Properties

Label 441.2.g.b.67.2
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 67.2
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.b.79.2

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.673648 + 1.16679i) q^{2} +(0.592396 - 1.62760i) q^{3} +(0.0923963 + 0.160035i) q^{4} -2.53209 q^{5} +(1.50000 + 1.78763i) q^{6} -2.94356 q^{8} +(-2.29813 - 1.92836i) q^{9} +O(q^{10})\) \(q+(-0.673648 + 1.16679i) q^{2} +(0.592396 - 1.62760i) q^{3} +(0.0923963 + 0.160035i) q^{4} -2.53209 q^{5} +(1.50000 + 1.78763i) q^{6} -2.94356 q^{8} +(-2.29813 - 1.92836i) q^{9} +(1.70574 - 2.95442i) q^{10} +0.467911 q^{11} +(0.315207 - 0.0555796i) q^{12} +(2.91147 - 5.04282i) q^{13} +(-1.50000 + 4.12122i) q^{15} +(1.79813 - 3.11446i) q^{16} +(1.93969 - 3.35965i) q^{17} +(3.79813 - 1.38241i) q^{18} +(-1.09240 - 1.89209i) q^{19} +(-0.233956 - 0.405223i) q^{20} +(-0.315207 + 0.545955i) q^{22} -0.106067 q^{23} +(-1.74376 + 4.79093i) q^{24} +1.41147 q^{25} +(3.92262 + 6.79417i) q^{26} +(-4.50000 + 2.59808i) q^{27} +(-4.39053 - 7.60462i) q^{29} +(-3.79813 - 4.52644i) q^{30} +(-3.84002 - 6.65111i) q^{31} +(-0.520945 - 0.902302i) q^{32} +(0.277189 - 0.761570i) q^{33} +(2.61334 + 4.52644i) q^{34} +(0.0962667 - 0.545955i) q^{36} +(3.84002 + 6.65111i) q^{37} +2.94356 q^{38} +(-6.48293 - 7.72605i) q^{39} +7.45336 q^{40} +(-1.11334 + 1.92836i) q^{41} +(-0.613341 - 1.06234i) q^{43} +(0.0432332 + 0.0748822i) q^{44} +(5.81908 + 4.88279i) q^{45} +(0.0714517 - 0.123758i) q^{46} +(-2.66637 + 4.61830i) q^{47} +(-4.00387 - 4.77163i) q^{48} +(-0.950837 + 1.64690i) q^{50} +(-4.31908 - 5.14728i) q^{51} +1.07604 q^{52} +(0.358441 - 0.620838i) q^{53} -7.00076i q^{54} -1.18479 q^{55} +(-3.72668 + 0.657115i) q^{57} +11.8307 q^{58} +(0.368241 + 0.637812i) q^{59} +(-0.798133 + 0.140732i) q^{60} +(0.479055 - 0.829748i) q^{61} +10.3473 q^{62} +8.59627 q^{64} +(-7.37211 + 12.7689i) q^{65} +(0.701867 + 0.836452i) q^{66} +(4.81908 + 8.34689i) q^{67} +0.716881 q^{68} +(-0.0628336 + 0.172634i) q^{69} +13.2344 q^{71} +(6.76470 + 5.67626i) q^{72} +(-5.13429 + 8.89284i) q^{73} -10.3473 q^{74} +(0.836152 - 2.29731i) q^{75} +(0.201867 - 0.349643i) q^{76} +(13.3819 - 2.35959i) q^{78} +(6.31908 - 10.9450i) q^{79} +(-4.55303 + 7.88609i) q^{80} +(1.56283 + 8.86327i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-1.36571 - 2.36549i) q^{83} +(-4.91147 + 8.50692i) q^{85} +1.65270 q^{86} +(-14.9782 + 2.64106i) q^{87} -1.37733 q^{88} +(-4.05690 - 7.02676i) q^{89} +(-9.61721 + 3.50038i) q^{90} +(-0.00980018 - 0.0169744i) q^{92} +(-13.1001 + 2.30991i) q^{93} +(-3.59240 - 6.22221i) q^{94} +(2.76604 + 4.79093i) q^{95} +(-1.77719 + 0.313366i) q^{96} +(-6.80200 - 11.7814i) q^{97} +(-1.07532 - 0.902302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q - 3q^{2} - 3q^{4} - 6q^{5} + 9q^{6} + 12q^{8} + O(q^{10}) \) \( 6q - 3q^{2} - 3q^{4} - 6q^{5} + 9q^{6} + 12q^{8} + 12q^{11} + 9q^{12} - 3q^{13} - 9q^{15} - 3q^{16} + 6q^{17} + 9q^{18} - 3q^{19} - 6q^{20} - 9q^{22} + 24q^{23} - 18q^{24} - 12q^{25} - 3q^{26} - 27q^{27} - 9q^{29} - 9q^{30} - 3q^{31} - 9q^{33} + 9q^{34} - 27q^{36} + 3q^{37} - 12q^{38} - 18q^{39} + 18q^{40} + 3q^{43} - 15q^{44} + 18q^{45} + 3q^{47} + 6q^{50} - 9q^{51} + 42q^{52} - 6q^{53} - 9q^{57} - 18q^{58} - 3q^{59} + 9q^{60} + 6q^{61} + 60q^{62} + 24q^{64} - 15q^{65} + 18q^{66} + 12q^{67} - 12q^{68} + 9q^{69} + 18q^{71} + 45q^{72} - 21q^{73} - 60q^{74} + 9q^{75} + 15q^{76} + 54q^{78} + 21q^{79} - 15q^{80} - 9q^{82} - 18q^{83} - 9q^{85} + 12q^{86} - 36q^{87} + 54q^{88} + 12q^{89} - 27q^{90} - 3q^{92} - 27q^{93} - 18q^{94} + 12q^{95} - 3q^{97} + 18q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.673648 + 1.16679i −0.476341 + 0.825047i −0.999633 0.0271067i \(-0.991371\pi\)
0.523291 + 0.852154i \(0.324704\pi\)
\(3\) 0.592396 1.62760i 0.342020 0.939693i
\(4\) 0.0923963 + 0.160035i 0.0461981 + 0.0800175i
\(5\) −2.53209 −1.13238 −0.566192 0.824273i \(-0.691584\pi\)
−0.566192 + 0.824273i \(0.691584\pi\)
\(6\) 1.50000 + 1.78763i 0.612372 + 0.729797i
\(7\) 0 0
\(8\) −2.94356 −1.04071
\(9\) −2.29813 1.92836i −0.766044 0.642788i
\(10\) 1.70574 2.95442i 0.539401 0.934271i
\(11\) 0.467911 0.141081 0.0705403 0.997509i \(-0.477528\pi\)
0.0705403 + 0.997509i \(0.477528\pi\)
\(12\) 0.315207 0.0555796i 0.0909926 0.0160444i
\(13\) 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
\(17\) 1.93969 3.35965i 0.470445 0.814834i −0.528984 0.848632i \(-0.677427\pi\)
0.999429 + 0.0337978i \(0.0107602\pi\)
\(18\) 3.79813 1.38241i 0.895229 0.325837i
\(19\) −1.09240 1.89209i −0.250613 0.434074i 0.713082 0.701081i \(-0.247299\pi\)
−0.963695 + 0.267007i \(0.913965\pi\)
