Properties

Label 441.2.f.c.148.2
Level $441$
Weight $2$
Character 441.148
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.f (of order \(3\), degree \(2\), 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 148.2
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.c.295.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.673648 - 1.16679i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(0.0923963 - 0.160035i) q^{4} +(1.26604 - 2.19285i) q^{5} +(1.50000 + 1.78763i) q^{6} -2.94356 q^{8} +(2.81908 - 1.02606i) q^{9} +O(q^{10})\) \(q+(-0.673648 - 1.16679i) q^{2} +(-1.70574 + 0.300767i) q^{3} +(0.0923963 - 0.160035i) q^{4} +(1.26604 - 2.19285i) q^{5} +(1.50000 + 1.78763i) q^{6} -2.94356 q^{8} +(2.81908 - 1.02606i) q^{9} -3.41147 q^{10} +(-0.233956 - 0.405223i) q^{11} +(-0.109470 + 0.300767i) q^{12} +(2.91147 - 5.04282i) q^{13} +(-1.50000 + 4.12122i) q^{15} +(1.79813 + 3.11446i) q^{16} -3.87939 q^{17} +(-3.09627 - 2.59808i) q^{18} +2.18479 q^{19} +(-0.233956 - 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} +(0.0530334 - 0.0918566i) q^{23} +(5.02094 - 0.885328i) q^{24} +(-0.705737 - 1.22237i) q^{25} -7.84524 q^{26} +(-4.50000 + 2.59808i) q^{27} +(-4.39053 - 7.60462i) q^{29} +(5.81908 - 1.02606i) q^{30} +(-3.84002 + 6.65111i) q^{31} +(-0.520945 + 0.902302i) q^{32} +(0.520945 + 0.620838i) q^{33} +(2.61334 + 4.52644i) q^{34} +(0.0962667 - 0.545955i) q^{36} -7.68004 q^{37} +(-1.47178 - 2.54920i) q^{38} +(-3.44949 + 9.47740i) q^{39} +(-3.72668 + 6.45480i) q^{40} +(-1.11334 + 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} -0.0864665 q^{44} +(1.31908 - 7.48086i) q^{45} -0.142903 q^{46} +(-2.66637 - 4.61830i) q^{47} +(-4.00387 - 4.77163i) q^{48} +(-0.950837 + 1.64690i) q^{50} +(6.61721 - 1.16679i) q^{51} +(-0.538019 - 0.931876i) q^{52} -0.716881 q^{53} +(6.06283 + 3.50038i) q^{54} -1.18479 q^{55} +(-3.72668 + 0.657115i) q^{57} +(-5.91534 + 10.2457i) q^{58} +(0.368241 - 0.637812i) q^{59} +(0.520945 + 0.620838i) q^{60} +(0.479055 + 0.829748i) q^{61} +10.3473 q^{62} +8.59627 q^{64} +(-7.37211 - 12.7689i) q^{65} +(0.373455 - 1.02606i) q^{66} +(4.81908 - 8.34689i) q^{67} +(-0.358441 + 0.620838i) q^{68} +(-0.0628336 + 0.172634i) q^{69} +13.2344 q^{71} +(-8.29813 + 3.02027i) q^{72} +10.2686 q^{73} +(5.17365 + 8.96102i) q^{74} +(1.57145 + 1.87278i) q^{75} +(0.201867 - 0.349643i) q^{76} +(13.3819 - 2.35959i) q^{78} +(6.31908 + 10.9450i) q^{79} +9.10607 q^{80} +(6.89440 - 5.78509i) q^{81} +3.00000 q^{82} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +(-0.826352 + 1.43128i) q^{86} +(9.77631 + 11.6510i) q^{87} +(0.688663 + 1.19280i) q^{88} +8.11381 q^{89} +(-9.61721 + 3.50038i) q^{90} +(-0.00980018 - 0.0169744i) q^{92} +(4.54963 - 12.5000i) q^{93} +(-3.59240 + 6.22221i) q^{94} +(2.76604 - 4.79093i) q^{95} +(0.617211 - 1.69577i) q^{96} +(-6.80200 - 11.7814i) q^{97} +(-1.07532 - 0.902302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{4} + 3q^{5} + 9q^{6} + 12q^{8} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{4} + 3q^{5} + 9q^{6} + 12q^{8} - 6q^{11} - 18q^{12} - 3q^{13} - 9q^{15} - 3q^{16} - 12q^{17} + 9q^{18} + 6q^{19} - 6q^{20} - 9q^{22} - 12q^{23} + 27q^{24} + 6q^{25} + 6q^{26} - 27q^{27} - 9q^{29} + 18q^{30} - 3q^{31} + 9q^{34} - 27q^{36} - 6q^{37} + 6q^{38} - 18q^{39} - 9q^{40} + 3q^{43} + 30q^{44} - 9q^{45} + 3q^{47} + 6q^{50} + 9q^{51} - 21q^{52} + 12q^{53} + 27q^{54} - 9q^{57} + 9q^{58} - 3q^{59} + 6q^{61} + 60q^{62} + 24q^{64} - 15q^{65} - 36q^{66} + 12q^{67} + 6q^{68} + 9q^{69} + 18q^{71} - 36q^{72} + 42q^{73} + 30q^{74} + 9q^{75} + 15q^{76} + 54q^{78} + 21q^{79} + 30q^{80} + 18q^{82} - 18q^{83} - 9q^{85} - 6q^{86} - 9q^{87} - 27q^{88} - 24q^{89} - 27q^{90} - 3q^{92} - 27q^{93} - 18q^{94} + 12q^{95} - 27q^{96} - 3q^{97} + 18q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.673648 1.16679i −0.476341 0.825047i 0.523291 0.852154i \(-0.324704\pi\)
−0.999633 + 0.0271067i \(0.991371\pi\)
\(3\) −1.70574 + 0.300767i −0.984808 + 0.173648i
\(4\) 0.0923963 0.160035i 0.0461981 0.0800175i
\(5\) 1.26604 2.19285i 0.566192 0.980674i −0.430745 0.902473i \(-0.641749\pi\)
0.996938 0.0782003i \(-0.0249174\pi\)
\(6\) 1.50000 + 1.78763i 0.612372 + 0.729797i
\(7\) 0 0
\(8\) −2.94356 −1.04071
\(9\) 2.81908 1.02606i 0.939693 0.342020i
\(10\) −3.41147 −1.07880
\(11\) −0.233956 0.405223i −0.0705403 0.122179i 0.828598 0.559844i \(-0.189139\pi\)
−0.899138 + 0.437665i \(0.855806\pi\)
\(12\) −0.109470 + 0.300767i −0.0316014 + 0.0868241i
\(13\) 2.91147 5.04282i 0.807498 1.39863i −0.107094 0.994249i \(-0.534155\pi\)
0.914592 0.404378i \(-0.132512\pi\)
\(14\) 0 0
\(15\) −1.50000 + 4.12122i −0.387298 + 1.06409i
\(16\) 1.79813 + 3.11446i 0.449533 + 0.778615i
\(17\) −3.87939 −0.940889 −0.470445 0.882430i \(-0.655906\pi\)
−0.470445 + 0.882430i \(0.655906\pi\)
\(18\) −3.09627 2.59808i −0.729797 0.612372i
\(19\) 2.18479 0.501226 0.250613 0.968087i \(-0.419368\pi\)
0.250613 + 0.968087i \(0.419368\pi\)
\(20\) −0.233956 0.405223i −0.0523141 0.0906106i
\(21\) 0 0
\(22\) −0.315207 + 0.545955i −0.0672025 + 0.116398i
\(23\) 0.0530334 0.0918566i 0.0110582 0.0191534i −0.860443 0.509546i \(-0.829813\pi\)
0.871502 + 0.490393i \(0.163147\pi\)
\(24\) 5.02094 0.885328i 1.02490 0.180717i
\(25\) −0.705737 1.22237i −0.141147 0.244474i
\(26\) −7.84524 −1.53858
\(27\) −4.50000 + 2.59808i −0.866025 + 0.500000i
\(28\) 0 0
\(29\) −4.39053 7.60462i −0.815301 1.41214i −0.909112 0.416552i \(-0.863238\pi\)
0.0938108 0.995590i \(-0.470095\pi\)
\(30\) 5.81908 1.02606i 1.06241 0.187332i
