Properties

Label 441.2.f.f.295.1
Level $441$
Weight $2$
Character 441.295
Analytic conductor $3.521$
Analytic rank $0$
Dimension $10$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(10\)
Relative dimension: \(5\) over \(\Q(\zeta_{3})\)
Coefficient field: 10.0.991381711347.1
Defining polynomial: \(x^{10} - 2 x^{9} + 9 x^{8} - 8 x^{7} + 40 x^{6} - 36 x^{5} + 90 x^{4} - 3 x^{3} + 36 x^{2} - 9 x + 9\)
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 295.1
Root \(-1.02682 + 1.77851i\) of defining polynomial
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.f.148.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.02682 + 1.77851i) q^{2} +(-0.608729 - 1.62156i) q^{3} +(-1.10873 - 1.92038i) q^{4} +(-0.0731228 - 0.126652i) q^{5} +(3.50901 + 0.582422i) q^{6} +0.446582 q^{8} +(-2.25890 + 1.97418i) q^{9} +O(q^{10})\) \(q+(-1.02682 + 1.77851i) q^{2} +(-0.608729 - 1.62156i) q^{3} +(-1.10873 - 1.92038i) q^{4} +(-0.0731228 - 0.126652i) q^{5} +(3.50901 + 0.582422i) q^{6} +0.446582 q^{8} +(-2.25890 + 1.97418i) q^{9} +0.300337 q^{10} +(-0.832020 + 1.44110i) q^{11} +(-2.43908 + 2.96686i) q^{12} +(-0.0999454 - 0.173111i) q^{13} +(-0.160862 + 0.195670i) q^{15} +(1.75890 - 3.04650i) q^{16} +6.27110 q^{17} +(-1.19161 - 6.04460i) q^{18} +6.91758 q^{19} +(-0.162147 + 0.280847i) q^{20} +(-1.70867 - 2.95951i) q^{22} +(3.09092 + 5.35363i) q^{23} +(-0.271848 - 0.724159i) q^{24} +(2.48931 - 4.31160i) q^{25} +0.410505 q^{26} +(4.57630 + 2.46119i) q^{27} +(-2.46757 + 4.27396i) q^{29} +(-0.182824 - 0.487013i) q^{30} +(-1.25890 - 2.18047i) q^{31} +(4.05873 + 7.02993i) q^{32} +(2.84330 + 0.471928i) q^{33} +(-6.43931 + 11.1532i) q^{34} +(6.29567 + 2.14910i) q^{36} +7.00046 q^{37} +(-7.10312 + 12.3030i) q^{38} +(-0.219869 + 0.267445i) q^{39} +(-0.0326554 - 0.0565608i) q^{40} +(-1.15895 - 2.00736i) q^{41} +(-0.940993 + 1.62985i) q^{43} +3.68994 q^{44} +(0.415212 + 0.141737i) q^{45} -12.6953 q^{46} +(-0.905887 + 1.56904i) q^{47} +(-6.01077 - 0.997660i) q^{48} +(5.11215 + 8.85451i) q^{50} +(-3.81740 - 10.1690i) q^{51} +(-0.221625 + 0.383865i) q^{52} +5.34614 q^{53} +(-9.07630 + 5.61178i) q^{54} +0.243359 q^{55} +(-4.21093 - 11.2172i) q^{57} +(-5.06752 - 8.77720i) q^{58} +(-2.28549 - 3.95859i) q^{59} +(0.554112 + 0.0919709i) q^{60} +(-0.339138 + 0.587404i) q^{61} +5.17066 q^{62} -9.63481 q^{64} +(-0.0146166 + 0.0253167i) q^{65} +(-3.75890 + 4.57226i) q^{66} +(3.09342 + 5.35796i) q^{67} +(-6.95296 - 12.0429i) q^{68} +(6.79968 - 8.27101i) q^{69} +1.27749 q^{71} +(-1.00878 + 0.881633i) q^{72} -1.55721 q^{73} +(-7.18823 + 12.4504i) q^{74} +(-8.50683 - 1.41195i) q^{75} +(-7.66972 - 13.2843i) q^{76} +(-0.249886 - 0.665657i) q^{78} +(-6.39787 + 11.0814i) q^{79} -0.514462 q^{80} +(1.20524 - 8.91894i) q^{81} +4.76015 q^{82} +(-3.75687 + 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-1.93247 - 3.34713i) q^{86} +(8.43256 + 1.39963i) q^{87} +(-0.371566 + 0.643571i) q^{88} +9.06788 q^{89} +(-0.678430 + 0.592918i) q^{90} +(6.85398 - 11.8714i) q^{92} +(-2.76944 + 3.36869i) q^{93} +(-1.86037 - 3.22226i) q^{94} +(-0.505833 - 0.876128i) q^{95} +(8.92877 - 10.8608i) q^{96} +(3.98514 - 6.90246i) q^{97} +(-0.965543 - 4.89786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q + 2q^{2} + q^{3} - 4q^{4} - 4q^{5} + 2q^{6} - 6q^{8} - 7q^{9} + O(q^{10}) \) \( 10q + 2q^{2} + q^{3} - 4q^{4} - 4q^{5} + 2q^{6} - 6q^{8} - 7q^{9} - 14q^{10} + 4q^{11} + 2q^{12} + 8q^{13} - 19q^{15} + 2q^{16} + 24q^{17} - 2q^{18} + 2q^{19} - 5q^{20} - q^{22} + 3q^{23} + 9q^{24} - q^{25} + 22q^{26} + 7q^{27} + 7q^{29} + 10q^{30} + 3q^{31} - 2q^{32} + 13q^{33} - 3q^{34} + 34q^{36} - 20q^{38} - 22q^{39} + 3q^{40} - 5q^{41} - 7q^{43} + 20q^{44} - 17q^{45} - 6q^{46} - 27q^{47} + 5q^{48} + 19q^{50} - 15q^{51} + 10q^{52} + 42q^{53} - 52q^{54} - 4q^{55} - 4q^{57} - 10q^{58} - 30q^{59} + 31q^{60} + 14q^{61} + 12q^{62} - 50q^{64} - 11q^{65} - 22q^{66} - 2q^{67} - 27q^{68} - 15q^{69} - 6q^{71} - 12q^{72} + 30q^{73} - 36q^{74} + 17q^{75} - 5q^{76} - 20q^{78} - 4q^{79} + 40q^{80} - 31q^{81} - 10q^{82} - 9q^{83} - 6q^{85} - 8q^{86} + 34q^{87} - 18q^{88} + 56q^{89} - 28q^{90} + 27q^{92} + 18q^{93} + 3q^{94} - 14q^{95} + 58q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.02682 + 1.77851i −0.726073 + 1.25760i 0.232458 + 0.972607i \(0.425323\pi\)
−0.958531 + 0.284989i \(0.908010\pi\)
\(3\) −0.608729 1.62156i −0.351450 0.936207i
\(4\) −1.10873 1.92038i −0.554365 0.960188i
\(5\) −0.0731228 0.126652i −0.0327015 0.0566407i 0.849211 0.528053i \(-0.177078\pi\)
−0.881913 + 0.471412i \(0.843744\pi\)
\(6\) 3.50901 + 0.582422i 1.43255 + 0.237773i
\(7\) 0 0
\(8\) 0.446582 0.157891
\(9\) −2.25890 + 1.97418i −0.752966 + 0.658060i
\(10\) 0.300337 0.0949748
\(11\) −0.832020 + 1.44110i −0.250864 + 0.434508i −0.963764 0.266757i \(-0.914048\pi\)
0.712900 + 0.701265i \(0.247381\pi\)
\(12\) −2.43908 + 2.96686i −0.704103 + 0.856458i
\(13\) −0.0999454 0.173111i −0.0277199 0.0480122i 0.851833 0.523814i \(-0.175491\pi\)
−0.879553 + 0.475802i \(0.842158\pi\)
\(14\) 0 0
\(15\) −0.160862 + 0.195670i −0.0415345 + 0.0505218i
\(16\) 1.75890 3.04650i 0.439724 0.761625i
\(17\) 6.27110 1.52097 0.760483 0.649358i \(-0.224962\pi\)
0.760483 + 0.649358i \(0.224962\pi\)
\(18\) −1.19161 6.04460i −0.280865 1.42473i
\(19\) 6.91758 1.58700 0.793500 0.608570i \(-0.208256\pi\)
0.793500 + 0.608570i \(0.208256\pi\)
\(20\) −0.162147 + 0.280847i −0.0362571 + 0.0627992i
\(21\) 0 0
\(22\) −1.70867 2.95951i −0.364291 0.630970i
\(23\) 3.09092 + 5.35363i 0.644501 + 1.11631i 0.984417 + 0.175852i \(0.0562682\pi\)
−0.339916 + 0.940456i \(0.610399\pi\)
