Properties

Label 1950.2.bc.f.751.4
Level $1950$
Weight $2$
Character 1950.751
Analytic conductor $15.571$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1950.bc (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(15.5708283941\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \(x^{8} - x^{4} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 751.4
Root \(-0.258819 - 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 1950.751
Dual form 1950.2.bc.f.901.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-0.417738 - 0.241181i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(-0.417738 - 0.241181i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-2.00731 + 1.15892i) q^{11} +1.00000 q^{12} +(3.08725 - 1.86250i) q^{13} -0.482362 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.39778 + 5.88512i) q^{17} +1.00000i q^{18} +(4.39778 + 2.53906i) q^{19} -0.482362i q^{21} +(-1.15892 + 2.00731i) q^{22} +(3.45327 + 5.98124i) q^{23} +(0.866025 - 0.500000i) q^{24} +(1.74238 - 3.15660i) q^{26} -1.00000 q^{27} +(-0.417738 + 0.241181i) q^{28} +(4.20478 + 7.28290i) q^{29} +0.952516i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-2.00731 - 1.15892i) q^{33} +6.79555i q^{34} +(0.500000 + 0.866025i) q^{36} +(5.35948 - 3.09429i) q^{37} +5.07812 q^{38} +(3.15660 + 1.74238i) q^{39} +(7.55607 - 4.36250i) q^{41} +(-0.241181 - 0.417738i) q^{42} +(5.64747 - 9.78170i) q^{43} +2.31784i q^{44} +(5.98124 + 3.45327i) q^{46} -5.77729i q^{47} +(0.500000 - 0.866025i) q^{48} +(-3.38366 - 5.86068i) q^{49} -6.79555 q^{51} +(-0.0693504 - 3.60488i) q^{52} -5.81017 q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.241181 + 0.417738i) q^{56} +5.07812i q^{57} +(7.28290 + 4.20478i) q^{58} +(10.2397 + 5.91189i) q^{59} +(-4.68764 + 8.11924i) q^{61} +(0.476258 + 0.824903i) q^{62} +(0.417738 - 0.241181i) q^{63} -1.00000 q^{64} -2.31784 q^{66} +(-6.40300 + 3.69677i) q^{67} +(3.39778 + 5.88512i) q^{68} +(-3.45327 + 5.98124i) q^{69} +(3.01876 + 1.74288i) q^{71} +(0.866025 + 0.500000i) q^{72} +8.53465i q^{73} +(3.09429 - 5.35948i) q^{74} +(4.39778 - 2.53906i) q^{76} +1.11804 q^{77} +(3.60488 - 0.0693504i) q^{78} +9.03820 q^{79} +(-0.500000 - 0.866025i) q^{81} +(4.36250 - 7.55607i) q^{82} +7.94887i q^{83} +(-0.417738 - 0.241181i) q^{84} -11.2949i q^{86} +(-4.20478 + 7.28290i) q^{87} +(1.15892 + 2.00731i) q^{88} +(7.80941 - 4.50877i) q^{89} +(-1.73886 + 0.0334520i) q^{91} +6.90654 q^{92} +(-0.824903 + 0.476258i) q^{93} +(-2.88865 - 5.00328i) q^{94} -1.00000i q^{96} +(-7.95189 - 4.59103i) q^{97} +(-5.86068 - 3.38366i) q^{98} -2.31784i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} + O(q^{10}) \) \( 8q + 4q^{3} + 4q^{4} - 4q^{9} - 12q^{11} + 8q^{12} - 8q^{14} - 4q^{16} - 4q^{17} + 12q^{19} - 8q^{22} - 4q^{23} - 8q^{27} + 4q^{29} - 12q^{33} + 4q^{36} + 24q^{37} - 4q^{42} + 4q^{43} + 12q^{46} + 4q^{48} - 16q^{49} - 8q^{51} + 8q^{53} - 4q^{56} - 12q^{58} - 12q^{59} - 16q^{61} - 4q^{62} - 8q^{64} - 16q^{66} - 24q^{67} + 4q^{68} + 4q^{69} + 60q^{71} + 16q^{74} + 12q^{76} + 8q^{77} - 8q^{79} - 4q^{81} + 20q^{82} - 4q^{87} + 8q^{88} + 24q^{89} + 8q^{91} - 8q^{92} + 24q^{93} + 16q^{94} - 12q^{97} - 12q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times\).

\(n\) \(301\) \(1301\) \(1327\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 0.500000i 0.612372 0.353553i
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 0 0
\(6\) 0.866025 + 0.500000i 0.353553 + 0.204124i
\(7\) −0.417738 0.241181i −0.157890 0.0911578i 0.418973 0.907999i \(-0.362390\pi\)
−0.576863 + 0.816841i \(0.695723\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −2.00731 + 1.15892i −0.605226 + 0.349427i −0.771095 0.636721i \(-0.780290\pi\)
0.165869 + 0.986148i \(0.446957\pi\)
\(12\) 1.00000 0.288675
\(13\) 3.08725 1.86250i 0.856248 0.516565i
\(14\) −0.482362 −0.128917
\(15\) 0 0
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.39778 + 5.88512i −0.824082 + 1.42735i 0.0785367 + 0.996911i \(0.474975\pi\)
−0.902619 + 0.430441i \(0.858358\pi\)
\(18\) 1.00000i 0.235702i
\(19\) 4.39778 + 2.53906i 1.00892 + 0.582500i 0.910875 0.412682i \(-0.135408\pi\)
0.0980443 + 0.995182i \(0.468741\pi\)
\(20\) 0 0
\(21\) 0.482362i 0.105260i
\(22\) −1.15892 + 2.00731i −0.247082 + 0.427959i
\(23\) 3.45327 + 5.98124i 0.720057 + 1.24718i 0.960976 + 0.276630i \(0.0892177\pi\)
−0.240920 + 0.970545i \(0.577449\pi\)
\(24\) 0.866025 0.500000i 0.176777 0.102062i
\(25\) 0 0
\(26\) 1.74238 3.15660i 0.341709 0.619060i
\(27\) −1.00000 −0.192450
\(28\) −0.417738 + 0.241181i −0.0789450 + 0.0455789i
\(29\) 4.20478 + 7.28290i 0.780809 + 1.35240i 0.931471 + 0.363815i \(0.118526\pi\)
−0.150662 + 0.988585i \(0.548141\pi\)
\(30\) 0 0
\(31\) 0.952516i 0.171077i 0.996335 + 0.0855385i \(0.0272611\pi\)
−0.996335 + 0.0855385i \(0.972739\pi\)
\(32\) −0.866025 0.500000i −0.153093 0.0883883i
\(33\) −2.00731 1.15892i −0.349427 0.201742i
\(34\) 6.79555i 1.16543i
\(35\) 0 0
\(36\) 0.500000 + 0.866025i 0.0833333 + 0.144338i
\(37\) 5.35948 3.09429i 0.881092 0.508699i 0.0100739 0.999949i \(-0.496793\pi\)
0.871018 + 0.491250i \(0.163460\pi\)
\(38\) 5.07812 0.823779
