Properties

Label 490.2.i.f.459.1
Level $490$
Weight $2$
Character 490.459
Analytic conductor $3.913$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.i (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 459.1
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 490.459
Dual form 490.2.i.f.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +2.44949 q^{6} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-2.03906 + 0.917738i) q^{5} +2.44949 q^{6} +1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.30701 - 1.81431i) q^{10} +(-2.44949 + 4.24264i) q^{11} +(-2.12132 + 1.22474i) q^{12} -0.449490i q^{13} +(5.44949 + 0.550510i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.73205 + 1.00000i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(-3.22474 - 5.58542i) q^{19} +(-0.224745 + 2.22474i) q^{20} -4.89898i q^{22} +(5.97469 - 3.44949i) q^{23} +(1.22474 - 2.12132i) q^{24} +(3.31552 - 3.74264i) q^{25} +(0.224745 + 0.389270i) q^{26} +2.89898 q^{29} +(-4.99465 + 2.24799i) q^{30} +(-0.449490 + 0.778539i) q^{31} +(0.866025 + 0.500000i) q^{32} +(10.3923 - 6.00000i) q^{33} -2.00000 q^{34} +3.00000 q^{36} +(1.73205 - 1.00000i) q^{37} +(5.58542 + 3.22474i) q^{38} +(-0.550510 + 0.953512i) q^{39} +(-0.917738 - 2.03906i) q^{40} +10.8990 q^{41} -8.89898i q^{43} +(2.44949 + 4.24264i) q^{44} +(-5.44294 - 3.92102i) q^{45} +(-3.44949 + 5.97469i) q^{46} +(0.778539 - 0.449490i) q^{47} +2.44949i q^{48} +(-1.00000 + 4.89898i) q^{50} +(-2.44949 - 4.24264i) q^{51} +(-0.389270 - 0.224745i) q^{52} +(-0.953512 - 0.550510i) q^{53} +(1.10102 - 10.8990i) q^{55} +15.7980i q^{57} +(-2.51059 + 1.44949i) q^{58} +(3.22474 - 5.58542i) q^{59} +(3.20150 - 4.44414i) q^{60} +(4.22474 + 7.31747i) q^{61} -0.898979i q^{62} -1.00000 q^{64} +(0.412514 + 0.916536i) q^{65} +(-6.00000 + 10.3923i) q^{66} +(6.92820 + 4.00000i) q^{67} +(1.73205 - 1.00000i) q^{68} -16.8990 q^{69} -10.8990 q^{71} +(-2.59808 + 1.50000i) q^{72} +(5.97469 + 3.44949i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-11.6170 + 3.87868i) q^{75} -6.44949 q^{76} -1.10102i q^{78} +(-1.44949 - 2.51059i) q^{79} +(1.81431 + 1.30701i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-9.43879 + 5.44949i) q^{82} +2.44949i q^{83} +(-4.44949 - 0.449490i) q^{85} +(4.44949 + 7.70674i) q^{86} +(-6.14966 - 3.55051i) q^{87} +(-4.24264 - 2.44949i) q^{88} +(5.00000 + 8.66025i) q^{89} +(6.67423 + 0.674235i) q^{90} -6.89898i q^{92} +(1.90702 - 1.10102i) q^{93} +(-0.449490 + 0.778539i) q^{94} +(11.7014 + 8.42953i) q^{95} +(-1.22474 - 2.12132i) q^{96} +3.79796i q^{97} -14.6969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4} + 4 q^{5} + 12 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} + 4 q^{5} + 12 q^{9} + 4 q^{10} + 24 q^{15} - 4 q^{16} - 16 q^{19} + 8 q^{20} - 8 q^{26} - 16 q^{29} - 12 q^{30} + 16 q^{31} - 16 q^{34} + 24 q^{36} - 24 q^{39} - 4 q^{40} + 48 q^{41} - 12 q^{45} - 8 q^{46} - 8 q^{50} + 48 q^{55} + 16 q^{59} + 12 q^{60} + 24 q^{61} - 8 q^{64} + 4 q^{65} - 48 q^{66} - 96 q^{69} - 48 q^{71} - 8 q^{74} - 32 q^{76} + 8 q^{79} + 4 q^{80} + 36 q^{81} - 16 q^{85} + 16 q^{86} + 40 q^{89} + 24 q^{90} + 16 q^{94} + 4 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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
\(3\) −2.12132 1.22474i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) −2.03906 + 0.917738i −0.911894 + 0.410425i
\(6\) 2.44949 1.00000
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 1.30701 1.81431i 0.413312 0.573736i
\(11\) −2.44949 + 4.24264i −0.738549 + 1.27920i 0.214600 + 0.976702i \(0.431155\pi\)
−0.953149 + 0.302502i \(0.902178\pi\)
\(12\) −2.12132 + 1.22474i −0.612372 + 0.353553i
\(13\) 0.449490i 0.124666i −0.998055 0.0623330i \(-0.980146\pi\)
0.998055 0.0623330i \(-0.0198541\pi\)
\(14\) 0 0
\(15\) 5.44949 + 0.550510i 1.40705 + 0.142141i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) 1.73205 + 1.00000i 0.420084 + 0.242536i 0.695113 0.718900i \(-0.255354\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) −2.59808 1.50000i −0.612372 0.353553i
\(19\) −3.22474 5.58542i −0.739807 1.28138i −0.952582 0.304282i \(-0.901583\pi\)
0.212775 0.977101i \(-0.431750\pi\)
\(20\) −0.224745 + 2.22474i −0.0502545 + 0.497468i
\(21\) 0 0
\(22\) 4.89898i 1.04447i
\(23\) 5.97469 3.44949i 1.24581 0.719268i 0.275538 0.961290i \(-0.411144\pi\)
0.970271 + 0.242022i \(0.0778105\pi\)
\(24\) 1.22474 2.12132i 0.250000 0.433013i
\(25\) 3.31552 3.74264i 0.663103 0.748528i
\(26\) 0.224745 + 0.389270i 0.0440761 + 0.0763420i
\(27\) 0 0
\(28\) 0 0
\(29\) 2.89898 0.538327 0.269163 0.963095i \(-0.413253\pi\)
0.269163 + 0.963095i \(0.413253\pi\)
\(30\) −4.99465 + 2.24799i −0.911894 + 0.410425i
\(31\) −0.449490 + 0.778539i −0.0807307 + 0.139830i −0.903564 0.428453i \(-0.859059\pi\)
0.822833 + 0.568283i \(0.192392\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 10.3923 6.00000i 1.80907 1.04447i
\(34\) −2.00000 −0.342997
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) 1.73205 1.00000i 0.284747 0.164399i −0.350823 0.936442i \(-0.614098\pi\)
0.635571 + 0.772043i \(0.280765\pi\)
\(38\) 5.58542 + 3.22474i 0.906075 + 0.523123i
\(39\) −0.550510 + 0.953512i −0.0881522 + 0.152684i
\(40\) −0.917738 2.03906i −0.145107 0.322403i
