Properties

Label 490.2.e.i.361.1
Level $490$
Weight $2$
Character 490.361
Analytic conductor $3.913$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 490.361
Dual form 490.2.e.i.471.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.70711 + 2.95680i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.41421 q^{6} -1.00000 q^{8} +(-4.32843 - 7.49706i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.70711 + 2.95680i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -3.41421 q^{6} -1.00000 q^{8} +(-4.32843 - 7.49706i) q^{9} +(0.500000 - 0.866025i) q^{10} +(0.414214 - 0.717439i) q^{11} +(-1.70711 - 2.95680i) q^{12} -4.82843 q^{13} +3.41421 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.29289 + 2.23936i) q^{17} +(4.32843 - 7.49706i) q^{18} +(-0.292893 - 0.507306i) q^{19} +1.00000 q^{20} +0.828427 q^{22} +(0.585786 + 1.01461i) q^{23} +(1.70711 - 2.95680i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.41421 - 4.18154i) q^{26} +19.3137 q^{27} -4.82843 q^{29} +(1.70711 + 2.95680i) q^{30} +(1.41421 - 2.44949i) q^{31} +(0.500000 - 0.866025i) q^{32} +(1.41421 + 2.44949i) q^{33} -2.58579 q^{34} +8.65685 q^{36} +(3.82843 + 6.63103i) q^{37} +(0.292893 - 0.507306i) q^{38} +(8.24264 - 14.2767i) q^{39} +(0.500000 + 0.866025i) q^{40} -3.07107 q^{41} -8.82843 q^{43} +(0.414214 + 0.717439i) q^{44} +(-4.32843 + 7.49706i) q^{45} +(-0.585786 + 1.01461i) q^{46} +(-2.58579 - 4.47871i) q^{47} +3.41421 q^{48} -1.00000 q^{50} +(-4.41421 - 7.64564i) q^{51} +(2.41421 - 4.18154i) q^{52} +(-3.24264 + 5.61642i) q^{53} +(9.65685 + 16.7262i) q^{54} -0.828427 q^{55} +2.00000 q^{57} +(-2.41421 - 4.18154i) q^{58} +(-4.29289 + 7.43551i) q^{59} +(-1.70711 + 2.95680i) q^{60} +(-4.65685 - 8.06591i) q^{61} +2.82843 q^{62} +1.00000 q^{64} +(2.41421 + 4.18154i) q^{65} +(-1.41421 + 2.44949i) q^{66} +(-0.828427 + 1.43488i) q^{67} +(-1.29289 - 2.23936i) q^{68} -4.00000 q^{69} -4.48528 q^{71} +(4.32843 + 7.49706i) q^{72} +(4.70711 - 8.15295i) q^{73} +(-3.82843 + 6.63103i) q^{74} +(-1.70711 - 2.95680i) q^{75} +0.585786 q^{76} +16.4853 q^{78} +(3.41421 + 5.91359i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-19.9853 + 34.6155i) q^{81} +(-1.53553 - 2.65962i) q^{82} -2.24264 q^{83} +2.58579 q^{85} +(-4.41421 - 7.64564i) q^{86} +(8.24264 - 14.2767i) q^{87} +(-0.414214 + 0.717439i) q^{88} +(-6.36396 - 11.0227i) q^{89} -8.65685 q^{90} -1.17157 q^{92} +(4.82843 + 8.36308i) q^{93} +(2.58579 - 4.47871i) q^{94} +(-0.292893 + 0.507306i) q^{95} +(1.70711 + 2.95680i) q^{96} -7.75736 q^{97} -7.17157 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 2q^{2} - 4q^{3} - 2q^{4} - 2q^{5} - 8q^{6} - 4q^{8} - 6q^{9} + O(q^{10}) \) \( 4q + 2q^{2} - 4q^{3} - 2q^{4} - 2q^{5} - 8q^{6} - 4q^{8} - 6q^{9} + 2q^{10} - 4q^{11} - 4q^{12} - 8q^{13} + 8q^{15} - 2q^{16} - 8q^{17} + 6q^{18} - 4q^{19} + 4q^{20} - 8q^{22} + 8q^{23} + 4q^{24} - 2q^{25} - 4q^{26} + 32q^{27} - 8q^{29} + 4q^{30} + 2q^{32} - 16q^{34} + 12q^{36} + 4q^{37} + 4q^{38} + 16q^{39} + 2q^{40} + 16q^{41} - 24q^{43} - 4q^{44} - 6q^{45} - 8q^{46} - 16q^{47} + 8q^{48} - 4q^{50} - 12q^{51} + 4q^{52} + 4q^{53} + 16q^{54} + 8q^{55} + 8q^{57} - 4q^{58} - 20q^{59} - 4q^{60} + 4q^{61} + 4q^{64} + 4q^{65} + 8q^{67} - 8q^{68} - 16q^{69} + 16q^{71} + 6q^{72} + 16q^{73} - 4q^{74} - 4q^{75} + 8q^{76} + 32q^{78} + 8q^{79} - 2q^{80} - 46q^{81} + 8q^{82} + 8q^{83} + 16q^{85} - 12q^{86} + 16q^{87} + 4q^{88} - 12q^{90} - 16q^{92} + 8q^{93} + 16q^{94} - 4q^{95} + 4q^{96} - 48q^{97} - 40q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −1.70711 + 2.95680i −0.985599 + 1.70711i −0.346353 + 0.938104i \(0.612580\pi\)
−0.639246 + 0.769002i \(0.720753\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) −3.41421 −1.39385
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −4.32843 7.49706i −1.44281 2.49902i
\(10\) 0.500000 0.866025i 0.158114 0.273861i
\(11\) 0.414214 0.717439i 0.124890 0.216316i −0.796800 0.604243i \(-0.793476\pi\)
0.921690 + 0.387927i \(0.126809\pi\)
\(12\) −1.70711 2.95680i −0.492799 0.853553i
\(13\) −4.82843 −1.33916 −0.669582 0.742738i \(-0.733527\pi\)
−0.669582 + 0.742738i \(0.733527\pi\)
\(14\) 0 0
\(15\) 3.41421 0.881546
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −1.29289 + 2.23936i −0.313573 + 0.543124i −0.979133 0.203220i \(-0.934859\pi\)
0.665560 + 0.746344i \(0.268193\pi\)
\(18\) 4.32843 7.49706i 1.02022 1.76707i
\(19\) −0.292893 0.507306i −0.0671943 0.116384i 0.830471 0.557062i \(-0.188071\pi\)
−0.897665 + 0.440678i \(0.854738\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 0.828427 0.176621
\(23\) 0.585786 + 1.01461i 0.122145 + 0.211561i 0.920613 0.390476i \(-0.127689\pi\)
−0.798468 + 0.602037i \(0.794356\pi\)
\(24\) 1.70711 2.95680i 0.348462 0.603553i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −2.41421 4.18154i −0.473466 0.820068i
\(27\) 19.3137 3.71692
\(28\) 0 0
\(29\) −4.82843 −0.896616 −0.448308 0.893879i \(-0.647973\pi\)
−0.448308 + 0.893879i \(0.647973\pi\)
\(30\) 1.70711 + 2.95680i 0.311674 + 0.539835i
\(31\) 1.41421 2.44949i 0.254000 0.439941i −0.710623 0.703573i \(-0.751587\pi\)
0.964623 + 0.263631i \(0.0849203\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 1.41421 + 2.44949i 0.246183 + 0.426401i
\(34\) −2.58579 −0.443459