\(39\) 3.15660 + 1.74238i 0.505460 + 0.279005i
\(40\) 0 0
\(41\) 7.55607 4.36250i 1.18006 0.681308i 0.224032 0.974582i \(-0.428078\pi\)
0.956029 + 0.293274i \(0.0947447\pi\)
\(42\) −0.241181 0.417738i −0.0372150 0.0644583i
\(43\) 5.64747 9.78170i 0.861231 1.49170i −0.00951136 0.999955i \(-0.503028\pi\)
0.870742 0.491740i \(-0.163639\pi\)
\(44\) 2.31784i 0.349427i
\(45\) 0 0
\(46\) 5.98124 + 3.45327i 0.881886 + 0.509157i
\(47\) 5.77729i 0.842705i −0.906897 0.421353i \(-0.861556\pi\)
0.906897 0.421353i \(-0.138444\pi\)
\(48\) 0.500000 0.866025i 0.0721688 0.125000i
\(49\) −3.38366 5.86068i −0.483380 0.837240i
\(50\) 0 0
\(51\) −6.79555 −0.951568
\(52\) −0.0693504 3.60488i −0.00961716 0.499908i
\(53\) −5.81017 −0.798088 −0.399044 0.916932i \(-0.630658\pi\)
−0.399044 + 0.916932i \(0.630658\pi\)
\(54\) −0.866025 + 0.500000i −0.117851 + 0.0680414i
\(55\) 0 0
\(56\) −0.241181 + 0.417738i −0.0322292 + 0.0558225i
\(57\) 5.07812i 0.672613i
\(58\) 7.28290 + 4.20478i 0.956292 + 0.552115i
\(59\) 10.2397 + 5.91189i 1.33309 + 0.769663i 0.985773 0.168083i \(-0.0537577\pi\)
0.347322 + 0.937746i \(0.387091\pi\)
\(60\) 0 0
\(61\) −4.68764 + 8.11924i −0.600191 + 1.03956i 0.392600 + 0.919709i \(0.371576\pi\)
−0.992792 + 0.119853i \(0.961758\pi\)
\(62\) 0.476258 + 0.824903i 0.0604848 + 0.104763i
\(63\) 0.417738 0.241181i 0.0526300 0.0303859i
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) −2.31784 −0.285306
\(67\) −6.40300 + 3.69677i −0.782251 + 0.451633i −0.837227 0.546855i \(-0.815825\pi\)
0.0549764 + 0.998488i \(0.482492\pi\)
\(68\) 3.39778 + 5.88512i 0.412041 + 0.713676i
\(69\) −3.45327 + 5.98124i −0.415725 + 0.720057i
\(70\) 0 0
\(71\) 3.01876 + 1.74288i 0.358261 + 0.206842i 0.668318 0.743876i \(-0.267015\pi\)
−0.310057 + 0.950718i \(0.600348\pi\)
\(72\) 0.866025 + 0.500000i 0.102062 + 0.0589256i
\(73\) 8.53465i 0.998906i 0.866341 + 0.499453i \(0.166466\pi\)
−0.866341 + 0.499453i \(0.833534\pi\)
\(74\) 3.09429 5.35948i 0.359704 0.623026i
\(75\) 0 0
\(76\) 4.39778 2.53906i 0.504460 0.291250i
\(77\) 1.11804 0.127412
\(78\) 3.60488 0.0693504i 0.408173 0.00785238i
\(79\) 9.03820 1.01688 0.508438 0.861098i \(-0.330223\pi\)
0.508438 + 0.861098i \(0.330223\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 4.36250 7.55607i 0.481758 0.834429i
\(83\) 7.94887i 0.872502i 0.899825 + 0.436251i \(0.143694\pi\)
−0.899825 + 0.436251i \(0.856306\pi\)
\(84\) −0.417738 0.241181i −0.0455789 0.0263150i
\(85\) 0 0
\(86\) 11.2949i 1.21796i
\(87\) −4.20478 + 7.28290i −0.450800 + 0.780809i
\(88\) 1.15892 + 2.00731i 0.123541 + 0.213980i
\(89\) 7.80941 4.50877i 0.827796 0.477928i −0.0253015 0.999680i \(-0.508055\pi\)
0.853097 + 0.521752i \(0.174721\pi\)
\(90\) 0 0
\(91\) −1.73886 + 0.0334520i −0.182282 + 0.00350672i
\(92\) 6.90654 0.720057
\(93\) −0.824903 + 0.476258i −0.0855385 + 0.0493857i
\(94\) −2.88865 5.00328i −0.297941 0.516049i
\(95\) 0 0
\(96\) 1.00000i 0.102062i
\(97\) −7.95189 4.59103i −0.807392 0.466148i 0.0386571 0.999253i \(-0.487692\pi\)
−0.846050 + 0.533104i \(0.821025\pi\)
\(98\) −5.86068 3.38366i −0.592018 0.341802i
\(99\) 2.31784i 0.232951i
\(100\) 0 0
\(101\) −5.34108 9.25102i −0.531457 0.920511i −0.999326 0.0367132i \(-0.988311\pi\)
0.467868 0.883798i \(-0.345022\pi\)
\(102\) −5.88512 + 3.39778i −0.582714 + 0.336430i
\(103\) −9.17449 −0.903990 −0.451995 0.892021i \(-0.649287\pi\)
−0.451995 + 0.892021i \(0.649287\pi\)
\(104\) −1.86250 3.08725i −0.182633 0.302729i
\(105\) 0 0
\(106\) −5.03175 + 2.90508i −0.488727 + 0.282167i
\(107\) −1.60867 2.78629i −0.155516 0.269361i 0.777731 0.628597i \(-0.216371\pi\)
−0.933247 + 0.359236i \(0.883037\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) 17.0669i 1.63471i 0.576132 + 0.817356i \(0.304561\pi\)
−0.576132 + 0.817356i \(0.695439\pi\)
\(110\) 0 0
\(111\) 5.35948 + 3.09429i 0.508699 + 0.293697i
\(112\) 0.482362i 0.0455789i
\(113\) −0.828427 + 1.43488i −0.0779319 + 0.134982i −0.902357 0.430988i \(-0.858165\pi\)
0.824426 + 0.565970i \(0.191498\pi\)
\(114\) 2.53906 + 4.39778i 0.237805 + 0.411890i
\(115\) 0 0
\(116\) 8.40957 0.780809
\(117\) 0.0693504 + 3.60488i 0.00641144 + 0.333272i
\(118\) 11.8238 1.08847
\(119\) 2.83876 1.63896i 0.260229 0.150243i
\(120\) 0 0
\(121\) −2.81382 + 4.87367i −0.255801 + 0.443061i
\(122\) 9.37529i 0.848799i
\(123\) 7.55607 + 4.36250i 0.681308 + 0.393353i
\(124\) 0.824903 + 0.476258i 0.0740785 + 0.0427692i
\(125\) 0 0
\(126\) 0.241181 0.417738i 0.0214861 0.0372150i
\(127\) −9.45946 16.3843i −0.839391 1.45387i −0.890405 0.455170i \(-0.849578\pi\)
0.0510134 0.998698i \(-0.483755\pi\)
\(128\) −0.866025 + 0.500000i −0.0765466 + 0.0441942i
\(129\) 11.2949 0.994463
\(130\) 0 0
\(131\) −6.96812 −0.608808 −0.304404 0.952543i \(-0.598457\pi\)
−0.304404 + 0.952543i \(0.598457\pi\)
\(132\) −2.00731 + 1.15892i −0.174714 + 0.100871i
\(133\) −1.22474 2.12132i −0.106199 0.183942i
\(134\) −3.69677 + 6.40300i −0.319353 + 0.553135i
\(135\) 0 0
\(136\) 5.88512 + 3.39778i 0.504645 + 0.291357i
\(137\) −17.7616 10.2547i −1.51748 0.876116i −0.999789 0.0205465i \(-0.993459\pi\)
−0.517688 0.855569i \(-0.673207\pi\)
\(138\) 6.90654i 0.587924i
