Properties

Label 441.2.h.d.373.1
Level $441$
Weight $2$
Character 441.373
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\zeta_{18})\)
Defining polynomial: \(x^{6} - x^{3} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.1
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.d.214.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.879385 q^{2} +(1.70574 - 0.300767i) q^{3} -1.22668 q^{4} +(-0.673648 - 1.16679i) q^{5} +(-1.50000 + 0.264490i) q^{6} +2.83750 q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\) \(q-0.879385 q^{2} +(1.70574 - 0.300767i) q^{3} -1.22668 q^{4} +(-0.673648 - 1.16679i) q^{5} +(-1.50000 + 0.264490i) q^{6} +2.83750 q^{8} +(2.81908 - 1.02606i) q^{9} +(0.592396 + 1.02606i) q^{10} +(-0.826352 + 1.43128i) q^{11} +(-2.09240 + 0.368946i) q^{12} +(1.68479 - 2.91815i) q^{13} +(-1.50000 - 1.78763i) q^{15} -0.0418891 q^{16} +(-0.233956 - 0.405223i) q^{17} +(-2.47906 + 0.902302i) q^{18} +(1.61334 - 2.79439i) q^{19} +(0.826352 + 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +(-4.47178 - 7.74535i) q^{23} +(4.84002 - 0.853427i) q^{24} +(1.59240 - 2.75811i) q^{25} +(-1.48158 + 2.56617i) q^{26} +(4.50000 - 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(1.31908 + 1.57202i) q^{30} +9.23442 q^{31} -5.63816 q^{32} +(-0.979055 + 2.68993i) q^{33} +(0.205737 + 0.356347i) q^{34} +(-3.45811 + 1.25865i) q^{36} +(-4.61721 + 7.99724i) q^{37} +(-1.41875 + 2.45734i) q^{38} +(1.99613 - 5.48432i) q^{39} +(-1.91147 - 3.31077i) q^{40} +(-1.70574 + 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(1.01367 - 1.75573i) q^{44} +(-3.09627 - 2.59808i) q^{45} +(3.93242 + 6.81115i) q^{46} +9.35504 q^{47} +(-0.0714517 + 0.0125989i) q^{48} +(-1.40033 + 2.42544i) q^{50} +(-0.520945 - 0.620838i) q^{51} +(-2.06670 + 3.57964i) q^{52} +(0.286989 + 0.497079i) q^{53} +(-3.95723 + 2.28471i) q^{54} +2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} +(2.75624 + 4.77396i) q^{58} -10.3969 q^{59} +(1.84002 + 2.19285i) q^{60} +7.63816 q^{61} -8.12061 q^{62} +5.04189 q^{64} -4.53983 q^{65} +(0.860967 - 2.36549i) q^{66} +0.596267 q^{67} +(0.286989 + 0.497079i) q^{68} +(-9.95723 - 11.8666i) q^{69} -0.554378 q^{71} +(7.99912 - 2.91144i) q^{72} +(-1.02481 - 1.77503i) q^{73} +(4.06031 - 7.03266i) q^{74} +(1.88666 - 5.18355i) q^{75} +(-1.97906 + 3.42782i) q^{76} +(-1.75537 + 4.82283i) q^{78} -2.40373 q^{79} +(0.0282185 + 0.0488759i) q^{80} +(6.89440 - 5.78509i) q^{81} +(1.50000 - 2.59808i) q^{82} +(7.52481 + 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +(-1.93969 - 3.35965i) q^{86} +(-6.97906 - 8.31731i) q^{87} +(-2.34477 + 4.06126i) q^{88} +(-4.54323 + 7.86911i) q^{89} +(2.72281 + 2.28471i) q^{90} +(5.48545 + 9.50108i) q^{92} +(15.7515 - 2.77741i) q^{93} -8.22668 q^{94} -4.34730 q^{95} +(-9.61721 + 1.69577i) q^{96} +(0.949493 + 1.64457i) q^{97} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} + 6q^{4} - 3q^{5} - 9q^{6} + 12q^{8} + O(q^{10}) \) \( 6q + 6q^{2} + 6q^{4} - 3q^{5} - 9q^{6} + 12q^{8} - 6q^{11} - 9q^{12} + 3q^{13} - 9q^{15} + 6q^{16} - 6q^{17} - 18q^{18} + 3q^{19} + 6q^{20} - 9q^{22} - 12q^{23} + 9q^{24} + 6q^{25} + 3q^{26} + 27q^{27} - 9q^{29} - 9q^{30} - 6q^{31} - 9q^{33} - 9q^{34} - 27q^{36} + 3q^{37} - 6q^{38} + 36q^{39} + 9q^{40} + 3q^{43} - 15q^{44} + 9q^{45} + 6q^{47} + 6q^{50} + 21q^{52} - 6q^{53} + 27q^{54} - 9q^{57} + 9q^{58} - 6q^{59} - 9q^{60} + 12q^{61} - 60q^{62} + 24q^{64} + 30q^{65} - 18q^{66} - 24q^{67} - 6q^{68} - 9q^{69} + 18q^{71} - 9q^{72} + 21q^{73} + 30q^{74} + 18q^{75} - 15q^{76} + 54q^{78} - 42q^{79} + 15q^{80} + 9q^{82} + 18q^{83} - 9q^{85} - 6q^{86} - 45q^{87} - 27q^{88} - 12q^{89} + 27q^{90} - 3q^{92} + 54q^{93} - 36q^{94} - 24q^{95} - 27q^{96} + 3q^{97} + 18q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.879385 −0.621819 −0.310910 0.950439i \(-0.600634\pi\)
−0.310910 + 0.950439i \(0.600634\pi\)
\(3\) 1.70574 0.300767i 0.984808 0.173648i
\(4\) −1.22668 −0.613341
\(5\) −0.673648 1.16679i −0.301265 0.521806i 0.675158 0.737673i \(-0.264075\pi\)
−0.976423 + 0.215867i \(0.930742\pi\)
\(6\) −1.50000 + 0.264490i −0.612372 + 0.107978i
\(7\) 0 0
\(8\) 2.83750 1.00321
\(9\) 2.81908 1.02606i 0.939693 0.342020i
\(10\) 0.592396 + 1.02606i 0.187332 + 0.324469i
\(11\) −0.826352 + 1.43128i −0.249154 + 0.431548i −0.963291 0.268458i \(-0.913486\pi\)
0.714137 + 0.700006i \(0.246819\pi\)
\(12\) −2.09240 + 0.368946i −0.604023 + 0.106506i
\(13\) 1.68479 2.91815i 0.467277 0.809348i −0.532024 0.846729i \(-0.678568\pi\)
0.999301 + 0.0373813i \(0.0119016\pi\)
\(14\) 0 0
\(15\) −1.50000 1.78763i −0.387298 0.461564i
\(16\) −0.0418891 −0.0104723
\(17\) −0.233956 0.405223i −0.0567426 0.0982810i 0.836259 0.548335i \(-0.184738\pi\)
−0.893001 + 0.450054i \(0.851405\pi\)
\(18\) −2.47906 + 0.902302i −0.584319 + 0.212675i
\(19\) 1.61334 2.79439i 0.370126 0.641077i −0.619459 0.785029i \(-0.712648\pi\)
0.989585 + 0.143953i \(0.0459813\pi\)
\(20\) 0.826352 + 1.43128i 0.184778 + 0.320045i
\(21\) 0 0
\(22\) 0.726682 1.25865i 0.154929 0.268345i
\(23\) −4.47178 7.74535i −0.932431 1.61502i −0.779152 0.626835i \(-0.784350\pi\)
−0.153279 0.988183i \(-0.548983\pi\)
\(24\) 4.84002 0.853427i 0.987965 0.174205i
\(25\) 1.59240 2.75811i 0.318479 0.551622i
\(26\) −1.48158 + 2.56617i −0.290562 + 0.503268i
\(27\) 4.50000 2.59808i 0.866025 0.500000i
\(28\) 0 0
\(29\) −3.13429 5.42874i −0.582022 1.00809i −0.995239 0.0974595i \(-0.968928\pi\)
0.413217 0.910632i \(-0.364405\pi\)
\(30\) 1.31908 + 1.57202i 0.240830 + 0.287010i