\(41\) 10.8990 1.70213 0.851067 0.525057i \(-0.175956\pi\)
0.851067 + 0.525057i \(0.175956\pi\)
\(42\) 0 0
\(43\) 8.89898i 1.35708i −0.734563 0.678541i \(-0.762613\pi\)
0.734563 0.678541i \(-0.237387\pi\)
\(44\) 2.44949 + 4.24264i 0.369274 + 0.639602i
\(45\) −5.44294 3.92102i −0.811386 0.584511i
\(46\) −3.44949 + 5.97469i −0.508600 + 0.880920i
\(47\) 0.778539 0.449490i 0.113562 0.0655648i −0.442143 0.896944i \(-0.645782\pi\)
0.555705 + 0.831380i \(0.312448\pi\)
\(48\) 2.44949i 0.353553i
\(49\) 0 0
\(50\) −1.00000 + 4.89898i −0.141421 + 0.692820i
\(51\) −2.44949 4.24264i −0.342997 0.594089i
\(52\) −0.389270 0.224745i −0.0539820 0.0311665i
\(53\) −0.953512 0.550510i −0.130975 0.0756184i 0.433081 0.901355i \(-0.357426\pi\)
−0.564056 + 0.825737i \(0.690760\pi\)
\(54\) 0 0
\(55\) 1.10102 10.8990i 0.148462 1.46962i
\(56\) 0 0
\(57\) 15.7980i 2.09249i
\(58\) −2.51059 + 1.44949i −0.329657 + 0.190327i
\(59\) 3.22474 5.58542i 0.419826 0.727160i −0.576096 0.817382i \(-0.695424\pi\)
0.995922 + 0.0902223i \(0.0287578\pi\)
\(60\) 3.20150 4.44414i 0.413312 0.573736i
\(61\) 4.22474 + 7.31747i 0.540923 + 0.936906i 0.998851 + 0.0479172i \(0.0152584\pi\)
−0.457928 + 0.888989i \(0.651408\pi\)
\(62\) 0.898979i 0.114171i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0.412514 + 0.916536i 0.0511660 + 0.113682i
\(66\) −6.00000 + 10.3923i −0.738549 + 1.27920i
\(67\) 6.92820 + 4.00000i 0.846415 + 0.488678i 0.859440 0.511237i \(-0.170813\pi\)
−0.0130248 + 0.999915i \(0.504146\pi\)
\(68\) 1.73205 1.00000i 0.210042 0.121268i
\(69\) −16.8990 −2.03440
\(70\) 0 0
\(71\) −10.8990 −1.29347 −0.646735 0.762714i \(-0.723866\pi\)
−0.646735 + 0.762714i \(0.723866\pi\)
\(72\) −2.59808 + 1.50000i −0.306186 + 0.176777i
\(73\) 5.97469 + 3.44949i 0.699285 + 0.403732i 0.807081 0.590441i \(-0.201046\pi\)
−0.107796 + 0.994173i \(0.534379\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) −11.6170 + 3.87868i −1.34142 + 0.447871i
\(76\) −6.44949 −0.739807
\(77\) 0 0
\(78\) 1.10102i 0.124666i
\(79\) −1.44949 2.51059i −0.163080 0.282463i 0.772892 0.634538i \(-0.218810\pi\)
−0.935972 + 0.352075i \(0.885476\pi\)
\(80\) 1.81431 + 1.30701i 0.202846 + 0.146128i
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) −9.43879 + 5.44949i −1.04234 + 0.601795i
\(83\) 2.44949i 0.268866i 0.990923 + 0.134433i \(0.0429214\pi\)
−0.990923 + 0.134433i \(0.957079\pi\)
\(84\) 0 0
\(85\) −4.44949 0.449490i −0.482615 0.0487540i
\(86\) 4.44949 + 7.70674i 0.479801 + 0.831039i
\(87\) −6.14966 3.55051i −0.659313 0.380655i
\(88\) −4.24264 2.44949i −0.452267 0.261116i
\(89\) 5.00000 + 8.66025i 0.529999 + 0.917985i 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) 6.67423 + 0.674235i 0.703526 + 0.0710706i
\(91\) 0 0
\(92\) 6.89898i 0.719268i
\(93\) 1.90702 1.10102i 0.197749 0.114171i
\(94\) −0.449490 + 0.778539i −0.0463613 + 0.0803002i
\(95\) 11.7014 + 8.42953i 1.20054 + 0.864851i
\(96\) −1.22474 2.12132i −0.125000 0.216506i
\(97\) 3.79796i 0.385624i 0.981236 + 0.192812i \(0.0617608\pi\)
−0.981236 + 0.192812i \(0.938239\pi\)
\(98\) 0 0
\(99\) −14.6969 −1.47710
\(100\) −1.58346 4.74264i −0.158346 0.474264i
\(101\) 4.22474 7.31747i 0.420378 0.728116i −0.575599 0.817732i \(-0.695231\pi\)
0.995976 + 0.0896167i \(0.0285642\pi\)
\(102\) 4.24264 + 2.44949i 0.420084 + 0.242536i
\(103\) 2.68556 1.55051i 0.264616 0.152776i −0.361822 0.932247i \(-0.617845\pi\)
0.626439 + 0.779471i \(0.284512\pi\)
\(104\) 0.449490 0.0440761
\(105\) 0 0
\(106\) 1.10102 0.106941
\(107\) −6.92820 + 4.00000i −0.669775 + 0.386695i −0.795991 0.605308i \(-0.793050\pi\)
0.126217 + 0.992003i \(0.459717\pi\)
\(108\) 0 0
\(109\) −1.44949 + 2.51059i −0.138836 + 0.240471i −0.927056 0.374922i \(-0.877669\pi\)
0.788220 + 0.615393i \(0.211003\pi\)
\(110\) 4.49598 + 9.98930i 0.428675 + 0.952443i
\(111\) −4.89898 −0.464991
\(112\) 0 0
\(113\) 0.202041i 0.0190064i −0.999955 0.00950321i \(-0.996975\pi\)
0.999955 0.00950321i \(-0.00302501\pi\)
\(114\) −7.89898 13.6814i −0.739807 1.28138i
\(115\) −9.01702 + 12.5169i −0.840841 + 1.16721i
\(116\) 1.44949 2.51059i 0.134582 0.233102i
\(117\) 1.16781 0.674235i 0.107964 0.0623330i
\(118\) 6.44949i 0.593724i
\(119\) 0 0
\(120\) −0.550510 + 5.44949i −0.0502545 + 0.497468i
\(121\) −6.50000 11.2583i −0.590909 1.02348i
\(122\) −7.31747 4.22474i −0.662493 0.382490i
\(123\) −23.1202 13.3485i −2.08468 1.20359i
\(124\) 0.449490 + 0.778539i 0.0403654 + 0.0699149i
\(125\) −3.32577 + 10.6742i −0.297465 + 0.954733i
\(126\) 0 0
\(127\) 5.10102i 0.452642i −0.974053 0.226321i \(-0.927330\pi\)
0.974053 0.226321i \(-0.0726699\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −10.8990 + 18.8776i −0.959602 + 1.66208i
\(130\) −0.815515 0.587486i −0.0715254 0.0515260i
\(131\) −0.775255 1.34278i −0.0677344 0.117319i 0.830169 0.557511i \(-0.188244\pi\)
−0.897904 + 0.440192i \(0.854910\pi\)
\(132\) 12.0000i 1.04447i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −1.00000 + 1.73205i −0.0857493 + 0.148522i
\(137\) −15.4135 8.89898i −1.31686 0.760291i −0.333640 0.942700i \(-0.608277\pi\)
−0.983223 + 0.182409i \(0.941610\pi\)
\(138\) 14.6349 8.44949i 1.24581 0.719268i
\(139\) 6.44949 0.547039 0.273519 0.961867i \(-0.411812\pi\)
0.273519 + 0.961867i \(0.411812\pi\)
\(140\) 0 0
