Properties

Label 441.2.h.d.373.2
Level $441$
Weight $2$
Character 441.373
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 373.2
Root \(-0.173648 - 0.984808i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.d.214.2

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 −0.996938 0.0782003i \(-0.975083\pi\)
0.430745 0.902473i \(-0.358251\pi\)
\(6\) −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 −0.899138 0.437665i \(-0.855806\pi\)
0.828598 + 0.559844i \(0.189139\pi\)
\(12\) 0.205737 + 0.245188i 0.0593912 + 0.0707796i
\(13\) −2.91147 + 5.04282i −0.807498 + 1.39863i 0.107094 + 0.994249i \(0.465845\pi\)
−0.914592 + 0.404378i \(0.867488\pi\)
\(14\) 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 \(-0.322573\pi\)
−0.999429 + 0.0337978i \(0.989240\pi\)
\(18\) −0.701867 + 3.98048i −0.165432 + 0.938209i
\(19\) 1.09240 1.89209i 0.250613 0.434074i −0.713082 0.701081i \(-0.752701\pi\)
0.963695 + 0.267007i \(0.0860345\pi\)
\(20\) 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 0.871502 0.490393i \(-0.163147\pi\)
−0.860443 + 0.509546i \(0.829813\pi\)
\(24\) 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 −0.909112 0.416552i \(-0.863238\pi\)
0.0938108 0.995590i \(-0.470095\pi\)
\(30\) −2.02094 + 5.55250i −0.368972 + 1.01374i
\(31\) −7.68004 −1.37938 −0.689688 0.724106i \(-0.742252\pi\)
−0.689688 + 0.724106i \(0.742252\pi\)
\(32\) 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 −0.355991 0.934489i \(-0.615857\pi\)
0.987287 0.158947i \(-0.0508099\pi\)
\(38\) 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 \(-0.777705\pi\)
0.939771 + 0.341804i \(0.111038\pi\)
\(42\) 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
\(45\) 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 \(-0.627155\pi\)
−0.388931 + 0.921267i \(0.627155\pi\)
\(48\) 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 0.889593 0.456754i \(-0.150988\pi\)
−0.840357 + 0.542033i \(0.817655\pi\)
\(54\) 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 \(-0.484734\pi\)
0.0479409 + 0.998850i \(0.484734\pi\)
\(60\) 0.277189 0.761570i 0.0357849 0.0983183i
\(61\) 0.958111 0.122674 0.0613368 0.998117i \(-0.480464\pi\)
0.0613368 + 0.998117i \(0.480464\pi\)
\(62\) −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 0.992682 + 0.120761i \(0.0385334\pi\)
−0.391759 + 0.920068i \(0.628133\pi\)
\(74\) 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 \(-0.118769\pi\)
−0.781286 + 0.624173i \(0.785436\pi\)
\(84\) 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 \(-0.691836\pi\)
0.996875 + 0.0789894i \(0.0251693\pi\)
\(90\) 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 0.971629 + 0.236511i \(0.0760039\pi\)
−0.280990 + 0.959711i \(0.590663\pi\)
\(98\) 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 \(-0.675303\pi\)
0.999632 + 0.0271271i \(0.00863590\pi\)
\(102\) −3.09627 + 8.50692i −0.306576 + 0.842311i
\(103\) −1.52094 2.63435i −0.149863 0.259571i 0.781314 0.624139i \(-0.214550\pi\)
−0.931177 + 0.364568i \(0.881217\pi\)
\(104\) 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 −0.664408 0.747370i \(-0.731316\pi\)
0.979445 + 0.201709i \(0.0646497\pi\)
\(108\) −0.831566 + 0.480105i −0.0800175 + 0.0461981i
\(109\) −5.31908 9.21291i −0.509475 0.882437i −0.999940 0.0109759i \(-0.996506\pi\)
0.490465 0.871461i \(-0.336827\pi\)
\(110\) 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 −0.961711 0.274065i \(-0.911632\pi\)
0.718203 + 0.695834i \(0.244965\pi\)
\(114\) −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 \(-0.332006\pi\)
−0.999991 + 0.00416893i \(0.998673\pi\)
\(132\) −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 −0.717459 0.696600i \(-0.754695\pi\)
0.962003 + 0.273038i \(0.0880285\pi\)
\(138\) 0.0846555 0.232589i 0.00720635 0.0197993i