\(31\) 9.23442 1.65855 0.829276 0.558840i \(-0.188753\pi\)
0.829276 + 0.558840i \(0.188753\pi\)
\(32\) −5.63816 −0.996695
\(33\) −0.979055 + 2.68993i −0.170432 + 0.468257i
\(34\) 0.205737 + 0.356347i 0.0352836 + 0.0611130i
\(35\) 0 0
\(36\) −3.45811 + 1.25865i −0.576352 + 0.209775i
\(37\) −4.61721 + 7.99724i −0.759065 + 1.31474i 0.184263 + 0.982877i \(0.441010\pi\)
−0.943328 + 0.331862i \(0.892323\pi\)
\(38\) −1.41875 + 2.45734i −0.230151 + 0.398634i
\(39\) 1.99613 5.48432i 0.319637 0.878194i
\(40\) −1.91147 3.31077i −0.302231 0.523479i
\(41\) −1.70574 + 2.95442i −0.266391 + 0.461403i −0.967927 0.251231i \(-0.919165\pi\)
0.701536 + 0.712634i \(0.252498\pi\)
\(42\) 0 0
\(43\) 2.20574 + 3.82045i 0.336372 + 0.582613i 0.983747 0.179558i \(-0.0574668\pi\)
−0.647376 + 0.762171i \(0.724133\pi\)
\(44\) 1.01367 1.75573i 0.152817 0.264686i
\(45\) −3.09627 2.59808i −0.461564 0.387298i
\(46\) 3.93242 + 6.81115i 0.579803 + 1.00425i
\(47\) 9.35504 1.36457 0.682286 0.731085i \(-0.260986\pi\)
0.682286 + 0.731085i \(0.260986\pi\)
\(48\) −0.0714517 + 0.0125989i −0.0103132 + 0.00181849i
\(49\) 0 0
\(50\) −1.40033 + 2.42544i −0.198037 + 0.343009i
\(51\) −0.520945 0.620838i −0.0729468 0.0869346i
\(52\) −2.06670 + 3.57964i −0.286600 + 0.496406i
\(53\) 0.286989 + 0.497079i 0.0394210 + 0.0682791i 0.885063 0.465472i \(-0.154115\pi\)
−0.845642 + 0.533751i \(0.820782\pi\)
\(54\) −3.95723 + 2.28471i −0.538511 + 0.310910i
\(55\) 2.22668 0.300246
\(56\) 0 0
\(57\) 1.91147 5.25173i 0.253181 0.695609i
\(58\) 2.75624 + 4.77396i 0.361913 + 0.626851i
\(59\) −10.3969 −1.35356 −0.676782 0.736183i \(-0.736626\pi\)
−0.676782 + 0.736183i \(0.736626\pi\)
\(60\) 1.84002 + 2.19285i 0.237546 + 0.283096i
\(61\) 7.63816 0.977966 0.488983 0.872293i \(-0.337368\pi\)
0.488983 + 0.872293i \(0.337368\pi\)
\(62\) −8.12061 −1.03132
\(63\) 0 0
\(64\) 5.04189 0.630236
\(65\) −4.53983 −0.563097
\(66\) 0.860967 2.36549i 0.105978 0.291171i
\(67\) 0.596267 0.0728456 0.0364228 0.999336i \(-0.488404\pi\)
0.0364228 + 0.999336i \(0.488404\pi\)
\(68\) 0.286989 + 0.497079i 0.0348025 + 0.0602797i
\(69\) −9.95723 11.8666i −1.19871 1.42857i
\(70\) 0 0
\(71\) −0.554378 −0.0657925 −0.0328963 0.999459i \(-0.510473\pi\)
−0.0328963 + 0.999459i \(0.510473\pi\)
\(72\) 7.99912 2.91144i 0.942706 0.343117i
\(73\) −1.02481 1.77503i −0.119946 0.207752i 0.799800 0.600266i \(-0.204939\pi\)
−0.919746 + 0.392514i \(0.871605\pi\)
\(74\) 4.06031 7.03266i 0.472001 0.817530i
\(75\) 1.88666 5.18355i 0.217853 0.598545i
\(76\) −1.97906 + 3.42782i −0.227013 + 0.393198i
\(77\) 0 0
\(78\) −1.75537 + 4.82283i −0.198756 + 0.546078i
\(79\) −2.40373 −0.270441 −0.135221 0.990816i \(-0.543174\pi\)
−0.135221 + 0.990816i \(0.543174\pi\)
\(80\) 0.0282185 + 0.0488759i 0.00315492 + 0.00546449i
\(81\) 6.89440 5.78509i 0.766044 0.642788i
\(82\) 1.50000 2.59808i 0.165647 0.286910i
\(83\) 7.52481 + 13.0334i 0.825956 + 1.43060i 0.901187 + 0.433431i \(0.142697\pi\)
−0.0752309 + 0.997166i \(0.523969\pi\)
\(84\) 0 0
\(85\) −0.315207 + 0.545955i −0.0341891 + 0.0592172i
\(86\) −1.93969 3.35965i −0.209162 0.362280i
\(87\) −6.97906 8.31731i −0.748233 0.891710i
\(88\) −2.34477 + 4.06126i −0.249953 + 0.432932i
\(89\) −4.54323 + 7.86911i −0.481582 + 0.834124i −0.999777 0.0211385i \(-0.993271\pi\)
0.518195 + 0.855263i \(0.326604\pi\)
\(90\) 2.72281 + 2.28471i 0.287010 + 0.240830i
\(91\) 0 0
\(92\) 5.48545 + 9.50108i 0.571898 + 0.990556i
\(93\) 15.7515 2.77741i 1.63335 0.288004i
\(94\) −8.22668 −0.848517
\(95\) −4.34730 −0.446023
\(96\) −9.61721 + 1.69577i −0.981553 + 0.173074i
\(97\) 0.949493 + 1.64457i 0.0964064 + 0.166981i 0.910195 0.414181i \(-0.135932\pi\)
−0.813788 + 0.581161i \(0.802598\pi\)
\(98\) 0 0
\(99\) −0.860967 + 4.88279i −0.0865304 + 0.490738i
\(100\) −1.95336 + 3.38332i −0.195336 + 0.338332i
\(101\) 0.854570 1.48016i 0.0850329 0.147281i −0.820372 0.571830i \(-0.806234\pi\)
0.905405 + 0.424548i \(0.139567\pi\)
\(102\) 0.458111 + 0.545955i 0.0453597 + 0.0540576i
\(103\) 1.81908 + 3.15074i 0.179239 + 0.310451i 0.941620 0.336677i \(-0.109303\pi\)
−0.762381 + 0.647128i \(0.775970\pi\)
\(104\) 4.78059 8.28023i 0.468776 0.811943i
\(105\) 0 0
\(106\) −0.252374 0.437124i −0.0245127 0.0424573i
\(107\) −3.56418 + 6.17334i −0.344562 + 0.596799i −0.985274 0.170982i \(-0.945306\pi\)
0.640712 + 0.767781i \(0.278639\pi\)
\(108\) −5.52007 + 3.18701i −0.531169 + 0.306670i
\(109\) −0.201867 0.349643i −0.0193353 0.0334898i 0.856196 0.516651i \(-0.172822\pi\)
−0.875531 + 0.483162i \(0.839488\pi\)
\(110\) −1.95811 −0.186699
\(111\) −5.47044 + 15.0299i −0.519231 + 1.42658i
\(112\) 0 0
\(113\) −7.18479 + 12.4444i −0.675888 + 1.17067i 0.300320 + 0.953839i \(0.402907\pi\)
−0.976208 + 0.216835i \(0.930427\pi\)
\(114\) −1.68092 + 4.61830i −0.157433 + 0.432543i
\(115\) −6.02481 + 10.4353i −0.561817 + 0.973095i
\(116\) 3.84477 + 6.65934i 0.356978 + 0.618304i
\(117\) 1.75537 9.95518i 0.162284 0.920357i
\(118\) 9.14290 0.841672
\(119\) 0 0
\(120\) −4.25624 5.07239i −0.388540 0.463044i
\(121\) 4.13429 + 7.16079i 0.375844 + 0.650981i
\(122\) −6.71688 −0.608118
\(123\) −2.02094 + 5.55250i −0.182222 + 0.500652i
\(124\) −11.3277 −1.01726
\(125\) −11.0273 −0.986315
\(126\) 0 0
\(127\) −20.7716 −1.84318 −0.921589 0.388167i \(-0.873108\pi\)
−0.921589 + 0.388167i \(0.873108\pi\)
\(128\) 6.84255 0.604802
\(129\) 4.91147 + 5.85327i 0.432431 + 0.515351i
\(130\) 3.99226 0.350144
\(131\) 3.58260 + 6.20524i 0.313013 + 0.542154i 0.979013 0.203797i \(-0.0653284\pi\)
−0.666000 + 0.745952i \(0.731995\pi\)
