Properties

Label 819.2.bm.f.550.5
Level $819$
Weight $2$
Character 819.550
Analytic conductor $6.540$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 819.bm (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(6.53974792554\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(\zeta_{6})\)
Coefficient field: 12.0.2346760387617129.1
Defining polynomial: \( x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + 16 x^{2} - 96 x + 64 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 550.5
Root \(-1.38488 + 0.286553i\) of defining polynomial
Character \(\chi\) \(=\) 819.550
Dual form 819.2.bm.f.478.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.37905i q^{2} +0.0982074 q^{4} +(0.697972 - 0.402974i) q^{5} +(0.0699870 + 2.64483i) q^{7} +2.89354i q^{8} +O(q^{10})\) \(q+1.37905i q^{2} +0.0982074 q^{4} +(0.697972 - 0.402974i) q^{5} +(0.0699870 + 2.64483i) q^{7} +2.89354i q^{8} +(0.555723 + 0.962541i) q^{10} +(-4.56532 + 2.63579i) q^{11} +(-2.36581 - 2.72084i) q^{13} +(-3.64736 + 0.0965159i) q^{14} -3.79394 q^{16} -0.560102 q^{17} +(5.06165 + 2.92234i) q^{19} +(0.0685460 - 0.0395750i) q^{20} +(-3.63490 - 6.29583i) q^{22} -1.60488 q^{23} +(-2.17522 + 3.76760i) q^{25} +(3.75219 - 3.26258i) q^{26} +(0.00687324 + 0.259741i) q^{28} +(1.14008 - 1.97467i) q^{29} +(3.01022 + 1.73795i) q^{31} +0.555034i q^{32} -0.772411i q^{34} +(1.11465 + 1.81781i) q^{35} +1.24196i q^{37} +(-4.03007 + 6.98029i) q^{38} +(1.16602 + 2.01961i) q^{40} +(-0.803413 - 0.463851i) q^{41} +(2.22356 + 3.85131i) q^{43} +(-0.448348 + 0.258854i) q^{44} -2.21321i q^{46} +(3.32915 - 1.92209i) q^{47} +(-6.99020 + 0.370207i) q^{49} +(-5.19572 - 2.99975i) q^{50} +(-0.232340 - 0.267207i) q^{52} +(2.72727 - 4.72377i) q^{53} +(-2.12431 + 3.67941i) q^{55} +(-7.65292 + 0.202510i) q^{56} +(2.72318 + 1.57223i) q^{58} +10.9940i q^{59} +(-3.65107 + 6.32385i) q^{61} +(-2.39673 + 4.15126i) q^{62} -8.35330 q^{64} +(-2.74769 - 0.945710i) q^{65} +(6.36144 - 3.67278i) q^{67} -0.0550061 q^{68} +(-2.50686 + 1.53716i) q^{70} +(8.06668 - 4.65730i) q^{71} +(4.33139 + 2.50073i) q^{73} -1.71273 q^{74} +(0.497091 + 0.286996i) q^{76} +(-7.29072 - 11.8900i) q^{77} +(-5.68437 - 9.84562i) q^{79} +(-2.64806 + 1.52886i) q^{80} +(0.639676 - 1.10795i) q^{82} -5.81962i q^{83} +(-0.390935 + 0.225707i) q^{85} +(-5.31117 + 3.06641i) q^{86} +(-7.62677 - 13.2100i) q^{88} -5.00946i q^{89} +(7.03057 - 6.44756i) q^{91} -0.157611 q^{92} +(2.65067 + 4.59109i) q^{94} +4.71051 q^{95} +(9.22171 - 5.32416i) q^{97} +(-0.510535 - 9.63988i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 8 q^{4} + 3 q^{5} - 3 q^{7} + 12 q^{10} - 12 q^{11} - 2 q^{13} - 4 q^{14} + 16 q^{16} + 34 q^{17} + 9 q^{19} + 3 q^{20} - 15 q^{22} + 6 q^{23} - 5 q^{25} + 6 q^{26} - 9 q^{28} + q^{29} + 18 q^{31} + 6 q^{35} - 19 q^{38} - q^{40} + 6 q^{41} + 11 q^{43} + 33 q^{44} + 15 q^{47} - 3 q^{49} - 18 q^{50} - 7 q^{52} + 8 q^{53} - 15 q^{55} - 27 q^{56} - 24 q^{58} + 5 q^{61} - 41 q^{62} + 2 q^{64} - 21 q^{65} + 15 q^{67} - 22 q^{68} + 3 q^{70} - 30 q^{71} + 42 q^{73} - 66 q^{74} - 45 q^{76} + 19 q^{77} - 35 q^{79} + 63 q^{80} + 5 q^{82} - 21 q^{85} + 57 q^{86} - 14 q^{88} - 7 q^{91} + 66 q^{92} + q^{94} + 4 q^{95} - 3 q^{97} + 18 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).

\(n\) \(92\) \(379\) \(703\)
\(\chi(n)\) \(1\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.37905i 0.975139i 0.873084 + 0.487570i \(0.162116\pi\)
−0.873084 + 0.487570i \(0.837884\pi\)
\(3\) 0 0
\(4\) 0.0982074 0.0491037
\(5\) 0.697972 0.402974i 0.312142 0.180216i −0.335742 0.941954i \(-0.608987\pi\)
0.647885 + 0.761738i \(0.275654\pi\)
\(6\) 0 0
\(7\) 0.0699870 + 2.64483i 0.0264526 + 0.999650i
\(8\) 2.89354i 1.02302i
\(9\) 0 0
\(10\) 0.555723 + 0.962541i 0.175735 + 0.304382i
\(11\) −4.56532 + 2.63579i −1.37650 + 0.794720i −0.991736 0.128296i \(-0.959049\pi\)
−0.384760 + 0.923017i \(0.625716\pi\)
\(12\) 0 0
\(13\) −2.36581 2.72084i −0.656156 0.754625i
\(14\) −3.64736 + 0.0965159i −0.974798 + 0.0257950i
\(15\) 0 0
\(16\) −3.79394 −0.948485
\(17\) −0.560102 −0.135845 −0.0679223 0.997691i \(-0.521637\pi\)
−0.0679223 + 0.997691i \(0.521637\pi\)
\(18\) 0 0
\(19\) 5.06165 + 2.92234i 1.16122 + 0.670431i 0.951596 0.307351i \(-0.0994424\pi\)
0.209625 + 0.977782i \(0.432776\pi\)
\(20\) 0.0685460 0.0395750i 0.0153273 0.00884925i
\(21\) 0 0
\(22\) −3.63490 6.29583i −0.774963 1.34228i
\(23\) −1.60488 −0.334640 −0.167320 0.985903i \(-0.553511\pi\)
−0.167320 + 0.985903i \(0.553511\pi\)
\(24\) 0 0
\(25\) −2.17522 + 3.76760i −0.435045 + 0.753520i
\(26\) 3.75219 3.26258i 0.735864 0.639844i
\(27\) 0 0
\(28\) 0.00687324 + 0.259741i 0.00129892 + 0.0490865i
\(29\) 1.14008 1.97467i 0.211707 0.366687i −0.740542 0.672010i \(-0.765431\pi\)
0.952249 + 0.305323i \(0.0987644\pi\)
\(30\) 0 0
\(31\) 3.01022 + 1.73795i 0.540651 + 0.312145i 0.745343 0.666681i \(-0.232286\pi\)