\(31\) −3.84002 + 6.65111i −0.689688 + 1.19458i 0.282250 + 0.959341i \(0.408919\pi\)
−0.971939 + 0.235235i \(0.924414\pi\)
\(32\) −0.520945 + 0.902302i −0.0920909 + 0.159506i
\(33\) 0.520945 + 0.620838i 0.0906848 + 0.108074i
\(34\) 2.61334 + 4.52644i 0.448184 + 0.776278i
\(35\) 0 0
\(36\) 0.0962667 0.545955i 0.0160444 0.0909926i
\(37\) −7.68004 −1.26259 −0.631296 0.775542i \(-0.717477\pi\)
−0.631296 + 0.775542i \(0.717477\pi\)
\(38\) −1.47178 2.54920i −0.238754 0.413535i
\(39\) −3.44949 + 9.47740i −0.552361 + 1.51760i
\(40\) −3.72668 + 6.45480i −0.589240 + 1.02059i
\(41\) −1.11334 + 1.92836i −0.173875 + 0.301160i −0.939771 0.341804i \(-0.888962\pi\)
0.765897 + 0.642964i \(0.222295\pi\)
\(42\) 0 0
\(43\) −0.613341 1.06234i −0.0935336 0.162005i 0.815462 0.578811i \(-0.196483\pi\)
−0.908996 + 0.416806i \(0.863150\pi\)
\(44\) −0.0864665 −0.0130353
\(45\) 1.31908 7.48086i 0.196637 1.11518i
\(46\) −0.142903 −0.0210700
\(47\) −2.66637 4.61830i −0.388931 0.673648i 0.603375 0.797457i \(-0.293822\pi\)
−0.992306 + 0.123810i \(0.960489\pi\)
\(48\) −4.00387 4.77163i −0.577909 0.688725i
\(49\) 0 0
\(50\) −0.950837 + 1.64690i −0.134469 + 0.232907i
\(51\) 6.61721 1.16679i 0.926595 0.163384i
\(52\) −0.538019 0.931876i −0.0746098 0.129228i
\(53\) −0.716881 −0.0984712 −0.0492356 0.998787i \(-0.515679\pi\)
−0.0492356 + 0.998787i \(0.515679\pi\)
\(54\) 6.06283 + 3.50038i 0.825047 + 0.476341i
\(55\) −1.18479 −0.159757
\(56\) 0 0
\(57\) −3.72668 + 0.657115i −0.493611 + 0.0870369i
\(58\) −5.91534 + 10.2457i −0.776723 + 1.34532i
\(59\) 0.368241 0.637812i 0.0479409 0.0830360i −0.841059 0.540943i \(-0.818067\pi\)
0.889000 + 0.457907i \(0.151401\pi\)
\(60\) 0.520945 + 0.620838i 0.0672537 + 0.0801498i
\(61\) 0.479055 + 0.829748i 0.0613368 + 0.106238i 0.895063 0.445939i \(-0.147130\pi\)
−0.833726 + 0.552178i \(0.813797\pi\)
\(62\) 10.3473 1.31411
\(63\) 0 0
\(64\) 8.59627 1.07453
\(65\) −7.37211 12.7689i −0.914398 1.58378i
\(66\) 0.373455 1.02606i 0.0459692 0.126299i
\(67\) 4.81908 8.34689i 0.588744 1.01973i −0.405653 0.914027i \(-0.632956\pi\)
0.994397 0.105708i \(-0.0337107\pi\)
\(68\) −0.358441 + 0.620838i −0.0434673 + 0.0752876i
\(69\) −0.0628336 + 0.172634i −0.00756428 + 0.0207827i
\(70\) 0 0
\(71\) 13.2344 1.57064 0.785318 0.619092i \(-0.212499\pi\)
0.785318 + 0.619092i \(0.212499\pi\)
\(72\) −8.29813 + 3.02027i −0.977944 + 0.355943i
\(73\) 10.2686 1.20185 0.600923 0.799307i \(-0.294800\pi\)
0.600923 + 0.799307i \(0.294800\pi\)
\(74\) 5.17365 + 8.96102i 0.601424 + 1.04170i
\(75\) 1.57145 + 1.87278i 0.181456 + 0.216250i
\(76\) 0.201867 0.349643i 0.0231557 0.0401068i
\(77\) 0 0
\(78\) 13.3819 2.35959i 1.51520 0.267171i
\(79\) 6.31908 + 10.9450i 0.710952 + 1.23140i 0.964500 + 0.264082i \(0.0850689\pi\)
−0.253548 + 0.967323i \(0.581598\pi\)
\(80\) 9.10607 1.01809
\(81\) 6.89440 5.78509i 0.766044 0.642788i
\(82\) 3.00000 0.331295
\(83\) −1.36571 2.36549i −0.149907 0.259646i 0.781286 0.624173i \(-0.214564\pi\)
−0.931193 + 0.364527i \(0.881231\pi\)
\(84\) 0 0
\(85\) −4.91147 + 8.50692i −0.532724 + 0.922705i
\(86\) −0.826352 + 1.43128i −0.0891078 + 0.154339i
\(87\) 9.77631 + 11.6510i 1.04813 + 1.24911i
\(88\) 0.688663 + 1.19280i 0.0734117 + 0.127153i
\(89\) 8.11381 0.860062 0.430031 0.902814i \(-0.358503\pi\)
0.430031 + 0.902814i \(0.358503\pi\)
\(90\) −9.61721 + 3.50038i −1.01374 + 0.368972i
\(91\) 0 0
\(92\) −0.00980018 0.0169744i −0.00102174 0.00176970i
\(93\) 4.54963 12.5000i 0.471775 1.29619i
\(94\) −3.59240 + 6.22221i −0.370527 + 0.641772i
\(95\) 2.76604 4.79093i 0.283790 0.491539i
\(96\) 0.617211 1.69577i 0.0629939 0.173074i
\(97\) −6.80200 11.7814i −0.690639 1.19622i −0.971629 0.236511i \(-0.923996\pi\)
0.280990 0.959711i \(-0.409337\pi\)
\(98\) 0 0
\(99\) −1.07532 0.902302i −0.108074 0.0906848i
\(100\) −0.260830 −0.0260830
\(101\) −4.78699 8.29131i −0.476323 0.825016i 0.523309 0.852143i \(-0.324697\pi\)
−0.999632 + 0.0271271i \(0.991364\pi\)
\(102\) −5.81908 6.93491i −0.576175 0.686658i
\(103\) 1.52094 2.63435i 0.149863 0.259571i −0.781314 0.624139i \(-0.785450\pi\)
0.931177 + 0.364568i \(0.118783\pi\)
\(104\) −8.57011 + 14.8439i −0.840368 + 1.45556i
\(105\) 0 0
\(106\) 0.482926 + 0.836452i 0.0469059 + 0.0812434i
\(107\) −6.51754 −0.630074 −0.315037 0.949079i \(-0.602017\pi\)
−0.315037 + 0.949079i \(0.602017\pi\)
\(108\) 0.960210i 0.0923963i
\(109\) 10.6382 1.01895 0.509475 0.860485i \(-0.329840\pi\)
0.509475 + 0.860485i \(0.329840\pi\)
\(110\) 0.798133 + 1.38241i 0.0760990 + 0.131807i
\(111\) 13.1001 2.30991i 1.24341 0.219247i
\(112\) 0 0
\(113\) −2.58853 + 4.48346i −0.243508 + 0.421768i −0.961711 0.274065i \(-0.911632\pi\)
0.718203 + 0.695834i \(0.244965\pi\)
\(114\) 3.27719 + 3.90560i 0.306937 + 0.365793i
\(115\) −0.134285 0.232589i −0.0125222 0.0216890i
\(116\) −1.62267 −0.150662
\(117\) 3.03343 17.2035i 0.280441 1.59046i
\(118\) −0.992259 −0.0913449
\(119\) 0 0
\(120\) 4.41534 12.1311i 0.403064 1.10741i
\(121\) 5.39053 9.33667i 0.490048 0.848788i
\(122\) 0.645430 1.11792i 0.0584345 0.101211i
\(123\) 1.31908 3.62414i 0.118937 0.326777i
\(124\) 0.709607 + 1.22908i 0.0637246 + 0.110374i
\(125\) 9.08647 0.812718
\(126\) 0 0
\(127\) −8.88207 −0.788157 −0.394078 0.919077i \(-0.628936\pi\)
−0.394078 + 0.919077i \(0.628936\pi\)
\(128\) −4.74897 8.22546i −0.419754 0.727035i
\(129\) 1.36571 + 1.62760i 0.120244 + 0.143302i
\(130\) −9.93242 + 17.2035i −0.871131 + 1.50884i
\(131\) 5.68139 9.84045i 0.496385 0.859764i −0.503606 0.863933i \(-0.667994\pi\)
0.999991 + 0.00416893i \(0.00132701\pi\)
