Properties

Label 441.2.f.e.295.4
Level $441$
Weight $2$
Character 441.295
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.4
Root \(0.920620 - 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.e.148.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.920620 - 1.59456i) q^{2} +(0.195084 - 1.72103i) q^{3} +(-0.695084 - 1.20392i) q^{4} +(-0.667377 - 1.15593i) q^{5} +(-2.56469 - 1.89549i) q^{6} +1.12285 q^{8} +(-2.92388 - 0.671489i) q^{9} +O(q^{10})\) \(q+(0.920620 - 1.59456i) q^{2} +(0.195084 - 1.72103i) q^{3} +(-0.695084 - 1.20392i) q^{4} +(-0.667377 - 1.15593i) q^{5} +(-2.56469 - 1.89549i) q^{6} +1.12285 q^{8} +(-2.92388 - 0.671489i) q^{9} -2.45760 q^{10} +(-0.756508 + 1.31031i) q^{11} +(-2.20758 + 0.961394i) q^{12} +(-2.58800 - 4.48254i) q^{13} +(-2.11958 + 0.923072i) q^{15} +(2.42388 - 4.19829i) q^{16} -1.54893 q^{17} +(-3.76252 + 4.04413i) q^{18} +2.50422 q^{19} +(-0.927765 + 1.60694i) q^{20} +(1.39291 + 2.41260i) q^{22} +(3.68039 + 6.37463i) q^{23} +(0.219049 - 1.93246i) q^{24} +(1.60922 - 2.78725i) q^{25} -9.53025 q^{26} +(-1.72605 + 4.90110i) q^{27} +(-0.0309713 + 0.0536439i) q^{29} +(-0.479438 + 4.22961i) q^{30} +(1.92388 + 3.33227i) q^{31} +(-3.34011 - 5.78523i) q^{32} +(2.10750 + 1.55759i) q^{33} +(-1.42597 + 2.46986i) q^{34} +(1.22392 + 3.98687i) q^{36} +0.563216 q^{37} +(2.30543 - 3.99313i) q^{38} +(-8.21946 + 3.57955i) q^{39} +(-0.749363 - 1.29794i) q^{40} +(4.51188 + 7.81481i) q^{41} +(5.09988 - 8.83325i) q^{43} +2.10335 q^{44} +(1.17514 + 3.82794i) q^{45} +13.5530 q^{46} +(4.75925 - 8.24327i) q^{47} +(-6.75252 - 4.99060i) q^{48} +(-2.96296 - 5.13199i) q^{50} +(-0.302170 + 2.66575i) q^{51} +(-3.59775 + 6.23148i) q^{52} -1.51075 q^{53} +(6.22605 + 7.26435i) q^{54} +2.01950 q^{55} +(0.488532 - 4.30983i) q^{57} +(0.0570257 + 0.0987714i) q^{58} +(4.22166 + 7.31212i) q^{59} +(2.58459 + 1.91020i) q^{60} +(-1.61958 + 2.80520i) q^{61} +7.08467 q^{62} -2.60434 q^{64} +(-3.45434 + 5.98309i) q^{65} +(4.42388 - 1.92659i) q^{66} +(-3.46670 - 6.00449i) q^{67} +(1.07663 + 1.86478i) q^{68} +(11.6889 - 5.09048i) q^{69} -12.3304 q^{71} +(-3.28308 - 0.753981i) q^{72} +2.75871 q^{73} +(0.518508 - 0.898083i) q^{74} +(-4.48300 - 3.31326i) q^{75} +(-1.74064 - 3.01488i) q^{76} +(-1.85920 + 16.4018i) q^{78} +(2.95969 - 5.12633i) q^{79} -6.47058 q^{80} +(8.09820 + 3.92671i) q^{81} +16.6149 q^{82} +(2.80111 - 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(-9.39010 - 16.2641i) q^{86} +(0.0862808 + 0.0637676i) q^{87} +(-0.849444 + 1.47128i) q^{88} -1.40657 q^{89} +(7.18575 + 1.65025i) q^{90} +(5.11636 - 8.86180i) q^{92} +(6.11025 - 2.66099i) q^{93} +(-8.76293 - 15.1778i) q^{94} +(-1.67126 - 2.89470i) q^{95} +(-10.6082 + 4.61982i) q^{96} +(-6.09713 + 10.5605i) q^{97} +(3.09180 - 3.32321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} - q^{3} - 4q^{4} + 4q^{5} - 2q^{6} - 6q^{8} - 7q^{9} + O(q^{10}) \) \( 10q + 2q^{2} - q^{3} - 4q^{4} + 4q^{5} - 2q^{6} - 6q^{8} - 7q^{9} + 14q^{10} + 4q^{11} - 2q^{12} - 8q^{13} - 19q^{15} + 2q^{16} - 24q^{17} - 2q^{18} - 2q^{19} + 5q^{20} - q^{22} + 3q^{23} - 9q^{24} - q^{25} - 22q^{26} - 7q^{27} + 7q^{29} + 10q^{30} - 3q^{31} - 2q^{32} - 13q^{33} + 3q^{34} + 34q^{36} + 20q^{38} - 22q^{39} - 3q^{40} + 5q^{41} - 7q^{43} + 20q^{44} + 17q^{45} - 6q^{46} + 27q^{47} - 5q^{48} + 19q^{50} - 15q^{51} - 10q^{52} + 42q^{53} + 52q^{54} + 4q^{55} - 4q^{57} - 10q^{58} + 30q^{59} + 31q^{60} - 14q^{61} - 12q^{62} - 50q^{64} - 11q^{65} + 22q^{66} - 2q^{67} + 27q^{68} + 15q^{69} - 6q^{71} - 12q^{72} - 30q^{73} - 36q^{74} - 17q^{75} + 5q^{76} - 20q^{78} - 4q^{79} - 40q^{80} - 31q^{81} + 10q^{82} + 9q^{83} - 6q^{85} - 8q^{86} - 34q^{87} - 18q^{88} - 56q^{89} + 28q^{90} + 27q^{92} + 18q^{93} - 3q^{94} - 14q^{95} - 58q^{96} - 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.920620 1.59456i 0.650977 1.12753i −0.331909 0.943311i \(-0.607693\pi\)
0.982886 0.184214i \(-0.0589739\pi\)
\(3\) 0.195084 1.72103i 0.112632 0.993637i
\(4\) −0.695084 1.20392i −0.347542 0.601960i
\(5\) −0.667377 1.15593i −0.298460 0.516948i 0.677324 0.735685i \(-0.263140\pi\)
−0.975784 + 0.218737i \(0.929806\pi\)
\(6\) −2.56469 1.89549i −1.04703 0.773830i
\(7\) 0 0
\(8\) 1.12285 0.396987
\(9\) −2.92388 0.671489i −0.974628 0.223830i
\(10\) −2.45760 −0.777162
\(11\) −0.756508 + 1.31031i −0.228096 + 0.395073i −0.957244 0.289283i \(-0.906583\pi\)
0.729148 + 0.684356i \(0.239917\pi\)
\(12\) −2.20758 + 0.961394i −0.637274 + 0.277531i
\(13\) −2.58800 4.48254i −0.717781 1.24323i −0.961877 0.273482i \(-0.911824\pi\)
0.244096 0.969751i \(-0.421509\pi\)
\(14\) 0 0
\(15\) −2.11958 + 0.923072i −0.547274 + 0.238336i
\(16\) 2.42388 4.19829i 0.605971 1.04957i
\(17\) −1.54893 −0.375670 −0.187835 0.982201i \(-0.560147\pi\)
−0.187835 + 0.982201i \(0.560147\pi\)
\(18\) −3.76252 + 4.04413i −0.886834 + 0.953210i
\(19\) 2.50422 0.574507 0.287254 0.957855i \(-0.407258\pi\)
0.287254 + 0.957855i \(0.407258\pi\)
\(20\) −0.927765 + 1.60694i −0.207455 + 0.359322i
\(21\) 0 0
\(22\) 1.39291 + 2.41260i 0.296970 + 0.514367i
\(23\) 3.68039 + 6.37463i 0.767415 + 1.32920i 0.938960 + 0.344025i \(0.111791\pi\)
−0.171545 + 0.985176i \(0.554876\pi\)
\(24\) 0.219049 1.93246i 0.0447133 0.394461i
\(25\) 1.60922 2.78725i 0.321843 0.557449i
\(26\) −9.53025 −1.86904
\(27\) −1.72605 + 4.90110i −0.332179 + 0.943216i
\(28\) 0 0
\(29\) −0.0309713 + 0.0536439i −0.00575123 + 0.00996143i −0.868887 0.495011i \(-0.835164\pi\)
0.863135 + 0.504972i \(0.168497\pi\)
\(30\) −0.479438 + 4.22961i −0.0875330 + 0.772217i