\(24\) −0.271848 0.724159i −0.0554907 0.147818i
\(25\) 2.48931 4.31160i 0.497861 0.862321i
\(26\) 0.410505 0.0805066
\(27\) 4.57630 + 2.46119i 0.880710 + 0.473657i
\(28\) 0 0
\(29\) −2.46757 + 4.27396i −0.458217 + 0.793655i −0.998867 0.0475930i \(-0.984845\pi\)
0.540650 + 0.841248i \(0.318178\pi\)
\(30\) −0.182824 0.487013i −0.0333789 0.0889160i
\(31\) −1.25890 2.18047i −0.226105 0.391625i 0.730546 0.682864i \(-0.239266\pi\)
−0.956650 + 0.291239i \(0.905932\pi\)
\(32\) 4.05873 + 7.02993i 0.717490 + 1.24273i
\(33\) 2.84330 + 0.471928i 0.494956 + 0.0821522i
\(34\) −6.43931 + 11.1532i −1.10433 + 1.91276i
\(35\) 0 0
\(36\) 6.29567 + 2.14910i 1.04928 + 0.358184i
\(37\) 7.00046 1.15087 0.575434 0.817848i \(-0.304833\pi\)
0.575434 + 0.817848i \(0.304833\pi\)
\(38\) −7.10312 + 12.3030i −1.15228 + 1.99581i
\(39\) −0.219869 + 0.267445i −0.0352072 + 0.0428254i
\(40\) −0.0326554 0.0565608i −0.00516327 0.00894304i
\(41\) −1.15895 2.00736i −0.180998 0.313498i 0.761223 0.648491i \(-0.224599\pi\)
−0.942221 + 0.334993i \(0.891266\pi\)
\(42\) 0 0
\(43\) −0.940993 + 1.62985i −0.143500 + 0.248550i −0.928812 0.370550i \(-0.879169\pi\)
0.785312 + 0.619100i \(0.212502\pi\)
\(44\) 3.68994 0.556280
\(45\) 0.415212 + 0.141737i 0.0618961 + 0.0211290i
\(46\) −12.6953 −1.87182
\(47\) −0.905887 + 1.56904i −0.132137 + 0.228868i −0.924500 0.381181i \(-0.875517\pi\)
0.792363 + 0.610050i \(0.208851\pi\)
\(48\) −6.01077 0.997660i −0.867579 0.144000i
\(49\) 0 0
\(50\) 5.11215 + 8.85451i 0.722967 + 1.25222i
\(51\) −3.81740 10.1690i −0.534543 1.42394i
\(52\) −0.221625 + 0.383865i −0.0307338 + 0.0532325i
\(53\) 5.34614 0.734348 0.367174 0.930152i \(-0.380325\pi\)
0.367174 + 0.930152i \(0.380325\pi\)
\(54\) −9.07630 + 5.61178i −1.23513 + 0.763667i
\(55\) 0.243359 0.0328145
\(56\) 0 0
\(57\) −4.21093 11.2172i −0.557751 1.48576i
\(58\) −5.06752 8.77720i −0.665398 1.15250i
\(59\) −2.28549 3.95859i −0.297546 0.515364i 0.678028 0.735036i \(-0.262835\pi\)
−0.975574 + 0.219672i \(0.929501\pi\)
\(60\) 0.554112 + 0.0919709i 0.0715356 + 0.0118734i
\(61\) −0.339138 + 0.587404i −0.0434221 + 0.0752094i −0.886920 0.461924i \(-0.847159\pi\)
0.843498 + 0.537133i \(0.180493\pi\)
\(62\) 5.17066 0.656674
\(63\) 0 0
\(64\) −9.63481 −1.20435
\(65\) −0.0146166 + 0.0253167i −0.00181296 + 0.00314015i
\(66\) −3.75890 + 4.57226i −0.462688 + 0.562806i
\(67\) 3.09342 + 5.35796i 0.377921 + 0.654579i 0.990760 0.135630i \(-0.0433057\pi\)
−0.612838 + 0.790208i \(0.709972\pi\)
\(68\) −6.95296 12.0429i −0.843170 1.46041i
\(69\) 6.79968 8.27101i 0.818586 0.995713i
\(70\) 0 0
\(71\) 1.27749 0.151611 0.0758053 0.997123i \(-0.475847\pi\)
0.0758053 + 0.997123i \(0.475847\pi\)
\(72\) −1.00878 + 0.881633i −0.118886 + 0.103901i
\(73\) −1.55721 −0.182257 −0.0911286 0.995839i \(-0.529047\pi\)
−0.0911286 + 0.995839i \(0.529047\pi\)
\(74\) −7.18823 + 12.4504i −0.835614 + 1.44733i
\(75\) −8.50683 1.41195i −0.982284 0.163038i
\(76\) −7.66972 13.2843i −0.879777 1.52382i
\(77\) 0 0
\(78\) −0.249886 0.665657i −0.0282940 0.0753708i
\(79\) −6.39787 + 11.0814i −0.719817 + 1.24676i 0.241255 + 0.970462i \(0.422441\pi\)
−0.961072 + 0.276298i \(0.910892\pi\)
\(80\) −0.514462 −0.0575186
\(81\) 1.20524 8.91894i 0.133915 0.990993i
\(82\) 4.76015 0.525671
\(83\) −3.75687 + 6.50709i −0.412370 + 0.714246i −0.995148 0.0983854i \(-0.968632\pi\)
0.582778 + 0.812631i \(0.301966\pi\)
\(84\) 0 0
\(85\) −0.458561 0.794251i −0.0497379 0.0861486i
\(86\) −1.93247 3.34713i −0.208383 0.360930i
\(87\) 8.43256 + 1.39963i 0.904065 + 0.150056i
\(88\) −0.371566 + 0.643571i −0.0396090 + 0.0686048i
\(89\) 9.06788 0.961193 0.480597 0.876942i \(-0.340420\pi\)
0.480597 + 0.876942i \(0.340420\pi\)
\(90\) −0.678430 + 0.592918i −0.0715128 + 0.0624991i
\(91\) 0 0
\(92\) 6.85398 11.8714i 0.714577 1.23768i
\(93\) −2.76944 + 3.36869i −0.287177 + 0.349317i
\(94\) −1.86037 3.22226i −0.191883 0.332350i
\(95\) −0.505833 0.876128i −0.0518973 0.0898888i
\(96\) 8.92877 10.8608i 0.911289 1.10848i
\(97\) 3.98514 6.90246i 0.404630 0.700839i −0.589649 0.807660i \(-0.700734\pi\)
0.994278 + 0.106821i \(0.0340671\pi\)
\(98\) 0 0
\(99\) −0.965543 4.89786i −0.0970408 0.492253i
\(100\) −11.0399 −1.10399
\(101\) 7.42150 12.8544i 0.738467 1.27906i −0.214719 0.976676i \(-0.568883\pi\)
0.953186 0.302386i \(-0.0977832\pi\)
\(102\) 22.0054 + 3.65243i 2.17886 + 0.361644i
\(103\) −0.101974 0.176624i −0.0100478 0.0174033i 0.860958 0.508676i \(-0.169865\pi\)
−0.871006 + 0.491273i \(0.836532\pi\)
\(104\) −0.0446339 0.0773081i −0.00437671 0.00758068i
\(105\) 0 0
\(106\) −5.48953 + 9.50815i −0.533191 + 0.923513i
\(107\) −6.96889 −0.673708 −0.336854 0.941557i \(-0.609363\pi\)
−0.336854 + 0.941557i \(0.609363\pi\)
\(108\) −0.347467 11.5170i −0.0334350 1.10822i
\(109\) −6.66116 −0.638024 −0.319012 0.947751i \(-0.603351\pi\)
−0.319012 + 0.947751i \(0.603351\pi\)
\(110\) −0.249886 + 0.432816i −0.0238257 + 0.0412674i
\(111\) −4.26138 11.3516i −0.404472 1.07745i
\(112\) 0 0
\(113\) −0.0193234 0.0334691i −0.00181779 0.00314851i 0.865115 0.501573i \(-0.167245\pi\)
−0.866933 + 0.498425i \(0.833912\pi\)
\(114\) 24.2739 + 4.02895i 2.27345 + 0.377345i
\(115\) 0.452033 0.782945i 0.0421523 0.0730100i
\(116\) 10.9435 1.01608
\(117\) 0.567518 + 0.193729i 0.0524670 + 0.0179102i
\(118\) 9.38718 0.864160
\(119\) 0 0
\(120\) −0.0718382 + 0.0873827i −0.00655790 + 0.00797692i
\(121\) 4.11548 + 7.12823i 0.374135 + 0.648021i
\(122\) −0.696469 1.20632i −0.0630553 0.109215i
\(123\) −2.54957 + 3.10125i −0.229887 + 0.279630i
\(124\) −2.79155 + 4.83511i −0.250689 + 0.434206i
\(125\) −1.45933 −0.130526
\(126\) 0 0
\(127\) 13.4788 1.19605 0.598027 0.801476i \(-0.295952\pi\)
