Properties

Label 1050.2.bc.g.943.2
Level $1050$
Weight $2$
Character 1050.943
Analytic conductor $8.384$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1050.bc (of order \(12\), degree \(4\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(8.38429221223\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(4\) over \(\Q(\zeta_{12})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} - \cdots)\)
Defining polynomial: \(x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} - 180 x^{7} + 358 x^{6} - 336 x^{5} + 390 x^{4} - 344 x^{3} + 164 x^{2} - 40 x + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 210)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 943.2
Root \(0.277956 - 0.213283i\) of defining polynomial
Character \(\chi\) \(=\) 1050.943
Dual form 1050.2.bc.g.157.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(1.87796 - 1.86367i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\) \(q+(-0.258819 - 0.965926i) q^{2} +(0.965926 + 0.258819i) q^{3} +(-0.866025 + 0.500000i) q^{4} -1.00000i q^{6} +(1.87796 - 1.86367i) q^{7} +(0.707107 + 0.707107i) q^{8} +(0.866025 + 0.500000i) q^{9} +(-2.74315 - 4.75127i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(2.41668 - 2.41668i) q^{13} +(-2.28622 - 1.33161i) q^{14} +(0.500000 - 0.866025i) q^{16} +(0.548242 - 2.04607i) q^{17} +(0.258819 - 0.965926i) q^{18} +(-3.49797 + 6.05866i) q^{19} +(2.29632 - 1.31412i) q^{21} +(-3.87940 + 3.87940i) q^{22} +(-1.69461 + 0.454069i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-2.95981 - 1.70885i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.694523 + 2.55297i) q^{28} -0.684610i q^{29} +(4.82932 - 2.78821i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-1.41996 - 5.29936i) q^{33} -2.11825 q^{34} -1.00000 q^{36} +(-2.53646 - 9.46620i) q^{37} +(6.75755 + 1.81068i) q^{38} +(2.95981 - 1.70885i) q^{39} +2.50597i q^{41} +(-1.86367 - 1.87796i) q^{42} +(1.95305 + 1.95305i) q^{43} +(4.75127 + 2.74315i) q^{44} +(0.877194 + 1.51935i) q^{46} +(3.40506 - 0.912383i) q^{47} +(0.707107 - 0.707107i) q^{48} +(0.0534500 - 6.99980i) q^{49} +(1.05912 - 1.83445i) q^{51} +(-0.884566 + 3.30124i) q^{52} +(2.43353 - 9.08204i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.64573 + 0.0101012i) q^{56} +(-4.94687 + 4.94687i) q^{57} +(-0.661282 + 0.177190i) q^{58} +(-5.08015 - 8.79907i) q^{59} +(1.01469 + 0.585830i) q^{61} +(-3.94312 - 3.94312i) q^{62} +(2.55820 - 0.675009i) q^{63} +1.00000i q^{64} +(-4.75127 + 2.74315i) q^{66} +(9.61398 + 2.57606i) q^{67} +(0.548242 + 2.04607i) q^{68} -1.75439 q^{69} -11.9716 q^{71} +(0.258819 + 0.965926i) q^{72} +(-4.70482 - 1.26065i) q^{73} +(-8.48716 + 4.90007i) q^{74} -6.99593i q^{76} +(-14.0063 - 3.81036i) q^{77} +(-2.41668 - 2.41668i) q^{78} +(7.21474 + 4.16543i) q^{79} +(0.500000 + 0.866025i) q^{81} +(2.42058 - 0.648592i) q^{82} +(4.05281 - 4.05281i) q^{83} +(-1.33161 + 2.28622i) q^{84} +(1.38101 - 2.39198i) q^{86} +(0.177190 - 0.661282i) q^{87} +(1.41996 - 5.29936i) q^{88} +(-3.59178 + 6.22115i) q^{89} +(0.0345228 - 9.04232i) q^{91} +(1.24054 - 1.24054i) q^{92} +(5.38640 - 1.44328i) q^{93} +(-1.76259 - 3.05289i) q^{94} +(-0.866025 - 0.500000i) q^{96} +(13.1212 + 13.1212i) q^{97} +(-6.77512 + 1.76005i) q^{98} -5.48630i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 4q^{7} + O(q^{10}) \) \( 16q + 4q^{7} + 4q^{11} - 16q^{13} - 16q^{14} + 8q^{16} - 12q^{17} + 8q^{19} + 8q^{21} - 4q^{22} + 40q^{23} + 8q^{24} - 12q^{26} + 4q^{28} - 24q^{31} - 4q^{33} - 16q^{34} - 16q^{36} + 8q^{37} + 20q^{38} + 12q^{39} - 8q^{42} + 24q^{43} - 4q^{46} - 52q^{49} + 8q^{51} - 8q^{52} + 28q^{53} + 8q^{54} + 8q^{56} + 8q^{57} + 12q^{58} - 8q^{59} + 24q^{61} + 8q^{62} + 4q^{63} + 84q^{67} - 12q^{68} + 8q^{69} - 32q^{71} - 16q^{73} + 24q^{74} - 44q^{77} + 16q^{78} - 12q^{79} + 8q^{81} - 36q^{82} - 16q^{83} - 4q^{84} - 8q^{86} - 48q^{87} + 4q^{88} + 16q^{89} + 8q^{91} - 8q^{92} + 32q^{93} - 8q^{94} + 44q^{97} - 24q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).

\(n\) \(127\) \(451\) \(701\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(e\left(\frac{5}{6}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.258819 0.965926i −0.183013 0.683013i
\(3\) 0.965926 + 0.258819i 0.557678 + 0.149429i
\(4\) −0.866025 + 0.500000i −0.433013 + 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 1.87796 1.86367i 0.709801 0.704402i
\(8\) 0.707107 + 0.707107i 0.250000 + 0.250000i
\(9\) 0.866025 + 0.500000i 0.288675 + 0.166667i
\(10\) 0 0
\(11\) −2.74315 4.75127i −0.827091 1.43256i −0.900311 0.435247i \(-0.856661\pi\)
0.0732202 0.997316i \(-0.476672\pi\)
\(12\) −0.965926 + 0.258819i −0.278839 + 0.0747146i
\(13\) 2.41668 2.41668i 0.670266 0.670266i −0.287511 0.957777i \(-0.592828\pi\)
0.957777 + 0.287511i \(0.0928279\pi\)
\(14\) −2.28622 1.33161i −0.611018 0.355889i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 0.548242 2.04607i 0.132968 0.496244i −0.867030 0.498256i \(-0.833974\pi\)
0.999998 + 0.00201209i \(0.000640467\pi\)
\(18\) 0.258819 0.965926i 0.0610042 0.227671i
\(19\) −3.49797 + 6.05866i −0.802489 + 1.38995i 0.115485 + 0.993309i \(0.463158\pi\)
−0.917974 + 0.396642i \(0.870176\pi\)
\(20\) 0 0
\(21\) 2.29632 1.31412i 0.501098 0.286764i
\(22\) −3.87940 + 3.87940i −0.827091 + 0.827091i
\(23\) −1.69461 + 0.454069i −0.353350 + 0.0946800i −0.431128 0.902291i \(-0.641884\pi\)
0.0777776 + 0.996971i \(0.475218\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) 0 0
\(26\) −2.95981 1.70885i −0.580467 0.335133i