\(132\) 1.20099 3.29969i 0.104533 0.287201i
\(133\) 0 0
\(134\) −0.524348 −0.0452968
\(135\) −6.06283 3.50038i −0.521806 0.301265i
\(136\) −0.663848 1.14982i −0.0569245 0.0985961i
\(137\) −1.28446 + 2.22475i −0.109739 + 0.190074i −0.915665 0.401943i \(-0.868335\pi\)
0.805925 + 0.592017i \(0.201668\pi\)
\(138\) 8.75624 + 10.4353i 0.745381 + 0.888310i
\(139\) 3.06670 5.31169i 0.260114 0.450531i −0.706158 0.708055i \(-0.749573\pi\)
0.966272 + 0.257523i \(0.0829064\pi\)
\(140\) 0 0
\(141\) 15.9572 2.81369i 1.34384 0.236956i
\(142\) 0.487511 0.0409111
\(143\) 2.78446 + 4.82283i 0.232848 + 0.403305i
\(144\) −0.118089 + 0.0429807i −0.00984071 + 0.00358173i
\(145\) −4.22281 + 7.31412i −0.350685 + 0.607405i
\(146\) 0.901207 + 1.56094i 0.0745844 + 0.129184i
\(147\) 0 0
\(148\) 5.66385 9.81007i 0.465565 0.806383i
\(149\) −0.215537 0.373321i −0.0176575 0.0305837i 0.857062 0.515214i \(-0.172288\pi\)
−0.874719 + 0.484630i \(0.838954\pi\)
\(150\) −1.65910 + 4.55834i −0.135465 + 0.372187i
\(151\) 1.23530 2.13960i 0.100527 0.174118i −0.811375 0.584526i \(-0.801280\pi\)
0.911902 + 0.410408i \(0.134614\pi\)
\(152\) 4.57785 7.92907i 0.371313 0.643132i
\(153\) −1.07532 0.902302i −0.0869346 0.0729468i
\(154\) 0 0
\(155\) −6.22075 10.7747i −0.499663 0.865441i
\(156\) −2.44862 + 6.72752i −0.196046 + 0.538632i
\(157\) 10.1334 0.808734 0.404367 0.914597i \(-0.367492\pi\)
0.404367 + 0.914597i \(0.367492\pi\)
\(158\) 2.11381 0.168166
\(159\) 0.639033 + 0.761570i 0.0506786 + 0.0603964i
\(160\) 3.79813 + 6.57856i 0.300269 + 0.520081i
\(161\) 0 0
\(162\) −6.06283 + 5.08732i −0.476341 + 0.399698i
\(163\) 1.29813 2.24843i 0.101678 0.176111i −0.810698 0.585464i \(-0.800912\pi\)
0.912376 + 0.409353i \(0.134246\pi\)
\(164\) 2.09240 3.62414i 0.163389 0.282998i
\(165\) 3.79813 0.669713i 0.295684 0.0521371i
\(166\) −6.61721 11.4613i −0.513595 0.889573i
\(167\) 11.5915 20.0771i 0.896979 1.55361i 0.0656422 0.997843i \(-0.479090\pi\)
0.831337 0.555769i \(-0.187576\pi\)
\(168\) 0 0
\(169\) 0.822948 + 1.42539i 0.0633037 + 0.109645i
\(170\) 0.277189 0.480105i 0.0212594 0.0368224i
\(171\) 1.68092 9.53298i 0.128543 0.729005i
\(172\) −2.70574 4.68647i −0.206311 0.357340i
\(173\) −4.75196 −0.361285 −0.180643 0.983549i \(-0.557818\pi\)
−0.180643 + 0.983549i \(0.557818\pi\)
\(174\) 6.13728 + 7.31412i 0.465266 + 0.554482i
\(175\) 0 0
\(176\) 0.0346151 0.0599551i 0.00260921 0.00451929i
\(177\) −17.7344 + 3.12706i −1.33300 + 0.235044i
\(178\) 3.99525 6.91998i 0.299457 0.518674i
\(179\) 4.26604 + 7.38901i 0.318859 + 0.552280i 0.980250 0.197761i \(-0.0633670\pi\)
−0.661391 + 0.750041i \(0.730034\pi\)
\(180\) 3.79813 + 3.18701i 0.283096 + 0.237546i
\(181\) −17.2344 −1.28102 −0.640512 0.767948i \(-0.721278\pi\)
−0.640512 + 0.767948i \(0.721278\pi\)
\(182\) 0 0
\(183\) 13.0287 2.29731i 0.963108 0.169822i
\(184\) −12.6887 21.9774i −0.935421 1.62020i
\(185\) 12.4415 0.914718
\(186\) −13.8516 + 2.44242i −1.01565 + 0.179087i
\(187\) 0.773318 0.0565506
\(188\) −11.4757 −0.836948
\(189\) 0 0
\(190\) 3.82295 0.277346
\(191\) 12.9094 0.934092 0.467046 0.884233i \(-0.345318\pi\)
0.467046 + 0.884233i \(0.345318\pi\)
\(192\) 8.60014 1.51644i 0.620661 0.109439i
\(193\) −0.638156 −0.0459355 −0.0229677 0.999736i \(-0.507311\pi\)
−0.0229677 + 0.999736i \(0.507311\pi\)
\(194\) −0.834970 1.44621i −0.0599473 0.103832i
\(195\) −7.74376 + 1.36543i −0.554542 + 0.0977807i
\(196\) 0 0
\(197\) 11.4456 0.815467 0.407733 0.913101i \(-0.366319\pi\)
0.407733 + 0.913101i \(0.366319\pi\)
\(198\) 0.757122 4.29385i 0.0538063 0.305151i
\(199\) 1.81908 + 3.15074i 0.128951 + 0.223350i 0.923270 0.384151i \(-0.125506\pi\)
−0.794319 + 0.607500i \(0.792172\pi\)
\(200\) 4.51842 7.82613i 0.319500 0.553391i
\(201\) 1.01707 0.179338i 0.0717389 0.0126495i
\(202\) −0.751497 + 1.30163i −0.0528751 + 0.0915824i
\(203\) 0 0
\(204\) 0.639033 + 0.761570i 0.0447413 + 0.0533206i
\(205\) 4.59627 0.321017
\(206\) −1.59967 2.77071i −0.111454 0.193045i
\(207\) −20.5535 17.2464i −1.42857 1.19871i
\(208\) −0.0705744 + 0.122238i −0.00489345 + 0.00847571i
\(209\) 2.66637 + 4.61830i 0.184437 + 0.319454i
\(210\) 0 0
\(211\) −2.91147 + 5.04282i −0.200434 + 0.347162i −0.948668 0.316273i \(-0.897569\pi\)
0.748234 + 0.663435i \(0.230902\pi\)
\(212\) −0.352044 0.609758i −0.0241785 0.0418784i
\(213\) −0.945622 + 0.166739i −0.0647930 + 0.0114248i
\(214\) 3.13429 5.42874i 0.214255 0.371101i
\(215\) 2.97178 5.14728i 0.202674 0.351041i
\(216\) 12.7687 7.37203i 0.868802 0.501603i
\(217\) 0 0
\(218\) 0.177519 + 0.307471i 0.0120231 + 0.0208246i
\(219\) −2.28194 2.71951i −0.154199 0.183767i
\(220\) −2.73143 −0.184153
\(221\) −1.57667 −0.106058
\(222\) 4.81062 13.2171i 0.322868 0.887072i
\(223\) −3.54189 6.13473i −0.237182 0.410812i 0.722722 0.691139i \(-0.242891\pi\)
−0.959905 + 0.280327i \(0.909557\pi\)
\(224\) 0 0
\(225\) 1.65910 9.40923i 0.110607 0.627282i
\(226\) 6.31820 10.9434i 0.420280 0.727947i
\(227\) 5.97178 10.3434i 0.396361 0.686517i −0.596913 0.802306i \(-0.703606\pi\)
0.993274 + 0.115789i \(0.0369395\pi\)
\(228\) −2.34477 + 6.44220i −0.155286 + 0.426645i
\(229\) 8.77631 + 15.2010i 0.579955 + 1.00451i 0.995484 + 0.0949315i \(0.0302632\pi\)
−0.415529 + 0.909580i \(0.636403\pi\)
\(230\) 5.29813 9.17664i 0.349349 0.605089i
\(231\) 0 0
\(232\) −8.89352 15.4040i −0.583888 1.01132i
\(233\) −8.12701 + 14.0764i −0.532418 + 0.922175i 0.466865 + 0.884328i \(0.345383\pi\)
−0.999284 + 0.0378470i \(0.987950\pi\)
\(234\) −1.54364 + 8.75444i −0.100911 + 0.572296i
\(235\) −6.30200 10.9154i −0.411097 0.712042i