0.598027 + 0.801476i \(0.295952\pi\)
\(128\) 1.77577 3.07572i 0.156957 0.271858i
\(129\) 3.21570 + 0.533739i 0.283127 + 0.0469931i
\(130\) −0.0300173 0.0519914i −0.00263269 0.00455995i
\(131\) −9.91665 17.1761i −0.866422 1.50069i −0.865628 0.500687i \(-0.833081\pi\)
−0.000793988 1.00000i \(-0.500253\pi\)
\(132\) −2.24617 5.98345i −0.195504 0.520793i
\(133\) 0 0
\(134\) −12.7056 −1.09759
\(135\) −0.0229161 0.759569i −0.00197230 0.0653733i
\(136\) 2.80056 0.240146
\(137\) 3.22255 5.58162i 0.275321 0.476870i −0.694895 0.719111i \(-0.744549\pi\)
0.970216 + 0.242241i \(0.0778826\pi\)
\(138\) 7.72800 + 20.5862i 0.657851 + 1.75241i
\(139\) −6.26527 10.8518i −0.531413 0.920435i −0.999328 0.0366611i \(-0.988328\pi\)
0.467914 0.883774i \(-0.345006\pi\)
\(140\) 0 0
\(141\) 3.09573 + 0.513826i 0.260708 + 0.0432720i
\(142\) −1.31176 + 2.27203i −0.110080 + 0.190665i
\(143\) 0.332626 0.0278156
\(144\) 2.04117 + 10.3541i 0.170097 + 0.862842i
\(145\) 0.721743 0.0599375
\(146\) 1.59897 2.76950i 0.132332 0.229206i
\(147\) 0 0
\(148\) −7.76161 13.4435i −0.638000 1.10505i
\(149\) −8.88364 15.3869i −0.727776 1.26054i −0.957821 0.287365i \(-0.907221\pi\)
0.230045 0.973180i \(-0.426113\pi\)
\(150\) 11.2462 13.6796i 0.918246 1.11694i
\(151\) −4.23300 + 7.33177i −0.344476 + 0.596651i −0.985259 0.171072i \(-0.945277\pi\)
0.640782 + 0.767723i \(0.278610\pi\)
\(152\) 3.08927 0.250573
\(153\) −14.1658 + 12.3803i −1.14524 + 1.00089i
\(154\) 0 0
\(155\) −0.184108 + 0.318885i −0.0147879 + 0.0256135i
\(156\) 0.757369 + 0.125707i 0.0606381 + 0.0100646i
\(157\) 2.84968 + 4.93579i 0.227429 + 0.393919i 0.957045 0.289938i \(-0.0936347\pi\)
−0.729616 + 0.683857i \(0.760301\pi\)
\(158\) −13.1390 22.7573i −1.04528 1.81048i
\(159\) −3.25435 8.66907i −0.258087 0.687502i
\(160\) 0.593572 1.02810i 0.0469260 0.0812782i
\(161\) 0 0
\(162\) 14.6248 + 11.3017i 1.14904 + 0.887944i
\(163\) 2.12535 0.166470 0.0832349 0.996530i \(-0.473475\pi\)
0.0832349 + 0.996530i \(0.473475\pi\)
\(164\) −2.56993 + 4.45125i −0.200678 + 0.347584i
\(165\) −0.148140 0.394620i −0.0115326 0.0307211i
\(166\) −7.71528 13.3632i −0.598821 1.03719i
\(167\) 5.78723 + 10.0238i 0.447829 + 0.775663i 0.998244 0.0592278i \(-0.0188638\pi\)
−0.550415 + 0.834891i \(0.685530\pi\)
\(168\) 0 0
\(169\) 6.48002 11.2237i 0.498463 0.863364i
\(170\) 1.88344 0.144453
\(171\) −15.6261 + 13.6565i −1.19496 + 1.04434i
\(172\) 4.17323 0.318206
\(173\) −7.95546 + 13.7793i −0.604842 + 1.04762i 0.387234 + 0.921981i \(0.373430\pi\)
−0.992076 + 0.125636i \(0.959903\pi\)
\(174\) −11.1480 + 13.5602i −0.845127 + 1.02800i
\(175\) 0 0
\(176\) 2.92688 + 5.06950i 0.220622 + 0.382128i
\(177\) −5.02783 + 6.11577i −0.377915 + 0.459689i
\(178\) −9.31110 + 16.1273i −0.697897 + 1.20879i
\(179\) −7.75331 −0.579509 −0.289755 0.957101i \(-0.593574\pi\)
−0.289755 + 0.957101i \(0.593574\pi\)
\(180\) −0.188168 0.954510i −0.0140252 0.0711450i
\(181\) 12.1618 0.903982 0.451991 0.892022i \(-0.350714\pi\)
0.451991 + 0.892022i \(0.350714\pi\)
\(182\) 0 0
\(183\) 1.15895 + 0.192362i 0.0856722 + 0.0142198i
\(184\) 1.38035 + 2.39084i 0.101761 + 0.176255i
\(185\) −0.511893 0.886625i −0.0376351 0.0651860i
\(186\) −3.14753 8.38452i −0.230788 0.614783i
\(187\) −5.21769 + 9.03730i −0.381555 + 0.660873i
\(188\) 4.01754 0.293009
\(189\) 0 0
\(190\) 2.07760 0.150725
\(191\) 2.48383 4.30211i 0.179723 0.311290i −0.762062 0.647504i \(-0.775813\pi\)
0.941786 + 0.336214i \(0.109146\pi\)
\(192\) 5.86499 + 15.6234i 0.423269 + 1.12752i
\(193\) 7.45221 + 12.9076i 0.536422 + 0.929110i 0.999093 + 0.0425800i \(0.0135577\pi\)
−0.462671 + 0.886530i \(0.653109\pi\)
\(194\) 8.18406 + 14.1752i 0.587581 + 1.01772i
\(195\) 0.0499500 + 0.00829064i 0.00357699 + 0.000593705i
\(196\) 0 0
\(197\) −21.2608 −1.51477 −0.757386 0.652968i \(-0.773524\pi\)
−0.757386 + 0.652968i \(0.773524\pi\)
\(198\) 9.70233 + 3.31200i 0.689514 + 0.235374i
\(199\) −19.9442 −1.41380 −0.706902 0.707311i \(-0.749908\pi\)
−0.706902 + 0.707311i \(0.749908\pi\)
\(200\) 1.11168 1.92549i 0.0786077 0.136152i
\(201\) 6.80518 8.27770i 0.480001 0.583864i
\(202\) 15.2411 + 26.3984i 1.07236 + 1.85739i
\(203\) 0 0
\(204\) −15.2957 + 18.6055i −1.07092 + 1.30264i
\(205\) −0.169492 + 0.293568i −0.0118378 + 0.0205037i
\(206\) 0.418838 0.0291818
\(207\) −17.5511 5.99127i −1.21988 0.416422i
\(208\) −0.703175 −0.0487564
\(209\) −5.75556 + 9.96893i −0.398121 + 0.689565i
\(210\) 0 0
\(211\) 11.7569 + 20.3636i 0.809381 + 1.40189i 0.913293 + 0.407303i \(0.133531\pi\)
−0.103912 + 0.994587i \(0.533136\pi\)
\(212\) −5.92742 10.2666i −0.407097 0.705112i
\(213\) −0.777647 2.07153i −0.0532835 0.141939i
\(214\) 7.15581 12.3942i 0.489161 0.847252i
\(215\) 0.275232 0.0187707
\(216\) 2.04370 + 1.09912i 0.139056 + 0.0747860i
\(217\) 0 0
\(218\) 6.83983 11.8469i 0.463252 0.802376i
\(219\) 0.947916 + 2.52510i 0.0640543 + 0.170630i
\(220\) −0.269819 0.467340i −0.0181912 0.0315081i
\(221\) −0.626768 1.08559i −0.0421610 0.0730250i
\(222\) 24.5647 + 4.07722i 1.64867 + 0.273645i
\(223\) −2.03052 + 3.51696i −0.135974 + 0.235513i −0.925969 0.377600i \(-0.876750\pi\)
0.789995 + 0.613113i \(0.210083\pi\)
\(224\) 0 0
\(225\) 2.88879 + 14.6538i 0.192586 + 0.976921i
\(226\) 0.0793667 0.00527940
\(227\) −1.92643 + 3.33667i −0.127861 + 0.221462i −0.922848 0.385165i \(-0.874145\pi\)
0.794986 + 0.606627i \(0.207478\pi\)
\(228\) −16.8725 + 20.5235i −1.11741 + 1.35920i
\(229\) 6.55812 + 11.3590i 0.433373 + 0.750624i 0.997161 0.0752952i \(-0.0239899\pi\)
−0.563788 + 0.825919i \(0.690657\pi\)
\(230\) 0.928316 + 1.60789i 0.0612113 + 0.106021i
\(231\) 0 0