\(27\) 0.707107 + 0.707107i 0.136083 + 0.136083i
\(28\) −0.694523 + 2.55297i −0.131252 + 0.482465i
\(29\) 0.684610i 0.127129i −0.997978 0.0635644i \(-0.979753\pi\)
0.997978 0.0635644i \(-0.0202468\pi\)
\(30\) 0 0
\(31\) 4.82932 2.78821i 0.867371 0.500777i 0.000897301 1.00000i \(-0.499714\pi\)
0.866474 + 0.499223i \(0.166381\pi\)
\(32\) −0.965926 0.258819i −0.170753 0.0457532i
\(33\) −1.41996 5.29936i −0.247183 0.922500i
\(34\) −2.11825 −0.363276
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) −2.53646 9.46620i −0.416992 1.55623i −0.780813 0.624765i \(-0.785195\pi\)
0.363821 0.931469i \(-0.381472\pi\)
\(38\) 6.75755 + 1.81068i 1.09622 + 0.293731i
\(39\) 2.95981 1.70885i 0.473950 0.273635i
\(40\) 0 0
\(41\) 2.50597i 0.391366i 0.980667 + 0.195683i \(0.0626924\pi\)
−0.980667 + 0.195683i \(0.937308\pi\)
\(42\) −1.86367 1.87796i −0.287571 0.289775i
\(43\) 1.95305 + 1.95305i 0.297837 + 0.297837i 0.840166 0.542329i \(-0.182457\pi\)
−0.542329 + 0.840166i \(0.682457\pi\)
\(44\) 4.75127 + 2.74315i 0.716282 + 0.413545i
\(45\) 0 0
\(46\) 0.877194 + 1.51935i 0.129335 + 0.224015i
\(47\) 3.40506 0.912383i 0.496679 0.133085i −0.00177938 0.999998i \(-0.500566\pi\)
0.498458 + 0.866914i \(0.333900\pi\)
\(48\) 0.707107 0.707107i 0.102062 0.102062i
\(49\) 0.0534500 6.99980i 0.00763571 0.999971i
\(50\) 0 0
\(51\) 1.05912 1.83445i 0.148307 0.256875i
\(52\) −0.884566 + 3.30124i −0.122667 + 0.457800i
\(53\) 2.43353 9.08204i 0.334270 1.24751i −0.570388 0.821376i \(-0.693207\pi\)
0.904658 0.426138i \(-0.140126\pi\)
\(54\) 0.500000 0.866025i 0.0680414 0.117851i
\(55\) 0 0
\(56\) 2.64573 + 0.0101012i 0.353551 + 0.00134983i
\(57\) −4.94687 + 4.94687i −0.655229 + 0.655229i
\(58\) −0.661282 + 0.177190i −0.0868306 + 0.0232662i
\(59\) −5.08015 8.79907i −0.661379 1.14554i −0.980253 0.197745i \(-0.936638\pi\)
0.318875 0.947797i \(-0.396695\pi\)
\(60\) 0 0
\(61\) 1.01469 + 0.585830i 0.129917 + 0.0750079i 0.563550 0.826082i \(-0.309435\pi\)
−0.433633 + 0.901090i \(0.642768\pi\)
\(62\) −3.94312 3.94312i −0.500777 0.500777i
\(63\) 2.55820 0.675009i 0.322302 0.0850431i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −4.75127 + 2.74315i −0.584841 + 0.337658i
\(67\) 9.61398 + 2.57606i 1.17454 + 0.314716i 0.792757 0.609538i \(-0.208645\pi\)
0.381778 + 0.924254i \(0.375312\pi\)
\(68\) 0.548242 + 2.04607i 0.0664841 + 0.248122i
\(69\) −1.75439 −0.211204
\(70\) 0 0
\(71\) −11.9716 −1.42077 −0.710383 0.703816i \(-0.751478\pi\)
−0.710383 + 0.703816i \(0.751478\pi\)
\(72\) 0.258819 + 0.965926i 0.0305021 + 0.113835i
\(73\) −4.70482 1.26065i −0.550657 0.147548i −0.0272467 0.999629i \(-0.508674\pi\)
−0.523411 + 0.852081i \(0.675341\pi\)
\(74\) −8.48716 + 4.90007i −0.986613 + 0.569621i
\(75\) 0 0
\(76\) 6.99593i 0.802489i
\(77\) −14.0063 3.81036i −1.59617 0.434231i
\(78\) −2.41668 2.41668i −0.273635 0.273635i
\(79\) 7.21474 + 4.16543i 0.811722 + 0.468648i 0.847553 0.530710i \(-0.178075\pi\)
−0.0358316 + 0.999358i \(0.511408\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 2.42058 0.648592i 0.267308 0.0716250i
\(83\) 4.05281 4.05281i 0.444854 0.444854i −0.448786 0.893639i \(-0.648143\pi\)
0.893639 + 0.448786i \(0.148143\pi\)
\(84\) −1.33161 + 2.28622i −0.145291 + 0.249447i
\(85\) 0 0
\(86\) 1.38101 2.39198i 0.148918 0.257934i
\(87\) 0.177190 0.661282i 0.0189968 0.0708969i
\(88\) 1.41996 5.29936i 0.151368 0.564913i
\(89\) −3.59178 + 6.22115i −0.380728 + 0.659440i −0.991166 0.132623i \(-0.957660\pi\)
0.610439 + 0.792064i \(0.290993\pi\)
\(90\) 0 0
\(91\) 0.0345228 9.04232i 0.00361897 0.947892i
\(92\) 1.24054 1.24054i 0.129335 0.129335i
\(93\) 5.38640 1.44328i 0.558544 0.149661i
\(94\) −1.76259 3.05289i −0.181797 0.314882i
\(95\) 0 0
\(96\) −0.866025 0.500000i −0.0883883 0.0510310i
\(97\) 13.1212 + 13.1212i 1.33226 + 1.33226i 0.903348 + 0.428909i \(0.141102\pi\)
0.428909 + 0.903348i \(0.358898\pi\)
\(98\) −6.77512 + 1.76005i −0.684390 + 0.177792i
\(99\) 5.48630i 0.551394i
\(100\) 0 0
\(101\) 7.16001 4.13383i 0.712447 0.411332i −0.0995192 0.995036i \(-0.531730\pi\)
0.811967 + 0.583704i \(0.198397\pi\)
\(102\) −2.04607 0.548242i −0.202591 0.0542841i
\(103\) 2.40862 + 8.98910i 0.237329 + 0.885722i 0.977085 + 0.212848i \(0.0682739\pi\)
−0.739757 + 0.672874i \(0.765059\pi\)
\(104\) 3.41770 0.335133
\(105\) 0 0
\(106\) −9.40242 −0.913244
\(107\) 3.17510 + 11.8496i 0.306949 + 1.14555i 0.931255 + 0.364369i \(0.118715\pi\)
−0.624306 + 0.781180i \(0.714618\pi\)
\(108\) −0.965926 0.258819i −0.0929463 0.0249049i
\(109\) −0.291523 + 0.168311i −0.0279228 + 0.0161213i −0.513896 0.857852i \(-0.671798\pi\)
0.485974 + 0.873973i \(0.338465\pi\)
\(110\) 0 0
\(111\) 9.80013i 0.930188i
\(112\) −0.675009 2.55820i −0.0637823 0.241727i
\(113\) −10.1896 10.1896i −0.958555 0.958555i 0.0406198 0.999175i \(-0.487067\pi\)
−0.999175 + 0.0406198i \(0.987067\pi\)
\(114\) 6.05866 + 3.49797i 0.567445 + 0.327615i
\(115\) 0 0
\(116\) 0.342305 + 0.592889i 0.0317822 + 0.0550484i
\(117\) 3.30124 0.884566i 0.305200 0.0817781i
\(118\) −7.18441 + 7.18441i −0.661379 + 0.661379i
\(119\) −2.78362 4.86417i −0.255174 0.445898i
\(120\) 0 0
\(121\) −9.54974 + 16.5406i −0.868158 + 1.50369i
\(122\) 0.303248 1.13174i 0.0274548 0.102463i
\(123\) −0.648592 + 2.42058i −0.0584816 + 0.218256i
\(124\) −2.78821 + 4.82932i −0.250388 + 0.433686i
\(125\) 0 0
\(126\) −1.31412 2.29632i −0.117071 0.204573i
\(127\) 4.77054 4.77054i 0.423317 0.423317i −0.463027 0.886344i \(-0.653237\pi\)
0.886344 + 0.463027i \(0.153237\pi\)
\(128\) 0.965926 0.258819i 0.0853766 0.0228766i
