Properties

Label 441.2.h.e.214.2
Level $441$
Weight $2$
Character 441.214
Analytic conductor $3.521$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

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

Embedding invariants

Embedding label 214.2
Root \(-0.173648 + 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.e.373.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.34730 q^{2} +(1.11334 - 1.32683i) q^{3} -0.184793 q^{4} +(1.26604 - 2.19285i) q^{5} +(1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(-0.520945 - 2.95442i) q^{9} +O(q^{10})\) \(q+1.34730 q^{2} +(1.11334 - 1.32683i) q^{3} -0.184793 q^{4} +(1.26604 - 2.19285i) q^{5} +(1.50000 - 1.78763i) q^{6} -2.94356 q^{8} +(-0.520945 - 2.95442i) q^{9} +(1.70574 - 2.95442i) q^{10} +(-0.233956 - 0.405223i) q^{11} +(-0.205737 + 0.245188i) q^{12} +(2.91147 + 5.04282i) q^{13} +(-1.50000 - 4.12122i) q^{15} -3.59627 q^{16} +(1.93969 - 3.35965i) q^{17} +(-0.701867 - 3.98048i) q^{18} +(-1.09240 - 1.89209i) q^{19} +(-0.233956 + 0.405223i) q^{20} +(-0.315207 - 0.545955i) q^{22} +(0.0530334 - 0.0918566i) q^{23} +(-3.27719 + 3.90560i) q^{24} +(-0.705737 - 1.22237i) q^{25} +(3.92262 + 6.79417i) q^{26} +(-4.50000 - 2.59808i) q^{27} +(-4.39053 + 7.60462i) q^{29} +(-2.02094 - 5.55250i) q^{30} +7.68004 q^{31} +1.04189 q^{32} +(-0.798133 - 0.140732i) q^{33} +(2.61334 - 4.52644i) q^{34} +(0.0962667 + 0.545955i) q^{36} +(3.84002 + 6.65111i) q^{37} +(-1.47178 - 2.54920i) q^{38} +(9.93242 + 1.75135i) q^{39} +(-3.72668 + 6.45480i) q^{40} +(-1.11334 - 1.92836i) q^{41} +(-0.613341 + 1.06234i) q^{43} +(0.0432332 + 0.0748822i) q^{44} +(-7.13816 - 2.59808i) q^{45} +(0.0714517 - 0.123758i) q^{46} +5.33275 q^{47} +(-4.00387 + 4.77163i) q^{48} +(-0.950837 - 1.64690i) q^{50} +(-2.29813 - 6.31407i) q^{51} +(-0.538019 - 0.931876i) q^{52} +(0.358441 - 0.620838i) q^{53} +(-6.06283 - 3.50038i) q^{54} -1.18479 q^{55} +(-3.72668 - 0.657115i) q^{57} +(-5.91534 + 10.2457i) q^{58} -0.736482 q^{59} +(0.277189 + 0.761570i) q^{60} -0.958111 q^{61} +10.3473 q^{62} +8.59627 q^{64} +14.7442 q^{65} +(-1.07532 - 0.189608i) q^{66} -9.63816 q^{67} +(-0.358441 + 0.620838i) q^{68} +(-0.0628336 - 0.172634i) q^{69} +13.2344 q^{71} +(1.53343 + 8.69653i) q^{72} +(-5.13429 + 8.89284i) q^{73} +(5.17365 + 8.96102i) q^{74} +(-2.40760 - 0.424525i) q^{75} +(0.201867 + 0.349643i) q^{76} +(13.3819 + 2.35959i) q^{78} -12.6382 q^{79} +(-4.55303 + 7.88609i) q^{80} +(-8.45723 + 3.07818i) q^{81} +(-1.50000 - 2.59808i) q^{82} +(-1.36571 + 2.36549i) q^{83} +(-4.91147 - 8.50692i) q^{85} +(-0.826352 + 1.43128i) q^{86} +(5.20187 + 14.2920i) q^{87} +(0.688663 + 1.19280i) q^{88} +(-4.05690 - 7.02676i) q^{89} +(-9.61721 - 3.50038i) q^{90} +(-0.00980018 + 0.0169744i) q^{92} +(8.55051 - 10.1901i) q^{93} +7.18479 q^{94} -5.53209 q^{95} +(1.15998 - 1.38241i) q^{96} +(-6.80200 + 11.7814i) q^{97} +(-1.07532 + 0.902302i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6q + 6q^{2} + 6q^{4} + 3q^{5} + 9q^{6} + 12q^{8} + O(q^{10}) \) \( 6q + 6q^{2} + 6q^{4} + 3q^{5} + 9q^{6} + 12q^{8} - 6q^{11} + 9q^{12} - 3q^{13} - 9q^{15} + 6q^{16} + 6q^{17} - 18q^{18} - 3q^{19} - 6q^{20} - 9q^{22} - 12q^{23} - 9q^{24} + 6q^{25} - 3q^{26} - 27q^{27} - 9q^{29} - 9q^{30} + 6q^{31} + 9q^{33} + 9q^{34} - 27q^{36} + 3q^{37} + 6q^{38} + 36q^{39} - 9q^{40} + 3q^{43} - 15q^{44} - 9q^{45} - 6q^{47} + 6q^{50} - 21q^{52} - 6q^{53} - 27q^{54} - 9q^{57} + 9q^{58} + 6q^{59} - 9q^{60} - 12q^{61} + 60q^{62} + 24q^{64} + 30q^{65} + 18q^{66} - 24q^{67} + 6q^{68} + 9q^{69} + 18q^{71} - 9q^{72} - 21q^{73} + 30q^{74} - 18q^{75} + 15q^{76} + 54q^{78} - 42q^{79} - 15q^{80} - 9q^{82} - 18q^{83} - 9q^{85} - 6q^{86} + 45q^{87} - 27q^{88} + 12q^{89} - 27q^{90} - 3q^{92} + 54q^{93} + 36q^{94} - 24q^{95} + 27q^{96} - 3q^{97} + 18q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.34730 0.952682 0.476341 0.879261i \(-0.341963\pi\)
0.476341 + 0.879261i \(0.341963\pi\)
\(3\) 1.11334 1.32683i 0.642788 0.766044i
\(4\) −0.184793 −0.0923963
\(5\) 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
\(9\) −0.520945 2.95442i −0.173648 0.984808i
\(10\) 1.70574 2.95442i 0.539401 0.934271i
\(11\) −0.233956 0.405223i −0.0705403 0.122179i 0.828598 0.559844i \(-0.189139\pi\)
−0.899138 + 0.437665i \(0.855806\pi\)
\(12\) −0.205737 + 0.245188i −0.0593912 + 0.0707796i
\(13\) 2.91147 + 5.04282i 0.807498 + 1.39863i 0.914592 + 0.404378i \(0.132512\pi\)
−0.107094 + 0.994249i \(0.534155\pi\)
\(14\) 0 0
\(15\) −1.50000 4.12122i −0.387298 1.06409i
\(16\) −3.59627 −0.899067