\(35\) 0 0
\(36\) 8.65685 1.44281
\(37\) 3.82843 + 6.63103i 0.629390 + 1.09013i 0.987674 + 0.156522i \(0.0500283\pi\)
−0.358285 + 0.933612i \(0.616638\pi\)
\(38\) 0.292893 0.507306i 0.0475136 0.0822959i
\(39\) 8.24264 14.2767i 1.31988 2.28610i
\(40\) 0.500000 + 0.866025i 0.0790569 + 0.136931i
\(41\) −3.07107 −0.479620 −0.239810 0.970820i \(-0.577085\pi\)
−0.239810 + 0.970820i \(0.577085\pi\)
\(42\) 0 0
\(43\) −8.82843 −1.34632 −0.673161 0.739496i \(-0.735064\pi\)
−0.673161 + 0.739496i \(0.735064\pi\)
\(44\) 0.414214 + 0.717439i 0.0624450 + 0.108158i
\(45\) −4.32843 + 7.49706i −0.645244 + 1.11760i
\(46\) −0.585786 + 1.01461i −0.0863695 + 0.149596i
\(47\) −2.58579 4.47871i −0.377176 0.653288i 0.613474 0.789715i \(-0.289771\pi\)
−0.990650 + 0.136427i \(0.956438\pi\)
\(48\) 3.41421 0.492799
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) −4.41421 7.64564i −0.618114 1.07060i
\(52\) 2.41421 4.18154i 0.334791 0.579875i
\(53\) −3.24264 + 5.61642i −0.445411 + 0.771474i −0.998081 0.0619259i \(-0.980276\pi\)
0.552670 + 0.833400i \(0.313609\pi\)
\(54\) 9.65685 + 16.7262i 1.31413 + 2.27614i
\(55\) −0.828427 −0.111705
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) −2.41421 4.18154i −0.317002 0.549063i
\(59\) −4.29289 + 7.43551i −0.558887 + 0.968021i 0.438703 + 0.898632i \(0.355438\pi\)
−0.997590 + 0.0693885i \(0.977895\pi\)
\(60\) −1.70711 + 2.95680i −0.220387 + 0.381721i
\(61\) −4.65685 8.06591i −0.596249 1.03273i −0.993369 0.114967i \(-0.963324\pi\)
0.397120 0.917767i \(-0.370010\pi\)
\(62\) 2.82843 0.359211
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 2.41421 + 4.18154i 0.299446 + 0.518656i
\(66\) −1.41421 + 2.44949i −0.174078 + 0.301511i
\(67\) −0.828427 + 1.43488i −0.101208 + 0.175298i −0.912183 0.409784i \(-0.865604\pi\)
0.810974 + 0.585082i \(0.198938\pi\)
\(68\) −1.29289 2.23936i −0.156786 0.271562i
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) −4.48528 −0.532305 −0.266152 0.963931i \(-0.585752\pi\)
−0.266152 + 0.963931i \(0.585752\pi\)
\(72\) 4.32843 + 7.49706i 0.510110 + 0.883536i
\(73\) 4.70711 8.15295i 0.550925 0.954230i −0.447283 0.894393i \(-0.647608\pi\)
0.998208 0.0598379i \(-0.0190584\pi\)
\(74\) −3.82843 + 6.63103i −0.445046 + 0.770842i
\(75\) −1.70711 2.95680i −0.197120 0.341421i
\(76\) 0.585786 0.0671943
\(77\) 0 0
\(78\) 16.4853 1.86659
\(79\) 3.41421 + 5.91359i 0.384129 + 0.665331i 0.991648 0.128974i \(-0.0411684\pi\)
−0.607519 + 0.794305i \(0.707835\pi\)
\(80\) −0.500000 + 0.866025i −0.0559017 + 0.0968246i
\(81\) −19.9853 + 34.6155i −2.22059 + 3.84617i
\(82\) −1.53553 2.65962i −0.169571 0.293706i
\(83\) −2.24264 −0.246162 −0.123081 0.992397i \(-0.539277\pi\)
−0.123081 + 0.992397i \(0.539277\pi\)
\(84\) 0 0
\(85\) 2.58579 0.280468
\(86\) −4.41421 7.64564i −0.475997 0.824451i
\(87\) 8.24264 14.2767i 0.883704 1.53062i
\(88\) −0.414214 + 0.717439i −0.0441553 + 0.0764792i
\(89\) −6.36396 11.0227i −0.674579 1.16840i −0.976592 0.215101i \(-0.930992\pi\)
0.302013 0.953304i \(-0.402341\pi\)
\(90\) −8.65685 −0.912513
\(91\) 0 0
\(92\) −1.17157 −0.122145
\(93\) 4.82843 + 8.36308i 0.500685 + 0.867211i
\(94\) 2.58579 4.47871i 0.266704 0.461944i
\(95\) −0.292893 + 0.507306i −0.0300502 + 0.0520485i
\(96\) 1.70711 + 2.95680i 0.174231 + 0.301777i
\(97\) −7.75736 −0.787641 −0.393820 0.919187i \(-0.628847\pi\)
−0.393820 + 0.919187i \(0.628847\pi\)
\(98\) 0 0
\(99\) −7.17157 −0.720770
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) −6.65685 + 11.5300i −0.662382 + 1.14728i 0.317606 + 0.948223i \(0.397121\pi\)
−0.979988 + 0.199056i \(0.936212\pi\)
\(102\) 4.41421 7.64564i 0.437072 0.757031i
\(103\) 7.41421 + 12.8418i 0.730544 + 1.26534i 0.956651 + 0.291237i \(0.0940669\pi\)
−0.226107 + 0.974103i \(0.572600\pi\)
\(104\) 4.82843 0.473466
\(105\) 0 0
\(106\) −6.48528 −0.629906
\(107\) −4.82843 8.36308i −0.466782 0.808490i 0.532498 0.846431i \(-0.321253\pi\)
−0.999280 + 0.0379415i \(0.987920\pi\)
\(108\) −9.65685 + 16.7262i −0.929231 + 1.60948i
\(109\) −1.24264 + 2.15232i −0.119023 + 0.206155i −0.919381 0.393368i \(-0.871310\pi\)
0.800358 + 0.599523i \(0.204643\pi\)
\(110\) −0.414214 0.717439i −0.0394937 0.0684051i
\(111\) −26.1421 −2.48130
\(112\) 0 0
\(113\) −15.3137 −1.44059 −0.720296 0.693667i \(-0.755994\pi\)
−0.720296 + 0.693667i \(0.755994\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 0.585786 1.01461i 0.0546249 0.0946130i
\(116\) 2.41421 4.18154i 0.224154 0.388246i
\(117\) 20.8995 + 36.1990i 1.93216 + 3.34660i
\(118\) −8.58579 −0.790386
\(119\) 0 0
\(120\) −3.41421 −0.311674
\(121\) 5.15685 + 8.93193i 0.468805 + 0.811994i
\(122\) 4.65685 8.06591i 0.421612 0.730253i
\(123\) 5.24264 9.08052i 0.472713 0.818763i
\(124\) 1.41421 + 2.44949i 0.127000 + 0.219971i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 2.82843 0.250982 0.125491 0.992095i \(-0.459949\pi\)
0.125491 + 0.992095i \(0.459949\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) 15.0711 26.1039i 1.32693 2.29832i
\(130\) −2.41421 + 4.18154i −0.211741 + 0.366745i
\(131\) 3.12132 + 5.40629i 0.272711 + 0.472349i 0.969555 0.244873i \(-0.0787464\pi\)
−0.696844 + 0.717223i \(0.745413\pi\)
\(132\) −2.82843 −0.246183
\(133\) 0 0
\(134\) −1.65685 −0.143130
\(135\) −9.65685 16.7262i −0.831130 1.43956i
