Properties

Label 1050.2.bc.h.607.3
Level $1050$
Weight $2$
Character 1050.607
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 607.3
Root \(0.277956 - 0.213283i\) of defining polynomial
Character \(\chi\) \(=\) 1050.607
Dual form 1050.2.bc.h.493.3

$q$-expansion

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

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.965926 0.258819i 0.683013 0.183013i
\(3\) 0.258819 0.965926i 0.149429 0.557678i
\(4\) 0.866025 0.500000i 0.433013 0.250000i
\(5\) 0 0
\(6\) 1.00000i 0.408248i
\(7\) 1.86367 + 1.87796i 0.704402 + 0.709801i
\(8\) 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 \(-0.476672\pi\)
\(12\) −0.258819 0.965926i −0.0747146 0.278839i
\(13\) −2.41668 2.41668i −0.670266 0.670266i 0.287511 0.957777i \(-0.407172\pi\)
−0.957777 + 0.287511i \(0.907172\pi\)
\(14\) 2.28622 + 1.33161i 0.611018 + 0.355889i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.125000 0.216506i
\(17\) 2.04607 + 0.548242i 0.496244 + 0.132968i 0.498256 0.867030i \(-0.333974\pi\)
−0.00201209 + 0.999998i \(0.500640\pi\)
\(18\) −0.965926 0.258819i −0.227671 0.0610042i
\(19\) 3.49797 6.05866i 0.802489 1.38995i −0.115485 0.993309i \(-0.536842\pi\)
0.917974 0.396642i \(-0.129824\pi\)
\(20\) 0 0
\(21\) 2.29632 1.31412i 0.501098 0.286764i
\(22\) −3.87940 3.87940i −0.827091 0.827091i
\(23\) 0.454069 + 1.69461i 0.0946800 + 0.353350i 0.996971 0.0777776i \(-0.0247824\pi\)
−0.902291 + 0.431128i \(0.858116\pi\)
\(24\) −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
\(28\) 2.55297 + 0.694523i 0.482465 + 0.131252i
\(29\) 0.684610i 0.127129i 0.997978 + 0.0635644i \(0.0202468\pi\)
−0.997978 + 0.0635644i \(0.979753\pi\)
\(30\) 0 0
\(31\) 4.82932 2.78821i 0.867371 0.500777i 0.000897301 1.00000i \(-0.499714\pi\)
0.866474 + 0.499223i \(0.166381\pi\)
\(32\) 0.258819 0.965926i 0.0457532 0.170753i
\(33\) −5.29936 + 1.41996i −0.922500 + 0.247183i
\(34\) 2.11825 0.363276
\(35\) 0 0
\(36\) −1.00000 −0.166667
\(37\) 9.46620 2.53646i 1.55623 0.416992i 0.624765 0.780813i \(-0.285195\pi\)
0.931469 + 0.363821i \(0.118528\pi\)
\(38\) 1.81068 6.75755i 0.293731 1.09622i
\(39\) −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 \(0.937308\pi\)
\(42\) 1.87796 1.86367i 0.289775 0.287571i
\(43\) 1.95305 1.95305i 0.297837 0.297837i −0.542329 0.840166i \(-0.682457\pi\)
0.840166 + 0.542329i \(0.182457\pi\)
\(44\) −4.75127 2.74315i −0.716282 0.413545i
\(45\) 0 0
\(46\) 0.877194 + 1.51935i 0.129335 + 0.224015i
\(47\) 0.912383 + 3.40506i 0.133085 + 0.496679i 0.999998 0.00177938i \(-0.000566396\pi\)
−0.866914 + 0.498458i \(0.833900\pi\)
\(48\) −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
\(52\) −3.30124 0.884566i −0.457800 0.122667i
\(53\) −9.08204 2.43353i −1.24751 0.334270i −0.426138 0.904658i \(-0.640126\pi\)
−0.821376 + 0.570388i \(0.806793\pi\)
\(54\) −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
\(58\) 0.177190 + 0.661282i 0.0232662 + 0.0868306i
\(59\) 5.08015 + 8.79907i 0.661379 + 1.14554i 0.980253 + 0.197745i \(0.0633618\pi\)
−0.318875 + 0.947797i \(0.603305\pi\)
\(60\) 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
\(63\) −0.675009 2.55820i −0.0850431 0.322302i
\(64\) 1.00000i 0.125000i
\(65\) 0 0
\(66\) −4.75127 + 2.74315i −0.584841 + 0.337658i
\(67\) −2.57606 + 9.61398i −0.314716 + 1.17454i 0.609538 + 0.792757i \(0.291355\pi\)
−0.924254 + 0.381778i \(0.875312\pi\)
\(68\) 2.04607 0.548242i 0.248122 0.0664841i
\(69\) 1.75439 0.211204
\(70\) 0 0
\(71\) −11.9716 −1.42077 −0.710383 0.703816i \(-0.751478\pi\)
−0.710383 + 0.703816i \(0.751478\pi\)
\(72\) −0.965926 + 0.258819i −0.113835 + 0.0305021i
\(73\) −1.26065 + 4.70482i −0.147548 + 0.550657i 0.852081 + 0.523411i \(0.175341\pi\)
−0.999629 + 0.0272467i \(0.991326\pi\)
\(74\) 8.48716 4.90007i 0.986613 0.569621i
\(75\) 0 0
\(76\) 6.99593i 0.802489i
\(77\) 3.81036 14.0063i 0.434231 1.59617i
\(78\) −2.41668 + 2.41668i −0.273635 + 0.273635i
\(79\) −7.21474 4.16543i −0.811722 0.468648i 0.0358316 0.999358i \(-0.488592\pi\)
−0.847553 + 0.530710i \(0.821925\pi\)
\(80\) 0 0
\(81\) 0.500000 + 0.866025i 0.0555556 + 0.0962250i
\(82\) 0.648592 + 2.42058i 0.0716250 + 0.267308i
