Properties

Label 450.2.h.e.271.2
Level $450$
Weight $2$
Character 450.271
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 271.2
Root \(-0.983224 + 0.644389i\) of defining polynomial
Character \(\chi\) \(=\) 450.271
Dual form 450.2.h.e.181.2

$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(127\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{5}\right)\)

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 −0.982344 0.187083i \(-0.940097\pi\)
0.904698 + 0.426054i \(0.140097\pi\)
\(12\) 0 0
\(13\) 1.41027 + 4.34038i 0.391140 + 1.20380i 0.931927 + 0.362645i \(0.118126\pi\)
−0.540787 + 0.841159i \(0.681874\pi\)
\(14\) 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 0.0937997 0.995591i \(-0.470099\pi\)
0.975849 + 0.218446i \(0.0700987\pi\)
\(18\) 0 0
\(19\) 7.00116 5.08664i 1.60618 1.16696i 0.732062 0.681238i \(-0.238558\pi\)
0.874116 0.485718i \(-0.161442\pi\)
\(20\) −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 0.770566 + 0.637361i \(0.219974\pi\)
−0.998032 + 0.0627085i \(0.980026\pi\)
\(24\) 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 0.805645 0.592399i \(-0.201819\pi\)
−0.314447 + 0.949275i \(0.601819\pi\)
\(30\) 0 0
\(31\) −4.85599 + 3.52808i −0.872161 + 0.633662i −0.931166 0.364596i \(-0.881207\pi\)
0.0590050 + 0.998258i \(0.481207\pi\)
\(32\) −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 0.945737 + 0.324932i \(0.105342\pi\)
−0.574127 + 0.818766i \(0.694658\pi\)
\(38\) 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 0.895847 0.444362i \(-0.146570\pi\)
−0.985945 + 0.167069i \(0.946570\pi\)
\(42\) 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 0.537527 0.843247i \(-0.319359\pi\)
−0.635870 + 0.771796i \(0.719359\pi\)
\(48\) 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 0.884538 0.466469i \(-0.154474\pi\)
−0.170301 + 0.985392i \(0.554474\pi\)
\(54\) 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 −0.722362 0.691515i \(-0.756943\pi\)
0.177940 0.984041i \(-0.443057\pi\)
\(60\) 0 0
\(61\) 1.81832 5.59621i 0.232812 0.716521i −0.764592 0.644514i \(-0.777060\pi\)
0.997404 0.0720066i \(-0.0229403\pi\)
\(62\) −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 −0.659436 0.751761i \(-0.729205\pi\)
0.511190 + 0.859468i \(0.329205\pi\)
\(68\) −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 0.468633 0.883393i \(-0.344747\pi\)
−0.695341 + 0.718680i \(0.744747\pi\)
\(72\) 0 0
\(73\) −1.02903 + 3.16703i −0.120439 + 0.370672i −0.993043 0.117756i \(-0.962430\pi\)
0.872604 + 0.488429i \(0.162430\pi\)
\(74\) −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 0.327144 0.944974i \(-0.393914\pi\)
−0.797631 + 0.603146i \(0.793914\pi\)
\(80\) 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 −0.980306 0.197487i \(-0.936722\pi\)
−0.115110 + 0.993353i \(0.536722\pi\)
\(84\) 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 −0.768326 0.640058i \(-0.778910\pi\)
0.997806 0.0662073i \(-0.0210899\pi\)
\(90\) 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 0.0302807 0.999541i \(-0.490360\pi\)
−0.941263 + 0.337674i \(0.890360\pi\)
\(98\) 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 0.271959 0.962309i \(-0.412328\pi\)
−0.831170 + 0.556018i \(0.812328\pi\)
\(104\) 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 −0.975839 0.218491i \(-0.929886\pi\)
0.661044 0.750347i \(-0.270114\pi\)
\(110\) −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 0.922543 0.385894i \(-0.126107\pi\)
−0.973176 + 0.230063i \(0.926107\pi\)
\(114\) 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 −0.842813 0.538206i \(-0.819102\pi\)
0.998200 + 0.0599756i \(0.0191023\pi\)
\(128\) 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 −0.990338 0.138673i \(-0.955716\pi\)
−0.174145 + 0.984720i \(0.555716\pi\)
