Properties

Label 490.2.i.f.79.2
Level $490$
Weight $2$
Character 490.79
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 79.2
Root \(-0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 490.79
Dual form 490.2.i.f.459.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.866025 - 0.500000i) q^{2} +(2.12132 - 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.30701 - 1.81431i) q^{5} -2.44949 q^{6} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-0.866025 - 0.500000i) q^{2} +(2.12132 - 1.22474i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.30701 - 1.81431i) q^{5} -2.44949 q^{6} -1.00000i q^{8} +(1.50000 - 2.59808i) q^{9} +(-2.03906 + 0.917738i) q^{10} +(2.44949 + 4.24264i) q^{11} +(2.12132 + 1.22474i) q^{12} -4.44949i q^{13} +(0.550510 - 5.44949i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.73205 - 1.00000i) q^{17} +(-2.59808 + 1.50000i) q^{18} +(-0.775255 + 1.34278i) q^{19} +(2.22474 + 0.224745i) q^{20} -4.89898i q^{22} +(-2.51059 - 1.44949i) q^{23} +(-1.22474 - 2.12132i) q^{24} +(-1.58346 - 4.74264i) q^{25} +(-2.22474 + 3.85337i) q^{26} -6.89898 q^{29} +(-3.20150 + 4.44414i) q^{30} +(4.44949 + 7.70674i) 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} +(1.34278 - 0.775255i) q^{38} +(-5.44949 - 9.43879i) q^{39} +(-1.81431 - 1.30701i) q^{40} +1.10102 q^{41} -0.898979i q^{43} +(-2.44949 + 4.24264i) q^{44} +(-2.75321 - 6.11717i) q^{45} +(1.44949 + 2.51059i) q^{46} +(-7.70674 - 4.44949i) q^{47} +2.44949i q^{48} +(-1.00000 + 4.89898i) q^{50} +(2.44949 - 4.24264i) q^{51} +(3.85337 - 2.22474i) q^{52} +(-9.43879 + 5.44949i) q^{53} +(10.8990 + 1.10102i) q^{55} +3.79796i q^{57} +(5.97469 + 3.44949i) q^{58} +(0.775255 + 1.34278i) q^{59} +(4.99465 - 2.24799i) q^{60} +(1.77526 - 3.07483i) q^{61} -8.89898i q^{62} -1.00000 q^{64} +(-8.07277 - 5.81552i) q^{65} +(-6.00000 - 10.3923i) q^{66} +(6.92820 - 4.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} -7.10102 q^{69} -1.10102 q^{71} +(-2.59808 - 1.50000i) q^{72} +(-2.51059 + 1.44949i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(-9.16756 - 8.12132i) q^{75} -1.55051 q^{76} +10.8990i q^{78} +(3.44949 - 5.97469i) q^{79} +(0.917738 + 2.03906i) q^{80} +(4.50000 + 7.79423i) q^{81} +(-0.953512 - 0.550510i) q^{82} +2.44949i q^{83} +(0.449490 - 4.44949i) q^{85} +(-0.449490 + 0.778539i) q^{86} +(-14.6349 + 8.44949i) q^{87} +(4.24264 - 2.44949i) q^{88} +(5.00000 - 8.66025i) q^{89} +(-0.674235 + 6.67423i) q^{90} -2.89898i q^{92} +(18.8776 + 10.8990i) q^{93} +(4.44949 + 7.70674i) q^{94} +(1.42296 + 3.16158i) q^{95} +(1.22474 - 2.12132i) q^{96} +15.7980i 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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

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

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 \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 1.30701 1.81431i 0.584511 0.811386i
\(6\) −2.44949 −1.00000
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −2.03906 + 0.917738i −0.644807 + 0.290214i
\(11\) 2.44949 + 4.24264i 0.738549 + 1.27920i 0.953149 + 0.302502i \(0.0978220\pi\)
−0.214600 + 0.976702i \(0.568845\pi\)
\(12\) 2.12132 + 1.22474i 0.612372 + 0.353553i
\(13\) 4.44949i 1.23407i −0.786937 0.617033i \(-0.788334\pi\)
0.786937 0.617033i \(-0.211666\pi\)
\(14\) 0 0
\(15\) 0.550510 5.44949i 0.142141 1.40705i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.73205 1.00000i 0.420084 0.242536i −0.275029 0.961436i \(-0.588688\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) −2.59808 + 1.50000i −0.612372 + 0.353553i
\(19\) −0.775255 + 1.34278i −0.177856 + 0.308055i −0.941146 0.338001i \(-0.890249\pi\)
0.763290 + 0.646056i \(0.223583\pi\)
\(20\) 2.22474 + 0.224745i 0.497468 + 0.0502545i
\(21\) 0 0
\(22\) 4.89898i 1.04447i
\(23\) −2.51059 1.44949i −0.523494 0.302240i 0.214869 0.976643i \(-0.431068\pi\)
−0.738363 + 0.674403i \(0.764401\pi\)
\(24\) −1.22474 2.12132i −0.250000 0.433013i
\(25\) −1.58346 4.74264i −0.316693 0.948528i
\(26\) −2.22474 + 3.85337i −0.436308 + 0.755708i
\(27\) 0 0
\(28\) 0 0
\(29\) −6.89898 −1.28111 −0.640554 0.767913i \(-0.721295\pi\)
−0.640554 + 0.767913i \(0.721295\pi\)
\(30\) −3.20150 + 4.44414i −0.584511 + 0.811386i
\(31\) 4.44949 + 7.70674i 0.799152 + 1.38417i 0.920169 + 0.391521i \(0.128051\pi\)
−0.121017 + 0.992650i \(0.538616\pi\)
\(32\) 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 0.635571 0.772043i \(-0.280765\pi\)
−0.350823 + 0.936442i \(0.614098\pi\)
\(38\) 1.34278 0.775255i 0.217828 0.125763i
\(39\) −5.44949 9.43879i −0.872617 1.51142i
\(40\) −1.81431 1.30701i −0.286868 0.206656i
\(41\) 1.10102 0.171951 0.0859753 0.996297i \(-0.472599\pi\)
0.0859753 + 0.996297i \(0.472599\pi\)
\(42\) 0 0
\(43\) 0.898979i 0.137093i −0.997648 0.0685465i \(-0.978164\pi\)
0.997648 0.0685465i \(-0.0218362\pi\)
\(44\) −2.44949 + 4.24264i −0.369274 + 0.639602i
\(45\) −2.75321 6.11717i −0.410425 0.911894i
\(46\) 1.44949 + 2.51059i 0.213716 + 0.370166i
\(47\) −7.70674 4.44949i −1.12414 0.649025i −0.181688 0.983356i \(-0.558156\pi\)
−0.942456 + 0.334331i \(0.891490\pi\)
\(48\) 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