\(236\) 12.7537 0.830196
\(237\) −4.10014 + 0.722965i −0.266333 + 0.0469616i
\(238\) 0 0
\(239\) 7.54963 13.0763i 0.488345 0.845838i −0.511565 0.859244i \(-0.670934\pi\)
0.999910 + 0.0134062i \(0.00426745\pi\)
\(240\) 0.0628336 + 0.0748822i 0.00405589 + 0.00483362i
\(241\) 7.81908 13.5430i 0.503671 0.872384i −0.496320 0.868140i \(-0.665316\pi\)
0.999991 0.00424420i \(-0.00135097\pi\)
\(242\) −3.63563 6.29710i −0.233707 0.404793i
\(243\) 10.0201 11.9415i 0.642788 0.766044i
\(244\) −9.36959 −0.599826
\(245\) 0 0
\(246\) 1.77719 4.88279i 0.113309 0.311315i
\(247\) −5.43629 9.41593i −0.345903 0.599121i
\(248\) 26.2026 1.66387
\(249\) 16.7554 + 19.9683i 1.06183 + 1.26544i
\(250\) 9.69728 0.613310
\(251\) 19.0651 1.20338 0.601690 0.798730i \(-0.294494\pi\)
0.601690 + 0.798730i \(0.294494\pi\)
\(252\) 0 0
\(253\) 14.7811 0.929277
\(254\) 18.2662 1.14612
\(255\) −0.373455 + 1.02606i −0.0233867 + 0.0642544i
\(256\) −16.1010 −1.00631
\(257\) −13.2909 23.0204i −0.829061 1.43598i −0.898776 0.438409i \(-0.855542\pi\)
0.0697146 0.997567i \(-0.477791\pi\)
\(258\) −4.31908 5.14728i −0.268894 0.320455i
\(259\) 0 0
\(260\) 5.56893 0.345370
\(261\) −14.4060 12.0881i −0.891710 0.748233i
\(262\) −3.15048 5.45680i −0.194637 0.337122i
\(263\) 0.367059 0.635765i 0.0226338 0.0392029i −0.854487 0.519473i \(-0.826128\pi\)
0.877120 + 0.480270i \(0.159461\pi\)
\(264\) −2.77807 + 7.63267i −0.170978 + 0.469759i
\(265\) 0.386659 0.669713i 0.0237523 0.0411402i
\(266\) 0 0
\(267\) −5.38279 + 14.7891i −0.329421 + 0.905078i
\(268\) −0.731429 −0.0446792
\(269\) 10.4251 + 18.0569i 0.635632 + 1.10095i 0.986381 + 0.164478i \(0.0525939\pi\)
−0.350749 + 0.936470i \(0.614073\pi\)
\(270\) 5.33157 + 3.07818i 0.324469 + 0.187332i
\(271\) −3.47906 + 6.02590i −0.211338 + 0.366047i −0.952133 0.305683i \(-0.901115\pi\)
0.740796 + 0.671730i \(0.234449\pi\)
\(272\) 0.00980018 + 0.0169744i 0.000594223 + 0.00102922i
\(273\) 0 0
\(274\) 1.12954 1.95642i 0.0682379 0.118191i
\(275\) 2.63176 + 4.55834i 0.158701 + 0.274878i
\(276\) 12.2144 + 14.5565i 0.735218 + 0.876198i
\(277\) −8.93629 + 15.4781i −0.536930 + 0.929989i 0.462138 + 0.886808i \(0.347083\pi\)
−0.999067 + 0.0431811i \(0.986251\pi\)
\(278\) −2.69681 + 4.67102i −0.161744 + 0.280149i
\(279\) 26.0326 9.47508i 1.55853 0.567258i
\(280\) 0 0
\(281\) −11.1552 19.3214i −0.665465 1.15262i −0.979159 0.203095i \(-0.934900\pi\)
0.313694 0.949524i \(-0.398433\pi\)
\(282\) −14.0326 + 2.47432i −0.835627 + 0.147344i
\(283\) −18.5945 −1.10533 −0.552665 0.833404i \(-0.686389\pi\)
−0.552665 + 0.833404i \(0.686389\pi\)
\(284\) 0.680045 0.0403532
\(285\) −7.41534 + 1.30753i −0.439247 + 0.0774511i
\(286\) −2.44862 4.24113i −0.144790 0.250783i
\(287\) 0 0
\(288\) −15.8944 + 5.78509i −0.936587 + 0.340890i
\(289\) 8.39053 14.5328i 0.493561 0.854872i
\(290\) 3.71348 6.43193i 0.218063 0.377696i
\(291\) 2.11422 + 2.51963i 0.123938 + 0.147703i
\(292\) 1.25712 + 2.17740i 0.0735675 + 0.127423i
\(293\) −6.54576 + 11.3376i −0.382407 + 0.662349i −0.991406 0.130822i \(-0.958238\pi\)
0.608998 + 0.793171i \(0.291572\pi\)
\(294\) 0 0
\(295\) 7.00387 + 12.1311i 0.407781 + 0.706298i
\(296\) −13.1013 + 22.6922i −0.761499 + 1.31895i
\(297\) 8.58770i 0.498309i
\(298\) 0.189540 + 0.328293i 0.0109798 + 0.0190175i
\(299\) −30.1361 −1.74282
\(300\) −2.31433 + 6.35857i −0.133618 + 0.367112i
\(301\) 0 0
\(302\) −1.08630 + 1.88153i −0.0625098 + 0.108270i
\(303\) 1.01249 2.78179i 0.0581659 0.159810i
\(304\) −0.0675813 + 0.117054i −0.00387606 + 0.00671353i
\(305\) −5.14543 8.91215i −0.294626 0.510308i
\(306\) 0.945622 + 0.793471i 0.0540576 + 0.0453597i
\(307\) 6.31046 0.360157 0.180078 0.983652i \(-0.442365\pi\)
0.180078 + 0.983652i \(0.442365\pi\)
\(308\) 0 0
\(309\) 4.05051 + 4.82721i 0.230425 + 0.274610i
\(310\) 5.47044 + 9.47508i 0.310700 + 0.538148i
\(311\) −9.52435 −0.540076 −0.270038 0.962850i \(-0.587036\pi\)
−0.270038 + 0.962850i \(0.587036\pi\)
\(312\) 5.66401 15.5617i 0.320661 0.881010i
\(313\) −17.6287 −0.996431 −0.498215 0.867053i \(-0.666011\pi\)
−0.498215 + 0.867053i \(0.666011\pi\)
\(314\) −8.91117 −0.502886
\(315\) 0 0
\(316\) 2.94862 0.165873
\(317\) 8.07697 0.453648 0.226824 0.973936i \(-0.427166\pi\)
0.226824 + 0.973936i \(0.427166\pi\)
\(318\) −0.561956 0.669713i −0.0315129 0.0375557i
\(319\) 10.3601 0.580054
\(320\) −3.39646 5.88284i −0.189868 0.328861i
\(321\) −4.22281 + 11.6021i −0.235694 + 0.647565i
\(322\) 0 0
\(323\) −1.50980 −0.0840075
\(324\) −8.45723 + 7.09646i −0.469846 + 0.394248i
\(325\) −5.36571 9.29369i −0.297636 0.515521i
\(326\) −1.14156 + 1.97724i −0.0632251 + 0.109509i
\(327\) −0.449493 0.535685i −0.0248570 0.0296234i
\(328\) −4.84002 + 8.38316i −0.267246 + 0.462883i
\(329\) 0 0
\(330\) −3.34002 + 0.588936i −0.183862 + 0.0324199i
\(331\) 23.0496 1.26692 0.633461 0.773775i \(-0.281634\pi\)
0.633461 + 0.773775i \(0.281634\pi\)
\(332\) −9.23055 15.9878i −0.506592 0.877444i
\(333\) −4.81062 + 27.2824i −0.263620 + 1.49507i
\(334\) −10.1934 + 17.6555i −0.557759 + 0.966066i
\(335\) −0.401674 0.695720i −0.0219458 0.0380112i
\(336\) 0 0
\(337\) −14.5116 + 25.1348i −0.790498 + 1.36918i 0.135161 + 0.990824i \(0.456845\pi\)
−0.925659 + 0.378359i \(0.876489\pi\)
\(338\) −0.723689 1.25347i −0.0393635 0.0681795i
\(339\) −8.51249 + 23.3879i −0.462335 + 1.27025i
\(340\) 0.386659 0.669713i 0.0209695 0.0363203i
\(341\) −7.63088 + 13.2171i −0.413235 + 0.715745i
\(342\) −1.47818 + 8.38316i −0.0799307 + 0.453310i
\(343\) 0 0
\(344\) 6.25877 + 10.8405i 0.337450 + 0.584481i
