Properties

Label 441.2.f.e.148.4
Level $441$
Weight $2$
Character 441.148
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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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 148.4
Root \(0.920620 + 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.e.295.4

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.920620 + 1.59456i 0.650977 + 1.12753i 0.982886 + 0.184214i \(0.0589739\pi\)
−0.331909 + 0.943311i \(0.607693\pi\)
\(3\) 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 −0.975784 0.218737i \(-0.929806\pi\)
0.677324 + 0.735685i \(0.263140\pi\)
\(6\) −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 0.729148 0.684356i \(-0.239917\pi\)
−0.957244 + 0.289283i \(0.906583\pi\)
\(12\) −2.20758 0.961394i −0.637274 0.277531i
\(13\) −2.58800 + 4.48254i −0.717781 + 1.24323i 0.244096 + 0.969751i \(0.421509\pi\)
−0.961877 + 0.273482i \(0.911824\pi\)
\(14\) 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 −0.171545 0.985176i \(-0.554876\pi\)
0.938960 0.344025i \(-0.111791\pi\)
\(24\) 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 0.863135 0.504972i \(-0.168497\pi\)
−0.868887 + 0.495011i \(0.835164\pi\)
\(30\) −0.479438 4.22961i −0.0875330 0.772217i
\(31\) 1.92388 3.33227i 0.345540 0.598493i −0.639912 0.768448i \(-0.721029\pi\)
0.985452 + 0.169956i \(0.0543625\pi\)
\(32\) −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 −0.262185 0.965018i \(-0.584443\pi\)
0.966822 0.255450i \(-0.0822237\pi\)
\(42\) 0 0
\(43\) 5.09988 + 8.83325i 0.777724 + 1.34706i 0.933251 + 0.359226i \(0.116959\pi\)
−0.155526 + 0.987832i \(0.549707\pi\)
\(44\) 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 0.970447 + 0.241315i \(0.0775788\pi\)
−0.276238 + 0.961089i \(0.589088\pi\)
\(48\) −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 −0.448688 0.893688i \(-0.648109\pi\)
0.998301 0.0582689i \(-0.0185581\pi\)
\(60\) 2.58459 1.91020i 0.333670 0.246606i
\(61\) −1.61958 2.80520i −0.207367 0.359169i 0.743518 0.668716i \(-0.233156\pi\)
−0.950884 + 0.309547i \(0.899823\pi\)
\(62\) 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 −0.996281 0.0861595i \(-0.972541\pi\)
0.572757 + 0.819725i \(0.305874\pi\)
\(68\) 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 0.983097 0.183086i \(-0.0586087\pi\)
−0.650106 + 0.759844i \(0.725275\pi\)
\(80\) −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 0.977806 0.209510i \(-0.0671870\pi\)
−0.670344 + 0.742050i \(0.733854\pi\)
\(84\) 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 −0.989656 0.143462i \(-0.954176\pi\)
0.370586 0.928798i \(-0.379157\pi\)
\(98\) 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 0.836855 0.547425i \(-0.184392\pi\)
−0.892511 + 0.451025i \(0.851058\pi\)
\(102\) 3.97251 2.93597i 0.393338 0.290704i
\(103\) −0.965224 + 1.67182i −0.0951063 + 0.164729i −0.909653 0.415369i \(-0.863652\pi\)
0.814547 + 0.580098i \(0.196986\pi\)
\(104\) −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 −0.292211 0.956354i \(-0.594391\pi\)
0.974332 0.225115i \(-0.0722758\pi\)
\(114\) −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 −0.818690 0.574236i \(-0.805299\pi\)
0.906648 + 0.421888i \(0.138632\pi\)
\(132\) 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 0.814770 0.579784i \(-0.196863\pi\)
−0.909493 + 0.415720i \(0.863530\pi\)
\(138\) 2.64396 + 23.3251i 0.225069 + 1.98556i
