Properties

Label 441.2.f.f.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.f.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 −0.677324 0.735685i \(-0.736860\pi\)
0.975784 + 0.218737i \(0.0701937\pi\)
\(6\) 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 \(-0.578491\pi\)
0.961877 0.273482i \(-0.0881755\pi\)
\(14\) 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 \(-0.439853\pi\)
0.187835 + 0.982201i \(0.439853\pi\)
\(18\) −3.76252 4.04413i −0.886834 0.953210i
\(19\) −2.50422 −0.574507 −0.287254 0.957855i \(-0.592742\pi\)
−0.287254 + 0.957855i \(0.592742\pi\)
\(20\) 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 −0.985452 0.169956i \(-0.945638\pi\)
0.639912 + 0.768448i \(0.278971\pi\)
\(32\) −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 \(0.415557\pi\)
−0.966822 + 0.255450i \(0.917776\pi\)
\(42\) 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 \(-0.922421\pi\)
0.276238 0.961089i \(-0.410912\pi\)
\(48\) 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 \(0.351891\pi\)
−0.998301 + 0.0582689i \(0.981442\pi\)
\(60\) 2.58459 1.91020i 0.333670 0.246606i
\(61\) 1.61958 + 2.80520i 0.207367 + 0.359169i 0.950884 0.309547i \(-0.100177\pi\)
−0.743518 + 0.668716i \(0.766844\pi\)
\(62\) −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 \(-0.551614\pi\)
−0.161442 + 0.986882i \(0.551614\pi\)
\(74\) 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 0.670344 0.742050i \(-0.266146\pi\)
−0.977806 + 0.209510i \(0.932813\pi\)
\(84\) 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 \(-0.476249\pi\)
0.0745483 + 0.997217i \(0.476249\pi\)
\(90\) −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 \(0.0458236\pi\)
−0.370586 + 0.928798i \(0.620843\pi\)
\(98\) 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 \(-0.148942\pi\)
−0.836855 + 0.547425i \(0.815608\pi\)
\(102\) 3.97251 2.93597i 0.393338 0.290704i
\(103\) 0.965224 1.67182i 0.0951063 0.164729i −0.814547 0.580098i \(-0.803014\pi\)
0.909653 + 0.415369i \(0.136348\pi\)
\(104\) 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 −0.906648 0.421888i \(-0.861368\pi\)
0.818690 + 0.574236i \(0.194701\pi\)
\(132\) −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 −0.881598 0.472002i \(-0.843532\pi\)
0.849564 + 0.527485i \(0.176865\pi\)
\(140\) 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 \(0.409338\pi\)
−0.971628 + 0.236515i \(0.923995\pi\)
\(158\) −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 \(-0.876882\pi\)
0.789741 + 0.613440i \(0.210215\pi\)
\(168\) 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 \(-0.0406958\pi\)
−0.606339 + 0.795206i \(0.707362\pi\)
\(174\) −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 \(-0.282406\pi\)
0.631581 + 0.775310i \(0.282406\pi\)
\(182\) 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 \(-0.599538\pi\)
−0.307636 + 0.951504i \(0.599538\pi\)
\(200\) 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 0.600276 0.799793i \(-0.295058\pi\)
−0.992779 + 0.119957i \(0.961724\pi\)
\(224\) 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 \(-0.0456394\pi\)
−0.618615 + 0.785694i \(0.712306\pi\)
\(228\) −5.52827 2.40754i −0.366118 0.159443i
\(229\) −4.82824 + 8.36275i −0.319059 + 0.552626i −0.980292 0.197554i \(-0.936700\pi\)
0.661233 + 0.750181i \(0.270033\pi\)
\(230\) 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 0.984909 0.173075i \(-0.0553703\pi\)
−0.642342 + 0.766419i \(0.722037\pi\)
\(242\) 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 \(-0.467129\pi\)
0.103083 + 0.994673i \(0.467129\pi\)
\(252\) 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 \(-0.880120\pi\)
0.783459 + 0.621443i \(0.213453\pi\)
\(258\) 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 \(-0.340392\pi\)
0.480675 + 0.876899i \(0.340392\pi\)
\(270\) 4.24196 + 12.0449i 0.258157 + 0.733032i
\(271\) 14.7976 0.898893 0.449446 0.893307i \(-0.351621\pi\)
0.449446 + 0.893307i \(0.351621\pi\)
\(272\) 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 \(-0.645115\pi\)
0.997709 0.0676550i \(-0.0215517\pi\)
\(284\) 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 \(-0.810424\pi\)
0.899738 + 0.436430i \(0.143757\pi\)
\(294\) 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 \(-0.457520\pi\)
0.133059 + 0.991108i \(0.457520\pi\)
\(308\) 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 \(-0.548968\pi\)
0.932413 0.361393i \(-0.117699\pi\)
