830i −0.224972 + 0.163452i
\(372\) 0 0
\(373\) 4.09435 + 12.6011i 0.211997 + 0.652460i 0.999353 + 0.0359616i \(0.0114494\pi\)
−0.787356 + 0.616499i \(0.788551\pi\)
\(374\) −4.54301 −0.234913
\(375\) 0 0
\(376\) −0.833366 −0.0429776
\(377\) −4.61106 14.1914i −0.237482 0.730894i
\(378\) 0 0
\(379\) −18.0702 + 13.1288i −0.928203 + 0.674379i −0.945552 0.325470i \(-0.894477\pi\)
0.0173488 + 0.999849i \(0.494477\pi\)
\(380\) −18.6702 5.08664i −0.957762 0.260939i
\(381\) 0 0
\(382\) −5.27521 −0.269903
\(383\) 19.7019 + 14.3143i 1.00672 + 0.731425i 0.963519 0.267642i \(-0.0862443\pi\)
0.0432012 + 0.999066i \(0.486244\pi\)
\(384\) 0 0
\(385\) 0.0747738 + 1.55114i 0.00381082 + 0.0790536i
\(386\) 4.15508 + 12.7880i 0.211488 + 0.650893i
\(387\) 0 0
\(388\) 3.42705 10.5474i 0.173982 0.535462i
\(389\) −9.30500 28.6378i −0.471782 1.45200i −0.850249 0.526381i \(-0.823548\pi\)
0.378467 0.925615i \(-0.376452\pi\)
\(390\) 0 0
\(391\) 5.94688 18.3026i 0.300746 0.925602i
\(392\) −5.10126 3.70628i −0.257652 0.187195i
\(393\) 0 0
\(394\) 4.39991 + 3.19672i 0.221664 + 0.161048i
\(395\) −10.8077 + 4.09681i −0.543796 + 0.206133i
\(396\) 0 0
\(397\) −28.6152 + 20.7902i −1.43616 + 1.04343i −0.447328 + 0.894370i \(0.647624\pi\)
−0.988828 + 0.149059i \(0.952376\pi\)
\(398\) 5.37968 + 16.5569i 0.269659 + 0.829924i
\(399\) 0 0
\(400\) 3.74364 3.31439i 0.187182 0.165719i
\(401\) 5.66794 0.283043 0.141522 0.989935i \(-0.454801\pi\)
0.141522 + 0.989935i \(0.454801\pi\)
\(402\) 0 0
\(403\) −22.1615 + 16.1013i −1.10394 + 0.802061i
\(404\) 10.2814 7.46988i 0.511519 0.371640i
\(405\) 0 0
\(406\) 2.20440 + 1.60159i 0.109403 + 0.0794856i
\(407\) −6.09595 −0.302165
\(408\) 0 0
\(409\) 5.98493 18.4197i 0.295936 0.910797i −0.686970 0.726686i \(-0.741060\pi\)
0.982906 0.184111i \(-0.0589405\pi\)
\(410\) 4.02775 + 1.09735i 0.198916 + 0.0541941i
\(411\) 0 0
\(412\) 2.16780 6.67180i 0.106800 0.328696i
\(413\) 3.48495 10.7256i 0.171483 0.527771i
\(414\) 0 0
\(415\) −17.2687 21.5088i −0.847687 1.05582i
\(416\) −1.41027 + 4.34038i −0.0691444 + 0.212805i
\(417\) 0 0
\(418\) −7.21188 −0.352744
\(419\) 18.5906 + 13.5068i 0.908209 + 0.659853i 0.940561 0.339624i \(-0.110300\pi\)
−0.0323520 + 0.999477i \(0.510300\pi\)
\(420\) 0 0
\(421\) 8.19306 5.95261i 0.399305 0.290112i −0.369953 0.929051i \(-0.620626\pi\)
0.769258 + 0.638938i \(0.220626\pi\)
