Properties

Label 441.2.g.c.79.3
Level $441$
Weight $2$
Character 441.79
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 79.3
Root \(0.939693 - 0.342020i\) of defining polynomial
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.c.67.3

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

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 0.978560 0.205964i \(-0.0660330\pi\)
−0.667650 + 0.744475i \(0.732700\pi\)
\(3\) −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 \(-0.402591\pi\)
0.301265 + 0.953541i \(0.402591\pi\)
\(6\) −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 \(-0.0119016\pi\)
−0.532024 + 0.846729i \(0.678568\pi\)
\(14\) 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 \(-0.184738\pi\)
−0.893001 + 0.450054i \(0.851405\pi\)
\(18\) 2.02094 1.69577i 0.476341 0.399698i
\(19\) 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
\(23\) 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 0.413217 + 0.910632i \(0.364405\pi\)
−0.995239 + 0.0974595i \(0.968928\pi\)
\(30\) −2.02094 0.356347i −0.368972 0.0650598i
\(31\) −4.61721 + 7.99724i −0.829276 + 1.43635i 0.0693317 + 0.997594i \(0.477913\pi\)
−0.898607 + 0.438754i \(0.855420\pi\)
\(32\) 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 0.184263 + 0.982877i \(0.441010\pi\)
−0.943328 + 0.331862i \(0.892323\pi\)
\(38\) 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 \(-0.252498\pi\)
−0.967927 + 0.251231i \(0.919165\pi\)
\(42\) 0 0
\(43\) 2.20574 3.82045i 0.336372 0.582613i −0.647376 0.762171i \(-0.724133\pi\)
0.983747 + 0.179558i \(0.0574668\pi\)
\(44\) 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 −0.974281 0.225335i \(-0.927652\pi\)
0.291995 0.956420i \(-0.405681\pi\)
\(48\) −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 0.885063 0.465472i \(-0.154115\pi\)
−0.845642 + 0.533751i \(0.820782\pi\)
\(54\) 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 −0.299162 0.954202i \(-0.596707\pi\)
0.975945 0.218019i \(-0.0699595\pi\)
\(60\) 0.979055 + 2.68993i 0.126396 + 0.347269i
\(61\) −3.81908 6.61484i −0.488983 0.846943i 0.510937 0.859618i \(-0.329299\pi\)
−0.999920 + 0.0126752i \(0.995965\pi\)
\(62\) −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 −0.883662 0.468125i \(-0.844930\pi\)
0.847239 + 0.531211i \(0.178263\pi\)
\(68\) −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 \(-0.204939\pi\)
−0.919746 + 0.392514i \(0.871605\pi\)
\(74\) −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 0.925682 0.378303i \(-0.123492\pi\)
−0.790461 + 0.612512i \(0.790159\pi\)
\(80\) 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 −0.0752309 0.997166i \(-0.523969\pi\)
0.901187 0.433431i \(-0.142697\pi\)
\(84\) 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 \(-0.993271\pi\)
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
\(93\) −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 \(-0.802598\pi\)
0.910195 + 0.414181i \(0.135932\pi\)
\(98\) 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 \(-0.527100\pi\)
−0.0850329 + 0.996378i \(0.527100\pi\)
\(102\) 0.243756 + 0.669713i 0.0241354 + 0.0663115i
\(103\) −3.63816 −0.358478 −0.179239 0.983806i \(-0.557364\pi\)
−0.179239 + 0.983806i \(0.557364\pi\)
\(104\) 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 \(0.839488\pi\)
\(110\) 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 −0.976208 0.216835i \(-0.930427\pi\)
0.300320 0.953839i \(-0.402907\pi\)
\(114\) −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 \(-0.601338\pi\)
−0.313013 + 0.949749i \(0.601338\pi\)
\(132\) 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 \(-0.0829064\pi\)
−0.706158 + 0.708055i \(0.749573\pi\)
\(140\) 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 \(-0.965841\pi\)
0.589881 + 0.807491i \(0.299175\pi\)