\(17\) 1.93969 3.35965i 0.470445 0.814834i −0.528984 0.848632i \(-0.677427\pi\)
0.999429 + 0.0337978i \(0.0107602\pi\)
\(18\) −0.701867 3.98048i −0.165432 0.938209i
\(19\) −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
\(23\) 0.0530334 0.0918566i 0.0110582 0.0191534i −0.860443 0.509546i \(-0.829813\pi\)
0.871502 + 0.490393i \(0.163147\pi\)
\(24\) −3.27719 + 3.90560i −0.668953 + 0.797228i
\(25\) −0.705737 1.22237i −0.141147 0.244474i
\(26\) 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 0.0938108 + 0.995590i \(0.470095\pi\)
−0.909112 + 0.416552i \(0.863238\pi\)
\(30\) −2.02094 5.55250i −0.368972 1.01374i
\(31\) 7.68004 1.37938 0.689688 0.724106i \(-0.257748\pi\)
0.689688 + 0.724106i \(0.257748\pi\)
\(32\) 1.04189 0.184182
\(33\) −0.798133 0.140732i −0.138937 0.0244984i
\(34\) 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 \(0.615857\pi\)
\(38\) −1.47178 2.54920i −0.238754 0.413535i
\(39\) 9.93242 + 1.75135i 1.59046 + 0.280441i
\(40\) −3.72668 + 6.45480i −0.589240 + 1.02059i
\(41\) −1.11334 1.92836i −0.173875 0.301160i 0.765897 0.642964i \(-0.222295\pi\)
−0.939771 + 0.341804i \(0.888962\pi\)
\(42\) 0 0
\(43\) −0.613341 + 1.06234i −0.0935336 + 0.162005i −0.908996 0.416806i \(-0.863150\pi\)
0.815462 + 0.578811i \(0.196483\pi\)
\(44\) 0.0432332 + 0.0748822i 0.00651766 + 0.0112889i
\(45\) −7.13816 2.59808i −1.06409 0.387298i
\(46\) 0.0714517 0.123758i 0.0105350 0.0182471i
\(47\) 5.33275 0.777861 0.388931 0.921267i \(-0.372845\pi\)
0.388931 + 0.921267i \(0.372845\pi\)
\(48\) −4.00387 + 4.77163i −0.577909 + 0.688725i
\(49\) 0 0
\(50\) −0.950837 1.64690i −0.134469 0.232907i
\(51\) −2.29813 6.31407i −0.321803 0.884147i
\(52\) −0.538019 0.931876i −0.0746098 0.129228i
\(53\) 0.358441 0.620838i 0.0492356 0.0852786i −0.840357 0.542033i \(-0.817655\pi\)
0.889593 + 0.456754i \(0.150988\pi\)
\(54\) −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
\(59\) −0.736482 −0.0958818 −0.0479409 0.998850i \(-0.515266\pi\)
−0.0479409 + 0.998850i \(0.515266\pi\)
\(60\) 0.277189 + 0.761570i 0.0357849 + 0.0983183i
\(61\) −0.958111 −0.122674 −0.0613368 0.998117i \(-0.519536\pi\)
−0.0613368 + 0.998117i \(0.519536\pi\)
\(62\) 10.3473 1.31411
\(63\) 0 0
\(64\) 8.59627 1.07453
\(65\) 14.7442 1.82880
\(66\) −1.07532 0.189608i −0.132363 0.0233392i
\(67\) −9.63816 −1.17749 −0.588744 0.808320i \(-0.700377\pi\)
−0.588744 + 0.808320i \(0.700377\pi\)
\(68\) −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 \(0.212499\pi\)
\(72\) 1.53343 + 8.69653i 0.180717 + 1.02490i
\(73\) −5.13429 + 8.89284i −0.600923 + 1.04083i 0.391759 + 0.920068i \(0.371867\pi\)
−0.992682 + 0.120761i \(0.961467\pi\)
\(74\) 5.17365 + 8.96102i 0.601424 + 1.04170i
\(75\) −2.40760 0.424525i −0.278006 0.0490200i
\(76\) 0.201867 + 0.349643i 0.0231557 + 0.0401068i
\(77\) 0 0
\(78\) 13.3819 + 2.35959i 1.51520 + 0.267171i
\(79\) −12.6382 −1.42190 −0.710952 0.703241i \(-0.751736\pi\)
−0.710952 + 0.703241i \(0.751736\pi\)
\(80\) −4.55303 + 7.88609i −0.509045 + 0.881691i
\(81\) −8.45723 + 3.07818i −0.939693 + 0.342020i
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) −1.36571 + 2.36549i −0.149907 + 0.259646i −0.931193 0.364527i \(-0.881231\pi\)
0.781286 + 0.624173i \(0.214564\pi\)
\(84\) 0 0
\(85\) −4.91147 8.50692i −0.532724 0.922705i
\(86\) −0.826352 + 1.43128i −0.0891078 + 0.154339i
\(87\) 5.20187 + 14.2920i 0.557699 + 1.53226i
\(88\) 0.688663 + 1.19280i 0.0734117 + 0.127153i
\(89\) −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
\(93\) 8.55051 10.1901i 0.886646 1.05666i
\(94\) 7.18479 0.741055
\(95\) −5.53209 −0.567580
\(96\) 1.15998 1.38241i 0.118390 0.141091i
\(97\) −6.80200 + 11.7814i −0.690639 + 1.19622i 0.280990 + 0.959711i \(0.409337\pi\)
−0.971629 + 0.236511i \(0.923996\pi\)
\(98\) 0 0
\(99\) −1.07532 + 0.902302i −0.108074 + 0.0906848i
\(100\) 0.130415 + 0.225885i 0.0130415 + 0.0225885i
\(101\) −4.78699 8.29131i −0.476323 0.825016i 0.523309 0.852143i \(-0.324697\pi\)
−0.999632 + 0.0271271i \(0.991364\pi\)
\(102\) −3.09627 8.50692i −0.306576 0.842311i
\(103\) 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
\(107\) 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 \(0.996506\pi\)
\(110\) −1.59627 −0.152198
\(111\) 13.1001 + 2.30991i 1.24341 + 0.219247i
\(112\) 0 0
\(113\) −2.58853 4.48346i −0.243508 0.421768i 0.718203 0.695834i \(-0.244965\pi\)
−0.961711 + 0.274065i \(0.911632\pi\)
\(114\) −5.02094 0.885328i −0.470255 0.0829186i
\(115\) −0.134285 0.232589i −0.0125222 0.0216890i
\(116\) 0.811337 1.40528i 0.0753308 0.130477i