\(422\) −0.218381 + 0.158663i −0.0106306 + 0.00772361i
\(423\) 0 0
\(424\) 6.42721 0.312133
\(425\) 10.8773 + 24.9926i 0.527626 + 1.21232i
\(426\) 0 0
\(427\) −1.51532 4.66369i −0.0733316 0.225692i
\(428\) −8.71314 + 6.33047i −0.421165 + 0.305995i
\(429\) 0 0
\(430\) 0.176440 + 3.66015i 0.00850867 + 0.176508i
\(431\) −23.0589 16.7533i −1.11071 0.806978i −0.127935 0.991783i \(-0.540835\pi\)
−0.982775 + 0.184804i \(0.940835\pi\)
\(432\) 0 0
\(433\) −12.8550 9.33971i −0.617772 0.448838i 0.234370 0.972147i \(-0.424697\pi\)
−0.852143 + 0.523309i \(0.824697\pi\)
\(434\) 1.54574 4.75731i 0.0741981 0.228358i
\(435\) 0 0
\(436\) −3.28655 10.1150i −0.157397 0.484419i
\(437\) 9.44047 29.0548i 0.451599 1.38988i
\(438\) 0 0
\(439\) 0.910550 + 2.80238i 0.0434582 + 0.133751i 0.970431 0.241377i \(-0.0775990\pi\)
−0.926973 + 0.375127i \(0.877599\pi\)
\(440\) 1.02146 1.55856i 0.0486960 0.0743016i
\(441\) 0 0
\(442\) −20.1274 14.6234i −0.957362 0.695564i
\(443\) 5.27327 0.250541 0.125270 0.992123i \(-0.460020\pi\)
0.125270 + 0.992123i \(0.460020\pi\)
\(444\) 0 0
\(445\) 0.754284 + 15.6472i 0.0357565 + 0.741750i
\(446\) 18.7460 13.6197i 0.887647 0.644914i
\(447\) 0 0
\(448\) −0.257524 0.792578i −0.0121669 0.0374458i
\(449\) 6.81659 0.321695 0.160847 0.986979i \(-0.448577\pi\)
0.160847 + 0.986979i \(0.448577\pi\)
\(450\) 0 0
\(451\) 1.55583 0.0732609
\(452\) −0.538232 1.65651i −0.0253163 0.0779156i
\(453\) 0 0
\(454\) 0.204401 0.148506i 0.00959300 0.00696972i
\(455\) −4.66167 + 7.11289i −0.218542 + 0.333457i
\(456\) 0 0
\(457\) 4.17712 0.195397 0.0976987 0.995216i \(-0.468852\pi\)
0.0976987 + 0.995216i \(0.468852\pi\)
\(458\) −17.0625 12.3966i −0.797277 0.579255i
\(459\) 0 0
\(460\) 4.94194 + 6.15537i 0.230419 + 0.286995i
\(461\) 11.5678 + 35.6020i 0.538766 + 1.65815i 0.735367 + 0.677669i \(0.237010\pi\)
−0.196601 + 0.980484i \(0.562990\pi\)
\(462\) 0 0
\(463\) −4.28879 + 13.1995i −0.199317 + 0.613434i 0.800582 + 0.599223i \(0.204524\pi\)
−0.999899 + 0.0142111i \(0.995476\pi\)
\(464\) −1.01037 3.10959i −0.0469052 0.144359i
\(465\) 0 0
\(466\) −4.51398 + 13.8926i −0.209106 + 0.643562i
\(467\) 11.2134 + 8.14705i 0.518896 + 0.377000i 0.816188 0.577786i \(-0.196083\pi\)
−0.297292 + 0.954787i \(0.596083\pi\)
\(468\) 0 0
\(469\) 1.01125 + 0.734713i 0.0466950 + 0.0339259i
\(470\) 1.16663 + 1.45309i 0.0538128 + 0.0670258i
\(471\) 0 0