\(136\) 1.29289 2.23936i 0.110865 0.192023i
\(137\) 8.00000 13.8564i 0.683486 1.18383i −0.290424 0.956898i \(-0.593796\pi\)
0.973910 0.226935i \(-0.0728704\pi\)
\(138\) −2.00000 3.46410i −0.170251 0.294884i
\(139\) 19.8995 1.68785 0.843927 0.536459i \(-0.180238\pi\)
0.843927 + 0.536459i \(0.180238\pi\)
\(140\) 0 0
\(141\) 17.6569 1.48698
\(142\) −2.24264 3.88437i −0.188198 0.325969i
\(143\) −2.00000 + 3.46410i −0.167248 + 0.289683i
\(144\) −4.32843 + 7.49706i −0.360702 + 0.624755i
\(145\) 2.41421 + 4.18154i 0.200490 + 0.347258i
\(146\) 9.41421 0.779126
\(147\) 0 0
\(148\) −7.65685 −0.629390
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 1.70711 2.95680i 0.139385 0.241421i
\(151\) 5.65685 9.79796i 0.460348 0.797347i −0.538630 0.842542i \(-0.681058\pi\)
0.998978 + 0.0451959i \(0.0143912\pi\)
\(152\) 0.292893 + 0.507306i 0.0237568 + 0.0411479i
\(153\) 22.3848 1.80970
\(154\) 0 0
\(155\) −2.82843 −0.227185
\(156\) 8.24264 + 14.2767i 0.659939 + 1.14305i
\(157\) −3.24264 + 5.61642i −0.258791 + 0.448239i −0.965918 0.258847i \(-0.916657\pi\)
0.707127 + 0.707086i \(0.249991\pi\)
\(158\) −3.41421 + 5.91359i −0.271620 + 0.470460i
\(159\) −11.0711 19.1757i −0.877993 1.52073i
\(160\) −1.00000 −0.0790569
\(161\) 0 0
\(162\) −39.9706 −3.14038
\(163\) 10.0711 + 17.4436i 0.788827 + 1.36629i 0.926686 + 0.375836i \(0.122645\pi\)
−0.137859 + 0.990452i \(0.544022\pi\)
\(164\) 1.53553 2.65962i 0.119905 0.207682i
\(165\) 1.41421 2.44949i 0.110096 0.190693i
\(166\) −1.12132 1.94218i −0.0870313 0.150743i
\(167\) 15.7990 1.22256 0.611281 0.791413i \(-0.290654\pi\)
0.611281 + 0.791413i \(0.290654\pi\)
\(168\) 0 0
\(169\) 10.3137 0.793362
\(170\) 1.29289 + 2.23936i 0.0991604 + 0.171751i
\(171\) −2.53553 + 4.39167i −0.193897 + 0.335840i
\(172\) 4.41421 7.64564i 0.336581 0.582975i
\(173\) 4.41421 + 7.64564i 0.335606 + 0.581287i 0.983601 0.180357i \(-0.0577254\pi\)
−0.647995 + 0.761645i \(0.724392\pi\)
\(174\) 16.4853 1.24975
\(175\) 0 0
\(176\) −0.828427 −0.0624450
\(177\) −14.6569 25.3864i −1.10168 1.90816i
\(178\) 6.36396 11.0227i 0.476999 0.826187i
\(179\) −2.00000 + 3.46410i −0.149487 + 0.258919i −0.931038 0.364922i \(-0.881096\pi\)
0.781551 + 0.623841i \(0.214429\pi\)
\(180\) −4.32843 7.49706i −0.322622 0.558798i
\(181\) −2.48528 −0.184730 −0.0923648 0.995725i \(-0.529443\pi\)
−0.0923648 + 0.995725i \(0.529443\pi\)
\(182\) 0 0
\(183\) 31.7990 2.35065
\(184\) −0.585786 1.01461i −0.0431847 0.0747982i
\(185\) 3.82843 6.63103i 0.281472 0.487523i
\(186\) −4.82843 + 8.36308i −0.354037 + 0.613211i
\(187\) 1.07107 + 1.85514i 0.0783242 + 0.135662i
\(188\) 5.17157 0.377176
\(189\) 0 0
\(190\) −0.585786 −0.0424974
\(191\) −5.07107 8.78335i −0.366930 0.635541i 0.622154 0.782895i \(-0.286258\pi\)
−0.989084 + 0.147354i \(0.952924\pi\)
\(192\) −1.70711 + 2.95680i −0.123200 + 0.213388i
\(193\) −2.82843 + 4.89898i −0.203595 + 0.352636i −0.949684 0.313210i \(-0.898596\pi\)
0.746089 + 0.665846i \(0.231929\pi\)
\(194\) −3.87868 6.71807i −0.278473 0.482329i
\(195\) −16.4853 −1.18054
\(196\) 0 0
\(197\) −25.7990 −1.83810 −0.919051 0.394139i \(-0.871043\pi\)
−0.919051 + 0.394139i \(0.871043\pi\)
\(198\) −3.58579 6.21076i −0.254831 0.441380i
\(199\) −8.24264 + 14.2767i −0.584305 + 1.01205i 0.410656 + 0.911790i \(0.365300\pi\)
−0.994962 + 0.100256i \(0.968034\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) −2.82843 4.89898i −0.199502 0.345547i
\(202\) −13.3137 −0.936749
\(203\) 0 0
\(204\) 8.82843 0.618114
\(205\) 1.53553 + 2.65962i 0.107246 + 0.185756i
\(206\) −7.41421 + 12.8418i −0.516573 + 0.894730i
\(207\) 5.07107 8.78335i 0.352464 0.610485i
\(208\) 2.41421 + 4.18154i 0.167396 + 0.289938i
\(209\) −0.485281 −0.0335676
\(210\) 0 0
\(211\) 18.6274 1.28236 0.641182 0.767389i \(-0.278444\pi\)
0.641182 + 0.767389i \(0.278444\pi\)
\(212\) −3.24264 5.61642i −0.222705 0.385737i
\(213\) 7.65685 13.2621i 0.524639 0.908701i
\(214\) 4.82843 8.36308i 0.330064 0.571688i
\(215\) 4.41421 + 7.64564i 0.301047 + 0.521428i
\(216\) −19.3137 −1.31413
\(217\) 0 0
\(218\) −2.48528 −0.168324
\(219\) 16.0711 + 27.8359i 1.08598 + 1.88098i
\(220\) 0.414214 0.717439i 0.0279263 0.0483697i
\(221\) 6.24264 10.8126i 0.419925 0.727332i
\(222\) −13.0711 22.6398i −0.877273 1.51948i
\(223\) −7.31371 −0.489762 −0.244881 0.969553i \(-0.578749\pi\)
−0.244881 + 0.969553i \(0.578749\pi\)
\(224\) 0 0
\(225\) 8.65685 0.577124
\(226\) −7.65685 13.2621i −0.509326 0.882179i
\(227\) −9.12132 + 15.7986i −0.605403 + 1.04859i 0.386584 + 0.922254i \(0.373655\pi\)
−0.991988 + 0.126335i \(0.959679\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) 8.07107 + 13.9795i 0.533351 + 0.923791i 0.999241 + 0.0389487i \(0.0124009\pi\)
−0.465890 + 0.884843i \(0.654266\pi\)
\(230\) 1.17157 0.0772512
\(231\) 0 0
\(232\) 4.82843 0.317002
\(233\) −11.6569 20.1903i −0.763666 1.32271i −0.940949 0.338548i \(-0.890064\pi\)
0.177283 0.984160i \(-0.443269\pi\)
\(234\) −20.8995 + 36.1990i −1.36624 + 2.36640i
\(235\) −2.58579 + 4.47871i −0.168678 + 0.292159i
\(236\) −4.29289 7.43551i −0.279444 0.484010i
\(237\) −23.3137 −1.51439
\(238\) 0 0
\(239\) 1.65685 0.107173 0.0535865 0.998563i \(-0.482935\pi\)
0.0535865 + 0.998563i \(0.482935\pi\)
\(240\) −1.70711 2.95680i −0.110193 0.190860i