\(232\) −1.10197 + 1.90868i −0.0723481 + 0.125311i
\(233\) 17.5023 1.14661 0.573307 0.819340i \(-0.305660\pi\)
0.573307 + 0.819340i \(0.305660\pi\)
\(234\) −0.927288 + 0.810410i −0.0606187 + 0.0529781i
\(235\) 0.264964 0.0172844
\(236\) −5.06798 + 8.77801i −0.329898 + 0.571400i
\(237\) 21.8638 + 3.62892i 1.42020 + 0.235724i
\(238\) 0 0
\(239\) 3.65857 + 6.33683i 0.236653 + 0.409895i 0.959752 0.280849i \(-0.0906161\pi\)
−0.723099 + 0.690745i \(0.757283\pi\)
\(240\) 0.313168 + 0.834230i 0.0202149 + 0.0538493i
\(241\) 3.11553 5.39626i 0.200689 0.347604i −0.748062 0.663629i \(-0.769015\pi\)
0.948751 + 0.316026i \(0.102349\pi\)
\(242\) −16.9035 −1.08660
\(243\) −15.1962 + 3.47486i −0.974839 + 0.222912i
\(244\) 1.50405 0.0962868
\(245\) 0 0
\(246\) −2.89764 7.71886i −0.184747 0.492137i
\(247\) −0.691380 1.19751i −0.0439915 0.0761954i
\(248\) −0.562201 0.973761i −0.0356998 0.0618339i
\(249\) 12.8385 + 2.13092i 0.813609 + 0.135042i
\(250\) 1.49847 2.59543i 0.0947717 0.164149i
\(251\) −5.65283 −0.356803 −0.178402 0.983958i \(-0.557093\pi\)
−0.178402 + 0.983958i \(0.557093\pi\)
\(252\) 0 0
\(253\) −10.2868 −0.646727
\(254\) −13.8404 + 23.9722i −0.868422 + 1.50415i
\(255\) −1.00878 + 1.22707i −0.0631725 + 0.0768419i
\(256\) −5.98801 10.3715i −0.374250 0.648221i
\(257\) 5.90082 + 10.2205i 0.368083 + 0.637539i 0.989266 0.146127i \(-0.0466808\pi\)
−0.621183 + 0.783666i \(0.713347\pi\)
\(258\) −4.25121 + 5.17110i −0.264669 + 0.321939i
\(259\) 0 0
\(260\) 0.0648233 0.00402017
\(261\) −2.86357 14.5259i −0.177250 0.899129i
\(262\) 40.7306 2.51634
\(263\) 11.1200 19.2605i 0.685691 1.18765i −0.287528 0.957772i \(-0.592834\pi\)
0.973219 0.229879i \(-0.0738331\pi\)
\(264\) 1.26977 + 0.210755i 0.0781489 + 0.0129711i
\(265\) −0.390925 0.677101i −0.0240143 0.0415940i
\(266\) 0 0
\(267\) −5.51988 14.7041i −0.337811 0.899876i
\(268\) 6.85953 11.8810i 0.419012 0.725750i
\(269\) −2.38884 −0.145650 −0.0728251 0.997345i \(-0.523201\pi\)
−0.0728251 + 0.997345i \(0.523201\pi\)
\(270\) 1.37443 + 0.739186i 0.0836452 + 0.0449854i
\(271\) −23.2258 −1.41087 −0.705435 0.708775i \(-0.749248\pi\)
−0.705435 + 0.708775i \(0.749248\pi\)
\(272\) 11.0302 19.1049i 0.668806 1.15841i
\(273\) 0 0
\(274\) 6.61797 + 11.4627i 0.399806 + 0.692484i
\(275\) 4.14231 + 7.17469i 0.249790 + 0.432650i
\(276\) −23.4224 3.88763i −1.40987 0.234008i
\(277\) 2.30900 3.99931i 0.138734 0.240295i −0.788283 0.615312i \(-0.789030\pi\)
0.927018 + 0.375017i \(0.122363\pi\)
\(278\) 25.7333 1.54338
\(279\) 7.14837 + 2.44018i 0.427962 + 0.146090i
\(280\) 0 0
\(281\) 5.90841 10.2337i 0.352466 0.610489i −0.634215 0.773157i \(-0.718676\pi\)
0.986681 + 0.162668i \(0.0520098\pi\)
\(282\) −4.09261 + 4.97818i −0.243712 + 0.296446i
\(283\) 7.92483 + 13.7262i 0.471082 + 0.815939i 0.999453 0.0330753i \(-0.0105301\pi\)
−0.528370 + 0.849014i \(0.677197\pi\)
\(284\) −1.41639 2.45327i −0.0840475 0.145575i
\(285\) −1.11278 + 1.35356i −0.0659152 + 0.0801781i
\(286\) −0.341548 + 0.591579i −0.0201962 + 0.0349808i
\(287\) 0 0
\(288\) −23.0466 7.86723i −1.35803 0.463581i
\(289\) 22.3267 1.31334
\(290\) −0.741102 + 1.28363i −0.0435190 + 0.0753772i
\(291\) −13.6186 2.26040i −0.798337 0.132507i
\(292\) 1.72652 + 2.99042i 0.101037 + 0.175001i
\(293\) −7.04804 12.2076i −0.411751 0.713173i 0.583330 0.812235i \(-0.301749\pi\)
−0.995081 + 0.0990615i \(0.968416\pi\)
\(294\) 0 0
\(295\) −0.334243 + 0.578927i −0.0194604 + 0.0337064i
\(296\) 3.12628 0.181711
\(297\) −7.35440 + 4.54715i −0.426746 + 0.263853i
\(298\) 36.4877 2.11367
\(299\) 0.617846 1.07014i 0.0357310 0.0618878i
\(300\) 6.72029 + 17.9018i 0.387996 + 1.03356i
\(301\) 0 0
\(302\) −8.69307 15.0568i −0.500230 0.866424i
\(303\) −25.3619 4.20953i −1.45700 0.241831i
\(304\) 12.1673 21.0744i 0.697843 1.20870i
\(305\) 0.0991949 0.00567988
\(306\) −7.47269 37.9063i −0.427185 2.16696i
\(307\) −27.3916 −1.56332 −0.781660 0.623704i \(-0.785627\pi\)
−0.781660 + 0.623704i \(0.785627\pi\)
\(308\) 0 0
\(309\) −0.224332 + 0.272873i −0.0127618 + 0.0155232i
\(310\) −0.378093 0.654877i −0.0214742 0.0371945i
\(311\) −7.02785 12.1726i −0.398513 0.690244i 0.595030 0.803704i \(-0.297140\pi\)
−0.993543 + 0.113459i \(0.963807\pi\)
\(312\) −0.0981896 + 0.119436i −0.00555889 + 0.00676174i
\(313\) 10.8723 18.8314i 0.614540 1.06441i −0.375925 0.926650i \(-0.622675\pi\)
0.990465 0.137764i \(-0.0439916\pi\)
\(314\) −11.7045 −0.660520
\(315\) 0 0
\(316\) 28.3740 1.59616
\(317\) −4.28148 + 7.41575i −0.240472 + 0.416510i −0.960849 0.277073i \(-0.910636\pi\)
0.720377 + 0.693583i \(0.243969\pi\)
\(318\) 18.7597 + 3.11371i 1.05199 + 0.174608i
\(319\) −4.10614 7.11204i −0.229900 0.398198i
\(320\) 0.704524 + 1.22027i 0.0393841 + 0.0682153i
\(321\) 4.24217 + 11.3005i 0.236775 + 0.630730i
\(322\) 0 0
\(323\) 43.3808 2.41377
\(324\) −18.4640 + 7.57418i −1.02578 + 0.420788i
\(325\) −0.995179 −0.0552026
\(326\) −2.18235 + 3.77995i −0.120869 + 0.209352i
\(327\) 4.05484 + 10.8015i 0.224233 + 0.597322i
\(328\) −0.517568 0.896453i −0.0285779 0.0494984i
\(329\) 0 0
\(330\) 0.853949 + 0.141737i 0.0470083 + 0.00780239i
\(331\) −5.42360 + 9.39396i −0.298108 + 0.516339i −0.975703 0.219097i \(-0.929689\pi\)
0.677595 + 0.735435i \(0.263022\pi\)
\(332\) 16.6614 0.914413
\(333\) −15.8133 + 13.8201i −0.866564 + 0.757340i
\(334\) −23.7698 −1.30063
\(335\) 0.452399 0.783578i 0.0247172 0.0428114i
\(336\) 0 0
\(337\) 1.67411 + 2.89964i 0.0911945 + 0.157954i 0.908014 0.418940i \(-0.137598\pi\)
−0.816819 + 0.576893i \(0.804265\pi\)
\(338\) 13.3077 + 23.0496i 0.723842 + 1.25373i
\(339\) −0.0425093 + 0.0517076i −0.00230879 + 0.00280837i