\(129\) 1.38101 + 2.39198i 0.121591 + 0.210602i
\(130\) 0 0
\(131\) 15.7695 + 9.10455i 1.37779 + 0.795468i 0.991893 0.127074i \(-0.0405585\pi\)
0.385898 + 0.922542i \(0.373892\pi\)
\(132\) 3.87940 + 3.87940i 0.337658 + 0.337658i
\(133\) 4.72232 + 17.8970i 0.409477 + 1.55186i
\(134\) 9.95313i 0.859819i
\(135\) 0 0
\(136\) 1.83445 1.05912i 0.157303 0.0908190i
\(137\) 2.11024 + 0.565438i 0.180290 + 0.0483086i 0.347835 0.937556i \(-0.386917\pi\)
−0.167544 + 0.985865i \(0.553584\pi\)
\(138\) 0.454069 + 1.69461i 0.0386529 + 0.144255i
\(139\) −18.1446 −1.53900 −0.769501 0.638645i \(-0.779495\pi\)
−0.769501 + 0.638645i \(0.779495\pi\)
\(140\) 0 0
\(141\) 3.52518 0.296873
\(142\) 3.09847 + 11.5637i 0.260018 + 0.970401i
\(143\) −18.1116 4.85299i −1.51457 0.405828i
\(144\) 0.866025 0.500000i 0.0721688 0.0416667i
\(145\) 0 0
\(146\) 4.87079i 0.403109i
\(147\) 1.86331 6.74745i 0.153683 0.556520i
\(148\) 6.92974 + 6.92974i 0.569621 + 0.569621i
\(149\) −0.167711 0.0968279i −0.0137394 0.00793245i 0.493115 0.869964i \(-0.335858\pi\)
−0.506854 + 0.862032i \(0.669192\pi\)
\(150\) 0 0
\(151\) 10.6614 + 18.4660i 0.867610 + 1.50274i 0.864432 + 0.502750i \(0.167678\pi\)
0.00317777 + 0.999995i \(0.498988\pi\)
\(152\) −6.75755 + 1.81068i −0.548110 + 0.146866i
\(153\) 1.49783 1.49783i 0.121092 0.121092i
\(154\) −0.0554181 + 14.5153i −0.00446571 + 1.16967i
\(155\) 0 0
\(156\) −1.70885 + 2.95981i −0.136817 + 0.236975i
\(157\) 0.952462 3.55464i 0.0760147 0.283691i −0.917447 0.397859i \(-0.869753\pi\)
0.993461 + 0.114168i \(0.0364201\pi\)
\(158\) 2.15619 8.04700i 0.171537 0.640185i
\(159\) 4.70121 8.14273i 0.372830 0.645761i
\(160\) 0 0
\(161\) −2.33617 + 4.01092i −0.184116 + 0.316105i
\(162\) 0.707107 0.707107i 0.0555556 0.0555556i
\(163\) −13.6012 + 3.64443i −1.06533 + 0.285454i −0.748572 0.663054i \(-0.769260\pi\)
−0.316756 + 0.948507i \(0.602594\pi\)
\(164\) −1.25298 2.17023i −0.0978416 0.169467i
\(165\) 0 0
\(166\) −4.96366 2.86577i −0.385255 0.222427i
\(167\) −6.07259 6.07259i −0.469911 0.469911i 0.431974 0.901886i \(-0.357817\pi\)
−0.901886 + 0.431974i \(0.857817\pi\)
\(168\) 2.55297 + 0.694523i 0.196966 + 0.0535836i
\(169\) 1.31933i 0.101487i
\(170\) 0 0
\(171\) −6.05866 + 3.49797i −0.463317 + 0.267496i
\(172\) −2.66791 0.714864i −0.203426 0.0545079i
\(173\) 1.04797 + 3.91108i 0.0796757 + 0.297354i 0.994253 0.107058i \(-0.0341430\pi\)
−0.914577 + 0.404412i \(0.867476\pi\)
\(174\) −0.684610 −0.0519001
\(175\) 0 0
\(176\) −5.48630 −0.413545
\(177\) −2.62968 9.81409i −0.197659 0.737672i
\(178\) 6.93879 + 1.85924i 0.520084 + 0.139356i
\(179\) 3.17428 1.83267i 0.237256 0.136980i −0.376659 0.926352i \(-0.622927\pi\)
0.613915 + 0.789372i \(0.289594\pi\)
\(180\) 0 0
\(181\) 2.39985i 0.178379i −0.996015 0.0891896i \(-0.971572\pi\)
0.996015 0.0891896i \(-0.0284277\pi\)
\(182\) −8.74314 + 2.30698i −0.648085 + 0.171005i
\(183\) 0.828489 + 0.828489i 0.0612437 + 0.0612437i
\(184\) −1.51935 0.877194i −0.112008 0.0646676i
\(185\) 0 0
\(186\) −2.78821 4.82932i −0.204441 0.354103i
\(187\) −11.2253 + 3.00782i −0.820878 + 0.219954i
\(188\) −2.49268 + 2.49268i −0.181797 + 0.181797i
\(189\) 2.64573 + 0.0101012i 0.192449 + 0.000734752i
\(190\) 0 0
\(191\) −4.03766 + 6.99344i −0.292155 + 0.506027i −0.974319 0.225172i \(-0.927706\pi\)
0.682164 + 0.731199i \(0.261039\pi\)
\(192\) −0.258819 + 0.965926i −0.0186787 + 0.0697097i
\(193\) 0.445821 1.66383i 0.0320909 0.119765i −0.948022 0.318204i \(-0.896920\pi\)
0.980113 + 0.198439i \(0.0635871\pi\)
\(194\) 9.27809 16.0701i 0.666128 1.15377i
\(195\) 0 0
\(196\) 3.45361 + 6.08873i 0.246686 + 0.434909i
\(197\) −6.01174 + 6.01174i −0.428319 + 0.428319i −0.888055 0.459737i \(-0.847944\pi\)
0.459737 + 0.888055i \(0.347944\pi\)
\(198\) −5.29936 + 1.41996i −0.376609 + 0.100912i
\(199\) 5.50897 + 9.54181i 0.390520 + 0.676401i 0.992518 0.122097i \(-0.0389618\pi\)
−0.601998 + 0.798498i \(0.705628\pi\)
\(200\) 0 0
\(201\) 8.61966 + 4.97656i 0.607984 + 0.351020i
\(202\) −5.84612 5.84612i −0.411332 0.411332i
\(203\) −1.27589 1.28567i −0.0895498 0.0902362i
\(204\) 2.11825i 0.148307i
\(205\) 0 0
\(206\) 8.05941 4.65310i 0.561526 0.324197i
\(207\) −1.69461 0.454069i −0.117783 0.0315600i
\(208\) −0.884566 3.30124i −0.0613336 0.228900i
\(209\) 38.3818 2.65492
\(210\) 0 0
\(211\) 10.3323 0.711302 0.355651 0.934619i \(-0.384259\pi\)
0.355651 + 0.934619i \(0.384259\pi\)
\(212\) 2.43353 + 9.08204i 0.167135 + 0.623757i
\(213\) −11.5637 3.09847i −0.792329 0.212304i
\(214\) 10.6241 6.13383i 0.726249 0.419300i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 3.87295 14.2364i 0.262913 0.966430i
\(218\) 0.238027 + 0.238027i 0.0161213 + 0.0161213i
\(219\) −4.21822 2.43539i −0.285041 0.164569i
\(220\) 0 0
\(221\) −3.61976 6.26961i −0.243492 0.421740i
\(222\) −9.46620 + 2.53646i −0.635330 + 0.170236i
\(223\) −3.41183 + 3.41183i −0.228473 + 0.228473i −0.812054 0.583582i \(-0.801651\pi\)
0.583582 + 0.812054i \(0.301651\pi\)
\(224\) −2.29632 + 1.31412i −0.153429 + 0.0878032i
\(225\) 0 0
\(226\) −7.20512 + 12.4796i −0.479277 + 0.830133i
\(227\) 4.68301 17.4772i 0.310822 1.16000i −0.616994 0.786968i \(-0.711650\pi\)
0.927816 0.373037i \(-0.121684\pi\)
\(228\) 1.81068 6.75755i 0.119915 0.447530i
\(229\) 4.82375 8.35497i 0.318762 0.552112i −0.661468 0.749973i \(-0.730066\pi\)
0.980230 + 0.197861i \(0.0633996\pi\)
\(230\) 0 0
\(231\) −12.5429 7.30563i −0.825262 0.480675i
\(232\) 0.484092 0.484092i 0.0317822 0.0317822i
\(233\) 13.9801 3.74597i 0.915870 0.245407i 0.230051 0.973179i \(-0.426111\pi\)
