Properties

Label 441.2.g.b.67.3
Level $441$
Weight $2$
Character 441.67
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.g (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 67.3
Root \(0.939693 + 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.b.79.3

$q$-expansion

\(f(q)\) \(=\) \(q+(0.439693 - 0.761570i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} -1.34730 q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +O(q^{10})\) \(q+(0.439693 - 0.761570i) q^{2} +(1.11334 + 1.32683i) q^{3} +(0.613341 + 1.06234i) q^{4} -1.34730 q^{5} +(1.50000 - 0.264490i) q^{6} +2.83750 q^{8} +(-0.520945 + 2.95442i) q^{9} +(-0.592396 + 1.02606i) q^{10} +1.65270 q^{11} +(-0.726682 + 1.99654i) q^{12} +(-1.68479 + 2.91815i) q^{13} +(-1.50000 - 1.78763i) q^{15} +(0.0209445 - 0.0362770i) q^{16} +(0.233956 - 0.405223i) q^{17} +(2.02094 + 1.69577i) q^{18} +(-1.61334 - 2.79439i) q^{19} +(-0.826352 - 1.43128i) q^{20} +(0.726682 - 1.25865i) q^{22} +8.94356 q^{23} +(3.15910 + 3.76487i) q^{24} -3.18479 q^{25} +(1.48158 + 2.56617i) q^{26} +(-4.50000 + 2.59808i) q^{27} +(-3.13429 - 5.42874i) q^{29} +(-2.02094 + 0.356347i) q^{30} +(4.61721 + 7.99724i) q^{31} +(2.81908 + 4.88279i) q^{32} +(1.84002 + 2.19285i) q^{33} +(-0.205737 - 0.356347i) q^{34} +(-3.45811 + 1.25865i) q^{36} +(-4.61721 - 7.99724i) q^{37} -2.83750 q^{38} +(-5.74763 + 1.01346i) q^{39} -3.82295 q^{40} +(1.70574 - 2.95442i) q^{41} +(2.20574 + 3.82045i) q^{43} +(1.01367 + 1.75573i) q^{44} +(0.701867 - 3.98048i) q^{45} +(3.93242 - 6.81115i) q^{46} +(4.67752 - 8.10170i) q^{47} +(0.0714517 - 0.0125989i) q^{48} +(-1.40033 + 2.42544i) q^{50} +(0.798133 - 0.140732i) q^{51} -4.13341 q^{52} +(0.286989 - 0.497079i) q^{53} +4.56942i q^{54} -2.22668 q^{55} +(1.91147 - 5.25173i) q^{57} -5.51249 q^{58} +(-5.19846 - 9.00400i) q^{59} +(0.979055 - 2.68993i) q^{60} +(3.81908 - 6.61484i) q^{61} +8.12061 q^{62} +5.04189 q^{64} +(2.26991 - 3.93161i) q^{65} +(2.47906 - 0.437124i) q^{66} +(-0.298133 - 0.516382i) q^{67} +0.573978 q^{68} +(9.95723 + 11.8666i) q^{69} -0.554378 q^{71} +(-1.47818 + 8.38316i) q^{72} +(1.02481 - 1.77503i) q^{73} -8.12061 q^{74} +(-3.54576 - 4.22567i) q^{75} +(1.97906 - 3.42782i) q^{76} +(-1.75537 + 4.82283i) q^{78} +(1.20187 - 2.08169i) q^{79} +(-0.0282185 + 0.0488759i) q^{80} +(-8.45723 - 3.07818i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-7.52481 - 13.0334i) q^{83} +(-0.315207 + 0.545955i) q^{85} +3.87939 q^{86} +(3.71348 - 10.2027i) q^{87} +4.68954 q^{88} +(4.54323 + 7.86911i) q^{89} +(-2.72281 - 2.28471i) q^{90} +(5.48545 + 9.50108i) q^{92} +(-5.47044 + 15.0299i) q^{93} +(-4.11334 - 7.12452i) q^{94} +(2.17365 + 3.76487i) q^{95} +(-3.34002 + 9.17664i) q^{96} +(-0.949493 - 1.64457i) q^{97} +(-0.860967 + 4.88279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{4} - 6q^{5} + 9q^{6} + 12q^{8} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{4} - 6q^{5} + 9q^{6} + 12q^{8} + 12q^{11} + 9q^{12} - 3q^{13} - 9q^{15} - 3q^{16} + 6q^{17} + 9q^{18} - 3q^{19} - 6q^{20} - 9q^{22} + 24q^{23} - 18q^{24} - 12q^{25} - 3q^{26} - 27q^{27} - 9q^{29} - 9q^{30} - 3q^{31} - 9q^{33} + 9q^{34} - 27q^{36} + 3q^{37} - 12q^{38} - 18q^{39} + 18q^{40} + 3q^{43} - 15q^{44} + 18q^{45} + 3q^{47} + 6q^{50} - 9q^{51} + 42q^{52} - 6q^{53} - 9q^{57} - 18q^{58} - 3q^{59} + 9q^{60} + 6q^{61} + 60q^{62} + 24q^{64} - 15q^{65} + 18q^{66} + 12q^{67} - 12q^{68} + 9q^{69} + 18q^{71} + 45q^{72} - 21q^{73} - 60q^{74} + 9q^{75} + 15q^{76} + 54q^{78} + 21q^{79} - 15q^{80} - 9q^{82} - 18q^{83} - 9q^{85} + 12q^{86} - 36q^{87} + 54q^{88} + 12q^{89} - 27q^{90} - 3q^{92} - 27q^{93} - 18q^{94} + 12q^{95} - 3q^{97} + 18q^{99} + O(q^{100}) \)

Character values

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

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.439693 0.761570i 0.310910 0.538511i −0.667650 0.744475i \(-0.732700\pi\)
0.978560 + 0.205964i \(0.0660330\pi\)
\(3\) 1.11334 + 1.32683i 0.642788 + 0.766044i
\(4\) 0.613341 + 1.06234i 0.306670 + 0.531169i
\(5\) −1.34730 −0.602529 −0.301265 0.953541i \(-0.597409\pi\)
−0.301265 + 0.953541i \(0.597409\pi\)
\(6\) 1.50000 0.264490i 0.612372 0.107978i
\(7\) 0 0
\(8\) 2.83750 1.00321
\(9\) −0.520945 + 2.95442i −0.173648 + 0.984808i
\(10\) −0.592396 + 1.02606i −0.187332 + 0.324469i
\(11\) 1.65270 0.498309 0.249154 0.968464i \(-0.419847\pi\)
0.249154 + 0.968464i \(0.419847\pi\)
\(12\) −0.726682 + 1.99654i −0.209775 + 0.576352i
\(13\) −1.68479 + 2.91815i −0.467277 + 0.809348i −0.999301 0.0373813i \(-0.988098\pi\)
0.532024 + 0.846729i \(0.321432\pi\)
\(14\) 0 0
\(15\) −1.50000 1.78763i −0.387298 0.461564i
\(16\) 0.0209445 0.0362770i 0.00523613 0.00906925i
\(17\) 0.233956 0.405223i 0.0567426 0.0982810i −0.836259 0.548335i \(-0.815262\pi\)
0.893001 + 0.450054i \(0.148595\pi\)
\(18\) 2.02094 + 1.69577i 0.476341 + 0.399698i
\(19\) −1.61334 2.79439i −0.370126 0.641077i 0.619459 0.785029i \(-0.287352\pi\)
−0.989585 + 0.143953i \(0.954019\pi\)