\(117\) 13.3819 11.2288i 1.23716 1.03810i
\(118\) −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
\(122\) −1.29086 −0.116869
\(123\) −3.79813 0.669713i −0.342466 0.0603860i
\(124\) −1.41921 −0.127449
\(125\) 9.08647 0.812718
\(126\) 0 0
\(127\) −8.88207 −0.788157 −0.394078 0.919077i \(-0.628936\pi\)
−0.394078 + 0.919077i \(0.628936\pi\)
\(128\) 9.49794 0.839507
\(129\) 0.726682 + 1.99654i 0.0639807 + 0.175786i
\(130\) 19.8648 1.74226
\(131\) 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
\(135\) −11.3944 + 6.57856i −0.980674 + 0.566192i
\(136\) −5.70961 + 9.88933i −0.489595 + 0.848003i
\(137\) 2.86231 + 4.95767i 0.244544 + 0.423562i 0.962003 0.273038i \(-0.0880285\pi\)
−0.717459 + 0.696600i \(0.754695\pi\)
\(138\) −0.0846555 0.232589i −0.00720635 0.0197993i
\(139\) −0.461981 0.800175i −0.0391847 0.0678700i 0.845768 0.533551i \(-0.179143\pi\)
−0.884953 + 0.465681i \(0.845809\pi\)
\(140\) 0 0
\(141\) 5.93717 7.07564i 0.500000 0.595876i
\(142\) 17.8307 1.49632
\(143\) 1.36231 2.35959i 0.113922 0.197319i
\(144\) 1.87346 + 10.6249i 0.156121 + 0.885408i
\(145\) 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
\(149\) −4.36231 + 7.55574i −0.357374 + 0.618991i −0.987521 0.157485i \(-0.949661\pi\)
0.630147 + 0.776476i \(0.282995\pi\)
\(150\) −3.24376 0.571962i −0.264852 0.0467005i
\(151\) −9.21348 15.9582i −0.749782 1.29866i −0.947927 0.318488i \(-0.896825\pi\)
0.198145 0.980173i \(-0.436508\pi\)
\(152\) 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
\(156\) −1.83544 0.323637i −0.146953 0.0259117i
\(157\) −4.92396 −0.392975 −0.196488 0.980506i \(-0.562954\pi\)
−0.196488 + 0.980506i \(0.562954\pi\)
\(158\) −17.0273 −1.35462
\(159\) −0.424678 1.16679i −0.0336791 0.0925327i
\(160\) 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 \(0.930031\pi\)
\(164\) 0.205737 + 0.356347i 0.0160654 + 0.0278260i
\(165\) −1.31908 + 1.57202i −0.102690 + 0.122381i
\(166\) −1.84002 + 3.18701i −0.142813 + 0.247360i
\(167\) −2.82770 4.89771i −0.218814 0.378996i 0.735632 0.677382i \(-0.236885\pi\)
−0.954446 + 0.298385i \(0.903552\pi\)
\(168\) 0 0
\(169\) −10.4534 + 18.1058i −0.804105 + 1.39275i
\(170\) −6.61721 11.4613i −0.507517 0.879045i
\(171\) −5.02094 + 4.21307i −0.383961 + 0.322182i
\(172\) 0.113341 0.196312i 0.00864215 0.0149687i
\(173\) −21.0692 −1.60186 −0.800932 0.598755i \(-0.795662\pi\)
−0.800932 + 0.598755i \(0.795662\pi\)
\(174\) 7.00846 + 19.2556i 0.531310 + 1.45976i
\(175\) 0 0
\(176\) 0.841367 + 1.45729i 0.0634204 + 0.109847i
\(177\) −0.819955 + 0.977185i −0.0616316 + 0.0734497i
\(178\) −5.46585 9.46713i −0.409683 0.709592i
\(179\) 2.56031 4.43458i 0.191366 0.331456i −0.754337 0.656487i \(-0.772041\pi\)
0.945703 + 0.325031i \(0.105375\pi\)
\(180\) 1.31908 + 0.480105i 0.0983183 + 0.0357849i
\(181\) 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
\(185\) 19.4466 1.42974
\(186\) 11.5201 13.7291i 0.844692 1.00667i
\(187\) −1.81521 −0.132741
\(188\) −0.985452 −0.0718715
\(189\) 0 0
\(190\) −7.45336 −0.540724
\(191\) −15.5672 −1.12640 −0.563200 0.826320i \(-0.690430\pi\)
−0.563200 + 0.826320i \(0.690430\pi\)
\(192\) 9.57057 11.4058i 0.690697 0.823140i
\(193\) 6.04189 0.434905 0.217452 0.976071i \(-0.430225\pi\)
0.217452 + 0.976071i \(0.430225\pi\)
\(194\) −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 \(0.144339\pi\)
\(198\) −1.44878 + 1.21567i −0.102960 + 0.0863938i
\(199\) 1.52094 2.63435i 0.107817 0.186744i −0.807069 0.590458i \(-0.798947\pi\)
0.914886 + 0.403713i \(0.132281\pi\)
\(200\) 2.07738 + 3.59813i 0.146893 + 0.254426i
\(201\) −10.7306 + 12.7882i −0.756875 + 0.902008i
\(202\) −6.44949 11.1708i −0.453785 0.785978i
\(203\) 0 0
\(204\) 0.424678 + 1.16679i 0.0297334 + 0.0816918i
\(205\) −5.63816 −0.393786
\(206\) 2.04916 3.54925i 0.142772 0.247288i
\(207\) −0.299011 0.108831i −0.0207827 0.00756428i
\(208\) −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 0.944487 0.328548i \(-0.106559\pi\)
−0.756775 + 0.653676i \(0.773226\pi\)
\(212\) −0.0662372 + 0.114726i −0.00454919 + 0.00787942i
\(213\) 14.7344 17.5598i 1.00959 1.20318i
\(214\) 4.39053 + 7.60462i 0.300130 + 0.519841i
\(215\) 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
\(219\) 6.08306 + 16.7131i 0.411055 + 1.12937i
\(220\) 0.218941 0.0147610
\(221\) 22.5895 1.51953
\(222\) 17.6498 + 3.11213i 1.18457 + 0.208872i
\(223\) 7.09627 12.2911i 0.475201 0.823073i −0.524395 0.851475i \(-0.675709\pi\)
0.999597 + 0.0284023i \(0.00904195\pi\)
\(224\) 0 0
\(225\) −3.24376 + 2.72183i −0.216250 + 0.181456i