\(83\) −4.05281 4.05281i −0.444854 0.444854i 0.448786 0.893639i \(-0.351857\pi\)
−0.893639 + 0.448786i \(0.851857\pi\)
\(84\) 1.33161 2.28622i 0.145291 0.249447i
\(85\) 0 0
\(86\) 1.38101 2.39198i 0.148918 0.257934i
\(87\) 0.661282 + 0.177190i 0.0708969 + 0.0189968i
\(88\) −5.29936 1.41996i −0.564913 0.151368i
\(89\) 3.59178 6.22115i 0.380728 0.659440i −0.610439 0.792064i \(-0.709007\pi\)
0.991166 + 0.132623i \(0.0423401\pi\)
\(90\) 0 0
\(91\) 0.0345228 9.04232i 0.00361897 0.947892i
\(92\) 1.24054 + 1.24054i 0.129335 + 0.129335i
\(93\) −1.44328 5.38640i −0.149661 0.558544i
\(94\) 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 −0.428909 + 0.903348i \(0.641102\pi\)
−0.903348 + 0.428909i \(0.858898\pi\)
\(98\) 1.76005 + 6.77512i 0.177792 + 0.684390i
\(99\) 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 \(0.198397\pi\)
\(102\) 0.548242 2.04607i 0.0542841 0.202591i
\(103\) 8.98910 2.40862i 0.885722 0.237329i 0.212848 0.977085i \(-0.431726\pi\)
0.672874 + 0.739757i \(0.265059\pi\)
\(104\) −3.41770 −0.335133
\(105\) 0 0
\(106\) −9.40242 −0.913244
\(107\) −11.8496 + 3.17510i −1.14555 + 0.306949i −0.781180 0.624306i \(-0.785382\pi\)
−0.364369 + 0.931255i \(0.618715\pi\)
\(108\) −0.258819 + 0.965926i −0.0249049 + 0.0929463i
\(109\) 0.291523 0.168311i 0.0279228 0.0161213i −0.485974 0.873973i \(-0.661535\pi\)
0.513896 + 0.857852i \(0.328202\pi\)
\(110\) 0 0
\(111\) 9.80013i 0.930188i
\(112\) 2.55820 0.675009i 0.241727 0.0637823i
\(113\) −10.1896 + 10.1896i −0.958555 + 0.958555i −0.999175 0.0406198i \(-0.987067\pi\)
0.0406198 + 0.999175i \(0.487067\pi\)
\(114\) −6.05866 3.49797i −0.567445 0.327615i
\(115\) 0 0
\(116\) 0.342305 + 0.592889i 0.0317822 + 0.0550484i
\(117\) 0.884566 + 3.30124i 0.0817781 + 0.305200i
\(118\) 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
\(122\) 1.13174 + 0.303248i 0.102463 + 0.0274548i
\(123\) 2.42058 + 0.648592i 0.218256 + 0.0584816i
\(124\) 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 0.886344 0.463027i \(-0.153237\pi\)
−0.463027 + 0.886344i \(0.653237\pi\)
\(128\) −0.258819 0.965926i −0.0228766 0.0853766i
\(129\) −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
\(133\) 17.8970 4.72232i 1.55186 0.409477i
\(134\) 9.95313i 0.859819i
\(135\) 0 0
\(136\) 1.83445 1.05912i 0.157303 0.0908190i
\(137\) −0.565438 + 2.11024i −0.0483086 + 0.180290i −0.985865 0.167544i \(-0.946416\pi\)
0.937556 + 0.347835i \(0.113083\pi\)
\(138\) 1.69461 0.454069i 0.144255 0.0386529i
\(139\) 18.1446 1.53900 0.769501 0.638645i \(-0.220505\pi\)
0.769501 + 0.638645i \(0.220505\pi\)
\(140\) 0 0
\(141\) 3.52518 0.296873
\(142\) −11.5637 + 3.09847i −0.970401 + 0.260018i
\(143\) −4.85299 + 18.1116i −0.405828 + 1.51457i
\(144\) −0.866025 + 0.500000i −0.0721688 + 0.0416667i
\(145\) 0 0
\(146\) 4.87079i 0.403109i
\(147\) 6.74745 + 1.86331i 0.556520 + 0.153683i
\(148\) 6.92974 6.92974i 0.569621 0.569621i
\(149\) 0.167711 + 0.0968279i 0.0137394 + 0.00793245i 0.506854 0.862032i \(-0.330808\pi\)
−0.493115 + 0.869964i \(0.664142\pi\)
\(150\) 0 0
\(151\) 10.6614 + 18.4660i 0.867610 + 1.50274i 0.864432 + 0.502750i \(0.167678\pi\)
0.00317777 + 0.999995i \(0.498988\pi\)
\(152\) −1.81068 6.75755i −0.146866 0.548110i
\(153\) −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
\(157\) 3.55464 + 0.952462i 0.283691 + 0.0760147i 0.397859 0.917447i \(-0.369753\pi\)
−0.114168 + 0.993461i \(0.536420\pi\)
\(158\) −8.04700 2.15619i −0.640185 0.171537i
\(159\) −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
\(163\) 3.64443 + 13.6012i 0.285454 + 1.06533i 0.948507 + 0.316756i \(0.102594\pi\)
−0.663054 + 0.748572i \(0.730740\pi\)
\(164\) 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 \(-0.642183\pi\)
0.901886 + 0.431974i \(0.142183\pi\)
\(168\) 0.694523 2.55297i 0.0535836 0.196966i
\(169\) 1.31933i 0.101487i
\(170\) 0 0
\(171\) −6.05866 + 3.49797i −0.463317 + 0.267496i
\(172\) 0.714864 2.66791i 0.0545079 0.203426i
\(173\) 3.91108 1.04797i 0.297354 0.0796757i −0.107058 0.994253i \(-0.534143\pi\)
0.404412 + 0.914577i \(0.367476\pi\)
\(174\) 0.684610 0.0519001
\(175\) 0 0
\(176\) −5.48630 −0.413545
\(177\) 9.81409 2.62968i 0.737672 0.197659i