\(139\) 0.461981 0.800175i 0.0391847 0.0678700i −0.845768 0.533551i \(-0.820857\pi\)
0.884953 + 0.465681i \(0.154191\pi\)
\(140\) 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 0.630147 0.776476i \(-0.282995\pi\)
−0.987521 + 0.157485i \(0.949661\pi\)
\(150\) 3.24376 0.571962i 0.264852 0.0467005i
\(151\) −9.21348 + 15.9582i −0.749782 + 1.29866i 0.198145 + 0.980173i \(0.436508\pi\)
−0.947927 + 0.318488i \(0.896825\pi\)
\(152\) −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 \(-0.437046\pi\)
0.196488 + 0.980506i \(0.437046\pi\)
\(158\) −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 −0.975938 0.218049i \(-0.930031\pi\)
0.676805 + 0.736163i \(0.263364\pi\)
\(164\) −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 \(-0.763115\pi\)
0.954446 + 0.298385i \(0.0964480\pi\)
\(168\) 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 \(-0.204338\pi\)
0.800932 + 0.598755i \(0.204338\pi\)
\(174\) −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 0.945703 0.325031i \(-0.105375\pi\)
−0.754337 + 0.656487i \(0.772041\pi\)
\(180\) −1.31908 + 0.480105i −0.0983183 + 0.0357849i
\(181\) −0.319955 −0.0237821 −0.0118910 0.999929i \(-0.503785\pi\)
−0.0118910 + 0.999929i \(0.503785\pi\)
\(182\) 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 \(-0.201053\pi\)
−0.914886 + 0.403713i \(0.867719\pi\)
\(200\) 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 −0.756775 0.653676i \(-0.773226\pi\)
0.944487 + 0.328548i \(0.106559\pi\)
\(212\) −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 \(-0.324291\pi\)
−0.999597 + 0.0284023i \(0.990958\pi\)
\(224\) 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 \(-0.802716\pi\)
0.910042 + 0.414517i \(0.136049\pi\)
\(228\) 0.688663 0.121430i 0.0456078 0.00804189i
\(229\) −4.58378 7.93934i −0.302905 0.524646i 0.673888 0.738834i \(-0.264623\pi\)
−0.976793 + 0.214187i \(0.931290\pi\)
\(230\) 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 −0.997272 0.0738103i \(-0.976484\pi\)
0.562558 + 0.826758i \(0.309817\pi\)
\(234\) −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 −0.978024 0.208491i \(-0.933145\pi\)
0.669571 + 0.742748i \(0.266478\pi\)
\(240\) 5.39440 14.8210i 0.348207 0.956691i
\(241\) 4.47906 7.75795i 0.288521 0.499734i −0.684936 0.728604i \(-0.740170\pi\)
0.973457 + 0.228870i \(0.0735031\pi\)
\(242\) 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 \(-0.789369\pi\)
−0.788938 + 0.614473i \(0.789369\pi\)
\(252\) 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 \(-0.276575\pi\)
−0.984144 + 0.177369i \(0.943241\pi\)
\(258\) −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 0.112448 + 0.993658i \(0.464131\pi\)
−0.916757 + 0.399446i \(0.869202\pi\)
\(264\) −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 \(-0.0919109\pi\)
−0.725902 + 0.687798i \(0.758578\pi\)
\(270\) −15.3516 8.86327i −0.934271 0.539401i
\(271\) −1.70187 + 2.94772i −0.103381 + 0.179061i −0.913076 0.407790i \(-0.866299\pi\)
0.809695 + 0.586852i \(0.199633\pi\)
\(272\) 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 −0.767185 0.641426i \(-0.778343\pi\)
0.939084 + 0.343689i \(0.111676\pi\)
\(278\) 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 \(-0.487916\pi\)
\(282\) 7.99912 + 9.53298i 0.476341 + 0.567681i
\(283\) 4.57129 0.271735 0.135867 0.990727i \(-0.456618\pi\)
0.135867 + 0.990727i \(0.456618\pi\)
\(284\) −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 \(-0.873680\pi\)
0.795871 + 0.605466i \(0.207013\pi\)
\(294\) 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 \(-0.385092\pi\)
0.353206 + 0.935546i \(0.385092\pi\)
\(308\) 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 \(-0.714225\pi\)
−0.623340 + 0.781951i \(0.714225\pi\)
\(312\) −29.2367 + 5.15522i −1.65520 + 0.291857i
\(313\) −13.8898 −0.785099 −0.392549 0.919731i \(-0.628407\pi\)
−0.392549 + 0.919731i \(0.628407\pi\)