\(226\) −3.48751 6.04055i −0.231986 0.401811i
\(227\) −1.44697 2.50622i −0.0960385 0.166344i 0.814003 0.580861i \(-0.197284\pi\)
−0.910042 + 0.414517i \(0.863951\pi\)
\(228\) 0.688663 + 0.121430i 0.0456078 + 0.00804189i
\(229\) 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
\(233\) −6.63563 11.4932i −0.434715 0.752948i 0.562558 0.826758i \(-0.309817\pi\)
−0.997272 + 0.0738103i \(0.976484\pi\)
\(234\) 18.0294 15.1285i 1.17862 0.988979i
\(235\) 6.75150 11.6939i 0.440419 0.762828i
\(236\) 0.136096 0.00885912
\(237\) −14.0706 + 16.7687i −0.913982 + 1.08924i
\(238\) 0 0
\(239\) −4.76857 8.25941i −0.308453 0.534257i 0.669571 0.742748i \(-0.266478\pi\)
−0.978024 + 0.208491i \(0.933145\pi\)
\(240\) 5.39440 + 14.8210i 0.348207 + 0.956691i
\(241\) −4.47906 7.75795i −0.288521 0.499734i 0.684936 0.728604i \(-0.259830\pi\)
−0.973457 + 0.228870i \(0.926497\pi\)
\(242\) 7.26264 12.5793i 0.466860 0.808626i
\(243\) −5.33157 + 14.6484i −0.342020 + 0.939693i
\(244\) 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
\(248\) −22.6067 −1.43553
\(249\) 1.61809 + 4.44566i 0.102542 + 0.281732i
\(250\) 12.2422 0.774262
\(251\) 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
\(254\) −11.9668 −0.750863
\(255\) −16.7554 2.95442i −1.04926 0.185013i
\(256\) −4.39599 −0.274750
\(257\) 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
\(261\) 24.7545 + 9.00990i 1.53226 + 0.557699i
\(262\) 7.65451 13.2580i 0.472897 0.819082i
\(263\) −13.0437 22.5924i −0.804309 1.39310i −0.916757 0.399446i \(-0.869202\pi\)
0.112448 0.993658i \(-0.464131\pi\)
\(264\) 2.34936 + 0.414255i 0.144593 + 0.0254956i
\(265\) −0.907604 1.57202i −0.0557537 0.0965682i
\(266\) 0 0
\(267\) −13.8400 2.44037i −0.846996 0.149348i
\(268\) 1.78106 0.108796
\(269\) −3.81655 + 6.61046i −0.232699 + 0.403047i −0.958602 0.284751i \(-0.908089\pi\)
0.725902 + 0.687798i \(0.241422\pi\)
\(270\) −15.3516 + 8.86327i −0.934271 + 0.539401i
\(271\) 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
\(275\) −0.330222 + 0.571962i −0.0199131 + 0.0344906i
\(276\) 0.0116112 + 0.0319015i 0.000698911 + 0.00192024i
\(277\) 2.86097 + 4.95534i 0.171899 + 0.297738i 0.939084 0.343689i \(-0.111676\pi\)
−0.767185 + 0.641426i \(0.778343\pi\)
\(278\) −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 0.0379535 + 0.999280i \(0.487916\pi\)
−0.884378 + 0.466771i \(0.845417\pi\)
\(282\) 7.99912 9.53298i 0.476341 0.567681i
\(283\) −4.57129 −0.271735 −0.135867 0.990727i \(-0.543382\pi\)
−0.135867 + 0.990727i \(0.543382\pi\)
\(284\) −2.44562 −0.145121
\(285\) −6.15910 + 7.34013i −0.364834 + 0.434792i
\(286\) 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
\(290\) 14.9782 + 25.9430i 0.879549 + 1.52342i
\(291\) 8.05896 + 22.1418i 0.472425 + 1.29798i
\(292\) 0.948778 1.64333i 0.0555230 0.0961687i
\(293\) 2.16385 + 3.74789i 0.126413 + 0.218954i 0.922285 0.386512i \(-0.126320\pi\)
−0.795871 + 0.605466i \(0.792987\pi\)
\(294\) 0 0
\(295\) −0.932419 + 1.61500i −0.0542875 + 0.0940287i
\(296\) −11.3033 19.5780i −0.656994 1.13795i
\(297\) 2.43134i 0.141081i
\(298\) −5.87733 + 10.1798i −0.340464 + 0.589702i
\(299\) 0.617622 0.0357180
\(300\) 0.444907 + 0.0784491i 0.0256867 + 0.00452926i
\(301\) 0 0
\(302\) −12.4133 21.5004i −0.714304 1.23721i
\(303\) −16.3307 2.87954i −0.938174 0.165425i
\(304\) 3.92855 + 6.80445i 0.225318 + 0.390262i
\(305\) −1.21301 + 2.10100i −0.0694568 + 0.120303i
\(306\) −14.7344 5.36289i −0.842311 0.306576i
\(307\) −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
\(311\) 21.9855 1.24668 0.623340 0.781951i \(-0.285775\pi\)
0.623340 + 0.781951i \(0.285775\pi\)
\(312\) −29.2367 5.15522i −1.65520 0.291857i
\(313\) 13.8898 0.785099 0.392549 0.919731i \(-0.371593\pi\)
0.392549 + 0.919731i \(0.371593\pi\)
\(314\) −6.63404 −0.374380
\(315\) 0 0
\(316\) 2.33544 0.131379
\(317\) −6.18210 −0.347222 −0.173611 0.984814i \(-0.555543\pi\)
−0.173611 + 0.984814i \(0.555543\pi\)
\(318\) −0.572167 1.57202i −0.0320855 0.0881543i
\(319\) 4.10876 0.230046
\(320\) 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
\(324\) 1.56283 0.568825i 0.0868241 0.0316014i
\(325\) 4.10947 7.11781i 0.227952 0.394825i
\(326\) −5.14543 8.91215i −0.284979 0.493598i
\(327\) 6.30200 + 17.3146i 0.348502 + 0.957500i
\(328\) 3.27719 + 5.67626i 0.180952 + 0.313419i
\(329\) 0 0
\(330\) −1.77719 + 2.11797i −0.0978310 + 0.116590i
\(331\) 10.7314 0.589853 0.294926 0.955520i \(-0.404705\pi\)
0.294926 + 0.955520i \(0.404705\pi\)
\(332\) 0.252374 0.437124i 0.0138508 0.0239903i