\(139\) 0.377669 0.654143i 0.0320335 0.0554836i −0.849564 0.527485i \(-0.823135\pi\)
0.881598 + 0.472002i \(0.156468\pi\)
\(140\) 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 −0.968792 0.247873i \(-0.920268\pi\)
0.699061 + 0.715062i \(0.253602\pi\)
\(150\) −9.41033 4.09817i −0.768350 0.334614i
\(151\) −6.33356 10.9700i −0.515417 0.892729i −0.999840 0.0178950i \(-0.994304\pi\)
0.484422 0.874834i \(-0.339030\pi\)
\(152\) 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 −0.280986 0.959712i \(-0.590662\pi\)
0.971628 0.236515i \(-0.0760052\pi\)
\(158\) −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 −0.789741 0.613440i \(-0.789785\pi\)
0.926126 + 0.377215i \(0.123118\pi\)
\(168\) 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 0.606339 0.795206i \(-0.292638\pi\)
−0.991838 + 0.127502i \(0.959304\pi\)
\(174\) 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 −0.904910 0.425603i \(-0.860062\pi\)
0.0838717 0.996477i \(-0.473271\pi\)
\(192\) −0.508064 4.48215i −0.0366664 0.323471i
\(193\) −3.09349 + 5.35808i −0.222674 + 0.385683i −0.955619 0.294605i \(-0.904812\pi\)
0.732945 + 0.680288i \(0.238145\pi\)
\(194\) 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 −0.947118 0.320885i \(-0.896020\pi\)
0.751453 + 0.659786i \(0.229353\pi\)
\(212\) 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 0.992779 0.119957i \(-0.0382758\pi\)
−0.600276 + 0.799793i \(0.704942\pi\)
\(224\) 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 0.618615 0.785694i \(-0.287694\pi\)
−0.989739 + 0.142890i \(0.954361\pi\)
\(228\) −5.52827 2.40754i −0.366118 0.159443i
\(229\) 4.82824 8.36275i 0.319059 0.552626i −0.661233 0.750181i \(-0.729967\pi\)
0.980292 + 0.197554i \(0.0632999\pi\)
\(230\) −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 −0.872252 0.489057i \(-0.837341\pi\)
0.859662 + 0.510864i \(0.170674\pi\)
\(240\) −1.26230 11.1361i −0.0814813 0.718829i
\(241\) −5.31807 9.21117i −0.342567 0.593344i 0.642342 0.766419i \(-0.277963\pi\)
−0.984909 + 0.173075i \(0.944630\pi\)
\(242\) 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 −0.783459 0.621443i \(-0.786547\pi\)
0.929915 + 0.367774i \(0.119880\pi\)
\(258\) −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 −0.992403 0.123028i \(-0.960740\pi\)
0.389656 0.920960i \(-0.372594\pi\)
\(264\) 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 0.955974 0.293452i \(-0.0948040\pi\)
−0.732124 + 0.681172i \(0.761471\pi\)
\(278\) 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 −0.934712 0.355406i \(-0.884343\pi\)
0.159566 0.987187i \(-0.448991\pi\)
\(282\) −27.8310 12.1203i −1.65731 0.721754i
\(283\) −9.37768 + 16.2426i −0.557445 + 0.965524i 0.440263 + 0.897869i \(0.354885\pi\)
−0.997709 + 0.0676550i \(0.978448\pi\)
\(284\) 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 −0.899738 0.436430i \(-0.856243\pi\)
0.827829 + 0.560981i \(0.189576\pi\)
\(294\) 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 0.153231 + 0.988190i \(0.451032\pi\)
−0.932413 + 0.361393i \(0.882301\pi\)
\(312\) −9.22921 4.01929i −0.522501 0.227548i
\(313\) −2.74666 4.75735i −0.155250 0.268901i 0.777900 0.628388i \(-0.216285\pi\)
−0.933150 + 0.359487i \(0.882952\pi\)
\(314\) 31.8671 1.79837
\(315\) 0 0
\(316\) −8.22893 −0.462914
\(317\) −4.93879 8.55424i −0.277390 0.480454i 0.693345 0.720606i \(-0.256136\pi\)
−0.970735 + 0.240152i \(0.922803\pi\)