\(345\) −7.13816 + 19.6119i −0.384305 + 1.05587i
\(346\) 4.17881 0.224654
\(347\) 12.9463 0.694991 0.347496 0.937682i \(-0.387032\pi\)
0.347496 + 0.937682i \(0.387032\pi\)
\(348\) 8.56108 + 10.2027i 0.458922 + 0.546922i
\(349\) −0.731429 1.26687i −0.0391525 0.0678141i 0.845785 0.533524i \(-0.179132\pi\)
−0.884938 + 0.465710i \(0.845799\pi\)
\(350\) 0 0
\(351\) 17.5089i 0.934555i
\(352\) 4.65910 8.06980i 0.248331 0.430122i
\(353\) −7.16637 + 12.4125i −0.381428 + 0.660652i −0.991267 0.131873i \(-0.957901\pi\)
0.609839 + 0.792525i \(0.291234\pi\)
\(354\) 15.5954 2.74989i 0.828886 0.146155i
\(355\) 0.373455 + 0.646844i 0.0198210 + 0.0343309i
\(356\) 5.57310 9.65289i 0.295374 0.511602i
\(357\) 0 0
\(358\) −3.75150 6.49778i −0.198273 0.343418i
\(359\) 10.4684 18.1318i 0.552500 0.956958i −0.445593 0.895235i \(-0.647007\pi\)
0.998093 0.0617224i \(-0.0196594\pi\)
\(360\) −8.78564 7.37203i −0.463044 0.388540i
\(361\) 4.29426 + 7.43788i 0.226014 + 0.391467i
\(362\) 15.1557 0.796566
\(363\) 9.20574 + 10.9710i 0.483176 + 0.575827i
\(364\) 0 0
\(365\) −1.38073 + 2.39149i −0.0722707 + 0.125176i
\(366\) −11.4572 + 2.02022i −0.598879 + 0.105599i
\(367\) 6.02869 10.4420i 0.314695 0.545067i −0.664678 0.747130i \(-0.731431\pi\)
0.979373 + 0.202063i \(0.0647645\pi\)
\(368\) 0.187319 + 0.324446i 0.00976466 + 0.0169129i
\(369\) −1.77719 + 10.0789i −0.0925168 + 0.524689i
\(370\) −10.9409 −0.568789
\(371\) 0 0
\(372\) −19.3221 + 3.40700i −1.00180 + 0.176645i
\(373\) 0.390530 + 0.676417i 0.0202209 + 0.0350235i 0.875959 0.482386i \(-0.160230\pi\)
−0.855738 + 0.517410i \(0.826896\pi\)
\(374\) −0.680045 −0.0351643
\(375\) −18.8097 + 3.31667i −0.971331 + 0.171272i
\(376\) 26.5449 1.36895
\(377\) −21.1225 −1.08786
\(378\) 0 0
\(379\) −6.92396 −0.355660 −0.177830 0.984061i \(-0.556908\pi\)
−0.177830 + 0.984061i \(0.556908\pi\)
\(380\) 5.33275 0.273564
\(381\) −35.4308 + 6.24741i −1.81518 + 0.320065i
\(382\) −11.3523 −0.580837
\(383\) −3.86618 6.69642i −0.197553 0.342171i 0.750182 0.661232i \(-0.229966\pi\)
−0.947734 + 0.319061i \(0.896633\pi\)
\(384\) 11.6716 2.05802i 0.595613 0.105023i
\(385\) 0 0
\(386\) 0.561185 0.0285636
\(387\) 10.1382 + 8.50692i 0.515351 + 0.432431i
\(388\) −1.16473 2.01736i −0.0591300 0.102416i
\(389\) −2.69981 + 4.67620i −0.136886 + 0.237093i −0.926316 0.376747i \(-0.877043\pi\)
0.789431 + 0.613840i \(0.210376\pi\)
\(390\) 6.80974 1.20074i 0.344825 0.0608019i
\(391\) −2.09240 + 3.62414i −0.105817 + 0.183280i
\(392\) 0 0
\(393\) 7.97730 + 9.50698i 0.402402 + 0.479564i
\(394\) −10.0651 −0.507073
\(395\) 1.61927 + 2.80466i 0.0814743 + 0.141118i
\(396\) 1.05613 5.98962i 0.0530726 0.300990i
\(397\) 14.6172 25.3178i 0.733617 1.27066i −0.221711 0.975112i \(-0.571164\pi\)
0.955328 0.295549i \(-0.0955026\pi\)
\(398\) −1.59967 2.77071i −0.0801842 0.138883i
\(399\) 0 0
\(400\) −0.0667040 + 0.115535i −0.00333520 + 0.00577674i
\(401\) 13.6989 + 23.7272i 0.684092 + 1.18488i 0.973721 + 0.227743i \(0.0731346\pi\)
−0.289629 + 0.957139i \(0.593532\pi\)
\(402\) −0.894400 + 0.157707i −0.0446086 + 0.00786570i
\(403\) 15.5581 26.9474i 0.775003 1.34235i
\(404\) −1.04829 + 1.81568i −0.0521542 + 0.0903337i
\(405\) −11.3944 4.14722i −0.566192 0.206077i
\(406\) 0 0
\(407\) −7.63088 13.2171i −0.378249 0.655146i
\(408\) −1.47818 1.76162i −0.0731807 0.0872134i
\(409\) −9.02498 −0.446256 −0.223128 0.974789i \(-0.571627\pi\)
−0.223128 + 0.974789i \(0.571627\pi\)
\(410\) −4.04189 −0.199615
\(411\) −1.52182 + 4.18117i −0.0750659 + 0.206242i
\(412\) −2.23143 3.86495i −0.109935 0.190412i
\(413\) 0 0
\(414\) 18.0744 + 15.1663i 0.888310 + 0.745381i
\(415\) 10.1382 17.5598i 0.497662 0.861977i
\(416\) −9.49912 + 16.4530i −0.465733 + 0.806673i
\(417\) 3.63341 9.98271i 0.177929 0.488855i
\(418\) −2.34477 4.06126i −0.114686 0.198643i
\(419\) −0.0876485 + 0.151812i −0.00428191 + 0.00741649i −0.868158 0.496287i \(-0.834696\pi\)
0.863877 + 0.503704i \(0.168030\pi\)
\(420\) 0 0
\(421\) 12.3525 + 21.3952i 0.602025 + 1.04274i 0.992514 + 0.122130i \(0.0389724\pi\)
−0.390490 + 0.920607i \(0.627694\pi\)
\(422\) 2.56031 4.43458i 0.124634 0.215872i
\(423\) 26.3726 9.59883i 1.28228 0.466711i
\(424\) 0.814330 + 1.41046i 0.0395474 + 0.0684980i
\(425\) −1.49020 −0.0722853
\(426\) 0.831566 0.146628i 0.0402895 0.00710413i
\(427\) 0 0
\(428\) 4.37211 7.57272i 0.211334 0.366041i
\(429\) 6.20011 + 7.38901i 0.299344 + 0.356745i
\(430\) −2.61334 + 4.52644i −0.126026 + 0.218284i
\(431\) 14.6596 + 25.3911i 0.706126 + 1.22305i 0.966283 + 0.257481i \(0.0828924\pi\)
−0.260157 + 0.965566i \(0.583774\pi\)
\(432\) −0.188501 + 0.108831i −0.00906925 + 0.00523613i
\(433\) 19.6554 0.944578 0.472289 0.881444i \(-0.343428\pi\)
0.472289 + 0.881444i \(0.343428\pi\)
\(434\) 0 0
\(435\) −5.00316 + 13.7461i −0.239883 + 0.659073i
\(436\) 0.247626 + 0.428901i 0.0118591 + 0.0205406i
\(437\) −28.8580 −1.38047
\(438\) 2.00670 + 2.39149i 0.0958839 + 0.114270i
\(439\) −21.9299 −1.04666 −0.523330 0.852130i \(-0.675310\pi\)
−0.523330 + 0.852130i \(0.675310\pi\)
\(440\) 6.31820 0.301208
\(441\) 0 0
\(442\) 1.38650 0.0659489
\(443\) −18.7101 −0.888942 −0.444471 0.895793i \(-0.646608\pi\)
−0.444471 + 0.895793i \(0.646608\pi\)
\(444\) 6.71048 18.4369i 0.318466 0.874977i
\(445\) 12.2422 0.580334
\(446\) 3.11468 + 5.39479i 0.147485 + 0.255451i
\(447\) −0.479933 0.571962i −0.0227000 0.0270529i
\(448\) 0 0
\(449\) 6.68004 0.315251 0.157625 0.987499i \(-0.449616\pi\)
0.157625 + 0.987499i \(0.449616\pi\)
\(450\) −1.45899 + 8.27433i −0.0687774 + 0.390056i
