Properties

Label 490.2.i.f.459.3
Level $490$
Weight $2$
Character 490.459
Analytic conductor $3.913$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

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 459.3
Root \(-0.258819 + 0.965926i\) of defining polynomial
Character \(\chi\) \(=\) 490.459
Dual form 490.2.i.f.79.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 - 0.500000i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.917738 + 2.03906i) q^{5} -2.44949 q^{6} -1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(0.866025 - 0.500000i) q^{2} +(-2.12132 - 1.22474i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.917738 + 2.03906i) q^{5} -2.44949 q^{6} -1.00000i q^{8} +(1.50000 + 2.59808i) q^{9} +(1.81431 + 1.30701i) 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} +(-3.31552 + 3.74264i) q^{25} +(-2.22474 - 3.85337i) q^{26} -6.89898 q^{29} +(-2.24799 - 4.99465i) 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} +(2.03906 - 0.917738i) q^{40} +1.10102 q^{41} -0.898979i q^{43} +(-2.44949 - 4.24264i) q^{44} +(-3.92102 + 5.44294i) 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} +(-4.44414 - 3.20150i) q^{60} +(1.77526 + 3.07483i) q^{61} -8.89898i q^{62} -1.00000 q^{64} +(9.07277 - 4.08346i) 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} +(11.6170 - 3.87868i) q^{75} -1.55051 q^{76} +10.8990i q^{78} +(3.44949 + 5.97469i) q^{79} +(1.30701 - 1.81431i) 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} +(2.02653 - 2.81311i) 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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

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

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
\(5\) 0.917738 + 2.03906i 0.410425 + 0.911894i
\(6\) −2.44949 −1.00000
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 1.81431 + 1.30701i 0.573736 + 0.413312i
\(11\) 2.44949 4.24264i 0.738549 1.27920i −0.214600 0.976702i \(-0.568845\pi\)
0.953149 0.302502i \(-0.0978220\pi\)
\(12\) −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 \(-0.411312\pi\)
−0.695113 + 0.718900i \(0.744646\pi\)
\(18\) 2.59808 + 1.50000i 0.612372 + 0.353553i
\(19\) −0.775255 1.34278i −0.177856 0.308055i 0.763290 0.646056i \(-0.223583\pi\)
−0.941146 + 0.338001i \(0.890249\pi\)
\(20\) 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 \(-0.568932\pi\)
0.738363 + 0.674403i \(0.235599\pi\)
\(24\) −1.22474 + 2.12132i −0.250000 + 0.433013i
\(25\) −3.31552 + 3.74264i −0.663103 + 0.748528i
\(26\) −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 \(0.721295\pi\)
\(30\) −2.24799 4.99465i −0.410425 0.911894i
\(31\) 4.44949 7.70674i 0.799152 1.38417i −0.121017 0.992650i \(-0.538616\pi\)
0.920169 0.391521i \(-0.128051\pi\)
\(32\) −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 \(-0.719235\pi\)
0.350823 + 0.936442i \(0.385902\pi\)
\(38\) −1.34278 0.775255i −0.217828 0.125763i
\(39\) −5.44949 + 9.43879i −0.872617 + 1.51142i
\(40\) 2.03906 0.917738i 0.322403 0.145107i
\(41\) 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
\(45\) −3.92102 + 5.44294i −0.584511 + 0.811386i
\(46\) 1.44949 2.51059i 0.213716 0.370166i
\(47\) 7.70674 4.44949i 1.12414 0.649025i 0.181688 0.983356i \(-0.441844\pi\)
0.942456 + 0.334331i \(0.108510\pi\)