\(132\) 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 0.981957 0.189104i \(-0.0605582\pi\)
−0.905572 + 0.424192i \(0.860558\pi\)
\(138\) 0 0
\(139\) 1.54184 4.74531i 0.130778 0.402492i −0.864132 0.503266i \(-0.832132\pi\)
0.994909 + 0.100774i \(0.0321318\pi\)
\(140\) 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 0.963597 + 0.267358i \(0.0861505\pi\)
−0.622418 + 0.782685i \(0.713849\pi\)
\(164\) −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 −0.813053 0.582190i \(-0.802196\pi\)
0.302448 + 0.953166i \(0.402196\pi\)
\(168\) 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 −0.917333 0.398120i \(-0.869663\pi\)
0.976147 + 0.217109i \(0.0696626\pi\)
\(174\) 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 −0.215995 0.976394i \(-0.569300\pi\)
−0.995352 + 0.0962986i \(0.969300\pi\)
\(180\) 0 0
\(181\) −6.37367 + 4.63074i −0.473751 + 0.344201i −0.798902 0.601462i \(-0.794585\pi\)
0.325150 + 0.945662i \(0.394585\pi\)
\(182\) 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 0.992551 0.121827i \(-0.0388755\pi\)
−0.874599 + 0.484847i \(0.838875\pi\)
\(192\) 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 0.419908 0.907567i \(-0.362062\pi\)
−0.733388 + 0.679810i \(0.762062\pi\)
\(198\) 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 −0.953887 0.300167i \(-0.902958\pi\)
0.948144 + 0.317840i \(0.102958\pi\)
\(212\) −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 −0.360313 0.932831i \(-0.617330\pi\)
0.839804 0.542889i \(-0.182670\pi\)
\(224\) 0.833366 0.0556816
\(225\) 0 0
\(226\) 1.74176 0.115860
\(227\) 0.0780741 0.240287i 0.00518196 0.0159484i −0.948432 0.316980i \(-0.897331\pi\)
0.953614 + 0.301032i \(0.0973311\pi\)
\(228\) 0 0
\(229\) 17.0625 + 12.3966i 1.12752 + 0.819191i 0.985332 0.170649i \(-0.0545864\pi\)
0.142187 + 0.989840i \(0.454586\pi\)
\(230\) −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 −0.903235 0.429147i \(-0.858814\pi\)
0.129028 + 0.991641i \(0.458814\pi\)
\(234\) 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 −0.992216 0.124532i \(-0.960257\pi\)
0.875917 + 0.482461i \(0.160257\pi\)
\(240\) 0 0
\(241\) 4.24254 + 13.0572i 0.273286 + 0.841087i 0.989668 + 0.143379i \(0.0457968\pi\)
−0.716382 + 0.697708i \(0.754203\pi\)
\(242\) −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 0.917592 + 0.397524i \(0.130130\pi\)
−0.508689 + 0.860951i \(0.669870\pi\)
\(264\) 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 0.0817787 0.996651i \(-0.473940\pi\)
0.973142 + 0.230206i \(0.0739399\pi\)
\(270\) 0 0
\(271\) 21.1400 + 15.3591i 1.28417 + 0.933001i 0.999670 0.0256766i \(-0.00817402\pi\)
0.284495 + 0.958677i \(0.408174\pi\)
\(272\) 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 0.614712 + 0.788752i \(0.289272\pi\)
−0.960929 + 0.276795i \(0.910728\pi\)
\(278\) 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 −0.169661 0.985503i \(-0.554267\pi\)
0.884841 + 0.465894i \(0.154267\pi\)
\(282\) 0 0
\(283\) −12.7663 + 9.27523i −0.758875 + 0.551355i −0.898565 0.438840i \(-0.855389\pi\)
0.139690 + 0.990195i \(0.455389\pi\)
\(284\) 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 −0.769462 0.638692i \(-0.779476\pi\)
0.997922 0.0644345i \(-0.0205243\pi\)
\(312\) 0 0
\(313\) 1.07619 + 3.31217i 0.0608298 + 0.187215i 0.976854 0.213909i \(-0.0686196\pi\)
−0.916024 + 0.401124i \(0.868620\pi\)
\(314\) −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 −0.472859 0.881138i \(-0.656778\pi\)
0.691891 + 0.722002i \(0.256778\pi\)
\(318\) 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 −0.761673 0.647961i \(-0.775622\pi\)
0.380878 + 0.924625i \(0.375622\pi\)
\(332\) 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 −0.995307 0.0967646i \(-0.969151\pi\)