\(141\) −2.20204 −0.185445
\(142\) 9.43879 5.44949i 0.792086 0.457311i
\(143\) 1.90702 + 1.10102i 0.159473 + 0.0920720i
\(144\) 1.50000 2.59808i 0.125000 0.216506i
\(145\) −5.91119 + 2.66050i −0.490897 + 0.220943i
\(146\) −6.89898 −0.570964
\(147\) 0 0
\(148\) 2.00000i 0.164399i
\(149\) 7.89898 + 13.6814i 0.647110 + 1.12083i 0.983810 + 0.179215i \(0.0573557\pi\)
−0.336700 + 0.941612i \(0.609311\pi\)
\(150\) 8.12132 9.16756i 0.663103 0.748528i
\(151\) 9.79796 16.9706i 0.797347 1.38104i −0.123992 0.992283i \(-0.539570\pi\)
0.921338 0.388762i \(-0.127097\pi\)
\(152\) 5.58542 3.22474i 0.453038 0.261561i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 0.202041 2.00000i 0.0162283 0.160644i
\(156\) 0.550510 + 0.953512i 0.0440761 + 0.0763420i
\(157\) 7.31747 + 4.22474i 0.583998 + 0.337171i 0.762721 0.646728i \(-0.223863\pi\)
−0.178723 + 0.983899i \(0.557196\pi\)
\(158\) 2.51059 + 1.44949i 0.199732 + 0.115315i
\(159\) 1.34847 + 2.33562i 0.106941 + 0.185226i
\(160\) −2.22474 0.224745i −0.175882 0.0177676i
\(161\) 0 0
\(162\) 9.00000i 0.707107i
\(163\) 14.6349 8.44949i 1.14630 0.661815i 0.198315 0.980138i \(-0.436453\pi\)
0.947982 + 0.318323i \(0.103120\pi\)
\(164\) 5.44949 9.43879i 0.425534 0.737046i
\(165\) −15.6841 + 21.7718i −1.22100 + 1.69493i
\(166\) −1.22474 2.12132i −0.0950586 0.164646i
\(167\) 4.89898i 0.379094i −0.981872 0.189547i \(-0.939298\pi\)
0.981872 0.189547i \(-0.0607020\pi\)
\(168\) 0 0
\(169\) 12.7980 0.984458
\(170\) 4.07812 1.83548i 0.312777 0.140775i
\(171\) 9.67423 16.7563i 0.739807 1.28138i
\(172\) −7.70674 4.44949i −0.587634 0.339270i
\(173\) 15.8028 9.12372i 1.20146 0.693664i 0.240581 0.970629i \(-0.422662\pi\)
0.960880 + 0.276965i \(0.0893286\pi\)
\(174\) 7.10102 0.538327
\(175\) 0 0
\(176\) 4.89898 0.369274
\(177\) −13.6814 + 7.89898i −1.02836 + 0.593724i
\(178\) −8.66025 5.00000i −0.649113 0.374766i
\(179\) −2.89898 + 5.02118i −0.216680 + 0.375301i −0.953791 0.300471i \(-0.902856\pi\)
0.737111 + 0.675772i \(0.236189\pi\)
\(180\) −6.11717 + 2.75321i −0.455947 + 0.205212i
\(181\) −14.2474 −1.05900 −0.529502 0.848309i \(-0.677621\pi\)
−0.529502 + 0.848309i \(0.677621\pi\)
\(182\) 0 0
\(183\) 20.6969i 1.52996i
\(184\) 3.44949 + 5.97469i 0.254300 + 0.440460i
\(185\) −2.61401 + 3.62863i −0.192186 + 0.266782i
\(186\) −1.10102 + 1.90702i −0.0807307 + 0.139830i
\(187\) −8.48528 + 4.89898i −0.620505 + 0.358249i
\(188\) 0.898979i 0.0655648i
\(189\) 0 0
\(190\) −14.3485 1.44949i −1.04095 0.105157i
\(191\) 8.34847 + 14.4600i 0.604074 + 1.04629i 0.992197 + 0.124679i \(0.0397902\pi\)
−0.388123 + 0.921608i \(0.626876\pi\)
\(192\) 2.12132 + 1.22474i 0.153093 + 0.0883883i
\(193\) 15.2385 + 8.79796i 1.09689 + 0.633291i 0.935403 0.353584i \(-0.115037\pi\)
0.161489 + 0.986874i \(0.448370\pi\)
\(194\) −1.89898 3.28913i −0.136339 0.236146i
\(195\) 0.247449 2.44949i 0.0177202 0.175412i
\(196\) 0 0
\(197\) 9.10102i 0.648421i 0.945985 + 0.324210i \(0.105099\pi\)
−0.945985 + 0.324210i \(0.894901\pi\)
\(198\) 12.7279 7.34847i 0.904534 0.522233i
\(199\) −3.55051 + 6.14966i −0.251689 + 0.435938i −0.963991 0.265935i \(-0.914319\pi\)
0.712302 + 0.701873i \(0.247653\pi\)
\(200\) 3.74264 + 3.31552i 0.264645 + 0.234442i
\(201\) −9.79796 16.9706i −0.691095 1.19701i
\(202\) 8.44949i 0.594504i
\(203\) 0 0
\(204\) −4.89898 −0.342997
\(205\) −22.2237 + 10.0024i −1.55217 + 0.698598i
\(206\) −1.55051 + 2.68556i −0.108029 + 0.187112i
\(207\) 17.9241 + 10.3485i 1.24581 + 0.719268i
\(208\) −0.389270 + 0.224745i −0.0269910 + 0.0155833i
\(209\) 31.5959 2.18554
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −0.953512 + 0.550510i −0.0654875 + 0.0378092i
\(213\) 23.1202 + 13.3485i 1.58417 + 0.914622i
\(214\) 4.00000 6.92820i 0.273434 0.473602i
\(215\) 8.16693 + 18.1455i 0.556980 + 1.23752i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.89898i 0.196344i
\(219\) −8.44949 14.6349i −0.570964 0.988938i
\(220\) −8.88828 6.40300i −0.599248 0.431690i
\(221\) 0.449490 0.778539i 0.0302360 0.0523702i
\(222\) 4.24264 2.44949i 0.284747 0.164399i
\(223\) 4.00000i 0.267860i −0.990991 0.133930i \(-0.957240\pi\)
0.990991 0.133930i \(-0.0427597\pi\)
\(224\) 0 0
\(225\) 14.6969 + 3.00000i 0.979796 + 0.200000i
\(226\) 0.101021 + 0.174973i 0.00671978 + 0.0116390i
\(227\) −6.36396 3.67423i −0.422391 0.243868i 0.273709 0.961813i \(-0.411750\pi\)
−0.696100 + 0.717945i \(0.745083\pi\)
\(228\) 13.6814 + 7.89898i 0.906075 + 0.523123i
\(229\) −7.57321 13.1172i −0.500452 0.866808i −1.00000 0.000522089i \(-0.999834\pi\)
0.499548 0.866286i \(-0.333500\pi\)
\(230\) 1.55051 15.3485i 0.102238 1.01205i
\(231\) 0 0
\(232\) 2.89898i 0.190327i
\(233\) −8.83523 + 5.10102i −0.578815 + 0.334179i −0.760662 0.649148i \(-0.775126\pi\)
0.181847 + 0.983327i \(0.441792\pi\)
\(234\) −0.674235 + 1.16781i −0.0440761 + 0.0763420i
\(235\) −1.17497 + 1.63103i −0.0766468 + 0.106397i
\(236\) −3.22474 5.58542i −0.209913 0.363580i
\(237\) 7.10102i 0.461261i
\(238\) 0 0
\(239\) 25.7980 1.66873 0.834366 0.551211i \(-0.185834\pi\)
0.834366 + 0.551211i \(0.185834\pi\)
\(240\) −2.24799 4.99465i −0.145107 0.322403i
\(241\) 10.3485 17.9241i 0.666604 1.15459i −0.312244 0.950002i \(-0.601081\pi\)
0.978848 0.204589i \(-0.0655859\pi\)
\(242\) 11.2583 + 6.50000i 0.723713 + 0.417836i