\(31\) 1.92388 + 3.33227i 0.345540 + 0.598493i 0.985452 0.169956i \(-0.0543625\pi\)
−0.639912 + 0.768448i \(0.721029\pi\)
\(32\) −3.34011 5.78523i −0.590453 1.02269i
\(33\) 2.10750 + 1.55759i 0.366869 + 0.271142i
\(34\) −1.42597 + 2.46986i −0.244552 + 0.423577i
\(35\) 0 0
\(36\) 1.22392 + 3.98687i 0.203987 + 0.664478i
\(37\) 0.563216 0.0925922 0.0462961 0.998928i \(-0.485258\pi\)
0.0462961 + 0.998928i \(0.485258\pi\)
\(38\) 2.30543 3.99313i 0.373991 0.647771i
\(39\) −8.21946 + 3.57955i −1.31617 + 0.573186i
\(40\) −0.749363 1.29794i −0.118485 0.205222i
\(41\) 4.51188 + 7.81481i 0.704638 + 1.22047i 0.966822 + 0.255450i \(0.0822237\pi\)
−0.262185 + 0.965018i \(0.584443\pi\)
\(42\) 0 0
\(43\) 5.09988 8.83325i 0.777724 1.34706i −0.155526 0.987832i \(-0.549707\pi\)
0.933251 0.359226i \(-0.116959\pi\)
\(44\) 2.10335 0.317091
\(45\) 1.17514 + 3.82794i 0.175179 + 0.570636i
\(46\) 13.5530 1.99828
\(47\) 4.75925 8.24327i 0.694209 1.20240i −0.276238 0.961089i \(-0.589088\pi\)
0.970447 0.241315i \(-0.0775788\pi\)
\(48\) −6.75252 4.99060i −0.974643 0.720330i
\(49\) 0 0
\(50\) −2.96296 5.13199i −0.419025 0.725773i
\(51\) −0.302170 + 2.66575i −0.0423123 + 0.373279i
\(52\) −3.59775 + 6.23148i −0.498918 + 0.864151i
\(53\) −1.51075 −0.207517 −0.103759 0.994603i \(-0.533087\pi\)
−0.103759 + 0.994603i \(0.533087\pi\)
\(54\) 6.22605 + 7.26435i 0.847259 + 0.988553i
\(55\) 2.01950 0.272310
\(56\) 0 0
\(57\) 0.488532 4.30983i 0.0647077 0.570851i
\(58\) 0.0570257 + 0.0987714i 0.00748784 + 0.0129693i
\(59\) 4.22166 + 7.31212i 0.549613 + 0.951957i 0.998301 + 0.0582689i \(0.0185581\pi\)
−0.448688 + 0.893688i \(0.648109\pi\)
\(60\) 2.58459 + 1.91020i 0.333670 + 0.246606i
\(61\) −1.61958 + 2.80520i −0.207367 + 0.359169i −0.950884 0.309547i \(-0.899823\pi\)
0.743518 + 0.668716i \(0.233156\pi\)
\(62\) 7.08467 0.899754
\(63\) 0 0
\(64\) −2.60434 −0.325543
\(65\) −3.45434 + 5.98309i −0.428458 + 0.742111i
\(66\) 4.42388 1.92659i 0.544543 0.237146i
\(67\) −3.46670 6.00449i −0.423524 0.733566i 0.572757 0.819725i \(-0.305874\pi\)
−0.996281 + 0.0861595i \(0.972541\pi\)
\(68\) 1.07663 + 1.86478i 0.130561 + 0.226138i
\(69\) 11.6889 5.09048i 1.40718 0.612822i
\(70\) 0 0
\(71\) −12.3304 −1.46335 −0.731673 0.681656i \(-0.761260\pi\)
−0.731673 + 0.681656i \(0.761260\pi\)
\(72\) −3.28308 0.753981i −0.386915 0.0888575i
\(73\) 2.75871 0.322883 0.161442 0.986882i \(-0.448386\pi\)
0.161442 + 0.986882i \(0.448386\pi\)
\(74\) 0.518508 0.898083i 0.0602754 0.104400i
\(75\) −4.48300 3.31326i −0.517652 0.382582i
\(76\) −1.74064 3.01488i −0.199665 0.345830i
\(77\) 0 0
\(78\) −1.85920 + 16.4018i −0.210512 + 1.85714i
\(79\) 2.95969 5.12633i 0.332991 0.576758i −0.650106 0.759844i \(-0.725275\pi\)
0.983097 + 0.183086i \(0.0586087\pi\)
\(80\) −6.47058 −0.723432
\(81\) 8.09820 + 3.92671i 0.899800 + 0.436302i
\(82\) 16.6149 1.83481
\(83\) 2.80111 4.85167i 0.307462 0.532540i −0.670344 0.742050i \(-0.733854\pi\)
0.977806 + 0.209510i \(0.0671870\pi\)
\(84\) 0 0
\(85\) 1.03372 + 1.79045i 0.112122 + 0.194202i
\(86\) −9.39010 16.2641i −1.01256 1.75381i
\(87\) 0.0862808 + 0.0637676i 0.00925027 + 0.00683661i
\(88\) −0.849444 + 1.47128i −0.0905511 + 0.156839i
\(89\) −1.40657 −0.149097 −0.0745483 0.997217i \(-0.523751\pi\)
−0.0745483 + 0.997217i \(0.523751\pi\)
\(90\) 7.18575 + 1.65025i 0.757444 + 0.173952i
\(91\) 0 0
\(92\) 5.11636 8.86180i 0.533418 0.923906i
\(93\) 6.11025 2.66099i 0.633603 0.275932i
\(94\) −8.76293 15.1778i −0.903827 1.56548i
\(95\) −1.67126 2.89470i −0.171467 0.296990i
\(96\) −10.6082 + 4.61982i −1.08269 + 0.471508i
\(97\) −6.09713 + 10.5605i −0.619070 + 1.07226i 0.370586 + 0.928798i \(0.379157\pi\)
−0.989656 + 0.143462i \(0.954176\pi\)
\(98\) 0 0
\(99\) 3.09180 3.32321i 0.310738 0.333995i
\(100\) −4.47416 −0.447416
\(101\) −0.559336 + 0.968798i −0.0556560 + 0.0963990i −0.892511 0.451025i \(-0.851058\pi\)
0.836855 + 0.547425i \(0.184392\pi\)
\(102\) 3.97251 + 2.93597i 0.393338 + 0.290704i
\(103\) −0.965224 1.67182i −0.0951063 0.164729i 0.814547 0.580098i \(-0.196986\pi\)
−0.909653 + 0.415369i \(0.863652\pi\)
\(104\) −2.90593 5.03322i −0.284950 0.493548i
\(105\) 0 0
\(106\) −1.39082 + 2.40898i −0.135089 + 0.233981i
\(107\) −5.77938 −0.558714 −0.279357 0.960187i \(-0.590121\pi\)
−0.279357 + 0.960187i \(0.590121\pi\)
\(108\) 7.10028 1.32864i 0.683225 0.127848i
\(109\) 8.24211 0.789451 0.394726 0.918799i \(-0.370840\pi\)
0.394726 + 0.918799i \(0.370840\pi\)
\(110\) 1.85920 3.22022i 0.177267 0.307036i
\(111\) 0.109874 0.969312i 0.0104288 0.0920030i
\(112\) 0 0
\(113\) 7.25105 + 12.5592i 0.682121 + 1.18147i 0.974332 + 0.225115i \(0.0722758\pi\)
−0.292211 + 0.956354i \(0.594391\pi\)
\(114\) −6.42254 4.74672i −0.601526 0.444571i
\(115\) 4.91242 8.50856i 0.458085 0.793427i
\(116\) 0.0861107 0.00799518
\(117\) 4.55703 + 14.8442i 0.421297 + 1.37235i
\(118\) 15.5462 1.43114
\(119\) 0 0
\(120\) −2.37997 + 1.03647i −0.217261 + 0.0946164i
\(121\) 4.35539 + 7.54376i 0.395945 + 0.685796i
\(122\) 2.98204 + 5.16505i 0.269982 + 0.467622i
\(123\) 14.3297 6.24054i 1.29207 0.562691i
\(124\) 2.67452 4.63241i 0.240179 0.416002i
\(125\) −10.9696 −0.981149
\(126\) 0 0
\(127\) 8.50004 0.754257 0.377128 0.926161i \(-0.376912\pi\)
0.377128 + 0.926161i \(0.376912\pi\)
\(128\) 4.28260 7.41769i 0.378532 0.655637i
\(129\) −14.2074 10.5003i −1.25089 0.924497i
\(130\) 6.36027 + 11.0163i 0.557832 + 0.966194i
\(131\) 1.00673 + 1.74371i 0.0879585 + 0.152349i 0.906648 0.421888i \(-0.138632\pi\)
−0.818690 + 0.574236i \(0.805299\pi\)