\(20\) −0.233956 0.405223i −0.0523141 0.0906106i
\(21\) 0 0
\(22\) −0.315207 + 0.545955i −0.0672025 + 0.116398i
\(23\) −0.106067 −0.0221165 −0.0110582 0.999939i \(-0.503520\pi\)
−0.0110582 + 0.999939i \(0.503520\pi\)
\(24\) −1.74376 + 4.79093i −0.355943 + 0.977944i
\(25\) 1.41147 0.282295
\(26\) 3.92262 + 6.79417i 0.769289 + 1.33245i
\(27\) −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 \(-0.470095\pi\)
\(30\) −3.79813 4.52644i −0.693441 0.826411i
\(31\) −3.84002 6.65111i −0.689688 1.19458i −0.971939 0.235235i \(-0.924414\pi\)
0.282250 0.959341i \(-0.408919\pi\)
\(32\) −0.520945 0.902302i −0.0920909 0.159506i
\(33\) 0.277189 0.761570i 0.0482524 0.132572i
\(34\) 2.61334 + 4.52644i 0.448184 + 0.776278i
\(35\) 0 0
\(36\) 0.0962667 0.545955i 0.0160444 0.0909926i
\(37\) 3.84002 + 6.65111i 0.631296 + 1.09344i 0.987287 + 0.158947i \(0.0508099\pi\)
−0.355991 + 0.934489i \(0.615857\pi\)
\(38\) 2.94356 0.477509
\(39\) −6.48293 7.72605i −1.03810 1.23716i
\(40\) 7.45336 1.17848
\(41\) −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 \(0.863150\pi\)
\(44\) 0.0432332 + 0.0748822i 0.00651766 + 0.0112889i
\(45\) 5.81908 + 4.88279i 0.867457 + 0.727883i
\(46\) 0.0714517 0.123758i 0.0105350 0.0182471i
\(47\) −2.66637 + 4.61830i −0.388931 + 0.673648i −0.992306 0.123810i \(-0.960489\pi\)
0.603375 + 0.797457i \(0.293822\pi\)
\(48\) −4.00387 4.77163i −0.577909 0.688725i
\(49\) 0 0
\(50\) −0.950837 + 1.64690i −0.134469 + 0.232907i
\(51\) −4.31908 5.14728i −0.604792 0.720763i
\(52\) 1.07604 0.149220
\(53\) 0.358441 0.620838i 0.0492356 0.0852786i −0.840357 0.542033i \(-0.817655\pi\)
0.889593 + 0.456754i \(0.150988\pi\)
\(54\) 7.00076i 0.952682i
\(55\) −1.18479 −0.159757
\(56\) 0 0
\(57\) −3.72668 + 0.657115i −0.493611 + 0.0870369i
\(58\) 11.8307 1.55345
\(59\) 0.368241 + 0.637812i 0.0479409 + 0.0830360i 0.889000 0.457907i \(-0.151401\pi\)
−0.841059 + 0.540943i \(0.818067\pi\)
\(60\) −0.798133 + 0.140732i −0.103039 + 0.0181685i
\(61\) 0.479055 0.829748i 0.0613368 0.106238i −0.833726 0.552178i \(-0.813797\pi\)
0.895063 + 0.445939i \(0.147130\pi\)
\(62\) 10.3473 1.31411
\(63\) 0 0
\(64\) 8.59627 1.07453
\(65\) −7.37211 + 12.7689i −0.914398 + 1.58378i
\(66\) 0.701867 + 0.836452i 0.0863938 + 0.102960i
\(67\) 4.81908 + 8.34689i 0.588744 + 1.01973i 0.994397 + 0.105708i \(0.0337107\pi\)
−0.405653 + 0.914027i \(0.632956\pi\)
\(68\) 0.716881 0.0869346
\(69\) −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 \(0.212499\pi\)
\(72\) 6.76470 + 5.67626i 0.797228 + 0.668953i
\(73\) −5.13429 + 8.89284i −0.600923 + 1.04083i 0.391759 + 0.920068i \(0.371867\pi\)
−0.992682 + 0.120761i \(0.961467\pi\)
\(74\) −10.3473 −1.20285
\(75\) 0.836152 2.29731i 0.0965505 0.265270i
\(76\) 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 −0.253548 0.967323i \(-0.581598\pi\)
0.964500 0.264082i \(-0.0850689\pi\)
\(80\) −4.55303 + 7.88609i −0.509045 + 0.881691i
\(81\) 1.56283 + 8.86327i 0.173648 + 0.984808i
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) −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
\(86\) 1.65270 0.178216
\(87\) −14.9782 + 2.64106i −1.60583 + 0.283151i
\(88\) −1.37733 −0.146823
\(89\) −4.05690 7.02676i −0.430031 0.744835i 0.566845 0.823825i \(-0.308164\pi\)
−0.996875 + 0.0789894i \(0.974831\pi\)
\(90\) −9.61721 + 3.50038i −1.01374 + 0.368972i
\(91\) 0 0
\(92\) −0.00980018 0.0169744i −0.00102174 0.00176970i
\(93\) −13.1001 + 2.30991i −1.35842 + 0.239526i
\(94\) −3.59240 6.22221i −0.370527 0.641772i
\(95\) 2.76604 + 4.79093i 0.283790 + 0.491539i
\(96\) −1.77719 + 0.313366i −0.181384 + 0.0319828i
\(97\) −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
\(100\) 0.130415 + 0.225885i 0.0130415 + 0.0225885i
\(101\) 9.57398 0.952646 0.476323 0.879270i \(-0.341969\pi\)
0.476323 + 0.879270i \(0.341969\pi\)
\(102\) 8.91534 1.57202i 0.882751 0.155653i
\(103\) −3.04189 −0.299726 −0.149863 0.988707i \(-0.547883\pi\)
−0.149863 + 0.988707i \(0.547883\pi\)
\(104\) −8.57011 + 14.8439i −0.840368 + 1.45556i
\(105\) 0 0
\(106\) 0.482926 + 0.836452i 0.0469059 + 0.0812434i
\(107\) 3.25877 + 5.64436i 0.315037 + 0.545660i 0.979445 0.201709i \(-0.0646497\pi\)
−0.664408 + 0.747370i \(0.731316\pi\)
\(108\) −0.831566 0.480105i −0.0800175 0.0461981i
\(109\) −5.31908 + 9.21291i −0.509475 + 0.882437i 0.490465 + 0.871461i \(0.336827\pi\)
−0.999940 + 0.0109759i \(0.996506\pi\)
\(110\) 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 \(0.244965\pi\)
\(114\) 1.74376 4.79093i 0.163318 0.448712i
\(115\) 0.268571 0.0250443
\(116\) 0.811337 1.40528i 0.0753308 0.130477i
\(117\) −16.4153 + 5.97470i −1.51760 + 0.552361i