\(243\) −19.0919 + 11.0227i −1.22474 + 0.707107i
\(244\) 8.44949 0.540923
\(245\) 0 0
\(246\) 26.6969 1.70213
\(247\) −2.51059 + 1.44949i −0.159745 + 0.0922288i
\(248\) −0.778539 0.449490i −0.0494373 0.0285426i
\(249\) 3.00000 5.19615i 0.190117 0.329293i
\(250\) −2.45692 10.9070i −0.155389 0.689822i
\(251\) 1.55051 0.0978673 0.0489337 0.998802i \(-0.484418\pi\)
0.0489337 + 0.998802i \(0.484418\pi\)
\(252\) 0 0
\(253\) 33.7980i 2.12486i
\(254\) 2.55051 + 4.41761i 0.160033 + 0.277186i
\(255\) 8.88828 + 6.40300i 0.556606 + 0.400972i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −17.9241 + 10.3485i −1.11807 + 0.645520i −0.940908 0.338661i \(-0.890026\pi\)
−0.177165 + 0.984181i \(0.556693\pi\)
\(258\) 21.7980i 1.35708i
\(259\) 0 0
\(260\) 1.00000 + 0.101021i 0.0620174 + 0.00626503i
\(261\) 4.34847 + 7.53177i 0.269163 + 0.466205i
\(262\) 1.34278 + 0.775255i 0.0829573 + 0.0478954i
\(263\) −8.48528 4.89898i −0.523225 0.302084i 0.215028 0.976608i \(-0.431016\pi\)
−0.738253 + 0.674524i \(0.764349\pi\)
\(264\) 6.00000 + 10.3923i 0.369274 + 0.639602i
\(265\) 2.44949 + 0.247449i 0.150471 + 0.0152007i
\(266\) 0 0
\(267\) 24.4949i 1.49906i
\(268\) 6.92820 4.00000i 0.423207 0.244339i
\(269\) 7.57321 13.1172i 0.461747 0.799769i −0.537301 0.843390i \(-0.680556\pi\)
0.999048 + 0.0436212i \(0.0138895\pi\)
\(270\) 0 0
\(271\) 6.00000 + 10.3923i 0.364474 + 0.631288i 0.988692 0.149963i \(-0.0479155\pi\)
−0.624218 + 0.781251i \(0.714582\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) 17.7980 1.07521
\(275\) 7.75736 + 23.2341i 0.467786 + 1.40107i
\(276\) −8.44949 + 14.6349i −0.508600 + 0.880920i
\(277\) 4.41761 + 2.55051i 0.265429 + 0.153245i 0.626808 0.779173i \(-0.284361\pi\)
−0.361380 + 0.932419i \(0.617694\pi\)
\(278\) −5.58542 + 3.22474i −0.334991 + 0.193407i
\(279\) −2.69694 −0.161461
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 1.90702 1.10102i 0.113562 0.0655648i
\(283\) −24.4630 14.1237i −1.45417 0.839568i −0.455460 0.890256i \(-0.650525\pi\)
−0.998715 + 0.0506878i \(0.983859\pi\)
\(284\) −5.44949 + 9.43879i −0.323368 + 0.560089i
\(285\) −14.4984 32.2130i −0.858810 1.90813i
\(286\) −2.20204 −0.130209
\(287\) 0 0
\(288\) 3.00000i 0.176777i
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 3.78899 5.25966i 0.222497 0.308858i
\(291\) 4.65153 8.05669i 0.272678 0.472291i
\(292\) 5.97469 3.44949i 0.349642 0.201866i
\(293\) 6.24745i 0.364980i −0.983208 0.182490i \(-0.941584\pi\)
0.983208 0.182490i \(-0.0584157\pi\)
\(294\) 0 0
\(295\) −1.44949 + 14.3485i −0.0843926 + 0.835400i
\(296\) 1.00000 + 1.73205i 0.0581238 + 0.100673i
\(297\) 0 0
\(298\) −13.6814 7.89898i −0.792544 0.457576i
\(299\) −1.55051 2.68556i −0.0896683 0.155310i
\(300\) −2.44949 + 12.0000i −0.141421 + 0.692820i
\(301\) 0 0
\(302\) 19.5959i 1.12762i
\(303\) −17.9241 + 10.3485i −1.02971 + 0.594504i
\(304\) −3.22474 + 5.58542i −0.184952 + 0.320346i
\(305\) −15.3300 11.0435i −0.877794 0.632351i
\(306\) −3.00000 5.19615i −0.171499 0.297044i
\(307\) 4.24745i 0.242415i −0.992627 0.121207i \(-0.961323\pi\)
0.992627 0.121207i \(-0.0386766\pi\)
\(308\) 0 0
\(309\) −7.59592 −0.432117
\(310\) 0.825027 + 1.83307i 0.0468584 + 0.104111i
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) −0.953512 0.550510i −0.0539820 0.0311665i
\(313\) 15.2385 8.79796i 0.861332 0.497290i −0.00312637 0.999995i \(-0.500995\pi\)
0.864458 + 0.502705i \(0.167662\pi\)
\(314\) −8.44949 −0.476832
\(315\) 0 0
\(316\) −2.89898 −0.163080
\(317\) 22.9453 13.2474i 1.28873 0.744051i 0.310305 0.950637i \(-0.399569\pi\)
0.978428 + 0.206586i \(0.0662353\pi\)
\(318\) −2.33562 1.34847i −0.130975 0.0756184i
\(319\) −7.10102 + 12.2993i −0.397581 + 0.688630i
\(320\) 2.03906 0.917738i 0.113987 0.0513031i
\(321\) 19.5959 1.09374
\(322\) 0 0
\(323\) 12.8990i 0.717718i
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) −1.68228 1.49029i −0.0933160 0.0826664i
\(326\) −8.44949 + 14.6349i −0.467974 + 0.810555i
\(327\) 6.14966 3.55051i 0.340077 0.196344i
\(328\) 10.8990i 0.601795i
\(329\) 0 0
\(330\) 2.69694 26.6969i 0.148462 1.46962i
\(331\) −5.34847 9.26382i −0.293978 0.509186i 0.680768 0.732499i \(-0.261646\pi\)
−0.974747 + 0.223313i \(0.928313\pi\)
\(332\) 2.12132 + 1.22474i 0.116423 + 0.0672166i
\(333\) 5.19615 + 3.00000i 0.284747 + 0.164399i
\(334\) 2.44949 + 4.24264i 0.134030 + 0.232147i
\(335\) −17.7980 1.79796i −0.972406 0.0982330i
\(336\) 0 0
\(337\) 29.5959i 1.61219i −0.591785 0.806096i \(-0.701576\pi\)
0.591785 0.806096i \(-0.298424\pi\)
\(338\) −11.0834 + 6.39898i −0.602855 + 0.348059i
\(339\) −0.247449 + 0.428594i −0.0134396 + 0.0232780i
\(340\) −2.61401 + 3.62863i −0.141765 + 0.196790i
\(341\) −2.20204 3.81405i −0.119247 0.206542i
\(342\) 19.3485i 1.04625i
\(343\) 0 0
\(344\) 8.89898 0.479801
\(345\) 34.4580 15.5088i 1.85516 0.834967i
\(346\) −9.12372 + 15.8028i −0.490494 + 0.849561i
\(347\) −16.5420 9.55051i −0.888019 0.512698i −0.0147253 0.999892i \(-0.504687\pi\)
−0.873294 + 0.487193i \(0.838021\pi\)
\(348\) −6.14966 + 3.55051i −0.329657 + 0.190327i
\(349\) −3.55051 −0.190054 −0.0950272 0.995475i \(-0.530294\pi\)
−0.0950272 + 0.995475i \(0.530294\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.24264 + 2.44949i −0.226134 + 0.130558i