−0.204692 + 0.978827i \(0.565619\pi\)
\(32\) 0.555034i 0.0981171i
\(33\) 0 0
\(34\) 0.772411i 0.132467i
\(35\) 1.11465 + 1.81781i 0.188409 + 0.307266i
\(36\) 0 0
\(37\) 1.24196i 0.204177i 0.994775 + 0.102088i \(0.0325524\pi\)
−0.994775 + 0.102088i \(0.967448\pi\)
\(38\) −4.03007 + 6.98029i −0.653764 + 1.13235i
\(39\) 0 0
\(40\) 1.16602 + 2.01961i 0.184364 + 0.319329i
\(41\) −0.803413 0.463851i −0.125472 0.0724413i 0.435950 0.899971i \(-0.356412\pi\)
−0.561422 + 0.827529i \(0.689746\pi\)
\(42\) 0 0
\(43\) 2.22356 + 3.85131i 0.339089 + 0.587320i 0.984262 0.176717i \(-0.0565478\pi\)
−0.645172 + 0.764037i \(0.723214\pi\)
\(44\) −0.448348 + 0.258854i −0.0675910 + 0.0390237i
\(45\) 0 0
\(46\) 2.21321i 0.326320i
\(47\) 3.32915 1.92209i 0.485607 0.280365i −0.237143 0.971475i \(-0.576211\pi\)
0.722750 + 0.691109i \(0.242878\pi\)
\(48\) 0 0
\(49\) −6.99020 + 0.370207i −0.998601 + 0.0528867i
\(50\) −5.19572 2.99975i −0.734786 0.424229i
\(51\) 0 0
\(52\) −0.232340 0.267207i −0.0322197 0.0370549i
\(53\) 2.72727 4.72377i 0.374620 0.648860i −0.615650 0.788019i \(-0.711107\pi\)
0.990270 + 0.139159i \(0.0444400\pi\)
\(54\) 0 0
\(55\) −2.12431 + 3.67941i −0.286442 + 0.496132i
\(56\) −7.65292 + 0.202510i −1.02266 + 0.0270616i
\(57\) 0 0
\(58\) 2.72318 + 1.57223i 0.357571 + 0.206444i
\(59\) 10.9940i 1.43129i 0.698463 + 0.715646i \(0.253868\pi\)
−0.698463 + 0.715646i \(0.746132\pi\)
\(60\) 0 0
\(61\) −3.65107 + 6.32385i −0.467472 + 0.809686i −0.999309 0.0371610i \(-0.988169\pi\)
0.531837 + 0.846847i \(0.321502\pi\)
\(62\) −2.39673 + 4.15126i −0.304385 + 0.527210i
\(63\) 0 0
\(64\) −8.35330 −1.04416
\(65\) −2.74769 0.945710i −0.340809 0.117301i
\(66\) 0 0
\(67\) 6.36144 3.67278i 0.777174 0.448701i −0.0582541 0.998302i \(-0.518553\pi\)
0.835428 + 0.549600i \(0.185220\pi\)
\(68\) −0.0550061 −0.00667047
\(69\) 0 0
\(70\) −2.50686 + 1.53716i −0.299627 + 0.183725i
\(71\) 8.06668 4.65730i 0.957339 0.552720i 0.0619857 0.998077i \(-0.480257\pi\)
0.895353 + 0.445357i \(0.146923\pi\)
\(72\) 0 0
\(73\) 4.33139 + 2.50073i 0.506951 + 0.292688i 0.731579 0.681756i \(-0.238784\pi\)
−0.224629 + 0.974444i \(0.572117\pi\)
\(74\) −1.71273 −0.199101
\(75\) 0 0
\(76\) 0.497091 + 0.286996i 0.0570202 + 0.0329207i
\(77\) −7.29072 11.8900i −0.830854 1.35499i
\(78\) 0 0
\(79\) −5.68437 9.84562i −0.639542 1.10772i −0.985533 0.169481i \(-0.945791\pi\)
0.345992 0.938238i \(-0.387543\pi\)
\(80\) −2.64806 + 1.52886i −0.296062 + 0.170932i
\(81\) 0 0
\(82\) 0.639676 1.10795i 0.0706404 0.122353i
\(83\) 5.81962i 0.638786i −0.947622 0.319393i \(-0.896521\pi\)
0.947622 0.319393i \(-0.103479\pi\)
\(84\) 0 0
\(85\) −0.390935 + 0.225707i −0.0424029 + 0.0244813i
\(86\) −5.31117 + 3.06641i −0.572719 + 0.330659i
\(87\) 0 0
\(88\) −7.62677 13.2100i −0.813016 1.40819i
\(89\) 5.00946i 0.531001i −0.964111 0.265501i \(-0.914463\pi\)
0.964111 0.265501i \(-0.0855373\pi\)
\(90\) 0 0
\(91\) 7.03057 6.44756i 0.737004 0.675888i
\(92\) −0.157611 −0.0164320
\(93\) 0 0
\(94\) 2.65067 + 4.59109i 0.273395 + 0.473534i
\(95\) 4.71051 0.483289
\(96\) 0 0
\(97\) 9.22171 5.32416i 0.936323 0.540586i 0.0475172 0.998870i \(-0.484869\pi\)
0.888806 + 0.458284i \(0.151536\pi\)
\(98\) −0.510535 9.63988i −0.0515719 0.973774i
\(99\) 0 0
\(100\) −0.213623 + 0.370006i −0.0213623 + 0.0370006i
\(101\) −1.95777 3.39096i −0.194805 0.337413i 0.752031 0.659127i \(-0.229074\pi\)
−0.946837 + 0.321715i \(0.895741\pi\)
\(102\) 0 0
\(103\) 4.22690 + 7.32120i 0.416488 + 0.721379i 0.995583 0.0938810i \(-0.0299273\pi\)
−0.579095 + 0.815260i \(0.696594\pi\)
\(104\) 7.87287 6.84556i 0.771998 0.671262i
\(105\) 0 0
\(106\) 6.51434 + 3.76106i 0.632729 + 0.365306i
\(107\) 9.67522 0.935339 0.467670 0.883903i \(-0.345094\pi\)
0.467670 + 0.883903i \(0.345094\pi\)
\(108\) 0 0
\(109\) −12.6126 7.28189i −1.20807 0.697478i −0.245731 0.969338i \(-0.579028\pi\)
−0.962337 + 0.271860i \(0.912361\pi\)
\(110\) −5.07411 2.92954i −0.483798 0.279321i
\(111\) 0 0
\(112\) −0.265526 10.0343i −0.0250899 0.948153i
\(113\) 9.75572 + 16.8974i 0.917741 + 1.58957i 0.802838 + 0.596197i \(0.203322\pi\)
0.114903 + 0.993377i \(0.463344\pi\)
\(114\) 0 0
\(115\) −1.12016 + 0.646723i −0.104455 + 0.0603073i
\(116\) 0.111964 0.193927i 0.0103956 0.0180057i
\(117\) 0 0
\(118\) −15.1613 −1.39571
\(119\) −0.0391998 1.48137i −0.00359344 0.135797i
\(120\) 0 0
\(121\) 8.39477 14.5402i 0.763161 1.32183i
\(122\) −8.72093 5.03503i −0.789556 0.455850i
\(123\) 0 0
\(124\) 0.295626 + 0.170680i 0.0265480 + 0.0153275i
\(125\) 7.53598i 0.674038i
\(126\) 0 0
\(127\) −0.958656 + 1.66044i −0.0850670 + 0.147340i −0.905420 0.424517i \(-0.860444\pi\)
0.820353 + 0.571858i \(0.193777\pi\)
\(128\) 10.4096i 0.920087i
\(129\) 0 0
\(130\) 1.30419 3.78922i 0.114385 0.332337i
\(131\) 7.79078 + 13.4940i 0.680684 + 1.17898i 0.974772 + 0.223201i \(0.0716506\pi\)
−0.294089 + 0.955778i \(0.595016\pi\)
\(132\) 0 0