\(48\) 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 \(-0.0640861\pi\)
0.316717 + 0.948520i \(0.397419\pi\)
\(54\) 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 −0.811138 0.584854i \(-0.801152\pi\)
0.912068 + 0.410039i \(0.134485\pi\)
\(60\) −4.44414 3.20150i −0.573736 0.413312i
\(61\) 1.77526 + 3.07483i 0.227298 + 0.393692i 0.957006 0.290067i \(-0.0936775\pi\)
−0.729708 + 0.683759i \(0.760344\pi\)
\(62\) 8.89898i 1.13017i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 9.07277 4.08346i 1.12534 0.506491i
\(66\) −6.00000 + 10.3923i −0.738549 + 1.27920i
\(67\) −6.92820 4.00000i −0.846415 0.488678i 0.0130248 0.999915i \(-0.495854\pi\)
−0.859440 + 0.511237i \(0.829187\pi\)
\(68\) −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 \(-0.279070\pi\)
−0.345831 + 0.938297i \(0.612403\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 11.6170 3.87868i 1.34142 0.447871i
\(76\) −1.55051 −0.177856
\(77\) 0 0
\(78\) 10.8990i 1.23407i
\(79\) 3.44949 + 5.97469i 0.388098 + 0.672205i 0.992194 0.124706i \(-0.0397989\pi\)
−0.604096 + 0.796912i \(0.706466\pi\)
\(80\) 1.30701 1.81431i 0.146128 0.202846i
\(81\) 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 0.999388 + 0.0349934i \(0.0111410\pi\)
−0.469389 + 0.882992i \(0.655526\pi\)
\(90\) −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
\(95\) 2.02653 2.81311i 0.207917 0.288619i
\(96\) 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
\(100\) 1.58346 + 4.74264i 0.158346 + 0.474264i
\(101\) 1.77526 3.07483i 0.176644 0.305957i −0.764085 0.645116i \(-0.776809\pi\)
0.940729 + 0.339159i \(0.110142\pi\)
\(102\) 4.24264 + 2.44949i 0.420084 + 0.242536i
\(103\) −11.1708 + 6.44949i −1.10070 + 0.635487i −0.936404 0.350925i \(-0.885867\pi\)
−0.164292 + 0.986412i \(0.552534\pi\)
\(104\) −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 \(-0.540283\pi\)
0.795991 + 0.605308i \(0.206950\pi\)
\(108\) 0 0
\(109\) 3.44949 5.97469i 0.330401 0.572272i −0.652189 0.758056i \(-0.726149\pi\)
0.982591 + 0.185784i \(0.0594826\pi\)
\(110\) 9.98930 4.49598i 0.952443 0.428675i
\(111\) 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
\(115\) 5.25966 + 3.78899i 0.490466 + 0.353325i
\(116\) −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
\(130\) 5.81552 8.07277i 0.510054 0.708029i
\(131\) −3.22474 5.58542i −0.281747 0.488001i 0.690068 0.723745i \(-0.257581\pi\)
−0.971815 + 0.235744i \(0.924247\pi\)
\(132\) 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 \(-0.357805\pi\)
−0.565038 + 0.825065i \(0.691139\pi\)
\(138\) −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
\(145\) −6.33145 14.0674i −0.525799 1.16824i
\(146\) 2.89898 0.239921
\(147\) 0 0
\(148\) 2.00000i 0.164399i
\(149\) −1.89898 3.28913i −0.155570 0.269456i 0.777696 0.628640i \(-0.216388\pi\)
−0.933267 + 0.359184i \(0.883055\pi\)
\(150\) 8.12132 9.16756i 0.663103 0.748528i
\(151\) −9.79796 + 16.9706i −0.797347 + 1.38104i 0.123992 + 0.992283i \(0.460430\pi\)
−0.921338 + 0.388762i \(0.872903\pi\)
\(152\) −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 \(-0.378584\pi\)
−0.617655 + 0.786449i \(0.711917\pi\)
\(158\) 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 \(-0.756370\pi\)
0.239437 + 0.970912i \(0.423037\pi\)
\(164\) 0.550510 0.953512i 0.0429876 0.0744568i
\(165\) −21.7718 15.6841i −1.69493 1.22100i