\(314\) 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 −0.493518 0.869735i \(-0.664289\pi\)
0.999972 0.00746831i \(-0.00237726\pi\)
\(338\) −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 \(-0.136274\pi\)
−0.814412 + 0.580288i \(0.802940\pi\)
\(350\) 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 \(-0.919272\pi\)
0.701296 + 0.712871i \(0.252605\pi\)
\(354\) −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 −0.963577 0.267431i \(-0.913825\pi\)
0.713391 + 0.700766i \(0.247159\pi\)
\(360\) −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 \(-0.971682\pi\)
0.574967 + 0.818177i \(0.305015\pi\)
\(368\) −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 0.624841 0.780752i \(-0.285164\pi\)
−0.988572 + 0.150752i \(0.951831\pi\)
\(374\) 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 0.907090 + 0.420936i \(0.138298\pi\)
−0.0890039 + 0.996031i \(0.528368\pi\)
\(384\) −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 −0.180402 0.983593i \(-0.557740\pi\)
0.942017 0.335564i \(-0.108927\pi\)
\(390\) −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 \(-0.733285\pi\)
0.978179 + 0.207764i \(0.0666187\pi\)
\(398\) −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 −0.999618 0.0276385i \(-0.991201\pi\)
0.475873 0.879514i \(-0.342132\pi\)
\(402\) 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 \(-0.281232\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(410\) −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 \(-0.821825\pi\)
0.883532 + 0.468370i \(0.155159\pi\)
\(420\) 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
\(423\) 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 0.569660 0.821881i \(-0.307075\pi\)
−0.996599 + 0.0823997i \(0.973742\pi\)
\(432\) −16.1832 + 9.34337i −0.778615 + 0.449533i
\(433\) −5.83843 −0.280577 −0.140289 0.990111i \(-0.544803\pi\)
−0.140289 + 0.990111i \(0.544803\pi\)
\(434\) 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 \(-0.247582\pi\)
0.712459 + 0.701714i \(0.247582\pi\)
\(440\) −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 \(-0.308121\pi\)
−0.996865 + 0.0791233i \(0.974788\pi\)
\(462\) 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
\(465\) 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 \(-0.808499\pi\)
0.902362 + 0.430980i \(0.141832\pi\)
\(468\) 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 −0.0499812 0.998750i \(-0.515916\pi\)
0.889934 0.456090i \(-0.150751\pi\)
\(480\) −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 0.883191 + 0.469014i \(0.155391\pi\)
−0.0354172 + 0.999373i \(0.511276\pi\)
\(488\) −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 −0.390734 0.920504i \(-0.627779\pi\)
0.992547 0.121866i \(-0.0388879\pi\)
\(492\) 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 −0.945215 0.326449i \(-0.894148\pi\)
0.189895 0.981804i \(-0.439185\pi\)
\(500\) 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 \(-0.753255\pi\)
−0.714299 + 0.699840i \(0.753255\pi\)
\(504\) 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 \(-0.110372\pi\)
−0.764550 + 0.644564i \(0.777039\pi\)
\(510\) 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 \(-0.0624926\pi\)
−0.659328 + 0.751855i \(0.729159\pi\)
\(522\) 33.3516 12.1390i 1.45976 0.531310i
\(523\) −14.1716 + 24.5459i −0.619680 + 1.07332i 0.369864 + 0.929086i \(0.379404\pi\)
−0.989544 + 0.144232i \(0.953929\pi\)
\(524\) 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 −0.961456 0.274958i \(-0.911336\pi\)
0.718849 + 0.695166i \(0.244669\pi\)
\(542\) −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 0.988519 + 0.151099i \(0.0482812\pi\)
−0.363404 + 0.931632i \(0.618385\pi\)
\(548\) −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 0.874125 0.485701i \(-0.161436\pi\)
−0.857692 + 0.514164i \(0.828102\pi\)