\(178\) 1.85924 6.93879i 0.139356 0.520084i
\(179\) −3.17428 + 1.83267i −0.237256 + 0.136980i −0.613915 0.789372i \(-0.710406\pi\)
0.376659 + 0.926352i \(0.377073\pi\)
\(180\) 0 0
\(181\) 2.39985i 0.178379i −0.996015 0.0891896i \(-0.971572\pi\)
0.996015 0.0891896i \(-0.0284277\pi\)
\(182\) −2.30698 8.74314i −0.171005 0.648085i
\(183\) 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
\(187\) −3.00782 11.2253i −0.219954 0.820878i
\(188\) 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 \(0.261039\pi\)
\(192\) −0.965926 0.258819i −0.0697097 0.0186787i
\(193\) −1.66383 0.445821i −0.119765 0.0320909i 0.198439 0.980113i \(-0.436413\pi\)
−0.318204 + 0.948022i \(0.603080\pi\)
\(194\) −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 0.459737 0.888055i \(-0.347944\pi\)
−0.888055 + 0.459737i \(0.847944\pi\)
\(198\) 1.41996 + 5.29936i 0.100912 + 0.376609i
\(199\) −5.50897 9.54181i −0.390520 0.676401i 0.601998 0.798498i \(-0.294372\pi\)
−0.992518 + 0.122097i \(0.961038\pi\)
\(200\) 0 0
\(201\) 8.61966 + 4.97656i 0.607984 + 0.351020i
\(202\) 5.84612 5.84612i 0.411332 0.411332i
\(203\) −1.28567 + 1.27589i −0.0902362 + 0.0895498i
\(204\) 2.11825i 0.148307i
\(205\) 0 0
\(206\) 8.05941 4.65310i 0.561526 0.324197i
\(207\) 0.454069 1.69461i 0.0315600 0.117783i
\(208\) −3.30124 + 0.884566i −0.228900 + 0.0613336i
\(209\) −38.3818 −2.65492
\(210\) 0 0
\(211\) 10.3323 0.711302 0.355651 0.934619i \(-0.384259\pi\)
0.355651 + 0.934619i \(0.384259\pi\)
\(212\) −9.08204 + 2.43353i −0.623757 + 0.167135i
\(213\) −3.09847 + 11.5637i −0.212304 + 0.792329i
\(214\) −10.6241 + 6.13383i −0.726249 + 0.419300i
\(215\) 0 0
\(216\) 1.00000i 0.0680414i
\(217\) 14.2364 + 3.87295i 0.966430 + 0.262913i
\(218\) 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
\(222\) −2.53646 9.46620i −0.170236 0.635330i
\(223\) 3.41183 + 3.41183i 0.228473 + 0.228473i 0.812054 0.583582i \(-0.198349\pi\)
−0.583582 + 0.812054i \(0.698349\pi\)
\(224\) 2.29632 1.31412i 0.153429 0.0878032i
\(225\) 0 0
\(226\) −7.20512 + 12.4796i −0.479277 + 0.830133i
\(227\) 17.4772 + 4.68301i 1.16000 + 0.310822i 0.786968 0.616994i \(-0.211650\pi\)
0.373037 + 0.927816i \(0.378316\pi\)
\(228\) −6.75755 1.81068i −0.447530 0.119915i
\(229\) −4.82375 + 8.35497i −0.318762 + 0.552112i −0.980230 0.197861i \(-0.936600\pi\)
0.661468 + 0.749973i \(0.269934\pi\)
\(230\) 0 0
\(231\) −12.5429 7.30563i −0.825262 0.480675i
\(232\) 0.484092 + 0.484092i 0.0317822 + 0.0317822i
\(233\) −3.74597 13.9801i −0.245407 0.915870i −0.973179 0.230051i \(-0.926111\pi\)
0.727772 0.685819i \(-0.240556\pi\)
\(234\) 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
\(238\) 3.94772 + 3.97798i 0.255892 + 0.257854i
\(239\) 29.9736i 1.93883i −0.245427 0.969415i \(-0.578928\pi\)
0.245427 0.969415i \(-0.421072\pi\)
\(240\) 0 0
\(241\) 14.3934 8.31003i 0.927161 0.535296i 0.0412481 0.999149i \(-0.486867\pi\)
0.885912 + 0.463853i \(0.153533\pi\)
\(242\) −4.94331 + 18.4487i −0.317768 + 1.18593i
\(243\) 0.965926 0.258819i 0.0619642 0.0166032i
\(244\) 1.17166 0.0750079
\(245\) 0 0
\(246\) 2.50597 0.159775
\(247\) −23.0953 + 6.18836i −1.46952 + 0.393756i
\(248\) 1.44328 5.38640i 0.0916485 0.342037i
\(249\) −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 \(0.889650\pi\)
\(252\) −1.86367 1.87796i −0.117400 0.118300i
\(253\) 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
\(257\) 3.89328 + 14.5299i 0.242856 + 0.906352i 0.974449 + 0.224610i \(0.0721107\pi\)
−0.731593 + 0.681742i \(0.761223\pi\)
\(258\) −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
\(262\) 17.5886 + 4.71286i 1.08663 + 0.291161i
\(263\) 21.7637 + 5.83157i 1.34201 + 0.359590i 0.857179 0.515019i \(-0.172215\pi\)
0.484829 + 0.874609i \(0.338882\pi\)
\(264\) −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
\(268\) 2.57606 + 9.61398i 0.157358 + 0.587268i
\(269\) −5.52122 9.56304i −0.336635 0.583069i 0.647163 0.762352i \(-0.275955\pi\)
−0.983797 + 0.179283i \(0.942622\pi\)
\(270\) 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
\(273\) −8.72527 2.37367i −0.528077 0.143661i
\(274\) 2.18468i 0.131982i
\(275\) 0 0
\(276\) 1.51935 0.877194i 0.0914538 0.0528009i