\(118\) −0.992259 −0.0913449
\(119\) 0 0
\(120\) 4.41534 12.1311i 0.403064 1.10741i
\(121\) −10.7811 −0.980096
\(122\) 0.645430 + 1.11792i 0.0584345 + 0.101211i
\(123\) 2.47906 + 2.95442i 0.223529 + 0.266391i
\(124\) 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
\(129\) −2.09240 + 0.368946i −0.184225 + 0.0324839i
\(130\) −9.93242 17.2035i −0.871131 1.50884i
\(131\) −11.3628 −0.992771 −0.496385 0.868102i \(-0.665340\pi\)
−0.496385 + 0.868102i \(0.665340\pi\)
\(132\) 0.147489 0.0260063i 0.0128373 0.00226356i
\(133\) 0 0
\(134\) −12.9855 −1.12177
\(135\) 11.3944 6.57856i 0.980674 0.566192i
\(136\) −5.70961 + 9.88933i −0.489595 + 0.848003i
\(137\) −5.72462 −0.489087 −0.244544 0.969638i \(-0.578638\pi\)
−0.244544 + 0.969638i \(0.578638\pi\)
\(138\) −0.159100 0.189608i −0.0135435 0.0161405i
\(139\) −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
\(143\) 1.36231 2.35959i 0.113922 0.197319i
\(144\) −10.1382 + 3.68999i −0.844846 + 0.307499i
\(145\) 11.1172 + 19.2556i 0.923234 + 1.59909i
\(146\) −6.91740 11.9813i −0.572488 0.991579i
\(147\) 0 0
\(148\) −0.709607 + 1.22908i −0.0583294 + 0.101029i
\(149\) 8.72462 0.714749 0.357374 0.933961i \(-0.383672\pi\)
0.357374 + 0.933961i \(0.383672\pi\)
\(150\) 2.11721 + 2.52319i 0.172870 + 0.206018i
\(151\) 18.4270 1.49956 0.749782 0.661685i \(-0.230158\pi\)
0.749782 + 0.661685i \(0.230158\pi\)
\(152\) 3.21554 + 5.56947i 0.260815 + 0.451744i
\(153\) −10.9363 + 3.98048i −0.884147 + 0.321803i
\(154\) 0 0
\(155\) 9.72328 + 16.8412i 0.780992 + 1.35272i
\(156\) 0.637441 1.75135i 0.0510361 0.140220i
\(157\) 2.46198 + 4.26428i 0.196488 + 0.340326i 0.947387 0.320090i \(-0.103713\pi\)
−0.750900 + 0.660416i \(0.770380\pi\)
\(158\) 8.51367 + 14.7461i 0.677311 + 1.17314i
\(159\) −0.798133 0.951178i −0.0632961 0.0754333i
\(160\) 1.31908 + 2.28471i 0.104282 + 0.180622i
\(161\) 0 0
\(162\) −11.3944 4.14722i −0.895229 0.325837i
\(163\) −3.81908 6.61484i −0.299133 0.518114i 0.676805 0.736163i \(-0.263364\pi\)
−0.975938 + 0.218049i \(0.930031\pi\)
\(164\) −0.411474 −0.0321307
\(165\) −0.701867 + 1.92836i −0.0546402 + 0.150123i
\(166\) 3.68004 0.285627
\(167\) −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
\(170\) −6.61721 11.4613i −0.507517 0.879045i
\(171\) −1.13816 + 6.45480i −0.0870369 + 0.493611i
\(172\) 0.113341 0.196312i 0.00864215 0.0149687i
\(173\) 10.5346 18.2465i 0.800932 1.38725i −0.118071 0.993005i \(-0.537671\pi\)
0.919003 0.394250i \(-0.128995\pi\)
\(174\) 7.00846 19.2556i 0.531310 1.45976i
\(175\) 0 0
\(176\) 0.841367 1.45729i 0.0634204 0.109847i
\(177\) 1.25624 0.221510i 0.0944251 0.0166497i
\(178\) 10.9317 0.819366
\(179\) 2.56031 4.43458i 0.191366 0.331456i −0.754337 0.656487i \(-0.772041\pi\)
0.945703 + 0.325031i \(0.105375\pi\)
\(180\) −0.243756 + 1.38241i −0.0181685 + 0.103039i
\(181\) 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
\(184\) 0.312214 0.0230168
\(185\) −9.72328 16.8412i −0.714870 1.23819i
\(186\) 6.12970 16.8412i 0.449451 1.23486i
\(187\) 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 −0.434014 0.900906i \(-0.642903\pi\)
0.997215 0.0745858i \(-0.0237635\pi\)
\(192\) 5.09240 13.9912i 0.367512 1.00973i
\(193\) −3.02094 5.23243i −0.217452 0.376639i 0.736576 0.676355i \(-0.236441\pi\)
−0.954028 + 0.299716i \(0.903108\pi\)
\(194\) 18.3286 1.31592
\(195\) 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 \(0.144339\pi\)
\(198\) 1.77719 0.646844i 0.126299 0.0459692i
\(199\) 1.52094 2.63435i 0.107817 0.186744i −0.807069 0.590458i \(-0.798947\pi\)
0.914886 + 0.403713i \(0.132281\pi\)
\(200\) −4.15476 −0.293786
\(201\) 16.4402 2.89884i 1.15960 0.204469i
\(202\) −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
\(206\) 2.04916 3.54925i 0.142772 0.247288i
\(207\) 0.243756 + 0.204535i 0.0169422 + 0.0142162i
\(208\) −10.4704 18.1353i −0.725994 1.25746i
\(209\) −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 \(0.106559\pi\)
\(212\) 0.132474 0.00909837
\(213\) 7.84002 21.5403i 0.537189 1.47592i
\(214\) −8.78106 −0.600261
\(215\) 1.55303 + 2.68993i 0.105916 + 0.183452i
\(216\) 13.2460 7.64760i 0.901278 0.520353i
\(217\) 0 0
\(218\) −7.16637 12.4125i −0.485368 0.840682i
\(219\) 11.4324 + 13.6246i 0.772531 + 0.920667i
\(220\) −0.109470 0.189608i −0.00738049 0.0127834i
\(221\) −11.2947 19.5630i −0.759766 1.31595i
\(222\) −6.12970 + 16.8412i −0.411399 + 1.13031i
\(223\) 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
\(226\) −3.48751 6.04055i −0.231986 0.401811i
\(227\) 2.89393 0.192077 0.0960385 0.995378i \(-0.469383\pi\)
0.0960385 + 0.995378i \(0.469383\pi\)
\(228\) −0.449493 0.535685i −0.0297684 0.0354766i