\(558\) 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 \(-0.323764\pi\)
0.525806 + 0.850605i \(0.323764\pi\)
\(564\) −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 \(-0.0803096\pi\)
−0.700358 + 0.713792i \(0.746976\pi\)
\(578\) 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 −0.790190 0.612861i \(-0.790018\pi\)
−0.135658 0.990756i \(-0.543315\pi\)
\(588\) 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 \(-0.857936\pi\)
0.824833 + 0.565376i \(0.191269\pi\)
\(594\) 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 \(-0.0195913\pi\)
−0.552322 + 0.833631i \(0.686258\pi\)
\(602\) 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 \(-0.331525\pi\)
−0.999984 + 0.00568063i \(0.998192\pi\)
\(608\) 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 −0.882444 0.470418i \(-0.844103\pi\)
0.0338284 0.999428i \(-0.489230\pi\)
\(614\) 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 −0.158125 + 0.987419i \(0.550545\pi\)
−0.776068 + 0.630650i \(0.782788\pi\)
\(618\) −2.42783 + 6.67042i −0.0976618 + 0.268324i
\(619\) 13.6047 23.5641i 0.546820 0.947120i −0.451670 0.892185i \(-0.649172\pi\)
0.998490 0.0549349i \(-0.0174951\pi\)
\(620\) −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 −0.863257 0.504764i \(-0.831579\pi\)
0.868767 + 0.495221i \(0.164913\pi\)
\(642\) −14.9782 + 2.64106i −0.591142 + 0.104234i
\(643\) 9.12196 15.7997i 0.359735 0.623079i −0.628181 0.778067i \(-0.716200\pi\)
0.987916 + 0.154988i \(0.0495338\pi\)
\(644\) 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 \(-0.312198\pi\)
−0.997796 + 0.0663498i \(0.978865\pi\)
\(648\) 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 0.624066 + 0.781372i \(0.285480\pi\)
0.364655 + 0.931143i \(0.381187\pi\)
\(654\) −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 0.890879 0.454241i \(-0.150089\pi\)
−0.838824 + 0.544403i \(0.816756\pi\)
\(660\) 0.243756 + 0.290497i 0.00948818 + 0.0113076i
\(661\) −34.6100 −1.34617 −0.673086 0.739564i \(-0.735032\pi\)
−0.673086 + 0.739564i \(0.735032\pi\)
\(662\) 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 0.661869 0.749619i \(-0.269763\pi\)
−0.980124 + 0.198386i \(0.936430\pi\)
\(674\) 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 \(-0.817960\pi\)
−0.840877 + 0.541226i \(0.817960\pi\)
\(678\) 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 −0.998886 0.0471895i \(-0.984974\pi\)
0.458576 0.888655i \(-0.348360\pi\)
\(684\) −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 \(-0.686458\pi\)
−0.552844 + 0.833284i \(0.686458\pi\)
\(692\) −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 −0.357751 0.933817i \(-0.616456\pi\)
0.987585 0.157087i \(-0.0502103\pi\)
\(720\) −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 \(-0.267538\pi\)
−0.978713 + 0.205234i \(0.934204\pi\)
\(728\) 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 \(-0.0856323\pi\)
−0.712195 + 0.701981i \(0.752299\pi\)
\(734\) −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 0.994319 + 0.106441i \(0.0339455\pi\)
−0.404979 + 0.914326i \(0.632721\pi\)
\(740\) 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 0.370507 + 0.928830i \(0.379184\pi\)
−0.989644 + 0.143547i \(0.954149\pi\)
\(744\) −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 0.523135 0.852250i \(-0.324762\pi\)
−0.999637 + 0.0269236i \(0.991429\pi\)
\(752\) 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 −0.953009 0.302943i \(-0.902031\pi\)
0.214148 0.976801i \(-0.431302\pi\)
\(762\) 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 0.253639 + 0.967299i \(0.418373\pi\)
−0.964525 + 0.263992i \(0.914961\pi\)
\(770\) 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 \(-0.314474\pi\)
−0.998245 + 0.0592135i \(0.981141\pi\)
\(774\) 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