\(166\) 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
\(170\) −1.83548 4.07812i −0.140775 0.312777i
\(171\) 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 \(-0.590341\pi\)
0.691369 + 0.722502i \(0.257008\pi\)
\(174\) 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 −0.484181 0.874968i \(-0.660882\pi\)
0.999835 0.0181709i \(-0.00578431\pi\)
\(180\) 2.75321 + 6.11717i 0.205212 + 0.455947i
\(181\) 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
\(185\) −3.62863 2.61401i −0.266782 0.192186i
\(186\) −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 0.539568 0.841942i \(-0.318588\pi\)
−0.998927 + 0.0463087i \(0.985254\pi\)
\(192\) 2.12132 + 1.22474i 0.153093 + 0.0883883i
\(193\) 18.7026 + 10.7980i 1.34624 + 0.777254i 0.987715 0.156265i \(-0.0499453\pi\)
0.358528 + 0.933519i \(0.383279\pi\)
\(194\) 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 0.394005 + 0.919108i \(0.371089\pi\)
−0.992974 + 0.118336i \(0.962244\pi\)
\(200\) 3.74264 + 3.31552i 0.264645 + 0.234442i
\(201\) 9.79796 + 16.9706i 0.691095 + 1.19701i
\(202\) 3.55051i 0.249813i
\(203\) 0 0
\(204\) 4.89898 0.342997
\(205\) 1.01045 + 2.24504i 0.0705727 + 0.156801i
\(206\) −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
\(215\) 1.83307 0.825027i 0.125014 0.0562664i
\(216\) 0 0
\(217\) 0 0
\(218\) 6.89898i 0.467258i
\(219\) −3.55051 6.14966i −0.239921 0.415556i
\(220\) 6.40300 8.88828i 0.431690 0.599248i
\(221\) −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 \(-0.411750\pi\)
−0.696100 + 0.717945i \(0.745083\pi\)
\(228\) 3.28913 + 1.89898i 0.217828 + 0.125763i
\(229\) 9.57321 + 16.5813i 0.632616 + 1.09572i 0.987015 + 0.160628i \(0.0513521\pi\)
−0.354399 + 0.935094i \(0.615315\pi\)
\(230\) 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 0.736556 0.676376i \(-0.236451\pi\)
0.954037 0.299688i \(-0.0968827\pi\)
\(234\) 6.67423 11.5601i 0.436308 0.755708i
\(235\) 16.1455 + 11.6310i 1.05322 + 0.758725i
\(236\) −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 \(0.435715\pi\)
\(240\) −4.99465 + 2.24799i −0.322403 + 0.145107i
\(241\) −4.34847 + 7.53177i −0.280110 + 0.485164i −0.971411 0.237402i \(-0.923704\pi\)
0.691302 + 0.722566i \(0.257037\pi\)
\(242\) −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
\(250\) −10.9070 + 2.45692i −0.689822 + 0.155389i
\(251\) 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
\(255\) −6.40300 + 8.88828i −0.400972 + 0.556606i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −7.53177 + 4.34847i −0.469819 + 0.271250i −0.716164 0.697932i \(-0.754104\pi\)
0.246345 + 0.969182i \(0.420770\pi\)
\(258\) 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 \(-0.431016\pi\)
−0.738253 + 0.674524i \(0.764349\pi\)
\(264\) 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 0.411348 + 0.911478i \(0.365058\pi\)
−0.995037 + 0.0995010i \(0.968275\pi\)
\(270\) 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
\(274\) −1.79796 −0.108619
\(275\) 7.75736 + 23.2341i 0.467786 + 1.40107i
\(276\) −3.55051 + 6.14966i −0.213716 + 0.370166i
\(277\) −12.9029 7.44949i −0.775260 0.447596i 0.0594879 0.998229i \(-0.481053\pi\)
−0.834748 + 0.550633i \(0.814387\pi\)
\(278\) 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 \(-0.297757\pi\)
−0.400290 + 0.916389i \(0.631091\pi\)