\(158\) −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 −0.810698 0.585464i \(-0.800912\pi\)
0.912376 + 0.409353i \(0.134246\pi\)
\(164\) −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 0.831337 + 0.555769i \(0.187576\pi\)
0.0656422 + 0.997843i \(0.479090\pi\)
\(168\) 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 \(-0.108849\pi\)
−0.761457 + 0.648215i \(0.775516\pi\)
\(174\) 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 0.980250 0.197761i \(-0.0633670\pi\)
−0.661391 + 0.750041i \(0.730034\pi\)
\(180\) −4.65910 1.69577i −0.347269 0.126396i
\(181\) −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
\(184\) 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 0.532245 0.846590i \(-0.321349\pi\)
−0.999291 + 0.0376425i \(0.988015\pi\)
\(192\) −5.61334 + 6.68972i −0.405108 + 0.482789i
\(193\) 0.319078 0.552659i 0.0229677 0.0397813i −0.854313 0.519759i \(-0.826022\pi\)
0.877281 + 0.479977i \(0.159355\pi\)
\(194\) 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 \(-0.125506\pi\)
−0.794319 + 0.607500i \(0.792172\pi\)
\(200\) −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 0.748234 0.663435i \(-0.230902\pi\)
−0.948668 + 0.316273i \(0.897569\pi\)
\(212\) 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 \(-0.909557\pi\)
0.722722 + 0.691139i \(0.242891\pi\)
\(224\) 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 \(-0.629727\pi\)
−0.396361 + 0.918095i \(0.629727\pi\)
\(228\) 6.75150 + 1.19047i 0.447129 + 0.0788409i
\(229\) −17.5526 −1.15991 −0.579955 0.814649i \(-0.696930\pi\)
−0.579955 + 0.814649i \(0.696930\pi\)
\(230\) 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 \(0.987950\pi\)
\(234\) 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 0.999910 0.0134062i \(-0.00426745\pi\)
−0.511565 + 0.859244i \(0.670934\pi\)
\(240\) −0.0962667 0.0169744i −0.00621399 0.00109569i
\(241\) −15.6382 −1.00734 −0.503671 0.863896i \(-0.668018\pi\)
−0.503671 + 0.863896i \(0.668018\pi\)
\(242\) −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 \(-0.294494\pi\)
0.601690 + 0.798730i \(0.294494\pi\)
\(252\) 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 \(-0.188876\pi\)
0.829061 + 0.559158i \(0.188876\pi\)
\(258\) −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 0.986381 + 0.164478i \(0.0525939\pi\)
−0.350749 + 0.936470i \(0.614073\pi\)
\(270\) 6.15636i 0.374664i
\(271\) −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
\(275\) −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 0.313694 + 0.949524i \(0.398433\pi\)
−0.979159 + 0.203095i \(0.934900\pi\)
\(282\) 4.87346 + 13.3897i 0.290210 + 0.797346i
\(283\) 9.29726 16.1033i 0.552665 0.957243i −0.445417 0.895323i \(-0.646944\pi\)
0.998081 0.0619196i \(-0.0197222\pi\)
\(284\) −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 \(-0.291572\pi\)
−0.991406 + 0.130822i \(0.958238\pi\)
\(294\) 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 \(-0.442365\pi\)
0.180078 + 0.983652i \(0.442365\pi\)
\(308\) 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 \(-0.746297\pi\)
0.968871 + 0.247565i \(0.0796304\pi\)
\(312\) −16.3089 2.87569i −0.923308 0.162804i
\(313\) 8.81433 + 15.2669i 0.498215 + 0.862934i 0.999998 0.00205946i \(-0.000655547\pi\)
−0.501782 + 0.864994i \(0.667322\pi\)
\(314\) −8.91117 −0.502886
\(315\) 0 0
\(316\) 2.94862 0.165873
\(317\) −4.03849 6.99486i −0.226824 0.392871i 0.730041 0.683403i \(-0.239501\pi\)
−0.956865 + 0.290533i \(0.906168\pi\)
\(318\) −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 −0.986839 0.161706i \(-0.948300\pi\)
0.353378 0.935481i \(-0.385033\pi\)
\(332\) −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 −0.925659 0.378359i \(-0.876489\pi\)
0.135161 0.990824i \(-0.456845\pi\)
\(338\) 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 −0.985804 0.167901i \(-0.946301\pi\)