\(20\) −0.826352 1.43128i −0.184778 0.320045i
\(21\) 0 0
\(22\) 0.726682 1.25865i 0.154929 0.268345i
\(23\) 8.94356 1.86486 0.932431 0.361348i \(-0.117683\pi\)
0.932431 + 0.361348i \(0.117683\pi\)
\(24\) 3.15910 + 3.76487i 0.644849 + 0.768501i
\(25\) −3.18479 −0.636959
\(26\) 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 \(-0.364405\pi\)
\(30\) −2.02094 + 0.356347i −0.368972 + 0.0650598i
\(31\) 4.61721 + 7.99724i 0.829276 + 1.43635i 0.898607 + 0.438754i \(0.144580\pi\)
−0.0693317 + 0.997594i \(0.522087\pi\)
\(32\) 2.81908 + 4.88279i 0.498347 + 0.863163i
\(33\) 1.84002 + 2.19285i 0.320307 + 0.381727i
\(34\) −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 −0.943328 0.331862i \(-0.892323\pi\)
0.184263 0.982877i \(-0.441010\pi\)
\(38\) −2.83750 −0.460303
\(39\) −5.74763 + 1.01346i −0.920357 + 0.162284i
\(40\) −3.82295 −0.604461
\(41\) 1.70574 2.95442i 0.266391 0.461403i −0.701536 0.712634i \(-0.747502\pi\)
0.967927 + 0.251231i \(0.0808353\pi\)
\(42\) 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
\(45\) 0.701867 3.98048i 0.104628 0.593375i
\(46\) 3.93242 6.81115i 0.579803 1.00425i
\(47\) 4.67752 8.10170i 0.682286 1.18175i −0.291995 0.956420i \(-0.594319\pi\)
0.974281 0.225335i \(-0.0723475\pi\)
\(48\) 0.0714517 0.0125989i 0.0103132 0.00181849i
\(49\) 0 0
\(50\) −1.40033 + 2.42544i −0.198037 + 0.343009i
\(51\) 0.798133 0.140732i 0.111761 0.0197065i
\(52\) −4.13341 −0.573201
\(53\) 0.286989 0.497079i 0.0394210 0.0682791i −0.845642 0.533751i \(-0.820782\pi\)
0.885063 + 0.465472i \(0.154115\pi\)
\(54\) 4.56942i 0.621819i
\(55\) −2.22668 −0.300246
\(56\) 0 0
\(57\) 1.91147 5.25173i 0.253181 0.695609i
\(58\) −5.51249 −0.723825
\(59\) −5.19846 9.00400i −0.676782 1.17222i −0.975945 0.218019i \(-0.930041\pi\)
0.299162 0.954202i \(-0.403293\pi\)
\(60\) 0.979055 2.68993i 0.126396 0.347269i
\(61\) 3.81908 6.61484i 0.488983 0.846943i −0.510937 0.859618i \(-0.670701\pi\)
0.999920 + 0.0126752i \(0.00403474\pi\)
\(62\) 8.12061 1.03132
\(63\) 0 0
\(64\) 5.04189 0.630236
\(65\) 2.26991 3.93161i 0.281548 0.487656i
\(66\) 2.47906 0.437124i 0.305151 0.0538063i
\(67\) −0.298133 0.516382i −0.0364228 0.0630861i 0.847239 0.531211i \(-0.178263\pi\)
−0.883662 + 0.468125i \(0.844930\pi\)
\(68\) 0.573978 0.0696051
\(69\) 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 \(0.510473\pi\)
\(72\) −1.47818 + 8.38316i −0.174205 + 0.987965i
\(73\) 1.02481 1.77503i 0.119946 0.207752i −0.799800 0.600266i \(-0.795061\pi\)
0.919746 + 0.392514i \(0.128395\pi\)
\(74\) −8.12061 −0.944002
\(75\) −3.54576 4.22567i −0.409429 0.487939i
\(76\) 1.97906 3.42782i 0.227013 0.393198i
\(77\) 0 0
\(78\) −1.75537 + 4.82283i −0.198756 + 0.546078i
\(79\) 1.20187 2.08169i 0.135221 0.234209i −0.790461 0.612512i \(-0.790159\pi\)
0.925682 + 0.378303i \(0.123492\pi\)
\(80\) −0.0282185 + 0.0488759i −0.00315492 + 0.00546449i
\(81\) −8.45723 3.07818i −0.939693 0.342020i
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) −7.52481 13.0334i −0.825956 1.43060i −0.901187 0.433431i \(-0.857303\pi\)
0.0752309 0.997166i \(-0.476031\pi\)
\(84\) 0 0
\(85\) −0.315207 + 0.545955i −0.0341891 + 0.0592172i
\(86\) 3.87939 0.418325
\(87\) 3.71348 10.2027i 0.398127 1.09384i
\(88\) 4.68954 0.499907
\(89\) 4.54323 + 7.86911i 0.481582 + 0.834124i 0.999777 0.0211385i \(-0.00672911\pi\)
−0.518195 + 0.855263i \(0.673396\pi\)
\(90\) −2.72281 2.28471i −0.287010 0.240830i
\(91\) 0 0
\(92\) 5.48545 + 9.50108i 0.571898 + 0.990556i
\(93\) −5.47044 + 15.0299i −0.567258 + 1.55853i
\(94\) −4.11334 7.12452i −0.424259 0.734838i
\(95\) 2.17365 + 3.76487i 0.223012 + 0.386267i
\(96\) −3.34002 + 9.17664i −0.340890 + 0.936587i
\(97\) −0.949493 1.64457i −0.0964064 0.166981i 0.813788 0.581161i \(-0.197402\pi\)
−0.910195 + 0.414181i \(0.864068\pi\)
\(98\) 0 0
\(99\) −0.860967 + 4.88279i −0.0865304 + 0.490738i
\(100\) −1.95336 3.38332i −0.195336 0.338332i
\(101\) 1.70914 0.170066 0.0850329 0.996378i \(-0.472900\pi\)
0.0850329 + 0.996378i \(0.472900\pi\)
\(102\) 0.243756 0.669713i 0.0241354 0.0663115i
\(103\) 3.63816 0.358478 0.179239 0.983806i \(-0.442636\pi\)
0.179239 + 0.983806i \(0.442636\pi\)
\(104\) −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 0.640712 0.767781i \(-0.278639\pi\)
−0.985274 + 0.170982i \(0.945306\pi\)
\(108\) −5.52007 3.18701i −0.531169 0.306670i
\(109\) −0.201867 + 0.349643i −0.0193353 + 0.0334898i −0.875531 0.483162i \(-0.839488\pi\)
0.856196 + 0.516651i \(0.172822\pi\)
\(110\) −0.979055 + 1.69577i −0.0933493 + 0.161686i
\(111\) 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 \(0.930427\pi\)
\(114\) −3.15910 3.76487i −0.295877 0.352612i
\(115\) −12.0496 −1.12363
\(116\) 3.84477 6.65934i 0.356978 0.618304i
\(117\) −7.74376 6.49778i −0.715910 0.600720i
\(118\) −9.14290 −0.841672
\(119\) 0 0
\(120\) −4.25624 5.07239i −0.388540 0.463044i
\(121\) −8.26857 −0.751688
\(122\) −3.35844 5.81699i −0.304059 0.526646i
\(123\) 5.81908 1.02606i 0.524689 0.0925168i