\(340\) −1.01684 + 1.76122i −0.0551459 + 0.0955154i
\(341\) 4.18971 0.226886
\(342\) −8.24304 41.8140i −0.445732 2.26104i
\(343\) 0 0
\(344\) −0.420231 + 0.727861i −0.0226573 + 0.0392437i
\(345\) −1.54476 0.256397i −0.0831669 0.0138039i
\(346\) −16.3377 28.2977i −0.878319 1.52129i
\(347\) 5.76652 + 9.98790i 0.309563 + 0.536178i 0.978267 0.207350i \(-0.0664840\pi\)
−0.668704 + 0.743529i \(0.733151\pi\)
\(348\) −6.66161 17.7455i −0.357100 0.951257i
\(349\) 4.44917 7.70619i 0.238159 0.412503i −0.722027 0.691865i \(-0.756789\pi\)
0.960186 + 0.279362i \(0.0901228\pi\)
\(350\) 0 0
\(351\) −0.0313221 1.03819i −0.00167185 0.0554145i
\(352\) −13.5078 −0.719968
\(353\) −1.32349 + 2.29236i −0.0704424 + 0.122010i −0.899095 0.437753i \(-0.855774\pi\)
0.828653 + 0.559763i \(0.189108\pi\)
\(354\) −5.71425 15.2219i −0.303709 0.809032i
\(355\) −0.0934139 0.161798i −0.00495790 0.00858733i
\(356\) −10.0538 17.4137i −0.532852 0.922926i
\(357\) 0 0
\(358\) 7.96127 13.7893i 0.420766 0.728789i
\(359\) 25.9671 1.37049 0.685245 0.728312i \(-0.259695\pi\)
0.685245 + 0.728312i \(0.259695\pi\)
\(360\) 0.185426 + 0.0632974i 0.00977282 + 0.00333607i
\(361\) 28.8529 1.51857
\(362\) −12.4880 + 21.6299i −0.656357 + 1.13684i
\(363\) 9.05362 11.0127i 0.475192 0.578014i
\(364\) 0 0
\(365\) 0.113867 + 0.197224i 0.00596009 + 0.0103232i
\(366\) −1.53215 + 1.86369i −0.0800870 + 0.0974164i
\(367\) 8.79371 15.2312i 0.459028 0.795060i −0.539882 0.841741i \(-0.681531\pi\)
0.998910 + 0.0466808i \(0.0148644\pi\)
\(368\) 21.7464 1.13361
\(369\) 6.58085 + 2.24645i 0.342585 + 0.116946i
\(370\) 2.10249 0.109303
\(371\) 0 0
\(372\) 9.53971 + 1.58339i 0.494611 + 0.0820950i
\(373\) −0.407538 0.705876i −0.0211015 0.0365489i 0.855282 0.518163i \(-0.173384\pi\)
−0.876383 + 0.481614i \(0.840051\pi\)
\(374\) −10.7153 18.5594i −0.554074 0.959684i
\(375\) 0.888336 + 2.36639i 0.0458735 + 0.122200i
\(376\) −0.404553 + 0.700707i −0.0208632 + 0.0361362i
\(377\) 0.986490 0.0508068
\(378\) 0 0
\(379\) −20.4312 −1.04948 −0.524741 0.851262i \(-0.675838\pi\)
−0.524741 + 0.851262i \(0.675838\pi\)
\(380\) −1.12166 + 1.94278i −0.0575401 + 0.0996624i
\(381\) −8.20496 21.8567i −0.420353 1.11975i
\(382\) 5.10090 + 8.83501i 0.260985 + 0.452039i
\(383\) 8.94638 + 15.4956i 0.457139 + 0.791788i 0.998808 0.0488039i \(-0.0155409\pi\)
−0.541670 + 0.840591i \(0.682208\pi\)
\(384\) −6.06843 1.00723i −0.309678 0.0514000i
\(385\) 0 0
\(386\) −30.6084 −1.55793
\(387\) −1.09200 5.53935i −0.0555097 0.281581i
\(388\) −17.6738 −0.897249
\(389\) −7.81392 + 13.5341i −0.396181 + 0.686206i −0.993251 0.115983i \(-0.962998\pi\)
0.597070 + 0.802189i \(0.296331\pi\)
\(390\) −0.0660347 + 0.0803234i −0.00334380 + 0.00406734i
\(391\) 19.3835 + 33.5731i 0.980264 + 1.69787i
\(392\) 0 0
\(393\) −21.8156 + 26.5360i −1.10045 + 1.33857i
\(394\) 21.8311 37.8126i 1.09984 1.90497i
\(395\) 1.87132 0.0941564
\(396\) −8.33520 + 7.28460i −0.418860 + 0.366065i
\(397\) 19.2613 0.966696 0.483348 0.875428i \(-0.339421\pi\)
0.483348 + 0.875428i \(0.339421\pi\)
\(398\) 20.4791 35.4709i 1.02653 1.77799i
\(399\) 0 0
\(400\) −8.75687 15.1673i −0.437843 0.758367i
\(401\) −7.15064 12.3853i −0.357086 0.618491i 0.630387 0.776281i \(-0.282896\pi\)
−0.987473 + 0.157790i \(0.949563\pi\)
\(402\) 7.73425 + 20.6028i 0.385749 + 1.02757i
\(403\) −0.251642 + 0.435857i −0.0125352 + 0.0217116i
\(404\) −32.9137 −1.63752
\(405\) −1.21774 + 0.499532i −0.0605098 + 0.0248219i
\(406\) 0 0
\(407\) −5.82452 + 10.0884i −0.288711 + 0.500062i
\(408\) −1.70479 4.54128i −0.0843994 0.224827i
\(409\) 15.9305 + 27.5924i 0.787712 + 1.36436i 0.927366 + 0.374156i \(0.122068\pi\)
−0.139654 + 0.990200i \(0.544599\pi\)
\(410\) −0.348076 0.602885i −0.0171902 0.0297744i
\(411\) −11.0126 1.82785i −0.543210 0.0901614i
\(412\) −0.226124 + 0.391657i −0.0111403 + 0.0192956i
\(413\) 0 0
\(414\) 28.6774 25.0628i 1.40942 1.23177i
\(415\) 1.09885 0.0539405
\(416\) 0.811304 1.40522i 0.0397774 0.0688965i
\(417\) −13.7829 + 16.7653i −0.674952 + 0.821000i
\(418\) −11.8199 20.4726i −0.578130 1.00135i
\(419\) −11.9480 20.6945i −0.583697 1.01099i −0.995036 0.0995110i \(-0.968272\pi\)
0.411339 0.911482i \(-0.365061\pi\)
\(420\) 0 0
\(421\) −1.22251 + 2.11744i −0.0595813 + 0.103198i −0.894278 0.447513i \(-0.852310\pi\)
0.834696 + 0.550711i \(0.185643\pi\)
\(422\) −48.2892 −2.35068
\(423\) −1.05126 5.33269i −0.0511142 0.259284i
\(424\) 2.38749 0.115947
\(425\) 15.6107 27.0385i 0.757230 1.31156i
\(426\) 4.48274 + 0.744039i 0.217189 + 0.0360488i
\(427\) 0 0
\(428\) 7.72661 + 13.3829i 0.373480 + 0.646886i
\(429\) −0.202479 0.539373i −0.00977580 0.0260412i
\(430\) −0.282615 + 0.489503i −0.0136289 + 0.0236059i
\(431\) −4.92764 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(432\) 15.5473 9.61272i 0.748018 0.462492i
\(433\) −30.8539 −1.48274 −0.741371 0.671095i \(-0.765824\pi\)
−0.741371 + 0.671095i \(0.765824\pi\)
\(434\) 0 0
\(435\) −0.439346 1.17035i −0.0210650 0.0561139i
\(436\) 7.38543 + 12.7919i 0.353698 + 0.612622i
\(437\) 21.3817 + 37.0341i 1.02282 + 1.77158i
\(438\) −5.46425 0.906950i −0.261092 0.0433358i
\(439\) 1.22411 2.12022i 0.0584235 0.101192i −0.835334 0.549742i \(-0.814726\pi\)
0.893758 + 0.448550i \(0.148059\pi\)
\(440\) 0.108680 0.00518110
\(441\) 0 0
\(442\) 2.57432 0.122448
\(443\) 13.1475 22.7722i 0.624657 1.08194i −0.363950 0.931419i \(-0.618572\pi\)
0.988607 0.150520i \(-0.0480946\pi\)
\(444\) −17.0747 + 20.7693i −0.810329 + 0.985670i
\(445\) −0.663069 1.14847i −0.0314325 0.0544427i
\(446\) −4.16996 7.22259i −0.197453 0.341999i
\(447\) −19.5430 + 23.7718i −0.924354 + 1.12437i
\(448\) 0 0