\(139\) 4.25467 7.36931i 0.360877 0.625057i −0.627229 0.778835i \(-0.715811\pi\)
0.988105 + 0.153778i \(0.0491442\pi\)
\(140\) 0 0
\(141\) 5.00328 2.88865i 0.421353 0.243268i
\(142\) 3.48576 0.292519
\(143\) −4.03856 + 7.31648i −0.337721 + 0.611835i
\(144\) 1.00000 0.0833333
\(145\) 0 0
\(146\) 4.26733 + 7.39123i 0.353166 + 0.611702i
\(147\) 3.38366 5.86068i 0.279080 0.483380i
\(148\) 6.18859i 0.508699i
\(149\) 6.27439 + 3.62252i 0.514018 + 0.296769i 0.734484 0.678626i \(-0.237424\pi\)
−0.220466 + 0.975395i \(0.570758\pi\)
\(150\) 0 0
\(151\) 7.82743i 0.636987i 0.947925 + 0.318494i \(0.103177\pi\)
−0.947925 + 0.318494i \(0.896823\pi\)
\(152\) 2.53906 4.39778i 0.205945 0.356707i
\(153\) −3.39778 5.88512i −0.274694 0.475784i
\(154\) 0.968248 0.559018i 0.0780236 0.0450470i
\(155\) 0 0
\(156\) 3.08725 1.86250i 0.247178 0.149119i
\(157\) −4.42267 −0.352967 −0.176484 0.984304i \(-0.556472\pi\)
−0.176484 + 0.984304i \(0.556472\pi\)
\(158\) 7.82731 4.51910i 0.622707 0.359520i
\(159\) −2.90508 5.03175i −0.230388 0.399044i
\(160\) 0 0
\(161\) 3.33145i 0.262555i
\(162\) −0.866025 0.500000i −0.0680414 0.0392837i
\(163\) −9.72060 5.61219i −0.761376 0.439581i 0.0684135 0.997657i \(-0.478206\pi\)
−0.829790 + 0.558076i \(0.811540\pi\)
\(164\) 8.72500i 0.681308i
\(165\) 0 0
\(166\) 3.97443 + 6.88392i 0.308476 + 0.534296i
\(167\) 13.0406 7.52898i 1.00911 0.582610i 0.0981794 0.995169i \(-0.468698\pi\)
0.910931 + 0.412558i \(0.135365\pi\)
\(168\) −0.482362 −0.0372150
\(169\) 6.06218 11.5000i 0.466321 0.884615i
\(170\) 0 0
\(171\) −4.39778 + 2.53906i −0.336306 + 0.194167i
\(172\) −5.64747 9.78170i −0.430615 0.745848i
\(173\) −7.37429 + 12.7727i −0.560657 + 0.971087i 0.436782 + 0.899567i \(0.356118\pi\)
−0.997439 + 0.0715193i \(0.977215\pi\)
\(174\) 8.40957i 0.637528i
\(175\) 0 0
\(176\) 2.00731 + 1.15892i 0.151306 + 0.0873568i
\(177\) 11.8238i 0.888730i
\(178\) 4.50877 7.80941i 0.337946 0.585340i
\(179\) 4.30589 + 7.45802i 0.321837 + 0.557438i 0.980867 0.194678i \(-0.0623663\pi\)
−0.659030 + 0.752117i \(0.729033\pi\)
\(180\) 0 0
\(181\) 2.84493 0.211462 0.105731 0.994395i \(-0.466282\pi\)
0.105731 + 0.994395i \(0.466282\pi\)
\(182\) −1.48917 + 0.898400i −0.110385 + 0.0665938i
\(183\) −9.37529 −0.693041
\(184\) 5.98124 3.45327i 0.440943 0.254579i
\(185\) 0 0
\(186\) −0.476258 + 0.824903i −0.0349209 + 0.0604848i
\(187\) 15.7510i 1.15183i
\(188\) −5.00328 2.88865i −0.364902 0.210676i
\(189\) 0.417738 + 0.241181i 0.0303859 + 0.0175433i
\(190\) 0 0
\(191\) 1.71794 2.97555i 0.124306 0.215304i −0.797156 0.603774i \(-0.793663\pi\)
0.921461 + 0.388470i \(0.126996\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 2.30090 1.32843i 0.165623 0.0956223i −0.414898 0.909868i \(-0.636183\pi\)
0.580520 + 0.814246i \(0.302849\pi\)
\(194\) −9.18206 −0.659233
\(195\) 0 0
\(196\) −6.76733 −0.483380
\(197\) −18.2868 + 10.5579i −1.30288 + 0.752219i −0.980897 0.194526i \(-0.937683\pi\)
−0.321984 + 0.946745i \(0.604350\pi\)
\(198\) −1.15892 2.00731i −0.0823608 0.142653i
\(199\) 5.26941 9.12688i 0.373538 0.646988i −0.616569 0.787301i \(-0.711478\pi\)
0.990107 + 0.140314i \(0.0448110\pi\)
\(200\) 0 0
\(201\) −6.40300 3.69677i −0.451633 0.260750i
\(202\) −9.25102 5.34108i −0.650900 0.375797i
\(203\) 4.05646i 0.284707i
\(204\) −3.39778 + 5.88512i −0.237892 + 0.412041i
\(205\) 0 0
\(206\) −7.94534 + 4.58725i −0.553578 + 0.319609i
\(207\) −6.90654 −0.480038
\(208\) −3.15660 1.74238i −0.218871 0.120813i
\(209\) −11.7702 −0.814165
\(210\) 0 0
\(211\) 5.74384 + 9.94863i 0.395422 + 0.684892i 0.993155 0.116804i \(-0.0372649\pi\)
−0.597733 + 0.801696i \(0.703932\pi\)
\(212\) −2.90508 + 5.03175i −0.199522 + 0.345582i
\(213\) 3.48576i 0.238840i
\(214\) −2.78629 1.60867i −0.190467 0.109966i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 0.229729 0.397902i 0.0155950 0.0270113i
\(218\) 8.53345 + 14.7804i 0.577958 + 1.00105i
\(219\) −7.39123 + 4.26733i −0.499453 + 0.288359i
\(220\) 0 0
\(221\) 0.471274 + 24.4972i 0.0317013 + 1.64786i
\(222\) 6.18859 0.415351
\(223\) 4.52739 2.61389i 0.303176 0.175039i −0.340693 0.940175i \(-0.610662\pi\)
0.643869 + 0.765136i \(0.277328\pi\)
\(224\) 0.241181 + 0.417738i 0.0161146 + 0.0279113i
\(225\) 0 0
\(226\) 1.65685i 0.110212i
\(227\) 9.41271 + 5.43443i 0.624744 + 0.360696i 0.778714 0.627380i \(-0.215873\pi\)
−0.153970 + 0.988076i \(0.549206\pi\)
\(228\) 4.39778 + 2.53906i 0.291250 + 0.168153i
\(229\) 21.1932i 1.40048i −0.713905 0.700242i \(-0.753075\pi\)
0.713905 0.700242i \(-0.246925\pi\)
\(230\) 0 0
\(231\) 0.559018 + 0.968248i 0.0367807 + 0.0637060i
\(232\) 7.28290 4.20478i 0.478146 0.276058i
\(233\) 21.8423 1.43094 0.715469 0.698645i \(-0.246213\pi\)
0.715469 + 0.698645i \(0.246213\pi\)
\(234\) 1.86250 + 3.08725i 0.121756 + 0.201820i
\(235\) 0 0
\(236\) 10.2397 5.91189i 0.666547 0.384831i
\(237\) 4.51910 + 7.82731i 0.293547 + 0.508438i
\(238\) 1.63896 2.83876i 0.106238 0.184009i
\(239\) 8.23027i 0.532372i 0.963922 + 0.266186i \(0.0857635\pi\)
−0.963922 + 0.266186i \(0.914236\pi\)
\(240\) 0 0
\(241\) −2.68678 1.55121i −0.173071 0.0999225i 0.410962 0.911652i \(-0.365193\pi\)
−0.584033 + 0.811730i \(0.698526\pi\)
\(242\) 5.62763i 0.361758i