\(52\) 3.85337 2.22474i 0.534366 0.308517i
\(53\) −9.43879 + 5.44949i −1.29652 + 0.748545i −0.979801 0.199975i \(-0.935914\pi\)
−0.316717 + 0.948520i \(0.602581\pi\)
\(54\) 0 0
\(55\) 10.8990 + 1.10102i 1.46962 + 0.148462i
\(56\) 0 0
\(57\) 3.79796i 0.503052i
\(58\) 5.97469 + 3.44949i 0.784515 + 0.452940i
\(59\) 0.775255 + 1.34278i 0.100930 + 0.174815i 0.912068 0.410039i \(-0.134485\pi\)
−0.811138 + 0.584854i \(0.801152\pi\)
\(60\) 4.99465 2.24799i 0.644807 0.290214i
\(61\) 1.77526 3.07483i 0.227298 0.393692i −0.729708 0.683759i \(-0.760344\pi\)
0.957006 + 0.290067i \(0.0936775\pi\)
\(62\) 8.89898i 1.13017i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −8.07277 5.81552i −1.00130 0.721326i
\(66\) −6.00000 10.3923i −0.738549 1.27920i
\(67\) 6.92820 4.00000i 0.846415 0.488678i −0.0130248 0.999915i \(-0.504146\pi\)
0.859440 + 0.511237i \(0.170813\pi\)
\(68\) 1.73205 + 1.00000i 0.210042 + 0.121268i
\(69\) −7.10102 −0.854862
\(70\) 0 0
\(71\) −1.10102 −0.130667 −0.0653335 0.997863i \(-0.520811\pi\)
−0.0653335 + 0.997863i \(0.520811\pi\)
\(72\) −2.59808 1.50000i −0.306186 0.176777i
\(73\) −2.51059 + 1.44949i −0.293842 + 0.169650i −0.639673 0.768647i \(-0.720930\pi\)
0.345831 + 0.938297i \(0.387597\pi\)
\(74\) −1.00000 1.73205i −0.116248 0.201347i
\(75\) −9.16756 8.12132i −1.05858 0.937769i
\(76\) −1.55051 −0.177856
\(77\) 0 0
\(78\) 10.8990i 1.23407i
\(79\) 3.44949 5.97469i 0.388098 0.672205i −0.604096 0.796912i \(-0.706466\pi\)
0.992194 + 0.124706i \(0.0397989\pi\)
\(80\) 0.917738 + 2.03906i 0.102606 + 0.227974i
\(81\) 4.50000 + 7.79423i 0.500000 + 0.866025i
\(82\) −0.953512 0.550510i −0.105298 0.0607937i
\(83\) 2.44949i 0.268866i 0.990923 + 0.134433i \(0.0429214\pi\)
−0.990923 + 0.134433i \(0.957079\pi\)
\(84\) 0 0
\(85\) 0.449490 4.44949i 0.0487540 0.482615i
\(86\) −0.449490 + 0.778539i −0.0484697 + 0.0839520i
\(87\) −14.6349 + 8.44949i −1.56903 + 0.905880i
\(88\) 4.24264 2.44949i 0.452267 0.261116i
\(89\) 5.00000 8.66025i 0.529999 0.917985i −0.469389 0.882992i \(-0.655526\pi\)
0.999388 0.0349934i \(-0.0111410\pi\)
\(90\) −0.674235 + 6.67423i −0.0710706 + 0.703526i
\(91\) 0 0
\(92\) 2.89898i 0.302240i
\(93\) 18.8776 + 10.8990i 1.95751 + 1.13017i
\(94\) 4.44949 + 7.70674i 0.458930 + 0.794890i
\(95\) 1.42296 + 3.16158i 0.145993 + 0.324371i
\(96\) 1.22474 2.12132i 0.125000 0.216506i
\(97\) 15.7980i 1.60404i 0.597297 + 0.802020i \(0.296241\pi\)
−0.597297 + 0.802020i \(0.703759\pi\)
\(98\) 0 0
\(99\) 14.6969 1.47710
\(100\) 3.31552 3.74264i 0.331552 0.374264i
\(101\) 1.77526 + 3.07483i 0.176644 + 0.305957i 0.940729 0.339159i \(-0.110142\pi\)
−0.764085 + 0.645116i \(0.776809\pi\)
\(102\) −4.24264 + 2.44949i −0.420084 + 0.242536i
\(103\) 11.1708 + 6.44949i 1.10070 + 0.635487i 0.936404 0.350925i \(-0.114133\pi\)
0.164292 + 0.986412i \(0.447466\pi\)
\(104\) −4.44949 −0.436308
\(105\) 0 0
\(106\) 10.8990 1.05860
\(107\) −6.92820 4.00000i −0.669775 0.386695i 0.126217 0.992003i \(-0.459717\pi\)
−0.795991 + 0.605308i \(0.793050\pi\)
\(108\) 0 0
\(109\) 3.44949 + 5.97469i 0.330401 + 0.572272i 0.982591 0.185784i \(-0.0594826\pi\)
−0.652189 + 0.758056i \(0.726149\pi\)
\(110\) −8.88828 6.40300i −0.847465 0.610502i
\(111\) 4.89898 0.464991
\(112\) 0 0
\(113\) 19.7980i 1.86244i 0.364464 + 0.931218i \(0.381252\pi\)
−0.364464 + 0.931218i \(0.618748\pi\)
\(114\) 1.89898 3.28913i 0.177856 0.308055i
\(115\) −5.91119 + 2.66050i −0.551221 + 0.248093i
\(116\) −3.44949 5.97469i −0.320277 0.554736i
\(117\) −11.5601 6.67423i −1.06873 0.617033i
\(118\) 1.55051i 0.142736i
\(119\) 0 0
\(120\) −5.44949 0.550510i −0.497468 0.0502545i
\(121\) −6.50000 + 11.2583i −0.590909 + 1.02348i
\(122\) −3.07483 + 1.77526i −0.278382 + 0.160724i
\(123\) 2.33562 1.34847i 0.210596 0.121587i
\(124\) −4.44949 + 7.70674i −0.399576 + 0.692086i
\(125\) −10.6742 3.32577i −0.954733 0.297465i
\(126\) 0 0
\(127\) 14.8990i 1.32207i 0.750355 + 0.661035i \(0.229883\pi\)
−0.750355 + 0.661035i \(0.770117\pi\)
\(128\) 0.866025 + 0.500000i 0.0765466 + 0.0441942i
\(129\) −1.10102 1.90702i −0.0969395 0.167904i
\(130\) 4.08346 + 9.07277i 0.358144 + 0.795734i
\(131\) −3.22474 + 5.58542i −0.281747 + 0.488001i −0.971815 0.235744i \(-0.924247\pi\)
0.690068 + 0.723745i \(0.257581\pi\)
\(132\) 12.0000i 1.04447i
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) 0 0
\(136\) −1.00000 1.73205i −0.0857493 0.148522i
\(137\) 1.55708 0.898979i 0.133030 0.0768050i −0.432008 0.901870i \(-0.642195\pi\)
0.565038 + 0.825065i \(0.308861\pi\)
\(138\) 6.14966 + 3.55051i 0.523494 + 0.302240i
\(139\) 1.55051 0.131513 0.0657563 0.997836i \(-0.479054\pi\)
0.0657563 + 0.997836i \(0.479054\pi\)
\(140\) 0 0
\(141\) −21.7980 −1.83572
\(142\) 0.953512 + 0.550510i 0.0800169 + 0.0461978i
\(143\) 18.8776 10.8990i 1.57862 0.911418i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) −9.01702 + 12.5169i −0.748822 + 1.03947i
\(146\) 2.89898 0.239921
\(147\) 0 0
\(148\) 2.00000i 0.164399i
\(149\) −1.89898 + 3.28913i −0.155570 + 0.269456i −0.933267 0.359184i \(-0.883055\pi\)
0.777696 + 0.628640i \(0.216388\pi\)
\(150\) 3.87868 + 11.6170i 0.316693 + 0.948528i