\(472\) −10.9480 + 7.95422i −0.503924 + 0.366123i
\(473\) 0.422023 + 1.29885i 0.0194046 + 0.0597213i
\(474\) 0 0
\(475\) 17.2673 + 39.6749i 0.792279 + 1.82041i
\(476\) 4.54301 0.208228
\(477\) 0 0
\(478\) −4.70704 + 3.41986i −0.215295 + 0.156421i
\(479\) 23.2976 16.9267i 1.06450 0.773401i 0.0895806 0.995980i \(-0.471447\pi\)
0.974915 + 0.222578i \(0.0714473\pi\)
\(480\) 0 0
\(481\) −27.0076 19.6221i −1.23144 0.894692i
\(482\) −13.7291 −0.625345
\(483\) 0 0
\(484\) −3.18458 + 9.80111i −0.144753 + 0.445505i
\(485\) −23.1883 + 8.78982i −1.05293 + 0.399125i
\(486\) 0 0
\(487\) 12.0366 37.0449i 0.545430 1.67866i −0.174534 0.984651i \(-0.555842\pi\)
0.719964 0.694011i \(-0.244158\pi\)
\(488\) −1.81832 + 5.59621i −0.0823114 + 0.253328i
\(489\) 0 0
\(490\) 0.678887 + 14.0832i 0.0306690 + 0.636213i
\(491\) 7.26403 22.3564i 0.327821 1.00893i −0.642330 0.766428i \(-0.722032\pi\)
0.970151 0.242501i \(-0.0779679\pi\)
\(492\) 0 0
\(493\) 17.8240 0.802753
\(494\) −31.9515 23.2141i −1.43757 1.04445i
\(495\) 0 0
\(496\) −4.85599 + 3.52808i −0.218040 + 0.158416i
\(497\) 1.59196 1.15662i 0.0714091 0.0518817i
\(498\) 0 0
\(499\) 28.2651 1.26532 0.632660 0.774430i \(-0.281963\pi\)
0.632660 + 0.774430i \(0.281963\pi\)
\(500\) −11.0198 1.88771i −0.492822 0.0844209i
\(501\) 0 0
\(502\) −4.91144 15.1159i −0.219208 0.674654i
\(503\) 5.58565 4.05821i 0.249052 0.180947i −0.456255 0.889849i \(-0.650809\pi\)
0.705306 + 0.708903i \(0.250809\pi\)
\(504\) 0 0
\(505\) −27.4178 7.46988i −1.22007 0.332405i
\(506\) 2.38008 + 1.72923i 0.105808 + 0.0768737i
\(507\) 0 0
\(508\) −4.58448 3.33082i −0.203403 0.147781i
\(509\) −10.3641 + 31.8975i −0.459382 + 1.41383i 0.406531 + 0.913637i \(0.366738\pi\)
−0.865913 + 0.500195i \(0.833262\pi\)
\(510\) 0 0
\(511\) 0.857557 + 2.63929i 0.0379361 + 0.116755i
\(512\) −0.309017 + 0.951057i −0.0136568 + 0.0420312i
\(513\) 0 0
\(514\) −0.714612 2.19935i −0.0315202 0.0970091i
\(515\) −14.6679 + 5.56005i −0.646345 + 0.245005i
\(516\) 0 0
\(517\) 0.561861 + 0.408216i 0.0247106 + 0.0179533i
\(518\) 6.09595 0.267841
\(519\) 0 0
\(520\) 9.54229 3.61712i 0.418457 0.158621i
\(521\) 0.997861 0.724989i 0.0437171 0.0317623i −0.565712 0.824603i \(-0.691399\pi\)
0.609429 + 0.792840i \(0.291399\pi\)
\(522\) 0 0
\(523\) 7.11681 + 21.9033i 0.311196 + 0.957764i 0.977292 + 0.211898i \(0.0679643\pi\)
−0.666095 + 0.745867i \(0.732036\pi\)