\(243\) 0.500000 0.866025i 0.0320750 0.0555556i
\(244\) 4.68764 + 8.11924i 0.300096 + 0.519781i
\(245\) 0 0
\(246\) 8.72500 0.556286
\(247\) 18.3060 0.352169i 1.16478 0.0224080i
\(248\) 0.952516 0.0604848
\(249\) −6.88392 + 3.97443i −0.436251 + 0.251870i
\(250\) 0 0
\(251\) 7.81042 13.5281i 0.492990 0.853883i −0.506978 0.861959i \(-0.669237\pi\)
0.999967 + 0.00807605i \(0.00257072\pi\)
\(252\) 0.482362i 0.0303859i
\(253\) −13.8635 8.00412i −0.871594 0.503215i
\(254\) −16.3843 9.45946i −1.02804 0.593539i
\(255\) 0 0
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 1.76210 + 3.05205i 0.109917 + 0.190382i 0.915736 0.401780i \(-0.131608\pi\)
−0.805819 + 0.592161i \(0.798275\pi\)
\(258\) 9.78170 5.64747i 0.608982 0.351596i
\(259\) −2.98514 −0.185488
\(260\) 0 0
\(261\) −8.40957 −0.520539
\(262\) −6.03457 + 3.48406i −0.372817 + 0.215246i
\(263\) −11.6415 20.1637i −0.717845 1.24334i −0.961852 0.273571i \(-0.911795\pi\)
0.244006 0.969774i \(-0.421538\pi\)
\(264\) −1.15892 + 2.00731i −0.0713265 + 0.123541i
\(265\) 0 0
\(266\) −2.12132 1.22474i −0.130066 0.0750939i
\(267\) 7.80941 + 4.50877i 0.477928 + 0.275932i
\(268\) 7.39355i 0.451633i
\(269\) −4.90873 + 8.50217i −0.299291 + 0.518387i −0.975974 0.217888i \(-0.930083\pi\)
0.676683 + 0.736274i \(0.263417\pi\)
\(270\) 0 0
\(271\) −18.8862 + 10.9040i −1.14726 + 0.662369i −0.948217 0.317623i \(-0.897115\pi\)
−0.199039 + 0.979992i \(0.563782\pi\)
\(272\) 6.79555 0.412041
\(273\) −0.898400 1.48917i −0.0543736 0.0901287i
\(274\) −20.5093 −1.23901
\(275\) 0 0
\(276\) 3.45327 + 5.98124i 0.207863 + 0.360028i
\(277\) −6.73753 + 11.6697i −0.404819 + 0.701167i −0.994300 0.106615i \(-0.965999\pi\)
0.589481 + 0.807782i \(0.299332\pi\)
\(278\) 8.50935i 0.510357i
\(279\) −0.824903 0.476258i −0.0493857 0.0285128i
\(280\) 0 0
\(281\) 29.6167i 1.76678i −0.468635 0.883392i \(-0.655254\pi\)
0.468635 0.883392i \(-0.344746\pi\)
\(282\) 2.88865 5.00328i 0.172016 0.297941i
\(283\) −6.09197 10.5516i −0.362130 0.627228i 0.626181 0.779678i \(-0.284617\pi\)
−0.988311 + 0.152450i \(0.951284\pi\)
\(284\) 3.01876 1.74288i 0.179130 0.103421i
\(285\) 0 0
\(286\) 0.160743 + 8.35554i 0.00950492 + 0.494073i
\(287\) −4.20861 −0.248426
\(288\) 0.866025 0.500000i 0.0510310 0.0294628i
\(289\) −14.5898 25.2702i −0.858223 1.48649i
\(290\) 0 0
\(291\) 9.18206i 0.538262i
\(292\) 7.39123 + 4.26733i 0.432539 + 0.249726i
\(293\) −13.0085 7.51047i −0.759965 0.438766i 0.0693181 0.997595i \(-0.477918\pi\)
−0.829283 + 0.558829i \(0.811251\pi\)
\(294\) 6.76733i 0.394679i
\(295\) 0 0
\(296\) −3.09429 5.35948i −0.179852 0.311513i
\(297\) 2.00731 1.15892i 0.116476 0.0672473i
\(298\) 7.24504 0.419694
\(299\) 21.8012 + 12.0338i 1.26079 + 0.695935i
\(300\) 0 0
\(301\) −4.71832 + 2.72412i −0.271959 + 0.157016i
\(302\) 3.91372 + 6.77875i 0.225209 + 0.390073i
\(303\) 5.34108 9.25102i 0.306837 0.531457i
\(304\) 5.07812i 0.291250i
\(305\) 0 0
\(306\) −5.88512 3.39778i −0.336430 0.194238i
\(307\) 27.9569i 1.59558i −0.602934 0.797791i \(-0.706002\pi\)
0.602934 0.797791i \(-0.293998\pi\)
\(308\) 0.559018 0.968248i 0.0318530 0.0551710i
\(309\) −4.58725 7.94534i −0.260959 0.451995i
\(310\) 0 0
\(311\) 14.3067 0.811256 0.405628 0.914038i \(-0.367053\pi\)
0.405628 + 0.914038i \(0.367053\pi\)
\(312\) 1.74238 3.15660i 0.0986430 0.178707i
\(313\) −13.9895 −0.790731 −0.395366 0.918524i \(-0.629382\pi\)
−0.395366 + 0.918524i \(0.629382\pi\)
\(314\) −3.83014 + 2.21134i −0.216148 + 0.124793i
\(315\) 0 0
\(316\) 4.51910 7.82731i 0.254219 0.440320i
\(317\) 7.29868i 0.409935i −0.978769 0.204967i \(-0.934291\pi\)
0.978769 0.204967i \(-0.0657089\pi\)
\(318\) −5.03175 2.90508i −0.282167 0.162909i
\(319\) −16.8806 9.74601i −0.945131 0.545672i
\(320\) 0 0
\(321\) 1.60867 2.78629i 0.0897870 0.155516i
\(322\) −1.66573 2.88512i −0.0928273 0.160782i
\(323\) −29.8853 + 17.2543i −1.66286 + 0.960055i
\(324\) −1.00000 −0.0555556
\(325\) 0 0
\(326\) −11.2244 −0.621661
\(327\) −14.7804 + 8.53345i −0.817356 + 0.471901i
\(328\) −4.36250 7.55607i −0.240879 0.417214i
\(329\) −1.39337 + 2.41339i −0.0768192 + 0.133055i
\(330\) 0 0
\(331\) 22.8279 + 13.1797i 1.25474 + 0.724423i 0.972046 0.234788i \(-0.0754397\pi\)
0.282690 + 0.959211i \(0.408773\pi\)
\(332\) 6.88392 + 3.97443i 0.377804 + 0.218125i
\(333\) 6.18859i 0.339133i
\(334\) 7.52898 13.0406i 0.411968 0.713549i
\(335\) 0 0
\(336\) −0.417738 + 0.241181i −0.0227895 + 0.0131575i
\(337\) 24.4240 1.33046 0.665229 0.746639i \(-0.268334\pi\)
0.665229 + 0.746639i \(0.268334\pi\)
\(338\) −0.500000 12.9904i −0.0271964 0.706584i
\(339\) −1.65685 −0.0899880
\(340\) 0 0
\(341\) −1.10389 1.91199i −0.0597789 0.103540i
\(342\) −2.53906 + 4.39778i −0.137297 + 0.237805i
\(343\) 6.64083i 0.358571i
\(344\) −9.78170 5.64747i −0.527394 0.304491i
\(345\) 0 0
\(346\) 14.7486i 0.792889i
\(347\) 6.70818 11.6189i 0.360114 0.623736i −0.627865 0.778322i \(-0.716071\pi\)
0.987979 + 0.154586i \(0.0494044\pi\)
\(348\) 4.20478 + 7.28290i 0.225400 + 0.390404i
\(349\) 0.824457 0.476000i 0.0441322 0.0254797i −0.477772 0.878484i \(-0.658555\pi\)
0.521904 + 0.853004i \(0.325222\pi\)
\(350\) 0 0