0.748344 0.663311i \(-0.230849\pi\)
\(338\) −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 −0.0366088 0.999330i \(-0.511656\pi\)
−0.961732 + 0.273993i \(0.911656\pi\)
\(348\) 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 0.459672 0.888089i \(-0.347967\pi\)
−0.702576 + 0.711609i \(0.747967\pi\)
\(354\) 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 0.989024 + 0.147754i \(0.0472043\pi\)
−0.713290 + 0.700869i \(0.752796\pi\)
\(360\) 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 −0.288688 0.957423i \(-0.593219\pi\)
0.821354 + 0.570419i \(0.193219\pi\)
\(368\) −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 −0.787356 0.616499i \(-0.788551\pi\)
0.999353 0.0359616i \(-0.0114494\pi\)
\(374\) −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 0.0173488 0.999849i \(-0.494477\pi\)
−0.945552 + 0.325470i \(0.894477\pi\)
\(380\) −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 0.0432012 0.999066i \(-0.486244\pi\)
0.963519 + 0.267642i \(0.0862443\pi\)
\(384\) 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 0.378467 + 0.925615i \(0.376452\pi\)
−0.850249 + 0.526381i \(0.823548\pi\)
\(390\) 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 −0.988828 0.149059i \(-0.952376\pi\)
−0.447328 0.894370i \(-0.647624\pi\)
\(398\) 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 0.982906 + 0.184111i \(0.0589405\pi\)
−0.686970 + 0.726686i \(0.741060\pi\)
\(410\) 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 −0.0323520 0.999477i \(-0.510300\pi\)
0.940561 + 0.339624i \(0.110300\pi\)
\(420\) 0 0
\(421\) 8.19306 + 5.95261i 0.399305 + 0.290112i 0.769258 0.638938i \(-0.220626\pi\)
−0.369953 + 0.929051i \(0.620626\pi\)
\(422\) −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 −0.982775 0.184804i \(-0.940835\pi\)
−0.127935 + 0.991783i \(0.540835\pi\)
\(432\) 0 0
\(433\) −12.8550 + 9.33971i −0.617772 + 0.448838i −0.852143 0.523309i \(-0.824697\pi\)
0.234370 + 0.972147i \(0.424697\pi\)
\(434\) 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 −0.926973 0.375127i \(-0.877599\pi\)
0.970431 + 0.241377i \(0.0775990\pi\)
\(440\) 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 −0.196601 0.980484i \(-0.562990\pi\)
0.735367 0.677669i \(-0.237010\pi\)
\(462\) 0 0
\(463\) −4.28879 13.1995i −0.199317 0.613434i −0.999899 0.0142111i \(-0.995476\pi\)
0.800582 0.599223i \(-0.204524\pi\)
\(464\) −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 −0.297292 0.954787i \(-0.596083\pi\)
0.816188 + 0.577786i \(0.196083\pi\)
\(468\) 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 0.974915 0.222578i \(-0.0714473\pi\)
0.0895806 + 0.995980i \(0.471447\pi\)
\(480\) 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 0.719964 + 0.694011i \(0.244158\pi\)
−0.174534 + 0.984651i \(0.555842\pi\)
\(488\) −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 0.970151 + 0.242501i \(0.0779679\pi\)
−0.642330 + 0.766428i \(0.722032\pi\)
\(492\) 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 0.705306 0.708903i \(-0.250809\pi\)
−0.456255 + 0.889849i \(0.650809\pi\)
\(504\) 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 −0.865913 0.500195i \(-0.833262\pi\)
0.406531 0.913637i \(-0.366738\pi\)
\(510\) 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 0.609429 0.792840i \(-0.291399\pi\)
−0.565712 + 0.824603i \(0.691399\pi\)
\(522\) 0 0
\(523\) 7.11681 21.9033i 0.311196 0.957764i −0.666095 0.745867i \(-0.732036\pi\)
0.977292 0.211898i \(-0.0679643\pi\)
\(524\) 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 −0.955627 0.294578i \(-0.904821\pi\)
0.599970 0.800023i \(-0.295179\pi\)
\(542\) −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 0.471054 0.882104i \(-0.343874\pi\)
−0.693367 + 0.720584i \(0.743874\pi\)