\(449\) −38.7077 −1.82673 −0.913365 0.407141i \(-0.866526\pi\)
−0.913365 + 0.407141i \(0.866526\pi\)
\(450\) −29.0282 9.90912i −1.36840 0.467120i
\(451\) 3.85709 0.181623
\(452\) −0.0428488 + 0.0742163i −0.00201544 + 0.00349084i
\(453\) 14.4656 + 2.40099i 0.679655 + 0.112808i
\(454\) −3.95620 6.85233i −0.185673 0.321596i
\(455\) 0 0
\(456\) −1.88053 5.00943i −0.0880638 0.234588i
\(457\) 4.57756 7.92856i 0.214129 0.370882i −0.738874 0.673844i \(-0.764642\pi\)
0.953003 + 0.302961i \(0.0979754\pi\)
\(458\) −26.9361 −1.25864
\(459\) 28.6985 + 15.4344i 1.33953 + 0.720416i
\(460\) −2.00473 −0.0934710
\(461\) −14.6152 + 25.3143i −0.680698 + 1.17900i 0.294070 + 0.955784i \(0.404990\pi\)
−0.974768 + 0.223220i \(0.928343\pi\)
\(462\) 0 0
\(463\) −8.21031 14.2207i −0.381565 0.660891i 0.609721 0.792616i \(-0.291282\pi\)
−0.991286 + 0.131726i \(0.957948\pi\)
\(464\) 8.68041 + 15.0349i 0.402978 + 0.697978i
\(465\) 0.629162 + 0.104428i 0.0291767 + 0.00484272i
\(466\) −17.9718 + 31.1280i −0.832526 + 1.44198i
\(467\) 15.3726 0.711361 0.355680 0.934608i \(-0.384249\pi\)
0.355680 + 0.934608i \(0.384249\pi\)
\(468\) −0.257191 1.30464i −0.0118887 0.0603070i
\(469\) 0 0
\(470\) −0.272071 + 0.471241i −0.0125497 + 0.0217367i
\(471\) 6.26898 7.62547i 0.288859 0.351363i
\(472\) −1.02066 1.76784i −0.0469797 0.0813713i
\(473\) −1.56585 2.71213i −0.0719979 0.124704i
\(474\) −28.9043 + 35.1586i −1.32762 + 1.61489i
\(475\) 17.2200 29.8259i 0.790106 1.36850i
\(476\) 0 0
\(477\) −12.0764 + 10.5542i −0.552939 + 0.483245i
\(478\) −15.0268 −0.687310
\(479\) −18.9646 + 32.8476i −0.866513 + 1.50084i −0.000975329 1.00000i \(0.500310\pi\)
−0.865537 + 0.500844i \(0.833023\pi\)
\(480\) −2.02844 0.336679i −0.0925854 0.0153672i
\(481\) −0.699663 1.21185i −0.0319019 0.0552557i
\(482\) 6.39820 + 11.0820i 0.291430 + 0.504772i
\(483\) 0 0
\(484\) 9.12591 15.8065i 0.414814 0.718479i
\(485\) −1.16562 −0.0529280
\(486\) 9.42377 30.5947i 0.427471 1.38780i
\(487\) −4.60495 −0.208670 −0.104335 0.994542i \(-0.533271\pi\)
−0.104335 + 0.994542i \(0.533271\pi\)
\(488\) −0.151453 + 0.262324i −0.00685595 + 0.0118749i
\(489\) −1.29376 3.44637i −0.0585058 0.155850i
\(490\) 0 0
\(491\) −15.1876 26.3056i −0.685405 1.18716i −0.973309 0.229497i \(-0.926292\pi\)
0.287904 0.957659i \(-0.407042\pi\)
\(492\) 8.78234 + 1.45768i 0.395939 + 0.0657174i
\(493\) −15.4744 + 26.8024i −0.696932 + 1.20712i
\(494\) 2.83970 0.127764
\(495\) −0.549722 + 0.480434i −0.0247082 + 0.0215939i
\(496\) −8.85709 −0.397695
\(497\) 0 0
\(498\) −16.9728 + 20.6454i −0.760568 + 0.925141i
\(499\) −4.63436 8.02694i −0.207462 0.359335i 0.743452 0.668789i \(-0.233187\pi\)
−0.950914 + 0.309454i \(0.899854\pi\)
\(500\) 1.61800 + 2.80246i 0.0723592 + 0.125330i
\(501\) 12.7313 15.4861i 0.568792 0.691868i
\(502\) 5.80445 10.0536i 0.259065 0.448715i
\(503\) 22.4230 0.999791 0.499896 0.866086i \(-0.333372\pi\)
0.499896 + 0.866086i \(0.333372\pi\)
\(504\) 0 0
\(505\) −2.17072 −0.0965960
\(506\) 10.5627 18.2952i 0.469571 0.813321i
\(507\) −22.1445 3.67552i −0.983472 0.163235i
\(508\) −14.9444 25.8844i −0.663050 1.14844i
\(509\) −18.8207 32.5984i −0.834213 1.44490i −0.894670 0.446728i \(-0.852589\pi\)
0.0604572 0.998171i \(-0.480744\pi\)
\(510\) −1.14651 3.05411i −0.0507682 0.135238i
\(511\) 0 0
\(512\) 31.6976 1.40085
\(513\) 31.6569 + 17.0255i 1.39769 + 0.751694i
\(514\) −24.2364 −1.06902
\(515\) −0.0149133 + 0.0258306i −0.000657158 + 0.00113823i
\(516\) −2.54036 6.76713i −0.111833 0.297906i
\(517\) −1.50743 2.61095i −0.0662969 0.114830i
\(518\) 0 0
\(519\) 27.1866 + 4.51240i 1.19336 + 0.198072i
\(520\) −0.00652751 + 0.0113060i −0.000286250 + 0.000495800i
\(521\) 34.9283 1.53023 0.765117 0.643891i \(-0.222681\pi\)
0.765117 + 0.643891i \(0.222681\pi\)
\(522\) 28.7748 + 9.82260i 1.25944 + 0.429924i
\(523\) −23.7471 −1.03839 −0.519194 0.854656i \(-0.673768\pi\)
−0.519194 + 0.854656i \(0.673768\pi\)
\(524\) −21.9898 + 38.0874i −0.960628 + 1.66386i
\(525\) 0 0
\(526\) 22.8366 + 39.5542i 0.995723 + 1.72464i
\(527\) −7.89468 13.6740i −0.343898 0.595648i
\(528\) 6.43881 7.83205i 0.280213 0.340846i
\(529\) −7.60755 + 13.1767i −0.330763 + 0.572898i
\(530\) 1.60564 0.0697446
\(531\) 12.9777 + 4.43008i 0.563182 + 0.192249i
\(532\) 0 0
\(533\) −0.231664 + 0.401254i −0.0100345 + 0.0173802i
\(534\) 31.8193 + 5.28133i 1.37696 + 0.228545i
\(535\) 0.509585 + 0.882627i 0.0220313 + 0.0381593i
\(536\) 1.38147 + 2.39277i 0.0596702 + 0.103352i
\(537\) 4.71967 + 12.5724i 0.203669 + 0.542541i
\(538\) 2.45292 4.24857i 0.105753 0.183169i
\(539\) 0 0
\(540\) −1.43325 + 0.886164i −0.0616773 + 0.0381344i
\(541\) −17.1708 −0.738232 −0.369116 0.929383i \(-0.620340\pi\)
−0.369116 + 0.929383i \(0.620340\pi\)
\(542\) 23.8488 41.3074i 1.02439 1.77430i
\(543\) −7.40327 19.7211i −0.317705 0.846314i
\(544\) 25.4527 + 44.0854i 1.09128 + 1.89015i
\(545\) 0.487083 + 0.843653i 0.0208643 + 0.0361381i
\(546\) 0 0
\(547\) −10.0046 + 17.3284i −0.427765 + 0.740910i −0.996674 0.0814901i \(-0.974032\pi\)
0.568910 + 0.822400i \(0.307365\pi\)
\(548\) −14.2917 −0.610512
\(549\) −0.393563 1.99640i −0.0167968 0.0852044i
\(550\) −17.0137 −0.725465
\(551\) −17.0696 + 29.5654i −0.727190 + 1.25953i
\(552\) 3.03662 3.69369i 0.129247 0.157214i
\(553\) 0 0
\(554\) 4.74187 + 8.21316i 0.201463 + 0.348944i
\(555\) −1.12611 + 1.36978i −0.0478007 + 0.0581439i
\(556\) −13.8930 + 24.0633i −0.589193 + 1.02051i
\(557\) 0.245481 0.0104014 0.00520068 0.999986i \(-0.498345\pi\)
0.00520068 + 0.999986i \(0.498345\pi\)
\(558\) −11.6800 + 10.2078i −0.494453 + 0.432131i
\(559\) 0.376192 0.0159112
\(560\) 0 0
\(561\) 17.8307 + 2.95951i 0.752811 + 0.124951i