\(353\) −11.3458 6.55051i −0.603877 0.348648i 0.166688 0.986010i \(-0.446693\pi\)
−0.770565 + 0.637361i \(0.780026\pi\)
\(354\) 7.89898 13.6814i 0.419826 0.727160i
\(355\) 22.2237 10.0024i 1.17951 0.530872i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 5.79796i 0.306432i
\(359\) 5.79796 + 10.0424i 0.306005 + 0.530015i 0.977484 0.211007i \(-0.0676744\pi\)
−0.671480 + 0.741023i \(0.734341\pi\)
\(360\) 3.92102 5.44294i 0.206656 0.286868i
\(361\) −11.2980 + 19.5686i −0.594629 + 1.02993i
\(362\) 12.3387 7.12372i 0.648505 0.374415i
\(363\) 31.8434i 1.67134i
\(364\) 0 0
\(365\) −15.3485 1.55051i −0.803376 0.0811574i
\(366\) 10.3485 + 17.9241i 0.540923 + 0.936906i
\(367\) 27.7128 + 16.0000i 1.44660 + 0.835193i 0.998277 0.0586798i \(-0.0186891\pi\)
0.448320 + 0.893873i \(0.352022\pi\)
\(368\) −5.97469 3.44949i −0.311452 0.179817i
\(369\) 16.3485 + 28.3164i 0.851067 + 1.47409i
\(370\) 0.449490 4.44949i 0.0233679 0.231318i
\(371\) 0 0
\(372\) 2.20204i 0.114171i
\(373\) −21.3882 + 12.3485i −1.10744 + 0.639380i −0.938165 0.346190i \(-0.887475\pi\)
−0.169273 + 0.985569i \(0.554142\pi\)
\(374\) 4.89898 8.48528i 0.253320 0.438763i
\(375\) 20.1282 18.5703i 1.03942 0.958964i
\(376\) 0.449490 + 0.778539i 0.0231807 + 0.0401501i
\(377\) 1.30306i 0.0671111i
\(378\) 0 0
\(379\) −1.30306 −0.0669338 −0.0334669 0.999440i \(-0.510655\pi\)
−0.0334669 + 0.999440i \(0.510655\pi\)
\(380\) 13.1509 5.91894i 0.674626 0.303635i
\(381\) −6.24745 + 10.8209i −0.320066 + 0.554371i
\(382\) −14.4600 8.34847i −0.739837 0.427145i
\(383\) −14.6349 + 8.44949i −0.747811 + 0.431749i −0.824902 0.565275i \(-0.808770\pi\)
0.0770916 + 0.997024i \(0.475437\pi\)
\(384\) −2.44949 −0.125000
\(385\) 0 0
\(386\) −17.5959 −0.895609
\(387\) 23.1202 13.3485i 1.17527 0.678541i
\(388\) 3.28913 + 1.89898i 0.166980 + 0.0964061i
\(389\) 11.4495 19.8311i 0.580512 1.00548i −0.414906 0.909864i \(-0.636186\pi\)
0.995419 0.0956125i \(-0.0304810\pi\)
\(390\) 1.01045 + 2.24504i 0.0511660 + 0.113682i
\(391\) 13.7980 0.697793
\(392\) 0 0
\(393\) 3.79796i 0.191582i
\(394\) −4.55051 7.88171i −0.229251 0.397075i
\(395\) 5.25966 + 3.78899i 0.264642 + 0.190645i
\(396\) −7.34847 + 12.7279i −0.369274 + 0.639602i
\(397\) 15.0242 8.67423i 0.754044 0.435347i −0.0731094 0.997324i \(-0.523292\pi\)
0.827153 + 0.561977i \(0.189959\pi\)
\(398\) 7.10102i 0.355942i
\(399\) 0 0
\(400\) −4.89898 1.00000i −0.244949 0.0500000i
\(401\) −14.6969 25.4558i −0.733930 1.27120i −0.955191 0.295990i \(-0.904351\pi\)
0.221261 0.975215i \(-0.428983\pi\)
\(402\) 16.9706 + 9.79796i 0.846415 + 0.488678i
\(403\) 0.349945 + 0.202041i 0.0174320 + 0.0100644i
\(404\) −4.22474 7.31747i −0.210189 0.364058i
\(405\) −2.02270 + 20.0227i −0.100509 + 0.994936i
\(406\) 0 0
\(407\) 9.79796i 0.485667i
\(408\) 4.24264 2.44949i 0.210042 0.121268i
\(409\) 7.24745 12.5529i 0.358363 0.620703i −0.629324 0.777143i \(-0.716668\pi\)
0.987688 + 0.156439i \(0.0500016\pi\)
\(410\) 14.2450 19.7742i 0.703513 0.976576i
\(411\) 21.7980 + 37.7552i 1.07521 + 1.86233i
\(412\) 3.10102i 0.152776i
\(413\) 0 0
\(414\) −20.6969 −1.01720
\(415\) −2.24799 4.99465i −0.110349 0.245178i
\(416\) 0.224745 0.389270i 0.0110190 0.0190855i
\(417\) −13.6814 7.89898i −0.669983 0.386815i
\(418\) −27.3629 + 15.7980i −1.33836 + 0.772703i
\(419\) −6.44949 −0.315078 −0.157539 0.987513i \(-0.550356\pi\)
−0.157539 + 0.987513i \(0.550356\pi\)
\(420\) 0 0
\(421\) −23.7980 −1.15984 −0.579921 0.814673i \(-0.696917\pi\)
−0.579921 + 0.814673i \(0.696917\pi\)
\(422\) −10.3923 + 6.00000i −0.505889 + 0.292075i
\(423\) 2.33562 + 1.34847i 0.113562 + 0.0655648i
\(424\) 0.550510 0.953512i 0.0267351 0.0463066i
\(425\) 9.48528 3.16693i 0.460104 0.153619i
\(426\) −26.6969 −1.29347
\(427\) 0 0
\(428\) 8.00000i 0.386695i
\(429\) −2.69694 4.67123i −0.130209 0.225529i
\(430\) −16.1455 11.6310i −0.778607 0.560898i
\(431\) −8.89898 + 15.4135i −0.428649 + 0.742441i −0.996753 0.0805149i \(-0.974344\pi\)
0.568105 + 0.822956i \(0.307677\pi\)
\(432\) 0 0
\(433\) 19.7980i 0.951429i −0.879600 0.475715i \(-0.842190\pi\)
0.879600 0.475715i \(-0.157810\pi\)
\(434\) 0 0
\(435\) 15.7980 + 1.59592i 0.757454 + 0.0765184i
\(436\) 1.44949 + 2.51059i 0.0694180 + 0.120235i
\(437\) −38.5337 22.2474i −1.84332 1.06424i
\(438\) 14.6349 + 8.44949i 0.699285 + 0.403732i
\(439\) −18.6969 32.3840i −0.892356 1.54561i −0.837043 0.547137i \(-0.815718\pi\)
−0.0553132 0.998469i \(-0.517616\pi\)
\(440\) 10.8990 + 1.10102i 0.519588 + 0.0524891i
\(441\) 0 0
\(442\) 0.898979i 0.0427601i
\(443\) 8.48528 4.89898i 0.403148 0.232758i −0.284693 0.958619i \(-0.591892\pi\)
0.687841 + 0.725861i \(0.258558\pi\)
\(444\) −2.44949 + 4.24264i −0.116248 + 0.201347i
\(445\) −18.1431 13.0701i −0.860067 0.619581i
\(446\) 2.00000 + 3.46410i 0.0947027 + 0.164030i
\(447\) 38.6969i 1.83030i
\(448\) 0 0
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) −14.2279 + 4.75039i −0.670711 + 0.223936i
\(451\) −26.6969 + 46.2405i −1.25711 + 2.17738i
\(452\) −0.174973 0.101021i −0.00823002 0.00475161i
\(453\) −41.5692 + 24.0000i −1.95309 + 1.12762i
\(454\) 7.34847 0.344881
\(455\) 0 0
\(456\) −15.7980 −0.739807
\(457\) −8.31031 + 4.79796i −0.388740 + 0.224439i −0.681614 0.731712i \(-0.738722\pi\)
0.292874 + 0.956151i \(0.405388\pi\)