\(277\) −1.63963 + 6.11920i −0.0985161 + 0.367667i −0.997529 0.0702549i \(-0.977619\pi\)
0.899013 + 0.437922i \(0.144285\pi\)
\(278\) 17.5263 4.69616i 1.05116 0.281657i
\(279\) −5.57642 −0.333851
\(280\) 0 0
\(281\) −29.4723 −1.75817 −0.879085 0.476665i \(-0.841846\pi\)
−0.879085 + 0.476665i \(0.841846\pi\)
\(282\) 3.40506 0.912383i 0.202768 0.0543316i
\(283\) 0.0253192 0.0944925i 0.00150507 0.00561700i −0.965169 0.261626i \(-0.915741\pi\)
0.966674 + 0.256009i \(0.0824078\pi\)
\(284\) −10.3677 + 5.98579i −0.615210 + 0.355191i
\(285\) 0 0
\(286\) 18.7505i 1.10874i
\(287\) −4.70610 + 4.67030i −0.277792 + 0.275679i
\(288\) −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
\(292\) 1.26065 + 4.70482i 0.0737741 + 0.275329i
\(293\) −14.0076 14.0076i −0.818330 0.818330i 0.167536 0.985866i \(-0.446419\pi\)
−0.985866 + 0.167536i \(0.946419\pi\)
\(294\) 6.99980 + 0.0534500i 0.408236 + 0.00311727i
\(295\) 0 0
\(296\) 4.90007 8.48716i 0.284811 0.493306i
\(297\) 5.29936 + 1.41996i 0.307500 + 0.0823944i
\(298\) 0.187057 + 0.0501218i 0.0108359 + 0.00290348i
\(299\) 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
\(303\) −2.13983 7.98595i −0.122930 0.458781i
\(304\) −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 \(-0.789321\pi\)
0.614591 + 0.788846i \(0.289321\pi\)
\(308\) −3.70330 14.0350i −0.211015 0.799720i
\(309\) 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 \(0.410299\pi\)
\(312\) −0.884566 + 3.30124i −0.0500787 + 0.186896i
\(313\) 18.7482 5.02358i 1.05971 0.283949i 0.313453 0.949604i \(-0.398514\pi\)
0.746260 + 0.665654i \(0.231847\pi\)
\(314\) 3.68003 0.207676
\(315\) 0 0
\(316\) −8.33087 −0.468648
\(317\) −15.0204 + 4.02471i −0.843632 + 0.226050i −0.654652 0.755931i \(-0.727185\pi\)
−0.188980 + 0.981981i \(0.560518\pi\)
\(318\) −2.43353 + 9.08204i −0.136465 + 0.509296i
\(319\) 3.25277 1.87799i 0.182120 0.105147i
\(320\) 0 0
\(321\) 12.2677i 0.684714i
\(322\) −1.21846 + 4.47890i −0.0679023 + 0.249599i
\(323\) 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
\(327\) −0.0871241 0.325151i −0.00481797 0.0179809i
\(328\) 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 \(0.313402\pi\)
\(332\) −5.53624 1.48343i −0.303841 0.0814139i
\(333\) −9.46620 2.53646i −0.518745 0.138997i
\(334\) 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 −0.998880 0.0473073i \(-0.984936\pi\)
−0.0473073 0.998880i \(-0.515064\pi\)
\(338\) −0.341468 1.27438i −0.0185734 0.0693169i
\(339\) 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
\(343\) −13.2449 + 12.9450i −0.715159 + 0.698962i
\(344\) 2.76202i 0.148918i
\(345\) 0 0
\(346\) 3.50658 2.02452i 0.188515 0.108839i
\(347\) −2.65696 + 9.91592i −0.142633 + 0.532315i 0.857216 + 0.514957i \(0.172192\pi\)
−0.999849 + 0.0173577i \(0.994475\pi\)
\(348\) 0.661282 0.177190i 0.0354484 0.00949838i
\(349\) −6.61441 −0.354061 −0.177031 0.984205i \(-0.556649\pi\)
−0.177031 + 0.984205i \(0.556649\pi\)
\(350\) 0 0
\(351\) 3.41770 0.182423
\(352\) −5.29936 + 1.41996i −0.282457 + 0.0756841i
\(353\) −3.52633 + 13.1604i −0.187688 + 0.700460i 0.806352 + 0.591436i \(0.201439\pi\)
−0.994039 + 0.109023i \(0.965228\pi\)
\(354\) 8.79907 5.08015i 0.467666 0.270007i
\(355\) 0 0
\(356\) 7.18356i 0.380728i
\(357\) 5.41889 1.42983i 0.286798 0.0756749i
\(358\) −2.59178 + 2.59178i −0.136980 + 0.136980i
\(359\) 14.9791 + 8.64822i 0.790569 + 0.456435i 0.840163 0.542334i \(-0.182459\pi\)
−0.0495937 + 0.998769i \(0.515793\pi\)
\(360\) 0 0
\(361\) −14.9715 25.9315i −0.787976 1.36481i
\(362\) −0.621126 2.31807i −0.0326457 0.121835i
\(363\) 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
\(367\) 24.9992 + 6.69852i 1.30495 + 0.349660i 0.843319 0.537413i \(-0.180598\pi\)
0.461629 + 0.887073i \(0.347265\pi\)
\(368\) 1.69461 + 0.454069i 0.0883376 + 0.0236700i
\(369\) 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
\(373\) −2.37243 8.85404i −0.122840 0.458445i 0.876914 0.480648i \(-0.159599\pi\)
−0.999753 + 0.0222033i \(0.992932\pi\)
\(374\) −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
\(378\) −2.55820 + 0.675009i −0.131579 + 0.0347187i
\(379\) 18.6871i 0.959891i −0.877298 0.479946i \(-0.840656\pi\)