\(312\) −9.22921 4.01929i −0.522501 0.227548i
\(313\) 2.74666 + 4.75735i 0.155250 + 0.268901i 0.933150 0.359487i \(-0.117048\pi\)
−0.777900 + 0.628388i \(0.783715\pi\)
\(314\) −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 \(-0.752872\pi\)
−0.250094 0.968222i \(-0.580461\pi\)
\(350\) 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 \(-0.879393\pi\)
0.144196 0.989549i \(-0.453940\pi\)
\(354\) 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 \(-0.960840\pi\)
0.389946 0.920838i \(-0.372494\pi\)
\(368\) 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 \(0.517496\pi\)
−0.837248 + 0.546823i \(0.815837\pi\)
\(384\) 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 \(-0.409444\pi\)
0.280667 + 0.959805i \(0.409444\pi\)
\(398\) −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 \(0.347245\pi\)
−0.999045 + 0.0436908i \(0.986088\pi\)
\(410\) −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 \(0.377547\pi\)
−0.990369 + 0.138455i \(0.955787\pi\)
\(420\) 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 \(-0.574992\pi\)
−0.233420 + 0.972376i \(0.574992\pi\)
\(434\) 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 \(-0.281758\pi\)
−0.986902 + 0.161320i \(0.948425\pi\)
\(440\) −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 0.831181 0.556003i \(-0.187666\pi\)
−0.897103 + 0.441822i \(0.854332\pi\)
\(462\) 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 \(-0.711436\pi\)
−0.616464 + 0.787383i \(0.711436\pi\)
\(468\) −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 \(-0.910146\pi\)
0.238979 0.971025i \(-0.423187\pi\)
\(480\) 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 \(-0.375703\pi\)
0.380642 + 0.924722i \(0.375703\pi\)
\(504\) 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 \(-0.530082\pi\)
0.909343 0.416048i \(-0.136585\pi\)
\(510\) −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 \(-0.637796\pi\)
−0.419504 + 0.907754i \(0.637796\pi\)
\(522\) −0.100413 + 0.327088i −0.00439494 + 0.0143163i
\(523\) −41.9429 −1.83404 −0.917018 0.398847i \(-0.869411\pi\)
−0.917018 + 0.398847i \(0.869411\pi\)
\(524\) −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 −0.862975 0.505247i \(-0.831401\pi\)
0.869044 + 0.494734i \(0.164735\pi\)
\(564\) −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 \(-0.332248\pi\)
0.502949 + 0.864316i \(0.332248\pi\)
\(578\) −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 \(-0.899814\pi\)
0.207339 0.978269i \(-0.433520\pi\)
\(588\) 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 \(-0.328923\pi\)
0.511951 + 0.859014i \(0.328923\pi\)
\(594\) 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 0.825490 0.564416i \(-0.190899\pi\)
−0.901544 + 0.432688i \(0.857565\pi\)
\(602\) 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 \(-0.673964\pi\)
0.999737 + 0.0229218i \(0.00729686\pi\)
\(608\) 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 0.571138 0.820854i \(-0.306502\pi\)
−0.996449 + 0.0841934i \(0.973169\pi\)
\(620\) −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 \(0.500368\pi\)
−0.865448 + 0.501000i \(0.832966\pi\)
\(644\) 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 \(-0.162484\pi\)
0.872521 + 0.488577i \(0.162484\pi\)
\(648\) 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 −0.867836 0.496852i \(-0.834489\pi\)
0.864204 + 0.503142i \(0.167823\pi\)
\(662\) −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 \(0.0170162\pi\)
−0.453012 + 0.891505i \(0.649650\pi\)
\(678\) −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 \(-0.0939361\pi\)
−0.730264 + 0.683165i \(0.760603\pi\)
\(692\) −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 \(-0.349686\pi\)
0.454869 + 0.890558i \(0.349686\pi\)
\(720\) −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 \(0.0809980\pi\)
−0.265899 + 0.964001i \(0.585669\pi\)
\(728\) 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 \(-0.819211\pi\)
0.887349 + 0.461098i \(0.152544\pi\)
\(734\) 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 \(0.606045\pi\)
−0.654897 + 0.755718i \(0.727288\pi\)
\(762\) 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 \(-0.710561\pi\)
0.990507 + 0.137462i \(0.0438943\pi\)
\(770\) 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 \(-0.952759\pi\)
−0.989007 + 0.147868i \(0.952759\pi\)
\(774\) 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 + 16.1566i 0.333783 + 0.578129i