\(458\) 13.1172 + 7.57321i 0.612926 + 0.353873i
\(459\) 0 0
\(460\) 6.33145 + 14.0674i 0.295206 + 0.655897i
\(461\) −2.65153 −0.123494 −0.0617470 0.998092i \(-0.519667\pi\)
−0.0617470 + 0.998092i \(0.519667\pi\)
\(462\) 0 0
\(463\) 35.5959i 1.65428i 0.561994 + 0.827141i \(0.310034\pi\)
−0.561994 + 0.827141i \(0.689966\pi\)
\(464\) −1.44949 2.51059i −0.0672909 0.116551i
\(465\) −2.87808 + 3.99519i −0.133468 + 0.185273i
\(466\) 5.10102 8.83523i 0.236300 0.409284i
\(467\) −4.80688 + 2.77526i −0.222436 + 0.128423i −0.607078 0.794642i \(-0.707658\pi\)
0.384642 + 0.923066i \(0.374325\pi\)
\(468\) 1.34847i 0.0623330i
\(469\) 0 0
\(470\) 0.202041 2.00000i 0.00931946 0.0922531i
\(471\) −10.3485 17.9241i −0.476832 0.825898i
\(472\) 5.58542 + 3.22474i 0.257090 + 0.148431i
\(473\) 37.7552 + 21.7980i 1.73598 + 1.00227i
\(474\) −3.55051 6.14966i −0.163080 0.282463i
\(475\) −31.5959 6.44949i −1.44972 0.295923i
\(476\) 0 0
\(477\) 3.30306i 0.151237i
\(478\) −22.3417 + 12.8990i −1.02189 + 0.589986i
\(479\) −19.3485 + 33.5125i −0.884054 + 1.53123i −0.0372602 + 0.999306i \(0.511863\pi\)
−0.846794 + 0.531921i \(0.821470\pi\)
\(480\) 4.44414 + 3.20150i 0.202846 + 0.146128i
\(481\) −0.449490 0.778539i −0.0204950 0.0354983i
\(482\) 20.6969i 0.942720i
\(483\) 0 0
\(484\) −13.0000 −0.590909
\(485\) −3.48553 7.74426i −0.158270 0.351649i
\(486\) 11.0227 19.0919i 0.500000 0.866025i
\(487\) 31.7805 + 18.3485i 1.44011 + 0.831449i 0.997856 0.0654410i \(-0.0208454\pi\)
0.442255 + 0.896890i \(0.354179\pi\)
\(488\) −7.31747 + 4.22474i −0.331246 + 0.191245i
\(489\) −41.3939 −1.87190
\(490\) 0 0
\(491\) −19.5959 −0.884351 −0.442176 0.896928i \(-0.645793\pi\)
−0.442176 + 0.896928i \(0.645793\pi\)
\(492\) −23.1202 + 13.3485i −1.04234 + 0.601795i
\(493\) 5.02118 + 2.89898i 0.226143 + 0.130563i
\(494\) 1.44949 2.51059i 0.0652156 0.112957i
\(495\) 29.9679 13.4879i 1.34696 0.606238i
\(496\) 0.898979 0.0403654
\(497\) 0 0
\(498\) 6.00000i 0.268866i
\(499\) 12.8990 + 22.3417i 0.577438 + 1.00015i 0.995772 + 0.0918583i \(0.0292807\pi\)
−0.418334 + 0.908293i \(0.637386\pi\)
\(500\) 7.58128 + 8.21731i 0.339045 + 0.367489i
\(501\) −6.00000 + 10.3923i −0.268060 + 0.464294i
\(502\) −1.34278 + 0.775255i −0.0599313 + 0.0346013i
\(503\) 4.00000i 0.178351i −0.996016 0.0891756i \(-0.971577\pi\)
0.996016 0.0891756i \(-0.0284232\pi\)
\(504\) 0 0
\(505\) −1.89898 + 18.7980i −0.0845035 + 0.836498i
\(506\) −16.8990 29.2699i −0.751251 1.30121i
\(507\) −27.1486 15.6742i −1.20571 0.696117i
\(508\) −4.41761 2.55051i −0.196000 0.113161i
\(509\) 18.2247 + 31.5662i 0.807798 + 1.39915i 0.914386 + 0.404843i \(0.132674\pi\)
−0.106588 + 0.994303i \(0.533993\pi\)
\(510\) −10.8990 1.10102i −0.482615 0.0487540i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 10.3485 17.9241i 0.456451 0.790597i
\(515\) −4.05306 + 5.62622i −0.178599 + 0.247921i
\(516\) 10.8990 + 18.8776i 0.479801 + 0.831039i
\(517\) 4.40408i 0.193691i
\(518\) 0 0
\(519\) −44.6969 −1.96198
\(520\) −0.916536 + 0.412514i −0.0401927 + 0.0180899i
\(521\) 1.65153 2.86054i 0.0723549 0.125322i −0.827578 0.561351i \(-0.810282\pi\)
0.899933 + 0.436028i \(0.143615\pi\)
\(522\) −7.53177 4.34847i −0.329657 0.190327i
\(523\) 0.992836 0.573214i 0.0434137 0.0250649i −0.478136 0.878286i \(-0.658687\pi\)
0.521550 + 0.853221i \(0.325354\pi\)
\(524\) −1.55051 −0.0677344
\(525\) 0 0
\(526\) 9.79796 0.427211
\(527\) −1.55708 + 0.898979i −0.0678274 + 0.0391602i
\(528\) −10.3923 6.00000i −0.452267 0.261116i
\(529\) 12.2980 21.3007i 0.534694 0.926117i
\(530\) −2.24504 + 1.01045i −0.0975185 + 0.0438911i
\(531\) 19.3485 0.839652
\(532\) 0 0
\(533\) 4.89898i 0.212198i
\(534\) 12.2474 + 21.2132i 0.529999 + 0.917985i
\(535\) 10.4561 14.5145i 0.452055 0.627517i
\(536\) −4.00000 + 6.92820i −0.172774 + 0.299253i
\(537\) 12.2993 7.10102i 0.530755 0.306432i
\(538\) 15.1464i 0.653009i
\(539\) 0 0
\(540\) 0 0
\(541\) 14.7980 + 25.6308i 0.636214 + 1.10195i 0.986257 + 0.165221i \(0.0528338\pi\)
−0.350043 + 0.936734i \(0.613833\pi\)
\(542\) −10.3923 6.00000i −0.446388 0.257722i
\(543\) 30.2234 + 17.4495i 1.29701 + 0.748829i
\(544\) 1.00000 + 1.73205i 0.0428746 + 0.0742611i
\(545\) 0.651531 6.44949i 0.0279085 0.276266i
\(546\) 0 0
\(547\) 10.6969i 0.457368i 0.973501 + 0.228684i \(0.0734423\pi\)
−0.973501 + 0.228684i \(0.926558\pi\)
\(548\) −15.4135 + 8.89898i −0.658431 + 0.380146i
\(549\) −12.6742 + 21.9524i −0.540923 + 0.936906i
\(550\) −18.3351 16.2426i −0.781812 0.692589i
\(551\) −9.34847 16.1920i −0.398258 0.689803i
\(552\) 16.8990i 0.719268i
\(553\) 0 0
\(554\) −5.10102 −0.216722
\(555\) 9.98930 4.49598i 0.424022 0.190844i
\(556\) 3.22474 5.58542i 0.136760 0.236875i
\(557\) 14.4600 + 8.34847i 0.612689 + 0.353736i 0.774017 0.633165i \(-0.218244\pi\)
−0.161328 + 0.986901i \(0.551578\pi\)
\(558\) 2.33562 1.34847i 0.0988746 0.0570853i
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) 15.5885 9.00000i 0.657559 0.379642i
\(563\) −12.1637 7.02270i −0.512638 0.295972i 0.221279 0.975210i \(-0.428977\pi\)
−0.733917 + 0.679239i \(0.762310\pi\)
\(564\) −1.10102 + 1.90702i −0.0463613 + 0.0803002i
\(565\) 0.185421 + 0.411973i 0.00780071 + 0.0173319i
\(566\) 28.2474 1.18733
\(567\) 0 0
\(568\) 10.8990i 0.457311i