\(284\) −0.550510 + 0.953512i −0.0326668 + 0.0565805i
\(285\) −7.74426 + 3.48553i −0.458730 + 0.206465i
\(286\) −21.7980 −1.28894
\(287\) 0 0
\(288\) 3.00000i 0.176777i
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) −12.5169 9.01702i −0.735018 0.529497i
\(291\) 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
\(305\) −4.64054 + 6.44174i −0.265717 + 0.368853i
\(306\) −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
\(310\) 18.1455 8.16693i 1.03060 0.463850i
\(311\) 6.00000 10.3923i 0.340229 0.589294i −0.644246 0.764818i \(-0.722829\pi\)
0.984475 + 0.175525i \(0.0561621\pi\)
\(312\) 9.43879 + 5.44949i 0.534366 + 0.308517i
\(313\) 18.7026 10.7980i 1.05713 0.610337i 0.132496 0.991184i \(-0.457701\pi\)
0.924638 + 0.380847i \(0.124367\pi\)
\(314\) −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 \(-0.449016\pi\)
0.934684 + 0.355480i \(0.115683\pi\)
\(318\) −23.1202 13.3485i −1.29652 0.748545i
\(319\) −16.8990 + 29.2699i −0.946161 + 1.63880i
\(320\) −0.917738 2.03906i −0.0513031 0.113987i
\(321\) −19.5959 −1.09374
\(322\) 0 0
\(323\) 3.10102i 0.172545i
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) 16.6528 + 14.7524i 0.923733 + 0.818313i
\(326\) −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 0.999871 + 0.0160535i \(0.00511022\pi\)
−0.486033 + 0.873941i \(0.661556\pi\)
\(332\) 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
\(340\) −3.62863 2.61401i −0.196790 0.141765i
\(341\) −21.7980 37.7552i −1.18043 2.04456i
\(342\) 4.65153i 0.251526i
\(343\) 0 0
\(344\) −0.898979 −0.0484697
\(345\) −6.51687 14.4794i −0.350857 0.779544i
\(346\) 3.12372 5.41045i 0.167932 0.290868i
\(347\) 25.0273 + 14.4495i 1.34353 + 0.775689i 0.987324 0.158717i \(-0.0507358\pi\)
0.356209 + 0.934406i \(0.384069\pi\)
\(348\) 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 \(-0.124746\pi\)
0.131318 + 0.991340i \(0.458079\pi\)
\(354\) −1.89898 + 3.28913i −0.100930 + 0.174815i
\(355\) −1.01045 2.24504i −0.0536290 0.119155i
\(356\) 10.0000 0.529999
\(357\) 0 0
\(358\) 13.7980i 0.729245i
\(359\) −13.7980 23.8988i −0.728228 1.26133i −0.957631 0.287997i \(-0.907011\pi\)
0.229403 0.973332i \(-0.426323\pi\)
\(360\) 5.44294 + 3.92102i 0.286868 + 0.206656i
\(361\) 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 \(-0.647978\pi\)
−0.998277 + 0.0586798i \(0.981311\pi\)
\(368\) −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 \(-0.705469\pi\)
0.390982 + 0.920398i \(0.372136\pi\)
\(374\) −4.89898 + 8.48528i −0.253320 + 0.438763i
\(375\) 18.5703 + 20.1282i 0.958964 + 1.03942i
\(376\) −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 \(0.789089\pi\)
\(380\) −1.42296 3.16158i −0.0729964 0.162186i
\(381\) 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 \(-0.608596\pi\)
0.648819 + 0.760943i \(0.275263\pi\)
\(384\) 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 −0.650804 0.759246i \(-0.725568\pi\)
0.982928 + 0.183990i \(0.0589014\pi\)
\(390\) −22.2237 + 10.0024i −1.12534 + 0.506491i
\(391\) −5.79796 −0.293215
\(392\) 0 0
\(393\) 15.7980i 0.796902i
\(394\) −9.44949 16.3670i −0.476058 0.824557i
\(395\) −9.01702 + 12.5169i −0.453695 + 0.629794i
\(396\) 7.34847 12.7279i 0.369274 0.639602i
\(397\) −2.29629 + 1.32577i −0.115248 + 0.0665383i −0.556516 0.830837i \(-0.687862\pi\)