\(132\) 0.147489 0.0260063i 0.0128373 0.00226356i
\(133\) 0 0
\(134\) −12.9855 −1.12177
\(135\) 13.1571i 1.13238i
\(136\) 11.4192 0.979190
\(137\) 2.86231 + 4.95767i 0.244544 + 0.423562i 0.962003 0.273038i \(-0.0880285\pi\)
−0.717459 + 0.696600i \(0.754695\pi\)
\(138\) 0.243756 0.0429807i 0.0207499 0.00365876i
\(139\) −0.461981 + 0.800175i −0.0391847 + 0.0678700i −0.884953 0.465681i \(-0.845809\pi\)
0.845768 + 0.533551i \(0.179143\pi\)
\(140\) 0 0
\(141\) 5.93717 + 7.07564i 0.500000 + 0.595876i
\(142\) −8.91534 15.4418i −0.748159 1.29585i
\(143\) −2.72462 −0.227844
\(144\) 8.26470 + 6.93491i 0.688725 + 0.577909i
\(145\) −22.2344 −1.84647
\(146\) −6.91740 11.9813i −0.572488 0.991579i
\(147\) 0 0
\(148\) −0.709607 + 1.22908i −0.0583294 + 0.101029i
\(149\) −4.36231 + 7.55574i −0.357374 + 0.618991i −0.987521 0.157485i \(-0.949661\pi\)
0.630147 + 0.776476i \(0.282995\pi\)
\(150\) 1.12654 3.09516i 0.0919820 0.252718i
\(151\) −9.21348 15.9582i −0.749782 1.29866i −0.947927 0.318488i \(-0.896825\pi\)
0.198145 0.980173i \(-0.436508\pi\)
\(152\) −6.43107 −0.521629
\(153\) −10.9363 + 3.98048i −0.884147 + 0.321803i
\(154\) 0 0
\(155\) 9.72328 + 16.8412i 0.780992 + 1.35272i
\(156\) 1.19800 + 1.42772i 0.0959165 + 0.114309i
\(157\) 2.46198 4.26428i 0.196488 0.340326i −0.750900 0.660416i \(-0.770380\pi\)
0.947387 + 0.320090i \(0.103713\pi\)
\(158\) 8.51367 14.7461i 0.677311 1.17314i
\(159\) 1.22281 0.215615i 0.0969752 0.0170994i
\(160\) 1.31908 + 2.28471i 0.104282 + 0.180622i
\(161\) 0 0
\(162\) −11.3944 4.14722i −0.895229 0.325837i
\(163\) 7.63816 0.598267 0.299133 0.954211i \(-0.403302\pi\)
0.299133 + 0.954211i \(0.403302\pi\)
\(164\) 0.205737 + 0.356347i 0.0160654 + 0.0278260i
\(165\) 2.02094 0.356347i 0.157330 0.0277416i
\(166\) −1.84002 + 3.18701i −0.142813 + 0.247360i
\(167\) −2.82770 + 4.89771i −0.218814 + 0.378996i −0.954446 0.298385i \(-0.903552\pi\)
0.735632 + 0.677382i \(0.236885\pi\)
\(168\) 0 0
\(169\) −10.4534 18.1058i −0.804105 1.39275i
\(170\) 13.2344 1.01503
\(171\) 6.15910 2.24173i 0.470998 0.171429i
\(172\) −0.226682 −0.0172843
\(173\) 10.5346 + 18.2465i 0.800932 + 1.38725i 0.919003 + 0.394250i \(0.128995\pi\)
−0.118071 + 0.993005i \(0.537671\pi\)
\(174\) 7.00846 19.2556i 0.531310 1.45976i
\(175\) 0 0
\(176\) 0.841367 1.45729i 0.0634204 0.109847i
\(177\) −0.436289 + 1.19869i −0.0327935 + 0.0900994i
\(178\) −5.46585 9.46713i −0.409683 0.709592i
\(179\) −5.12061 −0.382733 −0.191366 0.981519i \(-0.561292\pi\)
−0.191366 + 0.981519i \(0.561292\pi\)
\(180\) −1.07532 0.902302i −0.0801498 0.0672537i
\(181\) 0.319955 0.0237821 0.0118910 0.999929i \(-0.496215\pi\)
0.0118910 + 0.999929i \(0.496215\pi\)
\(182\) 0 0
\(183\) −1.06670 1.27125i −0.0788530 0.0939734i
\(184\) −0.156107 + 0.270386i −0.0115084 + 0.0199331i
\(185\) −9.72328 + 16.8412i −0.714870 + 1.23819i
\(186\) −17.6498 + 3.11213i −1.29414 + 0.228192i
\(187\) 0.907604 + 1.57202i 0.0663706 + 0.114957i
\(188\) −0.985452 −0.0718715
\(189\) 0 0
\(190\) −7.45336 −0.540724
\(191\) 7.78359 + 13.4816i 0.563200 + 0.975492i 0.997215 + 0.0745858i \(0.0237635\pi\)
−0.434014 + 0.900906i \(0.642903\pi\)
\(192\) −14.6630 + 2.58548i −1.05821 + 0.186591i
\(193\) −3.02094 + 5.23243i −0.217452 + 0.376639i −0.954028 0.299716i \(-0.903108\pi\)
0.736576 + 0.676355i \(0.236441\pi\)
\(194\) −9.16431 + 15.8731i −0.657959 + 1.13962i
\(195\) 16.4153 + 19.5630i 1.17553 + 1.40094i
\(196\) 0 0
\(197\) 25.2344 1.79788 0.898939 0.438074i \(-0.144339\pi\)
0.898939 + 0.438074i \(0.144339\pi\)
\(198\) −0.328411 + 1.86251i −0.0233392 + 0.132363i
\(199\) −3.04189 −0.215634 −0.107817 0.994171i \(-0.534386\pi\)
−0.107817 + 0.994171i \(0.534386\pi\)
\(200\) 2.07738 + 3.59813i 0.146893 + 0.254426i
\(201\) −5.70961 + 15.6870i −0.402725 + 1.10648i
\(202\) −6.44949 + 11.1708i −0.453785 + 0.785978i
\(203\) 0 0
\(204\) 0.424678 1.16679i 0.0297334 0.0816918i
\(205\) 2.81908 + 4.88279i 0.196893 + 0.341029i
\(206\) −4.09833 −0.285544
\(207\) 0.0552549 0.313366i 0.00384048 0.0217805i
\(208\) 20.9409 1.45199
\(209\) −0.511144 0.885328i −0.0353566 0.0612394i
\(210\) 0 0
\(211\) 2.72668 4.72275i 0.187713 0.325128i −0.756775 0.653676i \(-0.773226\pi\)
0.944487 + 0.328548i \(0.106559\pi\)
\(212\) −0.0662372 + 0.114726i −0.00454919 + 0.00787942i
\(213\) −22.5744 + 3.98048i −1.54678 + 0.272738i
\(214\) 4.39053 + 7.60462i 0.300130 + 0.519841i
\(215\) −3.10607 −0.211832
\(216\) 13.2460 7.64760i 0.901278 0.520353i
\(217\) 0 0
\(218\) −7.16637 12.4125i −0.485368 0.840682i
\(219\) −17.5155 + 3.08845i −1.18359 + 0.208698i
\(220\) −0.109470 + 0.189608i −0.00738049 + 0.0127834i
\(221\) −11.2947 + 19.5630i −0.759766 + 1.31595i
\(222\) −11.5201 13.7291i −0.773176 0.921436i
\(223\) 7.09627 + 12.2911i 0.475201 + 0.823073i 0.999597 0.0284023i \(-0.00904195\pi\)
−0.524395 + 0.851475i \(0.675709\pi\)
\(224\) 0 0
\(225\) −3.24376 2.72183i −0.216250 0.181456i
\(226\) 6.97502 0.463972
\(227\) −1.44697 2.50622i −0.0960385 0.166344i 0.814003 0.580861i \(-0.197284\pi\)
−0.910042 + 0.414517i \(0.863951\pi\)
\(228\) −0.239170 + 0.657115i −0.0158394 + 0.0435185i
\(229\) 4.58378 7.93934i 0.302905 0.524646i −0.673888 0.738834i \(-0.735377\pi\)
0.976793 + 0.214187i \(0.0687103\pi\)
\(230\) −0.180922 + 0.313366i −0.0119297 + 0.0206628i
\(231\) 0 0
\(232\) 12.9238 + 22.3847i 0.848489 + 1.46963i
\(233\) 13.2713 0.869429 0.434715 0.900568i \(-0.356849\pi\)
0.434715 + 0.900568i \(0.356849\pi\)
\(234\) −22.1163 + 8.04969i −1.44579 + 0.526225i
\(235\) −13.5030 −0.880838