0.638308 + 0.769781i \(0.279635\pi\)
\(348\) −13.1163 2.31276i −0.703109 0.123977i
\(349\) −0.731429 + 1.26687i −0.0391525 + 0.0678141i −0.884938 0.465710i \(-0.845799\pi\)
0.845785 + 0.533524i \(0.179132\pi\)
\(350\) 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 \(-0.375433\pi\)
0.381428 + 0.924399i \(0.375433\pi\)
\(354\) −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 −0.445593 0.895235i \(-0.647007\pi\)
0.998093 0.0617224i \(-0.0196594\pi\)
\(360\) −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 \(-0.601902\pi\)
−0.314695 + 0.949193i \(0.601902\pi\)
\(368\) 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 \(-0.436701\pi\)
0.197553 + 0.980292i \(0.436701\pi\)
\(384\) 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 −0.221711 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
\(401\) −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 \(-0.761706\pi\)
0.955756 + 0.294160i \(0.0950398\pi\)
\(410\) 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 \(-0.168030\pi\)
−0.868158 + 0.496287i \(0.834696\pi\)
\(420\) 0 0
\(421\) 12.3525 21.3952i 0.602025 1.04274i −0.390490 0.920607i \(-0.627694\pi\)
0.992514 0.122130i \(-0.0389724\pi\)
\(422\) 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 0.966283 + 0.257481i \(0.0828924\pi\)
−0.260157 + 0.965566i \(0.583774\pi\)
\(432\) 0.217662i 0.0104723i
\(433\) 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
\(436\) −0.495252 −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 0.999631 + 0.0271516i \(0.00864370\pi\)
−0.476302 + 0.879282i \(0.658023\pi\)
\(440\) 6.31820 0.301208
\(441\) 0 0
\(442\) 1.38650 0.0659489
\(443\) 9.35504 + 16.2034i 0.444471 + 0.769847i 0.998015 0.0629732i \(-0.0200583\pi\)
−0.553544 + 0.832820i \(0.686725\pi\)
\(444\) −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 0.998655 0.0518563i \(-0.0165138\pi\)
−0.544236 + 0.838932i \(0.683180\pi\)
\(458\) −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 \(-0.826173\pi\)
0.877052 + 0.480395i \(0.159507\pi\)
\(462\) 0 0
\(463\) 0.222811 + 0.385920i 0.0103549 + 0.0179352i 0.871156 0.491006i \(-0.163371\pi\)
−0.860802 + 0.508941i \(0.830037\pi\)
\(464\) −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 −0.133317 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
\(471\) −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 \(-0.665885\pi\)
−0.497872 + 0.867251i \(0.665885\pi\)
\(480\) 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 0.558256 0.829669i \(-0.311471\pi\)
−0.997642 + 0.0686297i \(0.978137\pi\)
\(488\) −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 −0.994203 0.107519i \(-0.965709\pi\)
0.403987 0.914765i \(-0.367624\pi\)
\(492\) 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 \(-0.363092\pi\)
0.416969 + 0.908921i \(0.363092\pi\)
\(504\) 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 \(-0.692109\pi\)
−0.567551 + 0.823338i \(0.692109\pi\)
\(510\) 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 \(-0.0128431\pi\)
−0.534526 + 0.845152i \(0.679510\pi\)
\(522\) 2.87170 + 16.2862i 0.125691 + 0.712829i
\(523\) −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
\(527\) 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 0.421486 + 0.906835i \(0.361509\pi\)
−0.996085 + 0.0884001i \(0.971825\pi\)
\(542\) −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 0.142523 + 0.989792i \(0.454479\pi\)
−0.928446 + 0.371467i \(0.878855\pi\)
\(548\) 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 −0.973400 0.229114i \(-0.926417\pi\)
0.288282 0.957546i \(-0.406916\pi\)
\(558\) 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 \(-0.711366\pi\)
0.990156 + 0.139965i \(0.0446990\pi\)
\(564\) 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 0.997697 + 0.0678320i \(0.0216082\pi\)