0.685819 + 0.727772i \(0.259444\pi\)
\(234\) −1.70885 2.95981i −0.111711 0.193489i
\(235\) 0 0
\(236\) 8.79907 + 5.08015i 0.572771 + 0.330689i
\(237\) 5.89081 + 5.89081i 0.382649 + 0.382649i
\(238\) −3.97798 + 3.94772i −0.257854 + 0.255892i
\(239\) 29.9736i 1.93883i 0.245427 + 0.969415i \(0.421072\pi\)
−0.245427 + 0.969415i \(0.578928\pi\)
\(240\) 0 0
\(241\) 14.3934 8.31003i 0.927161 0.535296i 0.0412481 0.999149i \(-0.486867\pi\)
0.885912 + 0.463853i \(0.153533\pi\)
\(242\) 18.4487 + 4.94331i 1.18593 + 0.317768i
\(243\) 0.258819 + 0.965926i 0.0166032 + 0.0619642i
\(244\) −1.17166 −0.0750079
\(245\) 0 0
\(246\) 2.50597 0.159775
\(247\) 6.18836 + 23.0953i 0.393756 + 1.46952i
\(248\) 5.38640 + 1.44328i 0.342037 + 0.0916485i
\(249\) 4.96366 2.86577i 0.314559 0.181611i
\(250\) 0 0
\(251\) 10.7660i 0.679546i 0.940508 + 0.339773i \(0.110350\pi\)
−0.940508 + 0.339773i \(0.889650\pi\)
\(252\) −1.87796 + 1.86367i −0.118300 + 0.117400i
\(253\) 6.80597 + 6.80597i 0.427888 + 0.427888i
\(254\) −5.84270 3.37328i −0.366604 0.211659i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 14.5299 3.89328i 0.906352 0.242856i 0.224610 0.974449i \(-0.427889\pi\)
0.681742 + 0.731593i \(0.261223\pi\)
\(258\) 1.95305 1.95305i 0.121591 0.121591i
\(259\) −22.4053 13.0500i −1.39220 0.810887i
\(260\) 0 0
\(261\) 0.342305 0.592889i 0.0211881 0.0366989i
\(262\) 4.71286 17.5886i 0.291161 1.08663i
\(263\) −5.83157 + 21.7637i −0.359590 + 1.34201i 0.515019 + 0.857179i \(0.327785\pi\)
−0.874609 + 0.484829i \(0.838882\pi\)
\(264\) 2.74315 4.75127i 0.168829 0.292421i
\(265\) 0 0
\(266\) 16.0649 9.19348i 0.985003 0.563689i
\(267\) −5.07954 + 5.07954i −0.310863 + 0.310863i
\(268\) −9.61398 + 2.57606i −0.587268 + 0.157358i
\(269\) 5.52122 + 9.56304i 0.336635 + 0.583069i 0.983797 0.179283i \(-0.0573779\pi\)
−0.647163 + 0.762352i \(0.724045\pi\)
\(270\) 0 0
\(271\) 4.34433 + 2.50820i 0.263899 + 0.152362i 0.626112 0.779733i \(-0.284645\pi\)
−0.362213 + 0.932095i \(0.617979\pi\)
\(272\) −1.49783 1.49783i −0.0908190 0.0908190i
\(273\) 2.37367 8.72527i 0.143661 0.528077i
\(274\) 2.18468i 0.131982i
\(275\) 0 0
\(276\) 1.51935 0.877194i 0.0914538 0.0528009i
\(277\) 6.11920 + 1.63963i 0.367667 + 0.0985161i 0.437922 0.899013i \(-0.355715\pi\)
−0.0702549 + 0.997529i \(0.522381\pi\)
\(278\) 4.69616 + 17.5263i 0.281657 + 1.05116i
\(279\) 5.57642 0.333851
\(280\) 0 0
\(281\) −29.4723 −1.75817 −0.879085 0.476665i \(-0.841846\pi\)
−0.879085 + 0.476665i \(0.841846\pi\)
\(282\) −0.912383 3.40506i −0.0543316 0.202768i
\(283\) 0.0944925 + 0.0253192i 0.00561700 + 0.00150507i 0.261626 0.965169i \(-0.415741\pi\)
−0.256009 + 0.966674i \(0.582408\pi\)
\(284\) 10.3677 5.98579i 0.615210 0.355191i
\(285\) 0 0
\(286\) 18.7505i 1.10874i
\(287\) 4.67030 + 4.70610i 0.275679 + 0.277792i
\(288\) −0.707107 0.707107i −0.0416667 0.0416667i
\(289\) 10.8366 + 6.25652i 0.637447 + 0.368030i
\(290\) 0 0
\(291\) 9.27809 + 16.0701i 0.543891 + 0.942048i
\(292\) 4.70482 1.26065i 0.275329 0.0737741i
\(293\) 14.0076 14.0076i 0.818330 0.818330i −0.167536 0.985866i \(-0.553581\pi\)
0.985866 + 0.167536i \(0.0535810\pi\)
\(294\) −6.99980 0.0534500i −0.408236 0.00311727i
\(295\) 0 0
\(296\) 4.90007 8.48716i 0.284811 0.493306i
\(297\) 1.41996 5.29936i 0.0823944 0.307500i
\(298\) −0.0501218 + 0.187057i −0.00290348 + 0.0108359i
\(299\) −2.99799 + 5.19266i −0.173378 + 0.300300i
\(300\) 0 0
\(301\) 7.30758 + 0.0278997i 0.421202 + 0.00160811i
\(302\) 15.0775 15.0775i 0.867610 0.867610i
\(303\) 7.98595 2.13983i 0.458781 0.122930i
\(304\) 3.49797 + 6.05866i 0.200622 + 0.347488i
\(305\) 0 0
\(306\) −1.83445 1.05912i −0.104869 0.0605460i
\(307\) 3.05320 + 3.05320i 0.174255 + 0.174255i 0.788846 0.614591i \(-0.210679\pi\)
−0.614591 + 0.788846i \(0.710679\pi\)
\(308\) 14.0350 3.70330i 0.799720 0.211015i
\(309\) 9.30620i 0.529411i
\(310\) 0 0
\(311\) −7.31386 + 4.22266i −0.414731 + 0.239445i −0.692820 0.721110i \(-0.743632\pi\)
0.278089 + 0.960555i \(0.410299\pi\)
\(312\) 3.30124 + 0.884566i 0.186896 + 0.0500787i
\(313\) 5.02358 + 18.7482i 0.283949 + 1.05971i 0.949604 + 0.313453i \(0.101486\pi\)
−0.665654 + 0.746260i \(0.731847\pi\)
\(314\) −3.68003 −0.207676
\(315\) 0 0
\(316\) −8.33087 −0.468648
\(317\) 4.02471 + 15.0204i 0.226050 + 0.843632i 0.981981 + 0.188980i \(0.0605181\pi\)
−0.755931 + 0.654652i \(0.772815\pi\)
\(318\) −9.08204 2.43353i −0.509296 0.136465i
\(319\) −3.25277 + 1.87799i −0.182120 + 0.105147i
\(320\) 0 0
\(321\) 12.2677i 0.684714i
\(322\) 4.47890 + 1.21846i 0.249599 + 0.0679023i
\(323\) 10.4787 + 10.4787i 0.583050 + 0.583050i
\(324\) −0.866025 0.500000i −0.0481125 0.0277778i
\(325\) 0 0
\(326\) 7.04050 + 12.1945i 0.389937 + 0.675391i
\(327\) −0.325151 + 0.0871241i −0.0179809 + 0.00481797i
\(328\) −1.77199 + 1.77199i −0.0978416 + 0.0978416i
\(329\) 4.69417 8.05933i 0.258798 0.444325i
\(330\) 0 0
\(331\) −8.09296 + 14.0174i −0.444830 + 0.770467i −0.998040 0.0625739i \(-0.980069\pi\)
0.553211 + 0.833041i \(0.313402\pi\)
\(332\) −1.48343 + 5.53624i −0.0814139 + 0.303841i
\(333\) 2.53646 9.46620i 0.138997 0.518745i
\(334\) −4.29397 + 7.43738i −0.234956 + 0.406955i
\(335\) 0 0
\(336\) 0.0101012 2.64573i 0.000551064 0.144337i
\(337\) −19.2055 + 19.2055i −1.04619 + 1.04619i −0.0473073 + 0.998880i \(0.515064\pi\)
−0.998880 + 0.0473073i \(0.984936\pi\)
\(338\) 1.27438 0.341468i 0.0693169 0.0185734i
\(339\) −7.20512 12.4796i −0.391328 0.677801i
\(340\) 0 0
\(341\) −26.4951 15.2969i −1.43479 0.828376i