\(132\) 0.410328 3.61992i 0.0357145 0.315074i
\(133\) 0 0
\(134\) −12.7660 −1.10282
\(135\) 6.81725 1.27568i 0.586736 0.109793i
\(136\) −1.73921 −0.149136
\(137\) −1.10870 + 1.92032i −0.0947225 + 0.164064i −0.909493 0.415720i \(-0.863530\pi\)
0.814770 + 0.579784i \(0.196863\pi\)
\(138\) 2.64396 23.3251i 0.225069 1.98556i
\(139\) 0.377669 + 0.654143i 0.0320335 + 0.0554836i 0.881598 0.472002i \(-0.156468\pi\)
−0.849564 + 0.527485i \(0.823135\pi\)
\(140\) 0 0
\(141\) −13.2585 9.79894i −1.11656 0.825220i
\(142\) −11.3516 + 19.6615i −0.952604 + 1.64996i
\(143\) 7.83136 0.654891
\(144\) −9.90627 + 10.6477i −0.825522 + 0.887309i
\(145\) 0.0826782 0.00686605
\(146\) 2.53973 4.39894i 0.210189 0.364059i
\(147\) 0 0
\(148\) −0.391482 0.678068i −0.0321797 0.0557368i
\(149\) −3.29249 5.70277i −0.269732 0.467189i 0.699061 0.715062i \(-0.253602\pi\)
−0.968792 + 0.247873i \(0.920268\pi\)
\(150\) −9.41033 + 4.09817i −0.768350 + 0.334614i
\(151\) −6.33356 + 10.9700i −0.515417 + 0.892729i 0.484422 + 0.874834i \(0.339030\pi\)
−0.999840 + 0.0178950i \(0.994304\pi\)
\(152\) 2.81186 0.228072
\(153\) 4.52888 + 1.04009i 0.366138 + 0.0840861i
\(154\) 0 0
\(155\) 2.56791 4.44775i 0.206260 0.357252i
\(156\) 10.0227 + 7.40749i 0.802459 + 0.593074i
\(157\) 8.65372 + 14.9887i 0.690642 + 1.19623i 0.971628 + 0.236515i \(0.0760052\pi\)
−0.280986 + 0.959712i \(0.590662\pi\)
\(158\) −5.44950 9.43882i −0.433539 0.750912i
\(159\) −0.294722 + 2.60004i −0.0233730 + 0.206197i
\(160\) −4.45822 + 7.72186i −0.352453 + 0.610467i
\(161\) 0 0
\(162\) 13.7168 9.29807i 1.07769 0.730525i
\(163\) −12.2193 −0.957086 −0.478543 0.878064i \(-0.658835\pi\)
−0.478543 + 0.878064i \(0.658835\pi\)
\(164\) 6.27227 10.8639i 0.489782 0.848327i
\(165\) 0.393972 3.47562i 0.0306707 0.270577i
\(166\) −5.15752 8.93309i −0.400301 0.693342i
\(167\) 1.76248 + 3.05270i 0.136385 + 0.236225i 0.926126 0.377215i \(-0.123118\pi\)
−0.789741 + 0.613440i \(0.789785\pi\)
\(168\) 0 0
\(169\) −6.89546 + 11.9433i −0.530420 + 0.918714i
\(170\) 3.80665 0.291956
\(171\) −7.32205 1.68156i −0.559931 0.128592i
\(172\) −14.1794 −1.08117
\(173\) −5.07046 + 8.78229i −0.385500 + 0.667705i −0.991838 0.127502i \(-0.959304\pi\)
0.606339 + 0.795206i \(0.292638\pi\)
\(174\) 0.181113 0.0788742i 0.0137302 0.00597944i
\(175\) 0 0
\(176\) 3.66738 + 6.35208i 0.276439 + 0.478806i
\(177\) 13.4080 5.83912i 1.00780 0.438895i
\(178\) −1.29492 + 2.24287i −0.0970584 + 0.168110i
\(179\) −1.70116 −0.127150 −0.0635752 0.997977i \(-0.520250\pi\)
−0.0635752 + 0.997977i \(0.520250\pi\)
\(180\) 3.79172 4.07551i 0.282618 0.303771i
\(181\) −16.9941 −1.26316 −0.631581 0.775310i \(-0.717594\pi\)
−0.631581 + 0.775310i \(0.717594\pi\)
\(182\) 0 0
\(183\) 4.51188 + 3.33460i 0.333528 + 0.246501i
\(184\) 4.13252 + 7.15774i 0.304654 + 0.527676i
\(185\) −0.375877 0.651039i −0.0276351 0.0478653i
\(186\) 1.38210 12.1929i 0.101341 0.894029i
\(187\) 1.17178 2.02957i 0.0856887 0.148417i
\(188\) −13.2323 −0.965066
\(189\) 0 0
\(190\) −6.15437 −0.446485
\(191\) −11.3470 + 19.6535i −0.821038 + 1.42208i 0.0838717 + 0.996477i \(0.473271\pi\)
−0.904910 + 0.425603i \(0.860062\pi\)
\(192\) −0.508064 + 4.48215i −0.0366664 + 0.323471i
\(193\) −3.09349 5.35808i −0.222674 0.385683i 0.732945 0.680288i \(-0.238145\pi\)
−0.955619 + 0.294605i \(0.904812\pi\)
\(194\) 11.2263 + 19.4445i 0.806001 + 1.39603i
\(195\) 9.62319 + 7.11222i 0.689131 + 0.509317i
\(196\) 0 0
\(197\) 9.77010 0.696091 0.348045 0.937478i \(-0.386846\pi\)
0.348045 + 0.937478i \(0.386846\pi\)
\(198\) −2.45269 7.98948i −0.174305 0.567788i
\(199\) 8.67947 0.615271 0.307636 0.951504i \(-0.400462\pi\)
0.307636 + 0.951504i \(0.400462\pi\)
\(200\) 1.80691 3.12965i 0.127768 0.221300i
\(201\) −11.0102 + 4.79491i −0.776600 + 0.338207i
\(202\) 1.02987 + 1.78379i 0.0724615 + 0.125507i
\(203\) 0 0
\(204\) 3.41938 1.48913i 0.239405 0.104260i
\(205\) 6.02225 10.4308i 0.420612 0.728522i
\(206\) −3.55442 −0.247648
\(207\) −6.48055 21.1100i −0.450429 1.46725i
\(208\) −25.0920 −1.73982
\(209\) −1.89446 + 3.28130i −0.131043 + 0.226973i
\(210\) 0 0
\(211\) −2.84219 4.92283i −0.195665 0.338901i 0.751453 0.659786i \(-0.229353\pi\)
−0.947118 + 0.320885i \(0.896020\pi\)
\(212\) 1.05010 + 1.81882i 0.0721209 + 0.124917i
\(213\) −2.40545 + 21.2209i −0.164819 + 1.45403i
\(214\) −5.32062 + 9.21558i −0.363710 + 0.629964i
\(215\) −13.6142 −0.928478
\(216\) −1.93810 + 5.50319i −0.131871 + 0.374445i
\(217\) 0 0
\(218\) 7.58786 13.1426i 0.513915 0.890126i
\(219\) 0.538180 4.74783i 0.0363668 0.320828i
\(220\) −1.40372 2.43132i −0.0946390 0.163920i
\(221\) 4.00862 + 6.94313i 0.269649 + 0.467045i
\(222\) −1.44447 1.06757i −0.0969468 0.0716506i
\(223\) 5.86133 10.1521i 0.392503 0.679836i −0.600276 0.799793i \(-0.704942\pi\)
0.992779 + 0.119957i \(0.0382758\pi\)
\(224\) 0 0
\(225\) −6.57677 + 7.06901i −0.438451 + 0.471267i
\(226\) 26.7019 1.77618
\(227\) −5.59154 + 9.68482i −0.371123 + 0.642804i −0.989739 0.142890i \(-0.954361\pi\)
0.618615 + 0.785694i \(0.287694\pi\)
\(228\) −5.52827 + 2.40754i −0.366118 + 0.159443i
\(229\) 4.82824 + 8.36275i 0.319059 + 0.552626i 0.980292 0.197554i \(-0.0632999\pi\)
−0.661233 + 0.750181i \(0.729967\pi\)
\(230\) −9.04494 15.6663i −0.596406 1.03301i
\(231\) 0 0
\(232\) −0.0347761 + 0.0602340i −0.00228317 + 0.00395456i
\(233\) 19.2898 1.26372 0.631860 0.775083i \(-0.282292\pi\)
0.631860 + 0.775083i \(0.282292\pi\)
\(234\) 27.8654 + 6.39946i 1.82162 + 0.418346i
\(235\) −12.7049 −0.828774
\(236\) 5.86881 10.1651i 0.382027 0.661690i