\(451\) −2.81908 4.88279i −0.132745 0.229921i
\(452\) 8.81345 15.2653i 0.414550 0.718022i
\(453\) 1.46357 4.02114i 0.0687647 0.188929i
\(454\) −5.25150 + 9.09586i −0.246465 + 0.426890i
\(455\) 0 0
\(456\) 5.42380 14.9018i 0.253993 0.697839i
\(457\) −19.4287 −0.908837 −0.454418 0.890788i \(-0.650153\pi\)
−0.454418 + 0.890788i \(0.650153\pi\)
\(458\) −7.71776 13.3676i −0.360627 0.624625i
\(459\) −2.10560 1.21567i −0.0982810 0.0567426i
\(460\) 7.39053 12.8008i 0.344585 0.596839i
\(461\) 0.482926 + 0.836452i 0.0224921 + 0.0389575i 0.877052 0.480395i \(-0.159507\pi\)
−0.854560 + 0.519352i \(0.826173\pi\)
\(462\) 0 0
\(463\) 0.222811 0.385920i 0.0103549 0.0179352i −0.860802 0.508941i \(-0.830037\pi\)
0.871156 + 0.491006i \(0.163371\pi\)
\(464\) 0.131292 + 0.227405i 0.00609509 + 0.0105570i
\(465\) −13.8516 16.5077i −0.642354 0.765528i
\(466\) 7.14677 12.3786i 0.331068 0.573426i
\(467\) 17.1074 29.6309i 0.791637 1.37115i −0.133317 0.991074i \(-0.542563\pi\)
0.924953 0.380081i \(-0.124104\pi\)
\(468\) −2.15328 + 12.2118i −0.0995352 + 0.564492i
\(469\) 0 0
\(470\) 5.54189 + 9.59883i 0.255628 + 0.442761i
\(471\) 17.2849 3.04780i 0.796448 0.140435i
\(472\) −29.5012 −1.35790
\(473\) −7.29086 −0.335234
\(474\) 3.60560 0.635765i 0.165611 0.0292016i
\(475\) −5.13816 8.89955i −0.235755 0.408339i
\(476\) 0 0
\(477\) 1.31908 + 1.10684i 0.0603964 + 0.0506786i
\(478\) −6.63903 + 11.4991i −0.303662 + 0.525959i
\(479\) 10.8965 18.8732i 0.497872 0.862339i −0.502125 0.864795i \(-0.667448\pi\)
0.999997 + 0.00245553i \(0.000781622\pi\)
\(480\) 8.45723 + 10.0789i 0.386018 + 0.460038i
\(481\) 15.5581 + 26.9474i 0.709388 + 1.22870i
\(482\) −6.87598 + 11.9095i −0.313192 + 0.542465i
\(483\) 0 0
\(484\) −5.07145 8.78401i −0.230521 0.399273i
\(485\) 1.27925 2.21572i 0.0580877 0.100611i
\(486\) −8.81150 + 10.5011i −0.399698 + 0.476341i
\(487\) −9.69640 16.7947i −0.439386 0.761039i 0.558256 0.829669i \(-0.311471\pi\)
−0.997642 + 0.0686297i \(0.978137\pi\)
\(488\) 21.6732 0.981101
\(489\) 1.53802 4.22567i 0.0695516 0.191091i
\(490\) 0 0
\(491\) −13.0783 + 22.6523i −0.590216 + 1.02228i 0.403987 + 0.914765i \(0.367624\pi\)
−0.994203 + 0.107519i \(0.965709\pi\)
\(492\) 2.47906 6.81115i 0.111764 0.307070i
\(493\) −1.46657 + 2.54017i −0.0660509 + 0.114403i
\(494\) 4.78059 + 8.28023i 0.215089 + 0.372545i
\(495\) 6.27719 2.28471i 0.282139 0.102690i
\(496\) −0.386821 −0.0173688
\(497\) 0 0
\(498\) −14.7344 17.5598i −0.660265 0.786873i
\(499\) 7.15064 + 12.3853i 0.320107 + 0.554441i 0.980510 0.196470i \(-0.0629479\pi\)
−0.660403 + 0.750911i \(0.729615\pi\)
\(500\) 13.5270 0.604947
\(501\) 13.7335 37.7326i 0.613570 1.68577i
\(502\) −16.7656 −0.748284
\(503\) 18.7033 0.833937 0.416969 0.908921i \(-0.363092\pi\)
0.416969 + 0.908921i \(0.363092\pi\)
\(504\) 0 0
\(505\) −2.30272 −0.102470
\(506\) −12.9982 −0.577842
\(507\) 1.83244 + 2.18382i 0.0813817 + 0.0969869i
\(508\) 25.4801 1.13050
\(509\) 12.8045 + 22.1781i 0.567551 + 0.983027i 0.996807 + 0.0798442i \(0.0254423\pi\)
−0.429257 + 0.903183i \(0.641224\pi\)
\(510\) 0.328411 0.902302i 0.0145423 0.0399546i
\(511\) 0 0
\(512\) 0.473897 0.0209435
\(513\) 16.7663i 0.740252i
\(514\) 11.6878 + 20.2438i 0.515526 + 0.892917i
\(515\) 2.45084 4.24497i 0.107997 0.187056i
\(516\) −6.02481 7.18009i −0.265228 0.316086i
\(517\) −7.73055 + 13.3897i −0.339989 + 0.588879i
\(518\) 0 0
\(519\) −8.10560 + 1.42924i −0.355796 + 0.0627365i
\(520\) −12.8817 −0.564902
\(521\) 10.6061 + 18.3702i 0.464660 + 0.804815i 0.999186 0.0403370i \(-0.0128431\pi\)
−0.534526 + 0.845152i \(0.679510\pi\)
\(522\) 12.6684 + 10.6301i 0.554482 + 0.465266i
\(523\) −10.4029 + 18.0183i −0.454885 + 0.787884i −0.998682 0.0513330i \(-0.983653\pi\)
0.543796 + 0.839217i \(0.316986\pi\)
\(524\) −4.39470 7.61185i −0.191984 0.332525i
\(525\) 0 0
\(526\) −0.322786 + 0.559082i −0.0140741 + 0.0243771i
\(527\) −2.16044 3.74200i −0.0941104 0.163004i
\(528\) 0.0410117 0.112679i 0.00178481 0.00490371i
\(529\) −28.4937 + 49.3525i −1.23885 + 2.14576i
\(530\) −0.340022 + 0.588936i −0.0147696 + 0.0255817i
\(531\) −29.3097 + 10.6679i −1.27193 + 0.462946i
\(532\) 0 0
\(533\) 5.74763 + 9.95518i 0.248957 + 0.431207i
\(534\) 4.73355 13.0053i 0.204841 0.562795i
\(535\) 9.60401 0.415217
\(536\) 1.69190 0.0730791
\(537\) 9.49912 + 11.3206i 0.409917 + 0.488521i
\(538\) −9.16772 15.8790i −0.395248 0.684590i
\(539\) 0 0
\(540\) 7.43717 + 4.29385i 0.320045 + 0.184778i
\(541\) −13.3648 + 23.1486i −0.574599 + 0.995235i 0.421486 + 0.906835i \(0.361509\pi\)
−0.996085 + 0.0884001i \(0.971825\pi\)
\(542\) 3.05943 5.29909i 0.131414 0.227615i
\(543\) −29.3974 + 5.18355i −1.26156 + 0.222448i
\(544\) 1.31908 + 2.28471i 0.0565550 + 0.0979561i
\(545\) −0.271974 + 0.471073i −0.0116501 + 0.0201786i
\(546\) 0 0
\(547\) −18.3812 31.8372i −0.785923 1.36126i −0.928446 0.371467i \(-0.878855\pi\)
0.142523 0.989792i \(-0.454479\pi\)
\(548\) 1.57563 2.72907i 0.0673074 0.116580i
\(549\) 21.5326 7.83721i 0.918987 0.334484i
\(550\) −2.31433 4.00854i −0.0986834 0.170925i
\(551\) −20.2267 −0.861686
\(552\) −28.2536 33.6713i −1.20255 1.43315i
\(553\) 0 0
\(554\) 7.85844 13.6112i 0.333873 0.578285i
\(555\) 21.2219 3.74200i 0.900821 0.158839i
\(556\) −3.76187 + 6.51575i −0.159539 + 0.276329i
\(557\) −16.1694 28.0062i −0.685118 1.18666i −0.973400 0.229114i \(-0.926417\pi\)
0.288282 0.957546i \(-0.406916\pi\)
\(558\) −22.8926 + 8.33224i −0.969123 + 0.352732i
\(559\) 14.8648 0.628716
\(560\) 0 0
\(561\) 1.31908 0.232589i 0.0556915 0.00981992i