\(333\) 17.6498 14.8099i 0.967201 0.811578i
\(334\) −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 0.999972 + 0.00746831i \(0.00237726\pi\)
−0.493518 + 0.869735i \(0.664289\pi\)
\(338\) −14.0838 + 24.3938i −0.766057 + 1.32685i
\(339\) −8.83069 1.55709i −0.479617 0.0845695i
\(340\) 0.907604 + 1.57202i 0.0492217 + 0.0852545i
\(341\) −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
\(345\) −0.458111 0.0807773i −0.0246639 0.00434890i
\(346\) −28.3865 −1.52607
\(347\) −20.4124 −1.09580 −0.547898 0.836545i \(-0.684572\pi\)
−0.547898 + 0.836545i \(0.684572\pi\)
\(348\) −0.961266 2.64106i −0.0515293 0.141576i
\(349\) −1.78106 + 3.08489i −0.0953379 + 0.165130i −0.909750 0.415157i \(-0.863726\pi\)
0.814412 + 0.580288i \(0.197060\pi\)
\(350\) 0 0
\(351\) 30.2569i 1.61500i
\(352\) −0.243756 0.422197i −0.0129922 0.0225032i
\(353\) 5.01114 + 8.67956i 0.266716 + 0.461966i 0.968012 0.250904i \(-0.0807280\pi\)
−0.701296 + 0.712871i \(0.747395\pi\)
\(354\) −1.10472 + 1.31656i −0.0587153 + 0.0699742i
\(355\) 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
\(359\) −4.74035 8.21053i −0.250186 0.433335i 0.713391 0.700766i \(-0.247159\pi\)
−0.963577 + 0.267431i \(0.913825\pi\)
\(360\) 21.0116 + 7.64760i 1.10741 + 0.403064i
\(361\) 7.11334 12.3207i 0.374386 0.648456i
\(362\) 0.431074 0.0226568
\(363\) −6.38666 17.5472i −0.335213 0.920989i
\(364\) 0 0
\(365\) 13.0005 + 22.5175i 0.680476 + 1.17862i
\(366\) −1.43717 + 1.71275i −0.0751219 + 0.0895268i
\(367\) 8.06670 + 13.9719i 0.421079 + 0.729329i 0.996045 0.0888474i \(-0.0283183\pi\)
−0.574967 + 0.818177i \(0.694985\pi\)
\(368\) −0.190722 + 0.330341i −0.00994209 + 0.0172202i
\(369\) −5.11721 + 4.29385i −0.266391 + 0.223529i
\(370\) 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 \(0.285164\pi\)
\(374\) −2.44562 −0.126460
\(375\) 10.1163 12.0562i 0.522405 0.622578i
\(376\) −15.6973 −0.809525
\(377\) −51.1317 −2.63341
\(378\) 0 0
\(379\) 16.0574 0.824812 0.412406 0.911000i \(-0.364689\pi\)
0.412406 + 0.911000i \(0.364689\pi\)
\(380\) 1.02229 0.0524423
\(381\) −9.88877 + 11.7850i −0.506617 + 0.603763i
\(382\) −20.9736 −1.07310
\(383\) −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
\(387\) 3.45811 + 1.25865i 0.175786 + 0.0639807i
\(388\) 1.25696 2.17712i 0.0638124 0.110526i
\(389\) 15.0214 + 26.0178i 0.761616 + 1.31916i 0.942017 + 0.335564i \(0.108927\pi\)
−0.180402 + 0.983593i \(0.557740\pi\)
\(390\) 22.1163 26.3572i 1.11990 1.33465i
\(391\) −0.205737 0.356347i −0.0104046 0.0180212i
\(392\) 0 0
\(393\) −6.73127 18.4940i −0.339548 0.932899i
\(394\) 33.9982 1.71281
\(395\) −16.0005 + 27.7136i −0.805071 + 1.39442i
\(396\) 0.198711 0.166739i 0.00998563 0.00837894i
\(397\) −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
\(401\) −10.4880 + 18.1657i −0.523745 + 0.907152i 0.475873 + 0.879514i \(0.342132\pi\)
−0.999618 + 0.0276385i \(0.991201\pi\)
\(402\) −14.4572 + 17.2295i −0.721061 + 0.859327i
\(403\) 22.3603 + 38.7291i 1.11384 + 1.92923i
\(404\) 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
\(408\) 6.76470 + 18.5859i 0.334903 + 0.920137i
\(409\) −25.6614 −1.26887 −0.634437 0.772975i \(-0.718768\pi\)
−0.634437 + 0.772975i \(0.718768\pi\)
\(410\) −7.59627 −0.375153
\(411\) 9.76470 + 1.72178i 0.481657 + 0.0849291i
\(412\) −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
\(416\) 3.03343 + 5.25406i 0.148726 + 0.257601i
\(417\) −1.57604 0.277898i −0.0771789 0.0136087i
\(418\) −0.688663 + 1.19280i −0.0336836 + 0.0583417i
\(419\) −0.739885 1.28152i −0.0361458 0.0626063i 0.847387 0.530976i \(-0.178175\pi\)
−0.883532 + 0.468370i \(0.844841\pi\)
\(420\) 0 0
\(421\) −6.55350 + 11.3510i −0.319398 + 0.553214i −0.980363 0.197203i \(-0.936814\pi\)
0.660965 + 0.750417i \(0.270147\pi\)
\(422\) 3.67365 + 6.36295i 0.178830 + 0.309743i
\(423\) −2.77807 15.7552i −0.135074 0.766044i
\(424\) −1.05509 + 1.82747i −0.0512398 + 0.0887500i
\(425\) −5.47565 −0.265608
\(426\) 19.8516 23.6583i 0.961815 1.14625i
\(427\) 0 0
\(428\) −0.602196 1.04303i −0.0291083 0.0504170i
\(429\) −1.61406 4.43458i −0.0779274 0.214104i
\(430\) 2.09240 + 3.62414i 0.100904 + 0.174771i
\(431\) −8.86349 + 15.3520i −0.426939 + 0.739481i −0.996599 0.0823997i \(-0.973742\pi\)
0.569660 + 0.821881i \(0.307075\pi\)
\(432\) 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
\(437\) −0.231734 −0.0110853
\(438\) 8.19569 + 22.5175i 0.391605 + 1.07593i
\(439\) −29.8553 −1.42492 −0.712459 0.701714i \(-0.752418\pi\)
−0.712459 + 0.701714i \(0.752418\pi\)
\(440\) 3.48751 0.166261
\(441\) 0 0
\(442\) 30.4347 1.44763