\(342\) 4.94687 + 4.94687i 0.267496 + 0.267496i
\(343\) −12.9450 13.2449i −0.698962 0.715159i
\(344\) 2.76202i 0.148918i
\(345\) 0 0
\(346\) 3.50658 2.02452i 0.188515 0.108839i
\(347\) 9.91592 + 2.65696i 0.532315 + 0.142633i 0.514957 0.857216i \(-0.327808\pi\)
0.0173577 + 0.999849i \(0.494475\pi\)
\(348\) 0.177190 + 0.661282i 0.00949838 + 0.0354484i
\(349\) 6.61441 0.354061 0.177031 0.984205i \(-0.443351\pi\)
0.177031 + 0.984205i \(0.443351\pi\)
\(350\) 0 0
\(351\) 3.41770 0.182423
\(352\) 1.41996 + 5.29936i 0.0756841 + 0.282457i
\(353\) −13.1604 3.52633i −0.700460 0.187688i −0.109023 0.994039i \(-0.534772\pi\)
−0.591436 + 0.806352i \(0.701439\pi\)
\(354\) −8.79907 + 5.08015i −0.467666 + 0.270007i
\(355\) 0 0
\(356\) 7.18356i 0.380728i
\(357\) −1.42983 5.41889i −0.0756749 0.286798i
\(358\) −2.59178 2.59178i −0.136980 0.136980i
\(359\) −14.9791 8.64822i −0.790569 0.456435i 0.0495937 0.998769i \(-0.484207\pi\)
−0.840163 + 0.542334i \(0.817541\pi\)
\(360\) 0 0
\(361\) −14.9715 25.9315i −0.787976 1.36481i
\(362\) −2.31807 + 0.621126i −0.121835 + 0.0326457i
\(363\) −13.5054 + 13.5054i −0.708848 + 0.708848i
\(364\) 4.49126 + 7.84814i 0.235406 + 0.411354i
\(365\) 0 0
\(366\) 0.585830 1.01469i 0.0306218 0.0530386i
\(367\) 6.69852 24.9992i 0.349660 1.30495i −0.537413 0.843319i \(-0.680598\pi\)
0.887073 0.461629i \(-0.152735\pi\)
\(368\) −0.454069 + 1.69461i −0.0236700 + 0.0883376i
\(369\) −1.25298 + 2.17023i −0.0652277 + 0.112978i
\(370\) 0 0
\(371\) −12.3559 21.5910i −0.641486 1.12095i
\(372\) −3.94312 + 3.94312i −0.204441 + 0.204441i
\(373\) 8.85404 2.37243i 0.458445 0.122840i −0.0222033 0.999753i \(-0.507068\pi\)
0.480648 + 0.876914i \(0.340401\pi\)
\(374\) 5.81066 + 10.0644i 0.300462 + 0.520416i
\(375\) 0 0
\(376\) 3.05289 + 1.76259i 0.157441 + 0.0908985i
\(377\) −1.65448 1.65448i −0.0852101 0.0852101i
\(378\) −0.675009 2.55820i −0.0347187 0.131579i
\(379\) 18.6871i 0.959891i 0.877298 + 0.479946i \(0.159344\pi\)
−0.877298 + 0.479946i \(0.840656\pi\)
\(380\) 0 0
\(381\) 5.84270 3.37328i 0.299331 0.172819i
\(382\) 7.80016 + 2.09005i 0.399091 + 0.106936i
\(383\) 5.13534 + 19.1654i 0.262404 + 0.979304i 0.963820 + 0.266553i \(0.0858846\pi\)
−0.701417 + 0.712752i \(0.747449\pi\)
\(384\) 1.00000 0.0510310
\(385\) 0 0
\(386\) −1.72252 −0.0876740
\(387\) 0.714864 + 2.66791i 0.0363386 + 0.135618i
\(388\) −17.9239 4.80269i −0.909948 0.243820i
\(389\) −4.44026 + 2.56359i −0.225130 + 0.129979i −0.608323 0.793689i \(-0.708158\pi\)
0.383193 + 0.923668i \(0.374824\pi\)
\(390\) 0 0
\(391\) 3.71623i 0.187938i
\(392\) 4.98740 4.91181i 0.251902 0.248084i
\(393\) 12.8758 + 12.8758i 0.649497 + 0.649497i
\(394\) 7.36285 + 4.25094i 0.370935 + 0.214159i
\(395\) 0 0
\(396\) 2.74315 + 4.75127i 0.137848 + 0.238761i
\(397\) −25.4941 + 6.83113i −1.27951 + 0.342844i −0.833668 0.552266i \(-0.813763\pi\)
−0.445845 + 0.895110i \(0.647097\pi\)
\(398\) 7.79086 7.79086i 0.390520 0.390520i
\(399\) −0.0706671 + 18.5094i −0.00353778 + 0.926627i
\(400\) 0 0
\(401\) 8.61471 14.9211i 0.430198 0.745125i −0.566692 0.823930i \(-0.691777\pi\)
0.996890 + 0.0788050i \(0.0251104\pi\)
\(402\) 2.57606 9.61398i 0.128482 0.479502i
\(403\) 4.93271 18.4091i 0.245716 0.917023i
\(404\) −4.13383 + 7.16001i −0.205666 + 0.356224i
\(405\) 0 0
\(406\) −0.911636 + 1.56517i −0.0452437 + 0.0776780i
\(407\) −38.0186 + 38.0186i −1.88451 + 1.88451i
\(408\) 2.04607 0.548242i 0.101295 0.0271420i
\(409\) −17.8569 30.9290i −0.882967 1.52934i −0.848027 0.529954i \(-0.822209\pi\)
−0.0349400 0.999389i \(-0.511124\pi\)
\(410\) 0 0
\(411\) 1.89199 + 1.09234i 0.0933251 + 0.0538813i
\(412\) −6.58048 6.58048i −0.324197 0.324197i
\(413\) −25.9389 7.05656i −1.27637 0.347230i
\(414\) 1.75439i 0.0862235i
\(415\) 0 0
\(416\) −2.95981 + 1.70885i −0.145117 + 0.0837832i
\(417\) −17.5263 4.69616i −0.858267 0.229972i
\(418\) −9.93394 37.0740i −0.485885 1.81335i
\(419\) 14.0414 0.685966 0.342983 0.939342i \(-0.388563\pi\)
0.342983 + 0.939342i \(0.388563\pi\)
\(420\) 0 0
\(421\) 24.4332 1.19080 0.595401 0.803429i \(-0.296993\pi\)
0.595401 + 0.803429i \(0.296993\pi\)
\(422\) −2.67419 9.98020i −0.130177 0.485829i
\(423\) 3.40506 + 0.912383i 0.165560 + 0.0443616i
\(424\) 8.14273 4.70121i 0.395446 0.228311i
\(425\) 0 0
\(426\) 11.9716i 0.580025i
\(427\) 2.99734 0.790881i 0.145051 0.0382734i
\(428\) −8.67454 8.67454i −0.419300 0.419300i
\(429\) −16.2384 9.37526i −0.783999 0.452642i
\(430\) 0 0
\(431\) 19.3886 + 33.5820i 0.933914 + 1.61759i 0.776559 + 0.630044i \(0.216963\pi\)
0.157354 + 0.987542i \(0.449704\pi\)
\(432\) 0.965926 0.258819i 0.0464731 0.0124524i
\(433\) 7.85700 7.85700i 0.377583 0.377583i −0.492646 0.870230i \(-0.663970\pi\)
0.870230 + 0.492646i \(0.163970\pi\)
\(434\) −14.7537 0.0563283i −0.708200 0.00270385i
\(435\) 0 0
\(436\) 0.168311 0.291523i 0.00806063 0.0139614i
\(437\) 3.17664 11.8554i 0.151959 0.567119i
\(438\) −1.26065 + 4.70482i −0.0602363 + 0.224805i
\(439\) 10.5640 18.2973i 0.504190 0.873283i −0.495798 0.868438i \(-0.665124\pi\)
0.999988 0.00484487i \(-0.00154217\pi\)
\(440\) 0 0
\(441\) 3.54619 6.03528i 0.168866 0.287394i
\(442\) −5.11912 + 5.11912i −0.243492 + 0.243492i
\(443\) 6.48289 1.73709i 0.308011 0.0825314i −0.101503 0.994835i \(-0.532365\pi\)
0.409514 + 0.912304i \(0.365698\pi\)
\(444\) 4.90007 + 8.48716i 0.232547 + 0.402783i
\(445\) 0 0
\(446\) 4.17862 + 2.41253i 0.197863 + 0.114236i
\(447\) −0.136935 0.136935i −0.00647682 0.00647682i
\(448\) 1.86367 + 1.87796i 0.0880502 + 0.0887252i
\(449\) 8.28979i 0.391219i −0.980682 0.195610i \(-0.937331\pi\)