\(229\) −9.16756 −0.605809 −0.302905 0.953021i \(-0.597956\pi\)
−0.302905 + 0.953021i \(0.597956\pi\)
\(230\) −0.180922 + 0.313366i −0.0119297 + 0.0206628i
\(231\) 0 0
\(232\) 12.9238 + 22.3847i 0.848489 + 1.46963i
\(233\) −6.63563 11.4932i −0.434715 0.752948i 0.562558 0.826758i \(-0.309817\pi\)
−0.997272 + 0.0738103i \(0.976484\pi\)
\(234\) 4.08693 23.1782i 0.267171 1.51520i
\(235\) 6.75150 11.6939i 0.440419 0.762828i
\(236\) −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 \(0.266478\pi\)
\(240\) 10.1382 + 12.0822i 0.654415 + 0.779902i
\(241\) 8.95811 0.577043 0.288521 0.957473i \(-0.406836\pi\)
0.288521 + 0.957473i \(0.406836\pi\)
\(242\) 7.26264 12.5793i 0.466860 0.808626i
\(243\) 15.3516 + 2.70691i 0.984808 + 0.173648i
\(244\) 0.177052 0.0113346
\(245\) 0 0
\(246\) −5.11721 + 0.902302i −0.326261 + 0.0575287i
\(247\) −12.7219 −0.809477
\(248\) 11.3033 + 19.5780i 0.717763 + 1.24320i
\(249\) −4.65910 + 0.821525i −0.295258 + 0.0520620i
\(250\) −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
\(255\) 10.9363 + 13.0334i 0.684857 + 0.816181i
\(256\) 2.19800 + 3.80704i 0.137375 + 0.237940i
\(257\) −10.8520 −0.676932 −0.338466 0.940979i \(-0.609908\pi\)
−0.338466 + 0.940979i \(0.609908\pi\)
\(258\) 0.979055 2.68993i 0.0609533 0.167468i
\(259\) 0 0
\(260\) −2.72462 −0.168974
\(261\) −4.57444 + 25.9430i −0.283151 + 1.60583i
\(262\) 7.65451 13.2580i 0.472897 0.819082i
\(263\) 26.0874 1.60862 0.804309 0.594211i \(-0.202536\pi\)
0.804309 + 0.594211i \(0.202536\pi\)
\(264\) −0.815923 + 2.24173i −0.0502166 + 0.137969i
\(265\) −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
\(269\) −3.81655 + 6.61046i −0.232699 + 0.403047i −0.958602 0.284751i \(-0.908089\pi\)
0.725902 + 0.687798i \(0.241422\pi\)
\(270\) 17.7265i 1.07880i
\(271\) 1.70187 + 2.94772i 0.103381 + 0.179061i 0.913076 0.407790i \(-0.133701\pi\)
−0.809695 + 0.586852i \(0.800367\pi\)
\(272\) −6.97565 12.0822i −0.422961 0.732590i
\(273\) 0 0
\(274\) 3.85638 6.67945i 0.232973 0.403520i
\(275\) 0.660444 0.0398263
\(276\) −0.0334331 + 0.00589515i −0.00201243 + 0.000354846i
\(277\) −5.72193 −0.343798 −0.171899 0.985115i \(-0.554990\pi\)
−0.171899 + 0.985115i \(0.554990\pi\)
\(278\) −0.622426 1.07807i −0.0373306 0.0646585i
\(279\) −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 \(-0.487916\pi\)
\(282\) −12.2554 + 2.16095i −0.729796 + 0.128683i
\(283\) 2.28564 + 3.95885i 0.135867 + 0.235329i 0.925929 0.377699i \(-0.123285\pi\)
−0.790061 + 0.613028i \(0.789951\pi\)
\(284\) 1.22281 + 2.11797i 0.0725605 + 0.125678i
\(285\) 9.43629 1.66387i 0.558958 0.0985593i
\(286\) 1.83544 + 3.17907i 0.108532 + 0.187982i
\(287\) 0 0
\(288\) −0.542766 + 3.07818i −0.0319828 + 0.181384i
\(289\) 0.975185 + 1.68907i 0.0573638 + 0.0993571i
\(290\) −29.9564 −1.75910
\(291\) −23.2049 + 4.09164i −1.36029 + 0.239856i
\(292\) −1.89756 −0.111046
\(293\) 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
\(296\) −11.3033 19.5780i −0.656994 1.13795i
\(297\) −2.10560 + 1.21567i −0.122179 + 0.0705403i
\(298\) −5.87733 + 10.1798i −0.340464 + 0.589702i
\(299\) −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
\(303\) 5.67159 15.5826i 0.325824 0.895195i
\(304\) −7.85710 −0.450635
\(305\) −1.21301 + 2.10100i −0.0694568 + 0.120303i
\(306\) 2.72281 15.4418i 0.155653 0.882751i
\(307\) −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
\(310\) −26.2003 −1.48808
\(311\) −10.9927 19.0400i −0.623340 1.07966i −0.988859 0.148853i \(-0.952442\pi\)
0.365519 0.930804i \(-0.380892\pi\)
\(312\) 19.0829 + 22.7421i 1.08036 + 1.28752i
\(313\) −6.94491 + 12.0289i −0.392549 + 0.679915i −0.992785 0.119908i \(-0.961740\pi\)
0.600236 + 0.799823i \(0.295073\pi\)
\(314\) −6.63404 −0.374380
\(315\) 0 0
\(316\) 2.33544 0.131379
\(317\) 3.09105 5.35386i 0.173611 0.300703i −0.766069 0.642759i \(-0.777790\pi\)
0.939680 + 0.342056i \(0.111123\pi\)
\(318\) 1.64749 0.290497i 0.0923866 0.0162903i
\(319\) −2.05438 3.55829i −0.115023 0.199226i
\(320\) −21.7665 −1.21678
\(321\) 11.1172 1.96026i 0.620502 0.109411i
\(322\) 0 0
\(323\) −8.47565 −0.471598
\(324\) −1.27403 + 1.06904i −0.0707796 + 0.0593912i
\(325\) 4.10947 7.11781i 0.227952 0.394825i
\(326\) 10.2909 0.569958
\(327\) 11.8439 + 14.1150i 0.654969 + 0.780561i
\(328\) 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 −0.974968 0.222346i \(-0.928628\pi\)
0.680041 + 0.733174i \(0.261962\pi\)
\(332\) 0.252374 0.437124i 0.0138508 0.0239903i
\(333\) 4.00088 22.6901i 0.219247 1.24341i
\(334\) −3.80974 6.59867i −0.208460 0.361063i
\(335\) −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 \(-0.00237726\pi\)