\(562\) 12.1338 + 21.0163i 0.511833 + 0.886520i
\(563\) −22.1255 38.3224i −0.932477 1.61510i −0.779073 0.626934i \(-0.784310\pi\)
−0.153404 0.988164i \(-0.549024\pi\)
\(564\) −2.44559 6.51466i −0.102978 0.274317i
\(565\) −0.00282596 + 0.00489471i −0.000118889 + 0.000205922i
\(566\) −32.5496 −1.36816
\(567\) 0 0
\(568\) 0.570506 0.0239379
\(569\) 2.76767 4.79374i 0.116027 0.200964i −0.802163 0.597105i \(-0.796318\pi\)
0.918190 + 0.396141i \(0.129651\pi\)
\(570\) −1.26470 3.36895i −0.0529723 0.141110i
\(571\) 2.05191 + 3.55400i 0.0858696 + 0.148730i 0.905761 0.423788i \(-0.139300\pi\)
−0.819892 + 0.572518i \(0.805966\pi\)
\(572\) −0.368793 0.638768i −0.0154200 0.0267082i
\(573\) −8.48810 1.40884i −0.354595 0.0588553i
\(574\) 0 0
\(575\) 30.7770 1.28349
\(576\) 21.7640 19.0208i 0.906835 0.792535i
\(577\) −5.64550 −0.235025 −0.117513 0.993071i \(-0.537492\pi\)
−0.117513 + 0.993071i \(0.537492\pi\)
\(578\) −22.9256 + 39.7083i −0.953579 + 1.65165i
\(579\) 16.3941 19.9414i 0.681314 0.828737i
\(580\) −0.800218 1.38602i −0.0332272 0.0575513i
\(581\) 0 0
\(582\) 18.0040 21.8998i 0.746292 0.907776i
\(583\) −4.44809 + 7.70433i −0.184221 + 0.319081i
\(584\) −0.695420 −0.0287767
\(585\) −0.0169623 0.0860435i −0.000701303 0.00355746i
\(586\) 28.9483 1.19585
\(587\) −9.36644 + 16.2232i −0.386595 + 0.669601i −0.991989 0.126324i \(-0.959682\pi\)
0.605394 + 0.795926i \(0.293015\pi\)
\(588\) 0 0
\(589\) −8.70852 15.0836i −0.358828 0.621509i
\(590\) −0.686417 1.18891i −0.0282594 0.0489466i
\(591\) 12.9421 + 34.4757i 0.532366 + 1.41814i
\(592\) 12.3131 21.3269i 0.506065 0.876530i
\(593\) −18.8703 −0.774912 −0.387456 0.921888i \(-0.626646\pi\)
−0.387456 + 0.921888i \(0.626646\pi\)
\(594\) −0.535484 17.7490i −0.0219712 0.728250i
\(595\) 0 0
\(596\) −19.6991 + 34.1198i −0.806906 + 1.39760i
\(597\) 12.1406 + 32.3406i 0.496882 + 1.32361i
\(598\) 1.26884 + 2.19769i 0.0518866 + 0.0898702i
\(599\) −1.33726 2.31620i −0.0546388 0.0946372i 0.837412 0.546572i \(-0.184067\pi\)
−0.892051 + 0.451934i \(0.850734\pi\)
\(600\) −3.79900 0.630553i −0.155094 0.0257422i
\(601\) 6.60716 11.4439i 0.269511 0.466808i −0.699224 0.714902i \(-0.746471\pi\)
0.968736 + 0.248095i \(0.0798044\pi\)
\(602\) 0 0
\(603\) −17.5653 5.99612i −0.715313 0.244181i
\(604\) 18.7730 0.763862
\(605\) 0.601872 1.04247i 0.0244696 0.0423825i
\(606\) 33.5288 40.7838i 1.36201 1.65673i
\(607\) 12.9026 + 22.3480i 0.523701 + 0.907076i 0.999619 + 0.0275869i \(0.00878231\pi\)
−0.475919 + 0.879489i \(0.657884\pi\)
\(608\) 28.0766 + 48.6301i 1.13866 + 1.97221i
\(609\) 0 0
\(610\) −0.101856 + 0.176419i −0.00412401 + 0.00714299i
\(611\) 0.362157 0.0146513
\(612\) 39.4808 + 13.4772i 1.59592 + 0.544785i
\(613\) −26.9533 −1.08863 −0.544316 0.838880i \(-0.683211\pi\)
−0.544316 + 0.838880i \(0.683211\pi\)
\(614\) 28.1263 48.7162i 1.13509 1.96603i
\(615\) 0.579212 + 0.0961370i 0.0233561 + 0.00387662i
\(616\) 0 0
\(617\) −4.76588 8.25474i −0.191867 0.332323i 0.754002 0.656872i \(-0.228121\pi\)
−0.945869 + 0.324549i \(0.894788\pi\)
\(618\) −0.254959 0.679169i −0.0102559 0.0273202i
\(619\) 17.3536 30.0573i 0.697499 1.20810i −0.271832 0.962345i \(-0.587630\pi\)
0.969331 0.245759i \(-0.0790371\pi\)
\(620\) 0.816505 0.0327916
\(621\) 0.968668 + 32.1072i 0.0388713 + 1.28842i
\(622\) 28.8654 1.15740
\(623\) 0 0
\(624\) 0.428043 + 1.14024i 0.0171354 + 0.0456461i
\(625\) −12.3398 21.3732i −0.493593 0.854928i
\(626\) 22.3279 + 38.6730i 0.892402 + 1.54568i
\(627\) 19.6688 + 3.26460i 0.785495 + 0.130376i
\(628\) 6.31904 10.9449i 0.252157 0.436749i
\(629\) 43.9006 1.75043
\(630\) 0 0
\(631\) −36.7963 −1.46484 −0.732419 0.680854i \(-0.761609\pi\)
−0.732419 + 0.680854i \(0.761609\pi\)
\(632\) −2.85718 + 4.94877i −0.113652 + 0.196852i
\(633\) 25.8640 31.4605i 1.02800 1.25044i
\(634\) −8.79265 15.2293i −0.349201 0.604833i
\(635\) −0.985611 1.70713i −0.0391128 0.0677453i
\(636\) −13.0397 + 15.8612i −0.517057 + 0.628938i
\(637\) 0 0
\(638\) 16.8651 0.667696
\(639\) −2.88573 + 2.52200i −0.114158 + 0.0997688i
\(640\) −0.519397 −0.0205310
\(641\) 22.0922 38.2648i 0.872590 1.51137i 0.0132813 0.999912i \(-0.495772\pi\)
0.859308 0.511458i \(-0.170894\pi\)
\(642\) −24.4539 4.05883i −0.965119 0.160189i
\(643\) −7.24065 12.5412i −0.285543 0.494575i 0.687197 0.726471i \(-0.258841\pi\)
−0.972741 + 0.231895i \(0.925507\pi\)
\(644\) 0 0
\(645\) −0.167542 0.446305i −0.00659696 0.0175732i
\(646\) −44.5444 + 77.1532i −1.75258 + 3.03555i
\(647\) −33.3071 −1.30944 −0.654719 0.755872i \(-0.727213\pi\)
−0.654719 + 0.755872i \(0.727213\pi\)
\(648\) 0.538237 3.98304i 0.0211440 0.156469i
\(649\) 7.60631 0.298574
\(650\) 1.02187 1.76993i 0.0400811 0.0694225i
\(651\) 0 0
\(652\) −2.35643 4.08146i −0.0922850 0.159842i
\(653\) 4.53322 + 7.85176i 0.177398 + 0.307263i 0.940989 0.338438i \(-0.109899\pi\)
−0.763590 + 0.645701i \(0.776565\pi\)
\(654\) −23.3741 3.87961i −0.913999 0.151705i
\(655\) −1.45027 + 2.51194i −0.0566666 + 0.0981495i
\(656\) −8.15391 −0.318357
\(657\) 3.51757 3.07420i 0.137233 0.119936i
\(658\) 0 0
\(659\) 16.1806 28.0256i 0.630305 1.09172i −0.357184 0.934034i \(-0.616263\pi\)
0.987489 0.157686i \(-0.0504035\pi\)
\(660\) −0.593572 + 0.722010i −0.0231048 + 0.0281042i
\(661\) −4.32958 7.49905i −0.168401 0.291679i 0.769457 0.638699i \(-0.220527\pi\)
−0.937858 + 0.347020i \(0.887194\pi\)
\(662\) −11.1382 19.2919i −0.432897 0.749799i
\(663\) −1.37882 + 1.67717i −0.0535490 + 0.0651360i
\(664\) −1.67775 + 2.90595i −0.0651094 + 0.112773i
\(665\) 0 0
\(666\) −8.34179 42.3150i −0.323238 1.63967i
\(667\) −30.5083 −1.18128
\(668\) 12.8329 22.2273i 0.496522 0.860001i