\(124\) −5.66385 + 9.81007i −0.508629 + 0.880971i
\(125\) 11.0273 0.986315
\(126\) 0 0
\(127\) −20.7716 −1.84318 −0.921589 0.388167i \(-0.873108\pi\)
−0.921589 + 0.388167i \(0.873108\pi\)
\(128\) −3.42127 + 5.92582i −0.302401 + 0.523774i
\(129\) −2.61334 + 7.18009i −0.230092 + 0.632172i
\(130\) −1.99613 3.45740i −0.175072 0.303234i
\(131\) 7.16519 0.626026 0.313013 0.949749i \(-0.398662\pi\)
0.313013 + 0.949749i \(0.398662\pi\)
\(132\) −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
\(137\) 2.56893 0.219478 0.109739 0.993960i \(-0.464998\pi\)
0.109739 + 0.993960i \(0.464998\pi\)
\(138\) 13.4153 2.36549i 1.14199 0.201364i
\(139\) −3.06670 + 5.31169i −0.260114 + 0.450531i −0.966272 0.257523i \(-0.917094\pi\)
0.706158 + 0.708055i \(0.250427\pi\)
\(140\) 0 0
\(141\) 15.9572 2.81369i 1.34384 0.236956i
\(142\) −0.243756 + 0.422197i −0.0204555 + 0.0354300i
\(143\) −2.78446 + 4.82283i −0.232848 + 0.403305i
\(144\) 0.0962667 + 0.0807773i 0.00802222 + 0.00673144i
\(145\) 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
\(149\) 0.431074 0.0353150 0.0176575 0.999844i \(-0.494379\pi\)
0.0176575 + 0.999844i \(0.494379\pi\)
\(150\) −4.77719 + 0.842347i −0.390056 + 0.0687774i
\(151\) −2.47060 −0.201055 −0.100527 0.994934i \(-0.532053\pi\)
−0.100527 + 0.994934i \(0.532053\pi\)
\(152\) −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
\(156\) −4.60189 5.48432i −0.368446 0.439097i
\(157\) 5.06670 + 8.77579i 0.404367 + 0.700384i 0.994248 0.107106i \(-0.0341585\pi\)
−0.589881 + 0.807491i \(0.700825\pi\)
\(158\) −1.05690 1.83061i −0.0840828 0.145636i
\(159\) 0.979055 0.172634i 0.0776441 0.0136908i
\(160\) −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 0.912376 0.409353i \(-0.134246\pi\)
−0.810698 + 0.585464i \(0.800912\pi\)
\(164\) 4.18479 0.326777
\(165\) −2.47906 2.95442i −0.192994 0.230002i
\(166\) −13.2344 −1.02719
\(167\) −11.5915 + 20.0771i −0.896979 + 1.55361i −0.0656422 + 0.997843i \(0.520910\pi\)
−0.831337 + 0.555769i \(0.812424\pi\)
\(168\) 0 0
\(169\) 0.822948 + 1.42539i 0.0633037 + 0.109645i
\(170\) 0.277189 + 0.480105i 0.0212594 + 0.0368224i
\(171\) 9.09627 3.31077i 0.695609 0.253181i
\(172\) −2.70574 + 4.68647i −0.206311 + 0.357340i
\(173\) −2.37598 + 4.11532i −0.180643 + 0.312882i −0.942100 0.335333i \(-0.891151\pi\)
0.761457 + 0.648215i \(0.224484\pi\)
\(174\) −6.13728 7.31412i −0.465266 0.554482i
\(175\) 0 0
\(176\) 0.0346151 0.0599551i 0.00260921 0.00451929i
\(177\) 6.15910 16.9220i 0.462946 1.27193i
\(178\) 7.99050 0.598914
\(179\) 4.26604 7.38901i 0.318859 0.552280i −0.661391 0.750041i \(-0.730034\pi\)
0.980250 + 0.197761i \(0.0633670\pi\)
\(180\) 4.65910 1.69577i 0.347269 0.126396i
\(181\) 17.2344 1.28102 0.640512 0.767948i \(-0.278722\pi\)
0.640512 + 0.767948i \(0.278722\pi\)
\(182\) 0 0
\(183\) 13.0287 2.29731i 0.963108 0.169822i
\(184\) 25.3773 1.87084
\(185\) 6.22075 + 10.7747i 0.457359 + 0.792169i
\(186\) 9.04101 + 10.7747i 0.662919 + 0.790036i
\(187\) 0.386659 0.669713i 0.0282753 0.0489743i
\(188\) 11.4757 0.836948
\(189\) 0 0
\(190\) 3.82295 0.277346
\(191\) −6.45471 + 11.1799i −0.467046 + 0.808948i −0.999291 0.0376425i \(-0.988015\pi\)
0.532245 + 0.846590i \(0.321349\pi\)
\(192\) 5.61334 + 6.68972i 0.405108 + 0.482789i
\(193\) 0.319078 + 0.552659i 0.0229677 + 0.0397813i 0.877281 0.479977i \(-0.159355\pi\)
−0.854313 + 0.519759i \(0.826022\pi\)
\(194\) −1.66994 −0.119895
\(195\) 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 \(0.366319\pi\)
\(198\) 3.34002 + 2.80261i 0.237365 + 0.199173i
\(199\) −1.81908 + 3.15074i −0.128951 + 0.223350i −0.923270 0.384151i \(-0.874494\pi\)
0.794319 + 0.607500i \(0.207828\pi\)
\(200\) −9.03684 −0.639001
\(201\) 0.353226 0.970481i 0.0249147 0.0684524i
\(202\) 0.751497 1.30163i 0.0528751 0.0915824i
\(203\) 0 0
\(204\) 0.639033 + 0.761570i 0.0447413 + 0.0533206i
\(205\) −2.29813 + 3.98048i −0.160509 + 0.278009i
\(206\) 1.59967 2.77071i 0.111454 0.193045i
\(207\) −4.65910 + 26.4231i −0.323830 + 1.83653i
\(208\) 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 \(0.230902\pi\)
\(212\) 0.704088 0.0483570
\(213\) −0.617211 0.735564i −0.0422906 0.0504000i
\(214\) −6.26857 −0.428511
\(215\) −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
\(219\) 3.49613 0.616462i 0.236247 0.0416566i
\(220\) −1.36571 2.36549i −0.0920765 0.159481i
\(221\) 0.788333 + 1.36543i 0.0530290 + 0.0918490i
\(222\) −9.04101 10.7747i −0.606793 0.723148i
\(223\) 3.54189 + 6.13473i 0.237182 + 0.410812i 0.959905 0.280327i \(-0.0904428\pi\)
−0.722722 + 0.691139i \(0.757109\pi\)
\(224\) 0 0
\(225\) 1.65910 9.40923i 0.110607 0.627282i
\(226\) 6.31820 + 10.9434i 0.420280 + 0.727947i
\(227\) 11.9436 0.792722 0.396361 0.918095i \(-0.370273\pi\)
0.396361 + 0.918095i \(0.370273\pi\)
\(228\) 6.75150 1.19047i 0.447129 0.0788409i
\(229\) 17.5526 1.15991 0.579955 0.814649i \(-0.303070\pi\)
0.579955 + 0.814649i \(0.303070\pi\)