\(241\) 6.70711 11.6170i 0.432043 0.748320i −0.565006 0.825087i \(-0.691126\pi\)
0.997049 + 0.0767666i \(0.0244596\pi\)
\(242\) −5.15685 + 8.93193i −0.331495 + 0.574166i
\(243\) −39.2635 68.0063i −2.51875 4.36261i
\(244\) 9.31371 0.596249
\(245\) 0 0
\(246\) 10.4853 0.668517
\(247\) 1.41421 + 2.44949i 0.0899843 + 0.155857i
\(248\) −1.41421 + 2.44949i −0.0898027 + 0.155543i
\(249\) 3.82843 6.63103i 0.242617 0.420224i
\(250\) 0.500000 + 0.866025i 0.0316228 + 0.0547723i
\(251\) 0.585786 0.0369745 0.0184873 0.999829i \(-0.494115\pi\)
0.0184873 + 0.999829i \(0.494115\pi\)
\(252\) 0 0
\(253\) 0.970563 0.0610188
\(254\) 1.41421 + 2.44949i 0.0887357 + 0.153695i
\(255\) −4.41421 + 7.64564i −0.276429 + 0.478789i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 4.94975 + 8.57321i 0.308757 + 0.534782i 0.978091 0.208179i \(-0.0667538\pi\)
−0.669334 + 0.742962i \(0.733420\pi\)
\(258\) 30.1421 1.87657
\(259\) 0 0
\(260\) −4.82843 −0.299446
\(261\) 20.8995 + 36.1990i 1.29365 + 2.24066i
\(262\) −3.12132 + 5.40629i −0.192836 + 0.334001i
\(263\) −14.0000 + 24.2487i −0.863277 + 1.49524i 0.00547092 + 0.999985i \(0.498259\pi\)
−0.868748 + 0.495255i \(0.835075\pi\)
\(264\) −1.41421 2.44949i −0.0870388 0.150756i
\(265\) 6.48528 0.398388
\(266\) 0 0
\(267\) 43.4558 2.65945
\(268\) −0.828427 1.43488i −0.0506042 0.0876491i
\(269\) −9.24264 + 16.0087i −0.563534 + 0.976069i 0.433651 + 0.901081i \(0.357225\pi\)
−0.997184 + 0.0749880i \(0.976108\pi\)
\(270\) 9.65685 16.7262i 0.587697 1.01792i
\(271\) −6.00000 10.3923i −0.364474 0.631288i 0.624218 0.781251i \(-0.285418\pi\)
−0.988692 + 0.149963i \(0.952085\pi\)
\(272\) 2.58579 0.156786
\(273\) 0 0
\(274\) 16.0000 0.966595
\(275\) 0.414214 + 0.717439i 0.0249780 + 0.0432632i
\(276\) 2.00000 3.46410i 0.120386 0.208514i
\(277\) 4.07107 7.05130i 0.244607 0.423671i −0.717414 0.696647i \(-0.754674\pi\)
0.962021 + 0.272976i \(0.0880078\pi\)
\(278\) 9.94975 + 17.2335i 0.596746 + 1.03359i
\(279\) −24.4853 −1.46590
\(280\) 0 0
\(281\) 8.00000 0.477240 0.238620 0.971113i \(-0.423305\pi\)
0.238620 + 0.971113i \(0.423305\pi\)
\(282\) 8.82843 + 15.2913i 0.525725 + 0.910583i
\(283\) 1.12132 1.94218i 0.0666556 0.115451i −0.830772 0.556613i \(-0.812100\pi\)
0.897427 + 0.441163i \(0.145434\pi\)
\(284\) 2.24264 3.88437i 0.133076 0.230495i
\(285\) −1.00000 1.73205i −0.0592349 0.102598i
\(286\) −4.00000 −0.236525
\(287\) 0 0
\(288\) −8.65685 −0.510110
\(289\) 5.15685 + 8.93193i 0.303344 + 0.525408i
\(290\) −2.41421 + 4.18154i −0.141768 + 0.245549i
\(291\) 13.2426 22.9369i 0.776297 1.34459i
\(292\) 4.70711 + 8.15295i 0.275463 + 0.477115i
\(293\) −8.34315 −0.487412 −0.243706 0.969849i \(-0.578363\pi\)
−0.243706 + 0.969849i \(0.578363\pi\)
\(294\) 0 0
\(295\) 8.58579 0.499884
\(296\) −3.82843 6.63103i −0.222523 0.385421i
\(297\) 8.00000 13.8564i 0.464207 0.804030i
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) −2.82843 4.89898i −0.163572 0.283315i
\(300\) 3.41421 0.197120
\(301\) 0 0
\(302\) 11.3137 0.651031
\(303\) −22.7279 39.3659i −1.30569 2.26151i
\(304\) −0.292893 + 0.507306i −0.0167986 + 0.0290960i
\(305\) −4.65685 + 8.06591i −0.266651 + 0.461853i
\(306\) 11.1924 + 19.3858i 0.639826 + 1.10821i
\(307\) 14.9289 0.852039 0.426020 0.904714i \(-0.359915\pi\)
0.426020 + 0.904714i \(0.359915\pi\)
\(308\) 0 0
\(309\) −50.6274 −2.88009
\(310\) −1.41421 2.44949i −0.0803219 0.139122i
\(311\) −2.00000 + 3.46410i −0.113410 + 0.196431i −0.917143 0.398559i \(-0.869511\pi\)
0.803733 + 0.594990i \(0.202844\pi\)
\(312\) −8.24264 + 14.2767i −0.466648 + 0.808257i
\(313\) −7.19239 12.4576i −0.406538 0.704144i 0.587961 0.808889i \(-0.299931\pi\)
−0.994499 + 0.104745i \(0.966597\pi\)
\(314\) −6.48528 −0.365986
\(315\) 0 0
\(316\) −6.82843 −0.384129
\(317\) −5.24264 9.08052i −0.294456 0.510013i 0.680402 0.732839i \(-0.261805\pi\)
−0.974858 + 0.222826i \(0.928472\pi\)
\(318\) 11.0711 19.1757i 0.620835 1.07532i
\(319\) −2.00000 + 3.46410i −0.111979 + 0.193952i
\(320\) −0.500000 0.866025i −0.0279508 0.0484123i
\(321\) 32.9706 1.84024
\(322\) 0 0
\(323\) 1.51472 0.0842812
\(324\) −19.9853 34.6155i −1.11029 1.92308i
\(325\) 2.41421 4.18154i 0.133916 0.231950i
\(326\) −10.0711 + 17.4436i −0.557785 + 0.966112i
\(327\) −4.24264 7.34847i −0.234619 0.406371i
\(328\) 3.07107 0.169571
\(329\) 0 0
\(330\) 2.82843 0.155700
\(331\) −16.8995 29.2708i −0.928880 1.60887i −0.785199 0.619244i \(-0.787439\pi\)
−0.143681 0.989624i \(-0.545894\pi\)
\(332\) 1.12132 1.94218i 0.0615404 0.106591i
\(333\) 33.1421 57.4039i 1.81618 3.14571i
\(334\) 7.89949 + 13.6823i 0.432241 + 0.748664i
\(335\) 1.65685 0.0905236
\(336\) 0 0
\(337\) 6.00000 0.326841 0.163420 0.986557i \(-0.447747\pi\)
0.163420 + 0.986557i \(0.447747\pi\)
\(338\) 5.15685 + 8.93193i 0.280496 + 0.485833i
\(339\) 26.1421 45.2795i 1.41985 2.45925i
\(340\) −1.29289 + 2.23936i −0.0701170 + 0.121446i
\(341\) −1.17157 2.02922i −0.0634442 0.109889i
\(342\) −5.07107 −0.274212
\(343\) 0 0
\(344\) 8.82843 0.475997
\(345\) 2.00000 + 3.46410i 0.107676 + 0.186501i
\(346\) −4.41421 + 7.64564i −0.237310 + 0.411032i
\(347\) 1.58579 2.74666i 0.0851295 0.147449i −0.820317 0.571909i \(-0.806203\pi\)
0.905446 + 0.424461i \(0.139536\pi\)
\(348\) 8.24264 + 14.2767i 0.441852 + 0.765310i