\(237\) −8.24519 6.09378i −0.535582 0.395833i
\(238\) 0 0
\(239\) −0.194641 0.337128i −0.0125903 0.0218070i 0.859662 0.510864i \(-0.170674\pi\)
−0.872252 + 0.489057i \(0.837341\pi\)
\(240\) −1.26230 + 11.1361i −0.0814813 + 0.718829i
\(241\) −5.31807 + 9.21117i −0.342567 + 0.593344i −0.984909 0.173075i \(-0.944630\pi\)
0.642342 + 0.766419i \(0.277963\pi\)
\(242\) 16.0386 1.03100
\(243\) 8.33782 13.1712i 0.534871 0.844934i
\(244\) 4.50299 0.288274
\(245\) 0 0
\(246\) 3.24130 28.5948i 0.206658 1.82314i
\(247\) −6.48091 11.2253i −0.412370 0.714247i
\(248\) 2.16023 + 3.74163i 0.137175 + 0.237594i
\(249\) −7.80341 5.76728i −0.494521 0.365486i
\(250\) −10.0988 + 17.4917i −0.638705 + 1.10627i
\(251\) −3.26628 −0.206166 −0.103083 0.994673i \(-0.532871\pi\)
−0.103083 + 0.994673i \(0.532871\pi\)
\(252\) 0 0
\(253\) −11.1370 −0.700176
\(254\) 7.82531 13.5538i 0.491004 0.850443i
\(255\) 3.28308 1.42977i 0.205594 0.0895357i
\(256\) −10.4896 18.1686i −0.655603 1.13554i
\(257\) 2.34787 + 4.06663i 0.146456 + 0.253669i 0.929915 0.367774i \(-0.119880\pi\)
−0.783459 + 0.621443i \(0.786547\pi\)
\(258\) −29.8229 + 12.9878i −1.85669 + 0.808584i
\(259\) 0 0
\(260\) 9.60421 0.595628
\(261\) 0.126578 0.136052i 0.00783498 0.00842139i
\(262\) 3.70727 0.229036
\(263\) −9.77491 + 16.9306i −0.602747 + 1.04399i 0.389656 + 0.920960i \(0.372594\pi\)
−0.992403 + 0.123028i \(0.960740\pi\)
\(264\) 2.36640 + 1.74894i 0.145642 + 0.107640i
\(265\) 1.00824 + 1.74632i 0.0619355 + 0.107276i
\(266\) 0 0
\(267\) −0.274400 + 2.42076i −0.0167930 + 0.148148i
\(268\) −4.81929 + 8.34725i −0.294385 + 0.509890i
\(269\) −15.7673 −0.961349 −0.480675 0.876899i \(-0.659608\pi\)
−0.480675 + 0.876899i \(0.659608\pi\)
\(270\) 4.24196 12.0449i 0.258157 0.733032i
\(271\) −14.7976 −0.898893 −0.449446 0.893307i \(-0.648379\pi\)
−0.449446 + 0.893307i \(0.648379\pi\)
\(272\) −3.75442 + 6.50285i −0.227645 + 0.394293i
\(273\) 0 0
\(274\) 2.04138 + 3.53578i 0.123324 + 0.213604i
\(275\) 2.43477 + 4.21715i 0.146822 + 0.254304i
\(276\) −14.2533 10.5342i −0.857948 0.634084i
\(277\) 3.72561 6.45295i 0.223850 0.387720i −0.732124 0.681172i \(-0.761471\pi\)
0.955974 + 0.293452i \(0.0948040\pi\)
\(278\) 1.39076 0.0834123
\(279\) −3.38764 11.0350i −0.202812 0.660650i
\(280\) 0 0
\(281\) −12.9938 + 22.5060i −0.775146 + 1.34259i 0.159566 + 0.987187i \(0.448991\pi\)
−0.934712 + 0.355406i \(0.884343\pi\)
\(282\) −27.8310 + 12.1203i −1.65731 + 0.721754i
\(283\) −9.37768 16.2426i −0.557445 0.965524i −0.997709 0.0676550i \(-0.978448\pi\)
0.440263 0.897869i \(-0.354885\pi\)
\(284\) 8.57064 + 14.8448i 0.508574 + 0.880876i
\(285\) −5.30790 + 2.31157i −0.314413 + 0.136926i
\(286\) 7.20971 12.4876i 0.426319 0.738406i
\(287\) 0 0
\(288\) 5.88136 + 19.1582i 0.346563 + 1.12891i
\(289\) −14.6008 −0.858872
\(290\) 0.0761152 0.131835i 0.00446964 0.00774165i
\(291\) 16.9856 + 12.5535i 0.995711 + 0.735901i
\(292\) −1.91754 3.32127i −0.112215 0.194363i
\(293\) −1.23089 2.13196i −0.0719093 0.124551i 0.827829 0.560981i \(-0.189576\pi\)
−0.899738 + 0.436430i \(0.856243\pi\)
\(294\) 0 0
\(295\) 5.63487 9.75988i 0.328075 0.568242i
\(296\) 0.632407 0.0367579
\(297\) −5.11618 5.96939i −0.296871 0.346379i
\(298\) −12.1245 −0.702356
\(299\) 19.0497 32.9950i 1.10167 1.90815i
\(300\) −0.872835 + 7.70016i −0.0503932 + 0.444569i
\(301\) 0 0
\(302\) 11.6616 + 20.1985i 0.671050 + 1.16229i
\(303\) 1.55821 + 1.15163i 0.0895170 + 0.0661594i
\(304\) 6.06994 10.5134i 0.348135 0.602987i
\(305\) 4.32349 0.247562
\(306\) 5.82787 6.26405i 0.333157 0.358092i
\(307\) −4.66277 −0.266118 −0.133059 0.991108i \(-0.542480\pi\)
−0.133059 + 0.991108i \(0.542480\pi\)
\(308\) 0 0
\(309\) −3.06555 + 1.33503i −0.174393 + 0.0759475i
\(310\) −4.72814 8.18938i −0.268541 0.465126i
\(311\) −13.7410 23.8002i −0.779183 1.34958i −0.932413 0.361393i \(-0.882301\pi\)
0.153231 0.988190i \(-0.451032\pi\)
\(312\) −9.22921 + 4.01929i −0.522501 + 0.227548i
\(313\) −2.74666 + 4.75735i −0.155250 + 0.268901i −0.933150 0.359487i \(-0.882952\pi\)
0.777900 + 0.628388i \(0.216285\pi\)
\(314\) 31.8671 1.79837
\(315\) 0 0
\(316\) −8.22893 −0.462914
\(317\) −4.93879 + 8.55424i −0.277390 + 0.480454i −0.970735 0.240152i \(-0.922803\pi\)
0.693345 + 0.720606i \(0.256136\pi\)
\(318\) 3.87460 + 2.86360i 0.217277 + 0.160583i
\(319\) −0.0468601 0.0811641i −0.00262366 0.00454432i
\(320\) 1.73808 + 3.01044i 0.0971614 + 0.168288i
\(321\) −1.12746 + 9.94649i −0.0629288 + 0.555159i
\(322\) 0 0
\(323\) −3.87885 −0.215825
\(324\) −0.901478 12.4790i −0.0500821 0.693277i
\(325\) −16.6586 −0.924052
\(326\) −11.2493 + 19.4844i −0.623041 + 1.07914i
\(327\) 1.60790 14.1849i 0.0889172 0.784428i
\(328\) 5.06616 + 8.77485i 0.279732 + 0.484510i
\(329\) 0 0
\(330\) −5.17940 3.82794i −0.285116 0.210721i
\(331\) 10.3471 17.9217i 0.568729 0.985067i −0.427963 0.903796i \(-0.640769\pi\)
0.996692 0.0812710i \(-0.0258979\pi\)
\(332\) −7.78803 −0.427424
\(333\) −1.64678 0.378194i −0.0902430 0.0207249i
\(334\) 6.49029 0.355133
\(335\) −4.62718 + 8.01452i −0.252810 + 0.437880i
\(336\) 0 0
\(337\) 0.748747 + 1.29687i 0.0407869 + 0.0706449i 0.885698 0.464261i \(-0.153680\pi\)
−0.844911 + 0.534906i \(0.820347\pi\)
\(338\) 12.6962 + 21.9905i 0.690582 + 1.19612i
\(339\) 23.0293 10.0292i 1.25078 0.544710i
\(340\) 1.43704 2.48903i 0.0779344 0.134986i
\(341\) −5.82174 −0.315265
\(342\) −9.42217 + 10.1274i −0.509493 + 0.547626i
\(343\) 0 0
\(344\) 5.72639 9.91840i 0.308746 0.534764i
\(345\) −13.6851 10.1143i −0.736783 0.544535i