0.980682 0.195610i \(-0.0626685\pi\)
\(450\) 0 0
\(451\) 11.9065 6.87424i 0.560657 0.323695i
\(452\) 13.9192 + 3.72964i 0.654705 + 0.175428i
\(453\) 5.51873 + 20.5962i 0.259293 + 0.967693i
\(454\) −18.0938 −0.849182
\(455\) 0 0
\(456\) −6.99593 −0.327615
\(457\) −5.71524 21.3296i −0.267348 0.997755i −0.960798 0.277250i \(-0.910577\pi\)
0.693450 0.720505i \(-0.256090\pi\)
\(458\) −9.31876 2.49695i −0.435437 0.116675i
\(459\) 1.83445 1.05912i 0.0856250 0.0494356i
\(460\) 0 0
\(461\) 19.0130i 0.885524i −0.896639 0.442762i \(-0.853999\pi\)
0.896639 0.442762i \(-0.146001\pi\)
\(462\) −3.81036 + 14.0063i −0.177274 + 0.651634i
\(463\) 16.6091 + 16.6091i 0.771891 + 0.771891i 0.978437 0.206546i \(-0.0662222\pi\)
−0.206546 + 0.978437i \(0.566222\pi\)
\(464\) −0.592889 0.342305i −0.0275242 0.0158911i
\(465\) 0 0
\(466\) −7.23665 12.5343i −0.335232 0.580638i
\(467\) −15.4446 + 4.13837i −0.714691 + 0.191501i −0.597802 0.801644i \(-0.703959\pi\)
−0.116889 + 0.993145i \(0.537292\pi\)
\(468\) −2.41668 + 2.41668i −0.111711 + 0.111711i
\(469\) 22.8556 13.0796i 1.05537 0.603959i
\(470\) 0 0
\(471\) 1.84001 3.18700i 0.0847834 0.146849i
\(472\) 2.62968 9.81409i 0.121041 0.451730i
\(473\) 3.92196 14.6370i 0.180332 0.673008i
\(474\) 4.16543 7.21474i 0.191325 0.331384i
\(475\) 0 0
\(476\) 4.84278 + 2.82069i 0.221968 + 0.129286i
\(477\) 6.64852 6.64852i 0.304415 0.304415i
\(478\) 28.9523 7.75773i 1.32425 0.354831i
\(479\) 4.50526 + 7.80333i 0.205850 + 0.356543i 0.950403 0.311020i \(-0.100671\pi\)
−0.744553 + 0.667563i \(0.767337\pi\)
\(480\) 0 0
\(481\) −29.0066 16.7470i −1.32259 0.763595i
\(482\) −11.7522 11.7522i −0.535296 0.535296i
\(483\) −3.29467 + 3.26961i −0.149913 + 0.148772i
\(484\) 19.0995i 0.868158i
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) 9.02186 + 2.41740i 0.408820 + 0.109543i 0.457367 0.889278i \(-0.348793\pi\)
−0.0485475 + 0.998821i \(0.515459\pi\)
\(488\) 0.303248 + 1.13174i 0.0137274 + 0.0512313i
\(489\) −14.0810 −0.636764
\(490\) 0 0
\(491\) 2.08535 0.0941107 0.0470554 0.998892i \(-0.485016\pi\)
0.0470554 + 0.998892i \(0.485016\pi\)
\(492\) −0.648592 2.42058i −0.0292408 0.109128i
\(493\) −1.40076 0.375332i −0.0630870 0.0169041i
\(494\) 20.7067 11.9550i 0.931637 0.537881i
\(495\) 0 0
\(496\) 5.57642i 0.250388i
\(497\) −22.4821 + 22.3111i −1.00846 + 1.00079i
\(498\) −4.05281 4.05281i −0.181611 0.181611i
\(499\) −11.6260 6.71229i −0.520452 0.300483i 0.216668 0.976245i \(-0.430481\pi\)
−0.737120 + 0.675762i \(0.763815\pi\)
\(500\) 0 0
\(501\) −4.29397 7.43738i −0.191841 0.332278i
\(502\) 10.3992 2.78645i 0.464138 0.124366i
\(503\) 7.19669 7.19669i 0.320885 0.320885i −0.528222 0.849106i \(-0.677141\pi\)
0.849106 + 0.528222i \(0.177141\pi\)
\(504\) 2.28622 + 1.33161i 0.101836 + 0.0593148i
\(505\) 0 0
\(506\) 4.81255 8.33558i 0.213944 0.370562i
\(507\) −0.341468 + 1.27438i −0.0151651 + 0.0565970i
\(508\) −1.74614 + 6.51668i −0.0774724 + 0.289131i
\(509\) 2.14078 3.70794i 0.0948884 0.164352i −0.814674 0.579920i \(-0.803084\pi\)
0.909562 + 0.415568i \(0.136417\pi\)
\(510\) 0 0
\(511\) −11.1849 + 6.40079i −0.494791 + 0.283154i
\(512\) −0.707107 + 0.707107i −0.0312500 + 0.0312500i
\(513\) −6.75755 + 1.81068i −0.298353 + 0.0799435i
\(514\) −7.52124 13.0272i −0.331748 0.574604i
\(515\) 0 0
\(516\) −2.39198 1.38101i −0.105301 0.0607957i
\(517\) −13.6756 13.6756i −0.601451 0.601451i
\(518\) −6.80642 + 25.0194i −0.299057 + 1.09929i
\(519\) 4.04905i 0.177733i
\(520\) 0 0
\(521\) −12.6226 + 7.28768i −0.553007 + 0.319279i −0.750334 0.661059i \(-0.770107\pi\)
0.197327 + 0.980338i \(0.436774\pi\)
\(522\) −0.661282 0.177190i −0.0289435 0.00775540i
\(523\) −9.85794 36.7904i −0.431058 1.60873i −0.750328 0.661066i \(-0.770104\pi\)
0.319270 0.947664i \(-0.396562\pi\)
\(524\) −18.2091 −0.795468
\(525\) 0 0
\(526\) 22.5315 0.982418
\(527\) −3.05723 11.4097i −0.133175 0.497015i
\(528\) −5.29936 1.41996i −0.230625 0.0617958i
\(529\) −17.2531 + 9.96106i −0.750133 + 0.433090i
\(530\) 0 0
\(531\) 10.1603i 0.440919i
\(532\) −13.0381 13.1381i −0.565275 0.569607i
\(533\) 6.05612 + 6.05612i 0.262319 + 0.262319i
\(534\) 6.22115 + 3.59178i 0.269215 + 0.155432i
\(535\) 0 0
\(536\) 4.97656 + 8.61966i 0.214955 + 0.372313i
\(537\) 3.54044 0.948659i 0.152781 0.0409377i
\(538\) 7.80819 7.80819i 0.336635 0.336635i
\(539\) −33.4046 + 18.9475i −1.43884 + 0.816128i
\(540\) 0 0
\(541\) −8.43016 + 14.6015i −0.362441 + 0.627766i −0.988362 0.152121i \(-0.951390\pi\)
0.625921 + 0.779886i \(0.284723\pi\)
\(542\) 1.29834 4.84547i 0.0557684 0.208131i
\(543\) 0.621126 2.31807i 0.0266551 0.0994781i
\(544\) −1.05912 + 1.83445i −0.0454095 + 0.0786516i
\(545\) 0 0
\(546\) −9.04232 0.0345228i −0.386975 0.00147744i
\(547\) 2.04444 2.04444i 0.0874141 0.0874141i −0.662048 0.749462i \(-0.730312\pi\)
0.749462 + 0.662048i \(0.230312\pi\)
\(548\) −2.11024 + 0.565438i −0.0901451 + 0.0241543i
\(549\) 0.585830 + 1.01469i 0.0250026 + 0.0433058i
\(550\) 0 0
\(551\) 4.14781 + 2.39474i 0.176703 + 0.102019i
\(552\) −1.24054 1.24054i −0.0528009 0.0528009i
\(553\) 21.3120 5.62341i 0.906278 0.239132i
\(554\) 6.33506i 0.269151i
\(555\) 0 0
\(556\) 15.7137 9.07229i 0.666408 0.384751i
\(557\) 4.04187 + 1.08302i 0.171260 + 0.0458889i 0.343430 0.939178i \(-0.388411\pi\)
−0.172170 + 0.985067i \(0.555078\pi\)
\(558\) −1.44328 5.38640i −0.0610990 0.228025i
\(559\) 9.43977 0.399260
\(560\) 0 0
\(561\) −11.6213 −0.490653
\(562\) 7.62799 + 28.4681i 0.321767 + 1.20085i