\(669\) 6.93899 + 1.15173i 0.268277 + 0.0445283i
\(670\) 0.929067 + 1.60919i 0.0358930 + 0.0621685i
\(671\) −0.564339 0.977464i −0.0217861 0.0377346i
\(672\) 0 0
\(673\) 7.24842 12.5546i 0.279406 0.483946i −0.691831 0.722059i \(-0.743196\pi\)
0.971237 + 0.238114i \(0.0765291\pi\)
\(674\) −6.87605 −0.264856
\(675\) 22.0035 13.6045i 0.846915 0.523639i
\(676\) −28.7384 −1.10532
\(677\) 19.1657 33.1960i 0.736600 1.27583i −0.217418 0.976078i \(-0.569764\pi\)
0.954018 0.299749i \(-0.0969030\pi\)
\(678\) −0.0483128 0.128698i −0.00185544 0.00494260i
\(679\) 0 0
\(680\) −0.204785 0.354698i −0.00785315 0.0136021i
\(681\) 6.58327 + 1.09268i 0.252271 + 0.0418717i
\(682\) −4.30209 + 7.45144i −0.164736 + 0.285330i
\(683\) 6.63318 0.253812 0.126906 0.991915i \(-0.459495\pi\)
0.126906 + 0.991915i \(0.459495\pi\)
\(684\) 43.5508 + 14.8666i 1.66521 + 0.568438i
\(685\) −0.942567 −0.0360136
\(686\) 0 0
\(687\) 14.4272 17.5489i 0.550430 0.669534i
\(688\) 3.31022 + 5.73347i 0.126201 + 0.218587i
\(689\) −0.534322 0.925472i −0.0203560 0.0352577i
\(690\) 2.04219 2.48409i 0.0777450 0.0945676i
\(691\) −11.6938 + 20.2542i −0.444852 + 0.770506i −0.998042 0.0625490i \(-0.980077\pi\)
0.553190 + 0.833055i \(0.313410\pi\)
\(692\) 35.2818 1.34121
\(693\) 0 0
\(694\) −23.6848 −0.899061
\(695\) −0.916269 + 1.58702i −0.0347561 + 0.0601992i
\(696\) 3.76583 + 0.625048i 0.142743 + 0.0236924i
\(697\) −7.26791 12.5884i −0.275292 0.476819i
\(698\) 9.13702 + 15.8258i 0.345841 + 0.599015i
\(699\) −10.6542 28.3810i −0.402978 1.07347i
\(700\) 0 0
\(701\) 9.26736 0.350023 0.175012 0.984566i \(-0.444004\pi\)
0.175012 + 0.984566i \(0.444004\pi\)
\(702\) 1.87859 + 1.01033i 0.0709029 + 0.0381325i
\(703\) 48.4262 1.82643
\(704\) 8.01636 13.8847i 0.302128 0.523301i
\(705\) −0.161291 0.429655i −0.00607459 0.0161817i
\(706\) −2.71799 4.70769i −0.102293 0.177176i
\(707\) 0 0
\(708\) 17.3191 + 2.87460i 0.650891 + 0.108034i
\(709\) −7.11775 + 12.3283i −0.267313 + 0.462999i −0.968167 0.250305i \(-0.919469\pi\)
0.700854 + 0.713305i \(0.252802\pi\)
\(710\) 0.383678 0.0143992
\(711\) −7.42460 37.6624i −0.278444 1.41245i
\(712\) 4.04956 0.151763
\(713\) 7.78230 13.4793i 0.291449 0.504805i
\(714\) 0 0
\(715\) −0.0243226 0.0421280i −0.000909613 0.00157550i
\(716\) 8.59632 + 14.8893i 0.321260 + 0.556438i
\(717\) 8.04846 9.79000i 0.300575 0.365614i
\(718\) −26.6636 + 46.1827i −0.995077 + 1.72352i
\(719\) 13.8570 0.516777 0.258389 0.966041i \(-0.416808\pi\)
0.258389 + 0.966041i \(0.416808\pi\)
\(720\) 1.16212 1.01564i 0.0433096 0.0378507i
\(721\) 0 0
\(722\) −29.6268 + 51.3151i −1.10259 + 1.90975i
\(723\) −10.6469 1.76715i −0.395961 0.0657212i
\(724\) −13.4842 23.3553i −0.501136 0.867993i
\(725\) 12.2851 + 21.2784i 0.456257 + 0.790260i
\(726\) 10.2896 + 27.4100i 0.381885 + 1.01728i
\(727\) −15.7000 + 27.1932i −0.582280 + 1.00854i 0.412928 + 0.910764i \(0.364506\pi\)
−0.995208 + 0.0977755i \(0.968827\pi\)
\(728\) 0 0
\(729\) 14.8851 + 22.5263i 0.551299 + 0.834308i
\(730\) −0.467686 −0.0173098
\(731\) −5.90107 + 10.2209i −0.218259 + 0.378035i
\(732\) −0.915558 2.43890i −0.0338400 0.0901443i
\(733\) −13.3003 23.0368i −0.491257 0.850883i 0.508692 0.860949i \(-0.330129\pi\)
−0.999949 + 0.0100658i \(0.996796\pi\)
\(734\) 18.0592 + 31.2794i 0.666576 + 1.15454i
\(735\) 0 0
\(736\) −25.0904 + 43.4579i −0.924845 + 1.60188i
\(737\) −10.2951 −0.379227
\(738\) −10.7527 + 9.39739i −0.395812 + 0.345923i
\(739\) −33.0039 −1.21407 −0.607034 0.794676i \(-0.707641\pi\)
−0.607034 + 0.794676i \(0.707641\pi\)
\(740\) −1.13510 + 1.96605i −0.0417272 + 0.0722736i
\(741\) −1.52096 + 1.85007i −0.0558739 + 0.0679640i
\(742\) 0 0
\(743\) 19.3008 + 33.4299i 0.708076 + 1.22642i 0.965570 + 0.260144i \(0.0837701\pi\)
−0.257493 + 0.966280i \(0.582897\pi\)
\(744\) −1.23678 + 1.50440i −0.0453426 + 0.0551539i
\(745\) −1.29919 + 2.25027i −0.0475988 + 0.0824435i
\(746\) 1.67388 0.0612849
\(747\) −4.35977 22.1156i −0.159516 0.809167i
\(748\) 23.1400 0.846082
\(749\) 0 0
\(750\) −5.12080 0.849945i −0.186985 0.0310356i
\(751\) 18.9498 + 32.8220i 0.691487 + 1.19769i 0.971351 + 0.237651i \(0.0763776\pi\)
−0.279863 + 0.960040i \(0.590289\pi\)
\(752\) 3.18673 + 5.51957i 0.116208 + 0.201278i
\(753\) 3.44104 + 9.16639i 0.125399 + 0.334042i
\(754\) −1.01295 + 1.75448i −0.0368895 + 0.0638944i
\(755\) 1.23811 0.0450596
\(756\) 0 0
\(757\) 22.5927 0.821147 0.410573 0.911828i \(-0.365329\pi\)
0.410573 + 0.911828i \(0.365329\pi\)
\(758\) 20.9793 36.3371i 0.762001 1.31982i
\(759\) 6.26189 + 16.6807i 0.227292 + 0.605470i
\(760\) −0.225896 0.391263i −0.00819411 0.0141926i
\(761\) 13.8735 + 24.0296i 0.502913 + 0.871072i 0.999994 + 0.00336738i \(0.00107187\pi\)
−0.497081 + 0.867704i \(0.665595\pi\)
\(762\) 47.2974 + 7.85037i 1.71340 + 0.284389i
\(763\) 0 0
\(764\) −11.0156 −0.398529
\(765\) 2.60383 + 0.888850i 0.0941418 + 0.0321364i
\(766\) −36.7454 −1.32766
\(767\) −0.456849 + 0.791286i −0.0164959 + 0.0285717i
\(768\) −13.1730 + 16.0233i −0.475338 + 0.578193i
\(769\) 6.07668 + 10.5251i 0.219131 + 0.379546i 0.954542 0.298075i \(-0.0963445\pi\)
−0.735412 + 0.677621i \(0.763011\pi\)
\(770\) 0 0
\(771\) 12.9812 15.7901i 0.467505 0.568665i
\(772\) 16.5250 28.6221i 0.594747 1.03013i
\(773\) −41.5591 −1.49478 −0.747388 0.664388i \(-0.768692\pi\)
−0.747388 + 0.664388i \(0.768692\pi\)
\(774\) 10.9731 + 3.74579i 0.394419 + 0.134640i
\(775\) −12.5351 −0.450275
\(776\) 1.77969 3.08252i 0.0638873 0.110656i
\(777\) 0 0
\(778\) −16.0470 27.7942i −0.575313 0.996472i
\(779\) −8.01714 13.8861i −0.287244 0.497521i
\(780\) −0.0394598 0.105115i −0.00141289 0.00376371i