\(349\) 2.48528 0.133034 0.0665170 0.997785i \(-0.478811\pi\)
0.0665170 + 0.997785i \(0.478811\pi\)
\(350\) 0 0
\(351\) −93.2548 −4.97757
\(352\) −0.414214 0.717439i −0.0220777 0.0382396i
\(353\) 1.19239 2.06528i 0.0634644 0.109924i −0.832547 0.553954i \(-0.813118\pi\)
0.896012 + 0.444030i \(0.146452\pi\)
\(354\) 14.6569 25.3864i 0.779003 1.34927i
\(355\) 2.24264 + 3.88437i 0.119027 + 0.206161i
\(356\) 12.7279 0.674579
\(357\) 0 0
\(358\) −4.00000 −0.211407
\(359\) −14.1421 24.4949i −0.746393 1.29279i −0.949541 0.313643i \(-0.898450\pi\)
0.203148 0.979148i \(-0.434883\pi\)
\(360\) 4.32843 7.49706i 0.228128 0.395130i
\(361\) 9.32843 16.1573i 0.490970 0.850385i
\(362\) −1.24264 2.15232i −0.0653117 0.113123i
\(363\) −35.2132 −1.84821
\(364\) 0 0
\(365\) −9.41421 −0.492762
\(366\) 15.8995 + 27.5387i 0.831080 + 1.43947i
\(367\) −12.4853 + 21.6251i −0.651726 + 1.12882i 0.330977 + 0.943639i \(0.392622\pi\)
−0.982704 + 0.185185i \(0.940712\pi\)
\(368\) 0.585786 1.01461i 0.0305362 0.0528903i
\(369\) 13.2929 + 23.0240i 0.692000 + 1.19858i
\(370\) 7.65685 0.398061
\(371\) 0 0
\(372\) −9.65685 −0.500685
\(373\) 15.2426 + 26.4010i 0.789234 + 1.36699i 0.926437 + 0.376450i \(0.122855\pi\)
−0.137203 + 0.990543i \(0.543811\pi\)
\(374\) −1.07107 + 1.85514i −0.0553836 + 0.0959272i
\(375\) −1.70711 + 2.95680i −0.0881546 + 0.152688i
\(376\) 2.58579 + 4.47871i 0.133352 + 0.230972i
\(377\) 23.3137 1.20072
\(378\) 0 0
\(379\) 34.4853 1.77139 0.885695 0.464268i \(-0.153682\pi\)
0.885695 + 0.464268i \(0.153682\pi\)
\(380\) −0.292893 0.507306i −0.0150251 0.0260242i
\(381\) −4.82843 + 8.36308i −0.247368 + 0.428454i
\(382\) 5.07107 8.78335i 0.259458 0.449395i
\(383\) 16.2426 + 28.1331i 0.829960 + 1.43753i 0.898069 + 0.439855i \(0.144970\pi\)
−0.0681085 + 0.997678i \(0.521696\pi\)
\(384\) −3.41421 −0.174231
\(385\) 0 0
\(386\) −5.65685 −0.287926
\(387\) 38.2132 + 66.1872i 1.94249 + 3.36448i
\(388\) 3.87868 6.71807i 0.196910 0.341058i
\(389\) −14.0711 + 24.3718i −0.713431 + 1.23570i 0.250130 + 0.968212i \(0.419527\pi\)
−0.963561 + 0.267487i \(0.913807\pi\)
\(390\) −8.24264 14.2767i −0.417382 0.722927i
\(391\) −3.02944 −0.153205
\(392\) 0 0
\(393\) −21.3137 −1.07513
\(394\) −12.8995 22.3426i −0.649867 1.12560i
\(395\) 3.41421 5.91359i 0.171788 0.297545i
\(396\) 3.58579 6.21076i 0.180193 0.312103i
\(397\) −16.8995 29.2708i −0.848161 1.46906i −0.882847 0.469660i \(-0.844376\pi\)
0.0346859 0.999398i \(-0.488957\pi\)
\(398\) −16.4853 −0.826332
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 3.00000 + 5.19615i 0.149813 + 0.259483i 0.931158 0.364615i \(-0.118800\pi\)
−0.781345 + 0.624099i \(0.785466\pi\)
\(402\) 2.82843 4.89898i 0.141069 0.244339i
\(403\) −6.82843 + 11.8272i −0.340148 + 0.589154i
\(404\) −6.65685 11.5300i −0.331191 0.573639i
\(405\) 39.9706 1.98615
\(406\) 0 0
\(407\) 6.34315 0.314418
\(408\) 4.41421 + 7.64564i 0.218536 + 0.378516i
\(409\) 5.29289 9.16756i 0.261717 0.453307i −0.704981 0.709226i \(-0.749045\pi\)
0.966698 + 0.255919i \(0.0823781\pi\)
\(410\) −1.53553 + 2.65962i −0.0758346 + 0.131349i
\(411\) 27.3137 + 47.3087i 1.34729 + 2.33357i
\(412\) −14.8284 −0.730544
\(413\) 0 0
\(414\) 10.1421 0.498459
\(415\) 1.12132 + 1.94218i 0.0550435 + 0.0953381i
\(416\) −2.41421 + 4.18154i −0.118367 + 0.205017i
\(417\) −33.9706 + 58.8387i −1.66355 + 2.88135i
\(418\) −0.242641 0.420266i −0.0118679 0.0205559i
\(419\) −20.8701 −1.01957 −0.509785 0.860302i \(-0.670275\pi\)
−0.509785 + 0.860302i \(0.670275\pi\)
\(420\) 0 0
\(421\) 17.3137 0.843819 0.421909 0.906638i \(-0.361360\pi\)
0.421909 + 0.906638i \(0.361360\pi\)
\(422\) 9.31371 + 16.1318i 0.453384 + 0.785285i
\(423\) −22.3848 + 38.7716i −1.08839 + 1.88514i
\(424\) 3.24264 5.61642i 0.157477 0.272757i
\(425\) −1.29289 2.23936i −0.0627145 0.108625i
\(426\) 15.3137 0.741952
\(427\) 0 0
\(428\) 9.65685 0.466782
\(429\) −6.82843 11.8272i −0.329680 0.571022i
\(430\) −4.41421 + 7.64564i −0.212872 + 0.368706i
\(431\) 11.1716 19.3497i 0.538116 0.932044i −0.460890 0.887457i \(-0.652470\pi\)
0.999006 0.0445864i \(-0.0141970\pi\)
\(432\) −9.65685 16.7262i −0.464616 0.804738i
\(433\) 10.5858 0.508720 0.254360 0.967110i \(-0.418135\pi\)
0.254360 + 0.967110i \(0.418135\pi\)
\(434\) 0 0
\(435\) −16.4853 −0.790409
\(436\) −1.24264 2.15232i −0.0595117 0.103077i
\(437\) 0.343146 0.594346i 0.0164149 0.0284314i
\(438\) −16.0711 + 27.8359i −0.767905 + 1.33005i
\(439\) 12.4853 + 21.6251i 0.595890 + 1.03211i 0.993421 + 0.114523i \(0.0365339\pi\)
−0.397531 + 0.917589i \(0.630133\pi\)
\(440\) 0.828427 0.0394937
\(441\) 0 0
\(442\) 12.4853 0.593864
\(443\) −1.51472 2.62357i −0.0719665 0.124650i 0.827797 0.561028i \(-0.189594\pi\)
−0.899763 + 0.436379i \(0.856261\pi\)
\(444\) 13.0711 22.6398i 0.620325 1.07444i
\(445\) −6.36396 + 11.0227i −0.301681 + 0.522526i
\(446\) −3.65685 6.33386i −0.173157 0.299917i
\(447\) −20.4853 −0.968921
\(448\) 0 0
\(449\) −16.6274 −0.784696 −0.392348 0.919817i \(-0.628337\pi\)
−0.392348 + 0.919817i \(0.628337\pi\)
\(450\) 4.32843 + 7.49706i 0.204044 + 0.353415i
\(451\) −1.27208 + 2.20330i −0.0598998 + 0.103750i
\(452\) 7.65685 13.2621i 0.360148 0.623795i
\(453\) 19.3137 + 33.4523i 0.907437 + 1.57173i
\(454\) −18.2426 −0.856170