\(133\) −7.37484 + 13.5917i −0.639479 + 1.17855i
\(134\) 5.06496 + 8.77278i 0.437546 + 0.757852i
\(135\) 0 0
\(136\) 1.62068i 0.138972i
\(137\) 7.85105i 0.670761i 0.942083 + 0.335380i \(0.108865\pi\)
−0.942083 + 0.335380i \(0.891135\pi\)
\(138\) 0 0
\(139\) −4.96241 8.59514i −0.420906 0.729030i 0.575122 0.818067i \(-0.304954\pi\)
−0.996028 + 0.0890370i \(0.971621\pi\)
\(140\) 0.109466 + 0.178522i 0.00925160 + 0.0150879i
\(141\) 0 0
\(142\) 6.42267 + 11.1244i 0.538979 + 0.933538i
\(143\) 17.9722 + 6.18574i 1.50291 + 0.517278i
\(144\) 0 0
\(145\) 1.83769i 0.152612i
\(146\) −3.44864 + 5.97322i −0.285412 + 0.494347i
\(147\) 0 0
\(148\) 0.121969i 0.0100258i
\(149\) −6.85827 3.95962i −0.561851 0.324385i 0.192037 0.981388i \(-0.438491\pi\)
−0.753888 + 0.657003i \(0.771824\pi\)
\(150\) 0 0
\(151\) 1.30005 + 0.750582i 0.105796 + 0.0610815i 0.551965 0.833868i \(-0.313878\pi\)
−0.446168 + 0.894949i \(0.647212\pi\)
\(152\) −8.45592 + 14.6461i −0.685866 + 1.18795i
\(153\) 0 0
\(154\) 16.3970 10.0543i 1.32131 0.810198i
\(155\) 2.80140 0.225014
\(156\) 0 0
\(157\) −1.92846 + 3.34019i −0.153908 + 0.266576i −0.932661 0.360754i \(-0.882519\pi\)
0.778753 + 0.627331i \(0.215853\pi\)
\(158\) 13.5777 7.83906i 1.08018 0.623642i
\(159\) 0 0
\(160\) 0.223664 + 0.387398i 0.0176822 + 0.0306265i
\(161\) −0.112320 4.24462i −0.00885209 0.334523i
\(162\) 0 0
\(163\) 12.4369 + 7.18042i 0.974130 + 0.562414i 0.900493 0.434871i \(-0.143206\pi\)
0.0736372 + 0.997285i \(0.476539\pi\)
\(164\) −0.0789011 0.0455536i −0.00616114 0.00355714i
\(165\) 0 0
\(166\) 8.02557 0.622905
\(167\) 3.91563 + 2.26069i 0.303000 + 0.174937i 0.643790 0.765202i \(-0.277361\pi\)
−0.340790 + 0.940140i \(0.610694\pi\)
\(168\) 0 0
\(169\) −1.80593 + 12.8740i −0.138918 + 0.990304i
\(170\) −0.311262 0.539121i −0.0238727 0.0413487i
\(171\) 0 0
\(172\) 0.218370 + 0.378227i 0.0166505 + 0.0288396i
\(173\) 9.75896 16.9030i 0.741960 1.28511i −0.209642 0.977778i \(-0.567230\pi\)
0.951602 0.307334i \(-0.0994369\pi\)
\(174\) 0 0
\(175\) −10.1169 5.48940i −0.764764 0.414960i
\(176\) 17.3206 10.0000i 1.30559 0.753780i
\(177\) 0 0
\(178\) 6.90832 0.517800
\(179\) −10.4098 18.0303i −0.778065 1.34765i −0.933055 0.359733i \(-0.882868\pi\)
0.154990 0.987916i \(-0.450465\pi\)
\(180\) 0 0
\(181\) 16.5522 1.23031 0.615157 0.788405i \(-0.289093\pi\)
0.615157 + 0.788405i \(0.289093\pi\)
\(182\) 8.89155 + 9.69554i 0.659085 + 0.718681i
\(183\) 0 0
\(184\) 4.64378i 0.342344i
\(185\) 0.500477 + 0.866851i 0.0367958 + 0.0637322i
\(186\) 0 0
\(187\) 2.55704 1.47631i 0.186990 0.107958i
\(188\) 0.326948 0.188763i 0.0238451 0.0137670i
\(189\) 0 0
\(190\) 6.49606i 0.471274i
\(191\) −2.12504 + 3.68068i −0.153762 + 0.266324i −0.932608 0.360892i \(-0.882472\pi\)
0.778845 + 0.627216i \(0.215806\pi\)
\(192\) 0 0
\(193\) −10.0435 + 5.79861i −0.722946 + 0.417393i −0.815836 0.578283i \(-0.803723\pi\)
0.0928898 + 0.995676i \(0.470390\pi\)
\(194\) 7.34231 + 12.7172i 0.527147 + 0.913045i
\(195\) 0 0
\(196\) −0.686490 + 0.0363570i −0.0490350 + 0.00259693i
\(197\) 12.4892 + 7.21066i 0.889821 + 0.513738i 0.873884 0.486135i \(-0.161594\pi\)
0.0159371 + 0.999873i \(0.494927\pi\)
\(198\) 0 0
\(199\) −7.05924 −0.500416 −0.250208 0.968192i \(-0.580499\pi\)
−0.250208 + 0.968192i \(0.580499\pi\)
\(200\) −10.9017 6.29410i −0.770867 0.445060i
\(201\) 0 0
\(202\) 4.67632 2.69987i 0.329024 0.189962i
\(203\) 5.30245 + 2.87710i 0.372159 + 0.201933i
\(204\) 0 0
\(205\) −0.747680 −0.0522202
\(206\) −10.0963 + 5.82912i −0.703445 + 0.406134i
\(207\) 0 0
\(208\) 8.97572 + 10.3227i 0.622354 + 0.715751i
\(209\) −30.8107 −2.13122
\(210\) 0 0
\(211\) 13.2113 22.8827i 0.909505 1.57531i 0.0947513 0.995501i \(-0.469794\pi\)
0.814754 0.579807i \(-0.196872\pi\)
\(212\) 0.267838 0.463909i 0.0183952 0.0318614i
\(213\) 0 0
\(214\) 13.3427i 0.912086i
\(215\) 3.10396 + 1.79207i 0.211688 + 0.122218i
\(216\) 0 0
\(217\) −4.38590 + 8.08314i −0.297734 + 0.548719i
\(218\) 10.0421 17.3935i 0.680138 1.17803i
\(219\) 0 0
\(220\) −0.208623 + 0.361345i −0.0140654 + 0.0243619i
\(221\) 1.32509 + 1.52395i 0.0891353 + 0.102512i
\(222\) 0 0
\(223\) 19.9191 + 11.5003i 1.33388 + 0.770115i 0.985892 0.167384i \(-0.0535321\pi\)
0.347987 + 0.937499i \(0.386865\pi\)
\(224\) −1.46797 + 0.0388452i −0.0980828 + 0.00259545i
\(225\) 0 0
\(226\) −23.3024 + 13.4537i −1.55006 + 0.894925i
\(227\) 0.453367i 0.0300911i −0.999887 0.0150455i \(-0.995211\pi\)
0.999887 0.0150455i \(-0.00478932\pi\)
\(228\) 0 0
\(229\) 15.0112 8.66674i 0.991970 0.572714i 0.0861077 0.996286i \(-0.472557\pi\)
0.905863 + 0.423571i \(0.139224\pi\)
\(230\) −0.891867 1.54476i −0.0588080 0.101858i
\(231\) 0 0
\(232\) 5.71380 + 3.29886i 0.375129 + 0.216581i
\(233\) −3.90756 6.76809i −0.255992 0.443392i 0.709172 0.705035i \(-0.249069\pi\)
−0.965165 + 0.261643i \(0.915736\pi\)
\(234\) 0 0
\(235\) 1.54910 2.68313i 0.101052 0.175028i