\(318\) 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 0.996692 + 0.0812710i \(0.0258979\pi\)
−0.427963 + 0.903796i \(0.640769\pi\)
\(332\) −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 −0.844911 0.534906i \(-0.820347\pi\)
0.885698 + 0.464261i \(0.153680\pi\)
\(338\) 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 −0.131326 0.991339i \(-0.541923\pi\)
0.924188 0.381938i \(-0.124743\pi\)
\(348\) 0.0167988 + 0.148199i 0.000900509 + 0.00794430i
\(349\) 18.0006 + 31.1780i 0.963551 + 1.66892i 0.713458 + 0.700698i \(0.247128\pi\)
0.250094 + 0.968222i \(0.419539\pi\)
\(350\) 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 0.929073 + 0.369897i \(0.120607\pi\)
−0.144196 + 0.989549i \(0.546060\pi\)
\(354\) 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 0.992442 + 0.122715i \(0.0391602\pi\)
−0.389946 + 0.920838i \(0.627506\pi\)
\(368\) 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 0.441078 + 0.897469i \(0.354596\pi\)
−0.997770 + 0.0667498i \(0.978737\pi\)
\(374\) −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 0.0549390 0.998490i \(-0.482504\pi\)
0.837248 0.546823i \(-0.184163\pi\)
\(384\) −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 0.955944 + 0.293548i \(0.0948361\pi\)
−0.223752 + 0.974646i \(0.571831\pi\)
\(390\) 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 −0.852200 0.523217i \(-0.824732\pi\)
0.879219 + 0.476418i \(0.158065\pi\)
\(402\) −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 −0.461685 0.887044i \(-0.652755\pi\)
0.999045 0.0436908i \(-0.0139116\pi\)
\(410\) −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 −0.375279 0.926912i \(-0.622453\pi\)
0.990369 0.138455i \(-0.0442135\pi\)
\(420\) 0 0
\(421\) −14.8304 25.6869i −0.722788 1.25191i −0.959878 0.280418i \(-0.909527\pi\)
0.237090 0.971488i \(-0.423806\pi\)
\(422\) −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 0.986902 0.161320i \(-0.0515751\pi\)
−0.633158 + 0.774022i \(0.718242\pi\)
\(440\) 2.26760 0.108103
\(441\) 0 0
\(442\) 14.7617 0.702141
\(443\) 10.9510 + 18.9676i 0.520297 + 0.901180i 0.999722 + 0.0235972i \(0.00751192\pi\)
−0.479425 + 0.877583i \(0.659155\pi\)
\(444\) −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 −0.745009 0.667054i \(-0.767555\pi\)
−0.205181 0.978724i \(-0.565778\pi\)
\(458\) 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 0.897103 0.441822i \(-0.145668\pi\)
−0.831181 + 0.556003i \(0.812334\pi\)
\(462\) 0 0
\(463\) −13.9324 + 24.1317i −0.647494 + 1.12149i 0.336225 + 0.941782i \(0.390850\pi\)
−0.983719 + 0.179711i \(0.942484\pi\)
\(464\) 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 0.960422 + 0.278551i \(0.0898540\pi\)
−0.238979 + 0.971025i \(0.576813\pi\)
\(480\) 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 −0.994813 0.101720i \(-0.967566\pi\)
0.585498 + 0.810674i \(0.300899\pi\)
\(492\) −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 −0.522687 0.852524i \(-0.675070\pi\)
0.999652 + 0.0263983i \(0.00840381\pi\)
\(500\) 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 0.0943635 + 0.995538i \(0.469918\pi\)
−0.909343 + 0.416048i \(0.863415\pi\)
\(510\) 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 0.894160 0.447747i \(-0.147773\pi\)
−0.834840 + 0.550492i \(0.814440\pi\)
\(548\) 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 −0.869044 0.494734i \(-0.835265\pi\)
0.862975 + 0.505247i \(0.168599\pi\)