\(151\) −9.79796 16.9706i −0.797347 1.38104i −0.921338 0.388762i \(-0.872903\pi\)
0.123992 0.992283i \(-0.460430\pi\)
\(152\) 1.34278 + 0.775255i 0.108914 + 0.0628815i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) 19.7980 + 2.00000i 1.59021 + 0.160644i
\(156\) 5.44949 9.43879i 0.436308 0.755708i
\(157\) 3.07483 1.77526i 0.245398 0.141681i −0.372257 0.928130i \(-0.621416\pi\)
0.617655 + 0.786449i \(0.288083\pi\)
\(158\) −5.97469 + 3.44949i −0.475321 + 0.274427i
\(159\) −13.3485 + 23.1202i −1.05860 + 1.83355i
\(160\) 0.224745 2.22474i 0.0177676 0.175882i
\(161\) 0 0
\(162\) 9.00000i 0.707107i
\(163\) 6.14966 + 3.55051i 0.481679 + 0.278097i 0.721116 0.692814i \(-0.243630\pi\)
−0.239437 + 0.970912i \(0.576963\pi\)
\(164\) 0.550510 + 0.953512i 0.0429876 + 0.0744568i
\(165\) 24.4687 11.0129i 1.90489 0.857349i
\(166\) 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
\(169\) −6.79796 −0.522920
\(170\) −2.61401 + 3.62863i −0.200486 + 0.278303i
\(171\) 2.32577 + 4.02834i 0.177856 + 0.308055i
\(172\) 0.778539 0.449490i 0.0593630 0.0342733i
\(173\) −5.41045 3.12372i −0.411349 0.237492i 0.280020 0.959994i \(-0.409659\pi\)
−0.691369 + 0.722502i \(0.742992\pi\)
\(174\) 16.8990 1.28111
\(175\) 0 0
\(176\) −4.89898 −0.369274
\(177\) 3.28913 + 1.89898i 0.247226 + 0.142736i
\(178\) −8.66025 + 5.00000i −0.649113 + 0.374766i
\(179\) 6.89898 + 11.9494i 0.515654 + 0.893139i 0.999835 + 0.0181709i \(0.00578431\pi\)
−0.484181 + 0.874968i \(0.660882\pi\)
\(180\) 3.92102 5.44294i 0.292256 0.405693i
\(181\) 10.2474 0.761687 0.380843 0.924640i \(-0.375634\pi\)
0.380843 + 0.924640i \(0.375634\pi\)
\(182\) 0 0
\(183\) 8.69694i 0.642896i
\(184\) −1.44949 + 2.51059i −0.106858 + 0.185083i
\(185\) 4.07812 1.83548i 0.299829 0.134947i
\(186\) −10.8990 18.8776i −0.799152 1.38417i
\(187\) 8.48528 + 4.89898i 0.620505 + 0.358249i
\(188\) 8.89898i 0.649025i
\(189\) 0 0
\(190\) 0.348469 3.44949i 0.0252806 0.250252i
\(191\) −6.34847 + 10.9959i −0.459359 + 0.795633i −0.998927 0.0463087i \(-0.985254\pi\)
0.539568 + 0.841942i \(0.318588\pi\)
\(192\) −2.12132 + 1.22474i −0.153093 + 0.0883883i
\(193\) −18.7026 + 10.7980i −1.34624 + 0.777254i −0.987715 0.156265i \(-0.950055\pi\)
−0.358528 + 0.933519i \(0.616721\pi\)
\(194\) 7.89898 13.6814i 0.567114 0.982270i
\(195\) −24.2474 2.44949i −1.73640 0.175412i
\(196\) 0 0
\(197\) 18.8990i 1.34650i −0.739417 0.673248i \(-0.764899\pi\)
0.739417 0.673248i \(-0.235101\pi\)
\(198\) −12.7279 7.34847i −0.904534 0.522233i
\(199\) −8.44949 14.6349i −0.598968 1.03744i −0.992974 0.118336i \(-0.962244\pi\)
0.394005 0.919108i \(-0.371089\pi\)
\(200\) −4.74264 + 1.58346i −0.335355 + 0.111968i
\(201\) 9.79796 16.9706i 0.691095 1.19701i
\(202\) 3.55051i 0.249813i
\(203\) 0 0
\(204\) 4.89898 0.342997
\(205\) 1.43904 1.99760i 0.100507 0.139518i
\(206\) −6.44949 11.1708i −0.449357 0.778310i
\(207\) −7.53177 + 4.34847i −0.523494 + 0.302240i
\(208\) 3.85337 + 2.22474i 0.267183 + 0.154258i
\(209\) −7.59592 −0.525421
\(210\) 0 0
\(211\) 12.0000 0.826114 0.413057 0.910705i \(-0.364461\pi\)
0.413057 + 0.910705i \(0.364461\pi\)
\(212\) −9.43879 5.44949i −0.648259 0.374272i
\(213\) −2.33562 + 1.34847i −0.160034 + 0.0923956i
\(214\) 4.00000 + 6.92820i 0.273434 + 0.473602i
\(215\) −1.63103 1.17497i −0.111235 0.0801325i
\(216\) 0 0
\(217\) 0 0
\(218\) 6.89898i 0.467258i
\(219\) −3.55051 + 6.14966i −0.239921 + 0.415556i
\(220\) 4.49598 + 9.98930i 0.303119 + 0.673479i
\(221\) −4.44949 7.70674i −0.299305 0.518412i
\(222\) −4.24264 2.44949i −0.284747 0.164399i
\(223\) 4.00000i 0.267860i 0.990991 + 0.133930i \(0.0427597\pi\)
−0.990991 + 0.133930i \(0.957240\pi\)
\(224\) 0 0
\(225\) −14.6969 3.00000i −0.979796 0.200000i
\(226\) 9.89898 17.1455i 0.658470 1.14050i
\(227\) 6.36396 3.67423i 0.422391 0.243868i −0.273709 0.961813i \(-0.588250\pi\)
0.696100 + 0.717945i \(0.254917\pi\)
\(228\) −3.28913 + 1.89898i −0.217828 + 0.125763i
\(229\) 9.57321 16.5813i 0.632616 1.09572i −0.354399 0.935094i \(-0.615315\pi\)
0.987015 0.160628i \(-0.0513521\pi\)
\(230\) 6.44949 + 0.651531i 0.425267 + 0.0429607i
\(231\) 0 0
\(232\) 6.89898i 0.452940i
\(233\) −25.8058 14.8990i −1.69059 0.976065i −0.954037 0.299688i \(-0.903117\pi\)
−0.736556 0.676376i \(-0.763549\pi\)
\(234\) 6.67423 + 11.5601i 0.436308 + 0.755708i
\(235\) −18.1455 + 8.16693i −1.18368 + 0.532752i
\(236\) −0.775255 + 1.34278i −0.0504648 + 0.0874076i
\(237\) 16.8990i 1.09771i
\(238\) 0 0
\(239\) 6.20204 0.401177 0.200588 0.979676i \(-0.435715\pi\)
0.200588 + 0.979676i \(0.435715\pi\)
\(240\) 4.44414 + 3.20150i 0.286868 + 0.206656i
\(241\) −4.34847 7.53177i −0.280110 0.485164i 0.691302 0.722566i \(-0.257037\pi\)
−0.971411 + 0.237402i \(0.923704\pi\)
\(242\) 11.2583 6.50000i 0.723713 0.417836i
\(243\) 19.0919 + 11.0227i 1.22474 + 0.707107i
\(244\) 3.55051 0.227298
\(245\) 0 0
\(246\) −2.69694 −0.171951
\(247\) 5.97469 + 3.44949i 0.380161 + 0.219486i
\(248\) 7.70674 4.44949i 0.489379 0.282543i
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 7.58128 + 8.21731i 0.479482 + 0.519709i
\(251\) 6.44949 0.407088 0.203544 0.979066i \(-0.434754\pi\)
0.203544 + 0.979066i \(0.434754\pi\)