\(562\) 9.80974 + 16.9910i 0.413799 + 0.716721i
\(563\) −17.7419 −0.747730 −0.373865 0.927483i \(-0.621968\pi\)
−0.373865 + 0.927483i \(0.621968\pi\)
\(564\) −19.5744 + 3.45150i −0.824233 + 0.145334i
\(565\) 19.3601 0.814485
\(566\) 16.3517 0.687315
\(567\) 0 0
\(568\) −1.57304 −0.0660035
\(569\) −26.6013 −1.11519 −0.557593 0.830115i \(-0.688275\pi\)
−0.557593 + 0.830115i \(0.688275\pi\)
\(570\) 6.52094 1.14982i 0.273132 0.0481606i
\(571\) −10.0172 −0.419208 −0.209604 0.977786i \(-0.567218\pi\)
−0.209604 + 0.977786i \(0.567218\pi\)
\(572\) −3.41565 5.91608i −0.142815 0.247364i
\(573\) 22.0201 3.88273i 0.919902 0.162203i
\(574\) 0 0
\(575\) −28.4834 −1.18784
\(576\) 14.2135 5.17328i 0.592228 0.215553i
\(577\) 16.4572 + 28.5048i 0.685124 + 1.18667i 0.973398 + 0.229121i \(0.0735852\pi\)
−0.288274 + 0.957548i \(0.593082\pi\)
\(578\) −7.37851 + 12.7800i −0.306905 + 0.531576i
\(579\) −1.08853 + 0.191936i −0.0452376 + 0.00797661i
\(580\) 5.18004 8.97210i 0.215090 0.372546i
\(581\) 0 0
\(582\) −1.85921 2.21572i −0.0770668 0.0918447i
\(583\) −0.948615 −0.0392876
\(584\) −2.90791 5.03665i −0.120330 0.208418i
\(585\) −12.7981 + 4.65814i −0.529138 + 0.192590i
\(586\) 5.75624 9.97011i 0.237788 0.411861i
\(587\) 7.53643 + 13.0535i 0.311062 + 0.538774i 0.978592 0.205808i \(-0.0659821\pi\)
−0.667531 + 0.744582i \(0.732649\pi\)
\(588\) 0 0
\(589\) 14.8983 25.8046i 0.613873 1.06326i
\(590\) −6.15910 10.6679i −0.253566 0.439189i
\(591\) 19.5232 3.44247i 0.803078 0.141604i
\(592\) 0.193411 0.334997i 0.00794913 0.0137683i
\(593\) −20.5005 + 35.5079i −0.841853 + 1.45813i 0.0464729 + 0.998920i \(0.485202\pi\)
−0.888326 + 0.459213i \(0.848131\pi\)
\(594\) 7.55190i 0.309858i
\(595\) 0 0
\(596\) 0.264396 + 0.457947i 0.0108301 + 0.0187582i
\(597\) 4.05051 + 4.82721i 0.165776 + 0.197564i
\(598\) 26.5012 1.08372
\(599\) 6.07367 0.248164 0.124082 0.992272i \(-0.460401\pi\)
0.124082 + 0.992272i \(0.460401\pi\)
\(600\) 5.35339 14.7083i 0.218551 0.600464i
\(601\) 7.06758 + 12.2414i 0.288293 + 0.499338i 0.973402 0.229102i \(-0.0735791\pi\)
−0.685110 + 0.728440i \(0.740246\pi\)
\(602\) 0 0
\(603\) 1.68092 0.611806i 0.0684524 0.0249147i
\(604\) −1.51532 + 2.62461i −0.0616575 + 0.106794i
\(605\) 5.57011 9.64771i 0.226457 0.392235i
\(606\) −0.890367 + 2.44626i −0.0361687 + 0.0993727i
\(607\) −23.0449 39.9149i −0.935363 1.62010i −0.773986 0.633203i \(-0.781740\pi\)
−0.161377 0.986893i \(-0.551594\pi\)
\(608\) −9.09627 + 15.7552i −0.368902 + 0.638958i
\(609\) 0 0
\(610\) 4.52481 + 7.83721i 0.183204 + 0.317319i
\(611\) 15.7613 27.2994i 0.637634 1.10441i
\(612\) 1.31908 + 1.10684i 0.0533206 + 0.0447413i
\(613\) 13.2469 + 22.9443i 0.535038 + 0.926712i 0.999162 + 0.0409421i \(0.0130359\pi\)
−0.464124 + 0.885770i \(0.653631\pi\)
\(614\) −5.54933 −0.223953
\(615\) 7.84002 1.38241i 0.316140 0.0557440i
\(616\) 0 0
\(617\) 1.12495 1.94847i 0.0452889 0.0784426i −0.842492 0.538708i \(-0.818913\pi\)
0.887781 + 0.460266i \(0.152246\pi\)
\(618\) −3.56196 4.24497i −0.143283 0.170758i
\(619\) −3.09539 + 5.36137i −0.124414 + 0.215492i −0.921504 0.388369i \(-0.873038\pi\)
0.797090 + 0.603861i \(0.206372\pi\)
\(620\) 7.63088 + 13.2171i 0.306464 + 0.530811i
\(621\) −40.2460 23.2361i −1.61502 0.932431i
\(622\) 8.37557 0.335830
\(623\) 0 0
\(624\) −0.0836160 + 0.229733i −0.00334732 + 0.00919668i
\(625\) −0.533433 0.923933i −0.0213373 0.0369573i
\(626\) 15.5024 0.619600
\(627\) 5.93717 + 7.07564i 0.237108 + 0.282574i
\(628\) −12.4305 −0.496030
\(629\) 4.32089 0.172285
\(630\) 0 0
\(631\) 26.1661 1.04166 0.520829 0.853661i \(-0.325623\pi\)
0.520829 + 0.853661i \(0.325623\pi\)
\(632\) −6.82058 −0.271308
\(633\) −3.44949 + 9.47740i −0.137105 + 0.376693i
\(634\) −7.10277 −0.282087
\(635\) 13.9927 + 24.2361i 0.555284 + 0.961781i
\(636\) −0.783890 0.934204i −0.0310833 0.0370436i
\(637\) 0 0
\(638\) −9.11051 −0.360689
\(639\) −1.56283 + 0.568825i −0.0618247 + 0.0225024i
\(640\) −4.60947 7.98384i −0.182205 0.315589i
\(641\) −2.44444 + 4.23389i −0.0965496 + 0.167229i −0.910254 0.414050i \(-0.864114\pi\)
0.813705 + 0.581278i \(0.197447\pi\)
\(642\) 3.71348 10.2027i 0.146559 0.402668i
\(643\) 20.1839 34.9596i 0.795976 1.37867i −0.126242 0.992000i \(-0.540291\pi\)
0.922218 0.386671i \(-0.126375\pi\)
\(644\) 0 0
\(645\) 3.52094 9.67372i 0.138637 0.380902i
\(646\) 1.32770 0.0522375
\(647\) 1.14038 + 1.97519i 0.0448329 + 0.0776528i 0.887571 0.460671i \(-0.152391\pi\)
−0.842738 + 0.538324i \(0.819058\pi\)
\(648\) 19.5628 16.4152i 0.768501 0.644849i
\(649\) 8.59152 14.8809i 0.337247 0.584128i
\(650\) 4.71853 + 8.17273i 0.185076 + 0.320561i
\(651\) 0 0
\(652\) −1.59240 + 2.75811i −0.0623631 + 0.108016i
\(653\) −11.7396 20.3336i −0.459407 0.795717i 0.539522 0.841971i \(-0.318605\pi\)
−0.998930 + 0.0462542i \(0.985272\pi\)
\(654\) 0.395277 + 0.471073i 0.0154566 + 0.0184204i
\(655\) 4.82682 8.36030i 0.188599 0.326664i
\(656\) 0.0714517 0.123758i 0.00278972 0.00483194i
\(657\) −4.71032 3.95243i −0.183767 0.154199i
\(658\) 0 0
\(659\) 23.9812 + 41.5366i 0.934174 + 1.61804i 0.776101 + 0.630609i \(0.217195\pi\)
0.158073 + 0.987427i \(0.449472\pi\)
\(660\) −4.65910 + 0.821525i −0.181355 + 0.0319778i
\(661\) 29.3090 1.13999 0.569995 0.821648i \(-0.306945\pi\)
0.569995 + 0.821648i \(0.306945\pi\)
\(662\) −20.2695 −0.787797
\(663\) −2.68938 + 0.474210i −0.104447 + 0.0184168i
\(664\) 21.3516 + 36.9821i 0.828604 + 1.43518i
\(665\) 0 0
\(666\) 4.23039 23.9917i 0.163924 0.929661i
\(667\) −28.0317 + 48.5523i −1.08539 + 1.87995i