\(236\) 1.07969i 0.0702818i
\(237\) 0 0
\(238\) 2.04289 0.0540587i 0.132421 0.00350411i
\(239\) 13.5314i 0.875276i −0.899151 0.437638i \(-0.855815\pi\)
0.899151 0.437638i \(-0.144185\pi\)
\(240\) 0 0
\(241\) 22.5592i 1.45317i 0.687078 + 0.726583i \(0.258893\pi\)
−0.687078 + 0.726583i \(0.741107\pi\)
\(242\) 20.0517 + 11.5768i 1.28897 + 0.744188i
\(243\) 0 0
\(244\) −0.358563 + 0.621049i −0.0229546 + 0.0397586i
\(245\) −4.72978 + 3.07526i −0.302175 + 0.196471i
\(246\) 0 0
\(247\) −4.02364 20.6856i −0.256018 1.31619i
\(248\) −5.02884 + 8.71020i −0.319331 + 0.553098i
\(249\) 0 0
\(250\) −10.3925 −0.657281
\(251\) 3.36618 + 5.83039i 0.212471 + 0.368011i 0.952487 0.304578i \(-0.0985154\pi\)
−0.740016 + 0.672589i \(0.765182\pi\)
\(252\) 0 0
\(253\) 7.32677 4.23011i 0.460630 0.265945i
\(254\) −2.28984 1.32204i −0.143677 0.0829521i
\(255\) 0 0
\(256\) −2.35120 −0.146950
\(257\) 16.5381 1.03162 0.515811 0.856703i \(-0.327491\pi\)
0.515811 + 0.856703i \(0.327491\pi\)
\(258\) 0 0
\(259\) −3.28476 + 0.0869209i −0.204105 + 0.00540100i
\(260\) −0.269844 0.0928757i −0.0167350 0.00575991i
\(261\) 0 0
\(262\) −18.6090 + 10.7439i −1.14967 + 0.663761i
\(263\) −5.01137 8.67994i −0.309014 0.535228i 0.669133 0.743143i \(-0.266666\pi\)
−0.978147 + 0.207915i \(0.933332\pi\)
\(264\) 0 0
\(265\) 4.39608i 0.270049i
\(266\) −18.7437 10.1703i −1.14925 0.623581i
\(267\) 0 0
\(268\) 0.624740 0.360694i 0.0381621 0.0220329i
\(269\) 15.7230 0.958647 0.479323 0.877638i \(-0.340882\pi\)
0.479323 + 0.877638i \(0.340882\pi\)
\(270\) 0 0
\(271\) 5.21618i 0.316860i −0.987370 0.158430i \(-0.949357\pi\)
0.987370 0.158430i \(-0.0506433\pi\)
\(272\) 2.12499 0.128847
\(273\) 0 0
\(274\) −10.8270 −0.654085
\(275\) 22.9337i 1.38296i
\(276\) 0 0
\(277\) 19.2724 1.15797 0.578983 0.815340i \(-0.303450\pi\)
0.578983 + 0.815340i \(0.303450\pi\)
\(278\) 11.8532 6.84343i 0.710906 0.410442i
\(279\) 0 0
\(280\) −5.25991 + 3.22527i −0.314340 + 0.192747i
\(281\) 2.14283i 0.127831i −0.997955 0.0639153i \(-0.979641\pi\)
0.997955 0.0639153i \(-0.0203588\pi\)
\(282\) 0 0
\(283\) −7.87512 13.6401i −0.468127 0.810820i 0.531209 0.847241i \(-0.321738\pi\)
−0.999337 + 0.0364203i \(0.988405\pi\)
\(284\) 0.792207 0.457381i 0.0470089 0.0271406i
\(285\) 0 0
\(286\) −8.53048 + 24.7847i −0.504418 + 1.46555i
\(287\) 1.17058 2.15735i 0.0690969 0.127344i
\(288\) 0 0
\(289\) −16.6863 −0.981546
\(290\) 2.53427 0.148817
\(291\) 0 0
\(292\) 0.425374 + 0.245590i 0.0248932 + 0.0143721i
\(293\) 20.0474 11.5744i 1.17118 0.676182i 0.217223 0.976122i \(-0.430300\pi\)
0.953958 + 0.299940i \(0.0969668\pi\)
\(294\) 0 0
\(295\) 4.43029 + 7.67348i 0.257941 + 0.446767i
\(296\) −3.59366 −0.208877
\(297\) 0 0
\(298\) 5.46054 9.45793i 0.316320 0.547883i
\(299\) 3.79682 + 4.36661i 0.219576 + 0.252528i
\(300\) 0 0
\(301\) −10.0304 + 6.15046i −0.578145 + 0.354507i
\(302\) −1.03509 + 1.79283i −0.0595629 + 0.103166i
\(303\) 0 0
\(304\) −19.2036 11.0872i −1.10140 0.635894i
\(305\) 5.88515i 0.336983i
\(306\) 0 0
\(307\) 4.23590i 0.241756i −0.992667 0.120878i \(-0.961429\pi\)
0.992667 0.120878i \(-0.0385709\pi\)
\(308\) −0.716002 1.16769i −0.0407980 0.0665351i
\(309\) 0 0
\(310\) 3.86328i 0.219420i
\(311\) −13.6251 + 23.5993i −0.772606 + 1.33819i 0.163524 + 0.986539i \(0.447714\pi\)
−0.936130 + 0.351654i \(0.885619\pi\)
\(312\) 0 0
\(313\) −1.34849 2.33565i −0.0762209 0.132018i 0.825396 0.564555i \(-0.190952\pi\)
−0.901617 + 0.432536i \(0.857619\pi\)
\(314\) −4.60631 2.65945i −0.259949 0.150082i
\(315\) 0 0
\(316\) −0.558247 0.966913i −0.0314039 0.0543931i
\(317\) −20.8456 + 12.0352i −1.17081 + 0.675966i −0.953870 0.300220i \(-0.902940\pi\)
−0.216937 + 0.976186i \(0.569607\pi\)
\(318\) 0 0
\(319\) 12.0200i 0.672991i
\(320\) −5.83037 + 3.36617i −0.325928 + 0.188174i
\(321\) 0 0
\(322\) 5.85356 0.154896i 0.326206 0.00863202i
\(323\) −2.83504 1.63681i −0.157746 0.0910745i
\(324\) 0 0
\(325\) 15.3972 2.99497i 0.854082 0.166131i
\(326\) −9.90220 + 17.1511i −0.548432 + 0.949912i
\(327\) 0 0
\(328\) 1.34217 2.32471i 0.0741091 0.128361i
\(329\) 5.31659 + 8.67051i 0.293113 + 0.478021i
\(330\) 0 0
\(331\) 0.536696 + 0.309862i 0.0294995 + 0.0170315i 0.514677 0.857384i \(-0.327912\pi\)
−0.485178 + 0.874416i \(0.661245\pi\)
\(332\) 0.571530i 0.0313668i
\(333\) 0 0
\(334\) −3.11762 + 5.39987i −0.170588 + 0.295468i
\(335\) 2.96007 5.12699i 0.161726 0.280117i
\(336\) 0 0
\(337\) −5.72118 −0.311652 −0.155826 0.987784i \(-0.549804\pi\)
−0.155826 + 0.987784i \(0.549804\pi\)
\(338\) −17.7539 2.49048i −0.965684 0.135464i
\(339\) 0 0
\(340\) −0.0383927 + 0.0221660i −0.00208214 + 0.00120212i
\(341\) −18.3235 −0.992272
\(342\) 0 0
\(343\) −1.46836 18.4620i −0.0792837 0.996852i
\(344\) −11.1439 + 6.43396i −0.600841 + 0.346896i
\(345\) 0 0
\(346\) 23.3102 + 13.4581i 1.25316 + 0.723514i
\(347\) 1.86486 0.100111 0.0500554 0.998746i \(-0.484060\pi\)