\(252\) 0 0
\(253\) 14.2020i 0.892875i
\(254\) 7.44949 12.9029i 0.467423 0.809600i
\(255\) −4.49598 9.98930i −0.281549 0.625554i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 7.53177 + 4.34847i 0.469819 + 0.271250i 0.716164 0.697932i \(-0.245896\pi\)
−0.246345 + 0.969182i \(0.579230\pi\)
\(258\) 2.20204i 0.137093i
\(259\) 0 0
\(260\) 1.00000 9.89898i 0.0620174 0.613909i
\(261\) −10.3485 + 17.9241i −0.640554 + 1.10947i
\(262\) 5.58542 3.22474i 0.345069 0.199225i
\(263\) 8.48528 4.89898i 0.523225 0.302084i −0.215028 0.976608i \(-0.568984\pi\)
0.738253 + 0.674524i \(0.235651\pi\)
\(264\) 6.00000 10.3923i 0.369274 0.639602i
\(265\) −2.44949 + 24.2474i −0.150471 + 1.48951i
\(266\) 0 0
\(267\) 24.4949i 1.49906i
\(268\) 6.92820 + 4.00000i 0.423207 + 0.244339i
\(269\) −9.57321 16.5813i −0.583689 1.01098i −0.995037 0.0995010i \(-0.968275\pi\)
0.411348 0.911478i \(-0.365058\pi\)
\(270\) 0 0
\(271\) 6.00000 10.3923i 0.364474 0.631288i −0.624218 0.781251i \(-0.714582\pi\)
0.988692 + 0.149963i \(0.0479155\pi\)
\(272\) 2.00000i 0.121268i
\(273\) 0 0
\(274\) −1.79796 −0.108619
\(275\) 16.2426 18.3351i 0.979468 1.10565i
\(276\) −3.55051 6.14966i −0.213716 0.370166i
\(277\) 12.9029 7.44949i 0.775260 0.447596i −0.0594879 0.998229i \(-0.518947\pi\)
0.834748 + 0.550633i \(0.185613\pi\)
\(278\) −1.34278 0.775255i −0.0805347 0.0464967i
\(279\) 26.6969 1.59830
\(280\) 0 0
\(281\) −18.0000 −1.07379 −0.536895 0.843649i \(-0.680403\pi\)
−0.536895 + 0.843649i \(0.680403\pi\)
\(282\) 18.8776 + 10.8990i 1.12414 + 0.649025i
\(283\) −3.24980 + 1.87628i −0.193181 + 0.111533i −0.593471 0.804856i \(-0.702243\pi\)
0.400290 + 0.916389i \(0.368909\pi\)
\(284\) −0.550510 0.953512i −0.0326668 0.0565805i
\(285\) 6.89069 + 4.96396i 0.408169 + 0.294040i
\(286\) −21.7980 −1.28894
\(287\) 0 0
\(288\) 3.00000i 0.176777i
\(289\) −6.50000 + 11.2583i −0.382353 + 0.662255i
\(290\) 14.0674 6.33145i 0.826067 0.371796i
\(291\) 19.3485 + 33.5125i 1.13423 + 1.96454i
\(292\) −2.51059 1.44949i −0.146921 0.0848250i
\(293\) 18.2474i 1.06603i −0.846107 0.533014i \(-0.821059\pi\)
0.846107 0.533014i \(-0.178941\pi\)
\(294\) 0 0
\(295\) 3.44949 + 0.348469i 0.200837 + 0.0202887i
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 0 0
\(298\) 3.28913 1.89898i 0.190534 0.110005i
\(299\) −6.44949 + 11.1708i −0.372984 + 0.646027i
\(300\) 2.44949 12.0000i 0.141421 0.692820i
\(301\) 0 0
\(302\) 19.5959i 1.12762i
\(303\) 7.53177 + 4.34847i 0.432689 + 0.249813i
\(304\) −0.775255 1.34278i −0.0444639 0.0770138i
\(305\) −3.25844 7.23970i −0.186578 0.414544i
\(306\) −3.00000 + 5.19615i −0.171499 + 0.297044i
\(307\) 20.2474i 1.15558i −0.816184 0.577791i \(-0.803915\pi\)
0.816184 0.577791i \(-0.196085\pi\)
\(308\) 0 0
\(309\) 31.5959 1.79743
\(310\) −16.1455 11.6310i −0.917005 0.660598i
\(311\) 6.00000 + 10.3923i 0.340229 + 0.589294i 0.984475 0.175525i \(-0.0561621\pi\)
−0.644246 + 0.764818i \(0.722829\pi\)
\(312\) −9.43879 + 5.44949i −0.534366 + 0.308517i
\(313\) −18.7026 10.7980i −1.05713 0.610337i −0.132496 0.991184i \(-0.542299\pi\)
−0.924638 + 0.380847i \(0.875633\pi\)
\(314\) −3.55051 −0.200367
\(315\) 0 0
\(316\) 6.89898 0.388098
\(317\) −19.4812 11.2474i −1.09417 0.631720i −0.159487 0.987200i \(-0.550984\pi\)
−0.934684 + 0.355480i \(0.884317\pi\)
\(318\) 23.1202 13.3485i 1.29652 0.748545i
\(319\) −16.8990 29.2699i −0.946161 1.63880i
\(320\) −1.30701 + 1.81431i −0.0730639 + 0.101423i
\(321\) −19.5959 −1.09374
\(322\) 0 0
\(323\) 3.10102i 0.172545i
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) −21.1023 + 7.04561i −1.17055 + 0.390820i
\(326\) −3.55051 6.14966i −0.196645 0.340598i
\(327\) 14.6349 + 8.44949i 0.809314 + 0.467258i
\(328\) 1.10102i 0.0607937i
\(329\) 0 0
\(330\) −26.6969 2.69694i −1.46962 0.148462i
\(331\) 9.34847 16.1920i 0.513838 0.889994i −0.486033 0.873941i \(-0.661556\pi\)
0.999871 0.0160535i \(-0.00511022\pi\)
\(332\) −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
\(335\) 1.79796 17.7980i 0.0982330 0.972406i
\(336\) 0 0
\(337\) 9.59592i 0.522723i −0.965241 0.261361i \(-0.915829\pi\)
0.965241 0.261361i \(-0.0841715\pi\)
\(338\) 5.88721 + 3.39898i 0.320222 + 0.184880i
\(339\) 24.2474 + 41.9978i 1.31694 + 2.28101i
\(340\) 4.07812 1.83548i 0.221167 0.0995426i
\(341\) −21.7980 + 37.7552i −1.18043 + 2.04456i
\(342\) 4.65153i 0.251526i
\(343\) 0 0
\(344\) −0.898979 −0.0484697
\(345\) −9.28108 + 12.8835i −0.499677 + 0.693623i
\(346\) 3.12372 + 5.41045i 0.167932 + 0.290868i
\(347\) −25.0273 + 14.4495i −1.34353 + 0.775689i −0.987324 0.158717i \(-0.949264\pi\)
−0.356209 + 0.934406i \(0.615931\pi\)
\(348\) −14.6349 8.44949i −0.784515 0.452940i
\(349\) −8.44949 −0.452291 −0.226145 0.974094i \(-0.572612\pi\)
−0.226145 + 0.974094i \(0.572612\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 4.24264 + 2.44949i 0.226134 + 0.130558i
\(353\) −19.8311 + 11.4495i −1.05550 + 0.609395i −0.924185 0.381945i \(-0.875254\pi\)
−0.131318 + 0.991340i \(0.541921\pi\)
\(354\) −1.89898 3.28913i −0.100930 0.174815i
\(355\) −1.43904 + 1.99760i −0.0763764 + 0.106021i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 13.7980i 0.729245i