0.441268 + 0.897375i \(0.354529\pi\)
\(398\) 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 0.955191 + 0.295990i \(0.0956494\pi\)
−0.221261 + 0.975215i \(0.571017\pi\)
\(402\) 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 0.0258109 + 0.999667i \(0.491783\pi\)
−0.878642 + 0.477481i \(0.841550\pi\)
\(410\) 1.99760 + 1.43904i 0.0986542 + 0.0710692i
\(411\) 2.20204 + 3.81405i 0.108619 + 0.188133i
\(412\) 12.8990i 0.635487i
\(413\) 0 0
\(414\) 8.69694 0.427431
\(415\) −4.99465 + 2.24799i −0.245178 + 0.110349i
\(416\) −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
\(425\) 9.48528 3.16693i 0.460104 0.153619i
\(426\) 2.69694 0.130667
\(427\) 0 0
\(428\) 8.00000i 0.386695i
\(429\) 26.6969 + 46.2405i 1.28894 + 2.23251i
\(430\) 1.17497 1.63103i 0.0566622 0.0786553i
\(431\) 0.898979 1.55708i 0.0433023 0.0750018i −0.843562 0.537032i \(-0.819545\pi\)
0.886864 + 0.462030i \(0.152879\pi\)
\(432\) 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 0.999925 + 0.0122101i \(0.00388670\pi\)
−0.489388 + 0.872066i \(0.662780\pi\)
\(440\) 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 \(-0.591892\pi\)
0.687841 + 0.725861i \(0.258558\pi\)
\(444\) 2.44949 4.24264i 0.116248 0.201347i
\(445\) −13.0701 + 18.1431i −0.619581 + 0.860067i
\(446\) 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 \(0.424175\pi\)
\(450\) −14.2279 + 4.75039i −0.670711 + 0.223936i
\(451\) 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 \(-0.910034\pi\)
−0.238636 + 0.971109i \(0.576700\pi\)
\(458\) 16.5813 + 9.57321i 0.774793 + 0.447327i
\(459\) 0 0
\(460\) 5.91119 2.66050i 0.275611 0.124047i
\(461\) −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
\(465\) −39.5483 28.4901i −1.83401 1.32120i
\(466\) 14.8990 25.8058i 0.690182 1.19543i
\(467\) 9.04952 5.22474i 0.418762 0.241772i −0.275785 0.961219i \(-0.588938\pi\)
0.694548 + 0.719447i \(0.255605\pi\)
\(468\) 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 −0.952507 0.304517i \(-0.901505\pi\)
0.739973 + 0.672637i \(0.234838\pi\)
\(480\) −3.20150 + 4.44414i −0.146128 + 0.202846i
\(481\) 4.44949 + 7.70674i 0.202879 + 0.351397i
\(482\) 8.69694i 0.396135i
\(483\) 0 0
\(484\) −13.0000 −0.590909
\(485\) −32.2130 + 14.4984i −1.46271 + 0.658338i
\(486\) −11.0227 + 19.0919i −0.500000 + 0.866025i
\(487\) −6.32464 3.65153i −0.286597 0.165467i 0.349809 0.936821i \(-0.386246\pi\)
−0.636406 + 0.771354i \(0.719580\pi\)
\(488\) 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
\(495\) 13.4879 + 29.9679i 0.606238 + 1.34696i
\(496\) −8.89898 −0.399576
\(497\) 0 0
\(498\) 6.00000i 0.268866i
\(499\) 3.10102 + 5.37113i 0.138821 + 0.240445i 0.927051 0.374936i \(-0.122335\pi\)
−0.788230 + 0.615381i \(0.789002\pi\)
\(500\) −8.21731 + 7.58128i −0.367489 + 0.339045i
\(501\) −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 0.968735 + 0.248097i \(0.0798052\pi\)
−0.269509 + 0.962998i \(0.586861\pi\)
\(510\) −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
\(515\) −23.4028 16.8591i −1.03125 0.742899i
\(516\) 1.10102 + 1.90702i 0.0484697 + 0.0839520i
\(517\) 43.5959i 1.91735i
\(518\) 0 0
\(519\) −15.3031 −0.671730
\(520\) −4.08346 9.07277i −0.179072 0.397867i
\(521\) 16.3485 28.3164i 0.716239 1.24056i −0.246240 0.969209i \(-0.579195\pi\)
0.962480 0.271354i \(-0.0874715\pi\)