\(338\) 28.1676 1.53211
\(339\) 5.76382 + 6.86906i 0.313048 + 0.373076i
\(340\) −1.81521 −0.0984434
\(341\) −1.79679 3.11213i −0.0973016 0.168531i
\(342\) −6.76470 5.67626i −0.365793 0.306937i
\(343\) 0 0
\(344\) 1.80541 + 3.12706i 0.0973410 + 0.168600i
\(345\) 0.159100 0.437124i 0.00856567 0.0235340i
\(346\) 14.1932 + 24.5834i 0.763034 + 1.32161i
\(347\) 10.2062 + 17.6777i 0.547898 + 0.948987i 0.998418 + 0.0562207i \(0.0179050\pi\)
−0.450521 + 0.892766i \(0.648762\pi\)
\(348\) −1.80659 2.15301i −0.0968434 0.115413i
\(349\) −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
\(352\) −0.243756 0.422197i −0.0129922 0.0225032i
\(353\) −10.0223 −0.533433 −0.266716 0.963775i \(-0.585939\pi\)
−0.266716 + 0.963775i \(0.585939\pi\)
\(354\) −0.587811 + 1.61500i −0.0312418 + 0.0858361i
\(355\) −33.5107 −1.77857
\(356\) 0.749686 1.29849i 0.0397333 0.0688200i
\(357\) 0 0
\(358\) 3.44949 + 5.97470i 0.182311 + 0.315773i
\(359\) −4.74035 8.21053i −0.250186 0.433335i 0.713391 0.700766i \(-0.247159\pi\)
−0.963577 + 0.267431i \(0.913825\pi\)
\(360\) −17.1288 14.3728i −0.902768 0.757512i
\(361\) 7.11334 12.3207i 0.374386 0.648456i
\(362\) −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
\(366\) 2.20187 0.388249i 0.115093 0.0202941i
\(367\) −16.1334 −0.842157 −0.421079 0.907024i \(-0.638348\pi\)
−0.421079 + 0.907024i \(0.638348\pi\)
\(368\) −0.190722 + 0.330341i −0.00994209 + 0.0172202i
\(369\) 6.27719 2.28471i 0.326777 0.118937i
\(370\) 26.2003 1.36209
\(371\) 0 0
\(372\) −1.58007 1.88305i −0.0819228 0.0976318i
\(373\) 14.0496 0.727462 0.363731 0.931504i \(-0.381503\pi\)
0.363731 + 0.931504i \(0.381503\pi\)
\(374\) 1.22281 + 2.11797i 0.0632301 + 0.109518i
\(375\) 5.38279 14.7891i 0.277966 0.763705i
\(376\) 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
\(381\) −5.26171 + 14.4564i −0.269565 + 0.740625i
\(382\) 10.4868 + 18.1637i 0.536551 + 0.929334i
\(383\) 32.0205 1.63617 0.818086 0.575095i \(-0.195035\pi\)
0.818086 + 0.575095i \(0.195035\pi\)
\(384\) 10.5744 + 12.6021i 0.539625 + 0.643100i
\(385\) 0 0
\(386\) 8.14022 0.414326
\(387\) −0.639033 + 3.62414i −0.0324839 + 0.184225i
\(388\) 1.25696 2.17712i 0.0638124 0.110526i
\(389\) −30.0428 −1.52323 −0.761616 0.648029i \(-0.775594\pi\)
−0.761616 + 0.648029i \(0.775594\pi\)
\(390\) −33.8842 + 5.97470i −1.71579 + 0.302541i
\(391\) −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
\(395\) −16.0005 + 27.7136i −0.805071 + 1.39442i
\(396\) 0.0450442 0.255459i 0.00226356 0.0128373i
\(397\) −6.15998 10.6694i −0.309160 0.535482i 0.669019 0.743246i \(-0.266715\pi\)
−0.978179 + 0.207764i \(0.933381\pi\)
\(398\) 2.04916 + 3.54925i 0.102715 + 0.177908i
\(399\) 0 0
\(400\) 2.53802 4.39598i 0.126901 0.219799i
\(401\) 20.9760 1.04749 0.523745 0.851875i \(-0.324535\pi\)
0.523745 + 0.851875i \(0.324535\pi\)
\(402\) −7.69253 + 21.1351i −0.383669 + 1.05412i
\(403\) −44.7205 −2.22769
\(404\) 0.884600 + 1.53217i 0.0440105 + 0.0762284i
\(405\) −3.95723 22.4426i −0.196637 1.11518i
\(406\) 0 0
\(407\) 1.79679 + 3.11213i 0.0890635 + 0.154263i
\(408\) 12.7135 + 15.1513i 0.629411 + 0.750103i
\(409\) 12.8307 + 22.2234i 0.634437 + 1.09888i 0.986634 + 0.162951i \(0.0521012\pi\)
−0.352197 + 0.935926i \(0.614565\pi\)
\(410\) 3.79813 + 6.57856i 0.187576 + 0.324892i
\(411\) −3.39124 + 9.31737i −0.167278 + 0.459592i
\(412\) −0.281059 0.486809i −0.0138468 0.0239833i
\(413\) 0 0
\(414\) −0.402856 + 0.146628i −0.0197993 + 0.00720635i
\(415\) 3.45811 + 5.98962i 0.169752 + 0.294019i
\(416\) −6.06687 −0.297453
\(417\) 1.02869 + 1.22594i 0.0503749 + 0.0600345i
\(418\) 1.37733 0.0673672
\(419\) −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 \(0.936814\pi\)
\(422\) 3.67365 + 6.36295i 0.178830 + 0.309743i
\(423\) 15.0334 5.47172i 0.730951 0.266044i
\(424\) −1.05509 + 1.82747i −0.0512398 + 0.0887500i
\(425\) 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
\(429\) −3.03343 3.61510i −0.146456 0.174539i
\(430\) −4.18479 −0.201809
\(431\) −8.86349 + 15.3520i −0.426939 + 0.739481i −0.996599 0.0823997i \(-0.973742\pi\)
0.569660 + 0.821881i \(0.307075\pi\)
\(432\) 18.6867i 0.899067i
\(433\) 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
\(436\) −1.96585 −0.0941472
\(437\) 0.115867 + 0.200688i 0.00554267 + 0.00960019i
\(438\) −23.5985 + 4.16106i −1.12758 + 0.198823i
\(439\) 14.9277 25.8555i 0.712459 1.23401i −0.251473 0.967864i \(-0.580915\pi\)
0.963931 0.266151i \(-0.0857518\pi\)
\(440\) 3.48751 0.166261
\(441\) 0 0
\(442\) 30.4347 1.44763
\(443\) −5.33275 + 9.23659i −0.253367 + 0.438844i −0.964451 0.264263i \(-0.914871\pi\)
0.711084 + 0.703107i \(0.248205\pi\)