\(359\) −13.7980 + 23.8988i −0.728228 + 1.26133i 0.229403 + 0.973332i \(0.426323\pi\)
−0.957631 + 0.287997i \(0.907011\pi\)
\(360\) −6.11717 + 2.75321i −0.322403 + 0.145107i
\(361\) 8.29796 + 14.3725i 0.436735 + 0.756447i
\(362\) −8.87455 5.12372i −0.466436 0.269297i
\(363\) 31.8434i 1.67134i
\(364\) 0 0
\(365\) −0.651531 + 6.44949i −0.0341027 + 0.337582i
\(366\) −4.34847 + 7.53177i −0.227298 + 0.393692i
\(367\) 27.7128 16.0000i 1.44660 0.835193i 0.448320 0.893873i \(-0.352022\pi\)
0.998277 + 0.0586798i \(0.0186891\pi\)
\(368\) 2.51059 1.44949i 0.130874 0.0755599i
\(369\) 1.65153 2.86054i 0.0859753 0.148914i
\(370\) −4.44949 0.449490i −0.231318 0.0233679i
\(371\) 0 0
\(372\) 21.7980i 1.13017i
\(373\) 4.06767 + 2.34847i 0.210616 + 0.121599i 0.601598 0.798799i \(-0.294531\pi\)
−0.390982 + 0.920398i \(0.627864\pi\)
\(374\) −4.89898 8.48528i −0.253320 0.438763i
\(375\) −26.7167 + 6.01820i −1.37964 + 0.310779i
\(376\) −4.44949 + 7.70674i −0.229465 + 0.397445i
\(377\) 30.6969i 1.58097i
\(378\) 0 0
\(379\) −30.6969 −1.57680 −0.788398 0.615166i \(-0.789089\pi\)
−0.788398 + 0.615166i \(0.789089\pi\)
\(380\) −2.02653 + 2.81311i −0.103959 + 0.144310i
\(381\) 18.2474 + 31.6055i 0.934845 + 1.61920i
\(382\) 10.9959 6.34847i 0.562598 0.324816i
\(383\) −6.14966 3.55051i −0.314233 0.181423i 0.334586 0.942365i \(-0.391404\pi\)
−0.648819 + 0.760943i \(0.724737\pi\)
\(384\) 2.44949 0.125000
\(385\) 0 0
\(386\) 21.5959 1.09920
\(387\) −2.33562 1.34847i −0.118726 0.0685465i
\(388\) −13.6814 + 7.89898i −0.694570 + 0.401010i
\(389\) 6.55051 + 11.3458i 0.332124 + 0.575256i 0.982928 0.183990i \(-0.0589014\pi\)
−0.650804 + 0.759246i \(0.725568\pi\)
\(390\) 19.7742 + 14.2450i 1.00130 + 0.721326i
\(391\) −5.79796 −0.293215
\(392\) 0 0
\(393\) 15.7980i 0.796902i
\(394\) −9.44949 + 16.3670i −0.476058 + 0.824557i
\(395\) −6.33145 14.0674i −0.318570 0.707809i
\(396\) 7.34847 + 12.7279i 0.369274 + 0.639602i
\(397\) 2.29629 + 1.32577i 0.115248 + 0.0665383i 0.556516 0.830837i \(-0.312138\pi\)
−0.441268 + 0.897375i \(0.645471\pi\)
\(398\) 16.8990i 0.847069i
\(399\) 0 0
\(400\) 4.89898 + 1.00000i 0.244949 + 0.0500000i
\(401\) 14.6969 25.4558i 0.733930 1.27120i −0.221261 0.975215i \(-0.571017\pi\)
0.955191 0.295990i \(-0.0956494\pi\)
\(402\) −16.9706 + 9.79796i −0.846415 + 0.488678i
\(403\) 34.2911 19.7980i 1.70816 0.986207i
\(404\) −1.77526 + 3.07483i −0.0883222 + 0.152979i
\(405\) 20.0227 + 2.02270i 0.994936 + 0.100509i
\(406\) 0 0
\(407\) 9.79796i 0.485667i
\(408\) −4.24264 2.44949i −0.210042 0.121268i
\(409\) −17.2474 29.8735i −0.852831 1.47715i −0.878642 0.477481i \(-0.841550\pi\)
0.0258109 0.999667i \(-0.491783\pi\)
\(410\) −2.24504 + 1.01045i −0.110875 + 0.0499025i
\(411\) 2.20204 3.81405i 0.108619 0.188133i
\(412\) 12.8990i 0.635487i
\(413\) 0 0
\(414\) 8.69694 0.427431
\(415\) 4.44414 + 3.20150i 0.218154 + 0.157155i
\(416\) −2.22474 3.85337i −0.109077 0.188927i
\(417\) 3.28913 1.89898i 0.161069 0.0929934i
\(418\) 6.57826 + 3.79796i 0.321753 + 0.185764i
\(419\) −1.55051 −0.0757474 −0.0378737 0.999283i \(-0.512058\pi\)
−0.0378737 + 0.999283i \(0.512058\pi\)
\(420\) 0 0
\(421\) −4.20204 −0.204795 −0.102397 0.994744i \(-0.532651\pi\)
−0.102397 + 0.994744i \(0.532651\pi\)
\(422\) −10.3923 6.00000i −0.505889 0.292075i
\(423\) −23.1202 + 13.3485i −1.12414 + 0.649025i
\(424\) 5.44949 + 9.43879i 0.264651 + 0.458388i
\(425\) −7.48528 6.63103i −0.363089 0.321652i
\(426\) 2.69694 0.130667
\(427\) 0 0
\(428\) 8.00000i 0.386695i
\(429\) 26.6969 46.2405i 1.28894 2.23251i
\(430\) 0.825027 + 1.83307i 0.0397864 + 0.0883985i
\(431\) 0.898979 + 1.55708i 0.0433023 + 0.0750018i 0.886864 0.462030i \(-0.152879\pi\)
−0.843562 + 0.537032i \(0.819545\pi\)
\(432\) 0 0
\(433\) 0.202041i 0.00970947i 0.999988 + 0.00485474i \(0.00154532\pi\)
−0.999988 + 0.00485474i \(0.998455\pi\)
\(434\) 0 0
\(435\) −3.79796 + 37.5959i −0.182098 + 1.80259i
\(436\) −3.44949 + 5.97469i −0.165201 + 0.286136i
\(437\) 3.89270 2.24745i 0.186213 0.107510i
\(438\) 6.14966 3.55051i 0.293842 0.169650i
\(439\) 10.6969 18.5276i 0.510537 0.884276i −0.489388 0.872066i \(-0.662780\pi\)
0.999925 0.0122101i \(-0.00388670\pi\)
\(440\) 1.10102 10.8990i 0.0524891 0.519588i
\(441\) 0 0
\(442\) 8.89898i 0.423281i
\(443\) −8.48528 4.89898i −0.403148 0.232758i 0.284693 0.958619i \(-0.408108\pi\)
−0.687841 + 0.725861i \(0.741442\pi\)
\(444\) 2.44949 + 4.24264i 0.116248 + 0.201347i
\(445\) −9.17738 20.3906i −0.435049 0.966606i
\(446\) 2.00000 3.46410i 0.0947027 0.164030i
\(447\) 9.30306i 0.440020i
\(448\) 0 0
\(449\) 10.0000 0.471929 0.235965 0.971762i \(-0.424175\pi\)
0.235965 + 0.971762i \(0.424175\pi\)
\(450\) 11.2279 + 9.94655i 0.529289 + 0.468885i
\(451\) 2.69694 + 4.67123i 0.126994 + 0.219960i
\(452\) −17.1455 + 9.89898i −0.806458 + 0.465609i
\(453\) −41.5692 24.0000i −1.95309 1.12762i
\(454\) −7.34847 −0.344881
\(455\) 0 0
\(456\) 3.79796 0.177856
\(457\) 25.6308 + 14.7980i 1.19896 + 0.692219i 0.960323 0.278890i \(-0.0899664\pi\)
0.238636 + 0.971109i \(0.423300\pi\)
\(458\) −16.5813 + 9.57321i −0.774793 + 0.447327i
\(459\) 0 0
\(460\) −5.25966 3.78899i −0.245233 0.176662i