\(443\) 10.6655 0.506733 0.253367 0.967370i \(-0.418462\pi\)
0.253367 + 0.967370i \(0.418462\pi\)
\(444\) −2.42081 0.426854i −0.114886 0.0202576i
\(445\) −20.5449 −0.973921
\(446\) 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 \(0.473272\pi\)
\(450\) −4.37030 + 3.66712i −0.206018 + 0.172870i
\(451\) −0.520945 + 0.902302i −0.0245303 + 0.0424878i
\(452\) 0.478340 + 0.828510i 0.0224992 + 0.0389698i
\(453\) −31.4315 5.54223i −1.47678 0.260397i
\(454\) −1.94949 3.37662i −0.0914942 0.158473i
\(455\) 0 0
\(456\) 10.9697 + 1.93426i 0.513704 + 0.0905799i
\(457\) 5.02322 0.234976 0.117488 0.993074i \(-0.462516\pi\)
0.117488 + 0.993074i \(0.462516\pi\)
\(458\) 6.17571 10.6966i 0.288572 0.499821i
\(459\) −17.4572 + 10.0789i −0.814834 + 0.470445i
\(460\) 0.0248149 + 0.0429807i 0.00115700 + 0.00200399i
\(461\) 9.23055 15.9878i 0.429910 0.744625i −0.566955 0.823749i \(-0.691879\pi\)
0.996865 + 0.0791233i \(0.0252121\pi\)
\(462\) 0 0
\(463\) 7.11721 + 12.3274i 0.330765 + 0.572902i 0.982662 0.185406i \(-0.0593600\pi\)
−0.651897 + 0.758307i \(0.726027\pi\)
\(464\) 15.7895 27.3482i 0.733010 1.26961i
\(465\) −11.5201 31.6511i −0.534230 1.46779i
\(466\) −8.94016 15.4848i −0.414145 0.717320i
\(467\) −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
\(471\) −5.48205 + 6.53325i −0.252599 + 0.301036i
\(472\) 2.16788 0.0997848
\(473\) 0.573978 0.0263915
\(474\) −18.9572 + 22.5924i −0.870735 + 1.03770i
\(475\) −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
\(479\) −18.3833 31.8407i −0.839952 1.45484i −0.889934 0.456090i \(-0.849249\pi\)
0.0499812 0.998750i \(-0.484084\pi\)
\(480\) −1.56283 4.29385i −0.0713333 0.195987i
\(481\) −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
\(485\) 17.2233 + 29.8316i 0.782069 + 1.35458i
\(486\) −7.18320 + 19.7357i −0.325837 + 0.895229i
\(487\) 18.7087 32.4045i 0.847773 1.46839i −0.0354172 0.999373i \(-0.511276\pi\)
0.883191 0.469014i \(-0.155391\pi\)
\(488\) 2.82026 0.127667
\(489\) −13.0287 2.29731i −0.589178 0.103888i
\(490\) 0 0
\(491\) 13.3353 + 23.0974i 0.601813 + 1.04237i 0.992547 + 0.121866i \(0.0388879\pi\)
−0.390734 + 0.920504i \(0.627779\pi\)
\(492\) 0.701867 + 0.123758i 0.0316426 + 0.00557944i
\(493\) 17.0326 + 29.5013i 0.767108 + 1.32867i
\(494\) 8.57011 14.8439i 0.385587 0.667857i
\(495\) 0.617211 + 3.50038i 0.0277416 + 0.157330i
\(496\) −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 \(0.894148\pi\)
\(500\) −1.67911 −0.0750921
\(501\) −9.64661 1.70096i −0.430979 0.0759932i
\(502\) 33.6800 1.50321
\(503\) 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
\(506\) −0.0668661 −0.00297256
\(507\) 12.3851 + 34.0277i 0.550040 + 1.51122i
\(508\) 1.64134 0.0728227
\(509\) −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
\(513\) 11.3525i 0.501226i
\(514\) 7.31046 12.6621i 0.322451 0.558501i
\(515\) −3.85117 6.67042i −0.169703 0.293934i
\(516\) −0.134285 0.368946i −0.00591158 0.0162419i
\(517\) −1.24763 2.16095i −0.0548705 0.0950386i
\(518\) 0 0
\(519\) −23.4572 + 27.9552i −1.02966 + 1.22710i
\(520\) −43.4005 −1.90324
\(521\) −7.33750 + 12.7089i −0.321462 + 0.556788i −0.980790 0.195067i \(-0.937507\pi\)
0.659328 + 0.751855i \(0.270841\pi\)
\(522\) 33.3516 + 12.1390i 1.45976 + 0.531310i
\(523\) 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
\(527\) 14.8969 25.8022i 0.648920 1.12396i
\(528\) 2.87030 + 0.506111i 0.124914 + 0.0220257i
\(529\) 11.4944 + 19.9088i 0.499755 + 0.865602i
\(530\) −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
\(534\) −18.6466 3.28790i −0.806918 0.142281i
\(535\) 16.5030 0.713487
\(536\) 28.3705 1.22542
\(537\) −3.03343 8.33429i −0.130902 0.359651i
\(538\) −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 \(0.911336\pi\)
\(542\) 2.29292 + 3.97145i 0.0984893 + 0.170588i
\(543\) 0.356219 0.424525i 0.0152868 0.0182181i
\(544\) 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 −0.363404 0.931632i \(-0.618385\pi\)
0.988519 0.151099i \(-0.0482812\pi\)
\(548\) −0.528934 0.916140i −0.0225949 0.0391356i
\(549\) 0.499123 + 2.83067i 0.0213020 + 0.120810i
\(550\) −0.444907 + 0.770602i −0.0189709 + 0.0328586i
\(551\) 19.1848 0.817300
\(552\) 0.184955 + 0.508159i 0.00787219 + 0.0216287i
\(553\) 0 0
\(554\) 3.85457 + 6.67631i 0.163765 + 0.283649i
\(555\) 21.6506 25.8022i 0.919019 1.09524i
\(556\) 0.0853707 + 0.147866i 0.00362052 + 0.00627093i
\(557\) 0.387841 0.671761i 0.0164334 0.0284634i −0.857692 0.514164i \(-0.828102\pi\)
0.874125 + 0.485701i \(0.161436\pi\)
\(558\) −5.39037 30.5703i −0.228192 1.29414i