0.877298 0.479946i \(-0.159344\pi\)
\(380\) 0 0
\(381\) 5.84270 3.37328i 0.299331 0.172819i
\(382\) −2.09005 + 7.80016i −0.106936 + 0.399091i
\(383\) 19.1654 5.13534i 0.979304 0.262404i 0.266553 0.963820i \(-0.414115\pi\)
0.712752 + 0.701417i \(0.247449\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 0 0
\(386\) −1.72252 −0.0876740
\(387\) −2.66791 + 0.714864i −0.135618 + 0.0363386i
\(388\) −4.80269 + 17.9239i −0.243820 + 0.909948i
\(389\) 4.44026 2.56359i 0.225130 0.129979i −0.383193 0.923668i \(-0.625176\pi\)
0.608323 + 0.793689i \(0.291842\pi\)
\(390\) 0 0
\(391\) 3.71623i 0.187938i
\(392\) 4.91181 + 4.98740i 0.248084 + 0.251902i
\(393\) 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
\(397\) −6.83113 25.4941i −0.342844 1.27951i −0.895110 0.445845i \(-0.852903\pi\)
0.552266 0.833668i \(-0.313763\pi\)
\(398\) −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 \(0.0251104\pi\)
\(402\) 9.61398 + 2.57606i 0.479502 + 0.128482i
\(403\) −18.4091 4.93271i −0.917023 0.245716i
\(404\) 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
\(408\) −0.548242 2.04607i −0.0271420 0.101295i
\(409\) 17.8569 + 30.9290i 0.882967 + 1.52934i 0.848027 + 0.529954i \(0.177791\pi\)
0.0349400 + 0.999389i \(0.488876\pi\)
\(410\) 0 0
\(411\) 1.89199 + 1.09234i 0.0933251 + 0.0538813i
\(412\) 6.58048 6.58048i 0.324197 0.324197i
\(413\) −7.05656 + 25.9389i −0.347230 + 1.27637i
\(414\) 1.75439i 0.0862235i
\(415\) 0 0
\(416\) −2.95981 + 1.70885i −0.145117 + 0.0837832i
\(417\) 4.69616 17.5263i 0.229972 0.858267i
\(418\) −37.0740 + 9.93394i −1.81335 + 0.485885i
\(419\) −14.0414 −0.685966 −0.342983 0.939342i \(-0.611437\pi\)
−0.342983 + 0.939342i \(0.611437\pi\)
\(420\) 0 0
\(421\) 24.4332 1.19080 0.595401 0.803429i \(-0.296993\pi\)
0.595401 + 0.803429i \(0.296993\pi\)
\(422\) 9.98020 2.67419i 0.485829 0.130177i
\(423\) 0.912383 3.40506i 0.0443616 0.165560i
\(424\) −8.14273 + 4.70121i −0.395446 + 0.228311i
\(425\) 0 0
\(426\) 11.9716i 0.580025i
\(427\) 0.790881 + 2.99734i 0.0382734 + 0.145051i
\(428\) −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 \(0.449704\pi\)
\(432\) 0.258819 + 0.965926i 0.0124524 + 0.0464731i
\(433\) −7.85700 7.85700i −0.377583 0.377583i 0.492646 0.870230i \(-0.336030\pi\)
−0.870230 + 0.492646i \(0.836030\pi\)
\(434\) 14.7537 + 0.0563283i 0.708200 + 0.00270385i
\(435\) 0 0
\(436\) 0.168311 0.291523i 0.00806063 0.0139614i
\(437\) 11.8554 + 3.17664i 0.567119 + 0.151959i
\(438\) 4.70482 + 1.26065i 0.224805 + 0.0602363i
\(439\) −10.5640 + 18.2973i −0.504190 + 0.873283i 0.495798 + 0.868438i \(0.334876\pi\)
−0.999988 + 0.00484487i \(0.998458\pi\)
\(440\) 0 0
\(441\) 3.54619 6.03528i 0.168866 0.287394i
\(442\) −5.11912 5.11912i −0.243492 0.243492i
\(443\) −1.73709 6.48289i −0.0825314 0.308011i 0.912304 0.409514i \(-0.134302\pi\)
−0.994835 + 0.101503i \(0.967635\pi\)
\(444\) −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
\(448\) 1.87796 1.86367i 0.0887252 0.0880502i
\(449\) 8.28979i 0.391219i 0.980682 + 0.195610i \(0.0626685\pi\)
−0.980682 + 0.195610i \(0.937331\pi\)
\(450\) 0 0
\(451\) 11.9065 6.87424i 0.560657 0.323695i
\(452\) −3.72964 + 13.9192i −0.175428 + 0.654705i
\(453\) 20.5962 5.51873i 0.967693 0.259293i
\(454\) 18.0938 0.849182
\(455\) 0 0
\(456\) −6.99593 −0.327615
\(457\) 21.3296 5.71524i 0.997755 0.267348i 0.277250 0.960798i \(-0.410577\pi\)
0.720505 + 0.693450i \(0.243910\pi\)
\(458\) −2.49695 + 9.31876i −0.116675 + 0.435437i
\(459\) −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 \(-0.146001\pi\)
\(462\) −14.0063 3.81036i −0.651634 0.177274i
\(463\) 16.6091 16.6091i 0.771891 0.771891i −0.206546 0.978437i \(-0.566222\pi\)
0.978437 + 0.206546i \(0.0662222\pi\)
\(464\) 0.592889 + 0.342305i 0.0275242 + 0.0158911i
\(465\) 0 0
\(466\) −7.23665 12.5343i −0.335232 0.580638i
\(467\) −4.13837 15.4446i −0.191501 0.714691i −0.993145 0.116889i \(-0.962708\pi\)
0.801644 0.597802i \(-0.203959\pi\)
\(468\) 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
\(472\) 9.81409 + 2.62968i 0.451730 + 0.121041i
\(473\) −14.6370 3.92196i −0.673008 0.180332i
\(474\) −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
\(478\) −7.75773 28.9523i −0.354831 1.32425i