\(346\) 9.33593 + 16.1703i 0.501903 + 0.869321i
\(347\) 14.7694 + 25.5813i 0.792862 + 1.37328i 0.924188 + 0.381938i \(0.124743\pi\)
−0.131326 + 0.991339i \(0.541923\pi\)
\(348\) 0.0167988 0.148199i 0.000900509 0.00794430i
\(349\) 18.0006 31.1780i 0.963551 1.66892i 0.250094 0.968222i \(-0.419539\pi\)
0.713458 0.700698i \(-0.247128\pi\)
\(350\) 0 0
\(351\) 26.4364 4.94691i 1.41107 0.264046i
\(352\) 10.1073 0.538719
\(353\) 14.7465 25.5417i 0.784877 1.35945i −0.144196 0.989549i \(-0.546060\pi\)
0.929073 0.369897i \(-0.120607\pi\)
\(354\) 3.03280 26.7554i 0.161192 1.42203i
\(355\) 8.22900 + 14.2530i 0.436750 + 0.756473i
\(356\) 0.977687 + 1.69340i 0.0518173 + 0.0897502i
\(357\) 0 0
\(358\) −1.56612 + 2.71260i −0.0827720 + 0.143365i
\(359\) −5.41069 −0.285566 −0.142783 0.989754i \(-0.545605\pi\)
−0.142783 + 0.989754i \(0.545605\pi\)
\(360\) 1.31950 + 4.29820i 0.0695439 + 0.226535i
\(361\) −12.7289 −0.669942
\(362\) −15.6451 + 27.0981i −0.822289 + 1.42425i
\(363\) 13.8327 6.02409i 0.726028 0.316183i
\(364\) 0 0
\(365\) −1.84110 3.18888i −0.0963676 0.166914i
\(366\) 9.47096 4.12457i 0.495055 0.215595i
\(367\) 11.5422 19.9916i 0.602496 1.04355i −0.389946 0.920838i \(-0.627506\pi\)
0.992442 0.122715i \(-0.0391602\pi\)
\(368\) 35.6834 1.86013
\(369\) −7.94466 25.8793i −0.413583 1.34722i
\(370\) −1.38416 −0.0719591
\(371\) 0 0
\(372\) −7.45075 5.50664i −0.386304 0.285506i
\(373\) −10.7515 18.6222i −0.556692 0.964219i −0.997770 0.0667498i \(-0.978737\pi\)
0.441078 0.897469i \(-0.354596\pi\)
\(374\) −2.15752 3.73694i −0.111563 0.193232i
\(375\) −2.13999 + 18.8790i −0.110508 + 0.974906i
\(376\) 5.34392 9.25595i 0.275592 0.477339i
\(377\) 0.320615 0.0165125
\(378\) 0 0
\(379\) 5.72168 0.293903 0.146952 0.989144i \(-0.453054\pi\)
0.146952 + 0.989144i \(0.453054\pi\)
\(380\) −2.32333 + 4.02412i −0.119184 + 0.206433i
\(381\) 1.65822 14.6288i 0.0849531 0.749457i
\(382\) 20.8925 + 36.1869i 1.06895 + 1.85148i
\(383\) 17.4604 + 30.2424i 0.892187 + 1.54531i 0.837248 + 0.546823i \(0.184163\pi\)
0.0549390 + 0.998490i \(0.482504\pi\)
\(384\) −11.9306 8.81756i −0.608831 0.449969i
\(385\) 0 0
\(386\) −11.3917 −0.579823
\(387\) −20.8429 + 22.4029i −1.05950 + 1.13880i
\(388\) 16.9521 0.860611
\(389\) 14.4411 25.0127i 0.732192 1.26819i −0.223752 0.974646i \(-0.571831\pi\)
0.955944 0.293548i \(-0.0948361\pi\)
\(390\) 20.2002 8.79711i 1.02288 0.445459i
\(391\) −5.70066 9.87383i −0.288295 0.499341i
\(392\) 0 0
\(393\) 3.19737 1.39244i 0.161286 0.0702395i
\(394\) 8.99455 15.5790i 0.453139 0.784860i
\(395\) −7.90091 −0.397538
\(396\) −6.14994 1.41237i −0.309046 0.0709745i
\(397\) −11.1845 −0.561335 −0.280667 0.959805i \(-0.590556\pi\)
−0.280667 + 0.959805i \(0.590556\pi\)
\(398\) 7.99049 13.8399i 0.400527 0.693734i
\(399\) 0 0
\(400\) −7.80111 13.5119i −0.390056 0.675596i
\(401\) 0.541061 + 0.937146i 0.0270193 + 0.0467988i 0.879219 0.476418i \(-0.158065\pi\)
−0.852200 + 0.523217i \(0.824732\pi\)
\(402\) −2.49045 + 21.9707i −0.124212 + 1.09580i
\(403\) 9.95802 17.2478i 0.496044 0.859174i
\(404\) 1.55514 0.0773711
\(405\) −0.865544 11.9816i −0.0430092 0.595368i
\(406\) 0 0
\(407\) −0.426078 + 0.737988i −0.0211199 + 0.0365807i
\(408\) −0.339291 + 2.99323i −0.0167974 + 0.148187i
\(409\) 10.8674 + 18.8229i 0.537360 + 0.930735i 0.999045 + 0.0436908i \(0.0139116\pi\)
−0.461685 + 0.887044i \(0.652755\pi\)
\(410\) −11.0884 19.2057i −0.547618 0.948501i
\(411\) 3.08864 + 2.28273i 0.152351 + 0.112599i
\(412\) −1.34182 + 2.32410i −0.0661069 + 0.114500i
\(413\) 0 0
\(414\) −39.6273 9.10068i −1.94758 0.447274i
\(415\) −7.47759 −0.367060
\(416\) −17.2884 + 29.9443i −0.847632 + 1.46814i
\(417\) 1.19948 0.522368i 0.0587386 0.0255805i
\(418\) 3.48816 + 6.04167i 0.170611 + 0.295508i
\(419\) 12.5906 + 21.8075i 0.615090 + 1.06537i 0.990369 + 0.138455i \(0.0442135\pi\)
−0.375279 + 0.926912i \(0.622453\pi\)
\(420\) 0 0
\(421\) −14.8304 + 25.6869i −0.722788 + 1.25191i 0.237090 + 0.971488i \(0.423806\pi\)
−0.959878 + 0.280418i \(0.909527\pi\)
\(422\) −10.4663 −0.509493
\(423\) −19.4508 + 20.9066i −0.945729 + 1.01651i
\(424\) −1.69634 −0.0823816
\(425\) −2.49256 + 4.31724i −0.120907 + 0.209417i
\(426\) 31.6236 + 23.3721i 1.53217 + 1.13238i
\(427\) 0 0
\(428\) 4.01715 + 6.95791i 0.194176 + 0.336323i
\(429\) 1.52777 13.4780i 0.0737615 0.650724i
\(430\) −12.5335 + 21.7086i −0.604418 + 1.04688i
\(431\) −4.89034 −0.235559 −0.117780 0.993040i \(-0.537578\pi\)
−0.117780 + 0.993040i \(0.537578\pi\)
\(432\) 16.3925 + 19.1262i 0.788683 + 0.920208i
\(433\) 9.71430 0.466839 0.233420 0.972376i \(-0.425008\pi\)
0.233420 + 0.972376i \(0.425008\pi\)
\(434\) 0 0
\(435\) 0.0161292 0.142292i 0.000773334 0.00682236i
\(436\) −5.72896 9.92285i −0.274367 0.475218i
\(437\) 9.21651 + 15.9635i 0.440885 + 0.763636i
\(438\) −7.07524 5.22911i −0.338068 0.249856i
\(439\) 7.41176 12.8375i 0.353744 0.612703i −0.633158 0.774022i \(-0.718242\pi\)
0.986902 + 0.161320i \(0.0515751\pi\)
\(440\) 2.26760 0.108103
\(441\) 0 0
\(442\) 14.7617 0.702141
\(443\) 10.9510 18.9676i 0.520297 0.901180i −0.479425 0.877583i \(-0.659155\pi\)
0.999722 0.0235972i \(-0.00751192\pi\)
\(444\) −1.24335 + 0.541473i −0.0590066 + 0.0256972i
\(445\) 0.938715 + 1.62590i 0.0444994 + 0.0770751i
\(446\) −10.7921 18.6925i −0.511021 0.885115i
\(447\) −10.4569 + 4.55396i −0.494596 + 0.215395i
\(448\) 0 0
\(449\) 21.4952 1.01442 0.507212 0.861822i \(-0.330676\pi\)
0.507212 + 0.861822i \(0.330676\pi\)
\(450\) 5.21726 + 16.9949i 0.245944 + 0.801149i
\(451\) −13.6531 −0.642899