\(230\) −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 −0.999284 0.0378470i \(-0.987950\pi\)
0.466865 0.884328i \(-0.345383\pi\)
\(234\) −8.35339 + 3.04038i −0.546078 + 0.198756i
\(235\) −6.30200 + 10.9154i −0.411097 + 0.712042i
\(236\) 6.37686 11.0450i 0.415098 0.718971i
\(237\) 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 \(0.00426745\pi\)
\(240\) −0.0962667 + 0.0169744i −0.00621399 + 0.00109569i
\(241\) 15.6382 1.00734 0.503671 0.863896i \(-0.331982\pi\)
0.503671 + 0.863896i \(0.331982\pi\)
\(242\) −3.63563 + 6.29710i −0.233707 + 0.404793i
\(243\) −5.33157 14.6484i −0.342020 0.939693i
\(244\) 9.36959 0.599826
\(245\) 0 0
\(246\) 1.77719 4.88279i 0.113309 0.311315i
\(247\) 10.8726 0.691806
\(248\) 13.1013 + 22.6922i 0.831935 + 1.44095i
\(249\) 8.91534 24.4947i 0.564987 1.55229i
\(250\) 4.84864 8.39809i 0.306655 0.531142i
\(251\) −19.0651 −1.20338 −0.601690 0.798730i \(-0.705506\pi\)
−0.601690 + 0.798730i \(0.705506\pi\)
\(252\) 0 0
\(253\) 14.7811 0.929277
\(254\) −9.13310 + 15.8190i −0.573062 + 0.992572i
\(255\) −1.07532 + 0.189608i −0.0673393 + 0.0118737i
\(256\) 8.05051 + 13.9439i 0.503157 + 0.871493i
\(257\) −26.5817 −1.65812 −0.829061 0.559158i \(-0.811124\pi\)
−0.829061 + 0.559158i \(0.811124\pi\)
\(258\) 4.31908 + 5.14728i 0.268894 + 0.320455i
\(259\) 0 0
\(260\) 5.56893 0.345370
\(261\) 17.6716 6.43193i 1.09384 0.398127i
\(262\) 3.15048 5.45680i 0.194637 0.337122i
\(263\) −0.734118 −0.0452676 −0.0226338 0.999744i \(-0.507205\pi\)
−0.0226338 + 0.999744i \(0.507205\pi\)
\(264\) 5.22106 + 6.22221i 0.321334 + 0.382951i
\(265\) −0.386659 + 0.669713i −0.0237523 + 0.0411402i
\(266\) 0 0
\(267\) −5.38279 + 14.7891i −0.329421 + 0.905078i
\(268\) 0.365715 0.633436i 0.0223396 0.0386933i
\(269\) −10.4251 + 18.0569i −0.635632 + 1.10095i 0.350749 + 0.936470i \(0.385927\pi\)
−0.986381 + 0.164478i \(0.947406\pi\)
\(270\) 6.15636i 0.374664i
\(271\) 3.47906 + 6.02590i 0.211338 + 0.366047i 0.952133 0.305683i \(-0.0988847\pi\)
−0.740796 + 0.671730i \(0.765551\pi\)
\(272\) −0.00980018 0.0169744i −0.000594223 0.00102922i
\(273\) 0 0
\(274\) 1.12954 1.95642i 0.0682379 0.118191i
\(275\) −5.26352 −0.317402
\(276\) −6.49912 + 17.8562i −0.391201 + 1.07482i
\(277\) 17.8726 1.07386 0.536930 0.843627i \(-0.319584\pi\)
0.536930 + 0.843627i \(0.319584\pi\)
\(278\) 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 \(-0.398433\pi\)
\(282\) 4.87346 13.3897i 0.290210 0.797346i
\(283\) −9.29726 16.1033i −0.552665 0.957243i −0.998081 0.0619196i \(-0.980278\pi\)
0.445417 0.895323i \(-0.353056\pi\)
\(284\) −0.340022 0.588936i −0.0201766 0.0349469i
\(285\) −2.57532 + 7.07564i −0.152549 + 0.419125i
\(286\) 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
\(290\) 7.42696 0.436126
\(291\) 1.12495 3.09078i 0.0659459 0.181185i
\(292\) 2.51424 0.147135
\(293\) 6.54576 11.3376i 0.382407 0.662349i −0.608998 0.793171i \(-0.708428\pi\)
0.991406 + 0.130822i \(0.0417618\pi\)
\(294\) 0 0
\(295\) 7.00387 + 12.1311i 0.407781 + 0.706298i
\(296\) −13.1013 22.6922i −0.761499 1.31895i
\(297\) −7.43717 + 4.29385i −0.431548 + 0.249154i
\(298\) 0.189540 0.328293i 0.0109798 0.0190175i
\(299\) −15.0680 + 26.0986i −0.871408 + 1.50932i
\(300\) 2.31433 6.35857i 0.133618 0.367112i
\(301\) 0 0
\(302\) −1.08630 + 1.88153i −0.0625098 + 0.108270i
\(303\) 1.90286 + 2.26774i 0.109316 + 0.130278i
\(304\) −0.135163 −0.00775211
\(305\) −5.14543 + 8.91215i −0.294626 + 0.510308i
\(306\) 1.15998 0.422197i 0.0663115 0.0241354i
\(307\) −6.31046 −0.360157 −0.180078 0.983652i \(-0.557635\pi\)
−0.180078 + 0.983652i \(0.557635\pi\)
\(308\) 0 0
\(309\) 4.05051 + 4.82721i 0.230425 + 0.274610i
\(310\) −10.9409 −0.621400
\(311\) −4.76217 8.24833i −0.270038 0.467720i 0.698833 0.715285i \(-0.253703\pi\)
−0.968871 + 0.247565i \(0.920370\pi\)
\(312\) −16.3089 + 2.87569i −0.923308 + 0.162804i
\(313\) −8.81433 + 15.2669i −0.498215 + 0.862934i −0.999998 0.00205946i \(-0.999344\pi\)
0.501782 + 0.864994i \(0.332678\pi\)
\(314\) 8.91117 0.502886
\(315\) 0 0
\(316\) 2.94862 0.165873
\(317\) −4.03849 + 6.99486i −0.226824 + 0.392871i −0.956865 0.290533i \(-0.906168\pi\)
0.730041 + 0.683403i \(0.239501\pi\)
\(318\) 0.299011 0.821525i 0.0167677 0.0460688i
\(319\) −5.18004 8.97210i −0.290027 0.502341i
\(320\) −6.79292 −0.379736
\(321\) 4.22281 11.6021i 0.235694 0.647565i
\(322\) 0 0
\(323\) −1.50980 −0.0840075
\(324\) −1.91710 10.8724i −0.106506 0.604023i
\(325\) 5.36571 9.29369i 0.297636 0.515521i
\(326\) 2.28312 0.126450
\(327\) −0.688663 + 0.121430i −0.0380831 + 0.00671509i
\(328\) 4.84002 8.38316i 0.267246 0.462883i
\(329\) 0 0
\(330\) −3.34002 + 0.588936i −0.183862 + 0.0324199i
\(331\) −11.5248 + 19.9616i −0.633461 + 1.09719i 0.353378 + 0.935481i \(0.385033\pi\)
−0.986839 + 0.161706i \(0.948300\pi\)
\(332\) 9.23055 15.9878i 0.506592 0.877444i
\(333\) 26.0326 9.47508i 1.42658 0.519231i
\(334\) 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 \(0.876489\pi\)
\(338\) 1.44738 0.0787269