\(461\) −17.3485 −0.807999 −0.403999 0.914759i \(-0.632380\pi\)
−0.403999 + 0.914759i \(0.632380\pi\)
\(462\) 0 0
\(463\) 3.59592i 0.167116i 0.996503 + 0.0835582i \(0.0266285\pi\)
−0.996503 + 0.0835582i \(0.973372\pi\)
\(464\) 3.44949 5.97469i 0.160139 0.277368i
\(465\) 44.4473 20.0048i 2.06119 0.927701i
\(466\) 14.8990 + 25.8058i 0.690182 + 1.19543i
\(467\) −9.04952 5.22474i −0.418762 0.241772i 0.275785 0.961219i \(-0.411062\pi\)
−0.694548 + 0.719447i \(0.744395\pi\)
\(468\) 13.3485i 0.617033i
\(469\) 0 0
\(470\) 19.7980 + 2.00000i 0.913212 + 0.0922531i
\(471\) 4.34847 7.53177i 0.200367 0.347046i
\(472\) 1.34278 0.775255i 0.0618065 0.0356840i
\(473\) 3.81405 2.20204i 0.175370 0.101250i
\(474\) −8.44949 + 14.6349i −0.388098 + 0.672205i
\(475\) 7.59592 + 1.55051i 0.348525 + 0.0711423i
\(476\) 0 0
\(477\) 32.6969i 1.49709i
\(478\) −5.37113 3.10102i −0.245670 0.141837i
\(479\) −4.65153 8.05669i −0.212534 0.368119i 0.739973 0.672637i \(-0.234838\pi\)
−0.952507 + 0.304517i \(0.901505\pi\)
\(480\) −2.24799 4.99465i −0.102606 0.227974i
\(481\) 4.44949 7.70674i 0.202879 0.351397i
\(482\) 8.69694i 0.396135i
\(483\) 0 0
\(484\) −13.0000 −0.590909
\(485\) 28.6624 + 20.6480i 1.30149 + 0.937579i
\(486\) −11.0227 19.0919i −0.500000 0.866025i
\(487\) 6.32464 3.65153i 0.286597 0.165467i −0.349809 0.936821i \(-0.613754\pi\)
0.636406 + 0.771354i \(0.280420\pi\)
\(488\) −3.07483 1.77526i −0.139191 0.0803620i
\(489\) 17.3939 0.786578
\(490\) 0 0
\(491\) 19.5959 0.884351 0.442176 0.896928i \(-0.354207\pi\)
0.442176 + 0.896928i \(0.354207\pi\)
\(492\) 2.33562 + 1.34847i 0.105298 + 0.0607937i
\(493\) −11.9494 + 6.89898i −0.538173 + 0.310714i
\(494\) −3.44949 5.97469i −0.155200 0.268814i
\(495\) 19.2090 26.6648i 0.863381 1.19850i
\(496\) −8.89898 −0.399576
\(497\) 0 0
\(498\) 6.00000i 0.268866i
\(499\) 3.10102 5.37113i 0.138821 0.240445i −0.788230 0.615381i \(-0.789002\pi\)
0.927051 + 0.374936i \(0.122335\pi\)
\(500\) −2.45692 10.9070i −0.109877 0.487778i
\(501\) −6.00000 10.3923i −0.268060 0.464294i
\(502\) −5.58542 3.22474i −0.249290 0.143927i
\(503\) 4.00000i 0.178351i 0.996016 + 0.0891756i \(0.0284232\pi\)
−0.996016 + 0.0891756i \(0.971577\pi\)
\(504\) 0 0
\(505\) 7.89898 + 0.797959i 0.351500 + 0.0355087i
\(506\) −7.10102 + 12.2993i −0.315679 + 0.546772i
\(507\) −14.4206 + 8.32577i −0.640443 + 0.369760i
\(508\) −12.9029 + 7.44949i −0.572473 + 0.330518i
\(509\) 15.7753 27.3235i 0.699226 1.21109i −0.269509 0.962998i \(-0.586861\pi\)
0.968735 0.248097i \(-0.0798052\pi\)
\(510\) −1.10102 + 10.8990i −0.0487540 + 0.482615i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) −4.34847 7.53177i −0.191803 0.332212i
\(515\) 26.3018 11.8379i 1.15899 0.521639i
\(516\) 1.10102 1.90702i 0.0484697 0.0839520i
\(517\) 43.5959i 1.91735i
\(518\) 0 0
\(519\) −15.3031 −0.671730
\(520\) −5.81552 + 8.07277i −0.255027 + 0.354014i
\(521\) 16.3485 + 28.3164i 0.716239 + 1.24056i 0.962480 + 0.271354i \(0.0874715\pi\)
−0.246240 + 0.969209i \(0.579195\pi\)
\(522\) 17.9241 10.3485i 0.784515 0.452940i
\(523\) −28.7056 16.5732i −1.25521 0.724696i −0.283071 0.959099i \(-0.591353\pi\)
−0.972140 + 0.234403i \(0.924686\pi\)
\(524\) −6.44949 −0.281747
\(525\) 0 0
\(526\) −9.79796 −0.427211
\(527\) 15.4135 + 8.89898i 0.671422 + 0.387646i
\(528\) −10.3923 + 6.00000i −0.452267 + 0.261116i
\(529\) −7.29796 12.6404i −0.317303 0.549584i
\(530\) 14.2450 19.7742i 0.618765 0.858935i
\(531\) 4.65153 0.201859
\(532\) 0 0
\(533\) 4.89898i 0.212198i
\(534\) −12.2474 + 21.2132i −0.529999 + 0.917985i
\(535\) −16.3125 + 7.34190i −0.705249 + 0.317418i
\(536\) −4.00000 6.92820i −0.172774 0.299253i
\(537\) 29.2699 + 16.8990i 1.26309 + 0.729245i
\(538\) 19.1464i 0.825461i
\(539\) 0 0
\(540\) 0 0
\(541\) −4.79796 + 8.31031i −0.206280 + 0.357288i −0.950540 0.310602i \(-0.899469\pi\)
0.744260 + 0.667891i \(0.232803\pi\)
\(542\) −10.3923 + 6.00000i −0.446388 + 0.257722i
\(543\) 21.7381 12.5505i 0.932872 0.538594i
\(544\) 1.00000 1.73205i 0.0428746 0.0742611i
\(545\) 15.3485 + 1.55051i 0.657456 + 0.0664166i
\(546\) 0 0
\(547\) 18.6969i 0.799423i 0.916641 + 0.399712i \(0.130890\pi\)
−0.916641 + 0.399712i \(0.869110\pi\)
\(548\) 1.55708 + 0.898979i 0.0665151 + 0.0384025i
\(549\) −5.32577 9.22450i −0.227298 0.393692i
\(550\) −23.2341 + 7.75736i −0.990705 + 0.330775i
\(551\) 5.34847 9.26382i 0.227852 0.394652i
\(552\) 7.10102i 0.302240i
\(553\) 0 0
\(554\) −14.8990 −0.632997
\(555\) 6.40300 8.88828i 0.271792 0.377287i
\(556\) 0.775255 + 1.34278i 0.0328781 + 0.0569466i
\(557\) −10.9959 + 6.34847i −0.465910 + 0.268993i −0.714526 0.699609i \(-0.753358\pi\)
0.248616 + 0.968602i \(0.420024\pi\)
\(558\) −23.1202 13.3485i −0.978757 0.565086i
\(559\) −4.00000 −0.169182
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) 15.5885 + 9.00000i 0.657559 + 0.379642i
\(563\) 26.0201 15.0227i 1.09662 0.633131i 0.161286 0.986908i \(-0.448436\pi\)
0.935330 + 0.353776i \(0.115103\pi\)
\(564\) −10.8990 18.8776i −0.458930 0.794890i
\(565\) 35.9197 + 25.8761i 1.51115 + 1.08861i
\(566\) 3.75255 0.157731
\(567\) 0 0
\(568\) 1.10102i 0.0461978i
\(569\) 16.8990 29.2699i 0.708442 1.22706i −0.256993 0.966413i \(-0.582732\pi\)