\(452\) 10.0802 17.4594i 0.474131 0.821220i
\(453\) 17.6442 + 13.0403i 0.828996 + 0.612687i
\(454\) 10.2954 + 17.8321i 0.483185 + 0.836902i
\(455\) 0 0
\(456\) 0.548548 4.83929i 0.0256881 0.226621i
\(457\) −20.3128 + 35.1827i −0.950190 + 1.64578i −0.205181 + 0.978724i \(0.565778\pi\)
−0.745009 + 0.667054i \(0.767555\pi\)
\(458\) 17.7799 0.830800
\(459\) 2.67353 7.59144i 0.124790 0.354338i
\(460\) −13.6582 −0.636815
\(461\) 1.41541 2.45155i 0.0659220 0.114180i −0.831181 0.556003i \(-0.812334\pi\)
0.897103 + 0.441822i \(0.145668\pi\)
\(462\) 0 0
\(463\) −13.9324 24.1317i −0.647494 1.12149i −0.983719 0.179711i \(-0.942484\pi\)
0.336225 0.941782i \(-0.390850\pi\)
\(464\) 0.150142 + 0.260053i 0.00697016 + 0.0120727i
\(465\) −7.15376 5.28714i −0.331748 0.245185i
\(466\) 17.7586 30.7588i 0.822653 1.42488i
\(467\) 26.6438 1.23293 0.616464 0.787383i \(-0.288564\pi\)
0.616464 + 0.787383i \(0.288564\pi\)
\(468\) 14.7038 15.8043i 0.679682 0.730554i
\(469\) 0 0
\(470\) −11.6964 + 20.2587i −0.539513 + 0.934463i
\(471\) 27.4842 11.9693i 1.26640 0.551514i
\(472\) 4.74028 + 8.21041i 0.218189 + 0.377915i
\(473\) 7.71620 + 13.3648i 0.354791 + 0.614516i
\(474\) −17.3076 + 7.53740i −0.794964 + 0.346204i
\(475\) 4.02983 6.97987i 0.184901 0.320258i
\(476\) 0 0
\(477\) 4.41725 + 1.01445i 0.202252 + 0.0464485i
\(478\) −0.716762 −0.0327839
\(479\) 15.7895 27.3483i 0.721443 1.24958i −0.238979 0.971025i \(-0.576813\pi\)
0.960422 0.278551i \(-0.0898540\pi\)
\(480\) 12.4198 + 9.17913i 0.566885 + 0.418968i
\(481\) −1.45760 2.52464i −0.0664609 0.115114i
\(482\) 9.79185 + 16.9600i 0.446007 + 0.772506i
\(483\) 0 0
\(484\) 6.05472 10.4871i 0.275215 0.476686i
\(485\) 16.2763 0.739070
\(486\) −13.3263 25.4208i −0.604495 1.15311i
\(487\) 0.306174 0.0138741 0.00693703 0.999976i \(-0.497792\pi\)
0.00693703 + 0.999976i \(0.497792\pi\)
\(488\) −1.81855 + 3.14982i −0.0823218 + 0.142586i
\(489\) −2.38378 + 21.0297i −0.107798 + 0.950996i
\(490\) 0 0
\(491\) −9.06981 15.7094i −0.409315 0.708954i 0.585498 0.810674i \(-0.300899\pi\)
−0.994813 + 0.101720i \(0.967566\pi\)
\(492\) −17.4735 12.9141i −0.787764 0.582214i
\(493\) 0.0479723 0.0830905i 0.00216057 0.00374221i
\(494\) −23.8658 −1.07377
\(495\) −5.90480 1.35607i −0.265401 0.0609510i
\(496\) 18.6531 0.837549
\(497\) 0 0
\(498\) −16.3803 + 7.13355i −0.734017 + 0.319662i
\(499\) 10.6546 + 18.4543i 0.476964 + 0.826126i 0.999652 0.0263983i \(-0.00840381\pi\)
−0.522687 + 0.852524i \(0.675070\pi\)
\(500\) 7.62478 + 13.2065i 0.340990 + 0.590613i
\(501\) 5.59762 2.43774i 0.250083 0.108910i
\(502\) −3.00701 + 5.20829i −0.134209 + 0.232457i
\(503\) −17.0738 −0.761285 −0.380642 0.924722i \(-0.624297\pi\)
−0.380642 + 0.924722i \(0.624297\pi\)
\(504\) 0 0
\(505\) 1.49315 0.0664443
\(506\) −10.2529 + 17.7586i −0.455799 + 0.789466i
\(507\) 19.2096 + 14.1972i 0.853126 + 0.630521i
\(508\) −5.90824 10.2334i −0.262136 0.454032i
\(509\) −18.3868 31.8468i −0.814979 1.41159i −0.909343 0.416048i \(-0.863415\pi\)
0.0943635 0.995538i \(-0.469918\pi\)
\(510\) 0.742614 6.55135i 0.0328835 0.290099i
\(511\) 0 0
\(512\) −21.4975 −0.950065
\(513\) −4.32242 + 12.2734i −0.190839 + 0.541884i
\(514\) 8.64598 0.381358
\(515\) −1.28834 + 2.23146i −0.0567709 + 0.0983300i
\(516\) −2.76616 + 24.4031i −0.121774 + 1.07429i
\(517\) 7.20083 + 12.4722i 0.316692 + 0.548527i
\(518\) 0 0
\(519\) 14.1254 + 10.4397i 0.620037 + 0.458251i
\(520\) −3.87870 + 6.71810i −0.170092 + 0.294608i
\(521\) 19.1507 0.839008 0.419504 0.907754i \(-0.362204\pi\)
0.419504 + 0.907754i \(0.362204\pi\)
\(522\) −0.100413 0.327088i −0.00439494 0.0143163i
\(523\) 41.9429 1.83404 0.917018 0.398847i \(-0.130589\pi\)
0.917018 + 0.398847i \(0.130589\pi\)
\(524\) 1.39952 2.42405i 0.0611385 0.105895i
\(525\) 0 0
\(526\) 17.9980 + 31.1734i 0.784749 + 1.35922i
\(527\) −2.97996 5.16144i −0.129809 0.224836i
\(528\) 11.6476 5.07248i 0.506895 0.220751i
\(529\) −15.5906 + 27.0037i −0.677851 + 1.17407i
\(530\) 3.71282 0.161274
\(531\) −7.43362 24.2146i −0.322592 1.05082i
\(532\) 0 0
\(533\) 23.3535 40.4494i 1.01155 1.75206i
\(534\) 3.60743 + 2.66614i 0.156109 + 0.115375i
\(535\) 3.85702 + 6.68056i 0.166754 + 0.288826i
\(536\) −3.89258 6.74214i −0.168134 0.291216i
\(537\) −0.331868 + 2.92774i −0.0143212 + 0.126341i
\(538\) −14.5157 + 25.1419i −0.625816 + 1.08395i
\(539\) 0 0
\(540\) −6.27438 7.32073i −0.270006 0.315034i
\(541\) 2.88544 0.124055 0.0620273 0.998074i \(-0.480243\pi\)
0.0620273 + 0.998074i \(0.480243\pi\)
\(542\) −13.6230 + 23.5957i −0.585158 + 1.01352i
\(543\) −3.31527 + 29.2474i −0.142272 + 1.25512i
\(544\) 5.17358 + 8.96090i 0.221815 + 0.384196i
\(545\) −5.50059 9.52731i −0.235620 0.408105i
\(546\) 0 0
\(547\) 1.38738 2.40301i 0.0593201 0.102745i −0.834840 0.550492i \(-0.814440\pi\)
0.894160 + 0.447747i \(0.147773\pi\)
\(548\) 3.08255 0.131680
\(549\) 6.61914 7.11456i 0.282498 0.303642i
\(550\) 8.96600 0.382311
\(551\) −0.0775590 + 0.134336i −0.00330413 + 0.00572291i
\(552\) 13.1249 5.71584i 0.558632 0.243282i
\(553\) 0 0
\(554\) −6.85975 11.8814i −0.291443 0.504794i
\(555\) −1.19378 + 0.519889i −0.0506733 + 0.0220681i
\(556\) 0.525024 0.909368i 0.0222660 0.0385658i
\(557\) −31.0688 −1.31643 −0.658214 0.752831i \(-0.728688\pi\)
−0.658214 + 0.752831i \(0.728688\pi\)
\(558\) −20.7148 4.75728i −0.876926 0.201392i
\(559\) −52.7939 −2.23294
\(560\) 0 0
\(561\) −3.26436 2.41260i −0.137822 0.101860i
\(562\) 23.9248 + 41.4389i 1.00920 + 1.74799i
\(563\) −0.144020 0.249451i −0.00606973 0.0105131i 0.862975 0.505247i \(-0.168599\pi\)