\(524\) 16.4745 0.719690
\(525\) 0 0
\(526\) −21.4593 −0.935671
\(527\) −10.1114 31.1196i −0.440458 1.35559i
\(528\) 0 0
\(529\) 8.52520 6.19392i 0.370661 0.269301i
\(530\) −8.99749 11.2067i −0.390826 0.486788i
\(531\) 0 0
\(532\) 7.21188 0.312674
\(533\) 6.89294 + 5.00801i 0.298566 + 0.216921i
\(534\) 0 0
\(535\) 23.2356 + 6.33047i 1.00456 + 0.273690i
\(536\) −0.463496 1.42649i −0.0200200 0.0616151i
\(537\) 0 0
\(538\) 6.60877 20.3397i 0.284924 0.876907i
\(539\) 1.62382 + 4.99760i 0.0699428 + 0.215262i
\(540\) 0 0
\(541\) −8.27238 + 25.4598i −0.355657 + 1.09460i 0.599970 + 0.800023i \(0.295179\pi\)
−0.955627 + 0.294578i \(0.904821\pi\)
\(542\) −21.1400 15.3591i −0.908042 0.659731i
\(543\) 0 0
\(544\) −4.41027 3.20425i −0.189089 0.137381i
\(545\) −13.0359 + 19.8906i −0.558398 + 0.852018i
\(546\) 0 0
\(547\) −5.19947 + 3.77763i −0.222313 + 0.161520i −0.693367 0.720584i \(-0.743874\pi\)
0.471054 + 0.882104i \(0.343874\pi\)
\(548\) 0.894062 + 2.75164i 0.0381924 + 0.117544i
\(549\) 0 0
\(550\) −4.14751 + 0.400797i −0.176850 + 0.0170900i
\(551\) 28.2950 1.20541
\(552\) 0 0
\(553\) 3.48495 2.53197i 0.148195 0.107670i
\(554\) −15.0856 + 10.9604i −0.640928 + 0.465661i
\(555\) 0 0
\(556\) −4.03660 2.93276i −0.171190 0.124377i
\(557\) −44.0843 −1.86791 −0.933957 0.357386i \(-0.883668\pi\)
−0.933957 + 0.357386i \(0.883668\pi\)
\(558\) 0 0
\(559\) −2.31112 + 7.11289i −0.0977498 + 0.300843i
\(560\) −1.02146 + 1.55856i −0.0431644 + 0.0658613i
\(561\) 0 0
\(562\) 4.57924 14.0934i 0.193164 0.594496i
\(563\) −6.20440 + 19.0952i −0.261484 + 0.804766i 0.730998 + 0.682379i \(0.239055\pi\)
−0.992483 + 0.122387i \(0.960945\pi\)
\(564\) 0 0
\(565\) −2.13487 + 3.25744i −0.0898147 + 0.137041i
\(566\) −4.87628 + 15.0076i −0.204965 + 0.630818i
\(567\) 0 0
\(568\) −2.36123 −0.0990750
\(569\) −24.2170 17.5947i −1.01523 0.737609i −0.0499312 0.998753i \(-0.515900\pi\)
−0.965300 + 0.261144i \(0.915900\pi\)
\(570\) 0 0
\(571\) 11.5201 8.36985i 0.482102 0.350267i −0.320037 0.947405i \(-0.603695\pi\)
0.802139 + 0.597138i \(0.203695\pi\)
\(572\) 3.07691 2.23551i 0.128652 0.0934712i
\(573\) 0 0
\(574\) −1.55583 −0.0649389
\(575\) 3.81445 17.2339i 0.159074 0.718703i
\(576\) 0 0
\(577\) −5.62687 17.3177i −0.234250 0.720946i −0.997220 0.0745128i \(-0.976260\pi\)
0.762970 0.646433i \(-0.223740\pi\)
\(578\) 10.2889 7.47531i 0.427961 0.310932i