\(479\) −4.50526 7.80333i −0.205850 0.356543i 0.744553 0.667563i \(-0.232663\pi\)
−0.950403 + 0.311020i \(0.899329\pi\)
\(480\) 0 0
\(481\) −29.0066 16.7470i −1.32259 0.763595i
\(482\) 11.7522 11.7522i 0.535296 0.535296i
\(483\) 3.26961 + 3.29467i 0.148772 + 0.149913i
\(484\) 19.0995i 0.868158i
\(485\) 0 0
\(486\) 0.866025 0.500000i 0.0392837 0.0226805i
\(487\) −2.41740 + 9.02186i −0.109543 + 0.408820i −0.998821 0.0485475i \(-0.984541\pi\)
0.889278 + 0.457367i \(0.151207\pi\)
\(488\) 1.13174 0.303248i 0.0512313 0.0137274i
\(489\) 14.0810 0.636764
\(490\) 0 0
\(491\) 2.08535 0.0941107 0.0470554 0.998892i \(-0.485016\pi\)
0.0470554 + 0.998892i \(0.485016\pi\)
\(492\) 2.42058 0.648592i 0.109128 0.0292408i
\(493\) −0.375332 + 1.40076i −0.0169041 + 0.0630870i
\(494\) −20.7067 + 11.9550i −0.931637 + 0.537881i
\(495\) 0 0
\(496\) 5.57642i 0.250388i
\(497\) −22.3111 22.4821i −1.00079 1.00846i
\(498\) −4.05281 + 4.05281i −0.181611 + 0.181611i
\(499\) 11.6260 + 6.71229i 0.520452 + 0.300483i 0.737120 0.675762i \(-0.236185\pi\)
−0.216668 + 0.976245i \(0.569519\pi\)
\(500\) 0 0
\(501\) −4.29397 7.43738i −0.191841 0.332278i
\(502\) 2.78645 + 10.3992i 0.124366 + 0.464138i
\(503\) −7.19669 7.19669i −0.320885 0.320885i 0.528222 0.849106i \(-0.322859\pi\)
−0.849106 + 0.528222i \(0.822859\pi\)
\(504\) −2.28622 1.33161i −0.101836 0.0593148i
\(505\) 0 0
\(506\) 4.81255 8.33558i 0.213944 0.370562i
\(507\) −1.27438 0.341468i −0.0565970 0.0151651i
\(508\) 6.51668 + 1.74614i 0.289131 + 0.0774724i
\(509\) −2.14078 + 3.70794i −0.0948884 + 0.164352i −0.909562 0.415568i \(-0.863583\pi\)
0.814674 + 0.579920i \(0.196916\pi\)
\(510\) 0 0
\(511\) −11.1849 + 6.40079i −0.494791 + 0.283154i
\(512\) −0.707107 0.707107i −0.0312500 0.0312500i
\(513\) 1.81068 + 6.75755i 0.0799435 + 0.298353i
\(514\) 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
\(518\) 25.0194 + 6.80642i 1.09929 + 0.299057i
\(519\) 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 \(0.436774\pi\)
\(522\) 0.177190 0.661282i 0.00775540 0.0289435i
\(523\) −36.7904 + 9.85794i −1.60873 + 0.431058i −0.947664 0.319270i \(-0.896562\pi\)
−0.661066 + 0.750328i \(0.729896\pi\)
\(524\) 18.2091 0.795468
\(525\) 0 0
\(526\) 22.5315 0.982418
\(527\) 11.4097 3.05723i 0.497015 0.133175i
\(528\) −1.41996 + 5.29936i −0.0617958 + 0.230625i
\(529\) 17.2531 9.96106i 0.750133 0.433090i
\(530\) 0 0
\(531\) 10.1603i 0.440919i
\(532\) 13.1381 13.0381i 0.569607 0.565275i
\(533\) 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
\(537\) 0.948659 + 3.54044i 0.0409377 + 0.152781i
\(538\) −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 \(0.284723\pi\)
\(542\) 4.84547 + 1.29834i 0.208131 + 0.0557684i
\(543\) −2.31807 0.621126i −0.0994781 0.0266551i
\(544\) 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 0.749462 0.662048i \(-0.230312\pi\)
−0.662048 + 0.749462i \(0.730312\pi\)
\(548\) 0.565438 + 2.11024i 0.0241543 + 0.0901451i
\(549\) −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
\(553\) −5.62341 21.3120i −0.239132 0.906278i
\(554\) 6.33506i 0.269151i
\(555\) 0 0
\(556\) 15.7137 9.07229i 0.666408 0.384751i
\(557\) −1.08302 + 4.04187i −0.0458889 + 0.171260i −0.985067 0.172170i \(-0.944922\pi\)
0.939178 + 0.343430i \(0.111589\pi\)
\(558\) −5.38640 + 1.44328i −0.228025 + 0.0610990i
\(559\) −9.43977 −0.399260
\(560\) 0 0
\(561\) −11.6213 −0.490653
\(562\) −28.4681 + 7.62799i −1.20085 + 0.321767i
\(563\) −6.48217 + 24.1918i −0.273191 + 1.01956i 0.683853 + 0.729620i \(0.260303\pi\)
−0.957044 + 0.289943i \(0.906364\pi\)
\(564\) 3.05289 1.76259i 0.128550 0.0742183i
\(565\) 0 0
\(566\) 0.0978259i 0.00411193i
\(567\) −0.694523 + 2.55297i −0.0291672 + 0.107215i
\(568\) −8.46519 + 8.46519i −0.355191 + 0.355191i
\(569\) 1.99827 + 1.15370i 0.0837720 + 0.0483658i 0.541301 0.840829i \(-0.317932\pi\)
−0.457529 + 0.889195i \(0.651265\pi\)
\(570\) 0 0
\(571\) −7.94325 13.7581i −0.332415 0.575759i 0.650570 0.759446i \(-0.274530\pi\)
−0.982985 + 0.183687i \(0.941197\pi\)
\(572\) 4.85299 + 18.1116i 0.202914 + 0.757285i
\(573\) 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