\(444\) 1.58007 + 1.88305i 0.0749868 + 0.0893658i
\(445\) 10.2724 + 17.7924i 0.486960 + 0.843440i
\(446\) −19.1215 −0.905432
\(447\) 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 \(0.473272\pi\)
\(450\) 5.36097 1.95123i 0.252718 0.0919820i
\(451\) −0.520945 + 0.902302i −0.0245303 + 0.0424878i
\(452\) −0.956680 −0.0449985
\(453\) 10.9161 29.9916i 0.512881 1.40913i
\(454\) −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 −0.918772 0.394789i \(-0.870818\pi\)
0.801283 + 0.598285i \(0.204151\pi\)
\(458\) 6.17571 10.6966i 0.288572 0.499821i
\(459\) 20.1579i 0.940889i
\(460\) 0.0248149 + 0.0429807i 0.00115700 + 0.00200399i
\(461\) 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 \(0.0593600\pi\)
\(464\) −31.5790 −1.46602
\(465\) 33.1707 5.84889i 1.53825 0.271236i
\(466\) 17.8803 0.828290
\(467\) −1.68433 2.91734i −0.0779413 0.134998i 0.824420 0.565978i \(-0.191501\pi\)
−0.902362 + 0.430980i \(0.858168\pi\)
\(468\) −2.47288 2.07499i −0.114309 0.0959165i
\(469\) 0 0
\(470\) 9.09627 + 15.7552i 0.419579 + 0.726733i
\(471\) 8.39899 1.48097i 0.387005 0.0682394i
\(472\) −1.08394 1.87744i −0.0498924 0.0864162i
\(473\) −0.286989 0.497079i −0.0131958 0.0228557i
\(474\) 29.0442 5.12127i 1.33404 0.235228i
\(475\) −1.54189 2.67063i −0.0707467 0.122537i
\(476\) 0 0
\(477\) −2.02094 + 0.735564i −0.0925327 + 0.0336791i
\(478\) −6.42468 11.1279i −0.293858 0.508977i
\(479\) 36.7665 1.67990 0.839952 0.542660i \(-0.182583\pi\)
0.839952 + 0.542660i \(0.182583\pi\)
\(480\) 4.50000 0.793471i 0.205396 0.0362168i
\(481\) 44.7205 2.03908
\(482\) −6.03462 + 10.4523i −0.274869 + 0.476087i
\(483\) 0 0
\(484\) −0.996130 1.72535i −0.0452786 0.0784249i
\(485\) 17.2233 + 29.8316i 0.782069 + 1.35458i
\(486\) −13.5000 + 16.0887i −0.612372 + 0.729797i
\(487\) 18.7087 32.4045i 0.847773 1.46839i −0.0354172 0.999373i \(-0.511276\pi\)
0.883191 0.469014i \(-0.155391\pi\)
\(488\) −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 \(-0.0388879\pi\)
\(492\) −0.243756 + 0.669713i −0.0109894 + 0.0301930i
\(493\) −34.0651 −1.53422
\(494\) 8.57011 14.8439i 0.385587 0.667857i
\(495\) 2.72281 + 2.28471i 0.122381 + 0.102690i
\(496\) −27.6195 −1.24015
\(497\) 0 0
\(498\) 2.18004 5.98962i 0.0976901 0.268401i
\(499\) 33.7452 1.51064 0.755320 0.655356i \(-0.227481\pi\)
0.755320 + 0.655356i \(0.227481\pi\)
\(500\) 0.839556 + 1.45415i 0.0375461 + 0.0650317i
\(501\) 6.29638 + 7.50373i 0.281301 + 0.335242i
\(502\) −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
\(507\) −35.6614 + 6.28806i −1.58378 + 0.279263i
\(508\) −0.820670 1.42144i −0.0364114 0.0630663i
\(509\) 7.93851 0.351868 0.175934 0.984402i \(-0.443705\pi\)
0.175934 + 0.984402i \(0.443705\pi\)
\(510\) −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
\(514\) 7.31046 12.6621i 0.322451 0.558501i
\(515\) 7.70233 0.339405
\(516\) −0.252374 0.300767i −0.0111101 0.0132405i
\(517\) −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
\(521\) −7.33750 + 12.7089i −0.321462 + 0.556788i −0.980790 0.195067i \(-0.937507\pi\)
0.659328 + 0.751855i \(0.270841\pi\)
\(522\) −27.1885 22.8139i −1.19001 0.998536i
\(523\) 14.1716 + 24.5459i 0.619680 + 1.07332i 0.989544 + 0.144232i \(0.0460711\pi\)
−0.369864 + 0.929086i \(0.620596\pi\)
\(524\) −1.04988 1.81844i −0.0458641 0.0794390i
\(525\) 0 0
\(526\) −17.5737 + 30.4386i −0.766251 + 1.32719i
\(527\) −29.7939 −1.29784
\(528\) −1.87346 2.23270i −0.0815317 0.0971657i
\(529\) −22.9887 −0.999511
\(530\) −1.22281 2.11797i −0.0531155 0.0919988i
\(531\) 0.383666 2.17588i 0.0166497 0.0944251i
\(532\) 0 0
\(533\) 6.48293 + 11.2288i 0.280807 + 0.486371i
\(534\) 6.47590 17.7924i 0.280240 0.769952i
\(535\) −8.25150 14.2920i −0.356743 0.617898i
\(536\) −14.1853 24.5696i −0.612710 1.06124i
\(537\) −5.70099 6.79417i −0.246016 0.293190i
\(538\) −5.14203 8.90625i −0.221688 0.383976i
\(539\) 0 0
\(540\) 2.10560 + 1.21567i 0.0906106 + 0.0523141i
\(541\) −5.64290 9.77380i −0.242607 0.420208i 0.718849 0.695166i \(-0.244669\pi\)
−0.961456 + 0.274958i \(0.911336\pi\)
\(542\) −4.58584 −0.196979
\(543\) 0.189540 0.520758i 0.00813395 0.0223478i
\(544\) −4.04189 −0.173295
\(545\) 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 \(0.618385\pi\)
\(548\) −0.528934 0.916140i −0.0225949 0.0391356i
\(549\) −2.70099 + 0.983080i −0.115275 + 0.0419568i
\(550\) −0.444907 + 0.770602i −0.0189709 + 0.0328586i
\(551\) −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
\(555\) −33.1707 + 5.84889i −1.40802 + 0.248272i
\(556\) −0.170741 −0.00724105
\(557\) 0.387841 0.671761i 0.0164334 0.0284634i −0.857692 0.514164i \(-0.828102\pi\)
0.874125 + 0.485701i \(0.161436\pi\)