\(522\) −17.9241 10.3485i −0.784515 0.452940i
\(523\) 28.7056 16.5732i 1.25521 0.724696i 0.283071 0.959099i \(-0.408647\pi\)
0.972140 + 0.234403i \(0.0753135\pi\)
\(524\) −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
\(530\) 10.0024 + 22.2237i 0.434477 + 0.965334i
\(531\) 4.65153 0.201859
\(532\) 0 0
\(533\) 4.89898i 0.212198i
\(534\) −12.2474 21.2132i −0.529999 0.917985i
\(535\) 14.5145 + 10.4561i 0.627517 + 0.452055i
\(536\) −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 0.744260 0.667891i \(-0.232803\pi\)
−0.950540 + 0.310602i \(0.899469\pi\)
\(542\) 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
\(550\) 18.3351 + 16.2426i 0.781812 + 0.692589i
\(551\) 5.34847 + 9.26382i 0.227852 + 0.394652i
\(552\) 7.10102i 0.302240i
\(553\) 0 0
\(554\) −14.8990 −0.632997
\(555\) 4.49598 + 9.98930i 0.190844 + 0.424022i
\(556\) 0.775255 1.34278i 0.0328781 0.0569466i
\(557\) 10.9959 + 6.34847i 0.465910 + 0.268993i 0.714526 0.699609i \(-0.246642\pi\)
−0.248616 + 0.968602i \(0.579976\pi\)
\(558\) 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 \(-0.551564\pi\)
−0.935330 + 0.353776i \(0.884897\pi\)
\(564\) −10.8990 + 18.8776i −0.458930 + 0.794890i
\(565\) −40.3692 + 18.1693i −1.69834 + 0.764390i
\(566\) 3.75255 0.157731
\(567\) 0 0
\(568\) 1.10102i 0.0461978i
\(569\) 16.8990 + 29.2699i 0.708442 + 1.22706i 0.965435 + 0.260644i \(0.0839350\pi\)
−0.256993 + 0.966413i \(0.582732\pi\)
\(570\) −4.96396 + 6.89069i −0.207917 + 0.288619i
\(571\) 5.55051 9.61377i 0.232282 0.402324i −0.726198 0.687486i \(-0.758714\pi\)
0.958479 + 0.285162i \(0.0920476\pi\)
\(572\) −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 \(-0.316795\pi\)
−0.454351 + 0.890823i \(0.650129\pi\)
\(578\) −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
\(585\) 24.2183 + 17.4465i 1.00130 + 0.721326i
\(586\) −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
\(590\) 3.16158 1.42296i 0.130160 0.0585824i
\(591\) −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 \(-0.594826\pi\)
0.681122 + 0.732170i \(0.261492\pi\)
\(594\) 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 −0.968254 0.249970i \(-0.919579\pi\)
0.700607 + 0.713547i \(0.252913\pi\)
\(600\) −3.87868 11.6170i −0.158346 0.474264i
\(601\) 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
\(605\) 16.9911 23.5861i 0.690786 0.958910i
\(606\) −4.34847 + 7.53177i −0.176644 + 0.305957i
\(607\) 28.9199 16.6969i 1.17382 0.677708i 0.219247 0.975669i \(-0.429640\pi\)
0.954578 + 0.297962i \(0.0963068\pi\)
\(608\) 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 \(-0.143606\pi\)
0.0723836 + 0.997377i \(0.476939\pi\)
\(614\) −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 −0.0589796 0.998259i \(-0.518785\pi\)
0.894008 0.448052i \(-0.147882\pi\)
\(620\) 11.6310 16.1455i 0.467113 0.648420i
\(621\) 0 0
\(622\) 12.0000i 0.481156i
\(623\) 0 0
\(624\) 10.8990 0.436308
\(625\) −3.01472 24.8176i −0.120589 0.992703i
\(626\) 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
\(635\) −30.3799 + 13.6734i −1.20559 + 0.542611i
\(636\) −26.6969 −1.05860
\(637\) 0 0
\(638\) 33.7980i 1.33807i
\(639\) −1.65153 2.86054i −0.0653335 0.113161i
\(640\) −1.81431 1.30701i −0.0717170 0.0516640i
\(641\) −12.8990 + 22.3417i −0.509479 + 0.882444i 0.490461 + 0.871463i \(0.336829\pi\)