\(577\) −3.86453 1.03550i −0.160883 0.0431084i 0.177479 0.984125i \(-0.443206\pi\)
−0.338361 + 0.941016i \(0.609873\pi\)
\(578\) −12.0867 3.23861i −0.502739 0.134709i
\(579\) −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
\(583\) 13.3510 + 49.8268i 0.552944 + 2.06361i
\(584\) 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 \(-0.799603\pi\)
0.588793 + 0.808284i \(0.299603\pi\)
\(588\) 6.77512 1.76005i 0.279401 0.0725833i
\(589\) 39.0122i 1.60747i
\(590\) 0 0
\(591\) −7.36285 + 4.25094i −0.302867 + 0.174860i
\(592\) 2.53646 9.46620i 0.104248 0.389059i
\(593\) −17.0986 + 4.58156i −0.702156 + 0.188142i −0.592196 0.805794i \(-0.701739\pi\)
−0.109960 + 0.993936i \(0.535072\pi\)
\(594\) 5.48630 0.225106
\(595\) 0 0
\(596\) 0.193656 0.00793245
\(597\) −10.6425 + 2.85165i −0.435569 + 0.116710i
\(598\) 1.55187 5.79167i 0.0634608 0.236839i
\(599\) 27.0972 15.6446i 1.10716 0.639220i 0.169069 0.985604i \(-0.445924\pi\)
0.938093 + 0.346384i \(0.112591\pi\)
\(600\) 0 0
\(601\) 47.5637i 1.94016i −0.242776 0.970082i \(-0.578058\pi\)
0.242776 0.970082i \(-0.421942\pi\)
\(602\) 7.06580 1.86439i 0.287980 0.0759869i
\(603\) 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
\(607\) −6.35260 23.7082i −0.257844 0.962287i −0.966486 0.256719i \(-0.917359\pi\)
0.708642 0.705568i \(-0.249308\pi\)
\(608\) −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
\(612\) −2.04607 0.548242i −0.0827074 0.0221614i
\(613\) −26.8884 7.20472i −1.08601 0.290996i −0.328955 0.944345i \(-0.606697\pi\)
−0.757056 + 0.653349i \(0.773363\pi\)
\(614\) −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 0.999901 0.0140365i \(-0.00446811\pi\)
−0.0140365 + 0.999901i \(0.504468\pi\)
\(618\) −2.40862 8.98910i −0.0968890 0.361595i
\(619\) 15.9137 + 27.5634i 0.639627 + 1.10787i 0.985515 + 0.169590i \(0.0542445\pi\)
−0.345888 + 0.938276i \(0.612422\pi\)
\(620\) 0 0
\(621\) −1.51935 0.877194i −0.0609692 0.0352006i
\(622\) −5.97174 + 5.97174i −0.239445 + 0.239445i
\(623\) 18.3770 4.84897i 0.736257 0.194270i
\(624\) 3.41770i 0.136817i
\(625\) 0 0
\(626\) 16.8092 9.70480i 0.671831 0.387882i
\(627\) −9.93394 + 37.0740i −0.396723 + 1.48059i
\(628\) 3.55464 0.952462i 0.141845 0.0380074i
\(629\) 20.7591 0.827719
\(630\) 0 0
\(631\) −34.9471 −1.39122 −0.695610 0.718419i \(-0.744866\pi\)
−0.695610 + 0.718419i \(0.744866\pi\)
\(632\) −8.04700 + 2.15619i −0.320092 + 0.0857685i
\(633\) 2.67419 9.98020i 0.106289 0.396677i
\(634\) −13.4670 + 7.77515i −0.534841 + 0.308791i
\(635\) 0 0
\(636\) 9.40242i 0.372830i
\(637\) 17.0454 16.7871i 0.675364 0.665128i
\(638\) 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 \(0.762148\pi\)
\(642\) 3.17510 + 11.8496i 0.125311 + 0.467668i
\(643\) 9.89036 + 9.89036i 0.390038 + 0.390038i 0.874701 0.484663i \(-0.161058\pi\)
−0.484663 + 0.874701i \(0.661058\pi\)
\(644\) −0.0177214 + 4.64164i −0.000698320 + 0.182906i
\(645\) 0 0
\(646\) 7.40955 12.8337i 0.291525 0.504936i
\(647\) −15.1576 4.06147i −0.595908 0.159673i −0.0517559 0.998660i \(-0.516482\pi\)
−0.544152 + 0.838987i \(0.683148\pi\)
\(648\) 0.965926 + 0.258819i 0.0379452 + 0.0101674i
\(649\) 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
\(653\) −4.12761 15.4045i −0.161526 0.602823i −0.998458 0.0555160i \(-0.982320\pi\)
0.836932 0.547307i \(-0.184347\pi\)
\(654\) −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
\(658\) −2.44832 + 8.99966i −0.0954453 + 0.350843i
\(659\) 10.4778i 0.408157i −0.978955 0.204078i \(-0.934580\pi\)
0.978955 0.204078i \(-0.0654198\pi\)
\(660\) 0 0
\(661\) −20.9764 + 12.1107i −0.815888 + 0.471053i −0.848996 0.528399i \(-0.822793\pi\)
0.0331084 + 0.999452i \(0.489459\pi\)
\(662\) −4.18923 + 15.6344i −0.162819 + 0.607648i
\(663\) −6.99285 + 1.87373i −0.271580 + 0.0727695i
\(664\) −5.73154 −0.222427
\(665\) 0 0
\(666\) −9.80013 −0.379747
\(667\) −1.16015 + 0.310860i −0.0449210 + 0.0120366i
\(668\) 2.22272 8.29532i 0.0859998 0.320955i
\(669\) 4.17862 2.41253i 0.161555 0.0932736i
\(670\) 0 0
\(671\) 6.42808i 0.248153i
\(672\) −0.675009 2.55820i −0.0260390 0.0986845i
\(673\) 1.16725 1.16725i 0.0449943 0.0449943i −0.684252 0.729246i \(-0.739871\pi\)
0.729246 + 0.684252i \(0.239871\pi\)
\(674\) −23.5218 13.5803i −0.906025 0.523094i