\(236\) −0.0680482 0.117863i −0.00442956 0.00767222i
\(237\) −14.0706 16.7687i −0.913982 1.08924i
\(238\) 0 0
\(239\) −4.76857 + 8.25941i −0.308453 + 0.534257i −0.978024 0.208491i \(-0.933145\pi\)
0.669571 + 0.742748i \(0.266478\pi\)
\(240\) −15.5326 + 2.73881i −1.00262 + 0.176789i
\(241\) −4.47906 7.75795i −0.288521 0.499734i 0.684936 0.728604i \(-0.259830\pi\)
−0.973457 + 0.228870i \(0.926497\pi\)
\(242\) −14.5253 −0.933720
\(243\) −10.0201 + 11.9415i −0.642788 + 0.766044i
\(244\) 0.177052 0.0113346
\(245\) 0 0
\(246\) −5.11721 + 0.902302i −0.326261 + 0.0575287i
\(247\) 6.36097 11.0175i 0.404739 0.701028i
\(248\) 11.3033 19.5780i 0.717763 1.24320i
\(249\) 3.04101 + 3.62414i 0.192716 + 0.229670i
\(250\) −6.12108 10.6020i −0.387131 0.670531i
\(251\) 24.9982 1.57788 0.788938 0.614473i \(-0.210631\pi\)
0.788938 + 0.614473i \(0.210631\pi\)
\(252\) 0 0
\(253\) −0.0496299 −0.00312020
\(254\) 5.98339 + 10.3635i 0.375431 + 0.650266i
\(255\) 5.81908 15.9878i 0.364405 1.00119i
\(256\) 2.19800 3.80704i 0.137375 0.237940i
\(257\) 5.42602 9.39815i 0.338466 0.586240i −0.645678 0.763609i \(-0.723425\pi\)
0.984144 + 0.177369i \(0.0567587\pi\)
\(258\) 0.979055 2.68993i 0.0609533 0.167468i
\(259\) 0 0
\(260\) −2.72462 −0.168974
\(261\) −20.1800 16.9331i −1.24911 1.04813i
\(262\) −15.3090 −0.945795
\(263\) −13.0437 22.5924i −0.804309 1.39310i −0.916757 0.399446i \(-0.869202\pi\)
0.112448 0.993658i \(-0.464131\pi\)
\(264\) −1.53343 1.82747i −0.0943763 0.112473i
\(265\) −0.907604 + 1.57202i −0.0557537 + 0.0965682i
\(266\) 0 0
\(267\) −13.8400 + 2.44037i −0.846996 + 0.149348i
\(268\) −0.890530 1.54244i −0.0543978 0.0942197i
\(269\) 7.63310 0.465399 0.232699 0.972549i \(-0.425244\pi\)
0.232699 + 0.972549i \(0.425244\pi\)
\(270\) 15.3516 8.86327i 0.934271 0.539401i
\(271\) −3.40373 −0.206762 −0.103381 0.994642i \(-0.532966\pi\)
−0.103381 + 0.994642i \(0.532966\pi\)
\(272\) −6.97565 12.0822i −0.422961 0.732590i
\(273\) 0 0
\(274\) 3.85638 6.67945i 0.232973 0.403520i
\(275\) −0.330222 + 0.571962i −0.0199131 + 0.0344906i
\(276\) 0.0218219 + 0.0260063i 0.00131352 + 0.00156540i
\(277\) 2.86097 + 4.95534i 0.171899 + 0.297738i 0.939084 0.343689i \(-0.111676\pi\)
−0.767185 + 0.641426i \(0.778343\pi\)
\(278\) 1.24485 0.0746612
\(279\) −4.00088 + 22.6901i −0.239526 + 1.35842i
\(280\) 0 0
\(281\) −14.1887 24.5755i −0.846425 1.46605i −0.884378 0.466771i \(-0.845417\pi\)
0.0379535 0.999280i \(-0.487916\pi\)
\(282\) 4.25624 11.6939i 0.253456 0.696364i
\(283\) 2.28564 3.95885i 0.135867 0.235329i −0.790061 0.613028i \(-0.789951\pi\)
0.925929 + 0.377699i \(0.123285\pi\)
\(284\) 1.22281 2.11797i 0.0725605 0.125678i
\(285\) −3.27719 + 9.00400i −0.194124 + 0.533351i
\(286\) 1.83544 + 3.17907i 0.108532 + 0.187982i
\(287\) 0 0
\(288\) −0.542766 + 3.07818i −0.0319828 + 0.181384i
\(289\) −1.95037 −0.114728
\(290\) 14.9782 + 25.9430i 0.879549 + 1.52342i
\(291\) 15.1459 + 18.0502i 0.887868 + 1.05812i
\(292\) 0.948778 1.64333i 0.0555230 0.0961687i
\(293\) 2.16385 3.74789i 0.126413 0.218954i −0.795871 0.605466i \(-0.792987\pi\)
0.922285 + 0.386512i \(0.126320\pi\)
\(294\) 0 0
\(295\) −0.932419 1.61500i −0.0542875 0.0940287i
\(296\) 22.6067 1.31399
\(297\) 2.10560 + 1.21567i 0.122179 + 0.0705403i
\(298\) 11.7547 0.680929
\(299\) −0.308811 0.534876i −0.0178590 0.0309327i
\(300\) 0.444907 0.0784491i 0.0256867 0.00452926i
\(301\) 0 0
\(302\) −12.4133 + 21.5004i −0.714304 + 1.23721i
\(303\) 10.6591 + 12.7030i 0.612349 + 0.729769i
\(304\) 3.92855 + 6.80445i 0.225318 + 0.390262i
\(305\) 2.42602 0.138914
\(306\) 12.0116 + 10.0789i 0.686658 + 0.576175i
\(307\) −12.3773 −0.706411 −0.353206 0.935546i \(-0.614908\pi\)
−0.353206 + 0.935546i \(0.614908\pi\)
\(308\) 0 0
\(309\) −1.80200 + 4.95096i −0.102512 + 0.281651i
\(310\) 13.1001 22.6901i 0.744038 1.28871i
\(311\) −10.9927 + 19.0400i −0.623340 + 1.07966i 0.365519 + 0.930804i \(0.380892\pi\)
−0.988859 + 0.148853i \(0.952442\pi\)
\(312\) 10.1538 27.8973i 0.574846 1.57938i
\(313\) −6.94491 12.0289i −0.392549 0.679915i 0.600236 0.799823i \(-0.295073\pi\)
−0.992785 + 0.119908i \(0.961740\pi\)
\(314\) −6.63404 −0.374380
\(315\) 0 0
\(316\) 2.33544 0.131379
\(317\) 3.09105 + 5.35386i 0.173611 + 0.300703i 0.939680 0.342056i \(-0.111123\pi\)
−0.766069 + 0.642759i \(0.777790\pi\)
\(318\) −1.07532 1.28152i −0.0603011 0.0718640i
\(319\) −2.05438 + 3.55829i −0.115023 + 0.199226i
\(320\) 10.8833 18.8504i 0.608392 1.05377i
\(321\) 11.1172 1.96026i 0.620502 0.109411i
\(322\) 0 0
\(323\) −8.47565 −0.471598
\(324\) −0.288800 1.63787i −0.0160444 0.0909926i
\(325\) −8.21894 −0.455905
\(326\) −5.14543 8.91215i −0.284979 0.493598i
\(327\) −18.1459 + 3.19961i −1.00347 + 0.176939i
\(328\) 3.27719 5.67626i 0.180952 0.313419i
\(329\) 0 0
\(330\) −1.77719 2.11797i −0.0978310 0.116590i
\(331\) −5.36571 9.29369i −0.294926 0.510827i 0.680041 0.733174i \(-0.261962\pi\)
−0.974968 + 0.222346i \(0.928628\pi\)
\(332\) −0.504748 −0.0277016
\(333\) −21.6506 + 7.88019i −1.18645 + 0.431832i
\(334\) 7.61949 0.416920
\(335\) −12.2023 21.1351i −0.666685 1.15473i
\(336\) 0 0
\(337\) 9.29726 16.1033i 0.506454 0.877204i −0.493518 0.869735i \(-0.664289\pi\)
0.999972 0.00746831i \(-0.00237726\pi\)
\(338\) −14.0838 + 24.3938i −0.766057 + 1.32685i
\(339\) 3.06687 8.42615i 0.166569 0.457645i
\(340\) 0.907604 + 1.57202i 0.0492217 + 0.0852545i
\(341\) 3.59358 0.194603
\(342\) −6.76470 5.67626i −0.365793 0.306937i
\(343\) 0 0
\(344\) 1.80541 + 3.12706i 0.0973410 + 0.168600i
\(345\) 0.299011 + 0.356347i 0.0160982 + 0.0191851i