−0.869044 + 0.494734i \(0.835265\pi\)
\(564\) −2.58141 + 22.7732i −0.108697 + 0.958925i
\(565\) 9.67836 16.7634i 0.407172 0.705242i
\(566\) −34.5331 −1.45154
\(567\) 0 0
\(568\) −13.8451 −0.580929
\(569\) 8.04004 13.9258i 0.337056 0.583798i −0.646821 0.762641i \(-0.723902\pi\)
0.983878 + 0.178843i \(0.0572354\pi\)
\(570\) −1.20062 + 10.5919i −0.0502883 + 0.443644i
\(571\) 7.64289 + 13.2379i 0.319845 + 0.553988i 0.980456 0.196741i \(-0.0630358\pi\)
−0.660610 + 0.750729i \(0.729702\pi\)
\(572\) −5.44345 9.42834i −0.227602 0.394218i
\(573\) 31.6107 + 23.3626i 1.32056 + 0.975985i
\(574\) 0 0
\(575\) 23.6902 0.987950
\(576\) 7.61479 + 1.74879i 0.317283 + 0.0728661i
\(577\) −24.1625 −1.00590 −0.502949 0.864316i \(-0.667752\pi\)
−0.502949 + 0.864316i \(0.667752\pi\)
\(578\) −13.4418 + 23.2819i −0.559106 + 0.968400i
\(579\) −9.82490 + 4.27871i −0.408309 + 0.177817i
\(580\) −0.0574683 0.0995380i −0.00238624 0.00413309i
\(581\) 0 0
\(582\) 35.6546 15.5275i 1.47793 0.643634i
\(583\) 1.14289 1.97955i 0.0473338 0.0819845i
\(584\) 3.09762 0.128180
\(585\) 14.1177 15.1743i 0.583694 0.627381i
\(586\) −4.53273 −0.187245
\(587\) 18.0145 31.2020i 0.743537 1.28784i −0.207339 0.978269i \(-0.566480\pi\)
0.950875 0.309574i \(-0.100186\pi\)
\(588\) 0 0
\(589\) 4.81783 + 8.34472i 0.198515 + 0.343838i
\(590\) −10.3752 17.9703i −0.427138 0.739825i
\(591\) 1.90599 16.8146i 0.0784018 0.691661i
\(592\) 1.36517 2.36455i 0.0561082 0.0971823i
\(593\) −24.9337 −1.02390 −0.511951 0.859014i \(-0.671077\pi\)
−0.511951 + 0.859014i \(0.671077\pi\)
\(594\) −14.2286 + 2.66253i −0.583807 + 0.109245i
\(595\) 0 0
\(596\) −4.57712 + 7.92780i −0.187486 + 0.324735i
\(597\) 1.69322 14.9376i 0.0692990 0.611356i
\(598\) −35.0751 60.7518i −1.43433 2.48433i
\(599\) −19.7642 34.2325i −0.807542 1.39870i −0.914561 0.404447i \(-0.867464\pi\)
0.107019 0.994257i \(-0.465869\pi\)
\(600\) −5.03373 3.72028i −0.205501 0.151880i
\(601\) 1.86447 3.22936i 0.0760534 0.131728i −0.825490 0.564416i \(-0.809101\pi\)
0.901544 + 0.432688i \(0.142435\pi\)
\(602\) 0 0
\(603\) 6.10427 + 19.8843i 0.248585 + 0.809751i
\(604\) 17.6094 0.716516
\(605\) 5.81337 10.0691i 0.236347 0.409365i
\(606\) 3.27087 1.42445i 0.132870 0.0578644i
\(607\) −11.8264 20.4839i −0.480018 0.831415i 0.519719 0.854337i \(-0.326036\pi\)
−0.999737 + 0.0229218i \(0.992703\pi\)
\(608\) −8.36436 14.4875i −0.339219 0.587545i
\(609\) 0 0
\(610\) 3.98029 6.89407i 0.161157 0.279133i
\(611\) −49.2677 −1.99316
\(612\) −1.89577 6.17536i −0.0766320 0.249624i
\(613\) −3.79903 −0.153442 −0.0767208 0.997053i \(-0.524445\pi\)
−0.0767208 + 0.997053i \(0.524445\pi\)
\(614\) −4.29264 + 7.43507i −0.173237 + 0.300055i
\(615\) −16.7769 12.3994i −0.676512 0.499990i
\(616\) 0 0
\(617\) −17.5615 30.4174i −0.706999 1.22456i −0.965965 0.258672i \(-0.916715\pi\)
0.258966 0.965886i \(-0.416618\pi\)
\(618\) −0.693409 + 6.11726i −0.0278930 + 0.246072i
\(619\) 10.5816 18.3279i 0.425311 0.736660i −0.571138 0.820854i \(-0.693498\pi\)
0.996449 + 0.0841934i \(0.0268314\pi\)
\(620\) −7.13965 −0.286735
\(621\) −37.5952 + 7.03500i −1.50864 + 0.282305i
\(622\) −50.6011 −2.02892
\(623\) 0 0
\(624\) −4.89504 + 43.1841i −0.195959 + 1.72875i
\(625\) −0.725240 1.25615i −0.0290096 0.0502461i
\(626\) 5.05726 + 8.75943i 0.202129 + 0.350097i
\(627\) 5.27764 + 3.90055i 0.210769 + 0.155773i
\(628\) 12.0301 20.8368i 0.480054 0.831477i
\(629\) −0.872381 −0.0347841
\(630\) 0 0
\(631\) 4.74845 0.189033 0.0945164 0.995523i \(-0.469870\pi\)
0.0945164 + 0.995523i \(0.469870\pi\)
\(632\) 3.32329 5.75610i 0.132193 0.228965i
\(633\) −9.02679 + 3.93114i −0.358783 + 0.156249i
\(634\) 9.09350 + 15.7504i 0.361149 + 0.625529i
\(635\) −5.67273 9.82546i −0.225115 0.389911i
\(636\) 3.33510 1.45242i 0.132245 0.0575924i
\(637\) 0 0
\(638\) −0.172562 −0.00683178
\(639\) 36.0526 + 8.27971i 1.42622 + 0.327540i
\(640\) −11.4324 −0.451907
\(641\) 4.93735 8.55174i 0.195013 0.337773i −0.751891 0.659287i \(-0.770858\pi\)
0.946905 + 0.321514i \(0.104192\pi\)
\(642\) 14.8223 + 10.9547i 0.584990 + 0.432349i
\(643\) 21.9748 + 38.0615i 0.866602 + 1.50100i 0.865448 + 0.501000i \(0.167034\pi\)
0.00115462 + 0.999999i \(0.499632\pi\)
\(644\) 0 0
\(645\) −2.65590 + 23.4304i −0.104576 + 0.922570i
\(646\) −3.57095 + 6.18507i −0.140497 + 0.243348i
\(647\) −44.3872 −1.74504 −0.872521 0.488577i \(-0.837516\pi\)
−0.872521 + 0.488577i \(0.837516\pi\)
\(648\) 9.09306 + 4.40911i 0.357209 + 0.173206i
\(649\) −12.7749 −0.501457
\(650\) −15.3362 + 26.5631i −0.601537 + 1.04189i
\(651\) 0 0
\(652\) 8.49341 + 14.7110i 0.332628 + 0.576128i
\(653\) −20.9956 36.3655i −0.821622 1.42309i −0.904474 0.426529i \(-0.859736\pi\)
0.0828523 0.996562i \(-0.473597\pi\)
\(654\) −21.1385 15.6228i −0.826579 0.610901i
\(655\) 1.34374 2.32742i 0.0525042 0.0909399i
\(656\) 43.7451 1.70796
\(657\) −8.06616 1.85245i −0.314691 0.0722708i
\(658\) 0 0
\(659\) −19.6365 + 34.0114i −0.764928 + 1.32489i 0.175356 + 0.984505i \(0.443892\pi\)
−0.940284 + 0.340390i \(0.889441\pi\)
\(660\) −4.45822 + 1.94154i −0.173536 + 0.0755743i
\(661\) 0.0933694 + 0.161721i 0.00363165 + 0.00629020i 0.867836 0.496852i \(-0.165511\pi\)
−0.864204 + 0.503142i \(0.832177\pi\)
\(662\) −19.0515 32.9982i −0.740459 1.28251i
\(663\) 12.7313 5.54446i 0.494444 0.215329i
\(664\) 3.14522 5.44769i 0.122058 0.211411i
\(665\) 0 0
\(666\) −2.11911 + 2.27772i −0.0821139 + 0.0882598i
\(667\) −0.455947 −0.0176543
\(668\) 2.45014 4.24376i 0.0947987 0.164196i
\(669\) −16.3286 12.0680i −0.631302 0.466577i