\(558\) −23.7795 19.9533i −1.00667 0.844692i
\(559\) −7.14290 −0.302113
\(560\) 0 0
\(561\) −2.02094 2.40847i −0.0853243 0.101686i
\(562\) 38.2327 1.61275
\(563\) 12.4761 + 21.6093i 0.525806 + 0.910722i 0.999548 + 0.0300588i \(0.00956944\pi\)
−0.473742 + 0.880663i \(0.657097\pi\)
\(564\) −0.583778 + 1.60392i −0.0245815 + 0.0675371i
\(565\) 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 −0.479827 0.877363i \(-0.659301\pi\)
0.999732 0.0231391i \(-0.00736608\pi\)
\(570\) −4.41534 + 12.1311i −0.184938 + 0.508114i
\(571\) −4.39827 7.61803i −0.184062 0.318805i 0.759198 0.650860i \(-0.225591\pi\)
−0.943260 + 0.332055i \(0.892258\pi\)
\(572\) 0.503490 0.0210520
\(573\) −17.3316 20.6550i −0.724037 0.862873i
\(574\) 0 0
\(575\) −0.149711 −0.00624336
\(576\) −19.7554 16.5767i −0.823140 0.690697i
\(577\) −6.43717 + 11.1495i −0.267983 + 0.464160i −0.968341 0.249632i \(-0.919690\pi\)
0.700358 + 0.713792i \(0.253024\pi\)
\(578\) −2.62773 −0.109299
\(579\) −10.3059 + 1.81720i −0.428298 + 0.0755204i
\(580\) −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
\(584\) 15.1131 26.1766i 0.625384 1.08320i
\(585\) 41.5651 15.1285i 1.71851 0.625485i
\(586\) 2.91534 + 5.04952i 0.120432 + 0.208594i
\(587\) 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
\(590\) 2.51249 0.103438
\(591\) 14.9488 41.0714i 0.614911 1.68945i
\(592\) 27.6195 1.13515
\(593\) 1.88026 + 3.25671i 0.0772131 + 0.133737i 0.902047 0.431639i \(-0.142064\pi\)
−0.824833 + 0.565376i \(0.808731\pi\)
\(594\) 3.27573i 0.134405i
\(595\) 0 0
\(596\) 0.806123 + 1.39625i 0.0330201 + 0.0571924i
\(597\) −3.38666 4.03606i −0.138607 0.165185i
\(598\) −0.416060 0.720637i −0.0170139 0.0294690i
\(599\) 1.84524 + 3.19604i 0.0753943 + 0.130587i 0.901258 0.433283i \(-0.142645\pi\)
−0.825863 + 0.563870i \(0.809312\pi\)
\(600\) −2.46127 + 6.76227i −0.100481 + 0.276069i
\(601\) −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
\(604\) 1.70258 + 2.94896i 0.0692771 + 0.119991i
\(605\) 27.2986 1.10985
\(606\) 14.3610 + 17.1147i 0.583374 + 0.695239i
\(607\) −24.3946 −0.990145 −0.495072 0.868852i \(-0.664858\pi\)
−0.495072 + 0.868852i \(0.664858\pi\)
\(608\) −1.13816 + 1.97134i −0.0461583 + 0.0799485i
\(609\) 0 0
\(610\) −1.63429 2.83067i −0.0661703 0.114610i
\(611\) 15.5262 + 26.8921i 0.628121 + 1.08794i
\(612\) −1.64749 1.38241i −0.0665958 0.0558805i
\(613\) −21.0107 + 36.3917i −0.848616 + 1.46985i 0.0338284 + 0.999428i \(0.489230\pi\)
−0.882444 + 0.470418i \(0.844103\pi\)
\(614\) 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 \(0.782788\pi\)
\(618\) −4.56283 5.43777i −0.183544 0.218739i
\(619\) 27.2094 1.09364 0.546820 0.837250i \(-0.315838\pi\)
0.546820 + 0.837250i \(0.315838\pi\)
\(620\) −1.79679 + 3.11213i −0.0721608 + 0.124986i
\(621\) 0.477301 0.275570i 0.0191534 0.0110582i
\(622\) 29.6209 1.18769
\(623\) 0 0
\(624\) −35.7196 + 6.29833i −1.42993 + 0.252135i
\(625\) −30.0651 −1.20260
\(626\) −9.35685 16.2065i −0.373975 0.647743i
\(627\) −1.74376 + 0.307471i −0.0696389 + 0.0122792i
\(628\) −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
\(633\) −6.07145 7.23567i −0.241319 0.287592i
\(634\) 4.16456 + 7.21324i 0.165396 + 0.286474i
\(635\) 22.4902 0.892496
\(636\) 0.0784773 0.215615i 0.00311183 0.00854968i
\(637\) 0 0
\(638\) 5.53571 0.219161
\(639\) −30.4145 25.5208i −1.20318 1.00959i
\(640\) 12.0248 20.8276i 0.475323 0.823283i
\(641\) −0.279000 −0.0110198 −0.00550991 0.999985i \(-0.501754\pi\)
−0.00550991 + 0.999985i \(0.501754\pi\)
\(642\) −5.20187 + 14.2920i −0.205301 + 0.564061i
\(643\) −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
\(647\) 11.2285 19.4483i 0.441438 0.764592i −0.556359 0.830942i \(-0.687802\pi\)
0.997796 + 0.0663498i \(0.0211353\pi\)
\(648\) −4.60030 26.0896i −0.180717 1.02490i
\(649\) 0.172304 + 0.298439i 0.00676352 + 0.0117148i
\(650\) 5.53667 + 9.58980i 0.217166 + 0.376143i
\(651\) 0 0
\(652\) 0.705737 1.22237i 0.0276388 0.0478718i
\(653\) −50.5313 −1.97744 −0.988721 0.149771i \(-0.952146\pi\)
−0.988721 + 0.149771i \(0.952146\pi\)
\(654\) −24.4479 + 4.31082i −0.955989 + 0.168567i
\(655\) 28.7716 1.12420
\(656\) 4.00387 + 6.93491i 0.156325 + 0.270763i
\(657\) 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 \(0.816756\pi\)
\(660\) −0.373455 + 0.0658503i −0.0145367 + 0.00256322i
\(661\) −17.3050 29.9731i −0.673086 1.16582i −0.977024 0.213128i \(-0.931635\pi\)
0.303938 0.952692i \(-0.401698\pi\)
\(662\) −7.22921 12.5214i −0.280971 0.486656i
\(663\) −38.5317 + 6.79417i −1.49645 + 0.263864i
\(664\) 4.02007 + 6.96296i 0.156009 + 0.270215i
\(665\) 0 0
\(666\) 23.7795 + 19.9533i 0.921436 + 0.773176i