\(346\) 14.1932 24.5834i 0.763034 1.32161i
\(347\) 10.2062 17.6777i 0.547898 0.948987i −0.450521 0.892766i \(-0.648762\pi\)
0.998418 0.0562207i \(-0.0179050\pi\)
\(348\) 2.76786 0.488048i 0.148373 0.0261621i
\(349\) −1.78106 3.08489i −0.0953379 0.165130i 0.814412 0.580288i \(-0.197060\pi\)
−0.909750 + 0.415157i \(0.863726\pi\)
\(350\) 0 0
\(351\) 30.2569i 1.61500i
\(352\) 0.487511 0.0259844
\(353\) 5.01114 + 8.67956i 0.266716 + 0.461966i 0.968012 0.250904i \(-0.0807280\pi\)
−0.701296 + 0.712871i \(0.747395\pi\)
\(354\) 1.69253 0.298439i 0.0899571 0.0158619i
\(355\) 16.7554 29.0211i 0.889283 1.54028i
\(356\) 0.749686 1.29849i 0.0397333 0.0688200i
\(357\) 0 0
\(358\) 3.44949 + 5.97470i 0.182311 + 0.315773i
\(359\) 9.48070 0.500372 0.250186 0.968198i \(-0.419508\pi\)
0.250186 + 0.968198i \(0.419508\pi\)
\(360\) −3.88279 + 22.0204i −0.204641 + 1.16058i
\(361\) −14.2267 −0.748773
\(362\) −0.215537 0.373321i −0.0113284 0.0196213i
\(363\) −6.38666 + 17.5472i −0.335213 + 0.920989i
\(364\) 0 0
\(365\) 13.0005 22.5175i 0.680476 1.17862i
\(366\) −0.764700 + 2.10100i −0.0399715 + 0.109821i
\(367\) 8.06670 + 13.9719i 0.421079 + 0.729329i 0.996045 0.0888474i \(-0.0283183\pi\)
−0.574967 + 0.818177i \(0.694985\pi\)
\(368\) 0.381445 0.0198842
\(369\) −1.15998 + 6.57856i −0.0603860 + 0.342466i
\(370\) 26.2003 1.36209
\(371\) 0 0
\(372\) −1.58007 1.88305i −0.0819228 0.0976318i
\(373\) −7.02481 + 12.1673i −0.363731 + 0.630001i −0.988572 0.150752i \(-0.951831\pi\)
0.624841 + 0.780752i \(0.285164\pi\)
\(374\) 1.22281 2.11797i 0.0632301 0.109518i
\(375\) −15.4991 + 2.73291i −0.800371 + 0.141127i
\(376\) 7.84864 + 13.5942i 0.404763 + 0.701070i
\(377\) −51.1317 −2.63341
\(378\) 0 0
\(379\) 16.0574 0.824812 0.412406 0.911000i \(-0.364689\pi\)
0.412406 + 0.911000i \(0.364689\pi\)
\(380\) −0.511144 0.885328i −0.0262212 0.0454164i
\(381\) 15.1505 2.67144i 0.776183 0.136862i
\(382\) 10.4868 18.1637i 0.536551 0.929334i
\(383\) −16.0103 + 27.7306i −0.818086 + 1.41697i 0.0890039 + 0.996031i \(0.471632\pi\)
−0.907090 + 0.420936i \(0.861702\pi\)
\(384\) 10.5744 + 12.6021i 0.539625 + 0.643100i
\(385\) 0 0
\(386\) 8.14022 0.414326
\(387\) −2.81908 2.36549i −0.143302 0.120244i
\(388\) −2.51392 −0.127625
\(389\) 15.0214 + 26.0178i 0.761616 + 1.31916i 0.942017 + 0.335564i \(0.108927\pi\)
−0.180402 + 0.983593i \(0.557740\pi\)
\(390\) 11.7679 32.3319i 0.595889 1.63719i
\(391\) −0.205737 + 0.356347i −0.0104046 + 0.0180212i
\(392\) 0 0
\(393\) −6.73127 + 18.4940i −0.339548 + 0.932899i
\(394\) −16.9991 29.4433i −0.856403 1.48333i
\(395\) 32.0009 1.61014
\(396\) −0.243756 + 0.0887198i −0.0122492 + 0.00445834i
\(397\) 12.3200 0.618321 0.309160 0.951010i \(-0.399952\pi\)
0.309160 + 0.951010i \(0.399952\pi\)
\(398\) 2.04916 + 3.54925i 0.102715 + 0.177908i
\(399\) 0 0
\(400\) 2.53802 4.39598i 0.126901 0.219799i
\(401\) −10.4880 + 18.1657i −0.523745 + 0.907152i 0.475873 + 0.879514i \(0.342132\pi\)
−0.999618 + 0.0276385i \(0.991201\pi\)
\(402\) 22.1498 3.90560i 1.10473 0.194794i
\(403\) 22.3603 + 38.7291i 1.11384 + 1.92923i
\(404\) −1.76920 −0.0880210
\(405\) −3.95723 22.4426i −0.196637 1.11518i
\(406\) 0 0
\(407\) 1.79679 + 3.11213i 0.0890635 + 0.154263i
\(408\) −19.4782 + 3.43453i −0.964314 + 0.170034i
\(409\) 12.8307 22.2234i 0.634437 1.09888i −0.352197 0.935926i \(-0.614565\pi\)
0.986634 0.162951i \(-0.0521012\pi\)
\(410\) 3.79813 6.57856i 0.187576 0.324892i
\(411\) −6.37346 7.59559i −0.314379 0.374663i
\(412\) −0.281059 0.486809i −0.0138468 0.0239833i
\(413\) 0 0
\(414\) −0.402856 + 0.146628i −0.0197993 + 0.00720635i
\(415\) −6.91622 −0.339504
\(416\) 3.03343 + 5.25406i 0.148726 + 0.257601i
\(417\) 0.547352 1.50384i 0.0268039 0.0736432i
\(418\) −0.688663 + 1.19280i −0.0336836 + 0.0583417i
\(419\) −0.739885 + 1.28152i −0.0361458 + 0.0626063i −0.883532 0.468370i \(-0.844841\pi\)
0.847387 + 0.530976i \(0.178175\pi\)
\(420\) 0 0
\(421\) −6.55350 11.3510i −0.319398 0.553214i 0.660965 0.750417i \(-0.270147\pi\)
−0.980363 + 0.197203i \(0.936814\pi\)
\(422\) −7.34730 −0.357661
\(423\) −12.2554 10.2835i −0.595876 0.500000i
\(424\) 2.11019 0.102480
\(425\) 2.73783 + 4.74205i 0.132804 + 0.230023i
\(426\) 19.8516 + 23.6583i 0.961815 + 1.14625i
\(427\) 0 0
\(428\) −0.602196 + 1.04303i −0.0291083 + 0.0504170i
\(429\) 4.64749 0.819478i 0.224383 0.0395648i
\(430\) 2.09240 + 3.62414i 0.100904 + 0.174771i
\(431\) 17.7270 0.853879 0.426939 0.904280i \(-0.359592\pi\)
0.426939 + 0.904280i \(0.359592\pi\)
\(432\) −16.1832 9.34337i −0.778615 0.449533i
\(433\) 5.83843 0.280577 0.140289 0.990111i \(-0.455197\pi\)
0.140289 + 0.990111i \(0.455197\pi\)
\(434\) 0 0
\(435\) 37.9261 6.68739i 1.81842 0.320636i
\(436\) 0.982926 1.70248i 0.0470736 0.0815339i
\(437\) 0.115867 0.200688i 0.00554267 0.00960019i
\(438\) 15.4029 + 18.3564i 0.735977 + 0.877103i
\(439\) 14.9277 + 25.8555i 0.712459 + 1.23401i 0.963931 + 0.266151i \(0.0857518\pi\)
−0.251473 + 0.967864i \(0.580915\pi\)
\(440\) 3.48751 0.166261
\(441\) 0 0
\(442\) 30.4347 1.44763
\(443\) −5.33275 9.23659i −0.253367 0.438844i 0.711084 0.703107i \(-0.248205\pi\)
−0.964451 + 0.264263i \(0.914871\pi\)
\(444\) 0.840738 2.30991i 0.0398996 0.109623i
\(445\) 10.2724 17.7924i 0.486960 0.843440i
\(446\) 9.56077 16.5597i 0.452716 0.784127i
\(447\) 5.16843 14.2002i 0.244459 0.671644i
\(448\) 0 0
\(449\) 3.55438 0.167741 0.0838707 0.996477i \(-0.473272\pi\)
0.0838707 + 0.996477i \(0.473272\pi\)
\(450\) −0.990667 + 5.61835i −0.0467005 + 0.264852i
\(451\) 1.04189 0.0490606
\(452\) 0.478340 + 0.828510i 0.0224992 + 0.0389698i