\(559\) −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
\(563\) −24.9522 −1.05161 −0.525806 0.850605i \(-0.676236\pi\)
−0.525806 + 0.850605i \(0.676236\pi\)
\(564\) −1.09714 + 1.30753i −0.0461981 + 0.0550567i
\(565\) −13.1088 −0.551489
\(566\) −6.15888 −0.258877
\(567\) 0 0
\(568\) −38.9564 −1.63457
\(569\) −24.8033 −1.03981 −0.519905 0.854224i \(-0.674033\pi\)
−0.519905 + 0.854224i \(0.674033\pi\)
\(570\) −8.29813 + 9.88933i −0.347571 + 0.414218i
\(571\) 8.79654 0.368124 0.184062 0.982915i \(-0.441075\pi\)
0.184062 + 0.982915i \(0.441075\pi\)
\(572\) −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
\(576\) −4.47818 25.3970i −0.186591 1.05821i
\(577\) −6.43717 + 11.1495i −0.267983 + 0.464160i −0.968341 0.249632i \(-0.919690\pi\)
0.700358 + 0.713792i \(0.253024\pi\)
\(578\) 1.31386 + 2.27568i 0.0546495 + 0.0946557i
\(579\) 6.72668 8.01655i 0.279551 0.333156i
\(580\) −2.05438 3.55829i −0.0853034 0.147750i
\(581\) 0 0
\(582\) 10.8578 + 29.8316i 0.450071 + 1.23656i
\(583\) −0.335437 −0.0138924
\(584\) 15.1131 26.1766i 0.625384 1.08320i
\(585\) −7.68092 43.5607i −0.317567 1.80101i
\(586\) 2.91534 + 5.04952i 0.120432 + 0.208594i
\(587\) 22.4315 38.8526i 0.925849 1.60362i 0.135658 0.990756i \(-0.456685\pi\)
0.790190 0.612861i \(-0.209982\pi\)
\(588\) 0 0
\(589\) −8.38965 14.5313i −0.345690 0.598752i
\(590\) −1.25624 + 2.17588i −0.0517188 + 0.0895795i
\(591\) 28.0945 33.4817i 1.15565 1.37725i
\(592\) −13.8097 23.9192i −0.567577 0.983072i
\(593\) 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
\(597\) −1.80200 4.95096i −0.0737511 0.202629i
\(598\) 0.832119 0.0340279
\(599\) −3.69047 −0.150789 −0.0753943 0.997154i \(-0.524022\pi\)
−0.0753943 + 0.997154i \(0.524022\pi\)
\(600\) 7.08693 + 1.24962i 0.289323 + 0.0510154i
\(601\) −10.9285 + 18.9288i −0.445785 + 0.772122i −0.998107 0.0615091i \(-0.980409\pi\)
0.552322 + 0.833631i \(0.313742\pi\)
\(602\) 0 0
\(603\) 5.02094 + 28.4752i 0.204469 + 1.15960i
\(604\) 1.70258 + 2.94896i 0.0692771 + 0.119991i
\(605\) −13.6493 23.6413i −0.554923 0.961155i
\(606\) −22.0023 3.87960i −0.893781 0.157598i
\(607\) 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
\(611\) 15.5262 + 26.8921i 0.628121 + 1.08794i
\(612\) 2.02094 + 0.735564i 0.0816918 + 0.0297334i
\(613\) −21.0107 + 36.3917i −0.848616 + 1.46985i 0.0338284 + 0.999428i \(0.489230\pi\)
−0.882444 + 0.470418i \(0.844103\pi\)
\(614\) −16.6759 −0.672986
\(615\) −6.27719 + 7.48086i −0.253121 + 0.301657i
\(616\) 0 0
\(617\) −23.2049 40.1920i −0.934192 1.61807i −0.776068 0.630650i \(-0.782788\pi\)
−0.158125 0.987419i \(-0.550545\pi\)
\(618\) −2.42783 6.67042i −0.0976618 0.268324i
\(619\) −13.6047 23.5641i −0.546820 0.947120i −0.998490 0.0549349i \(-0.982505\pi\)
0.451670 0.892185i \(-0.350828\pi\)
\(620\) −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
\(625\) 15.0326 26.0372i 0.601302 1.04149i
\(626\) 18.7137 0.747950
\(627\) 0.605600 + 1.66387i 0.0241853 + 0.0664487i
\(628\) 0.909912 0.0363094
\(629\) 29.7939 1.18796
\(630\) 0 0
\(631\) −29.6023 −1.17845 −0.589224 0.807970i \(-0.700566\pi\)
−0.589224 + 0.807970i \(0.700566\pi\)
\(632\) 37.2012 1.47978
\(633\) 9.30200 + 1.64019i 0.369721 + 0.0651919i
\(634\) −8.32913 −0.330792
\(635\) −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
\(639\) −6.89440 39.1001i −0.272738 1.54678i
\(640\) 12.0248 20.8276i 0.475323 0.823283i
\(641\) 0.139500 + 0.241621i 0.00550991 + 0.00954345i 0.868767 0.495221i \(-0.164913\pi\)
−0.863257 + 0.504764i \(0.831579\pi\)
\(642\) 14.9782 + 2.64106i 0.591142 + 0.104234i
\(643\) −9.12196 15.7997i −0.359735 0.623079i 0.628181 0.778067i \(-0.283800\pi\)
−0.987916 + 0.154988i \(0.950466\pi\)
\(644\) 0 0
\(645\) 5.29813 + 0.934204i 0.208614 + 0.0367842i
\(646\) −11.4192 −0.449283
\(647\) 11.2285 19.4483i 0.441438 0.764592i −0.556359 0.830942i \(-0.687802\pi\)
0.997796 + 0.0663498i \(0.0211353\pi\)
\(648\) 24.8944 9.06082i 0.977944 0.355943i
\(649\) 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
\(653\) 25.2656 43.7614i 0.988721 1.71251i 0.364655 0.931143i \(-0.381187\pi\)
0.624066 0.781372i \(-0.285480\pi\)
\(654\) 8.49067 + 23.3279i 0.332011 + 0.912194i
\(655\) −14.3858 24.9169i −0.562099 0.973584i
\(656\) 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 −0.838824 0.544403i \(-0.816756\pi\)
0.890879 + 0.454241i \(0.150089\pi\)
\(660\) 0.243756 0.290497i 0.00948818 0.0113076i
\(661\) 34.6100 1.34617 0.673086 0.739564i \(-0.264968\pi\)
0.673086 + 0.739564i \(0.264968\pi\)
\(662\) 14.4584 0.561942