\(579\) 0 0
\(580\) −4.00757 + 6.11485i −0.166405 + 0.253905i
\(581\) 8.31675 + 6.04247i 0.345037 + 0.250684i
\(582\) 0 0
\(583\) −4.33327 3.14830i −0.179466 0.130389i
\(584\) 1.02903 3.16703i 0.0425815 0.131052i
\(585\) 0 0
\(586\) 5.68601 + 17.4998i 0.234887 + 0.722908i
\(587\) −1.59586 + 4.91155i −0.0658681 + 0.202721i −0.978574 0.205896i \(-0.933989\pi\)
0.912706 + 0.408618i \(0.133989\pi\)
\(588\) 0 0
\(589\) −16.0515 49.4014i −0.661389 2.03555i
\(590\) 29.1955 + 7.95422i 1.20196 + 0.327470i
\(591\) 0 0
\(592\) −5.91785 4.29957i −0.243222 0.176711i
\(593\) 35.6286 1.46309 0.731546 0.681793i \(-0.238799\pi\)
0.731546 + 0.681793i \(0.238799\pi\)
\(594\) 0 0
\(595\) −6.35979 7.92135i −0.260726 0.324744i
\(596\) 1.62271 1.17897i 0.0664690 0.0482925i
\(597\) 0 0
\(598\) 4.97854 + 15.3224i 0.203588 + 0.626579i
\(599\) 31.8284 1.30047 0.650236 0.759733i \(-0.274670\pi\)
0.650236 + 0.759733i \(0.274670\pi\)
\(600\) 0 0
\(601\) −12.6378 −0.515508 −0.257754 0.966211i \(-0.582982\pi\)
−0.257754 + 0.966211i \(0.582982\pi\)
\(602\) −0.422023 1.29885i −0.0172004 0.0529373i
\(603\) 0 0
\(604\) 1.59353 1.15777i 0.0648397 0.0471088i
\(605\) 21.5477 8.16791i 0.876037 0.332073i
\(606\) 0 0
\(607\) 34.9481 1.41850 0.709250 0.704957i \(-0.249034\pi\)
0.709250 + 0.704957i \(0.249034\pi\)
\(608\) −7.00116 5.08664i −0.283935 0.206291i
\(609\) 0 0
\(610\) 12.3032 4.66369i 0.498142 0.188827i
\(611\) 1.17527 + 3.61712i 0.0475465 + 0.146333i
\(612\) 0 0
\(613\) 2.20106 6.77418i 0.0889001 0.273606i −0.896716 0.442607i \(-0.854054\pi\)
0.985616 + 0.169000i \(0.0540538\pi\)
\(614\) 10.5430 + 32.4480i 0.425481 + 1.30950i
\(615\) 0 0
\(616\) −0.214612 + 0.660507i −0.00864696 + 0.0266126i
\(617\) −13.0147 9.45572i −0.523951 0.380673i 0.294139 0.955763i \(-0.404967\pi\)
−0.818090 + 0.575090i \(0.804967\pi\)
\(618\) 0 0
\(619\) 0.607103 + 0.441086i 0.0244015 + 0.0177287i 0.599919 0.800061i \(-0.295199\pi\)
−0.575518 + 0.817789i \(0.695199\pi\)
\(620\) 12.9496 + 3.52808i 0.520069 + 0.141691i
\(621\) 0 0
\(622\) 10.5479 7.66348i 0.422931 0.307278i
\(623\) −1.80416 5.55263i −0.0722821 0.222461i
\(624\) 0 0
\(625\) 12.1353 + 21.8572i 0.485410 + 0.874287i
\(626\) −3.48262 −0.139194
\(627\) 0 0
\(628\) −6.29793 + 4.57571i −0.251315 + 0.182591i
\(629\) 32.2606 23.4387i 1.28631 0.934561i
\(630\) 0 0