\(351\) −3.08725 + 1.86250i −0.164785 + 0.0994130i
\(352\) 2.31784 0.123541
\(353\) −12.5120 + 7.22380i −0.665946 + 0.384484i −0.794539 0.607213i \(-0.792287\pi\)
0.128593 + 0.991697i \(0.458954\pi\)
\(354\) 5.91189 + 10.2397i 0.314213 + 0.544234i
\(355\) 0 0
\(356\) 9.01753i 0.477928i
\(357\) 2.83876 + 1.63896i 0.150243 + 0.0867429i
\(358\) 7.45802 + 4.30589i 0.394168 + 0.227573i
\(359\) 8.11291i 0.428183i 0.976814 + 0.214092i \(0.0686791\pi\)
−0.976814 + 0.214092i \(0.931321\pi\)
\(360\) 0 0
\(361\) 3.39363 + 5.87794i 0.178612 + 0.309365i
\(362\) 2.46378 1.42246i 0.129493 0.0747630i
\(363\) −5.62763 −0.295374
\(364\) −0.840459 + 1.52262i −0.0440520 + 0.0798071i
\(365\) 0 0
\(366\) −8.11924 + 4.68764i −0.424399 + 0.245027i
\(367\) −11.9977 20.7806i −0.626274 1.08474i −0.988293 0.152568i \(-0.951246\pi\)
0.362019 0.932171i \(-0.382088\pi\)
\(368\) 3.45327 5.98124i 0.180014 0.311794i
\(369\) 8.72500i 0.454205i
\(370\) 0 0
\(371\) 2.42713 + 1.40130i 0.126010 + 0.0727520i
\(372\) 0.952516i 0.0493857i
\(373\) 13.4288 23.2593i 0.695316 1.20432i −0.274758 0.961513i \(-0.588598\pi\)
0.970074 0.242809i \(-0.0780689\pi\)
\(374\) −7.87550 13.6408i −0.407232 0.705347i
\(375\) 0 0
\(376\) −5.77729 −0.297941
\(377\) 26.5456 + 14.6527i 1.36717 + 0.754652i
\(378\) 0.482362 0.0248100
\(379\) −13.2638 + 7.65785i −0.681315 + 0.393357i −0.800350 0.599533i \(-0.795353\pi\)
0.119035 + 0.992890i \(0.462020\pi\)
\(380\) 0 0
\(381\) 9.45946 16.3843i 0.484623 0.839391i
\(382\) 3.43587i 0.175795i
\(383\) 30.5185 + 17.6198i 1.55942 + 0.900332i 0.997312 + 0.0732675i \(0.0233427\pi\)
0.562108 + 0.827064i \(0.309991\pi\)
\(384\) −0.866025 0.500000i −0.0441942 0.0255155i
\(385\) 0 0
\(386\) 1.32843 2.30090i 0.0676152 0.117113i
\(387\) 5.64747 + 9.78170i 0.287077 + 0.497232i
\(388\) −7.95189 + 4.59103i −0.403696 + 0.233074i
\(389\) −18.0946 −0.917433 −0.458717 0.888583i \(-0.651691\pi\)
−0.458717 + 0.888583i \(0.651691\pi\)
\(390\) 0 0
\(391\) −46.9338 −2.37354
\(392\) −5.86068 + 3.38366i −0.296009 + 0.170901i
\(393\) −3.48406 6.03457i −0.175748 0.304404i
\(394\) −10.5579 + 18.2868i −0.531899 + 0.921276i
\(395\) 0 0
\(396\) −2.00731 1.15892i −0.100871 0.0582379i
\(397\) −9.05105 5.22562i −0.454259 0.262267i 0.255368 0.966844i \(-0.417803\pi\)
−0.709627 + 0.704577i \(0.751137\pi\)
\(398\) 10.5388i 0.528263i
\(399\) 1.22474 2.12132i 0.0613139 0.106199i
\(400\) 0 0
\(401\) −1.21317 + 0.700423i −0.0605827 + 0.0349775i −0.529985 0.848007i \(-0.677803\pi\)
0.469403 + 0.882984i \(0.344469\pi\)
\(402\) −7.39355 −0.368757
\(403\) 1.77406 + 2.94065i 0.0883723 + 0.146484i
\(404\) −10.6822 −0.531457
\(405\) 0 0
\(406\) −2.02823 3.51299i −0.100659 0.174347i
\(407\) −7.17207 + 12.4224i −0.355506 + 0.615755i
\(408\) 6.79555i 0.336430i
\(409\) 5.83817 + 3.37067i 0.288679 + 0.166669i 0.637346 0.770578i \(-0.280032\pi\)
−0.348667 + 0.937247i \(0.613366\pi\)
\(410\) 0 0
\(411\) 20.5093i 1.01165i
\(412\) −4.58725 + 7.94534i −0.225997 + 0.391439i
\(413\) −2.85167 4.93924i −0.140322 0.243044i
\(414\) −5.98124 + 3.45327i −0.293962 + 0.169719i
\(415\) 0 0
\(416\) −3.60488 + 0.0693504i −0.176744 + 0.00340018i
\(417\) 8.50935 0.416704
\(418\) −10.1933 + 5.88512i −0.498572 + 0.287851i
\(419\) −18.2539 31.6166i −0.891760 1.54457i −0.837765 0.546032i \(-0.816138\pi\)
−0.0539949 0.998541i \(-0.517195\pi\)
\(420\) 0 0
\(421\) 40.8490i 1.99086i −0.0955005 0.995429i \(-0.530445\pi\)
0.0955005 0.995429i \(-0.469555\pi\)
\(422\) 9.94863 + 5.74384i 0.484292 + 0.279606i
\(423\) 5.00328 + 2.88865i 0.243268 + 0.140451i
\(424\) 5.81017i 0.282167i
\(425\) 0 0
\(426\) 1.74288 + 3.01876i 0.0844429 + 0.146259i
\(427\) 3.91641 2.26114i 0.189528 0.109424i
\(428\) −3.21733 −0.155516
\(429\) −8.35554 + 0.160743i −0.403409 + 0.00776074i
\(430\) 0 0
\(431\) −15.9145 + 9.18824i −0.766575 + 0.442582i −0.831651 0.555298i \(-0.812604\pi\)
0.0650767 + 0.997880i \(0.479271\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) 0.699097 1.21087i 0.0335964 0.0581907i −0.848738 0.528813i \(-0.822637\pi\)
0.882335 + 0.470622i \(0.155971\pi\)
\(434\) 0.459457i 0.0220547i
\(435\) 0 0
\(436\) 14.7804 + 8.53345i 0.707851 + 0.408678i
\(437\) 35.0722i 1.67773i
\(438\) −4.26733 + 7.39123i −0.203901 + 0.353166i
\(439\) −7.65685 13.2621i −0.365442 0.632964i 0.623405 0.781899i \(-0.285749\pi\)
−0.988847 + 0.148935i \(0.952415\pi\)
\(440\) 0 0
\(441\) 6.76733 0.322254
\(442\) 12.6567 + 20.9796i 0.602019 + 0.997895i
\(443\) 33.1769 1.57628 0.788141 0.615495i \(-0.211044\pi\)
0.788141 + 0.615495i \(0.211044\pi\)
\(444\) 5.35948 3.09429i 0.254349 0.146849i
\(445\) 0 0
\(446\) 2.61389 4.52739i 0.123771 0.214378i
\(447\) 7.24504i 0.342679i
\(448\) 0.417738 + 0.241181i 0.0197362 + 0.0113947i
\(449\) 13.3408 + 7.70234i 0.629593 + 0.363496i 0.780595 0.625038i \(-0.214916\pi\)
−0.151001 + 0.988534i \(0.548250\pi\)
\(450\) 0 0
\(451\) −10.1116 + 17.5137i −0.476135 + 0.824690i
\(452\) 0.828427 + 1.43488i 0.0389659 + 0.0674910i
\(453\) −6.77875 + 3.91372i −0.318494 + 0.183882i
\(454\) 10.8689 0.510101
\(455\) 0 0
\(456\) 5.07812 0.237805
\(457\) −6.46224 + 3.73097i −0.302291 + 0.174528i −0.643471 0.765470i \(-0.722506\pi\)