\(563\) −24.1918 6.48217i −1.01956 0.273191i −0.289943 0.957044i \(-0.593636\pi\)
−0.729620 + 0.683853i \(0.760303\pi\)
\(564\) −3.05289 + 1.76259i −0.128550 + 0.0742183i
\(565\) 0 0
\(566\) 0.0978259i 0.00411193i
\(567\) 2.55297 + 0.694523i 0.107215 + 0.0291672i
\(568\) −8.46519 8.46519i −0.355191 0.355191i
\(569\) −1.99827 1.15370i −0.0837720 0.0483658i 0.457529 0.889195i \(-0.348735\pi\)
−0.541301 + 0.840829i \(0.682068\pi\)
\(570\) 0 0
\(571\) −7.94325 13.7581i −0.332415 0.575759i 0.650570 0.759446i \(-0.274530\pi\)
−0.982985 + 0.183687i \(0.941197\pi\)
\(572\) 18.1116 4.85299i 0.757285 0.202914i
\(573\) −5.71012 + 5.71012i −0.238544 + 0.238544i
\(574\) 3.33698 5.72919i 0.139283 0.239132i
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −1.03550 + 3.86453i −0.0431084 + 0.160883i −0.984125 0.177479i \(-0.943206\pi\)
0.941016 + 0.338361i \(0.109873\pi\)
\(578\) 3.23861 12.0867i 0.134709 0.502739i
\(579\) 0.861260 1.49175i 0.0357928 0.0619949i
\(580\) 0 0
\(581\) 0.0578953 15.1641i 0.00240190 0.629114i
\(582\) 13.1212 13.1212i 0.543891 0.543891i
\(583\) −49.8268 + 13.3510i −2.06361 + 0.552944i
\(584\) −2.43539 4.21822i −0.100777 0.174551i
\(585\) 0 0
\(586\) −17.1557 9.90484i −0.708695 0.409165i
\(587\) 5.31785 + 5.31785i 0.219491 + 0.219491i 0.808284 0.588793i \(-0.200397\pi\)
−0.588793 + 0.808284i \(0.700397\pi\)
\(588\) 1.76005 + 6.77512i 0.0725833 + 0.279401i
\(589\) 39.0122i 1.60747i
\(590\) 0 0
\(591\) −7.36285 + 4.25094i −0.302867 + 0.174860i
\(592\) −9.46620 2.53646i −0.389059 0.104248i
\(593\) −4.58156 17.0986i −0.188142 0.702156i −0.993936 0.109960i \(-0.964928\pi\)
0.805794 0.592196i \(-0.201739\pi\)
\(594\) −5.48630 −0.225106
\(595\) 0 0
\(596\) 0.193656 0.00793245
\(597\) 2.85165 + 10.6425i 0.116710 + 0.435569i
\(598\) 5.79167 + 1.55187i 0.236839 + 0.0634608i
\(599\) −27.0972 + 15.6446i −1.10716 + 0.639220i −0.938093 0.346384i \(-0.887409\pi\)
−0.169069 + 0.985604i \(0.554076\pi\)
\(600\) 0 0
\(601\) 47.5637i 1.94016i −0.242776 0.970082i \(-0.578058\pi\)
0.242776 0.970082i \(-0.421942\pi\)
\(602\) −1.86439 7.06580i −0.0759869 0.287980i
\(603\) 7.03792 + 7.03792i 0.286606 + 0.286606i
\(604\) −18.4660 10.6614i −0.751372 0.433805i
\(605\) 0 0
\(606\) −4.13383 7.16001i −0.167925 0.290855i
\(607\) −23.7082 + 6.35260i −0.962287 + 0.257844i −0.705568 0.708642i \(-0.749308\pi\)
−0.256719 + 0.966486i \(0.582641\pi\)
\(608\) 4.94687 4.94687i 0.200622 0.200622i
\(609\) −0.899658 1.57208i −0.0364560 0.0637041i
\(610\) 0 0
\(611\) 6.02400 10.4339i 0.243705 0.422109i
\(612\) −0.548242 + 2.04607i −0.0221614 + 0.0827074i
\(613\) 7.20472 26.8884i 0.290996 1.08601i −0.653349 0.757056i \(-0.726637\pi\)
0.944345 0.328955i \(-0.106697\pi\)
\(614\) 2.15894 3.73939i 0.0871277 0.150910i
\(615\) 0 0
\(616\) −7.20965 12.5983i −0.290485 0.507600i
\(617\) 24.4884 24.4884i 0.985865 0.985865i −0.0140365 0.999901i \(-0.504468\pi\)
0.999901 + 0.0140365i \(0.00446811\pi\)
\(618\) 8.98910 2.40862i 0.361595 0.0968890i
\(619\) −15.9137 27.5634i −0.639627 1.10787i −0.985515 0.169590i \(-0.945756\pi\)
0.345888 0.938276i \(-0.387578\pi\)
\(620\) 0 0
\(621\) −1.51935 0.877194i −0.0609692 0.0352006i
\(622\) 5.97174 + 5.97174i 0.239445 + 0.239445i
\(623\) 4.84897 + 18.3770i 0.194270 + 0.736257i
\(624\) 3.41770i 0.136817i
\(625\) 0 0
\(626\) 16.8092 9.70480i 0.671831 0.387882i
\(627\) 37.0740 + 9.93394i 1.48059 + 0.396723i
\(628\) 0.952462 + 3.55464i 0.0380074 + 0.141845i
\(629\) −20.7591 −0.827719
\(630\) 0 0
\(631\) −34.9471 −1.39122 −0.695610 0.718419i \(-0.744866\pi\)
−0.695610 + 0.718419i \(0.744866\pi\)
\(632\) 2.15619 + 8.04700i 0.0857685 + 0.320092i
\(633\) 9.98020 + 2.67419i 0.396677 + 0.106289i
\(634\) 13.4670 7.77515i 0.534841 0.308791i
\(635\) 0 0
\(636\) 9.40242i 0.372830i
\(637\) −16.7871 17.0454i −0.665128 0.675364i
\(638\) 2.65587 + 2.65587i 0.105147 + 0.105147i
\(639\) −10.3677 5.98579i −0.410140 0.236794i
\(640\) 0 0
\(641\) 5.61488 + 9.72526i 0.221774 + 0.384125i 0.955347 0.295487i \(-0.0954818\pi\)
−0.733572 + 0.679611i \(0.762148\pi\)
\(642\) 11.8496 3.17510i 0.467668 0.125311i
\(643\) −9.89036 + 9.89036i −0.390038 + 0.390038i −0.874701 0.484663i \(-0.838942\pi\)
0.484663 + 0.874701i \(0.338942\pi\)
\(644\) 0.0177214 4.64164i 0.000698320 0.182906i
\(645\) 0 0
\(646\) 7.40955 12.8337i 0.291525 0.504936i
\(647\) −4.06147 + 15.1576i −0.159673 + 0.595908i 0.838987 + 0.544152i \(0.183148\pi\)
−0.998660 + 0.0517559i \(0.983518\pi\)
\(648\) −0.258819 + 0.965926i −0.0101674 + 0.0379452i
\(649\) −27.8712 + 48.2744i −1.09404 + 1.89493i
\(650\) 0 0
\(651\) 7.42563 12.7489i 0.291033 0.499669i
\(652\) 9.95676 9.95676i 0.389937 0.389937i
\(653\) 15.4045 4.12761i 0.602823 0.161526i 0.0555160 0.998458i \(-0.482320\pi\)
0.547307 + 0.836932i \(0.315653\pi\)
\(654\) 0.168311 + 0.291523i 0.00658147 + 0.0113994i
\(655\) 0 0
\(656\) 2.17023 + 1.25298i 0.0847333 + 0.0489208i
\(657\) −3.44417 3.44417i −0.134370 0.134370i
\(658\) −8.99966 2.44832i −0.350843 0.0954453i
\(659\) 10.4778i 0.408157i 0.978955 + 0.204078i \(0.0654198\pi\)
−0.978955 + 0.204078i \(0.934580\pi\)
\(660\) 0 0
\(661\) −20.9764 + 12.1107i −0.815888 + 0.471053i −0.848996 0.528399i \(-0.822793\pi\)
0.0331084 + 0.999452i \(0.489459\pi\)
\(662\) 15.6344 + 4.18923i 0.607648 + 0.162819i
\(663\) −1.87373 6.99285i −0.0727695 0.271580i
\(664\) 5.73154 0.222427
\(665\) 0 0
\(666\) −9.80013 −0.379747
\(667\) 0.310860 + 1.16015i 0.0120366 + 0.0449210i
\(668\) 8.29532 + 2.22272i 0.320955 + 0.0859998i
\(669\) −4.17862 + 2.41253i −0.161555 + 0.0932736i