\(339\) −24.5107 + 4.32190i −1.33124 + 0.234734i
\(340\) −0.773318 −0.0419391
\(341\) 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
\(345\) −13.4153 15.9878i −0.722258 0.860753i
\(346\) 2.08940 + 3.61895i 0.112327 + 0.194556i
\(347\) −6.47313 11.2118i −0.347496 0.601880i 0.638308 0.769781i \(-0.279635\pi\)
−0.985804 + 0.167901i \(0.946301\pi\)
\(348\) 13.1163 2.31276i 0.703109 0.123977i
\(349\) 0.731429 + 1.26687i 0.0391525 + 0.0678141i 0.884938 0.465710i \(-0.154201\pi\)
−0.845785 + 0.533524i \(0.820868\pi\)
\(350\) 0 0
\(351\) 17.5089i 0.934555i
\(352\) 4.65910 + 8.06980i 0.248331 + 0.430122i
\(353\) −14.3327 −0.762855 −0.381428 0.924399i \(-0.624567\pi\)
−0.381428 + 0.924399i \(0.624567\pi\)
\(354\) −10.1792 12.1311i −0.541017 0.644759i
\(355\) 0.746911 0.0396419
\(356\) −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 0.998093 + 0.0617224i \(0.0196594\pi\)
−0.445593 + 0.895235i \(0.647007\pi\)
\(360\) 1.99154 11.2946i 0.104964 0.595278i
\(361\) 4.29426 7.43788i 0.226014 0.391467i
\(362\) 7.57785 13.1252i 0.398283 0.689846i
\(363\) −9.20574 10.9710i −0.483176 0.575827i
\(364\) 0 0
\(365\) −1.38073 + 2.39149i −0.0722707 + 0.125176i
\(366\) 3.97906 10.9324i 0.207989 0.571444i
\(367\) 12.0574 0.629390 0.314695 0.949193i \(-0.398098\pi\)
0.314695 + 0.949193i \(0.398098\pi\)
\(368\) 0.187319 0.324446i 0.00976466 0.0169129i
\(369\) 7.84002 + 6.57856i 0.408135 + 0.342466i
\(370\) 10.9409 0.568789
\(371\) 0 0
\(372\) −19.3221 + 3.40700i −1.00180 + 0.176645i
\(373\) −0.781059 −0.0404417 −0.0202209 0.999796i \(-0.506437\pi\)
−0.0202209 + 0.999796i \(0.506437\pi\)
\(374\) −0.340022 0.588936i −0.0175821 0.0304532i
\(375\) 12.2772 + 14.6314i 0.633991 + 0.755561i
\(376\) 13.2724 22.9885i 0.684474 1.18554i
\(377\) 21.1225 1.08786
\(378\) 0 0
\(379\) −6.92396 −0.355660 −0.177830 0.984061i \(-0.556908\pi\)
−0.177830 + 0.984061i \(0.556908\pi\)
\(380\) −2.66637 + 4.61830i −0.136782 + 0.236914i
\(381\) −23.1258 27.5603i −1.18477 1.41196i
\(382\) 5.67617 + 9.83142i 0.290418 + 0.503019i
\(383\) −7.73236 −0.395105 −0.197553 0.980292i \(-0.563299\pi\)
−0.197553 + 0.980292i \(0.563299\pi\)
\(384\) −11.6716 + 2.05802i −0.595613 + 0.105023i
\(385\) 0 0
\(386\) 0.561185 0.0285636
\(387\) −12.4363 + 4.52644i −0.632172 + 0.230092i
\(388\) 1.16473 2.01736i 0.0591300 0.102416i
\(389\) 5.39961 0.273771 0.136886 0.990587i \(-0.456291\pi\)
0.136886 + 0.990587i \(0.456291\pi\)
\(390\) 2.36500 6.49778i 0.119756 0.329028i
\(391\) 2.09240 3.62414i 0.105817 0.183280i
\(392\) 0 0
\(393\) 7.97730 + 9.50698i 0.402402 + 0.479564i
\(394\) 5.03256 8.71664i 0.253536 0.439138i
\(395\) −1.61927 + 2.80466i −0.0814743 + 0.141118i
\(396\) −5.71523 + 2.08017i −0.287201 + 0.104533i
\(397\) −14.6172 25.3178i −0.733617 1.27066i −0.955328 0.295549i \(-0.904497\pi\)
0.221711 0.975112i \(-0.428836\pi\)
\(398\) 1.59967 + 2.77071i 0.0801842 + 0.138883i
\(399\) 0 0
\(400\) −0.0667040 + 0.115535i −0.00333520 + 0.00577674i
\(401\) −27.3979 −1.36818 −0.684092 0.729396i \(-0.739801\pi\)
−0.684092 + 0.729396i \(0.739801\pi\)
\(402\) −0.583778 0.695720i −0.0291162 0.0346993i
\(403\) −31.1162 −1.55001
\(404\) 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
\(408\) 2.26470 0.399328i 0.112119 0.0197697i
\(409\) −4.51249 7.81586i −0.223128 0.386469i 0.732628 0.680629i \(-0.238294\pi\)
−0.955756 + 0.294160i \(0.904960\pi\)
\(410\) 2.02094 + 3.50038i 0.0998073 + 0.172871i
\(411\) 2.86009 + 3.40852i 0.141078 + 0.168130i
\(412\) 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
\(416\) −18.9982 −0.931466
\(417\) −10.4620 + 1.84473i −0.512325 + 0.0903368i
\(418\) −4.68954 −0.229373
\(419\) 0.0876485 0.151812i 0.00428191 0.00741649i −0.863877 0.503704i \(-0.831970\pi\)
0.868158 + 0.496287i \(0.165304\pi\)
\(420\) 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
\(423\) 21.4991 + 18.0399i 1.04532 + 0.877130i
\(424\) 0.814330 1.41046i 0.0395474 0.0684980i
\(425\) −0.745100 + 1.29055i −0.0361427 + 0.0626009i
\(426\) −0.831566 + 0.146628i −0.0402895 + 0.00710413i
\(427\) 0 0
\(428\) 4.37211 7.57272i 0.211334 0.366041i
\(429\) −9.49912 + 1.67495i −0.458622 + 0.0808674i
\(430\) −5.22668 −0.252053
\(431\) 14.6596 25.3911i 0.706126 1.22305i −0.260157 0.965566i \(-0.583774\pi\)
0.966283 0.257481i \(-0.0828924\pi\)
\(432\) 0.217662i 0.0104723i
\(433\) −19.6554 −0.944578 −0.472289 0.881444i \(-0.656572\pi\)
−0.472289 + 0.881444i \(0.656572\pi\)
\(434\) 0 0
\(435\) −5.00316 + 13.7461i −0.239883 + 0.659073i
\(436\) −0.495252 −0.0237183
\(437\) −14.4290 24.9918i −0.690233 1.19552i
\(438\) 1.06774 2.93360i 0.0510188 0.140173i
\(439\) −10.9650 + 18.9919i −0.523330 + 0.906434i 0.476302 + 0.879282i \(0.341977\pi\)
−0.999631 + 0.0271516i \(0.991356\pi\)
\(440\) −6.31820 −0.301208
\(441\) 0 0
\(442\) 1.38650 0.0659489
\(443\) 9.35504 16.2034i 0.444471 0.769847i −0.553544 0.832820i \(-0.686725\pi\)
0.998015 + 0.0629732i \(0.0200583\pi\)
\(444\) 19.3221 3.40700i 0.916985 0.161689i