0.341181 + 0.939998i \(0.389173\pi\)
\(458\) −10.5966 18.3538i −0.495146 0.857618i
\(459\) 3.39778 5.88512i 0.158595 0.274694i
\(460\) 0 0
\(461\) −3.97457 2.29472i −0.185114 0.106876i 0.404579 0.914503i \(-0.367418\pi\)
−0.589693 + 0.807627i \(0.700751\pi\)
\(462\) 0.968248 + 0.559018i 0.0450470 + 0.0260079i
\(463\) 9.20888i 0.427973i 0.976837 + 0.213986i \(0.0686448\pi\)
−0.976837 + 0.213986i \(0.931355\pi\)
\(464\) 4.20478 7.28290i 0.195202 0.338100i
\(465\) 0 0
\(466\) 18.9160 10.9212i 0.876267 0.505913i
\(467\) 0.219469 0.0101558 0.00507792 0.999987i \(-0.498384\pi\)
0.00507792 + 0.999987i \(0.498384\pi\)
\(468\) 3.15660 + 1.74238i 0.145914 + 0.0805417i
\(469\) 3.56637 0.164680
\(470\) 0 0
\(471\) −2.21134 3.83014i −0.101893 0.176484i
\(472\) 5.91189 10.2397i 0.272117 0.471320i
\(473\) 26.1798i 1.20375i
\(474\) 7.82731 + 4.51910i 0.359520 + 0.207569i
\(475\) 0 0
\(476\) 3.27792i 0.150243i
\(477\) 2.90508 5.03175i 0.133015 0.230388i
\(478\) 4.11513 + 7.12762i 0.188222 + 0.326010i
\(479\) −5.49422 + 3.17209i −0.251037 + 0.144936i −0.620239 0.784413i \(-0.712964\pi\)
0.369202 + 0.929349i \(0.379631\pi\)
\(480\) 0 0
\(481\) 10.7829 19.5349i 0.491658 0.890714i
\(482\) −3.10243 −0.141312
\(483\) 2.88512 1.66573i 0.131278 0.0757932i
\(484\) 2.81382 + 4.87367i 0.127901 + 0.221530i
\(485\) 0 0
\(486\) 1.00000i 0.0453609i
\(487\) 32.2113 + 18.5972i 1.45963 + 0.842720i 0.998993 0.0448662i \(-0.0142862\pi\)
0.460641 + 0.887586i \(0.347619\pi\)
\(488\) 8.11924 + 4.68764i 0.367541 + 0.212200i
\(489\) 11.2244i 0.507584i
\(490\) 0 0
\(491\) 2.99901 + 5.19444i 0.135344 + 0.234422i 0.925729 0.378188i \(-0.123453\pi\)
−0.790385 + 0.612610i \(0.790120\pi\)
\(492\) 7.55607 4.36250i 0.340654 0.196677i
\(493\) −57.1477 −2.57380
\(494\) 15.6774 9.45800i 0.705359 0.425535i
\(495\) 0 0
\(496\) 0.824903 0.476258i 0.0370392 0.0213846i
\(497\) −0.840699 1.45613i −0.0377105 0.0653165i
\(498\) −3.97443 + 6.88392i −0.178099 + 0.308476i
\(499\) 21.2908i 0.953107i −0.879145 0.476554i \(-0.841886\pi\)
0.879145 0.476554i \(-0.158114\pi\)
\(500\) 0 0
\(501\) 13.0406 + 7.52898i 0.582610 + 0.336370i
\(502\) 15.6208i 0.697193i
\(503\) 9.52194 16.4925i 0.424562 0.735363i −0.571817 0.820381i \(-0.693761\pi\)
0.996379 + 0.0850178i \(0.0270947\pi\)
\(504\) −0.241181 0.417738i −0.0107431 0.0186075i
\(505\) 0 0
\(506\) −16.0082 −0.711653
\(507\) 12.9904 0.500000i 0.576923 0.0222058i
\(508\) −18.9189 −0.839391
\(509\) −24.6679 + 14.2420i −1.09339 + 0.631267i −0.934476 0.356026i \(-0.884132\pi\)
−0.158911 + 0.987293i \(0.550798\pi\)
\(510\) 0 0
\(511\) 2.05840 3.56525i 0.0910581 0.157717i
\(512\) 1.00000i 0.0441942i
\(513\) −4.39778 2.53906i −0.194167 0.112102i
\(514\) 3.05205 + 1.76210i 0.134620 + 0.0777230i
\(515\) 0 0
\(516\) 5.64747 9.78170i 0.248616 0.430615i
\(517\) 6.69541 + 11.5968i 0.294464 + 0.510027i
\(518\) −2.58521 + 1.49257i −0.113587 + 0.0655797i
\(519\) −14.7486 −0.647391
\(520\) 0 0
\(521\) −27.6617 −1.21188 −0.605940 0.795511i \(-0.707203\pi\)
−0.605940 + 0.795511i \(0.707203\pi\)
\(522\) −7.28290 + 4.20478i −0.318764 + 0.184038i
\(523\) −8.44709 14.6308i −0.369365 0.639759i 0.620101 0.784522i \(-0.287092\pi\)
−0.989466 + 0.144762i \(0.953758\pi\)
\(524\) −3.48406 + 6.03457i −0.152202 + 0.263622i
\(525\) 0 0
\(526\) −20.1637 11.6415i −0.879177 0.507593i
\(527\) −5.60567 3.23644i −0.244187 0.140981i
\(528\) 2.31784i 0.100871i
\(529\) −12.3502 + 21.3911i −0.536964 + 0.930049i
\(530\) 0 0
\(531\) −10.2397 + 5.91189i −0.444365 + 0.256554i
\(532\) −2.44949 −0.106199
\(533\) 15.2023 27.5413i 0.658485 1.19295i
\(534\) 9.01753 0.390227
\(535\) 0 0
\(536\) 3.69677 + 6.40300i 0.159676 + 0.276568i
\(537\) −4.30589 + 7.45802i −0.185813 + 0.321837i
\(538\) 9.81746i 0.423261i
\(539\) 13.5841 + 7.84278i 0.585108 + 0.337813i
\(540\) 0 0
\(541\) 30.6639i 1.31834i −0.751993 0.659171i \(-0.770907\pi\)
0.751993 0.659171i \(-0.229093\pi\)
\(542\) −10.9040 + 18.8862i −0.468365 + 0.811233i
\(543\) 1.42246 + 2.46378i 0.0610438 + 0.105731i
\(544\) 5.88512 3.39778i 0.252323 0.145679i
\(545\) 0 0
\(546\) −1.52262 0.840459i −0.0651622 0.0359683i
\(547\) 40.6726 1.73903 0.869517 0.493903i \(-0.164430\pi\)
0.869517 + 0.493903i \(0.164430\pi\)
\(548\) −17.7616 + 10.2547i −0.758739 + 0.438058i
\(549\) −4.68764 8.11924i −0.200064 0.346521i
\(550\) 0 0
\(551\) 42.7048i 1.81928i
\(552\) 5.98124 + 3.45327i 0.254579 + 0.146981i
\(553\) −3.77559 2.17984i −0.160555 0.0926963i
\(554\) 13.4751i 0.572501i
\(555\) 0 0
\(556\) −4.25467 7.36931i −0.180438 0.312528i
\(557\) −15.9822 + 9.22730i −0.677186 + 0.390973i −0.798794 0.601605i \(-0.794528\pi\)
0.121608 + 0.992578i \(0.461195\pi\)
\(558\) −0.952516 −0.0403232
\(559\) −0.783308 40.7169i −0.0331304 1.72214i
\(560\) 0 0
\(561\) 13.6408 7.87550i 0.575913 0.332504i
\(562\) −14.8083 25.6488i −0.624652 1.08193i
\(563\) 4.71770 8.17129i 0.198827 0.344379i −0.749321 0.662207i \(-0.769620\pi\)
0.948148 + 0.317828i \(0.102953\pi\)
\(564\) 5.77729i 0.243268i
\(565\) 0 0
\(566\) −10.5516 6.09197i −0.443517 0.256065i
\(567\) 0.482362i 0.0202573i
\(568\) 1.74288 3.01876i 0.0731297 0.126664i