\(670\) 0 0
\(671\) 6.42808i 0.248153i
\(672\) −2.55820 + 0.675009i −0.0986845 + 0.0260390i
\(673\) 1.16725 + 1.16725i 0.0449943 + 0.0449943i 0.729246 0.684252i \(-0.239871\pi\)
−0.684252 + 0.729246i \(0.739871\pi\)
\(674\) 23.5218 + 13.5803i 0.906025 + 0.523094i
\(675\) 0 0
\(676\) −0.659666 1.14257i −0.0253718 0.0439452i
\(677\) 12.4001 3.32260i 0.476575 0.127698i −0.0125322 0.999921i \(-0.503989\pi\)
0.489108 + 0.872223i \(0.337323\pi\)
\(678\) −10.1896 + 10.1896i −0.391328 + 0.391328i
\(679\) 49.0947 + 0.187439i 1.88408 + 0.00719326i
\(680\) 0 0
\(681\) 9.04688 15.6697i 0.346677 0.600463i
\(682\) −7.91828 + 29.5514i −0.303207 + 1.13158i
\(683\) −5.52974 + 20.6373i −0.211589 + 0.789663i 0.775750 + 0.631040i \(0.217372\pi\)
−0.987339 + 0.158622i \(0.949295\pi\)
\(684\) 3.49797 6.05866i 0.133748 0.231658i
\(685\) 0 0
\(686\) −9.44322 + 15.9319i −0.360544 + 0.608283i
\(687\) 6.82181 6.82181i 0.260268 0.260268i
\(688\) 2.66791 0.714864i 0.101713 0.0272540i
\(689\) −16.0673 27.8294i −0.612116 1.06022i
\(690\) 0 0
\(691\) −37.0127 21.3693i −1.40803 0.812927i −0.412833 0.910807i \(-0.635461\pi\)
−0.995198 + 0.0978797i \(0.968794\pi\)
\(692\) −2.86311 2.86311i −0.108839 0.108839i
\(693\) −10.2247 10.3030i −0.388403 0.391380i
\(694\) 10.2657i 0.389681i
\(695\) 0 0
\(696\) 0.592889 0.342305i 0.0224734 0.0129750i
\(697\) 5.12738 + 1.37388i 0.194213 + 0.0520393i
\(698\) −1.71194 6.38903i −0.0647977 0.241828i
\(699\) 14.4733 0.547431
\(700\) 0 0
\(701\) 44.5959 1.68436 0.842182 0.539194i \(-0.181271\pi\)
0.842182 + 0.539194i \(0.181271\pi\)
\(702\) −0.884566 3.30124i −0.0333858 0.124597i
\(703\) 66.2249 + 17.7449i 2.49772 + 0.669262i
\(704\) 4.75127 2.74315i 0.179070 0.103386i
\(705\) 0 0
\(706\) 13.6247i 0.512772i
\(707\) 5.74208 21.1071i 0.215953 0.793813i
\(708\) 7.18441 + 7.18441i 0.270007 + 0.270007i
\(709\) 35.8750 + 20.7125i 1.34732 + 0.777873i 0.987869 0.155293i \(-0.0496320\pi\)
0.359447 + 0.933166i \(0.382965\pi\)
\(710\) 0 0
\(711\) 4.16543 + 7.21474i 0.156216 + 0.270574i
\(712\) −6.93879 + 1.85924i −0.260042 + 0.0696781i
\(713\) −6.91777 + 6.91777i −0.259072 + 0.259072i
\(714\) −4.86417 + 2.78362i −0.182037 + 0.104175i
\(715\) 0 0
\(716\) −1.83267 + 3.17428i −0.0684900 + 0.118628i
\(717\) −7.75773 + 28.9523i −0.289718 + 1.08124i
\(718\) −4.47665 + 16.7071i −0.167067 + 0.623502i
\(719\) −11.7839 + 20.4103i −0.439464 + 0.761174i −0.997648 0.0685431i \(-0.978165\pi\)
0.558184 + 0.829717i \(0.311498\pi\)
\(720\) 0 0
\(721\) 21.2760 + 12.3923i 0.792361 + 0.461512i
\(722\) −21.1730 + 21.1730i −0.787976 + 0.787976i
\(723\) 16.0538 4.30159i 0.597046 0.159978i
\(724\) 1.19992 + 2.07833i 0.0445948 + 0.0772405i
\(725\) 0 0
\(726\) 16.5406 + 9.54974i 0.613881 + 0.354424i
\(727\) −3.38556 3.38556i −0.125563 0.125563i 0.641532 0.767096i \(-0.278299\pi\)
−0.767096 + 0.641532i \(0.778299\pi\)
\(728\) 6.41829 6.36947i 0.237878 0.236068i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 5.06681 2.92532i 0.187403 0.108197i
\(732\) −1.13174 0.303248i −0.0418302 0.0112084i
\(733\) −10.1653 37.9373i −0.375463 1.40125i −0.852667 0.522454i \(-0.825017\pi\)
0.477204 0.878792i \(-0.341650\pi\)
\(734\) −25.8811 −0.955288
\(735\) 0 0
\(736\) 1.75439 0.0646676
\(737\) −14.1330 52.7452i −0.520597 1.94289i
\(738\) 2.42058 + 0.648592i 0.0891027 + 0.0238750i
\(739\) 38.6211 22.2979i 1.42070 0.820242i 0.424343 0.905502i \(-0.360505\pi\)
0.996359 + 0.0852593i \(0.0271719\pi\)
\(740\) 0 0
\(741\) 23.9100i 0.878356i
\(742\) −17.6573 + 17.5230i −0.648222 + 0.643291i
\(743\) −24.7787 24.7787i −0.909041 0.909041i 0.0871537 0.996195i \(-0.472223\pi\)
−0.996195 + 0.0871537i \(0.972223\pi\)
\(744\) 4.82932 + 2.78821i 0.177051 + 0.102221i
\(745\) 0 0
\(746\) −4.58319 7.93832i −0.167802 0.290642i
\(747\) 5.53624 1.48343i 0.202561 0.0542759i
\(748\) 8.21752 8.21752i 0.300462 0.300462i
\(749\) 28.0466 + 16.3358i 1.02480 + 0.596897i
\(750\) 0 0
\(751\) −2.54731 + 4.41207i −0.0929526 + 0.160999i −0.908752 0.417336i \(-0.862964\pi\)
0.815800 + 0.578335i \(0.196297\pi\)
\(752\) 0.912383 3.40506i 0.0332712 0.124170i
\(753\) −2.78645 + 10.3992i −0.101544 + 0.378967i
\(754\) −1.16989 + 2.02632i −0.0426051 + 0.0737941i
\(755\) 0 0
\(756\) −2.29632 + 1.31412i −0.0835164 + 0.0477940i
\(757\) −18.2623 + 18.2623i −0.663754 + 0.663754i −0.956263 0.292509i \(-0.905510\pi\)
0.292509 + 0.956263i \(0.405510\pi\)
\(758\) 18.0503 4.83657i 0.655618 0.175672i
\(759\) 4.81255 + 8.33558i 0.174685 + 0.302562i
\(760\) 0 0
\(761\) 24.3626 + 14.0657i 0.883142 + 0.509882i 0.871693 0.490052i \(-0.163022\pi\)
0.0114488 + 0.999934i \(0.496356\pi\)
\(762\) −4.77054 4.77054i −0.172819 0.172819i
\(763\) −0.233791 + 0.859384i −0.00846382 + 0.0311118i
\(764\) 8.07532i 0.292155i
\(765\) 0 0
\(766\) 17.1832 9.92072i 0.620854 0.358450i
\(767\) −33.5416 8.98745i −1.21112 0.324518i
\(768\) −0.258819 0.965926i −0.00933933 0.0348548i
\(769\) −3.03517 −0.109451 −0.0547256 0.998501i \(-0.517428\pi\)
−0.0547256 + 0.998501i \(0.517428\pi\)
\(770\) 0 0
\(771\) 15.0425 0.541742
\(772\) 0.445821 + 1.66383i 0.0160455 + 0.0598825i
\(773\) 46.8575 + 12.5554i 1.68535 + 0.451588i 0.969183 0.246342i \(-0.0792288\pi\)
0.716166 + 0.697930i \(0.245895\pi\)
\(774\) 2.39198 1.38101i 0.0859781 0.0496395i
\(775\) 0 0
\(776\) 18.5562i 0.666128i
\(777\) −18.2642 18.4042i −0.655226 0.660248i
\(778\) 3.62546 + 3.62546i 0.129979 + 0.129979i
\(779\) −15.1828 8.76579i −0.543980 0.314067i
\(780\) 0 0
\(781\) 32.8398 + 56.8803i 1.17510 + 2.03534i