\(548\) 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 −0.992483 0.122387i \(-0.960945\pi\)
0.730998 0.682379i \(-0.239055\pi\)
\(564\) 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 −0.965300 0.261144i \(-0.915900\pi\)
−0.0499312 + 0.998753i \(0.515900\pi\)
\(570\) 0 0
\(571\) 11.5201 + 8.36985i 0.482102 + 0.350267i 0.802139 0.597138i \(-0.203695\pi\)
−0.320037 + 0.947405i \(0.603695\pi\)
\(572\) 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 0.762970 + 0.646433i \(0.223740\pi\)
−0.997220 + 0.0745128i \(0.976260\pi\)
\(578\) 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 0.912706 0.408618i \(-0.133989\pi\)
−0.978574 + 0.205896i \(0.933989\pi\)
\(588\) 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 0.985616 0.169000i \(-0.0540538\pi\)
−0.896716 + 0.442607i \(0.854054\pi\)
\(614\) 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 −0.818090 0.575090i \(-0.804967\pi\)
0.294139 + 0.955763i \(0.404967\pi\)
\(618\) 0 0
\(619\) 0.607103 0.441086i 0.0244015 0.0177287i −0.575518 0.817789i \(-0.695199\pi\)
0.599919 + 0.800061i \(0.295199\pi\)
\(620\) 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 −0.311985 0.950087i \(-0.600994\pi\)
0.807178 + 0.590309i \(0.200994\pi\)
\(632\) −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 0.876639 0.481148i \(-0.159780\pi\)
−0.992028 + 0.126019i \(0.959780\pi\)
\(642\) 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 0.834490 0.551022i \(-0.185762\pi\)
−0.266182 + 0.963923i \(0.585762\pi\)
\(648\) 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 −0.0473435 0.998879i \(-0.515076\pi\)
−0.964620 + 0.263644i \(0.915076\pi\)
\(654\) 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 0.995928 0.0901527i \(-0.0287355\pi\)
−0.858713 + 0.512457i \(0.828736\pi\)
\(660\) 0 0
\(661\) 2.26642 6.97531i 0.0881533 0.271308i −0.897256 0.441511i \(-0.854442\pi\)
0.985409 + 0.170203i \(0.0544425\pi\)
\(662\) −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 0.542325 + 0.840169i \(0.317544\pi\)
−0.932589 + 0.360940i \(0.882456\pi\)
\(674\) 14.6712 0.565113
\(675\) 0 0
\(676\) 7.82777 0.301068
\(677\) 10.0686 30.9879i 0.386967 1.19096i −0.548076 0.836428i \(-0.684640\pi\)
0.935043 0.354534i \(-0.115360\pi\)
\(678\) 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 −0.653067 0.757300i \(-0.726518\pi\)
0.518426 + 0.855123i \(0.326518\pi\)
\(684\) 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 −0.996686 0.0813423i \(-0.974079\pi\)
0.758524 0.651645i \(-0.225921\pi\)
\(692\) −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 0.963116 + 0.269088i \(0.0867222\pi\)
−0.621011 + 0.783802i \(0.713278\pi\)
\(710\) 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 −0.940994 0.338422i \(-0.890107\pi\)
0.0310756 + 0.999517i \(0.490107\pi\)
\(720\) 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 −0.911174 0.412021i \(-0.864823\pi\)
0.979336 + 0.202242i \(0.0648229\pi\)
\(728\) −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 −0.729355 0.684136i \(-0.760180\pi\)
0.425269 + 0.905067i \(0.360180\pi\)
\(734\) 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 −0.501289 0.865280i \(-0.667141\pi\)
0.914150 0.405376i \(-0.132859\pi\)
\(740\) 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 −0.988942 0.148305i \(-0.952618\pi\)
0.887242 + 0.461304i \(0.152618\pi\)
\(762\) 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 −0.150839 0.988558i \(-0.548198\pi\)
0.893563 + 0.448938i \(0.148198\pi\)
\(770\) 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 −1.00000 0.000583568i \(-0.999814\pi\)
0.809360 + 0.587313i \(0.199814\pi\)
\(774\) 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 0.993750 0.111632i \(-0.0356077\pi\)
−0.869576 + 0.493799i \(0.835608\pi\)
\(788\) 1.68061 + 5.17240i