\(569\) 5.33503 + 9.24054i 0.223656 + 0.387384i 0.955915 0.293642i \(-0.0948674\pi\)
−0.732259 + 0.681026i \(0.761534\pi\)
\(570\) 0 0
\(571\) 0.532730 0.0222941 0.0111470 0.999938i \(-0.496452\pi\)
0.0111470 + 0.999938i \(0.496452\pi\)
\(572\) 4.31697 + 7.15573i 0.180502 + 0.299196i
\(573\) 3.43587 0.143536
\(574\) −3.64476 + 2.10430i −0.152129 + 0.0878320i
\(575\) 0 0
\(576\) 0.500000 0.866025i 0.0208333 0.0360844i
\(577\) 26.0683i 1.08524i 0.839978 + 0.542620i \(0.182568\pi\)
−0.839978 + 0.542620i \(0.817432\pi\)
\(578\) −25.2702 14.5898i −1.05110 0.606855i
\(579\) 2.30090 + 1.32843i 0.0956223 + 0.0552075i
\(580\) 0 0
\(581\) 1.91712 3.32054i 0.0795354 0.137759i
\(582\) −4.59103 7.95189i −0.190304 0.329617i
\(583\) 11.6628 6.73351i 0.483023 0.278874i
\(584\) 8.53465 0.353166
\(585\) 0 0
\(586\) −15.0209 −0.620509
\(587\) 12.7739 7.37501i 0.527235 0.304399i −0.212655 0.977127i \(-0.568211\pi\)
0.739890 + 0.672728i \(0.234878\pi\)
\(588\) −3.38366 5.86068i −0.139540 0.241690i
\(589\) −2.41849 + 4.18895i −0.0996523 + 0.172603i
\(590\) 0 0
\(591\) −18.2868 10.5579i −0.752219 0.434294i
\(592\) −5.35948 3.09429i −0.220273 0.127175i
\(593\) 23.4887i 0.964566i 0.876015 + 0.482283i \(0.160192\pi\)
−0.876015 + 0.482283i \(0.839808\pi\)
\(594\) 1.15892 2.00731i 0.0475510 0.0823608i
\(595\) 0 0
\(596\) 6.27439 3.62252i 0.257009 0.148384i
\(597\) 10.5388 0.431325
\(598\) 24.8973 0.478971i 1.01813 0.0195866i
\(599\) 3.72087 0.152031 0.0760154 0.997107i \(-0.475780\pi\)
0.0760154 + 0.997107i \(0.475780\pi\)
\(600\) 0 0
\(601\) 21.1757 + 36.6773i 0.863773 + 1.49610i 0.868261 + 0.496109i \(0.165238\pi\)
−0.00448765 + 0.999990i \(0.501428\pi\)
\(602\) −2.72412 + 4.71832i −0.111027 + 0.192304i
\(603\) 7.39355i 0.301089i
\(604\) 6.77875 + 3.91372i 0.275824 + 0.159247i
\(605\) 0 0
\(606\) 10.6822i 0.433933i
\(607\) 9.50853 16.4692i 0.385939 0.668466i −0.605960 0.795495i \(-0.707211\pi\)
0.991899 + 0.127029i \(0.0405441\pi\)
\(608\) −2.53906 4.39778i −0.102972 0.178353i
\(609\) 3.51299 2.02823i 0.142354 0.0821879i
\(610\) 0 0
\(611\) −10.7602 17.8359i −0.435312 0.721565i
\(612\) −6.79555 −0.274694
\(613\) 19.7672 11.4126i 0.798390 0.460951i −0.0445178 0.999009i \(-0.514175\pi\)
0.842908 + 0.538058i \(0.180842\pi\)
\(614\) −13.9784 24.2114i −0.564124 0.977091i
\(615\) 0 0
\(616\) 1.11804i 0.0450470i
\(617\) −15.0114 8.66682i −0.604335 0.348913i 0.166410 0.986057i \(-0.446783\pi\)
−0.770745 + 0.637144i \(0.780116\pi\)
\(618\) −7.94534 4.58725i −0.319609 0.184526i
\(619\) 0.972021i 0.0390688i 0.999809 + 0.0195344i \(0.00621839\pi\)
−0.999809 + 0.0195344i \(0.993782\pi\)
\(620\) 0 0
\(621\) −3.45327 5.98124i −0.138575 0.240019i
\(622\) 12.3899 7.15333i 0.496791 0.286822i
\(623\) −4.34971 −0.174268
\(624\) −0.0693504 3.60488i −0.00277624 0.144311i
\(625\) 0 0
\(626\) −12.1152 + 6.99473i −0.484222 + 0.279566i
\(627\) −5.88512 10.1933i −0.235029 0.407082i
\(628\) −2.21134 + 3.83014i −0.0882419 + 0.152839i
\(629\) 42.0549i 1.67684i
\(630\) 0 0
\(631\) 4.53981 + 2.62106i 0.180727 + 0.104343i 0.587634 0.809127i \(-0.300059\pi\)
−0.406907 + 0.913470i \(0.633393\pi\)
\(632\) 9.03820i 0.359520i
\(633\) −5.74384 + 9.94863i −0.228297 + 0.395422i
\(634\) −3.64934 6.32085i −0.144934 0.251033i
\(635\) 0 0
\(636\) −5.81017 −0.230388
\(637\) −21.3617 11.7913i −0.846382 0.467187i
\(638\) −19.4920 −0.771696
\(639\) −3.01876 + 1.74288i −0.119420 + 0.0689473i
\(640\) 0 0
\(641\) −16.4075 + 28.4186i −0.648057 + 1.12247i 0.335529 + 0.942030i \(0.391085\pi\)
−0.983586 + 0.180439i \(0.942248\pi\)
\(642\) 3.21733i 0.126978i
\(643\) 10.0888 + 5.82478i 0.397864 + 0.229707i 0.685562 0.728014i \(-0.259557\pi\)
−0.287698 + 0.957721i \(0.592890\pi\)
\(644\) −2.88512 1.66573i −0.113690 0.0656388i
\(645\) 0 0
\(646\) −17.2543 + 29.8853i −0.678862 + 1.17582i
\(647\) −11.0922 19.2123i −0.436081 0.755314i 0.561303 0.827611i \(-0.310300\pi\)
−0.997383 + 0.0722970i \(0.976967\pi\)
\(648\) −0.866025 + 0.500000i −0.0340207 + 0.0196419i
\(649\) −27.4056 −1.07576
\(650\) 0 0
\(651\) 0.459457 0.0180076
\(652\) −9.72060 + 5.61219i −0.380688 + 0.219790i
\(653\) 16.6764 + 28.8844i 0.652598 + 1.13033i 0.982490 + 0.186314i \(0.0596542\pi\)
−0.329892 + 0.944019i \(0.607012\pi\)
\(654\) −8.53345 + 14.7804i −0.333684 + 0.577958i
\(655\) 0 0
\(656\) −7.55607 4.36250i −0.295015 0.170327i
\(657\) −7.39123 4.26733i −0.288359 0.166484i
\(658\) 2.78675i 0.108639i
\(659\) 12.2280 21.1796i 0.476337 0.825039i −0.523296 0.852151i \(-0.675298\pi\)
0.999632 + 0.0271118i \(0.00863100\pi\)
\(660\) 0 0
\(661\) 28.8737 16.6702i 1.12306 0.648396i 0.180876 0.983506i \(-0.442107\pi\)
0.942179 + 0.335109i \(0.108773\pi\)
\(662\) 26.3594 1.02449
\(663\) −20.9796 + 12.6567i −0.814778 + 0.491547i
\(664\) 7.94887 0.308476
\(665\) 0 0
\(666\) 3.09429 + 5.35948i 0.119901 + 0.207675i
\(667\) −29.0405 + 50.2997i −1.12445 + 1.94761i
\(668\) 15.0580i 0.582610i
\(669\) 4.52739 + 2.61389i 0.175039 + 0.101059i
\(670\) 0 0
\(671\) 21.7304i 0.838893i
\(672\) −0.241181 + 0.417738i −0.00930376 + 0.0161146i
\(673\) 16.9894 + 29.4265i 0.654893 + 1.13431i 0.981921 + 0.189293i \(0.0606195\pi\)