\(668\) −14.2191 + 24.6282i −0.550154 + 0.952894i
\(669\) −7.88666 9.39895i −0.304916 0.363385i
\(670\) 0.353226 + 0.611806i 0.0136463 + 0.0236361i
\(671\) −6.31180 + 10.9324i −0.243664 + 0.422039i
\(672\) 0 0
\(673\) −13.1591 22.7922i −0.507246 0.878576i −0.999965 0.00838731i \(-0.997330\pi\)
0.492719 0.870189i \(-0.336003\pi\)
\(674\) 12.7613 22.1032i 0.491547 0.851384i
\(675\) 16.5487i 0.636959i
\(676\) −1.00950 1.74850i −0.0388267 0.0672499i
\(677\) 35.8907 1.37939 0.689697 0.724098i \(-0.257744\pi\)
0.689697 + 0.724098i \(0.257744\pi\)
\(678\) 7.48576 20.5669i 0.287489 0.789869i
\(679\) 0 0
\(680\) −0.894400 + 1.54915i −0.0342987 + 0.0594070i
\(681\) 7.07532 19.4393i 0.271127 0.744915i
\(682\) 6.71048 11.6229i 0.256958 0.445064i
\(683\) −17.5321 30.3665i −0.670847 1.16194i −0.977664 0.210172i \(-0.932597\pi\)
0.306818 0.951768i \(-0.400736\pi\)
\(684\) −2.06196 + 11.6939i −0.0788409 + 0.447129i
\(685\) 3.46110 0.132242
\(686\) 0 0
\(687\) 19.5421 + 23.2893i 0.745576 + 0.888543i
\(688\) −0.0923963 0.160035i −0.00352257 0.00610128i
\(689\) 1.93407 0.0736821
\(690\) 6.27719 17.2464i 0.238968 0.656561i
\(691\) 2.06687 0.0786273 0.0393136 0.999227i \(-0.487483\pi\)
0.0393136 + 0.999227i \(0.487483\pi\)
\(692\) 5.82915 0.221591
\(693\) 0 0
\(694\) −11.3847 −0.432159
\(695\) −8.26352 −0.313453
\(696\) −19.8030 23.6003i −0.750632 0.894569i
\(697\) 1.59627 0.0604629
\(698\) 0.643208 + 1.11407i 0.0243458 + 0.0421681i
\(699\) −9.62882 + 26.4550i −0.364196 + 1.00062i
\(700\) 0 0
\(701\) −7.36009 −0.277987 −0.138993 0.990293i \(-0.544387\pi\)
−0.138993 + 0.990293i \(0.544387\pi\)
\(702\) 15.3970i 0.581124i
\(703\) 14.8983 + 25.8046i 0.561899 + 0.973237i
\(704\) −4.16637 + 7.21637i −0.157026 + 0.271977i
\(705\) −14.0326 16.7233i −0.528497 0.629838i
\(706\) 6.30200 10.9154i 0.237179 0.410806i
\(707\) 0 0
\(708\) 21.7545 3.83590i 0.817584 0.144162i
\(709\) 9.10876 0.342086 0.171043 0.985264i \(-0.445286\pi\)
0.171043 + 0.985264i \(0.445286\pi\)
\(710\) −0.328411 0.568825i −0.0123251 0.0213476i
\(711\) −6.77631 + 2.46638i −0.254132 + 0.0924963i
\(712\) −12.8914 + 22.3286i −0.483126 + 0.836799i
\(713\) −41.2943 71.5239i −1.54648 2.67859i
\(714\) 0 0
\(715\) 3.75150 6.49778i 0.140298 0.243003i
\(716\) −5.23308 9.06396i −0.195569 0.338736i
\(717\) 8.94475 24.5755i 0.334048 0.917788i
\(718\) −9.20574 + 15.9448i −0.343555 + 0.595055i
\(719\) 12.9768 22.4765i 0.483954 0.838233i −0.515876 0.856663i \(-0.672533\pi\)
0.999830 + 0.0184300i \(0.00586678\pi\)
\(720\) 0.129700 + 0.108831i 0.00483362 + 0.00405589i
\(721\) 0 0
\(722\) −3.77631 6.54076i −0.140540 0.243422i
\(723\) 9.26399 25.4526i 0.344531 0.946592i
\(724\) 21.1411 0.785705
\(725\) −19.9641 −0.741448
\(726\) −8.09539 9.64771i −0.300448 0.358060i
\(727\) 5.08007 + 8.79894i 0.188409 + 0.326335i 0.944720 0.327878i \(-0.106333\pi\)
−0.756311 + 0.654213i \(0.773000\pi\)
\(728\) 0 0
\(729\) 13.5000 23.3827i 0.500000 0.866025i
\(730\) 1.21419 2.10304i 0.0449393 0.0778372i
\(731\) 1.03209 1.78763i 0.0381732 0.0661179i
\(732\) −15.9820 + 2.81807i −0.590714 + 0.104159i
\(733\) −20.3307 35.2138i −0.750931 1.30065i −0.947372 0.320135i \(-0.896272\pi\)
0.196441 0.980516i \(-0.437062\pi\)
\(734\) −5.30154 + 9.18253i −0.195683 + 0.338933i
\(735\) 0 0
\(736\) 25.2126 + 43.6695i 0.929349 + 1.60968i
\(737\) −0.492726 + 0.853427i −0.0181498 + 0.0314364i
\(738\) 1.56283 8.86327i 0.0575287 0.326261i
\(739\) 12.6809 + 21.9640i 0.466475 + 0.807959i 0.999267 0.0382877i \(-0.0121903\pi\)
−0.532791 + 0.846247i \(0.678857\pi\)
\(740\) −15.2618 −0.561034
\(741\) −12.1049 14.4260i −0.444684 0.529954i
\(742\) 0 0
\(743\) 11.2221 19.4372i 0.411699 0.713083i −0.583377 0.812202i \(-0.698269\pi\)
0.995076 + 0.0991184i \(0.0316023\pi\)
\(744\) 44.6948 7.88090i 1.63859 0.288928i
\(745\) −0.290393 + 0.502975i −0.0106392 + 0.0184276i
\(746\) −0.343426 0.594831i −0.0125737 0.0217783i
\(747\) 34.5861 + 29.0211i 1.26544 + 1.06183i
\(748\) −0.948615 −0.0346848
\(749\) 0 0
\(750\) 16.5410 2.91663i 0.603992 0.106500i
\(751\) −12.1086 20.9727i −0.441849 0.765305i 0.555978 0.831197i \(-0.312344\pi\)
−0.997827 + 0.0658924i \(0.979011\pi\)
\(752\) −0.391874 −0.0142902
\(753\) 32.5201 5.73417i 1.18510 0.208965i
\(754\) 18.5748 0.676454
\(755\) −3.32863 −0.121141
\(756\) 0 0
\(757\) 9.11793 0.331397 0.165698 0.986176i \(-0.447012\pi\)
0.165698 + 0.986176i \(0.447012\pi\)
\(758\) 6.08883 0.221156
\(759\) 25.2126 4.44566i 0.915159 0.161367i
\(760\) −12.3354 −0.447453
\(761\) 9.13610 + 15.8242i 0.331183 + 0.573626i 0.982744 0.184970i \(-0.0592188\pi\)
−0.651561 + 0.758596i \(0.725886\pi\)
\(762\) 31.1573 5.49388i 1.12871 0.199022i
\(763\) 0 0
\(764\) −15.8357 −0.572917
\(765\) −0.328411 + 1.86251i −0.0118737 + 0.0673393i
\(766\) 3.39986 + 5.88874i 0.122842 + 0.212769i
\(767\) −17.5167 + 30.3398i −0.632490 + 1.09550i
\(768\) −27.4641 + 4.84266i −0.991025 + 0.174744i
\(769\) −9.26470 + 16.0469i −0.334094 + 0.578667i −0.983310 0.181936i \(-0.941764\pi\)
0.649217 + 0.760604i \(0.275097\pi\)
\(770\) 0 0
\(771\) −29.5945 35.2694i −1.06582 1.27020i
\(772\) 0.782814 0.0281741
\(773\) 1.48040 + 2.56413i 0.0532463 + 0.0922253i 0.891420 0.453178i \(-0.149710\pi\)
−0.838174 + 0.545403i \(0.816376\pi\)
\(774\) −8.91534 7.48086i −0.320455 0.268894i
\(775\) 14.7049 25.4696i 0.528214 0.914894i
\(776\) 2.69418 + 4.66646i 0.0967155 + 0.167516i
\(777\) 0 0
\(778\) 2.37417 4.11218i 0.0851181 0.147429i
\(779\) 5.50387 + 9.53298i 0.197197 + 0.341555i
\(780\) 9.49912 1.67495i 0.340123 0.0599729i