\(631\) 12.4391 + 9.03753i 0.495192 + 0.359778i 0.807178 0.590309i \(-0.200994\pi\)
−0.311985 + 0.950087i \(0.600994\pi\)
\(632\) −5.16896 −0.205610
\(633\) 0 0
\(634\) 1.48957 4.58443i 0.0591585 0.182071i
\(635\) 0.610113 + 12.6565i 0.0242116 + 0.502258i
\(636\) 0 0
\(637\) −8.89249 + 27.3683i −0.352333 + 1.08437i
\(638\) −0.842006 + 2.59143i −0.0333353 + 0.102596i
\(639\) 0 0
\(640\) 2.09089 0.792578i 0.0826497 0.0313294i
\(641\) −2.92140 + 8.99114i −0.115388 + 0.355129i −0.992028 0.126019i \(-0.959780\pi\)
0.876639 + 0.481148i \(0.159780\pi\)
\(642\) 0 0
\(643\) 32.8334 1.29482 0.647411 0.762141i \(-0.275852\pi\)
0.647411 + 0.762141i \(0.275852\pi\)
\(644\) −2.38008 1.72923i −0.0937883 0.0681412i
\(645\) 0 0
\(646\) 38.1661 27.7293i 1.50163 1.09100i
\(647\) 14.4556 10.5026i 0.568309 0.412901i −0.266182 0.963923i \(-0.585762\pi\)
0.834490 + 0.551022i \(0.185762\pi\)
\(648\) 0 0
\(649\) 11.2775 0.442682
\(650\) −19.6653 11.5746i −0.771335 0.453994i
\(651\) 0 0
\(652\) 4.35589 + 13.4060i 0.170590 + 0.525021i
\(653\) −25.8596 + 18.7881i −1.01196 + 0.735235i −0.964620 0.263644i \(-0.915076\pi\)
−0.0473435 + 0.998879i \(0.515076\pi\)
\(654\) 0 0
\(655\) −23.0627 28.7254i −0.901135 1.12240i
\(656\) 1.51037 + 1.09735i 0.0589700 + 0.0428442i
\(657\) 0 0
\(658\) −0.561861 0.408216i −0.0219036 0.0159139i
\(659\) 3.52244 10.8410i 0.137215 0.422304i −0.858713 0.512457i \(-0.828736\pi\)
0.995928 + 0.0901527i \(0.0287355\pi\)
\(660\) 0 0
\(661\) 2.26642 + 6.97531i 0.0881533 + 0.271308i 0.985409 0.170203i \(-0.0544425\pi\)
−0.897256 + 0.441511i \(0.854442\pi\)
\(662\) −2.64625 + 8.14431i −0.102849 + 0.316537i
\(663\) 0 0
\(664\) −3.81191 11.7319i −0.147931 0.455284i
\(665\) −10.0960 12.5749i −0.391504 0.487633i
\(666\) 0 0
\(667\) −9.33799 6.78445i −0.361568 0.262695i
\(668\) 8.15615 0.315571
\(669\) 0 0
\(670\) −1.83843 + 2.80512i −0.0710248 + 0.108371i
\(671\) 3.96717 2.88232i 0.153151 0.111271i
\(672\) 0 0
\(673\) −10.1243 31.1595i −0.390264 1.20111i −0.932589 0.360940i \(-0.882456\pi\)
0.542325 0.840169i \(-0.317544\pi\)
\(674\) 14.6712 0.565113
\(675\) 0 0
\(676\) 7.82777 0.301068
\(677\) 10.0686 + 30.9879i 0.386967 + 1.19096i 0.935043 + 0.354534i \(0.115360\pi\)
−0.548076 + 0.836428i \(0.684640\pi\)
\(678\) 0 0
\(679\) 7.47707 5.43241i 0.286944 0.208477i
\(680\) 0.586930 + 12.1756i 0.0225077 + 0.466911i
\(681\) 0 0
\(682\) 5.00214 0.191542