0.0500554 + 0.998746i \(0.484060\pi\)
\(348\) 0 0
\(349\) −19.3273 11.1586i −1.03457 0.597307i −0.116277 0.993217i \(-0.537096\pi\)
−0.918290 + 0.395909i \(0.870429\pi\)
\(350\) 7.57019 13.9517i 0.404644 0.745751i
\(351\) 0 0
\(352\) −1.46295 2.53391i −0.0779756 0.135058i
\(353\) −2.01956 + 1.16600i −0.107491 + 0.0620597i −0.552781 0.833326i \(-0.686434\pi\)
0.445291 + 0.895386i \(0.353100\pi\)
\(354\) 0 0
\(355\) 3.75354 6.50133i 0.199217 0.345055i
\(356\) 0.491966i 0.0260741i
\(357\) 0 0
\(358\) 24.8648 14.3557i 1.31415 0.758722i
\(359\) 2.83281 1.63553i 0.149510 0.0863197i −0.423379 0.905953i \(-0.639156\pi\)
0.572889 + 0.819633i \(0.305823\pi\)
\(360\) 0 0
\(361\) 7.58017 + 13.1292i 0.398956 + 0.691013i
\(362\) 22.8264i 1.19973i
\(363\) 0 0
\(364\) 0.690454 0.633198i 0.0361896 0.0331886i
\(365\) 4.03092 0.210988
\(366\) 0 0
\(367\) −2.07645 3.59652i −0.108390 0.187737i 0.806728 0.590923i \(-0.201236\pi\)
−0.915118 + 0.403186i \(0.867903\pi\)
\(368\) 6.08880 0.317401
\(369\) 0 0
\(370\) −1.19544 + 0.690185i −0.0621477 + 0.0358810i
\(371\) 12.6844 + 6.88256i 0.658543 + 0.357325i
\(372\) 0 0
\(373\) 5.55446 9.62061i 0.287599 0.498136i −0.685637 0.727944i \(-0.740476\pi\)
0.973236 + 0.229807i \(0.0738096\pi\)
\(374\) 2.03591 + 3.52630i 0.105275 + 0.182341i
\(375\) 0 0
\(376\) 5.56165 + 9.63305i 0.286820 + 0.496787i
\(377\) −8.06996 + 1.56972i −0.415624 + 0.0808447i
\(378\) 0 0
\(379\) −4.01862 2.32015i −0.206422 0.119178i 0.393225 0.919442i \(-0.371359\pi\)
−0.599648 + 0.800264i \(0.704693\pi\)
\(380\) 0.462607 0.0237312
\(381\) 0 0
\(382\) −5.07586 2.93055i −0.259703 0.149940i
\(383\) 3.17773 + 1.83466i 0.162374 + 0.0937469i 0.578985 0.815338i \(-0.303449\pi\)
−0.416611 + 0.909085i \(0.636782\pi\)
\(384\) 0 0
\(385\) −9.88008 5.36092i −0.503535 0.273218i
\(386\) −7.99661 13.8505i −0.407017 0.704973i
\(387\) 0 0
\(388\) 0.905640 0.522872i 0.0459769 0.0265448i
\(389\) −8.44156 + 14.6212i −0.428004 + 0.741324i −0.996696 0.0812262i \(-0.974116\pi\)
0.568692 + 0.822551i \(0.307450\pi\)
\(390\) 0 0
\(391\) 0.898894 0.0454590
\(392\) −1.07121 20.2265i −0.0541042 1.02159i
\(393\) 0 0
\(394\) −9.94390 + 17.2233i −0.500966 + 0.867699i
\(395\) −7.93506 4.58131i −0.399256 0.230511i
\(396\) 0 0
\(397\) −14.4700 8.35428i −0.726230 0.419289i 0.0908114 0.995868i \(-0.471054\pi\)
−0.817041 + 0.576579i \(0.804387\pi\)
\(398\) 9.73508i 0.487976i
\(399\) 0 0
\(400\) 8.25267 14.2940i 0.412633 0.714702i
\(401\) 25.3134i 1.26409i −0.774931 0.632046i \(-0.782215\pi\)
0.774931 0.632046i \(-0.217785\pi\)
\(402\) 0 0
\(403\) −2.39291 12.3020i −0.119199 0.612805i
\(404\) −0.192267 0.333017i −0.00956566 0.0165682i
\(405\) 0 0
\(406\) −3.96768 + 7.31237i −0.196913 + 0.362907i
\(407\) −3.27354 5.66994i −0.162263 0.281048i
\(408\) 0 0
\(409\) 5.73343i 0.283500i −0.989903 0.141750i \(-0.954727\pi\)
0.989903 0.141750i \(-0.0452729\pi\)
\(410\) 1.03109i 0.0509220i
\(411\) 0 0
\(412\) 0.415112 + 0.718996i 0.0204511 + 0.0354224i
\(413\) −29.0771 + 0.769435i −1.43079 + 0.0378614i
\(414\) 0 0
\(415\) −2.34516 4.06193i −0.115119 0.199392i
\(416\) 1.51016 1.31310i 0.0740416 0.0643801i
\(417\) 0 0
\(418\) 42.4897i 2.07824i
\(419\) −17.1729 + 29.7443i −0.838950 + 1.45310i 0.0518229 + 0.998656i \(0.483497\pi\)
−0.890773 + 0.454448i \(0.849836\pi\)
\(420\) 0 0
\(421\) 2.94167i 0.143368i 0.997427 + 0.0716842i \(0.0228374\pi\)
−0.997427 + 0.0716842i \(0.977163\pi\)
\(422\) 31.5565 + 18.2191i 1.53614 + 0.886894i
\(423\) 0 0
\(424\) 13.6684 + 7.89148i 0.663798 + 0.383244i
\(425\) 1.21835 2.11024i 0.0590985 0.102362i
\(426\) 0 0
\(427\) −16.9810 9.21387i −0.821768 0.445890i
\(428\) 0.950178 0.0459286
\(429\) 0 0
\(430\) −2.47137 + 4.28053i −0.119180 + 0.206426i
\(431\) −34.3773 + 19.8478i −1.65590 + 0.956033i −0.681321 + 0.731985i \(0.738594\pi\)
−0.974578 + 0.224048i \(0.928073\pi\)
\(432\) 0 0
\(433\) −4.91827 8.51869i −0.236357 0.409382i 0.723309 0.690524i \(-0.242620\pi\)
−0.959666 + 0.281142i \(0.909287\pi\)
\(434\) −11.1471 6.04840i −0.535078 0.290332i
\(435\) 0 0
\(436\) −1.23865 0.715135i −0.0593206 0.0342488i
\(437\) −8.12331 4.69000i −0.388591 0.224353i
\(438\) 0 0
\(439\) −28.5465 −1.36245 −0.681226 0.732073i \(-0.738553\pi\)
−0.681226 + 0.732073i \(0.738553\pi\)
\(440\) −10.6465 6.14678i −0.507554 0.293036i
\(441\) 0 0
\(442\) −2.10161 + 1.82737i −0.0999632 + 0.0869193i
\(443\) 1.66951 + 2.89167i 0.0793207 + 0.137387i 0.902957 0.429731i \(-0.141392\pi\)
−0.823636 + 0.567118i \(0.808058\pi\)
\(444\) 0 0
\(445\) −2.01868 3.49646i −0.0956947 0.165748i
\(446\) −15.8595 + 27.4695i −0.750969 + 1.30072i
\(447\) 0 0
\(448\) −0.584622 22.0930i −0.0276208 1.04380i
\(449\) −15.7487 + 9.09253i −0.743228 + 0.429103i −0.823242 0.567691i \(-0.807837\pi\)
0.0800136 + 0.996794i \(0.474504\pi\)
\(450\) 0 0
\(451\) 4.89045 0.230282
\(452\) 0.958084 + 1.65945i 0.0450645 + 0.0780539i
\(453\) 0 0