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) −10.8284 18.7554i −0.506532 0.877340i −0.999971 0.00755953i \(-0.997594\pi\)
0.493439 0.869780i \(-0.335740\pi\)
\(458\) −8.07107 + 13.9795i −0.377136 + 0.653219i
\(459\) −24.9706 + 43.2503i −1.16553 + 2.01875i
\(460\) 0.585786 + 1.01461i 0.0273124 + 0.0473065i
\(461\) −12.8284 −0.597479 −0.298740 0.954335i \(-0.596566\pi\)
−0.298740 + 0.954335i \(0.596566\pi\)
\(462\) 0 0
\(463\) −16.9706 −0.788689 −0.394344 0.918963i \(-0.629028\pi\)
−0.394344 + 0.918963i \(0.629028\pi\)
\(464\) 2.41421 + 4.18154i 0.112077 + 0.194123i
\(465\) 4.82843 8.36308i 0.223913 0.387829i
\(466\) 11.6569 20.1903i 0.539993 0.935296i
\(467\) 7.94975 + 13.7694i 0.367870 + 0.637170i 0.989232 0.146353i \(-0.0467537\pi\)
−0.621362 + 0.783524i \(0.713420\pi\)
\(468\) −41.7990 −1.93216
\(469\) 0 0
\(470\) −5.17157 −0.238547
\(471\) −11.0711 19.1757i −0.510128 0.883567i
\(472\) 4.29289 7.43551i 0.197596 0.342247i
\(473\) −3.65685 + 6.33386i −0.168142 + 0.291231i
\(474\) −11.6569 20.1903i −0.535417 0.927370i
\(475\) 0.585786 0.0268777
\(476\) 0 0
\(477\) 56.1421 2.57057
\(478\) 0.828427 + 1.43488i 0.0378914 + 0.0656298i
\(479\) 8.58579 14.8710i 0.392295 0.679474i −0.600457 0.799657i \(-0.705015\pi\)
0.992752 + 0.120183i \(0.0383480\pi\)
\(480\) 1.70711 2.95680i 0.0779184 0.134959i
\(481\) −18.4853 32.0174i −0.842856 1.45987i
\(482\) 13.4142 0.611001
\(483\) 0 0
\(484\) −10.3137 −0.468805
\(485\) 3.87868 + 6.71807i 0.176122 + 0.305052i
\(486\) 39.2635 68.0063i 1.78103 3.08483i
\(487\) −15.8995 + 27.5387i −0.720475 + 1.24790i 0.240335 + 0.970690i \(0.422743\pi\)
−0.960810 + 0.277209i \(0.910591\pi\)
\(488\) 4.65685 + 8.06591i 0.210806 + 0.365127i
\(489\) −68.7696 −3.10987
\(490\) 0 0
\(491\) 32.2843 1.45697 0.728484 0.685062i \(-0.240225\pi\)
0.728484 + 0.685062i \(0.240225\pi\)
\(492\) 5.24264 + 9.08052i 0.236356 + 0.409381i
\(493\) 6.24264 10.8126i 0.281154 0.486974i
\(494\) −1.41421 + 2.44949i −0.0636285 + 0.110208i
\(495\) 3.58579 + 6.21076i 0.161169 + 0.279153i
\(496\) −2.82843 −0.127000
\(497\) 0 0
\(498\) 7.65685 0.343112
\(499\) −15.1716 26.2779i −0.679173 1.17636i −0.975230 0.221192i \(-0.929005\pi\)
0.296057 0.955170i \(-0.404328\pi\)
\(500\) −0.500000 + 0.866025i −0.0223607 + 0.0387298i
\(501\) −26.9706 + 46.7144i −1.20496 + 2.08704i
\(502\) 0.292893 + 0.507306i 0.0130725 + 0.0226422i
\(503\) 17.6569 0.787280 0.393640 0.919265i \(-0.371216\pi\)
0.393640 + 0.919265i \(0.371216\pi\)
\(504\) 0 0
\(505\) 13.3137 0.592452
\(506\) 0.485281 + 0.840532i 0.0215734 + 0.0373662i
\(507\) −17.6066 + 30.4955i −0.781937 + 1.35435i
\(508\) −1.41421 + 2.44949i −0.0627456 + 0.108679i
\(509\) −2.89949 5.02207i −0.128518 0.222599i 0.794585 0.607153i \(-0.207689\pi\)
−0.923103 + 0.384554i \(0.874355\pi\)
\(510\) −8.82843 −0.390929
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −5.65685 9.79796i −0.249756 0.432590i
\(514\) −4.94975 + 8.57321i −0.218324 + 0.378148i
\(515\) 7.41421 12.8418i 0.326709 0.565877i
\(516\) 15.0711 + 26.1039i 0.663467 + 1.14916i
\(517\) −4.28427 −0.188422
\(518\) 0 0
\(519\) −30.1421 −1.32309
\(520\) −2.41421 4.18154i −0.105870 0.183373i
\(521\) −9.53553 + 16.5160i −0.417759 + 0.723580i −0.995714 0.0924887i \(-0.970518\pi\)
0.577954 + 0.816069i \(0.303851\pi\)
\(522\) −20.8995 + 36.1990i −0.914746 + 1.58439i
\(523\) −11.9497 20.6976i −0.522526 0.905042i −0.999656 0.0262091i \(-0.991656\pi\)
0.477131 0.878832i \(-0.341677\pi\)
\(524\) −6.24264 −0.272711
\(525\) 0 0
\(526\) −28.0000 −1.22086
\(527\) 3.65685 + 6.33386i 0.159295 + 0.275907i
\(528\) 1.41421 2.44949i 0.0615457 0.106600i
\(529\) 10.8137 18.7299i 0.470161 0.814343i
\(530\) 3.24264 + 5.61642i 0.140851 + 0.243962i
\(531\) 74.3259 3.22547
\(532\) 0 0
\(533\) 14.8284 0.642290
\(534\) 21.7279 + 37.6339i 0.940259 + 1.62858i
\(535\) −4.82843 + 8.36308i −0.208751 + 0.361568i
\(536\) 0.828427 1.43488i 0.0357826 0.0619773i
\(537\) −6.82843 11.8272i −0.294668 0.510381i
\(538\) −18.4853 −0.796957
\(539\) 0 0
\(540\) 19.3137 0.831130
\(541\) 7.48528 + 12.9649i 0.321817 + 0.557404i 0.980863 0.194699i \(-0.0623730\pi\)
−0.659046 + 0.752103i \(0.729040\pi\)
\(542\) 6.00000 10.3923i 0.257722 0.446388i
\(543\) 4.24264 7.34847i 0.182069 0.315353i
\(544\) 1.29289 + 2.23936i 0.0554323 + 0.0960116i
\(545\) 2.48528 0.106458
\(546\) 0 0
\(547\) −10.4853 −0.448318 −0.224159 0.974553i \(-0.571964\pi\)
−0.224159 + 0.974553i \(0.571964\pi\)
\(548\) 8.00000 + 13.8564i 0.341743 + 0.591916i
\(549\) −40.3137 + 69.8254i −1.72055 + 2.98008i
\(550\) −0.414214 + 0.717439i −0.0176621 + 0.0305917i
\(551\) 1.41421 + 2.44949i 0.0602475 + 0.104352i
\(552\) 4.00000 0.170251
\(553\) 0 0
\(554\) 8.14214 0.345926
\(555\) 13.0711 + 22.6398i 0.554836 + 0.961004i
\(556\) −9.94975 + 17.2335i −0.421963 + 0.730862i
\(557\) −7.58579 + 13.1390i −0.321420 + 0.556716i −0.980781 0.195110i \(-0.937493\pi\)
0.659361 + 0.751826i \(0.270827\pi\)
\(558\) −12.2426 21.2049i −0.518272 0.897674i
\(559\) 42.6274 1.80295
\(560\) 0 0
\(561\) −7.31371 −0.308785
\(562\) 4.00000 + 6.92820i 0.168730 + 0.292249i
\(563\) 18.2929 31.6842i 0.770954 1.33533i −0.166087 0.986111i \(-0.553113\pi\)
0.937041 0.349220i \(-0.113553\pi\)
\(564\) −8.82843 + 15.2913i −0.371744 + 0.643879i