\(683\) −3.51875 2.55652i −0.134641 0.0978227i 0.518426 0.855123i \(-0.326518\pi\)
−0.653067 + 0.757300i \(0.726518\pi\)
\(684\) 0 0
\(685\) 3.54625 5.41096i 0.135495 0.206742i
\(686\) −3.42649 10.5456i −0.130824 0.402635i
\(687\) 0 0
\(688\) −0.506408 + 1.55856i −0.0193066 + 0.0594197i
\(689\) −9.06413 27.8965i −0.345316 1.06277i
\(690\) 0 0
\(691\) −6.26053 + 19.2679i −0.238162 + 0.732987i 0.758524 + 0.651645i \(0.225921\pi\)
−0.996686 + 0.0813423i \(0.974079\pi\)
\(692\) −2.02526 1.47144i −0.0769888 0.0559356i
\(693\) 0 0
\(694\) 18.5970 + 13.5115i 0.705933 + 0.512891i
\(695\) 0.537200 + 11.1440i 0.0203772 + 0.422714i
\(696\) 0 0
\(697\) −8.23362 + 5.98208i −0.311871 + 0.226587i
\(698\) −1.09708 3.37647i −0.0415252 0.127801i
\(699\) 0 0
\(700\) 4.14751 0.400797i 0.156761 0.0151487i
\(701\) −12.5964 −0.475758 −0.237879 0.971295i \(-0.576452\pi\)
−0.237879 + 0.971295i \(0.576452\pi\)
\(702\) 0 0
\(703\) 51.2126 37.2081i 1.93152 1.40333i
\(704\) 0.674207 0.489840i 0.0254101 0.0184615i
\(705\) 0 0
\(706\) 4.56375 + 3.31576i 0.171759 + 0.124790i
\(707\) 10.5908 0.398310
\(708\) 0 0
\(709\) 9.10924 28.0354i 0.342105 1.05289i −0.621011 0.783802i \(-0.713278\pi\)
0.963116 0.269088i \(-0.0867222\pi\)
\(710\) 3.30550 + 4.11712i 0.124053 + 0.154513i
\(711\) 0 0
\(712\) −2.16491 + 6.66290i −0.0811333 + 0.249703i
\(713\) −6.54788 + 20.1523i −0.245220 + 0.754710i
\(714\) 0 0
\(715\) −8.20529 2.23551i −0.306860 0.0836032i
\(716\) 6.19042 19.0522i 0.231347 0.712012i
\(717\) 0 0
\(718\) −16.9066 −0.630948
\(719\) −24.3987 17.7267i −0.909919 0.661095i 0.0310756 0.999517i \(-0.490107\pi\)
−0.940994 + 0.338422i \(0.890107\pi\)
\(720\) 0 0
\(721\) 4.72966 3.43630i 0.176142 0.127974i
\(722\) 45.2162 32.8515i 1.68277 1.22261i
\(723\) 0 0
\(724\) 7.87829 0.292794
\(725\) 16.2723 1.57248i 0.604338 0.0584006i
\(726\) 0 0
\(727\) 1.83783 + 5.65626i 0.0681614 + 0.209779i 0.979336 0.202242i \(-0.0648229\pi\)
−0.911174 + 0.412021i \(0.864823\pi\)
\(728\) −3.07691 + 2.23551i −0.114038 + 0.0828533i
\(729\) 0 0
\(730\) −6.96268 + 2.63929i −0.257700 + 0.0976845i
\(731\) −7.22743 5.25103i −0.267316 0.194216i
\(732\) 0 0
\(733\) −8.23281 5.98148i −0.304086 0.220931i 0.425269 0.905067i \(-0.360180\pi\)
−0.729355 + 0.684136i \(0.760180\pi\)
\(734\) 3.89773 11.9960i 0.143868 0.442780i
\(735\) 0 0
\(736\) 1.09089 + 3.35741i 0.0402107 + 0.123756i