\(453\) 20.5155 + 24.4494i 0.963901 + 1.14873i
\(454\) −1.94949 + 3.37662i −0.0914942 + 0.158473i
\(455\) 0 0
\(456\) 10.9697 1.93426i 0.513704 0.0905799i
\(457\) −2.51161 4.35024i −0.117488 0.203496i 0.801283 0.598285i \(-0.204151\pi\)
−0.918772 + 0.394789i \(0.870818\pi\)
\(458\) −12.3514 −0.577144
\(459\) 17.4572 10.0789i 0.814834 0.470445i
\(460\) −0.0496299 −0.00231400
\(461\) 9.23055 + 15.9878i 0.429910 + 0.744625i 0.996865 0.0791233i \(-0.0252121\pi\)
−0.566955 + 0.823749i \(0.691879\pi\)
\(462\) 0 0
\(463\) 7.11721 12.3274i 0.330765 0.572902i −0.651897 0.758307i \(-0.726027\pi\)
0.982662 + 0.185406i \(0.0593600\pi\)
\(464\) 15.7895 27.3482i 0.733010 1.26961i
\(465\) −21.6506 25.8022i −1.00402 1.19655i
\(466\) −8.94016 15.4848i −0.414145 0.717320i
\(467\) 3.36865 0.155883 0.0779413 0.996958i \(-0.475165\pi\)
0.0779413 + 0.996958i \(0.475165\pi\)
\(468\) −2.47288 2.07499i −0.114309 0.0959165i
\(469\) 0 0
\(470\) 9.09627 + 15.7552i 0.419579 + 0.726733i
\(471\) −2.91694 + 8.01422i −0.134405 + 0.369276i
\(472\) −1.08394 + 1.87744i −0.0498924 + 0.0864162i
\(473\) −0.286989 + 0.497079i −0.0131958 + 0.0228557i
\(474\) −10.0869 + 27.7136i −0.463308 + 1.27293i
\(475\) −1.54189 2.67063i −0.0707467 0.122537i
\(476\) 0 0
\(477\) −2.02094 + 0.735564i −0.0925327 + 0.0336791i
\(478\) 12.8494 0.587716
\(479\) −18.3833 31.8407i −0.839952 1.45484i −0.889934 0.456090i \(-0.849249\pi\)
0.0499812 0.998750i \(-0.484084\pi\)
\(480\) −2.93717 3.50038i −0.134063 0.159770i
\(481\) −22.3603 + 38.7291i −1.01954 + 1.76589i
\(482\) −6.03462 + 10.4523i −0.274869 + 0.476087i
\(483\) 0 0
\(484\) −0.996130 1.72535i −0.0452786 0.0784249i
\(485\) −34.4466 −1.56414
\(486\) 20.6832 + 3.64701i 0.938209 + 0.165432i
\(487\) −37.4175 −1.69555 −0.847773 0.530358i \(-0.822057\pi\)
−0.847773 + 0.530358i \(0.822057\pi\)
\(488\) −1.41013 2.44242i −0.0638336 0.110563i
\(489\) −13.0287 + 2.29731i −0.589178 + 0.103888i
\(490\) 0 0
\(491\) 13.3353 23.0974i 0.601813 1.04237i −0.390734 0.920504i \(-0.627779\pi\)
0.992547 0.121866i \(-0.0388879\pi\)
\(492\) −0.458111 0.545955i −0.0206532 0.0246136i
\(493\) 17.0326 + 29.5013i 0.767108 + 1.32867i
\(494\) −17.1402 −0.771175
\(495\) −3.34002 + 1.21567i −0.150123 + 0.0546402i
\(496\) −27.6195 −1.24015
\(497\) 0 0
\(498\) 2.18004 5.98962i 0.0976901 0.268401i
\(499\) −16.8726 + 29.2242i −0.755320 + 1.30825i 0.189895 + 0.981804i \(0.439185\pi\)
−0.945215 + 0.326449i \(0.894148\pi\)
\(500\) 0.839556 1.45415i 0.0375461 0.0650317i
\(501\) 3.35023 9.20469i 0.149677 0.411235i
\(502\) −16.8400 29.1678i −0.751607 1.30182i
\(503\) 32.0401 1.42860 0.714299 0.699840i \(-0.246745\pi\)
0.714299 + 0.699840i \(0.246745\pi\)
\(504\) 0 0
\(505\) −24.2422 −1.07876
\(506\) 0.0334331 + 0.0579078i 0.00148628 + 0.00257431i
\(507\) 23.2763 + 27.7396i 1.03374 + 1.23196i
\(508\) −0.820670 + 1.42144i −0.0364114 + 0.0630663i
\(509\) −3.96926 + 6.87495i −0.175934 + 0.304727i −0.940484 0.339838i \(-0.889628\pi\)
0.764550 + 0.644564i \(0.222961\pi\)
\(510\) −22.5744 + 3.98048i −0.999613 + 0.176259i
\(511\) 0 0
\(512\) −24.9186 −1.10126
\(513\) −9.83157 + 5.67626i −0.434074 + 0.250613i
\(514\) −14.6209 −0.644901
\(515\) −3.85117 6.67042i −0.169703 0.293934i
\(516\) 0.386659 0.0681784i 0.0170217 0.00300139i
\(517\) −1.24763 + 2.16095i −0.0548705 + 0.0950386i
\(518\) 0 0
\(519\) −23.4572 27.9552i −1.02966 1.22710i
\(520\) 21.7003 + 37.5860i 0.951620 + 1.64825i
\(521\) 14.6750 0.642923 0.321462 0.946923i \(-0.395826\pi\)
0.321462 + 0.946923i \(0.395826\pi\)
\(522\) −6.16313 + 34.9529i −0.269753 + 1.52985i
\(523\) −28.3432 −1.23936 −0.619680 0.784854i \(-0.712738\pi\)
−0.619680 + 0.784854i \(0.712738\pi\)
\(524\) −1.04988 1.81844i −0.0458641 0.0794390i
\(525\) 0 0
\(526\) −17.5737 + 30.4386i −0.766251 + 1.32719i
\(527\) 14.8969 25.8022i 0.648920 1.12396i
\(528\) −0.996845 + 2.73881i −0.0433821 + 0.119191i
\(529\) 11.4944 + 19.9088i 0.499755 + 0.865602i
\(530\) 2.44562 0.106231
\(531\) 0.383666 2.17588i 0.0166497 0.0944251i
\(532\) 0 0
\(533\) 6.48293 + 11.2288i 0.280807 + 0.486371i
\(534\) 12.1707 + 14.5045i 0.526678 + 0.627671i
\(535\) −8.25150 + 14.2920i −0.356743 + 0.617898i
\(536\) −14.1853 + 24.5696i −0.612710 + 1.06124i
\(537\) 8.73442 1.54011i 0.376918 0.0664608i
\(538\) −5.14203 8.90625i −0.221688 0.383976i
\(539\) 0 0
\(540\) 2.10560 + 1.21567i 0.0906106 + 0.0523141i
\(541\) 11.2858 0.485215 0.242607 0.970125i \(-0.421997\pi\)
0.242607 + 0.970125i \(0.421997\pi\)
\(542\) 2.29292 + 3.97145i 0.0984893 + 0.170588i
\(543\) −0.545759 + 0.0962321i −0.0234208 + 0.00412972i
\(544\) 2.02094 3.50038i 0.0866473 0.150077i
\(545\) 13.4684 23.3279i 0.576922 0.999258i
\(546\) 0 0
\(547\) 14.6202 + 25.3229i 0.625115 + 1.08273i 0.988519 + 0.151099i \(0.0482812\pi\)
−0.363404 + 0.931632i \(0.618385\pi\)
\(548\) 1.05787 0.0451899
\(549\) 2.20187 + 1.84759i 0.0939734 + 0.0788530i
\(550\) 0.889814 0.0379418
\(551\) −9.59240 16.6145i −0.408650 0.707802i
\(552\) 0.184955 0.508159i 0.00787219 0.0216287i
\(553\) 0 0
\(554\) 3.85457 6.67631i 0.163765 0.283649i
\(555\) 11.5201 31.6511i 0.489000 1.34352i
\(556\) 0.0853707 + 0.147866i 0.00362052 + 0.00627093i
\(557\) −0.775682 −0.0328667 −0.0164334 0.999865i \(-0.505231\pi\)
−0.0164334 + 0.999865i \(0.505231\pi\)
\(558\) 29.1698 10.6170i 1.23486 0.449451i
\(559\) −7.14290 −0.302113
\(560\) 0 0
\(561\) −2.02094 2.40847i −0.0853243 0.101686i
\(562\) −19.1163 + 33.1105i −0.806374 + 1.39668i
\(563\) 12.4761 21.6093i 0.525806 0.910722i −0.473742 0.880663i \(-0.657097\pi\)