\(565\) 7.65685 + 13.2621i 0.322126 + 0.557939i
\(566\) 2.24264 0.0942652
\(567\) 0 0
\(568\) 4.48528 0.188198
\(569\) 14.6569 + 25.3864i 0.614447 + 1.06425i 0.990481 + 0.137648i \(0.0439543\pi\)
−0.376034 + 0.926606i \(0.622712\pi\)
\(570\) 1.00000 1.73205i 0.0418854 0.0725476i
\(571\) 1.10051 1.90613i 0.0460547 0.0797691i −0.842079 0.539354i \(-0.818668\pi\)
0.888134 + 0.459585i \(0.152002\pi\)
\(572\) −2.00000 3.46410i −0.0836242 0.144841i
\(573\) 34.6274 1.44658
\(574\) 0 0
\(575\) −1.17157 −0.0488580
\(576\) −4.32843 7.49706i −0.180351 0.312377i
\(577\) −3.05025 + 5.28319i −0.126984 + 0.219942i −0.922507 0.385981i \(-0.873863\pi\)
0.795523 + 0.605923i \(0.207196\pi\)
\(578\) −5.15685 + 8.93193i −0.214497 + 0.371519i
\(579\) −9.65685 16.7262i −0.401325 0.695116i
\(580\) −4.82843 −0.200490
\(581\) 0 0
\(582\) 26.4853 1.09785
\(583\) 2.68629 + 4.65279i 0.111255 + 0.192699i
\(584\) −4.70711 + 8.15295i −0.194781 + 0.337371i
\(585\) 20.8995 36.1990i 0.864088 1.49664i
\(586\) −4.17157 7.22538i −0.172326 0.298478i
\(587\) 17.0711 0.704598 0.352299 0.935887i \(-0.385400\pi\)
0.352299 + 0.935887i \(0.385400\pi\)
\(588\) 0 0
\(589\) −1.65685 −0.0682695
\(590\) 4.29289 + 7.43551i 0.176736 + 0.306115i
\(591\) 44.0416 76.2823i 1.81163 3.13784i
\(592\) 3.82843 6.63103i 0.157347 0.272534i
\(593\) −1.63604 2.83370i −0.0671841 0.116366i 0.830477 0.557053i \(-0.188068\pi\)
−0.897661 + 0.440687i \(0.854735\pi\)
\(594\) 16.0000 0.656488
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −28.1421 48.7436i −1.15178 1.99494i
\(598\) 2.82843 4.89898i 0.115663 0.200334i
\(599\) 5.41421 9.37769i 0.221219 0.383162i −0.733960 0.679193i \(-0.762330\pi\)
0.955178 + 0.296031i \(0.0956632\pi\)
\(600\) 1.70711 + 2.95680i 0.0696923 + 0.120711i
\(601\) 6.58579 0.268640 0.134320 0.990938i \(-0.457115\pi\)
0.134320 + 0.990938i \(0.457115\pi\)
\(602\) 0 0
\(603\) 14.3431 0.584098
\(604\) 5.65685 + 9.79796i 0.230174 + 0.398673i
\(605\) 5.15685 8.93193i 0.209656 0.363135i
\(606\) 22.7279 39.3659i 0.923259 1.59913i
\(607\) −8.14214 14.1026i −0.330479 0.572407i 0.652127 0.758110i \(-0.273877\pi\)
−0.982606 + 0.185703i \(0.940544\pi\)
\(608\) −0.585786 −0.0237568
\(609\) 0 0
\(610\) −9.31371 −0.377101
\(611\) 12.4853 + 21.6251i 0.505100 + 0.874860i
\(612\) −11.1924 + 19.3858i −0.452425 + 0.783624i
\(613\) 6.17157 10.6895i 0.249267 0.431744i −0.714055 0.700089i \(-0.753144\pi\)
0.963323 + 0.268345i \(0.0864768\pi\)
\(614\) 7.46447 + 12.9288i 0.301241 + 0.521765i
\(615\) −10.4853 −0.422807
\(616\) 0 0
\(617\) −33.3137 −1.34116 −0.670580 0.741837i \(-0.733955\pi\)
−0.670580 + 0.741837i \(0.733955\pi\)
\(618\) −25.3137 43.8446i −1.01827 1.76369i
\(619\) −14.5355 + 25.1763i −0.584232 + 1.01192i 0.410738 + 0.911753i \(0.365271\pi\)
−0.994971 + 0.100167i \(0.968062\pi\)
\(620\) 1.41421 2.44949i 0.0567962 0.0983739i
\(621\) 11.3137 + 19.5959i 0.454003 + 0.786357i
\(622\) −4.00000 −0.160385
\(623\) 0 0
\(624\) −16.4853 −0.659939
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 7.19239 12.4576i 0.287466 0.497905i
\(627\) 0.828427 1.43488i 0.0330842 0.0573035i
\(628\) −3.24264 5.61642i −0.129395 0.224119i
\(629\) −19.7990 −0.789437
\(630\) 0 0
\(631\) −12.4853 −0.497031 −0.248516 0.968628i \(-0.579943\pi\)
−0.248516 + 0.968628i \(0.579943\pi\)
\(632\) −3.41421 5.91359i −0.135810 0.235230i
\(633\) −31.7990 + 55.0775i −1.26390 + 2.18913i
\(634\) 5.24264 9.08052i 0.208212 0.360634i
\(635\) −1.41421 2.44949i −0.0561214 0.0972050i
\(636\) 22.1421 0.877993
\(637\) 0 0
\(638\) −4.00000 −0.158362
\(639\) 19.4142 + 33.6264i 0.768014 + 1.33024i
\(640\) 0.500000 0.866025i 0.0197642 0.0342327i
\(641\) 12.3137 21.3280i 0.486362 0.842404i −0.513515 0.858081i \(-0.671657\pi\)
0.999877 + 0.0156766i \(0.00499021\pi\)
\(642\) 16.4853 + 28.5533i 0.650622 + 1.12691i
\(643\) 4.78680 0.188773 0.0943864 0.995536i \(-0.469911\pi\)
0.0943864 + 0.995536i \(0.469911\pi\)
\(644\) 0 0
\(645\) −30.1421 −1.18685
\(646\) 0.757359 + 1.31178i 0.0297979 + 0.0516115i
\(647\) 11.5563 20.0162i 0.454327 0.786917i −0.544322 0.838876i \(-0.683213\pi\)
0.998649 + 0.0519588i \(0.0165465\pi\)
\(648\) 19.9853 34.6155i 0.785096 1.35983i
\(649\) 3.55635 + 6.15978i 0.139599 + 0.241792i
\(650\) 4.82843 0.189386
\(651\) 0 0
\(652\) −20.1421 −0.788827
\(653\) −2.17157 3.76127i −0.0849802 0.147190i 0.820403 0.571786i \(-0.193749\pi\)
−0.905383 + 0.424596i \(0.860416\pi\)
\(654\) 4.24264 7.34847i 0.165900 0.287348i
\(655\) 3.12132 5.40629i 0.121960 0.211241i
\(656\) 1.53553 + 2.65962i 0.0599525 + 0.103841i
\(657\) −81.4975 −3.17952
\(658\) 0 0
\(659\) −27.1716 −1.05845 −0.529227 0.848480i \(-0.677518\pi\)
−0.529227 + 0.848480i \(0.677518\pi\)
\(660\) 1.41421 + 2.44949i 0.0550482 + 0.0953463i
\(661\) 19.1421 33.1552i 0.744543 1.28959i −0.205865 0.978580i \(-0.566001\pi\)
0.950408 0.311006i \(-0.100666\pi\)
\(662\) 16.8995 29.2708i 0.656818 1.13764i
\(663\) 21.3137 + 36.9164i 0.827756 + 1.43372i
\(664\) 2.24264 0.0870313
\(665\) 0 0
\(666\) 66.2843 2.56846
\(667\) −2.82843 4.89898i −0.109517 0.189689i
\(668\) −7.89949 + 13.6823i −0.305641 + 0.529385i
\(669\) 12.4853 21.6251i 0.482709 0.836076i
\(670\) 0.828427 + 1.43488i 0.0320049 + 0.0554342i
\(671\) −7.71573 −0.297862
\(672\) 0 0