\(445\) −6.12108 10.6020i −0.290167 0.502584i
\(446\) 6.22937 0.294969
\(447\) 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 \(0.449616\pi\)
\(450\) −6.43629 5.40069i −0.303410 0.254591i
\(451\) 2.81908 4.88279i 0.132745 0.229921i
\(452\) −17.6269 −0.829100
\(453\) −2.75062 3.27806i −0.129235 0.154017i
\(454\) 5.25150 9.09586i 0.246465 0.426890i
\(455\) 0 0
\(456\) 5.42380 14.9018i 0.253993 0.697839i
\(457\) 9.71436 16.8258i 0.454418 0.787076i −0.544236 0.838932i \(-0.683180\pi\)
0.998655 + 0.0518563i \(0.0165138\pi\)
\(458\) 7.71776 13.3676i 0.360627 0.624625i
\(459\) 2.43134i 0.113485i
\(460\) −7.39053 12.8008i −0.344585 0.596839i
\(461\) −0.482926 0.836452i −0.0224921 0.0389575i 0.854560 0.519352i \(-0.173827\pi\)
−0.877052 + 0.480395i \(0.840493\pi\)
\(462\) 0 0
\(463\) 0.222811 0.385920i 0.0103549 0.0179352i −0.860802 0.508941i \(-0.830037\pi\)
0.871156 + 0.491006i \(0.163371\pi\)
\(464\) −0.262585 −0.0121902
\(465\) 7.37030 20.2497i 0.341789 0.939059i
\(466\) −14.2935 −0.662136
\(467\) −17.1074 29.6309i −0.791637 1.37115i −0.924953 0.380081i \(-0.875896\pi\)
0.133317 0.991074i \(-0.457437\pi\)
\(468\) 2.15328 12.2118i 0.0995352 0.564492i
\(469\) 0 0
\(470\) 5.54189 + 9.59883i 0.255628 + 0.442761i
\(471\) −6.00299 + 16.4931i −0.276603 + 0.759961i
\(472\) −14.7506 25.5488i −0.678952 1.17598i
\(473\) 3.64543 + 6.31407i 0.167617 + 0.290321i
\(474\) 1.25221 3.44042i 0.0575160 0.158024i
\(475\) 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
\(479\) 21.7929 0.995744 0.497872 0.867251i \(-0.334115\pi\)
0.497872 + 0.867251i \(0.334115\pi\)
\(480\) 4.50000 12.3636i 0.205396 0.564321i
\(481\) 31.1162 1.41878
\(482\) 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
\(486\) −13.5000 2.38041i −0.612372 0.107978i
\(487\) −9.69640 + 16.7947i −0.439386 + 0.761039i −0.997642 0.0686297i \(-0.978137\pi\)
0.558256 + 0.829669i \(0.311471\pi\)
\(488\) 10.8366 18.7696i 0.490551 0.849659i
\(489\) −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 \(0.965709\pi\)
\(492\) 4.65910 + 5.55250i 0.210048 + 0.250326i
\(493\) −2.93313 −0.132102
\(494\) 4.78059 8.28023i 0.215089 0.372545i
\(495\) 1.15998 6.57856i 0.0521371 0.295684i
\(496\) 0.386821 0.0173688
\(497\) 0 0
\(498\) −14.7344 17.5598i −0.660265 0.786873i
\(499\) −14.3013 −0.640214 −0.320107 0.947381i \(-0.603719\pi\)
−0.320107 + 0.947381i \(0.603719\pi\)
\(500\) 6.76352 + 11.7148i 0.302474 + 0.523900i
\(501\) −39.5442 + 6.97270i −1.76670 + 0.311517i
\(502\) −8.38279 + 14.5194i −0.374142 + 0.648033i
\(503\) −18.7033 −0.833937 −0.416969 0.908921i \(-0.636908\pi\)
−0.416969 + 0.908921i \(0.636908\pi\)
\(504\) 0 0
\(505\) −2.30272 −0.102470
\(506\) 6.49912 11.2568i 0.288921 0.500426i
\(507\) −0.975023 + 2.67885i −0.0433023 + 0.118972i
\(508\) −12.7400 22.0664i −0.565248 0.979039i
\(509\) 25.6091 1.13510 0.567551 0.823338i \(-0.307891\pi\)
0.567551 + 0.823338i \(0.307891\pi\)
\(510\) −0.328411 + 0.902302i −0.0145423 + 0.0399546i
\(511\) 0 0
\(512\) 0.473897 0.0209435
\(513\) 14.5201 + 8.38316i 0.641077 + 0.370126i
\(514\) −11.6878 + 20.2438i −0.515526 + 0.892917i
\(515\) −4.90167 −0.215994
\(516\) −9.23055 + 1.62760i −0.406352 + 0.0716509i
\(517\) 7.73055 13.3897i 0.339989 0.588879i
\(518\) 0 0
\(519\) −8.10560 + 1.42924i −0.355796 + 0.0627365i
\(520\) 6.44087 11.1559i 0.282451 0.489220i
\(521\) −10.6061 + 18.3702i −0.464660 + 0.804815i −0.999186 0.0403370i \(-0.987157\pi\)
0.534526 + 0.845152i \(0.320490\pi\)
\(522\) 2.87170 16.2862i 0.125691 0.712829i
\(523\) 10.4029 + 18.0183i 0.454885 + 0.787884i 0.998682 0.0513330i \(-0.0163470\pi\)
−0.543796 + 0.839217i \(0.683014\pi\)
\(524\) 4.39470 + 7.61185i 0.191984 + 0.332525i
\(525\) 0 0
\(526\) −0.322786 + 0.559082i −0.0140741 + 0.0243771i
\(527\) 4.32089 0.188221
\(528\) 0.118089 0.0208222i 0.00513914 0.000906170i
\(529\) 56.9873 2.47771
\(530\) 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
\(534\) 8.89615 + 10.6020i 0.384974 + 0.458794i
\(535\) 4.80200 + 8.31731i 0.207609 + 0.359589i
\(536\) −0.845952 1.46523i −0.0365396 0.0632884i
\(537\) 14.5535 2.56617i 0.628030 0.110739i
\(538\) 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 −0.996085 0.0884001i \(-0.971825\pi\)
0.421486 0.906835i \(-0.361509\pi\)
\(542\) 6.11886 0.262828
\(543\) 19.1878 + 22.8671i 0.823427 + 0.981322i
\(544\) 2.63816 0.113110
\(545\) 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
\(549\) 17.5535 + 14.7291i 0.749165 + 0.628624i
\(550\) −2.31433 + 4.00854i −0.0986834 + 0.170925i
\(551\) −10.1133 + 17.5168i −0.430843 + 0.746242i
\(552\) 28.2536 + 33.6713i 1.20255 + 1.43315i
\(553\) 0 0
\(554\) 7.85844 13.6112i 0.333873 0.578285i
\(555\) −7.37030 + 20.2497i −0.312852 + 0.859553i
\(556\) −7.52374 −0.319078
\(557\) −16.1694 + 28.0062i −0.685118 + 1.18666i 0.288282 + 0.957546i \(0.406916\pi\)
−0.973400 + 0.229114i \(0.926417\pi\)
\(558\) −4.23039 + 23.9917i −0.179087 + 1.01565i
\(559\) −14.8648 −0.628716
\(560\) 0 0