0.999548 0.0300588i \(-0.00956944\pi\)
\(564\) 1.68092 0.296392i 0.0707796 0.0124804i
\(565\) 6.55438 + 11.3525i 0.275745 + 0.477604i
\(566\) −6.15888 −0.258877
\(567\) 0 0
\(568\) −38.9564 −1.63457
\(569\) 12.4017 + 21.4803i 0.519905 + 0.900502i 0.999732 + 0.0231391i \(0.00736608\pi\)
−0.479827 + 0.877363i \(0.659301\pi\)
\(570\) 12.7135 2.24173i 0.532509 0.0938957i
\(571\) −4.39827 + 7.61803i −0.184062 + 0.318805i −0.943260 0.332055i \(-0.892258\pi\)
0.759198 + 0.650860i \(0.225591\pi\)
\(572\) −0.251745 + 0.436035i −0.0105260 + 0.0182315i
\(573\) −17.3316 20.6550i −0.724037 0.862873i
\(574\) 0 0
\(575\) −0.149711 −0.00624336
\(576\) 24.2335 8.82029i 1.00973 0.367512i
\(577\) 12.8743 0.535965 0.267983 0.963424i \(-0.413643\pi\)
0.267983 + 0.963424i \(0.413643\pi\)
\(578\) 1.31386 + 2.27568i 0.0546495 + 0.0946557i
\(579\) 3.57919 9.83375i 0.148746 0.408677i
\(580\) −2.05438 + 3.55829i −0.0853034 + 0.147750i
\(581\) 0 0
\(582\) 10.8578 29.8316i 0.450071 1.23656i
\(583\) 0.167718 + 0.290497i 0.00694619 + 0.0120311i
\(584\) −30.2262 −1.25077
\(585\) −33.8842 28.4322i −1.40094 1.17553i
\(586\) −5.83069 −0.240864
\(587\) 22.4315 + 38.8526i 0.925849 + 1.60362i 0.790190 + 0.612861i \(0.209982\pi\)
0.135658 + 0.990756i \(0.456685\pi\)
\(588\) 0 0
\(589\) −8.38965 + 14.5313i −0.345690 + 0.598752i
\(590\) −1.25624 + 2.17588i −0.0517188 + 0.0895795i
\(591\) −43.0433 + 7.58969i −1.77056 + 0.312198i
\(592\) −13.8097 23.9192i −0.567577 0.983072i
\(593\) −3.76053 −0.154426 −0.0772131 0.997015i \(-0.524602\pi\)
−0.0772131 + 0.997015i \(0.524602\pi\)
\(594\) 3.27573i 0.134405i
\(595\) 0 0
\(596\) 0.806123 + 1.39625i 0.0330201 + 0.0571924i
\(597\) 5.18866 0.914901i 0.212358 0.0374444i
\(598\) −0.416060 + 0.720637i −0.0170139 + 0.0294690i
\(599\) 1.84524 3.19604i 0.0753943 0.130587i −0.825863 0.563870i \(-0.809312\pi\)
0.901258 + 0.433283i \(0.142645\pi\)
\(600\) −4.62567 5.51266i −0.188842 0.225053i
\(601\) −10.9285 18.9288i −0.445785 0.772122i 0.552322 0.833631i \(-0.313742\pi\)
−0.998107 + 0.0615091i \(0.980409\pi\)
\(602\) 0 0
\(603\) 5.02094 28.4752i 0.204469 1.15960i
\(604\) −3.40516 −0.138554
\(605\) −13.6493 23.6413i −0.554923 0.961155i
\(606\) 7.64131 20.9943i 0.310407 0.852836i
\(607\) 12.1973 21.1263i 0.495072 0.857490i −0.504911 0.863171i \(-0.668475\pi\)
0.999984 + 0.00568063i \(0.00180821\pi\)
\(608\) −1.13816 + 1.97134i −0.0461583 + 0.0799485i
\(609\) 0 0
\(610\) −1.63429 2.83067i −0.0661703 0.114610i
\(611\) −31.0523 −1.25624
\(612\) −0.373455 + 2.11797i −0.0150960 + 0.0856139i
\(613\) 42.0215 1.69723 0.848616 0.529010i \(-0.177437\pi\)
0.848616 + 0.529010i \(0.177437\pi\)
\(614\) 8.33796 + 14.4418i 0.336493 + 0.582823i
\(615\) −6.27719 7.48086i −0.253121 0.301657i
\(616\) 0 0
\(617\) −23.2049 + 40.1920i −0.934192 + 1.61807i −0.158125 + 0.987419i \(0.550545\pi\)
−0.776068 + 0.630650i \(0.782788\pi\)
\(618\) 6.99067 1.23264i 0.281206 0.0495842i
\(619\) −13.6047 23.5641i −0.546820 0.947120i −0.998490 0.0549349i \(-0.982505\pi\)
0.451670 0.892185i \(-0.350828\pi\)
\(620\) 3.59358 0.144322
\(621\) 0.551139i 0.0221165i
\(622\) 29.6209 1.18769
\(623\) 0 0
\(624\) −35.7196 + 6.29833i −1.42993 + 0.252135i
\(625\) 15.0326 26.0372i 0.601302 1.04149i
\(626\) −9.35685 + 16.2065i −0.373975 + 0.647743i
\(627\) 1.13816 + 1.35640i 0.0454536 + 0.0541694i
\(628\) −0.454956 0.788006i −0.0181547 0.0314449i
\(629\) 29.7939 1.18796
\(630\) 0 0
\(631\) −29.6023 −1.17845 −0.589224 0.807970i \(-0.700566\pi\)
−0.589224 + 0.807970i \(0.700566\pi\)
\(632\) −18.6006 32.2172i −0.739892 1.28153i
\(633\) −3.23055 + 8.87587i −0.128403 + 0.352784i
\(634\) 4.16456 7.21324i 0.165396 0.286474i
\(635\) −11.2451 + 19.4771i −0.446248 + 0.772925i
\(636\) 0.0784773 0.215615i 0.00311183 0.00854968i
\(637\) 0 0
\(638\) 5.53571 0.219161
\(639\) 37.3089 13.5793i 1.47592 0.537189i
\(640\) −24.0496 −0.950645
\(641\) 0.139500 + 0.241621i 0.00550991 + 0.00954345i 0.868767 0.495221i \(-0.164913\pi\)
−0.863257 + 0.504764i \(0.831579\pi\)
\(642\) −9.77631 11.6510i −0.385840 0.459826i
\(643\) −9.12196 + 15.7997i −0.359735 + 0.623079i −0.987916 0.154988i \(-0.950466\pi\)
0.628181 + 0.778067i \(0.283800\pi\)
\(644\) 0 0
\(645\) 5.29813 0.934204i 0.208614 0.0367842i
\(646\) 5.70961 + 9.88933i 0.224642 + 0.389090i
\(647\) −22.4570 −0.882875 −0.441438 0.897292i \(-0.645531\pi\)
−0.441438 + 0.897292i \(0.645531\pi\)
\(648\) −20.2941 + 17.0288i −0.797228 + 0.668953i
\(649\) −0.344608 −0.0135270
\(650\) 5.53667 + 9.58980i 0.217166 + 0.376143i
\(651\) 0 0
\(652\) 0.705737 1.22237i 0.0276388 0.0478718i
\(653\) 25.2656 43.7614i 0.988721 1.71251i 0.364655 0.931143i \(-0.381187\pi\)
0.624066 0.781372i \(-0.285480\pi\)
\(654\) 15.9572 + 19.0171i 0.623977 + 0.743627i
\(655\) −14.3858 24.9169i −0.562099 0.973584i
\(656\) −8.00774 −0.312650
\(657\) 28.9479 10.5362i 1.12937 0.411055i
\(658\) 0 0
\(659\) 1.33631 + 2.31456i 0.0520554 + 0.0901626i 0.890879 0.454241i \(-0.150089\pi\)
−0.838824 + 0.544403i \(0.816756\pi\)
\(660\) 0.129700 0.356347i 0.00504855 0.0138708i
\(661\) −17.3050 + 29.9731i −0.673086 + 1.16582i 0.303938 + 0.952692i \(0.401698\pi\)
−0.977024 + 0.213128i \(0.931635\pi\)
\(662\) −7.22921 + 12.5214i −0.280971 + 0.486656i
\(663\) 13.3819 36.7665i 0.519710 1.42789i
\(664\) 4.02007 + 6.96296i 0.156009 + 0.270215i
\(665\) 0 0
\(666\) 23.7795 + 19.9533i 0.921436 + 0.773176i
\(667\) −0.931379 −0.0360631
\(668\) 0.522537 + 0.905061i 0.0202176 + 0.0350179i
\(669\) −15.8011 18.8310i −0.610907 0.728050i