\(673\) −48.0000 −1.85026 −0.925132 0.379646i \(-0.876046\pi\)
−0.925132 + 0.379646i \(0.876046\pi\)
\(674\) 3.00000 + 5.19615i 0.115556 + 0.200148i
\(675\) −9.65685 + 16.7262i −0.371692 + 0.643790i
\(676\) −5.15685 + 8.93193i −0.198341 + 0.343536i
\(677\) −19.7279 34.1698i −0.758206 1.31325i −0.943765 0.330618i \(-0.892743\pi\)
0.185559 0.982633i \(-0.440590\pi\)
\(678\) 52.2843 2.00797
\(679\) 0 0
\(680\) −2.58579 −0.0991604
\(681\) −31.1421 53.9398i −1.19337 2.06698i
\(682\) 1.17157 2.02922i 0.0448618 0.0777030i
\(683\) −16.8284 + 29.1477i −0.643922 + 1.11531i 0.340628 + 0.940198i \(0.389360\pi\)
−0.984549 + 0.175107i \(0.943973\pi\)
\(684\) −2.53553 4.39167i −0.0969486 0.167920i
\(685\) −16.0000 −0.611329
\(686\) 0 0
\(687\) −55.1127 −2.10268
\(688\) 4.41421 + 7.64564i 0.168290 + 0.291487i
\(689\) 15.6569 27.1185i 0.596479 1.03313i
\(690\) −2.00000 + 3.46410i −0.0761387 + 0.131876i
\(691\) −0.878680 1.52192i −0.0334265 0.0578965i 0.848828 0.528669i \(-0.177309\pi\)
−0.882255 + 0.470772i \(0.843975\pi\)
\(692\) −8.82843 −0.335606
\(693\) 0 0
\(694\) 3.17157 0.120391
\(695\) −9.94975 17.2335i −0.377415 0.653703i
\(696\) −8.24264 + 14.2767i −0.312436 + 0.541156i
\(697\) 3.97056 6.87722i 0.150396 0.260493i
\(698\) 1.24264 + 2.15232i 0.0470346 + 0.0814664i
\(699\) 79.5980 3.01067
\(700\) 0 0
\(701\) 2.48528 0.0938678 0.0469339 0.998898i \(-0.485055\pi\)
0.0469339 + 0.998898i \(0.485055\pi\)
\(702\) −46.6274 80.7611i −1.75984 3.04813i
\(703\) 2.24264 3.88437i 0.0845828 0.146502i
\(704\) 0.414214 0.717439i 0.0156113 0.0270395i
\(705\) −8.82843 15.2913i −0.332498 0.575903i
\(706\) 2.38478 0.0897522
\(707\) 0 0
\(708\) 29.3137 1.10168
\(709\) −22.5563 39.0687i −0.847121 1.46726i −0.883766 0.467929i \(-0.845000\pi\)
0.0366445 0.999328i \(-0.488333\pi\)
\(710\) −2.24264 + 3.88437i −0.0841648 + 0.145778i
\(711\) 29.5563 51.1931i 1.10845 1.91989i
\(712\) 6.36396 + 11.0227i 0.238500 + 0.413093i
\(713\) 3.31371 0.124099
\(714\) 0 0
\(715\) 4.00000 0.149592
\(716\) −2.00000 3.46410i −0.0747435 0.129460i
\(717\) −2.82843 + 4.89898i −0.105630 + 0.182956i
\(718\) 14.1421 24.4949i 0.527780 0.914141i
\(719\) −20.7279 35.9018i −0.773021 1.33891i −0.935900 0.352266i \(-0.885411\pi\)
0.162879 0.986646i \(-0.447922\pi\)
\(720\) 8.65685 0.322622
\(721\) 0 0
\(722\) 18.6569 0.694336
\(723\) 22.8995 + 39.6631i 0.851641 + 1.47509i
\(724\) 1.24264 2.15232i 0.0461824 0.0799902i
\(725\) 2.41421 4.18154i 0.0896616 0.155299i
\(726\) −17.6066 30.4955i −0.653442 1.13180i
\(727\) −3.51472 −0.130354 −0.0651768 0.997874i \(-0.520761\pi\)
−0.0651768 + 0.997874i \(0.520761\pi\)
\(728\) 0 0
\(729\) 148.196 5.48874
\(730\) −4.70711 8.15295i −0.174218 0.301754i
\(731\) 11.4142 19.7700i 0.422170 0.731220i
\(732\) −15.8995 + 27.5387i −0.587662 + 1.01786i
\(733\) −17.0000 29.4449i −0.627909 1.08757i −0.987971 0.154642i \(-0.950578\pi\)
0.360061 0.932929i \(-0.382756\pi\)
\(734\) −24.9706 −0.921680
\(735\) 0 0
\(736\) 1.17157 0.0431847
\(737\) 0.686292 + 1.18869i 0.0252799 + 0.0437860i
\(738\) −13.2929 + 23.0240i −0.489318 + 0.847524i
\(739\) −1.58579 + 2.74666i −0.0583341 + 0.101038i −0.893718 0.448630i \(-0.851912\pi\)
0.835384 + 0.549667i \(0.185246\pi\)
\(740\) 3.82843 + 6.63103i 0.140736 + 0.243762i
\(741\) −9.65685 −0.354753
\(742\) 0 0
\(743\) 51.7990 1.90032 0.950160 0.311762i \(-0.100919\pi\)
0.950160 + 0.311762i \(0.100919\pi\)
\(744\) −4.82843 8.36308i −0.177019 0.306605i
\(745\) 3.00000 5.19615i 0.109911 0.190372i
\(746\) −15.2426 + 26.4010i −0.558073 + 0.966610i
\(747\) 9.70711 + 16.8132i 0.355164 + 0.615163i
\(748\) −2.14214 −0.0783242
\(749\) 0 0
\(750\) −3.41421 −0.124669
\(751\) 19.6569 + 34.0467i 0.717289 + 1.24238i 0.962070 + 0.272802i \(0.0879505\pi\)
−0.244781 + 0.969578i \(0.578716\pi\)
\(752\) −2.58579 + 4.47871i −0.0942939 + 0.163322i
\(753\) −1.00000 + 1.73205i −0.0364420 + 0.0631194i
\(754\) 11.6569 + 20.1903i 0.424518 + 0.735286i
\(755\) −11.3137 −0.411748
\(756\) 0 0
\(757\) 3.65685 0.132911 0.0664553 0.997789i \(-0.478831\pi\)
0.0664553 + 0.997789i \(0.478831\pi\)
\(758\) 17.2426 + 29.8651i 0.626281 + 1.08475i
\(759\) −1.65685 + 2.86976i −0.0601400 + 0.104166i
\(760\) 0.292893 0.507306i 0.0106244 0.0184019i
\(761\) −11.1924 19.3858i −0.405724 0.702734i 0.588682 0.808365i \(-0.299647\pi\)
−0.994405 + 0.105631i \(0.966314\pi\)
\(762\) −9.65685 −0.349831
\(763\) 0 0
\(764\) 10.1421 0.366930
\(765\) −11.1924 19.3858i −0.404662 0.700895i
\(766\) −16.2426 + 28.1331i −0.586870 + 1.01649i
\(767\) 20.7279 35.9018i 0.748442 1.29634i
\(768\) −1.70711 2.95680i −0.0615999 0.106694i
\(769\) 19.5563 0.705220 0.352610 0.935770i \(-0.385294\pi\)
0.352610 + 0.935770i \(0.385294\pi\)
\(770\) 0 0
\(771\) −33.7990 −1.21724
\(772\) −2.82843 4.89898i −0.101797 0.176318i
\(773\) 1.00000 1.73205i 0.0359675 0.0622975i −0.847481 0.530825i \(-0.821882\pi\)
0.883449 + 0.468528i \(0.155215\pi\)
\(774\) −38.2132 + 66.1872i −1.37355 + 2.37905i
\(775\) 1.41421 + 2.44949i 0.0508001 + 0.0879883i
\(776\) 7.75736 0.278473
\(777\) 0 0
\(778\) −28.1421 −1.00894
\(779\) 0.899495 + 1.55797i 0.0322278 + 0.0558201i
\(780\) 8.24264 14.2767i 0.295134 0.511187i
\(781\) −1.85786 + 3.21792i −0.0664796 + 0.115146i
\(782\) −1.51472 2.62357i −0.0541662 0.0938187i