\(569\) 7.10102 + 12.2993i 0.297690 + 0.515615i 0.975607 0.219524i \(-0.0704504\pi\)
−0.677917 + 0.735139i \(0.737117\pi\)
\(570\) 28.6624 + 20.6480i 1.20054 + 0.864851i
\(571\) 10.4495 18.0990i 0.437298 0.757422i −0.560183 0.828369i \(-0.689269\pi\)
0.997480 + 0.0709477i \(0.0226023\pi\)
\(572\) 1.90702 1.10102i 0.0797367 0.0460360i
\(573\) 40.8990i 1.70858i
\(574\) 0 0
\(575\) 6.89898 33.7980i 0.287707 1.40947i
\(576\) −1.50000 2.59808i −0.0625000 0.108253i
\(577\) 40.2658 + 23.2474i 1.67629 + 0.967804i 0.963995 + 0.265919i \(0.0856753\pi\)
0.712290 + 0.701885i \(0.247658\pi\)
\(578\) 11.2583 + 6.50000i 0.468285 + 0.270364i
\(579\) −21.5505 37.3266i −0.895609 1.55124i
\(580\) −0.651531 + 6.44949i −0.0270533 + 0.267800i
\(581\) 0 0
\(582\) 9.30306i 0.385624i
\(583\) 4.67123 2.69694i 0.193463 0.111696i
\(584\) −3.44949 + 5.97469i −0.142741 + 0.247234i
\(585\) −1.76246 + 2.44655i −0.0728687 + 0.101152i
\(586\) 3.12372 + 5.41045i 0.129040 + 0.223504i
\(587\) 33.1464i 1.36810i 0.729435 + 0.684050i \(0.239783\pi\)
−0.729435 + 0.684050i \(0.760217\pi\)
\(588\) 0 0
\(589\) 5.79796 0.238901
\(590\) −5.91894 13.1509i −0.243679 0.541413i
\(591\) 11.1464 19.3062i 0.458503 0.794150i
\(592\) −1.73205 1.00000i −0.0711868 0.0410997i
\(593\) −0.953512 + 0.550510i −0.0391560 + 0.0226067i −0.519450 0.854501i \(-0.673863\pi\)
0.480294 + 0.877107i \(0.340530\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 15.7980 0.647110
\(597\) 15.0635 8.69694i 0.616510 0.355942i
\(598\) 2.68556 + 1.55051i 0.109821 + 0.0634051i
\(599\) −11.4495 + 19.8311i −0.467813 + 0.810277i −0.999324 0.0367753i \(-0.988291\pi\)
0.531510 + 0.847052i \(0.321625\pi\)
\(600\) −3.87868 11.6170i −0.158346 0.474264i
\(601\) −19.3939 −0.791093 −0.395546 0.918446i \(-0.629445\pi\)
−0.395546 + 0.918446i \(0.629445\pi\)
\(602\) 0 0
\(603\) 24.0000i 0.977356i
\(604\) −9.79796 16.9706i −0.398673 0.690522i
\(605\) 23.5861 + 16.9911i 0.958910 + 0.690786i
\(606\) 10.3485 17.9241i 0.420378 0.728116i
\(607\) 21.9917 12.6969i 0.892617 0.515353i 0.0178196 0.999841i \(-0.494328\pi\)
0.874798 + 0.484488i \(0.160994\pi\)
\(608\) 6.44949i 0.261561i
\(609\) 0 0
\(610\) 18.7980 + 1.89898i 0.761107 + 0.0768874i
\(611\) −0.202041 0.349945i −0.00817371 0.0141573i
\(612\) 5.19615 + 3.00000i 0.210042 + 0.121268i
\(613\) −7.10318 4.10102i −0.286895 0.165639i 0.349646 0.936882i \(-0.386302\pi\)
−0.636541 + 0.771243i \(0.719635\pi\)
\(614\) 2.12372 + 3.67840i 0.0857065 + 0.148448i
\(615\) 59.3939 + 6.00000i 2.39499 + 0.241943i
\(616\) 0 0
\(617\) 9.59592i 0.386317i −0.981168 0.193159i \(-0.938127\pi\)
0.981168 0.193159i \(-0.0618732\pi\)
\(618\) 6.57826 3.79796i 0.264616 0.152776i
\(619\) 23.2247 40.2264i 0.933481 1.61684i 0.156161 0.987732i \(-0.450088\pi\)
0.777320 0.629106i \(-0.216579\pi\)
\(620\) −1.63103 1.17497i −0.0655038 0.0471880i
\(621\) 0 0
\(622\) 12.0000i 0.481156i
\(623\) 0 0
\(624\) 1.10102 0.0440761
\(625\) −3.01472 24.8176i −0.120589 0.992703i
\(626\) −8.79796 + 15.2385i −0.351637 + 0.609053i
\(627\) −67.0251 38.6969i −2.67672 1.54541i
\(628\) 7.31747 4.22474i 0.291999 0.168586i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) 6.49490 0.258558 0.129279 0.991608i \(-0.458734\pi\)
0.129279 + 0.991608i \(0.458734\pi\)
\(632\) 2.51059 1.44949i 0.0998659 0.0576576i
\(633\) −25.4558 14.6969i −1.01178 0.584151i
\(634\) −13.2474 + 22.9453i −0.526123 + 0.911272i
\(635\) 4.68140 + 10.4013i 0.185776 + 0.412762i
\(636\) 2.69694 0.106941
\(637\) 0 0
\(638\) 14.2020i 0.562264i
\(639\) −16.3485 28.3164i −0.646735 1.12018i
\(640\) −1.30701 + 1.81431i −0.0516640 + 0.0717170i
\(641\) −3.10102 + 5.37113i −0.122483 + 0.212147i −0.920746 0.390162i \(-0.872419\pi\)
0.798263 + 0.602309i \(0.205752\pi\)
\(642\) −16.9706 + 9.79796i −0.669775 + 0.386695i
\(643\) 9.14643i 0.360700i −0.983603 0.180350i \(-0.942277\pi\)
0.983603 0.180350i \(-0.0577230\pi\)
\(644\) 0 0
\(645\) 4.89898 48.4949i 0.192897 1.90948i
\(646\) 6.44949 + 11.1708i 0.253752 + 0.439511i
\(647\) 19.3062 + 11.1464i 0.759004 + 0.438211i 0.828938 0.559340i \(-0.188945\pi\)
−0.0699339 + 0.997552i \(0.522279\pi\)
\(648\) 7.79423 + 4.50000i 0.306186 + 0.176777i
\(649\) 15.7980 + 27.3629i 0.620124 + 1.07409i
\(650\) 2.20204 + 0.449490i 0.0863712 + 0.0176304i
\(651\) 0 0
\(652\) 16.8990i 0.661815i
\(653\) 34.4660 19.8990i 1.34876 0.778707i 0.360687 0.932687i \(-0.382542\pi\)
0.988074 + 0.153980i \(0.0492091\pi\)
\(654\) −3.55051 + 6.14966i −0.138836 + 0.240471i
\(655\) 2.81311 + 2.02653i 0.109917 + 0.0791830i
\(656\) −5.44949 9.43879i −0.212767 0.368523i
\(657\) 20.6969i 0.807464i
\(658\) 0 0
\(659\) −7.10102 −0.276616 −0.138308 0.990389i \(-0.544166\pi\)
−0.138308 + 0.990389i \(0.544166\pi\)
\(660\) 11.0129 + 24.4687i 0.428675 + 0.952443i
\(661\) 6.47219 11.2102i 0.251739 0.436025i −0.712266 0.701910i \(-0.752331\pi\)
0.964005 + 0.265885i \(0.0856642\pi\)
\(662\) 9.26382 + 5.34847i 0.360049 + 0.207874i
\(663\) −1.90702 + 1.10102i −0.0740627 + 0.0427601i
\(664\) −2.44949 −0.0950586
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) 17.3205 10.0000i 0.670653 0.387202i
\(668\) −4.24264 2.44949i −0.164153 0.0947736i
\(669\) −4.89898 + 8.48528i −0.189405 + 0.328060i
\(670\) 16.3125 7.34190i 0.630205 0.283642i