0.965435 0.260644i \(-0.0839350\pi\)
\(570\) −3.48553 7.74426i −0.145993 0.324371i
\(571\) 5.55051 + 9.61377i 0.232282 + 0.402324i 0.958479 0.285162i \(-0.0920476\pi\)
−0.726198 + 0.687486i \(0.758714\pi\)
\(572\) 18.8776 + 10.8990i 0.789312 + 0.455709i
\(573\) 31.1010i 1.29926i
\(574\) 0 0
\(575\) −2.89898 + 14.2020i −0.120896 + 0.592266i
\(576\) −1.50000 + 2.59808i −0.0625000 + 0.108253i
\(577\) −2.16064 + 1.24745i −0.0899488 + 0.0519320i −0.544300 0.838891i \(-0.683205\pi\)
0.454351 + 0.890823i \(0.349871\pi\)
\(578\) 11.2583 6.50000i 0.468285 0.270364i
\(579\) −26.4495 + 45.8119i −1.09920 + 1.90388i
\(580\) −15.3485 1.55051i −0.637310 0.0643814i
\(581\) 0 0
\(582\) 38.6969i 1.60404i
\(583\) −46.2405 26.6969i −1.91508 1.10567i
\(584\) 1.44949 + 2.51059i 0.0599803 + 0.103889i
\(585\) −27.2183 + 12.2504i −1.12534 + 0.506491i
\(586\) −9.12372 + 15.8028i −0.376898 + 0.652806i
\(587\) 1.14643i 0.0473182i 0.999720 + 0.0236591i \(0.00753162\pi\)
−0.999720 + 0.0236591i \(0.992468\pi\)
\(588\) 0 0
\(589\) −13.7980 −0.568535
\(590\) −2.81311 2.02653i −0.115814 0.0834308i
\(591\) −23.1464 40.0908i −0.952117 1.64911i
\(592\) −1.73205 + 1.00000i −0.0711868 + 0.0410997i
\(593\) −9.43879 5.44949i −0.387605 0.223784i 0.293517 0.955954i \(-0.405174\pi\)
−0.681122 + 0.732170i \(0.738508\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −3.79796 −0.155570
\(597\) −35.8481 20.6969i −1.46717 0.847069i
\(598\) 11.1708 6.44949i 0.456810 0.263739i
\(599\) −6.55051 11.3458i −0.267647 0.463577i 0.700607 0.713547i \(-0.252913\pi\)
−0.968254 + 0.249970i \(0.919579\pi\)
\(600\) −8.12132 + 9.16756i −0.331552 + 0.374264i
\(601\) 39.3939 1.60691 0.803455 0.595366i \(-0.202993\pi\)
0.803455 + 0.595366i \(0.202993\pi\)
\(602\) 0 0
\(603\) 24.0000i 0.977356i
\(604\) 9.79796 16.9706i 0.398673 0.690522i
\(605\) 11.9306 + 26.5078i 0.485047 + 1.07769i
\(606\) −4.34847 7.53177i −0.176644 0.305957i
\(607\) −28.9199 16.6969i −1.17382 0.677708i −0.219247 0.975669i \(-0.570360\pi\)
−0.954578 + 0.297962i \(0.903693\pi\)
\(608\) 1.55051i 0.0628815i
\(609\) 0 0
\(610\) −0.797959 + 7.89898i −0.0323084 + 0.319820i
\(611\) −19.7980 + 34.2911i −0.800940 + 1.38727i
\(612\) 5.19615 3.00000i 0.210042 0.121268i
\(613\) −24.0737 + 13.8990i −0.972329 + 0.561374i −0.899946 0.436002i \(-0.856394\pi\)
−0.0723836 + 0.997377i \(0.523061\pi\)
\(614\) −10.1237 + 17.5348i −0.408560 + 0.707647i
\(615\) 0.606123 6.00000i 0.0244412 0.241943i
\(616\) 0 0
\(617\) 29.5959i 1.19149i −0.803175 0.595743i \(-0.796858\pi\)
0.803175 0.595743i \(-0.203142\pi\)
\(618\) −27.3629 15.7980i −1.10070 0.635487i
\(619\) 20.7753 + 35.9838i 0.835028 + 1.44631i 0.894008 + 0.448052i \(0.147882\pi\)
−0.0589796 + 0.998259i \(0.518785\pi\)
\(620\) 8.16693 + 18.1455i 0.327992 + 0.728742i
\(621\) 0 0
\(622\) 12.0000i 0.481156i
\(623\) 0 0
\(624\) 10.8990 0.436308
\(625\) −19.9853 + 15.0196i −0.799411 + 0.600784i
\(626\) 10.7980 + 18.7026i 0.431573 + 0.747507i
\(627\) −16.1134 + 9.30306i −0.643506 + 0.371528i
\(628\) 3.07483 + 1.77526i 0.122699 + 0.0708404i
\(629\) 4.00000 0.159490
\(630\) 0 0
\(631\) −42.4949 −1.69170 −0.845848 0.533425i \(-0.820905\pi\)
−0.845848 + 0.533425i \(0.820905\pi\)
\(632\) −5.97469 3.44949i −0.237660 0.137213i
\(633\) 25.4558 14.6969i 1.01178 0.584151i
\(634\) 11.2474 + 19.4812i 0.446693 + 0.773695i
\(635\) 27.0314 + 19.4731i 1.07271 + 0.772765i
\(636\) −26.6969 −1.05860
\(637\) 0 0
\(638\) 33.7980i 1.33807i
\(639\) −1.65153 + 2.86054i −0.0653335 + 0.113161i
\(640\) 2.03906 0.917738i 0.0806008 0.0362768i
\(641\) −12.8990 22.3417i −0.509479 0.882444i −0.999940 0.0109803i \(-0.996505\pi\)
0.490461 0.871463i \(-0.336829\pi\)
\(642\) 16.9706 + 9.79796i 0.669775 + 0.386695i
\(643\) 25.1464i 0.991678i −0.868414 0.495839i \(-0.834861\pi\)
0.868414 0.495839i \(-0.165139\pi\)
\(644\) 0 0
\(645\) −4.89898 0.494897i −0.192897 0.0194866i
\(646\) 1.55051 2.68556i 0.0610040 0.105662i
\(647\) −40.0908 + 23.1464i −1.57613 + 0.909980i −0.580740 + 0.814089i \(0.697237\pi\)
−0.995392 + 0.0958907i \(0.969430\pi\)
\(648\) 7.79423 4.50000i 0.306186 0.176777i
\(649\) −3.79796 + 6.57826i −0.149083 + 0.258219i
\(650\) 21.7980 + 4.44949i 0.854986 + 0.174523i
\(651\) 0 0
\(652\) 7.10102i 0.278097i
\(653\) 17.4955 + 10.1010i 0.684651 + 0.395283i 0.801605 0.597854i \(-0.203980\pi\)
−0.116954 + 0.993137i \(0.537313\pi\)
\(654\) −8.44949 14.6349i −0.330401 0.572272i
\(655\) 5.91894 + 13.1509i 0.231272 + 0.513848i
\(656\) −0.550510 + 0.953512i −0.0214938 + 0.0372284i
\(657\) 8.69694i 0.339300i
\(658\) 0 0
\(659\) −16.8990 −0.658291 −0.329145 0.944279i \(-0.606761\pi\)
−0.329145 + 0.944279i \(0.606761\pi\)
\(660\) 21.7718 + 15.6841i 0.847465 + 0.610502i
\(661\) −20.4722 35.4589i −0.796276 1.37919i −0.922026 0.387129i \(-0.873467\pi\)
0.125750 0.992062i \(-0.459866\pi\)
\(662\) −16.1920 + 9.34847i −0.629321 + 0.363339i
\(663\) −18.8776 10.8990i −0.733145 0.423281i
\(664\) 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
\(670\) −10.4561 + 14.5145i −0.403953 + 0.560744i
\(671\) 17.3939 0.671483
\(672\) 0 0
\(673\) 17.7980i 0.686061i −0.939324 0.343030i \(-0.888547\pi\)