\(670\) 8.51976 + 14.7567i 0.329147 + 0.570099i
\(671\) −2.45046 4.24432i −0.0945989 0.163850i
\(672\) 0 0
\(673\) −5.43382 + 9.41166i −0.209458 + 0.362793i −0.951544 0.307512i \(-0.900503\pi\)
0.742086 + 0.670305i \(0.233837\pi\)
\(674\) 2.75725 0.106205
\(675\) 10.8830 + 12.6979i 0.418885 + 0.488741i
\(676\) 19.1717 0.737372
\(677\) −14.1950 + 24.5865i −0.545560 + 0.944937i 0.453012 + 0.891505i \(0.350350\pi\)
−0.998571 + 0.0534326i \(0.982984\pi\)
\(678\) 5.20910 45.9547i 0.200054 1.76488i
\(679\) 0 0
\(680\) 1.16071 + 2.01041i 0.0445111 + 0.0770956i
\(681\) 15.5771 + 11.5125i 0.596914 + 0.441162i
\(682\) −5.35961 + 9.28312i −0.205230 + 0.355469i
\(683\) −11.8407 −0.453071 −0.226536 0.974003i \(-0.572740\pi\)
−0.226536 + 0.974003i \(0.572740\pi\)
\(684\) 3.06498 + 9.98398i 0.117192 + 0.381747i
\(685\) 2.95968 0.113083
\(686\) 0 0
\(687\) 15.3345 6.67810i 0.585046 0.254786i
\(688\) −24.7230 42.8216i −0.942557 1.63256i
\(689\) 3.90981 + 6.77199i 0.148952 + 0.257992i
\(690\) −28.7267 + 12.5104i −1.09361 + 0.476262i
\(691\) −5.95416 + 10.3129i −0.226507 + 0.392321i −0.956770 0.290844i \(-0.906064\pi\)
0.730264 + 0.683165i \(0.239397\pi\)
\(692\) 14.0976 0.535909
\(693\) 0 0
\(694\) 54.3880 2.06454
\(695\) 0.504096 0.873119i 0.0191214 0.0331193i
\(696\) 0.0968803 + 0.0716014i 0.00367224 + 0.00271405i
\(697\) −6.98857 12.1046i −0.264711 0.458493i
\(698\) −33.1435 57.4062i −1.25450 2.17286i
\(699\) 3.76313 33.1984i 0.142335 1.25568i
\(700\) 0 0
\(701\) −31.3902 −1.18559 −0.592795 0.805353i \(-0.701976\pi\)
−0.592795 + 0.805353i \(0.701976\pi\)
\(702\) 16.4497 46.7087i 0.620855 1.76291i
\(703\) 1.41042 0.0531949
\(704\) 1.97020 3.41249i 0.0742549 0.128613i
\(705\) −2.47851 + 21.8654i −0.0933461 + 0.823500i
\(706\) −27.1518 47.0284i −1.02187 1.76994i
\(707\) 0 0
\(708\) −16.3495 12.0834i −0.614451 0.454123i
\(709\) −0.312609 + 0.541455i −0.0117403 + 0.0203348i −0.871836 0.489798i \(-0.837070\pi\)
0.860096 + 0.510133i \(0.170404\pi\)
\(710\) 30.3031 1.13726
\(711\) −12.0961 + 13.0014i −0.453638 + 0.487591i
\(712\) −1.57937 −0.0591894
\(713\) −14.1613 + 24.5281i −0.530345 + 0.918584i
\(714\) 0 0
\(715\) −5.22647 9.05251i −0.195459 0.338545i
\(716\) 1.18245 + 2.04806i 0.0441901 + 0.0765395i
\(717\) −0.618179 + 0.269215i −0.0230863 + 0.0100540i
\(718\) −4.98119 + 8.62768i −0.185897 + 0.321982i
\(719\) −24.3939 −0.909739 −0.454869 0.890558i \(-0.650314\pi\)
−0.454869 + 0.890558i \(0.650314\pi\)
\(720\) 18.9192 + 4.34492i 0.705078 + 0.161926i
\(721\) 0 0
\(722\) −11.7185 + 20.2970i −0.436116 + 0.755376i
\(723\) 14.8152 + 10.9495i 0.550984 + 0.407217i
\(724\) 11.8123 + 20.4595i 0.439002 + 0.760373i
\(725\) 0.0996792 + 0.172649i 0.00370199 + 0.00641204i
\(726\) 3.12888 27.6030i 0.116124 1.02444i
\(727\) −18.9253 + 32.7796i −0.701900 + 1.21573i 0.265899 + 0.964001i \(0.414331\pi\)
−0.967799 + 0.251726i \(0.919002\pi\)
\(728\) 0 0
\(729\) −21.0415 16.9191i −0.779314 0.626634i
\(730\) −6.77982 −0.250932
\(731\) −7.89934 + 13.6821i −0.292168 + 0.506049i
\(732\) 0.878459 7.74977i 0.0324688 0.286440i
\(733\) −1.20077 2.07980i −0.0443516 0.0768193i 0.842997 0.537918i \(-0.180789\pi\)
−0.887349 + 0.461098i \(0.847456\pi\)
\(734\) −21.2519 36.8093i −0.784421 1.35866i
\(735\) 0 0
\(736\) 24.5858 42.5839i 0.906245 1.56966i
\(737\) 10.4903 0.386416
\(738\) −48.5801 11.1567i −1.78826 0.410685i
\(739\) 30.3880 1.11784 0.558920 0.829222i \(-0.311216\pi\)
0.558920 + 0.829222i \(0.311216\pi\)
\(740\) −0.522533 + 0.905053i −0.0192087 + 0.0332704i
\(741\) −20.5833 + 8.96397i −0.756148 + 0.329300i
\(742\) 0 0
\(743\) −2.54785 4.41300i −0.0934715 0.161897i 0.815498 0.578760i \(-0.196463\pi\)
−0.908970 + 0.416862i \(0.863130\pi\)
\(744\) 6.86088 2.98789i 0.251532 0.109541i
\(745\) −4.39467 + 7.61179i −0.161008 + 0.278874i
\(746\) −39.5922 −1.44957
\(747\) −11.4480 + 12.3048i −0.418859 + 0.450209i
\(748\) −3.25793 −0.119122
\(749\) 0 0
\(750\) 28.1336 + 20.7927i 1.02729 + 0.759242i
\(751\) 0.487506 + 0.844384i 0.0177893 + 0.0308120i 0.874783 0.484515i \(-0.161004\pi\)
−0.856994 + 0.515327i \(0.827671\pi\)
\(752\) −23.0718 39.9615i −0.841341 1.45724i
\(753\) −0.637198 + 5.62137i −0.0232208 + 0.204854i
\(754\) 0.295165 0.511240i 0.0107493 0.0186183i
\(755\) 16.9075 0.615326
\(756\) 0 0
\(757\) 11.6346 0.422865 0.211433 0.977393i \(-0.432187\pi\)
0.211433 + 0.977393i \(0.432187\pi\)
\(758\) 5.26750 9.12357i 0.191324 0.331383i
\(759\) −2.17264 + 19.1671i −0.0788620 + 0.695721i
\(760\) −1.87657 3.25031i −0.0680703 0.117901i
\(761\) 27.0875 + 46.9169i 0.981920 + 1.70073i 0.654897 + 0.755718i \(0.272712\pi\)
0.327023 + 0.945016i \(0.393955\pi\)
\(762\) −21.8000 16.1117i −0.789729 0.583666i
\(763\) 0 0
\(764\) 31.5484 1.14138
\(765\) −1.82020 5.92920i −0.0658095 0.214371i
\(766\) 64.2978 2.32317
\(767\) 21.8513 37.8475i 0.789004 1.36659i
\(768\) −33.3151 + 14.5086i −1.20215 + 0.523534i
\(769\) −10.4326 18.0698i −0.376208 0.651612i 0.614299 0.789074i \(-0.289439\pi\)
−0.990507 + 0.137462i \(0.956106\pi\)
\(770\) 0 0
\(771\) 7.45681 3.24742i 0.268551 0.116953i
\(772\) −4.30047 + 7.44863i −0.154777 + 0.268082i
\(773\) 54.9945 1.97801 0.989007 0.147868i \(-0.0472409\pi\)
0.989007 + 0.147868i \(0.0472409\pi\)
\(774\) 16.5344 + 53.8598i 0.594316 + 1.93595i
\(775\) 12.3838 0.444839
\(776\) −6.84616 + 11.8579i −0.245763 + 0.425674i
\(777\) 0 0
\(778\) −26.5895 46.0544i −0.953281 1.65113i
\(779\) 11.2987 + 19.5700i 0.404819 + 0.701168i
\(780\) 1.87363 16.5291i 0.0670865 0.591838i
\(781\) 9.32802