\(663\) 25.1498 29.9723i 0.976736 1.16403i
\(664\) 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
\(668\) 0.522537 + 0.905061i 0.0202176 + 0.0350179i
\(669\) −8.40760 23.0997i −0.325057 0.893086i
\(670\) −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 −0.980124 0.198386i \(-0.936430\pi\)
0.661869 + 0.749619i \(0.269763\pi\)
\(674\) 12.5262 + 21.6959i 0.482490 + 0.835697i
\(675\) 7.33423i 0.282295i
\(676\) 1.93170 3.34581i 0.0742963 0.128685i
\(677\) 43.7579 1.68175 0.840877 0.541226i \(-0.182040\pi\)
0.840877 + 0.541226i \(0.182040\pi\)
\(678\) −11.8976 2.09786i −0.456923 0.0805678i
\(679\) 0 0
\(680\) 14.4572 + 25.0407i 0.554410 + 0.960266i
\(681\) −4.93629 0.870401i −0.189159 0.0333538i
\(682\) −2.42081 4.19296i −0.0926975 0.160557i
\(683\) −14.1206 + 24.4576i −0.540310 + 0.935845i 0.458576 + 0.888655i \(0.348360\pi\)
−0.998886 + 0.0471895i \(0.984974\pi\)
\(684\) 0.927833 0.778544i 0.0354766 0.0297684i
\(685\) 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
\(689\) 4.17436 0.159031
\(690\) −0.617211 0.108831i −0.0234968 0.00414312i
\(691\) 29.0651 1.10569 0.552844 0.833284i \(-0.313542\pi\)
0.552844 + 0.833284i \(0.313542\pi\)
\(692\) 3.89344 0.148006
\(693\) 0 0
\(694\) −27.5016 −1.04395
\(695\) −2.33956 −0.0887444
\(696\) −15.3120 42.0694i −0.580401 1.59464i
\(697\) −8.63816 −0.327193
\(698\) −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 \(0.506665\pi\)
\(702\) 40.7650i 1.53858i
\(703\) 8.38965 14.5313i 0.316422 0.548059i
\(704\) −2.01114 3.48340i −0.0757979 0.131286i
\(705\) −7.99912 21.9774i −0.301264 0.827717i
\(706\) 6.75150 + 11.6939i 0.254096 + 0.440107i
\(707\) 0 0
\(708\) 0.151522 0.180576i 0.00569453 0.00678648i
\(709\) −18.4688 −0.693612 −0.346806 0.937937i \(-0.612734\pi\)
−0.346806 + 0.937937i \(0.612734\pi\)
\(710\) 22.5744 39.1001i 0.847204 1.46740i
\(711\) 6.58378 + 37.3385i 0.246911 + 1.40030i
\(712\) 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
\(716\) −0.473126 + 0.819478i −0.0176815 + 0.0306253i
\(717\) −16.2679 2.86846i −0.607534 0.107125i
\(718\) −6.38666 11.0620i −0.238348 0.412831i
\(719\) −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
\(723\) −15.2802 2.69431i −0.568276 0.100202i
\(724\) −0.0591253 −0.00219738
\(725\) 12.3942 0.460310
\(726\) −8.60472 23.6413i −0.319351 0.877410i
\(727\) 8.40214 14.5529i 0.311618 0.539738i −0.667095 0.744973i \(-0.732462\pi\)
0.978713 + 0.205234i \(0.0657957\pi\)
\(728\) 0 0
\(729\) 13.5000 + 23.3827i 0.500000 + 0.866025i
\(730\) 17.5155 + 30.3377i 0.648277 + 1.12285i
\(731\) 2.37939 + 4.12122i 0.0880047 + 0.152429i
\(732\) 0.197119 0.234917i 0.00728573 0.00868279i
\(733\) −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
\(737\) 2.25490 + 3.90560i 0.0830603 + 0.143865i
\(738\) −6.89440 + 5.78509i −0.253786 + 0.212952i
\(739\) 16.0209 27.7491i 0.589340 1.02077i −0.404979 0.914326i \(-0.632721\pi\)
0.994319 0.106441i \(-0.0339455\pi\)
\(740\) −3.59358 −0.132103
\(741\) −7.53643 20.7062i −0.276858 0.760660i
\(742\) 0 0
\(743\) −16.8764 29.2309i −0.619137 1.07238i −0.989644 0.143547i \(-0.954149\pi\)
0.370507 0.928830i \(-0.379184\pi\)
\(744\) −25.1690 + 29.9952i −0.922739 + 1.09968i
\(745\) 11.0458 + 19.1318i 0.404685 + 0.700936i
\(746\) −9.46451 + 16.3930i −0.346520 + 0.600191i
\(747\) 7.70011 + 2.80261i 0.281732 + 0.102542i
\(748\) 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 \(0.324762\pi\)
\(752\) −19.1780 −0.699349
\(753\) 27.8316 33.1684i 1.01424 1.20872i
\(754\) −68.8895 −2.50881
\(755\) −46.6587 −1.69808
\(756\) 0 0
\(757\) 35.6536 1.29585 0.647927 0.761703i \(-0.275636\pi\)
0.647927 + 0.761703i \(0.275636\pi\)
\(758\) 21.6340 0.785784
\(759\) −0.0552549 + 0.0658503i −0.00200563 + 0.00239021i
\(760\) 16.2841 0.590685
\(761\) 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
\(765\) −22.5744 + 18.9422i −0.816181 + 0.684857i
\(766\) −21.5706 + 37.3613i −0.779377 + 1.34992i
\(767\) −2.14425 3.71395i −0.0774243 0.134103i
\(768\) −4.89424 + 5.83273i −0.176606 + 0.210470i
\(769\) 19.7135 + 34.1447i 0.710886 + 1.23129i 0.964525 + 0.263992i \(0.0850392\pi\)
−0.253639 + 0.967299i \(0.581627\pi\)
\(770\) 0 0
\(771\) −6.42871 17.6627i −0.231524 0.636108i
\(772\) −1.11650 −0.0401836
\(773\) 12.4513 21.5663i 0.447842 0.775686i −0.550403 0.834899i \(-0.685526\pi\)
0.998245 + 0.0592135i \(0.0188593\pi\)
\(774\) 4.65910 + 1.69577i 0.167468 + 0.0609533i
\(775\) −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
\(779\) −2.43242 + 4.21307i −0.0871504 + 0.150949i
\(780\) −3.03343 + 3.61510i