Properties

Label 441.2.f.f.295.4
Level $441$
Weight $2$
Character 441.295
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 295.4
Root \(0.920620 - 1.59456i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.f.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 0.975784 0.218737i \(-0.0701937\pi\)
−0.677324 + 0.735685i \(0.736860\pi\)
\(6\) 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 \(0.0881755\pi\)
−0.244096 + 0.969751i \(0.578491\pi\)
\(14\) 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 0.938960 + 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 0.639912 0.768448i \(-0.278971\pi\)
−0.985452 + 0.169956i \(0.945638\pi\)
\(32\) −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 \(-0.917776\pi\)
0.262185 0.965018i \(-0.415557\pi\)
\(42\) 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 \(0.410912\pi\)
−0.970447 + 0.241315i \(0.922421\pi\)
\(48\) 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 \(-0.981442\pi\)
0.448688 0.893688i \(-0.351891\pi\)
\(60\) 2.58459 + 1.91020i 0.333670 + 0.246606i
\(61\) 1.61958 2.80520i 0.207367 0.359169i −0.743518 0.668716i \(-0.766844\pi\)
0.950884 + 0.309547i \(0.100177\pi\)
\(62\) −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 \(-0.551614\pi\)
−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 −0.650106 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 −0.977806 0.209510i \(-0.932813\pi\)
0.670344 + 0.742050i \(0.266146\pi\)
\(84\) 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 −0.370586 0.928798i \(-0.620843\pi\)
0.989656 0.143462i \(-0.0458236\pi\)
\(98\) 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 \(-0.815608\pi\)
0.892511 + 0.451025i \(0.148942\pi\)
\(102\) 3.97251 + 2.93597i 0.393338 + 0.290704i
\(103\) 0.965224 + 1.67182i 0.0951063 + 0.164729i 0.909653 0.415369i \(-0.136348\pi\)
−0.814547 + 0.580098i \(0.803014\pi\)
\(104\) 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 0.818690 0.574236i \(-0.194701\pi\)
−0.906648 + 0.421888i \(0.861368\pi\)
\(132\) −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 0.849564 0.527485i \(-0.176865\pi\)
−0.881598 + 0.472002i \(0.843532\pi\)
\(140\) 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 \(-0.923995\pi\)
0.280986 0.959712i \(-0.409338\pi\)
\(158\) −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 \(-0.210215\pi\)
−0.926126 + 0.377215i \(0.876882\pi\)
\(168\) 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 \(-0.707362\pi\)
0.991838 + 0.127502i \(0.0406958\pi\)
\(174\) −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 0.0838717 + 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 \(-0.599538\pi\)
−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 0.751453 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 −0.992779 0.119957i \(-0.961724\pi\)
0.600276 + 0.799793i \(0.295058\pi\)
\(224\) 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 \(-0.712306\pi\)
0.989739 + 0.142890i \(0.0456394\pi\)
\(228\) −5.52827 + 2.40754i −0.366118 + 0.159443i
\(229\) −4.82824 8.36275i −0.319059 0.552626i 0.661233 0.750181i \(-0.270033\pi\)
−0.980292 + 0.197554i \(0.936700\pi\)
\(230\) 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 −0.642342 0.766419i \(-0.722037\pi\)
0.984909 + 0.173075i \(0.0553703\pi\)
\(242\) 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 0.783459 0.621443i \(-0.213453\pi\)
−0.929915 + 0.367774i \(0.880120\pi\)
\(258\) 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 \(-0.340392\pi\)
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 −0.732124 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 \(0.0215517\pi\)
−0.440263 + 0.897869i \(0.645115\pi\)
\(284\) 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 \(-0.143757\pi\)
−0.827829 + 0.560981i \(0.810424\pi\)
\(294\) 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 0.932413 + 0.361393i \(0.117699\pi\)
−0.153231 + 0.988190i \(0.548968\pi\)
\(312\) −9.22921 + 4.01929i −0.522501 + 0.227548i
\(313\) 2.74666 4.75735i 0.155250 0.268901i −0.777900 0.628388i \(-0.783715\pi\)
0.933150 + 0.359487i \(0.117048\pi\)
\(314\) −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 \(0.580461\pi\)
−0.713458 + 0.700698i \(0.752872\pi\)
\(350\) 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 \(0.453940\pi\)
−0.929073 + 0.369897i \(0.879393\pi\)
\(354\) 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 \(0.372494\pi\)
−0.992442 + 0.122715i \(0.960840\pi\)
\(368\) 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 \(-0.815837\pi\)
−0.0549390 0.998490i \(-0.517496\pi\)
\(384\) 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 \(-0.409444\pi\)
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 0.879219 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 \(-0.986088\pi\)
0.461685 0.887044i \(-0.347245\pi\)
\(410\) −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 \(-0.955787\pi\)
0.375279 0.926912i \(-0.377547\pi\)
\(420\) 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 \(-0.574992\pi\)
−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 −0.986902 0.161320i \(-0.948425\pi\)
0.633158 + 0.774022i \(0.281758\pi\)
\(440\) −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 −0.897103 0.441822i \(-0.854332\pi\)
0.831181 + 0.556003i \(0.187666\pi\)
\(462\) 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 \(-0.711436\pi\)
−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 0.238979 + 0.971025i \(0.423187\pi\)
−0.960422 + 0.278551i \(0.910146\pi\)
\(480\) 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 \(-0.375703\pi\)
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 0.909343 + 0.416048i \(0.136585\pi\)
−0.0943635 + 0.995538i \(0.530082\pi\)
\(510\) −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 −0.834840 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 0.869044 0.494734i \(-0.164735\pi\)
−0.862975 + 0.505247i \(0.831401\pi\)
\(564\) −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 \(-0.332248\pi\)
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 0.207339 + 0.978269i \(0.433520\pi\)
−0.950875 + 0.309574i \(0.899814\pi\)
\(588\) 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 −0.914561 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 −0.901544 0.432688i \(-0.857565\pi\)
0.825490 + 0.564416i \(0.190899\pi\)
\(602\) 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 \(-0.00729686\pi\)
−0.519719 + 0.854337i \(0.673964\pi\)
\(608\) 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 −0.996449 0.0841934i \(-0.973169\pi\)
0.571138 + 0.820854i \(0.306502\pi\)
\(620\) −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 \(-0.832966\pi\)
−0.00115462 0.999999i \(-0.500368\pi\)
\(644\) 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 −0.904474 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 0.864204 0.503142i \(-0.167823\pi\)
−0.867836 + 0.496852i \(0.834489\pi\)
\(662\) −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 \(-0.649650\pi\)
0.998571 0.0534326i \(-0.0170162\pi\)
\(678\) −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 \(-0.760603\pi\)
0.956770 + 0.290844i \(0.0939361\pi\)
\(692\) −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 \(-0.349686\pi\)
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 −0.265899 0.964001i \(-0.585669\pi\)
0.967799 0.251726i \(-0.0809980\pi\)
\(728\) 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 \(-0.152544\pi\)
−0.842997 + 0.537918i \(0.819211\pi\)
\(734\) 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 \(-0.727288\pi\)
−0.327023 0.945016i \(-0.606045\pi\)
\(762\) 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 \(-0.0438943\pi\)
−0.614299 + 0.789074i \(0.710561\pi\)
\(770\) 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