\(671\) −41.3939 −1.59799
\(672\) 0 0
\(673\) 1.79796i 0.0693062i −0.999399 0.0346531i \(-0.988967\pi\)
0.999399 0.0346531i \(-0.0110326\pi\)
\(674\) 14.7980 + 25.6308i 0.569996 + 0.987262i
\(675\) 0 0
\(676\) 6.39898 11.0834i 0.246115 0.426283i
\(677\) 27.3235 15.7753i 1.05013 0.606292i 0.127444 0.991846i \(-0.459323\pi\)
0.922685 + 0.385554i \(0.125989\pi\)
\(678\) 0.494897i 0.0190064i
\(679\) 0 0
\(680\) 0.449490 4.44949i 0.0172371 0.170630i
\(681\) 9.00000 + 15.5885i 0.344881 + 0.597351i
\(682\) 3.81405 + 2.20204i 0.146047 + 0.0843205i
\(683\) −30.8270 17.7980i −1.17956 0.681020i −0.223648 0.974670i \(-0.571797\pi\)
−0.955913 + 0.293650i \(0.905130\pi\)
\(684\) −9.67423 16.7563i −0.369904 0.640692i
\(685\) 39.5959 + 4.00000i 1.51288 + 0.152832i
\(686\) 0 0
\(687\) 37.1010i 1.41549i
\(688\) −7.70674 + 4.44949i −0.293817 + 0.169635i
\(689\) −0.247449 + 0.428594i −0.00942705 + 0.0163281i
\(690\) −22.0871 + 30.6600i −0.840841 + 1.16721i
\(691\) −6.57321 11.3851i −0.250057 0.433111i 0.713484 0.700671i \(-0.247116\pi\)
−0.963541 + 0.267560i \(0.913783\pi\)
\(692\) 18.2474i 0.693664i
\(693\) 0 0
\(694\) 19.1010 0.725065
\(695\) −13.1509 + 5.91894i −0.498841 + 0.224518i
\(696\) 3.55051 6.14966i 0.134582 0.233102i
\(697\) 18.8776 + 10.8990i 0.715040 + 0.412828i
\(698\) 3.07483 1.77526i 0.116384 0.0671944i
\(699\) 24.9898 0.945201
\(700\) 0 0
\(701\) 40.6969 1.53710 0.768551 0.639788i \(-0.220978\pi\)
0.768551 + 0.639788i \(0.220978\pi\)
\(702\) 0 0
\(703\) −11.1708 6.44949i −0.421316 0.243247i
\(704\) 2.44949 4.24264i 0.0923186 0.159901i
\(705\) 4.49009 2.02090i 0.169107 0.0761113i
\(706\) 13.1010 0.493063
\(707\) 0 0
\(708\) 15.7980i 0.593724i
\(709\) 20.1464 + 34.8946i 0.756615 + 1.31050i 0.944567 + 0.328317i \(0.106482\pi\)
−0.187952 + 0.982178i \(0.560185\pi\)
\(710\) −14.2450 + 19.7742i −0.534607 + 0.742111i
\(711\) 4.34847 7.53177i 0.163080 0.282463i
\(712\) −8.66025 + 5.00000i −0.324557 + 0.187383i
\(713\) 6.20204i 0.232268i
\(714\) 0 0
\(715\) −4.89898 0.494897i −0.183211 0.0185081i
\(716\) 2.89898 + 5.02118i 0.108340 + 0.187650i
\(717\) −54.7257 31.5959i −2.04377 1.17997i
\(718\) −10.0424 5.79796i −0.374778 0.216378i
\(719\) −22.2474 38.5337i −0.829690 1.43706i −0.898282 0.439420i \(-0.855184\pi\)
0.0685918 0.997645i \(-0.478149\pi\)
\(720\) −0.674235 + 6.67423i −0.0251272 + 0.248734i
\(721\) 0 0
\(722\) 22.5959i 0.840933i
\(723\) −43.9048 + 25.3485i −1.63284 + 0.942720i
\(724\) −7.12372 + 12.3387i −0.264751 + 0.458562i
\(725\) 9.61161 10.8498i 0.356966 0.402953i
\(726\) −15.9217 27.5772i −0.590909 1.02348i
\(727\) 6.69694i 0.248376i 0.992259 + 0.124188i \(0.0396325\pi\)
−0.992259 + 0.124188i \(0.960367\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 14.0674 6.33145i 0.520659 0.234338i
\(731\) 8.89898 15.4135i 0.329141 0.570088i
\(732\) −17.9241 10.3485i −0.662493 0.382490i
\(733\) −37.7945 + 21.8207i −1.39597 + 0.805965i −0.993968 0.109673i \(-0.965020\pi\)
−0.402004 + 0.915638i \(0.631686\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) 6.89898 0.254300
\(737\) −33.9411 + 19.5959i −1.25024 + 0.721825i
\(738\) −28.3164 16.3485i −1.04234 0.601795i
\(739\) −22.2474 + 38.5337i −0.818386 + 1.41749i 0.0884855 + 0.996077i \(0.471797\pi\)
−0.906871 + 0.421408i \(0.861536\pi\)
\(740\) 1.83548 + 4.07812i 0.0674734 + 0.149915i
\(741\) 7.10102 0.260863
\(742\) 0 0
\(743\) 15.3031i 0.561415i 0.959793 + 0.280707i \(0.0905691\pi\)
−0.959793 + 0.280707i \(0.909431\pi\)
\(744\) 1.10102 + 1.90702i 0.0403654 + 0.0699149i
\(745\) −28.6624 20.6480i −1.05011 0.756486i
\(746\) 12.3485 21.3882i 0.452110 0.783077i
\(747\) −6.36396 + 3.67423i −0.232845 + 0.134433i
\(748\) 9.79796i 0.358249i
\(749\) 0 0
\(750\) −8.14643 + 26.1464i −0.297465 + 0.954733i
\(751\) 11.1010 + 19.2275i 0.405082 + 0.701623i 0.994331 0.106329i \(-0.0339096\pi\)
−0.589249 + 0.807951i \(0.700576\pi\)
\(752\) −0.778539 0.449490i −0.0283904 0.0163912i
\(753\) −3.28913 1.89898i −0.119863 0.0692027i
\(754\) 0.651531 + 1.12848i 0.0237274 + 0.0410970i
\(755\) −4.40408 + 43.5959i −0.160281 + 1.58662i
\(756\) 0 0
\(757\) 32.2020i 1.17040i −0.810888 0.585202i \(-0.801015\pi\)
0.810888 0.585202i \(-0.198985\pi\)
\(758\) 1.12848 0.651531i 0.0409884 0.0236647i
\(759\) 41.3939 71.6963i 1.50250 2.60241i
\(760\) −8.42953 + 11.7014i −0.305771 + 0.424454i
\(761\) −15.4495 26.7593i −0.560044 0.970024i −0.997492 0.0707804i \(-0.977451\pi\)
0.437448 0.899244i \(-0.355882\pi\)
\(762\) 12.4949i 0.452642i
\(763\) 0 0
\(764\) 16.6969 0.604074
\(765\) −5.50643 12.2343i −0.199085 0.442334i
\(766\) 8.44949 14.6349i 0.305292 0.528782i
\(767\) −2.51059 1.44949i −0.0906521 0.0523380i
\(768\) 2.12132 1.22474i 0.0765466 0.0441942i
\(769\) −11.3031 −0.407599 −0.203799 0.979013i \(-0.565329\pi\)
−0.203799 + 0.979013i \(0.565329\pi\)
\(770\) 0 0
\(771\) 50.6969 1.82581
\(772\) 15.2385 8.79796i 0.548446 0.316645i
\(773\) 11.5601 + 6.67423i 0.415788 + 0.240056i 0.693274 0.720674i \(-0.256168\pi\)
−0.277485 + 0.960730i \(0.589501\pi\)
\(774\) −13.3485 + 23.1202i −0.479801 + 0.831039i
\(775\) 1.42350 + 4.26354i 0.0511337 + 0.153151i
\(776\) −3.79796 −0.136339
\(777\) 0 0
\(778\) 22.8990i 0.820968i
\(779\) −35.1464 60.8754i −1.25925 2.18109i
\(780\) −1.99760