−0.440104 + 0.897947i \(0.645058\pi\)
\(570\) −4.25624 + 5.07239i −0.178274 + 0.212459i
\(571\) 5.00862 8.67518i 0.209604 0.363045i −0.741986 0.670416i \(-0.766116\pi\)
0.951590 + 0.307371i \(0.0994491\pi\)
\(572\) 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 0.973398 + 0.229121i \(0.0735852\pi\)
−0.288274 + 0.957548i \(0.593082\pi\)
\(578\) 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 \(-0.732649\pi\)
0.978592 + 0.205808i \(0.0659821\pi\)
\(588\) 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 0.0464729 + 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
\(597\) −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 −0.921374 0.388678i \(-0.872932\pi\)
0.797292 + 0.603594i \(0.206265\pi\)
\(600\) 10.0611 11.9903i 0.410742 0.489503i
\(601\) 7.06758 12.2414i 0.288293 0.499338i −0.685110 0.728440i \(-0.740246\pi\)
0.973402 + 0.229102i \(0.0735791\pi\)
\(602\) 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 \(-0.115073\pi\)
0.935363 + 0.353689i \(0.115073\pi\)
\(608\) −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 0.999162 + 0.0409421i \(0.0130359\pi\)
−0.464124 + 0.885770i \(0.653631\pi\)
\(614\) 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 0.887781 0.460266i \(-0.152246\pi\)
−0.842492 + 0.538708i \(0.818913\pi\)
\(618\) 5.45723 + 0.962258i 0.219522 + 0.0387077i
\(619\) 6.19078 0.248828 0.124414 0.992230i \(-0.460295\pi\)
0.124414 + 0.992230i \(0.460295\pi\)
\(620\) 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 0.922218 + 0.386671i \(0.126375\pi\)
−0.126242 + 0.992000i \(0.540291\pi\)
\(644\) 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 \(-0.152391\pi\)
−0.842738 + 0.538324i \(0.819058\pi\)
\(648\) −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 0.158073 0.987427i \(-0.449472\pi\)
0.776101 0.630609i \(-0.217195\pi\)
\(660\) 1.61809 + 4.44566i 0.0629840 + 0.173047i
\(661\) −14.6545 + 25.3824i −0.569995 + 0.987260i 0.426571 + 0.904454i \(0.359721\pi\)
−0.996566 + 0.0828055i \(0.973612\pi\)
\(662\) 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 0.492719 + 0.870189i \(0.336003\pi\)
−0.999965 + 0.00838731i \(0.997330\pi\)
\(674\) 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 −0.971936 0.235246i \(-0.924411\pi\)
0.282239 0.959344i \(-0.408923\pi\)
\(678\) 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 −0.977664 0.210172i \(-0.932597\pi\)
0.306818 0.951768i \(-0.400736\pi\)
\(684\) −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 \(-0.179184\pi\)
−0.885013 + 0.465567i \(0.845850\pi\)
\(692\) 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 0.767742 0.640760i \(-0.221380\pi\)
−0.938785 + 0.344504i \(0.888047\pi\)
\(710\) −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 \(-0.672533\pi\)
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
\(723\) 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 \(-0.773000\pi\)
0.944720 + 0.327878i \(0.106333\pi\)
\(728\) 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 \(-0.229605\pi\)
0.750931 + 0.660381i \(0.229605\pi\)
\(734\) −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 0.999267 0.0382877i \(-0.0121903\pi\)
−0.532791 + 0.846247i \(0.678857\pi\)
\(740\) 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 0.995076 0.0991184i \(-0.0316023\pi\)
−0.583377 + 0.812202i \(0.698269\pi\)
\(744\) −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 \(-0.607448\pi\)
−0.331183 + 0.943566i \(0.607448\pi\)
\(762\) 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 \(-0.275097\pi\)
−0.983310 + 0.181936i \(0.941764\pi\)
\(770\) 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 \(-0.149710\pi\)
−0.838174 + 0.545403i \(0.816376\pi\)
\(774\) −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