\(564\) −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 0.983878 0.178843i \(-0.0572354\pi\)
−0.646821 + 0.762641i \(0.723902\pi\)
\(570\) −1.20062 10.5919i −0.0502883 0.443644i
\(571\) 7.64289 13.2379i 0.319845 0.553988i −0.660610 0.750729i \(-0.729702\pi\)
0.980456 + 0.196741i \(0.0630358\pi\)
\(572\) −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 0.950875 + 0.309574i \(0.100186\pi\)
−0.207339 + 0.978269i \(0.566480\pi\)
\(588\) 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 0.107019 + 0.994257i \(0.465869\pi\)
−0.914561 + 0.404447i \(0.867464\pi\)
\(600\) −5.03373 + 3.72028i −0.205501 + 0.151880i
\(601\) 1.86447 + 3.22936i 0.0760534 + 0.131728i 0.901544 0.432688i \(-0.142435\pi\)
−0.825490 + 0.564416i \(0.809101\pi\)
\(602\) 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 −0.999737 0.0229218i \(-0.992703\pi\)
0.519719 + 0.854337i \(0.326036\pi\)
\(608\) −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 0.258966 + 0.965886i \(0.416618\pi\)
−0.965965 + 0.258672i \(0.916715\pi\)
\(618\) −0.693409 6.11726i −0.0278930 0.246072i
\(619\) 10.5816 + 18.3279i 0.425311 + 0.736660i 0.996449 0.0841934i \(-0.0268314\pi\)
−0.571138 + 0.820854i \(0.693498\pi\)
\(620\) −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 0.946905 0.321514i \(-0.104192\pi\)
−0.751891 + 0.659287i \(0.770858\pi\)
\(642\) 14.8223 10.9547i 0.584990 0.432349i
\(643\) 21.9748 38.0615i 0.866602 1.50100i 0.00115462 0.999999i \(-0.499632\pi\)
0.865448 0.501000i \(-0.167034\pi\)
\(644\) 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 0.0828523 + 0.996562i \(0.473597\pi\)
−0.904474 + 0.426529i \(0.859736\pi\)
\(654\) −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 −0.940284 0.340390i \(-0.889441\pi\)
0.175356 0.984505i \(-0.443892\pi\)
\(660\) −4.45822 1.94154i −0.173536 0.0755743i
\(661\) 0.0933694 0.161721i 0.00363165 0.00629020i −0.864204 0.503142i \(-0.832177\pi\)
0.867836 + 0.496852i \(0.165511\pi\)
\(662\) −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 0.742086 0.670305i \(-0.233837\pi\)
−0.951544 + 0.307512i \(0.900503\pi\)
\(674\) 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 −0.998571 0.0534326i \(-0.982984\pi\)
0.453012 0.891505i \(-0.350350\pi\)
\(678\) 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 0.730264 0.683165i \(-0.239397\pi\)
−0.956770 + 0.290844i \(0.906064\pi\)
\(692\) 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 0.860096 0.510133i \(-0.170404\pi\)
−0.871836 + 0.489798i \(0.837070\pi\)
\(710\) 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 −0.967799 0.251726i \(-0.919002\pi\)
0.265899 0.964001i \(-0.414331\pi\)
\(728\) 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 −0.887349 0.461098i \(-0.847456\pi\)
0.842997 + 0.537918i \(0.180789\pi\)
\(734\) −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 −0.908970 0.416862i \(-0.863130\pi\)
0.815498 + 0.578760i \(0.196463\pi\)
\(744\) 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 −0.856994 0.515327i \(-0.827671\pi\)
0.874783 + 0.484515i \(0.161004\pi\)
\(752\) −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 0.327023 0.945016i \(-0.393955\pi\)
0.654897 0.755718i \(-0.272712\pi\)
\(762\) −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 −0.990507 0.137462i \(-0.956106\pi\)
0.614299 + 0.789074i \(0.289439\pi\)
\(770\) 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 +