\(667\) 0.465690 + 0.806598i 0.0180316 + 0.0312316i
\(668\) −1.04507 −0.0404351
\(669\) 24.2087 4.26865i 0.935964 0.165036i
\(670\) 32.8803 1.27028
\(671\) 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 \(0.936430\pi\)
\(674\) 12.5262 + 21.6959i 0.482490 + 0.835697i
\(675\) −6.35163 + 3.66712i −0.244474 + 0.141147i
\(676\) 1.93170 3.34581i 0.0742963 0.128685i
\(677\) −21.8790 + 37.8955i −0.840877 + 1.45644i 0.0482766 + 0.998834i \(0.484627\pi\)
−0.889154 + 0.457608i \(0.848706\pi\)
\(678\) −11.8976 + 2.09786i −0.456923 + 0.0805678i
\(679\) 0 0
\(680\) 14.4572 25.0407i 0.554410 0.960266i
\(681\) 1.71436 4.71015i 0.0656942 0.180493i
\(682\) 4.84161 0.185395
\(683\) −14.1206 + 24.4576i −0.540310 + 0.935845i 0.458576 + 0.888655i \(0.348360\pi\)
−0.998886 + 0.0471895i \(0.984974\pi\)
\(684\) −1.13816 + 0.414255i −0.0435185 + 0.0158394i
\(685\) 14.4953 0.553835
\(686\) 0 0
\(687\) −5.43083 + 14.9211i −0.207199 + 0.569274i
\(688\) −4.41147 −0.168186
\(689\) −2.08718 3.61510i −0.0795153 0.137725i
\(690\) 0.402856 + 0.480105i 0.0153365 + 0.0182773i
\(691\) −14.5326 + 25.1711i −0.552844 + 0.957555i 0.445223 + 0.895420i \(0.353124\pi\)
−0.998068 + 0.0621351i \(0.980209\pi\)
\(692\) 3.89344 0.148006
\(693\) 0 0
\(694\) −27.5016 −1.04395
\(695\) 1.16978 2.02611i 0.0443722 0.0768549i
\(696\) 44.0892 7.77412i 1.67120 0.294677i
\(697\) 4.31908 + 7.48086i 0.163597 + 0.283358i
\(698\) 4.79923 0.181654
\(699\) −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
\(703\) 8.38965 14.5313i 0.316422 0.548059i
\(704\) 4.02229 0.151596
\(705\) −15.0334 17.9161i −0.566192 0.674761i
\(706\) 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 −0.638874 0.769311i \(-0.720600\pi\)
0.985680 + 0.168626i \(0.0539329\pi\)
\(710\) 22.5744 39.1001i 0.847204 1.46740i
\(711\) −35.6279 + 12.9675i −1.33615 + 0.486320i
\(712\) 11.9418 + 20.6837i 0.447536 + 0.775155i
\(713\) 0.407299 + 0.705463i 0.0152535 + 0.0264198i
\(714\) 0 0
\(715\) −3.44949 + 5.97470i −0.129004 + 0.223441i
\(716\) 0.946251 0.0353631
\(717\) 10.6181 + 12.6541i 0.396540 + 0.472578i
\(718\) 12.7733 0.476696
\(719\) −16.8885 29.2517i −0.629834 1.09090i −0.987585 0.157087i \(-0.949790\pi\)
0.357751 0.933817i \(-0.383544\pi\)
\(720\) 25.6707 9.34337i 0.956691 0.348207i
\(721\) 0 0
\(722\) 9.58378 + 16.5996i 0.356671 + 0.617773i
\(723\) 5.30675 14.5802i 0.197360 0.542243i
\(724\) 0.0295627 + 0.0512040i 0.00109869 + 0.00190298i
\(725\) −6.19712 10.7337i −0.230155 0.398641i
\(726\) −16.1716 19.2725i −0.600184 0.715271i
\(727\) 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
\(730\) 17.5155 + 30.3377i 0.648277 + 1.12285i
\(731\) −4.75877 −0.176009
\(732\) 0.104885 0.288169i 0.00387665 0.0106510i
\(733\) 13.6364 0.503672 0.251836 0.967770i \(-0.418966\pi\)
0.251836 + 0.967770i \(0.418966\pi\)
\(734\) 10.8682 18.8243i 0.401154 0.694819i
\(735\) 0 0
\(736\) 0.0552549 + 0.0957044i 0.00203672 + 0.00352771i
\(737\) 2.25490 + 3.90560i 0.0830603 + 0.143865i
\(738\) −1.56283 + 8.86327i −0.0575287 + 0.326261i
\(739\) 16.0209 27.7491i 0.589340 1.02077i −0.404979 0.914326i \(-0.632721\pi\)
0.994319 0.106441i \(-0.0339455\pi\)
\(740\) 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 \(0.954149\pi\)
\(744\) 38.5611 6.79936i 1.41372 0.249277i
\(745\) −22.0915 −0.809371
\(746\) −9.46451 + 16.3930i −0.346520 + 0.600191i
\(747\) −1.42292 + 8.06980i −0.0520620 + 0.295258i
\(748\) 0.335437 0.0122648
\(749\) 0 0
\(750\) 13.6297 + 16.2432i 0.497686 + 0.593119i
\(751\) 26.1165 0.953004 0.476502 0.879173i \(-0.341904\pi\)
0.476502 + 0.879173i \(0.341904\pi\)
\(752\) 9.58899 + 16.6086i 0.349675 + 0.605654i
\(753\) 14.8089 40.6870i 0.539665 1.48272i
\(754\) 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
\(759\) −0.0294005 + 0.0807773i −0.00106717 + 0.00293203i
\(760\) −8.14203 14.1024i −0.295342 0.511548i
\(761\) −40.7648 −1.47772 −0.738861 0.673858i \(-0.764636\pi\)
−0.738861 + 0.673858i \(0.764636\pi\)
\(762\) −13.3231 15.8779i −0.482645 0.575194i
\(763\) 0 0
\(764\) 2.87670 0.104075
\(765\) 27.6917 10.0789i 1.00119 0.364405i
\(766\) −21.5706 + 37.3613i −0.779377 + 1.34992i
\(767\) 4.28850 0.154849
\(768\) 7.49841 1.32217i 0.270575 0.0477098i
\(769\) 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
\(773\) 12.4513 21.5663i 0.447842 0.775686i −0.550403 0.834899i \(-0.685526\pi\)
0.998245 + 0.0592135i \(0.0188593\pi\)
\(774\) −3.79813 3.18701i −0.136521 0.114555i
\(775\) −5.42009 9.38788i −0.194695 0.337222i
\(776\) 20.0221 + 34.6793i 0.718752 + 1.24492i
\(777\) 0 0
\(778\) 20.2383 35.0538i 0.725578 1.25674i
\(779\) 4.86484 0.174301
\(780\) −1.61406 + 4.43458i