\(675\) 0 0
\(676\) −0.659666 1.14257i −0.0253718 0.0439452i
\(677\) 3.32260 + 12.4001i 0.127698 + 0.476575i 0.999921 0.0125322i \(-0.00398922\pi\)
−0.872223 + 0.489108i \(0.837323\pi\)
\(678\) 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
\(682\) −29.5514 7.91828i −1.13158 0.303207i
\(683\) 20.6373 + 5.52974i 0.789663 + 0.211589i 0.631040 0.775750i \(-0.282628\pi\)
0.158622 + 0.987339i \(0.449295\pi\)
\(684\) −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
\(688\) −0.714864 2.66791i −0.0272540 0.101713i
\(689\) 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
\(693\) −10.3030 + 10.2247i −0.391380 + 0.388403i
\(694\) 10.2657i 0.389681i
\(695\) 0 0
\(696\) 0.592889 0.342305i 0.0224734 0.0129750i
\(697\) −1.37388 + 5.12738i −0.0520393 + 0.194213i
\(698\) −6.38903 + 1.71194i −0.241828 + 0.0647977i
\(699\) −14.4733 −0.547431
\(700\) 0 0
\(701\) 44.5959 1.68436 0.842182 0.539194i \(-0.181271\pi\)
0.842182 + 0.539194i \(0.181271\pi\)
\(702\) 3.30124 0.884566i 0.124597 0.0333858i
\(703\) 17.7449 66.2249i 0.669262 2.49772i
\(704\) −4.75127 + 2.74315i −0.179070 + 0.103386i
\(705\) 0 0
\(706\) 13.6247i 0.512772i
\(707\) 21.1071 + 5.74208i 0.793813 + 0.215953i
\(708\) 7.18441 7.18441i 0.270007 0.270007i
\(709\) −35.8750 20.7125i −1.34732 0.777873i −0.359447 0.933166i \(-0.617035\pi\)
−0.987869 + 0.155293i \(0.950368\pi\)
\(710\) 0 0
\(711\) 4.16543 + 7.21474i 0.156216 + 0.270574i
\(712\) −1.85924 6.93879i −0.0696781 0.260042i
\(713\) 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
\(717\) −28.9523 7.75773i −1.08124 0.289718i
\(718\) 16.7071 + 4.47665i 0.623502 + 0.167067i
\(719\) 11.7839 20.4103i 0.439464 0.761174i −0.558184 0.829717i \(-0.688502\pi\)
0.997648 + 0.0685431i \(0.0218351\pi\)
\(720\) 0 0
\(721\) 21.2760 + 12.3923i 0.792361 + 0.461512i
\(722\) −21.1730 21.1730i −0.787976 0.787976i
\(723\) −4.30159 16.0538i −0.159978 0.597046i
\(724\) −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 \(-0.721701\pi\)
0.767096 + 0.641532i \(0.221701\pi\)
\(728\) −6.36947 6.41829i −0.236068 0.237878i
\(729\) 1.00000i 0.0370370i
\(730\) 0 0
\(731\) 5.06681 2.92532i 0.187403 0.108197i
\(732\) 0.303248 1.13174i 0.0112084 0.0418302i
\(733\) −37.9373 + 10.1653i −1.40125 + 0.375463i −0.878792 0.477204i \(-0.841650\pi\)
−0.522454 + 0.852667i \(0.674983\pi\)
\(734\) 25.8811 0.955288
\(735\) 0 0
\(736\) 1.75439 0.0646676
\(737\) 52.7452 14.1330i 1.94289 0.520597i
\(738\) 0.648592 2.42058i 0.0238750 0.0891027i
\(739\) −38.6211 + 22.2979i −1.42070 + 0.820242i −0.996359 0.0852593i \(-0.972828\pi\)
−0.424343 + 0.905502i \(0.639495\pi\)
\(740\) 0 0
\(741\) 23.9100i 0.878356i
\(742\) −17.5230 17.6573i −0.643291 0.648222i
\(743\) −24.7787 + 24.7787i −0.909041 + 0.909041i −0.996195 0.0871537i \(-0.972223\pi\)
0.0871537 + 0.996195i \(0.472223\pi\)
\(744\) −4.82932 2.78821i −0.177051 0.102221i
\(745\) 0 0
\(746\) −4.58319 7.93832i −0.167802 0.290642i
\(747\) 1.48343 + 5.53624i 0.0542759 + 0.202561i
\(748\) −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 \(0.196297\pi\)
\(752\) 3.40506 + 0.912383i 0.124170 + 0.0332712i
\(753\) 10.3992 + 2.78645i 0.378967 + 0.101544i
\(754\) 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 0.292509 0.956263i \(-0.405510\pi\)
−0.956263 + 0.292509i \(0.905510\pi\)
\(758\) −4.83657 18.0503i −0.175672 0.655618i
\(759\) −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
\(763\) 0.859384 + 0.233791i 0.0311118 + 0.00846382i
\(764\) 8.07532i 0.292155i
\(765\) 0 0
\(766\) 17.1832 9.92072i 0.620854 0.358450i
\(767\) 8.98745 33.5416i 0.324518 1.21112i
\(768\) −0.965926 + 0.258819i −0.0348548 + 0.00933933i
\(769\) 3.03517 0.109451 0.0547256 0.998501i \(-0.482572\pi\)
0.0547256 + 0.998501i \(0.482572\pi\)
\(770\) 0 0
\(771\) 15.0425 0.541742
\(772\) −1.66383 + 0.445821i −0.0598825 + 0.0160455i
\(773\) 12.5554 46.8575i 0.451588 1.68535i −0.246342 0.969183i \(-0.579229\pi\)
0.697930 0.716166i \(-0.254105\pi\)
\(774\) −2.39198 + 1.38101i −0.0859781 + 0.0496395i
\(775\) 0 0
\(776\) 18.5562i 0.666128i
\(777\) 18.4042 18.2642i 0.660248 0.655226i
\(778\) 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