\(561\) 1.31908 0.232589i 0.0556915 0.00981992i
\(562\) −19.6195 −0.827598
\(563\) −8.87093 15.3649i −0.373865 0.647553i 0.616291 0.787518i \(-0.288634\pi\)
−0.990156 + 0.139965i \(0.955301\pi\)
\(564\) 12.7763 + 15.2262i 0.537980 + 0.641139i
\(565\) 9.68004 16.7663i 0.407243 0.705365i
\(566\) −16.3517 −0.687315
\(567\) 0 0
\(568\) −1.57304 −0.0660035
\(569\) 13.3007 23.0374i 0.557593 0.965779i −0.440104 0.897947i \(-0.645058\pi\)
0.997697 0.0678320i \(-0.0216082\pi\)
\(570\) 4.25624 + 5.07239i 0.178274 + 0.212459i
\(571\) 5.00862 + 8.67518i 0.209604 + 0.363045i 0.951590 0.307371i \(-0.0994491\pi\)
−0.741986 + 0.670416i \(0.766116\pi\)
\(572\) −6.83130 −0.285631
\(573\) −22.0201 + 3.88273i −0.919902 + 0.162203i
\(574\) 0 0
\(575\) −28.4834 −1.18784
\(576\) −2.62654 + 14.8959i −0.109439 + 0.620661i
\(577\) −16.4572 + 28.5048i −0.685124 + 1.18667i 0.288274 + 0.957548i \(0.406918\pi\)
−0.973398 + 0.229121i \(0.926415\pi\)
\(578\) 14.7570 0.613811
\(579\) −0.378041 + 1.03866i −0.0157109 + 0.0431652i
\(580\) −5.18004 + 8.97210i −0.215090 + 0.372546i
\(581\) 0 0
\(582\) −1.85921 2.21572i −0.0770668 0.0918447i
\(583\) 0.474308 0.821525i 0.0196438 0.0340241i
\(584\) 2.90791 5.03665i 0.120330 0.208418i
\(585\) 10.4331 + 8.75444i 0.431357 + 0.361951i
\(586\) −5.75624 9.97011i −0.237788 0.411861i
\(587\) −7.53643 13.0535i −0.311062 0.538774i 0.667531 0.744582i \(-0.267351\pi\)
−0.978592 + 0.205808i \(0.934018\pi\)
\(588\) 0 0
\(589\) 14.8983 25.8046i 0.613873 1.06326i
\(590\) 12.3182 0.507132
\(591\) 12.7429 + 15.1864i 0.524172 + 0.624684i
\(592\) −0.386821 −0.0158983
\(593\) 20.5005 + 35.5079i 0.841853 + 1.45813i 0.888326 + 0.459213i \(0.151869\pi\)
−0.0464729 + 0.998920i \(0.514798\pi\)
\(594\) 7.55190i 0.309858i
\(595\) 0 0
\(596\) 0.264396 + 0.457947i 0.0108301 + 0.0187582i
\(597\) −6.20574 + 1.09424i −0.253984 + 0.0447842i
\(598\) 13.2506 + 22.9507i 0.541858 + 0.938526i
\(599\) −3.03684 5.25996i −0.124082 0.214916i 0.797292 0.603594i \(-0.206265\pi\)
−0.921374 + 0.388678i \(0.872932\pi\)
\(600\) −10.0611 11.9903i −0.410742 0.489503i
\(601\) −7.06758 12.2414i −0.288293 0.499338i 0.685110 0.728440i \(-0.259754\pi\)
−0.973402 + 0.229102i \(0.926421\pi\)
\(602\) 0 0
\(603\) 1.68092 0.611806i 0.0684524 0.0249147i
\(604\) −1.51532 2.62461i −0.0616575 0.106794i
\(605\) 11.1402 0.452914
\(606\) 2.56371 0.452051i 0.104144 0.0183633i
\(607\) −46.0898 −1.87073 −0.935363 0.353689i \(-0.884927\pi\)
−0.935363 + 0.353689i \(0.884927\pi\)
\(608\) 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
\(612\) −0.299011 + 1.69577i −0.0120868 + 0.0685476i
\(613\) 13.2469 22.9443i 0.535038 0.926712i −0.464124 0.885770i \(-0.653631\pi\)
0.999162 0.0409421i \(-0.0130359\pi\)
\(614\) −2.77466 + 4.80586i −0.111976 + 0.193949i
\(615\) −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 \(0.152246\pi\)
\(618\) 5.45723 0.962258i 0.219522 0.0387077i
\(619\) −6.19078 −0.248828 −0.124414 0.992230i \(-0.539705\pi\)
−0.124414 + 0.992230i \(0.539705\pi\)
\(620\) 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
\(625\) 1.06687 0.0426746
\(626\) 7.75119 + 13.4255i 0.309800 + 0.536589i
\(627\) 3.15910 8.67956i 0.126162 0.346628i
\(628\) −6.21523 + 10.7651i −0.248015 + 0.429574i
\(629\) −4.32089 −0.172285
\(630\) 0 0
\(631\) 26.1661 1.04166 0.520829 0.853661i \(-0.325623\pi\)
0.520829 + 0.853661i \(0.325623\pi\)
\(632\) 3.41029 5.90680i 0.135654 0.234960i
\(633\) −9.93242 + 1.75135i −0.394778 + 0.0696100i
\(634\) 3.55138 + 6.15118i 0.141043 + 0.244295i
\(635\) 27.9855 1.11057
\(636\) 0.783890 + 0.934204i 0.0310833 + 0.0370436i
\(637\) 0 0
\(638\) −9.11051 −0.360689
\(639\) 0.288800 1.63787i 0.0114248 0.0647930i
\(640\) 4.60947 7.98384i 0.182205 0.315589i
\(641\) 4.88888 0.193099 0.0965496 0.995328i \(-0.469219\pi\)
0.0965496 + 0.995328i \(0.469219\pi\)
\(642\) −6.97906 8.31731i −0.275441 0.328258i
\(643\) −20.1839 + 34.9596i −0.795976 + 1.37867i 0.126242 + 0.992000i \(0.459709\pi\)
−0.922218 + 0.386671i \(0.873625\pi\)
\(644\) 0 0
\(645\) 3.52094 9.67372i 0.138637 0.380902i
\(646\) −0.663848 + 1.14982i −0.0261188 + 0.0452390i
\(647\) −1.14038 + 1.97519i −0.0448329 + 0.0776528i −0.887571 0.460671i \(-0.847609\pi\)
0.842738 + 0.538324i \(0.180942\pi\)
\(648\) −23.9974 8.73433i −0.942706 0.343117i
\(649\) −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
\(653\) 23.4793 0.918815 0.459407 0.888226i \(-0.348062\pi\)
0.459407 + 0.888226i \(0.348062\pi\)
\(654\) −0.210323 + 0.577857i −0.00822427 + 0.0225960i
\(655\) −9.65364 −0.377199
\(656\) −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 \(0.449472\pi\)
\(660\) 1.61809 4.44566i 0.0629840 0.173047i
\(661\) 14.6545 + 25.3824i 0.569995 + 0.987260i 0.996566 + 0.0828055i \(0.0263880\pi\)
−0.426571 + 0.904454i \(0.640279\pi\)
\(662\) 10.1348 + 17.5539i 0.393898 + 0.682252i
\(663\) −0.934011 + 2.56617i −0.0362740 + 0.0996620i
\(664\) −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