0.939324 0.343030i \(-0.111453\pi\)
\(674\) −4.79796 + 8.31031i −0.184810 + 0.320101i
\(675\) 0 0
\(676\) −3.39898 5.88721i −0.130730 0.226431i
\(677\) 31.5662 + 18.2247i 1.21319 + 0.700434i 0.963452 0.267880i \(-0.0863232\pi\)
0.249735 + 0.968314i \(0.419657\pi\)
\(678\) 48.4949i 1.86244i
\(679\) 0 0
\(680\) −4.44949 0.449490i −0.170630 0.0172371i
\(681\) 9.00000 15.5885i 0.344881 0.597351i
\(682\) 37.7552 21.7980i 1.44572 0.834687i
\(683\) 3.11416 1.79796i 0.119160 0.0687970i −0.439235 0.898372i \(-0.644751\pi\)
0.558395 + 0.829575i \(0.311417\pi\)
\(684\) −2.32577 + 4.02834i −0.0889279 + 0.154028i
\(685\) 0.404082 4.00000i 0.0154392 0.152832i
\(686\) 0 0
\(687\) 46.8990i 1.78931i
\(688\) 0.778539 + 0.449490i 0.0296815 + 0.0171366i
\(689\) 24.2474 + 41.9978i 0.923754 + 1.59999i
\(690\) 14.4794 6.51687i 0.551221 0.248093i
\(691\) 10.5732 18.3133i 0.402224 0.696672i −0.591770 0.806107i \(-0.701571\pi\)
0.993994 + 0.109434i \(0.0349040\pi\)
\(692\) 6.24745i 0.237492i
\(693\) 0 0
\(694\) 28.8990 1.09699
\(695\) 2.02653 2.81311i 0.0768706 0.106707i
\(696\) 8.44949 + 14.6349i 0.320277 + 0.554736i
\(697\) 1.90702 1.10102i 0.0722337 0.0417041i
\(698\) 7.31747 + 4.22474i 0.276970 + 0.159909i
\(699\) −72.9898 −2.76073
\(700\) 0 0
\(701\) 11.3031 0.426911 0.213455 0.976953i \(-0.431528\pi\)
0.213455 + 0.976953i \(0.431528\pi\)
\(702\) 0 0
\(703\) −2.68556 + 1.55051i −0.101288 + 0.0584786i
\(704\) −2.44949 4.24264i −0.0923186 0.159901i
\(705\) −28.4901 + 39.5483i −1.07300 + 1.48948i
\(706\) 22.8990 0.861814
\(707\) 0 0
\(708\) 3.79796i 0.142736i
\(709\) −14.1464 + 24.5023i −0.531280 + 0.920204i 0.468053 + 0.883700i \(0.344956\pi\)
−0.999334 + 0.0365041i \(0.988378\pi\)
\(710\) 2.24504 1.01045i 0.0842550 0.0379214i
\(711\) −10.3485 17.9241i −0.388098 0.672205i
\(712\) −8.66025 5.00000i −0.324557 0.187383i
\(713\) 25.7980i 0.966141i
\(714\) 0 0
\(715\) 4.89898 48.4949i 0.183211 1.81361i
\(716\) −6.89898 + 11.9494i −0.257827 + 0.446569i
\(717\) 13.1565 7.59592i 0.491339 0.283675i
\(718\) 23.8988 13.7980i 0.891894 0.514935i
\(719\) 2.24745 3.89270i 0.0838157 0.145173i −0.821070 0.570827i \(-0.806623\pi\)
0.904886 + 0.425654i \(0.139956\pi\)
\(720\) 6.67423 + 0.674235i 0.248734 + 0.0251272i
\(721\) 0 0
\(722\) 16.5959i 0.617636i
\(723\) −18.4490 10.6515i −0.686125 0.396135i
\(724\) 5.12372 + 8.87455i 0.190422 + 0.329820i
\(725\) 10.9243 + 32.7194i 0.405718 + 1.21517i
\(726\) 15.9217 27.5772i 0.590909 1.02348i
\(727\) 22.6969i 0.841783i 0.907111 + 0.420891i \(0.138283\pi\)
−0.907111 + 0.420891i \(0.861717\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) 3.78899 5.25966i 0.140237 0.194669i
\(731\) −0.898979 1.55708i −0.0332500 0.0575906i
\(732\) 7.53177 4.34847i 0.278382 0.160724i
\(733\) 34.3304 + 19.8207i 1.26802 + 0.732093i 0.974613 0.223894i \(-0.0718770\pi\)
0.293409 + 0.955987i \(0.405210\pi\)
\(734\) −32.0000 −1.18114
\(735\) 0 0
\(736\) −2.89898 −0.106858
\(737\) 33.9411 + 19.5959i 1.25024 + 0.721825i
\(738\) −2.86054 + 1.65153i −0.105298 + 0.0607937i
\(739\) 2.24745 + 3.89270i 0.0826737 + 0.143195i 0.904398 0.426691i \(-0.140321\pi\)
−0.821724 + 0.569886i \(0.806987\pi\)
\(740\) 3.62863 + 2.61401i 0.133391 + 0.0960931i
\(741\) 16.8990 0.620800
\(742\) 0 0
\(743\) 44.6969i 1.63977i −0.572527 0.819886i \(-0.694037\pi\)
0.572527 0.819886i \(-0.305963\pi\)
\(744\) 10.8990 18.8776i 0.399576 0.692086i
\(745\) 3.48553 + 7.74426i 0.127700 + 0.283728i
\(746\) −2.34847 4.06767i −0.0859836 0.148928i
\(747\) 6.36396 + 3.67423i 0.232845 + 0.134433i
\(748\) 9.79796i 0.358249i
\(749\) 0 0
\(750\) 26.1464 + 8.14643i 0.954733 + 0.297465i
\(751\) 20.8990 36.1981i 0.762615 1.32089i −0.178884 0.983870i \(-0.557249\pi\)
0.941499 0.337017i \(-0.109418\pi\)
\(752\) 7.70674 4.44949i 0.281036 0.162256i
\(753\) 13.6814 7.89898i 0.498579 0.287855i
\(754\) 15.3485 26.5843i 0.558958 0.968144i
\(755\) −43.5959 4.40408i −1.58662 0.160281i
\(756\) 0 0
\(757\) 51.7980i 1.88263i 0.337531 + 0.941314i \(0.390408\pi\)
−0.337531 + 0.941314i \(0.609592\pi\)
\(758\) 26.5843 + 15.3485i 0.965586 + 0.557482i
\(759\) −17.3939 30.1271i −0.631358 1.09354i
\(760\) 3.16158 1.42296i 0.114683 0.0516162i
\(761\) −10.5505 + 18.2740i −0.382456 + 0.662433i −0.991413 0.130771i \(-0.958255\pi\)
0.608957 + 0.793203i \(0.291588\pi\)
\(762\) 36.4949i 1.32207i
\(763\) 0 0
\(764\) −12.6969 −0.459359
\(765\) −10.8859 7.84204i −0.393580 0.283530i
\(766\) 3.55051 + 6.14966i 0.128285 + 0.222196i
\(767\) 5.97469 3.44949i 0.215734 0.124554i
\(768\) −2.12132 1.22474i −0.0765466 0.0441942i
\(769\) −40.6969 −1.46757 −0.733785 0.679382i \(-0.762248\pi\)
−0.733785 + 0.679382i \(0.762248\pi\)
\(770\) 0 0
\(771\) 21.3031 0.767211
\(772\) −18.7026 10.7980i −0.673122 0.388627i
\(773\) −1.16781 + 0.674235i −0.0420032 + 0.0242505i −0.520855 0.853645i \(-0.674387\pi\)
0.478851 + 0.877896i \(0.341053\pi\)
\(774\) 1.34847 + 2.33562i 0.0484697 + 0.0839520i
\(775\) 29.5047 33.3057i 1.05984 1.19638i
\(776\) 15.7980 0.567114
\(777\) 0 0
\(778\) 13.1010i 0.469694i
\(779\) −0.853572 + 1.47843i −0.0305824 + 0.0529702i
\(780\) −10.0024 22.2237i −0.358144