\(454\) 0.625219 0.0293430
\(455\) 2.30894 7.33336i 0.108245 0.343793i
\(456\) 0 0
\(457\) 8.72932i 0.408341i 0.978935 + 0.204170i \(0.0654496\pi\)
−0.978935 + 0.204170i \(0.934550\pi\)
\(458\) 11.9519 + 20.7013i 0.558476 + 0.967309i
\(459\) 0 0
\(460\) −0.110008 + 0.0635130i −0.00512914 + 0.00296131i
\(461\) 1.96695 1.13562i 0.0916099 0.0528910i −0.453495 0.891259i \(-0.649823\pi\)
0.545105 + 0.838368i \(0.316490\pi\)
\(462\) 0 0
\(463\) 5.48326i 0.254829i 0.991850 + 0.127414i \(0.0406678\pi\)
−0.991850 + 0.127414i \(0.959332\pi\)
\(464\) −4.32538 + 7.49178i −0.200801 + 0.347797i
\(465\) 0 0
\(466\) 9.33356 5.38873i 0.432369 0.249628i
\(467\) −9.44095 16.3522i −0.436875 0.756690i 0.560572 0.828106i \(-0.310581\pi\)
−0.997447 + 0.0714164i \(0.977248\pi\)
\(468\) 0 0
\(469\) 10.1591 + 16.5679i 0.469103 + 0.765032i
\(470\) 3.70018 + 2.13630i 0.170677 + 0.0985401i
\(471\) 0 0
\(472\) −31.8115 −1.46424
\(473\) −20.3025 11.7217i −0.933510 0.538962i
\(474\) 0 0
\(475\) −22.0204 + 12.7135i −1.01037 + 0.583335i
\(476\) −0.00384971 0.145482i −0.000176451 0.00666814i
\(477\) 0 0
\(478\) 18.6606 0.853516
\(479\) 28.6961 16.5677i 1.31116 0.756997i 0.328869 0.944375i \(-0.393332\pi\)
0.982288 + 0.187378i \(0.0599991\pi\)
\(480\) 0 0
\(481\) 3.37917 2.93823i 0.154077 0.133972i
\(482\) −31.1104 −1.41704
\(483\) 0 0
\(484\) 0.824428 1.42795i 0.0374740 0.0649069i
\(485\) 4.29100 7.43222i 0.194844 0.337480i
\(486\) 0 0
\(487\) 15.9563i 0.723048i 0.932363 + 0.361524i \(0.117743\pi\)
−0.932363 + 0.361524i \(0.882257\pi\)
\(488\) −18.2983 10.5645i −0.828326 0.478234i
\(489\) 0 0
\(490\) −4.24096 6.52263i −0.191587 0.294662i
\(491\) 15.8464 27.4468i 0.715138 1.23866i −0.247769 0.968819i \(-0.579697\pi\)
0.962906 0.269836i \(-0.0869694\pi\)
\(492\) 0 0
\(493\) −0.638559 + 1.10602i −0.0287593 + 0.0498125i
\(494\) 28.5266 5.54882i 1.28347 0.249653i
\(495\) 0 0
\(496\) −11.4206 6.59368i −0.512800 0.296065i
\(497\) 12.8823 + 21.0090i 0.577850 + 0.942383i
\(498\) 0 0
\(499\) 20.9738 12.1092i 0.938916 0.542083i 0.0492955 0.998784i \(-0.484302\pi\)
0.889620 + 0.456701i \(0.150969\pi\)
\(500\) 0.740089i 0.0330978i
\(501\) 0 0
\(502\) −8.04043 + 4.64215i −0.358862 + 0.207189i
\(503\) 0.427249 + 0.740017i 0.0190501 + 0.0329957i 0.875393 0.483411i \(-0.160602\pi\)
−0.856343 + 0.516407i \(0.827269\pi\)
\(504\) 0 0
\(505\) −2.73294 1.57786i −0.121614 0.0702139i
\(506\) 5.83356 + 10.1040i 0.259333 + 0.449179i
\(507\) 0 0
\(508\) −0.0941471 + 0.163068i −0.00417710 + 0.00723495i
\(509\) 1.30000i 0.0576215i 0.999585 + 0.0288108i \(0.00917202\pi\)
−0.999585 + 0.0288108i \(0.990828\pi\)
\(510\) 0 0
\(511\) −6.31085 + 11.6308i −0.279176 + 0.514516i
\(512\) 24.0616i 1.06338i
\(513\) 0 0
\(514\) 22.8070i 1.00597i
\(515\) 5.90051 + 3.40666i 0.260007 + 0.150115i
\(516\) 0 0
\(517\) −10.1324 + 17.5499i −0.445624 + 0.771844i
\(518\) −0.119869 4.52987i −0.00526673 0.199031i
\(519\) 0 0
\(520\) 2.73645 7.95057i 0.120001 0.348655i
\(521\) −12.5228 + 21.6901i −0.548632 + 0.950259i 0.449736 + 0.893161i \(0.351518\pi\)
−0.998369 + 0.0570974i \(0.981815\pi\)
\(522\) 0 0
\(523\) 12.8239 0.560752 0.280376 0.959890i \(-0.409541\pi\)
0.280376 + 0.959890i \(0.409541\pi\)
\(524\) 0.765112 + 1.32521i 0.0334241 + 0.0578922i
\(525\) 0 0
\(526\) 11.9701 6.91095i 0.521922 0.301332i
\(527\) −1.68603 0.973429i −0.0734446 0.0424032i
\(528\) 0 0
\(529\) −20.4244 −0.888016
\(530\) 6.06244 0.263335
\(531\) 0 0
\(532\) −0.724263 + 1.33480i −0.0314008 + 0.0578711i
\(533\) 0.638656 + 3.28334i 0.0276632 + 0.142217i
\(534\) 0 0
\(535\) 6.75303 3.89886i 0.291959 0.168563i
\(536\) 10.6273 + 18.4071i 0.459031 + 0.795066i
\(537\) 0 0
\(538\) 21.6828i 0.934814i
\(539\) 30.9367 20.1148i 1.33254 0.866406i
\(540\) 0 0
\(541\) −24.8938 + 14.3725i −1.07027 + 0.617920i −0.928255 0.371944i \(-0.878691\pi\)
−0.142014 + 0.989865i \(0.545358\pi\)
\(542\) 7.19340 0.308983
\(543\) 0 0
\(544\) 0.310876i 0.0133287i
\(545\) −11.7376 −0.502785
\(546\) 0 0
\(547\) −8.88085 −0.379718 −0.189859 0.981811i \(-0.560803\pi\)
−0.189859 + 0.981811i \(0.560803\pi\)
\(548\) 0.771031i 0.0329368i
\(549\) 0 0
\(550\) 31.6269 1.34857
\(551\) 11.5413 6.66339i 0.491677 0.283870i
\(552\) 0 0
\(553\) 25.6421 15.7232i 1.09041 0.668620i
\(554\) 26.5777i 1.12918i
\(555\) 0 0
\(556\) −0.487345 0.844106i −0.0206680 0.0357981i
\(557\) −33.5389 + 19.3637i −1.42109 + 0.820465i −0.996392 0.0848711i \(-0.972952\pi\)
−0.424695 + 0.905336i \(0.639619\pi\)
\(558\) 0 0
\(559\) 5.21830 15.1614i 0.220711 0.641259i
\(560\) −4.22890 6.89666i −0.178704 0.291437i
\(561\) 0 0
\(562\) 2.95508 0.124653
\(563\) 6.90882 0.291172 0.145586 0.989346i \(-0.453493\pi\)
0.145586 + 0.989346i \(0.453493\pi\)
\(564\) 0 0
\(565\) 13.6184 + 7.86260i 0.572932 + 0.330782i
\(566\) 18.8105 10.8602i 0.790663 0.456489i
\(567\) 0 0
\(568\) 13.4761 + 23.3413i 0.565444 + 0.979379i