−0.999940 + 0.0109803i \(0.996505\pi\)
\(642\) −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 0.995392 + 0.0958907i \(0.0305699\pi\)
0.580740 + 0.814089i \(0.302763\pi\)
\(648\) −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 \(-0.796020\pi\)
0.116954 + 0.993137i \(0.462687\pi\)
\(654\) −8.44949 + 14.6349i −0.330401 + 0.572272i
\(655\) 8.42953 11.7014i 0.329369 0.457211i
\(656\) −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 \(0.606761\pi\)
\(660\) −24.4687 + 11.0129i −0.952443 + 0.428675i
\(661\) −20.4722 + 35.4589i −0.796276 + 1.37919i 0.125750 + 0.992062i \(0.459866\pi\)
−0.922026 + 0.387129i \(0.873467\pi\)
\(662\) 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
\(670\) −7.34190 16.3125i −0.283642 0.630205i
\(671\) 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 \(-0.913677\pi\)
−0.249735 + 0.968314i \(0.580343\pi\)
\(678\) 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 \(-0.355249\pi\)
−0.558395 + 0.829575i \(0.688583\pi\)
\(684\) −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
\(690\) −12.8835 9.28108i −0.490466 0.353325i
\(691\) 10.5732 + 18.3133i 0.402224 + 0.696672i 0.993994 0.109434i \(-0.0349040\pi\)
−0.591770 + 0.806107i \(0.701571\pi\)
\(692\) 6.24745i 0.237492i
\(693\) 0 0
\(694\) 28.8990 1.09699
\(695\) 1.42296 + 3.16158i 0.0539760 + 0.119926i
\(696\) 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
\(705\) −20.0048 44.4473i −0.753425 1.67398i
\(706\) 22.8990 0.861814
\(707\) 0 0
\(708\) 3.79796i 0.142736i
\(709\) −14.1464 24.5023i −0.531280 0.920204i −0.999334 0.0365041i \(-0.988378\pi\)
0.468053 0.883700i \(-0.344956\pi\)
\(710\) −1.99760 1.43904i −0.0749684 0.0540063i
\(711\) −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 0.904886 0.425654i \(-0.139956\pi\)
−0.821070 + 0.570827i \(0.806623\pi\)
\(720\) 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
\(725\) 22.8737 25.8204i 0.849507 0.958946i
\(726\) 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
\(730\) 2.66050 + 5.91119i 0.0984696 + 0.218783i
\(731\) −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 \(-0.928123\pi\)
−0.293409 + 0.955987i \(0.594790\pi\)
\(734\) −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 −0.821724 0.569886i \(-0.806987\pi\)
0.904398 + 0.426691i \(0.140321\pi\)
\(740\) −4.07812 + 1.83548i −0.149915 + 0.0674734i
\(741\) 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
\(745\) 4.96396 6.89069i 0.181865 0.252455i
\(746\) −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 0.941499 + 0.337017i \(0.109418\pi\)
−0.178884 + 0.983870i \(0.557249\pi\)
\(752\) −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
\(760\) −2.81311 2.02653i −0.102042 0.0735099i
\(761\) −10.5505 18.2740i −0.382456 0.662433i 0.608957 0.793203i \(-0.291588\pi\)
−0.991413 + 0.130771i \(0.958255\pi\)
\(762\) 36.4949i 1.32207i
\(763\) 0 0
\(764\) −12.6969 −0.459359
\(765\) 12.2343 5.50643i 0.442334 0.199085i
\(766\) 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 \(-0.325613\pi\)
−0.478851 + 0.877896i \(0.658947\pi\)
\(774\) 1.34847 2.33562i 0.0484697 0.0839520i
\(775\) 14.0912 + 42.2047i 0.506171 + 1.51604i
\(776\) 15.7980 0.567114
\(777\) 0 0
\(778\) 13.1010i 0.469694i
\(779\) −0.853572 1.47843i −0.0305824 0.0529702i
\(780\) −14.2450 + 19.7742i