\(668\) −28.4382 −1.10031
\(669\) −4.19640 + 11.5295i −0.162242 + 0.445757i
\(670\) 0.706452 0.0272926
\(671\) 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
\(675\) 14.3316 8.27433i 0.551622 0.318479i
\(676\) −1.00950 + 1.74850i −0.0388267 + 0.0672499i
\(677\) 17.9454 31.0823i 0.689697 1.19459i −0.282239 0.959344i \(-0.591077\pi\)
0.971936 0.235246i \(-0.0755895\pi\)
\(678\) −7.48576 + 20.5669i −0.287489 + 0.789869i
\(679\) 0 0
\(680\) −0.894400 + 1.54915i −0.0342987 + 0.0594070i
\(681\) 13.2973 + 15.8471i 0.509552 + 0.607260i
\(682\) 13.4210 0.513915
\(683\) −17.5321 + 30.3665i −0.670847 + 1.16194i 0.306818 + 0.951768i \(0.400736\pi\)
−0.977664 + 0.210172i \(0.932597\pi\)
\(684\) 9.09627 + 7.63267i 0.347804 + 0.291843i
\(685\) −3.46110 −0.132242
\(686\) 0 0
\(687\) 19.5421 + 23.2893i 0.745576 + 0.888543i
\(688\) 0.184793 0.00704515
\(689\) 0.967034 + 1.67495i 0.0368411 + 0.0638106i
\(690\) −18.0744 + 3.18701i −0.688082 + 0.121327i
\(691\) 1.03343 1.78996i 0.0393136 0.0680932i −0.845699 0.533660i \(-0.820816\pi\)
0.885013 + 0.465567i \(0.154150\pi\)
\(692\) −5.82915 −0.221591
\(693\) 0 0
\(694\) −11.3847 −0.432159
\(695\) 4.13176 7.15642i 0.156727 0.271458i
\(696\) 10.5370 28.9501i 0.399403 1.09735i
\(697\) −0.798133 1.38241i −0.0302315 0.0523624i
\(698\) 1.28642 0.0486916
\(699\) 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 \(0.544387\pi\)
\(702\) −13.3342 7.69852i −0.503268 0.290562i
\(703\) −14.8983 + 25.8046i −0.561899 + 0.973237i
\(704\) 8.33275 0.314052
\(705\) −21.4991 + 3.79088i −0.809704 + 0.142773i
\(706\) −6.30200 + 10.9154i −0.237179 + 0.410806i
\(707\) 0 0
\(708\) 21.7545 3.83590i 0.817584 0.144162i
\(709\) −4.55438 + 7.88841i −0.171043 + 0.296256i −0.938785 0.344504i \(-0.888047\pi\)
0.767742 + 0.640760i \(0.221380\pi\)
\(710\) 0.328411 0.568825i 0.0123251 0.0213476i
\(711\) 5.52410 + 4.63527i 0.207170 + 0.173836i
\(712\) 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
\(716\) 10.4662 0.391139
\(717\) 25.7554 4.54137i 0.961852 0.169600i
\(718\) 18.4115 0.687110
\(719\) −12.9768 22.4765i −0.483954 0.838233i 0.515876 0.856663i \(-0.327467\pi\)
−0.999830 + 0.0184300i \(0.994133\pi\)
\(720\) −0.129700 0.108831i −0.00483362 0.00405589i
\(721\) 0 0
\(722\) −3.77631 6.54076i −0.140540 0.243422i
\(723\) 17.4106 + 20.7491i 0.647507 + 0.771669i
\(724\) 10.5706 + 18.3088i 0.392852 + 0.680440i
\(725\) 9.98205 + 17.2894i 0.370724 + 0.642113i
\(726\) −12.4029 + 2.18696i −0.460313 + 0.0811656i
\(727\) −5.08007 8.79894i −0.188409 0.326335i 0.756311 0.654213i \(-0.227000\pi\)
−0.944720 + 0.327878i \(0.893667\pi\)
\(728\) 0 0
\(729\) 13.5000 23.3827i 0.500000 0.866025i
\(730\) 1.21419 + 2.10304i 0.0449393 + 0.0778372i
\(731\) 2.06418 0.0763464
\(732\) 10.4315 + 12.4318i 0.385561 + 0.459494i
\(733\) −40.6614 −1.50186 −0.750931 0.660381i \(-0.770395\pi\)
−0.750931 + 0.660381i \(0.770395\pi\)
\(734\) 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
\(738\) 8.45723 3.07818i 0.311315 0.113309i
\(739\) 12.6809 21.9640i 0.466475 0.807959i −0.532791 0.846247i \(-0.678857\pi\)
0.999267 + 0.0382877i \(0.0121903\pi\)
\(740\) −7.63088 + 13.2171i −0.280517 + 0.485869i
\(741\) 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 \(0.0316023\pi\)
\(744\) −15.5223 + 42.6473i −0.569077 + 1.56353i
\(745\) −0.580785 −0.0212783
\(746\) −0.343426 + 0.594831i −0.0125737 + 0.0217783i
\(747\) 42.4261 15.4418i 1.55229 0.564987i
\(748\) 0.948615 0.0346848
\(749\) 0 0
\(750\) 16.5410 2.91663i 0.603992 0.106500i
\(751\) 24.2172 0.883698 0.441849 0.897090i \(-0.354323\pi\)
0.441849 + 0.897090i \(0.354323\pi\)
\(752\) −0.195937 0.339373i −0.00714508 0.0123756i
\(753\) −21.2260 25.2961i −0.773517 0.921842i
\(754\) 9.28740 16.0862i 0.338227 0.585827i
\(755\) 3.32863 0.121141
\(756\) 0 0
\(757\) 9.11793 0.331397 0.165698 0.986176i \(-0.447012\pi\)
0.165698 + 0.986176i \(0.447012\pi\)
\(758\) −3.04442 + 5.27308i −0.110578 + 0.191527i
\(759\) 16.4564 + 19.6119i 0.597328 + 0.711868i
\(760\) 6.16772 + 10.6828i 0.223727 + 0.387506i
\(761\) 18.2722 0.662366 0.331183 0.943566i \(-0.392552\pi\)
0.331183 + 0.943566i \(0.392552\pi\)
\(762\) −31.1573 + 5.49388i −1.12871 + 0.199022i
\(763\) 0 0
\(764\) −15.8357 −0.572917
\(765\) −1.44878 1.21567i −0.0523807 0.0439526i
\(766\) −3.39986 + 5.88874i −0.122842 + 0.212769i
\(767\) 35.0333 1.26498
\(768\) −9.53818 + 26.2059i −0.344179 + 0.945625i
\(769\) 9.26470 16.0469i 0.334094 0.578667i −0.649217 0.760604i \(-0.724903\pi\)
0.983310 + 0.181936i \(0.0582365\pi\)
\(770\) 0 0
\(771\) −29.5945 35.2694i −1.06582 1.27020i
\(772\) −0.391407 + 0.677937i −0.0140870 + 0.0243995i
\(773\) −1.48040 + 2.56413i −0.0532463 + 0.0922253i −0.891420 0.453178i \(-0.850290\pi\)
0.838174 + 0.545403i \(0.183624\pi\)
\(774\) −2.02094 + 11.4613i −0.0726414 + 0.411970i
\(775\) −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
\(779\) −11.0077 −0.394393
\(780\) 6.20011 + 7.38901i 0.222000 + 0.264569i</