\(569\) −2.83745 −0.118952 −0.0594759 0.998230i \(-0.518943\pi\)
−0.0594759 + 0.998230i \(0.518943\pi\)
\(570\) 0 0
\(571\) −23.3362 + 40.4195i −0.976589 + 1.69150i −0.302001 + 0.953307i \(0.597655\pi\)
−0.674588 + 0.738195i \(0.735679\pi\)
\(572\) 1.76500 + 0.607485i 0.0737985 + 0.0254002i
\(573\) 0 0
\(574\) 2.97511 + 1.61429i 0.124179 + 0.0673791i
\(575\) 3.49096 6.04653i 0.145583 0.252158i
\(576\) 0 0
\(577\) −9.88033 5.70441i −0.411323 0.237478i 0.280035 0.959990i \(-0.409654\pi\)
−0.691358 + 0.722512i \(0.742987\pi\)
\(578\) 23.0113i 0.957144i
\(579\) 0 0
\(580\) 0.180474i 0.00749379i
\(581\) 15.3919 0.407298i 0.638563 0.0168975i
\(582\) 0 0
\(583\) 28.7541i 1.19087i
\(584\) −7.23597 + 12.5331i −0.299426 + 0.518622i
\(585\) 0 0
\(586\) 15.9617 + 27.6465i 0.659371 + 1.14206i
\(587\) 40.2191 + 23.2205i 1.66002 + 0.958413i 0.972702 + 0.232057i \(0.0745456\pi\)
0.687318 + 0.726356i \(0.258788\pi\)
\(588\) 0 0
\(589\) 10.1578 + 17.5938i 0.418544 + 0.724939i
\(590\) −10.5821 + 6.10961i −0.435660 + 0.251529i
\(591\) 0 0
\(592\) 4.71191i 0.193658i
\(593\) −17.5462 + 10.1303i −0.720535 + 0.416001i −0.814950 0.579532i \(-0.803235\pi\)
0.0944146 + 0.995533i \(0.469902\pi\)
\(594\) 0 0
\(595\) −0.624315 1.01816i −0.0255944 0.0417404i
\(596\) −0.673533 0.388864i −0.0275890 0.0159285i
\(597\) 0 0
\(598\) −6.02179 + 5.23603i −0.246249 + 0.214117i
\(599\) −19.4938 + 33.7642i −0.796494 + 1.37957i 0.125391 + 0.992107i \(0.459981\pi\)
−0.921886 + 0.387462i \(0.873352\pi\)
\(600\) 0 0
\(601\) −9.56951 + 16.5749i −0.390348 + 0.676103i −0.992495 0.122282i \(-0.960979\pi\)
0.602147 + 0.798385i \(0.294312\pi\)
\(602\) −8.48182 13.8325i −0.345693 0.563771i
\(603\) 0 0
\(604\) 0.127674 + 0.0737127i 0.00519499 + 0.00299933i
\(605\) 13.5315i 0.550134i
\(606\) 0 0
\(607\) −21.6668 + 37.5280i −0.879428 + 1.52321i −0.0274572 + 0.999623i \(0.508741\pi\)
−0.851970 + 0.523590i \(0.824592\pi\)
\(608\) −1.62200 + 2.80939i −0.0657808 + 0.113936i
\(609\) 0 0
\(610\) −8.11595 −0.328605
\(611\) −13.1058 4.51081i −0.530205 0.182488i
\(612\) 0 0
\(613\) 8.92834 5.15478i 0.360612 0.208200i −0.308737 0.951147i \(-0.599906\pi\)
0.669349 + 0.742948i \(0.266573\pi\)
\(614\) 5.84154 0.235745
\(615\) 0 0
\(616\) 34.4042 21.0960i 1.38619 0.849982i
\(617\) 9.58684 5.53497i 0.385952 0.222829i −0.294453 0.955666i \(-0.595137\pi\)
0.680405 + 0.732837i \(0.261804\pi\)
\(618\) 0 0
\(619\) 29.2384 + 16.8808i 1.17519 + 0.678498i 0.954897 0.296936i \(-0.0959647\pi\)
0.220295 + 0.975433i \(0.429298\pi\)
\(620\) 0.275118 0.0110490
\(621\) 0 0
\(622\) −32.5447 18.7897i −1.30492 0.753399i
\(623\) 13.2491 0.350597i 0.530816 0.0140464i
\(624\) 0 0
\(625\) −7.83931 13.5781i −0.313573 0.543124i
\(626\) 3.22098 1.85964i 0.128736 0.0743260i
\(627\) 0 0
\(628\) −0.189389 + 0.328031i −0.00755745 + 0.0130899i
\(629\) 0.695623i 0.0277363i
\(630\) 0 0
\(631\) 33.4264 19.2987i 1.33068 0.768271i 0.345280 0.938500i \(-0.387784\pi\)
0.985405 + 0.170229i \(0.0544507\pi\)
\(632\) 28.4887 16.4480i 1.13322 0.654265i
\(633\) 0 0
\(634\) −16.5972 28.7473i −0.659161 1.14170i
\(635\) 1.54525i 0.0613215i
\(636\) 0 0
\(637\) 17.5447 + 18.1434i 0.695148 + 0.718867i
\(638\) −16.5763 −0.656260
\(639\) 0 0
\(640\) −4.19480 7.26560i −0.165814 0.287198i
\(641\) 19.5228 0.771105 0.385553 0.922686i \(-0.374011\pi\)
0.385553 + 0.922686i \(0.374011\pi\)
\(642\) 0 0
\(643\) 10.8009 6.23589i 0.425945 0.245920i −0.271673 0.962390i \(-0.587577\pi\)
0.697618 + 0.716470i \(0.254243\pi\)
\(644\) −0.0110307 0.416853i −0.000434670 0.0164263i
\(645\) 0 0
\(646\) 2.25725 3.90967i 0.0888103 0.153824i
\(647\) −17.9695 31.1241i −0.706455 1.22362i −0.966164 0.257929i \(-0.916960\pi\)
0.259709 0.965687i \(-0.416373\pi\)
\(648\) 0 0
\(649\) −28.9778 50.1910i −1.13748 1.97017i
\(650\) 4.13023 + 21.2336i 0.162001 + 0.832849i
\(651\) 0 0
\(652\) 1.22139 + 0.705171i 0.0478334 + 0.0276166i
\(653\) −4.85888 −0.190143 −0.0950713 0.995470i \(-0.530308\pi\)
−0.0950713 + 0.995470i \(0.530308\pi\)
\(654\) 0 0
\(655\) 10.8755 + 6.27897i 0.424941 + 0.245340i
\(656\) 3.04810 + 1.75982i 0.119008 + 0.0687095i
\(657\) 0 0
\(658\) −11.9571 + 7.33186i −0.466137 + 0.285826i
\(659\) −11.8103 20.4560i −0.460063 0.796853i 0.538900 0.842370i \(-0.318840\pi\)
−0.998964 + 0.0455166i \(0.985507\pi\)
\(660\) 0 0
\(661\) 14.1970 8.19662i 0.552198 0.318812i −0.197810 0.980240i \(-0.563383\pi\)
0.750008 + 0.661429i \(0.230050\pi\)
\(662\) −0.427316 + 0.740134i −0.0166081 + 0.0287661i
\(663\) 0 0
\(664\) 16.8393 0.653492
\(665\) 0.329675 + 12.4585i 0.0127842 + 0.483119i
\(666\) 0 0
\(667\) −1.82968 + 3.16910i −0.0708456 + 0.122708i
\(668\) 0.384544 + 0.222016i 0.0148784 + 0.00859007i
\(669\) 0 0
\(670\) 7.07040 + 4.08210i 0.273154 + 0.157705i
\(671\) 38.4939i 1.48604i
\(672\) 0 0
\(673\) −7.12678 + 12.3439i −0.274717 + 0.475824i −0.970064 0.242851i \(-0.921918\pi\)