\(670\) −16.4402 + 28.4752i −0.635139 + 1.10009i
\(671\) 0.224155 0.388249i 0.00865342 0.0149882i
\(672\) 0 0
\(673\) −8.25624 14.3002i −0.318255 0.551234i 0.661869 0.749619i \(-0.269763\pi\)
−0.980124 + 0.198386i \(0.936430\pi\)
\(674\) −25.0523 −0.964979
\(675\) 6.35163 + 3.66712i 0.244474 + 0.141147i
\(676\) −3.86341 −0.148593
\(677\) −21.8790 37.8955i −0.840877 1.45644i −0.889154 0.457608i \(-0.848706\pi\)
0.0482766 0.998834i \(-0.484627\pi\)
\(678\) −11.8976 + 2.09786i −0.456923 + 0.0805678i
\(679\) 0 0
\(680\) 14.4572 25.0407i 0.554410 0.960266i
\(681\) 3.22193 + 3.83975i 0.123465 + 0.147140i
\(682\) −2.42081 4.19296i −0.0926975 0.160557i
\(683\) 28.2412 1.08062 0.540310 0.841466i \(-0.318307\pi\)
0.540310 + 0.841466i \(0.318307\pi\)
\(684\) 0.210323 1.19280i 0.00804189 0.0456078i
\(685\) 14.4953 0.553835
\(686\) 0 0
\(687\) −5.43083 + 14.9211i −0.207199 + 0.569274i
\(688\) 2.20574 3.82045i 0.0840929 0.145653i
\(689\) −2.08718 + 3.61510i −0.0795153 + 0.137725i
\(690\) 0.214355 0.588936i 0.00816036 0.0224204i
\(691\) −14.5326 25.1711i −0.552844 0.957555i −0.998068 0.0621351i \(-0.980209\pi\)
0.445223 0.895420i \(-0.353124\pi\)
\(692\) 3.89344 0.148006
\(693\) 0 0
\(694\) −27.5016 −1.04395
\(695\) 1.16978 + 2.02611i 0.0443722 + 0.0768549i
\(696\) −28.7772 34.2953i −1.09080 1.29996i
\(697\) 4.31908 7.48086i 0.163597 0.283358i
\(698\) −2.39961 + 4.15625i −0.0908268 + 0.157317i
\(699\) −22.6373 + 3.99156i −0.856221 + 0.150975i
\(700\) 0 0
\(701\) −1.10876 −0.0418771 −0.0209386 0.999781i \(-0.506665\pi\)
−0.0209386 + 0.999781i \(0.506665\pi\)
\(702\) 35.3036 20.3825i 1.33245 0.769289i
\(703\) −16.7793 −0.632843
\(704\) −2.01114 3.48340i −0.0757979 0.131286i
\(705\) 23.0326 4.06126i 0.867456 0.152956i
\(706\) 6.75150 11.6939i 0.254096 0.440107i
\(707\) 0 0
\(708\) 0.151522 + 0.180576i 0.00569453 + 0.00678648i
\(709\) 9.23442 + 15.9945i 0.346806 + 0.600686i 0.985680 0.168626i \(-0.0539329\pi\)
−0.638874 + 0.769311i \(0.720600\pi\)
\(710\) −45.1489 −1.69441
\(711\) 29.0442 + 24.3709i 1.08924 + 0.913982i
\(712\) −23.8835 −0.895072
\(713\) 0.407299 + 0.705463i 0.0152535 + 0.0264198i
\(714\) 0 0
\(715\) −3.44949 + 5.97470i −0.129004 + 0.223441i
\(716\) −0.473126 + 0.819478i −0.0176815 + 0.0306253i
\(717\) 5.64977 15.5226i 0.210994 0.579702i
\(718\) −6.38666 11.0620i −0.238348 0.412831i
\(719\) 33.7769 1.25967 0.629834 0.776730i \(-0.283123\pi\)
0.629834 + 0.776730i \(0.283123\pi\)
\(720\) 25.6707 9.34337i 0.956691 0.348207i
\(721\) 0 0
\(722\) 9.58378 + 16.5996i 0.356671 + 0.617773i
\(723\) 9.97343 + 11.8859i 0.370916 + 0.442040i
\(724\) 0.0295627 0.0512040i 0.00109869 0.00190298i
\(725\) −6.19712 + 10.7337i −0.230155 + 0.398641i
\(726\) 24.7763 4.36873i 0.919535 0.162139i
\(727\) 8.40214 + 14.5529i 0.311618 + 0.539738i 0.978713 0.205234i \(-0.0657957\pi\)
−0.667095 + 0.744973i \(0.732462\pi\)
\(728\) 0 0
\(729\) 13.5000 23.3827i 0.500000 0.866025i
\(730\) −35.0310 −1.29655
\(731\) 2.37939 + 4.12122i 0.0880047 + 0.152429i
\(732\) −0.302004 + 0.0532514i −0.0111624 + 0.00196823i
\(733\) −6.81820 + 11.8095i −0.251836 + 0.436193i −0.964031 0.265789i \(-0.914368\pi\)
0.712195 + 0.701981i \(0.247701\pi\)
\(734\) 10.8682 18.8243i 0.401154 0.694819i
\(735\) 0 0
\(736\) 0.0552549 + 0.0957044i 0.00203672 + 0.00352771i
\(737\) −4.50980 −0.166121
\(738\) 8.45723 3.07818i 0.311315 0.113309i
\(739\) −32.0419 −1.17868 −0.589340 0.807885i \(-0.700612\pi\)
−0.589340 + 0.807885i \(0.700612\pi\)
\(740\) 1.79679 + 3.11213i 0.0660513 + 0.114404i
\(741\) −7.53643 + 20.7062i −0.276858 + 0.760660i
\(742\) 0 0
\(743\) −16.8764 + 29.2309i −0.619137 + 1.07238i 0.370507 + 0.928830i \(0.379184\pi\)
−0.989644 + 0.143547i \(0.954149\pi\)
\(744\) −13.3921 + 36.7946i −0.490979 + 1.34895i
\(745\) 11.0458 + 19.1318i 0.404685 + 0.700936i
\(746\) 18.9290 0.693040
\(747\) −6.27719 5.26719i −0.229670 0.192716i
\(748\) 0.335437 0.0122648
\(749\) 0 0
\(750\) 13.6297 + 16.2432i 0.497686 + 0.593119i
\(751\) −13.0582 + 22.6175i −0.476502 + 0.825326i −0.999637 0.0269236i \(-0.991429\pi\)
0.523135 + 0.852250i \(0.324762\pi\)
\(752\) 9.58899 16.6086i 0.349675 0.605654i
\(753\) −42.6404 + 7.51866i −1.55390 + 0.273995i
\(754\) 34.4447 + 59.6600i 1.25440 + 2.17269i
\(755\) −46.6587 −1.69808
\(756\) 0 0
\(757\) 35.6536 1.29585 0.647927 0.761703i \(-0.275636\pi\)
0.647927 + 0.761703i \(0.275636\pi\)
\(758\) −10.8170 18.7356i −0.392892 0.680509i
\(759\) 0.0846555 0.0149270i 0.00307280 0.000541817i
\(760\) −8.14203 + 14.1024i −0.295342 + 0.511548i
\(761\) 20.3824 35.3033i 0.738861 1.27974i −0.214148 0.976801i \(-0.568698\pi\)
0.953009 0.302943i \(-0.0979692\pi\)
\(762\) −13.3231 15.8779i −0.482645 0.575194i
\(763\) 0 0
\(764\) 2.87670 0.104075
\(765\) −5.11721 + 29.0211i −0.185013 + 1.04926i
\(766\) 43.1411 1.55875
\(767\) −2.14425 3.71395i −0.0774243 0.134103i
\(768\) −2.60417 + 7.15490i −0.0939699 + 0.258180i
\(769\) 19.7135 34.1447i 0.710886 1.23129i −0.253639 0.967299i \(-0.581627\pi\)
0.964525 0.263992i \(-0.0850392\pi\)
\(770\) 0 0
\(771\) −6.42871 + 17.6627i −0.231524 + 0.636108i
\(772\) 0.558248 + 0.966914i 0.0200918 + 0.0348000i
\(773\) −24.9026 −0.895685 −0.447842 0.894113i \(-0.647807\pi\)
−0.447842 + 0.894113i \(0.647807\pi\)
\(774\) −0.860967 + 4.88279i −0.0309468 + 0.175508i
\(775\) 10.8402 0.389391
\(776\) 20.0221 + 34.6793i 0.718752 + 1.24492i
\(777\) 0 0
\(778\) 20.2383 35.0538i 0.725578 1.25674i
\(779\) −2.43242 + 4.21307i −0.0871504 + 0.150949i
\(780\) 4.64749 0.819478i 0.166407 0.0293420i