−0.327028 + 0.945015i \(0.606047\pi\)
\(674\) 21.1518 12.2120i 0.814736 0.470388i
\(675\) 0 0
\(676\) −6.92820 11.0000i −0.266469 0.423077i
\(677\) 10.3145 0.396417 0.198208 0.980160i \(-0.436488\pi\)
0.198208 + 0.980160i \(0.436488\pi\)
\(678\) −1.43488 + 0.828427i −0.0551062 + 0.0318156i
\(679\) 2.21454 + 3.83569i 0.0849861 + 0.147200i
\(680\) 0 0
\(681\) 10.8689i 0.416496i
\(682\) −1.91199 1.10389i −0.0732139 0.0422701i
\(683\) −42.4682 24.5191i −1.62500 0.938196i −0.985554 0.169362i \(-0.945829\pi\)
−0.639448 0.768834i \(-0.720837\pi\)
\(684\) 5.07812i 0.194167i
\(685\) 0 0
\(686\) 3.32042 + 5.75113i 0.126774 + 0.219579i
\(687\) 18.3538 10.5966i 0.700242 0.404285i
\(688\) −11.2949 −0.430615
\(689\) −17.9374 + 10.8214i −0.683361 + 0.412264i
\(690\) 0 0
\(691\) 29.7340 17.1669i 1.13113 0.653061i 0.186914 0.982376i \(-0.440151\pi\)
0.944220 + 0.329315i \(0.106818\pi\)
\(692\) 7.37429 + 12.7727i 0.280329 + 0.485543i
\(693\) −0.559018 + 0.968248i −0.0212353 + 0.0367807i
\(694\) 13.4164i 0.509278i
\(695\) 0 0
\(696\) 7.28290 + 4.20478i 0.276058 + 0.159382i
\(697\) 59.2912i 2.24582i
\(698\) 0.476000 0.824457i 0.0180169 0.0312061i
\(699\) 10.9212 + 18.9160i 0.413076 + 0.715469i
\(700\) 0 0
\(701\) −32.0303 −1.20977 −0.604885 0.796313i \(-0.706781\pi\)
−0.604885 + 0.796313i \(0.706781\pi\)
\(702\) −1.74238 + 3.15660i −0.0657620 + 0.119138i
\(703\) 31.4264 1.18527
\(704\) 2.00731 1.15892i 0.0756532 0.0436784i
\(705\) 0 0
\(706\) −7.22380 + 12.5120i −0.271871 + 0.470895i
\(707\) 5.15267i 0.193786i
\(708\) 10.2397 + 5.91189i 0.384831 + 0.222182i
\(709\) 27.0809 + 15.6352i 1.01704 + 0.587190i 0.913246 0.407408i \(-0.133567\pi\)
0.103797 + 0.994598i \(0.466901\pi\)
\(710\) 0 0
\(711\) −4.51910 + 7.82731i −0.169479 + 0.293547i
\(712\) −4.50877 7.80941i −0.168973 0.292670i
\(713\) −5.69723 + 3.28930i −0.213363 + 0.123185i
\(714\) 3.27792 0.122673
\(715\) 0 0
\(716\) 8.61177 0.321837
\(717\) −7.12762 + 4.11513i −0.266186 + 0.153683i
\(718\) 4.05646 + 7.02599i 0.151386 + 0.262208i
\(719\) −10.6716 + 18.4838i −0.397984 + 0.689328i −0.993477 0.114032i \(-0.963623\pi\)
0.595494 + 0.803360i \(0.296957\pi\)
\(720\) 0 0
\(721\) 3.83253 + 2.21271i 0.142731 + 0.0824057i
\(722\) 5.87794 + 3.39363i 0.218754 + 0.126298i
\(723\) 3.10243i 0.115381i
\(724\) 1.42246 2.46378i 0.0528655 0.0915656i
\(725\) 0 0
\(726\) −4.87367 + 2.81382i −0.180879 + 0.104430i
\(727\) 8.80283 0.326479 0.163240 0.986586i \(-0.447806\pi\)
0.163240 + 0.986586i \(0.447806\pi\)
\(728\) 0.0334520 + 1.73886i 0.00123981 + 0.0644464i
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) 38.3777 + 66.4721i 1.41945 + 2.45856i
\(732\) −4.68764 + 8.11924i −0.173260 + 0.300096i
\(733\) 7.86883i 0.290642i 0.989385 + 0.145321i \(0.0464215\pi\)
−0.989385 + 0.145321i \(0.953579\pi\)
\(734\) −20.7806 11.9977i −0.767026 0.442843i
\(735\) 0 0
\(736\) 6.90654i 0.254579i
\(737\) 8.56852 14.8411i 0.315626 0.546680i
\(738\) 4.36250 + 7.55607i 0.160586 + 0.278143i
\(739\) 15.6988 9.06368i 0.577488 0.333413i −0.182646 0.983179i \(-0.558466\pi\)
0.760134 + 0.649766i \(0.225133\pi\)
\(740\) 0 0
\(741\) 9.45800 + 15.6774i 0.347448 + 0.575923i
\(742\) 2.80260 0.102887
\(743\) 1.19048 0.687322i 0.0436744 0.0252154i −0.478004 0.878358i \(-0.658640\pi\)
0.521678 + 0.853142i \(0.325306\pi\)
\(744\) 0.476258 + 0.824903i 0.0174605 + 0.0302424i
\(745\) 0 0
\(746\) 26.8576i 0.983325i
\(747\) −6.88392 3.97443i −0.251870 0.145417i
\(748\) −13.6408 7.87550i −0.498756 0.287957i
\(749\) 1.55192i 0.0567059i
\(750\) 0 0
\(751\) −19.0127 32.9310i −0.693784 1.20167i −0.970589 0.240743i \(-0.922609\pi\)
0.276805 0.960926i \(-0.410724\pi\)
\(752\) −5.00328 + 2.88865i −0.182451 + 0.105338i
\(753\) 15.6208 0.569255
\(754\) 30.3155 0.583207i 1.10403 0.0212391i
\(755\) 0 0
\(756\) 0.417738 0.241181i 0.0151930 0.00877167i
\(757\) −18.4771 32.0033i −0.671562 1.16318i −0.977461 0.211115i \(-0.932290\pi\)
0.305899 0.952064i \(-0.401043\pi\)
\(758\) −7.65785 + 13.2638i −0.278146 + 0.481762i
\(759\) 16.0082i 0.581062i
\(760\) 0 0
\(761\) 25.9967 + 15.0092i 0.942380 + 0.544084i 0.890706 0.454580i \(-0.150211\pi\)
0.0516746 + 0.998664i \(0.483544\pi\)
\(762\) 18.9189i 0.685360i
\(763\) 4.11621 7.12949i 0.149017 0.258105i
\(764\) −1.71794 2.97555i −0.0621528 0.107652i
\(765\) 0 0
\(766\) 35.2397 1.27326
\(767\) 42.6234 0.819984i 1.53904 0.0296079i
\(768\) −1.00000 −0.0360844
\(769\) −39.3038 + 22.6921i −1.41733 + 0.818297i −0.996064 0.0886391i \(-0.971748\pi\)
−0.421268 + 0.906936i \(0.638415\pi\)
\(770\) 0 0
\(771\) −1.76210 + 3.05205i −0.0634606 + 0.109917i
\(772\) 2.65685i 0.0956223i
\(773\) 22.1132 + 12.7671i 0.795358 + 0.459200i 0.841845 0.539719i \(-0.181469\pi\)
−0.0464877 + 0.998919i \(0.514803\pi\)
\(774\) 9.78170 + 5.64747i 0.351596 + 0.202994i
\(775\) 0 0
\(776\) −4.59103 + 7.95189i −0.164808 + 0.285456i
\(777\) −1.49257 2.58521i −0.0535456 0.0927438i
\(778\) −15.6704 + 9.04731i −0.561811 + 0.324362i
\(779\) 44.3066 1.58745
\(780\) 0 0
\(781\) −8.07943 −0.289105
\(782\) −40.6459 + 23.4669i −1.45349 + 0.839175i
\(783\) −4.20478 7.28290i −0.150267 0.260270i
\(784\) −3.38366 + 5.86068i −0.120845 + 0.209310i