0.695347 + 0.718675i \(0.255251\pi\)
\(674\) 7.88982i 0.303904i
\(675\) 0 0
\(676\) −0.177356 + 1.26432i −0.00682138 + 0.0486276i
\(677\) −5.13574 8.89537i −0.197383 0.341877i 0.750296 0.661102i \(-0.229911\pi\)
−0.947679 + 0.319225i \(0.896577\pi\)
\(678\) 0 0
\(679\) 14.7269 + 24.0172i 0.565165 + 0.921695i
\(680\) −0.653092 1.13119i −0.0250449 0.0433791i
\(681\) 0 0
\(682\) 25.2691i 0.967604i
\(683\) 2.22201i 0.0850230i 0.999096 + 0.0425115i \(0.0135359\pi\)
−0.999096 + 0.0425115i \(0.986464\pi\)
\(684\) 0 0
\(685\) 3.16377 + 5.47981i 0.120881 + 0.209373i
\(686\) 25.4601 2.02494i 0.972069 0.0773127i
\(687\) 0 0
\(688\) −8.43604 14.6117i −0.321621 0.557064i
\(689\) −19.3048 + 3.75506i −0.735455 + 0.143056i
\(690\) 0 0
\(691\) 2.64015i 0.100436i 0.998738 + 0.0502179i \(0.0159916\pi\)
−0.998738 + 0.0502179i \(0.984008\pi\)
\(692\) 0.958402 1.66000i 0.0364330 0.0631038i
\(693\) 0 0
\(694\) 2.57174i 0.0976220i
\(695\) −6.92724 3.99944i −0.262765 0.151708i
\(696\) 0 0
\(697\) 0.449993 + 0.259804i 0.0170447 + 0.00984077i
\(698\) 15.3884 26.6534i 0.582458 1.00885i
\(699\) 0 0
\(700\) −0.993552 0.539100i −0.0375527 0.0203761i
\(701\) 8.89991 0.336145 0.168072 0.985775i \(-0.446246\pi\)
0.168072 + 0.985775i \(0.446246\pi\)
\(702\) 0 0
\(703\) −3.62943 + 6.28635i −0.136886 + 0.237094i
\(704\) 38.1355 22.0175i 1.43729 0.829818i
\(705\) 0 0
\(706\) −1.60797 2.78509i −0.0605168 0.104818i
\(707\) 8.83147 5.41528i 0.332142 0.203663i
\(708\) 0 0
\(709\) −35.1558 20.2972i −1.32030 0.762278i −0.336527 0.941674i \(-0.609252\pi\)
−0.983777 + 0.179396i \(0.942586\pi\)
\(710\) 8.96569 + 5.17634i 0.336476 + 0.194265i
\(711\) 0 0
\(712\) 14.4951 0.543226
\(713\) −4.83103 2.78920i −0.180923 0.104456i
\(714\) 0 0
\(715\) 15.0368 2.92487i 0.562344 0.109384i
\(716\) −1.02232 1.77071i −0.0382059 0.0661745i
\(717\) 0 0
\(718\) 2.25548 + 3.90661i 0.0841738 + 0.145793i
\(719\) −7.25674 + 12.5690i −0.270631 + 0.468746i −0.969024 0.246968i \(-0.920566\pi\)
0.698393 + 0.715715i \(0.253899\pi\)
\(720\) 0 0
\(721\) −19.0675 + 11.6918i −0.710109 + 0.435425i
\(722\) −18.1059 + 10.4535i −0.673834 + 0.389038i
\(723\) 0 0
\(724\) 1.62555 0.0604129
\(725\) 4.95984 + 8.59070i 0.184204 + 0.319051i
\(726\) 0 0
\(727\) 30.6942 1.13839 0.569193 0.822204i \(-0.307256\pi\)
0.569193 + 0.822204i \(0.307256\pi\)
\(728\) 18.6563 + 20.3433i 0.691449 + 0.753971i
\(729\) 0 0
\(730\) 5.55885i 0.205742i
\(731\) −1.24542 2.15713i −0.0460635 0.0797842i
\(732\) 0 0
\(733\) −11.4873 + 6.63218i −0.424292 + 0.244965i −0.696912 0.717157i \(-0.745443\pi\)
0.272620 + 0.962122i \(0.412110\pi\)
\(734\) 4.95980 2.86354i 0.183069 0.105695i
\(735\) 0 0
\(736\) 0.890761i 0.0328339i
\(737\) −19.3613 + 33.5348i −0.713184 + 1.23527i
\(738\) 0 0
\(739\) −6.28279 + 3.62737i −0.231116 + 0.133435i −0.611087 0.791564i \(-0.709267\pi\)
0.379971 + 0.924999i \(0.375934\pi\)
\(740\) 0.0491505 + 0.0851312i 0.00180681 + 0.00312948i
\(741\) 0 0
\(742\) −9.49142 + 17.4925i −0.348441 + 0.642171i
\(743\) 40.0705 + 23.1347i 1.47004 + 0.848730i 0.999435 0.0336128i \(-0.0107013\pi\)
0.470608 + 0.882342i \(0.344035\pi\)
\(744\) 0 0
\(745\) −6.38250 −0.233837
\(746\) 13.2673 + 7.65991i 0.485752 + 0.280449i
\(747\) 0 0
\(748\) 0.251121 0.144985i 0.00918188 0.00530116i
\(749\) 0.677140 + 25.5893i 0.0247421 + 0.935012i
\(750\) 0 0
\(751\) 36.0260 1.31461 0.657305 0.753625i \(-0.271697\pi\)
0.657305 + 0.753625i \(0.271697\pi\)
\(752\) −12.6306 + 7.29229i −0.460591 + 0.265922i
\(753\) 0 0
\(754\) −2.16473 11.1289i −0.0788349 0.405291i
\(755\) 1.20986 0.0440313
\(756\) 0 0
\(757\) 5.28132 9.14751i 0.191953 0.332472i −0.753945 0.656938i \(-0.771851\pi\)
0.945897 + 0.324466i \(0.105185\pi\)
\(758\) 3.19961 5.54189i 0.116215 0.201291i
\(759\) 0 0
\(760\) 13.6301i 0.494415i
\(761\) −6.76541 3.90601i −0.245246 0.141593i 0.372340 0.928097i \(-0.378556\pi\)
−0.617585 + 0.786504i \(0.711889\pi\)
\(762\) 0 0
\(763\) 18.3766 33.8678i 0.665278 1.22609i
\(764\) −0.208695 + 0.361470i −0.00755031 + 0.0130775i
\(765\) 0 0
\(766\) −2.53010 + 4.38226i −0.0914163 + 0.158338i
\(767\) 29.9128 26.0096i 1.08009 0.939152i
\(768\) 0 0
\(769\) 21.9030 + 12.6457i 0.789844 + 0.456017i 0.839908 0.542729i \(-0.182609\pi\)
−0.0500637 + 0.998746i \(0.515942\pi\)
\(770\) 7.39300 13.6252i 0.266425 0.491017i
\(771\) 0 0
\(772\) −0.986345 + 0.569467i −0.0354993 + 0.0204956i
\(773\) 46.6004i 1.67610i −0.545592 0.838051i \(-0.683695\pi\)
0.545592 0.838051i \(-0.316305\pi\)
\(774\) 0 0
\(775\) −13.0958 + 7.56086i −0.470415 + 0.271594i
\(776\) 15.4057 + 26.6834i 0.553032 + 0.957879i
\(777\) 0 0
\(778\) −20.1634 11.6414i −0.722895 0.417363i
\(779\) −2.71106 4.69570i −0.0971339 0.168241i
\(780\) 0 0
\(781\) −24.5513 + 42.5241i −0.878515 + 1.52163i
\(782\) 1.23962i 0.0443289i
\(783\) 0 0
\(784\) 26.5204 1.40454i 0.947158 0.0501622i
\(785\) 3.10848i 0.110946i
\(786\) 0 0