\(737\) −0.386261 + 1.18879i −0.0142281 + 0.0437896i
\(738\) 0 0
\(739\) 11.2234 + 34.5422i 0.412861 + 1.27066i 0.914150 + 0.405376i \(0.132859\pi\)
−0.501289 + 0.865280i \(0.667141\pi\)
\(740\) 0.787561 + 16.3376i 0.0289513 + 0.600581i
\(741\) 0 0
\(742\) 4.33327 + 3.14830i 0.159079 + 0.115578i
\(743\) −2.84832 −0.104495 −0.0522473 0.998634i \(-0.516638\pi\)
−0.0522473 + 0.998634i \(0.516638\pi\)
\(744\) 0 0
\(745\) −4.32734 1.17897i −0.158542 0.0431941i
\(746\) 10.7191 7.78791i 0.392455 0.285136i
\(747\) 0 0
\(748\) 1.40387 + 4.32066i 0.0513305 + 0.157979i
\(749\) −8.97537 −0.327953
\(750\) 0 0
\(751\) −31.5502 −1.15128 −0.575641 0.817702i \(-0.695248\pi\)
−0.575641 + 0.817702i \(0.695248\pi\)
\(752\) 0.257524 + 0.792578i 0.00939094 + 0.0289023i
\(753\) 0 0
\(754\) −12.0719 + 8.77076i −0.439633 + 0.319412i
\(755\) −4.24951 1.15777i −0.154656 0.0421354i
\(756\) 0 0
\(757\) −45.6446 −1.65898 −0.829491 0.558520i \(-0.811369\pi\)
−0.829491 + 0.558520i \(0.811369\pi\)
\(758\) 18.0702 + 13.1288i 0.656339 + 0.476858i
\(759\) 0 0
\(760\) 0.931731 + 19.3283i 0.0337974 + 0.701111i
\(761\) −2.80550 8.63445i −0.101699 0.312998i 0.887242 0.461304i \(-0.152618\pi\)
−0.988942 + 0.148305i \(0.952618\pi\)
\(762\) 0 0
\(763\) 2.73890 8.42947i 0.0991549 0.305167i
\(764\) 1.63013 + 5.01702i 0.0589760 + 0.181510i
\(765\) 0 0
\(766\) 7.52545 23.1610i 0.271906 0.836840i
\(767\) 49.9641 + 36.3010i 1.80410 + 1.31075i
\(768\) 0 0
\(769\) 20.5964 + 14.9641i 0.742724 + 0.539621i 0.893563 0.448938i \(-0.148198\pi\)
−0.150839 + 0.988558i \(0.548198\pi\)
\(770\) 1.45212 0.550444i 0.0523308 0.0198366i
\(771\) 0 0
\(772\) 10.8781 7.90343i 0.391513 0.284451i
\(773\) −5.30034 16.3128i −0.190640 0.586729i 0.809360 0.587313i \(-0.199814\pi\)
−1.00000 0.000583568i \(0.999814\pi\)
\(774\) 0 0
\(775\) −11.9766 27.5184i −0.430211 0.988489i
\(776\) −11.0902 −0.398114
\(777\) 0 0
\(778\) −24.3608 + 17.6992i −0.873377 + 0.634546i
\(779\) −13.0706 + 9.49635i −0.468303 + 0.340242i
\(780\) 0 0
\(781\) 1.59196 + 1.15662i 0.0569647 + 0.0413873i
\(782\) −19.2445 −0.688182
\(783\) 0 0
\(784\) −1.94851 + 5.99689i −0.0695895 + 0.214175i
\(785\) 16.7949 + 4.57571i 0.599435 + 0.163314i
\(786\) 0 0
\(787\) 3.48351 10.7211i 0.124174 0.382168i −0.869576 0.493799i \(-0.835608\pi\)
0.993750 + 0.111632i \(0.0356077\pi\)
\(788\) 1.68061