Properties

Label 441.2.h.f.214.5
Level $441$
Weight $2$
Character 441.214
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.h (of order \(3\), degree \(2\), not 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 214.5
Root \(-1.02682 + 1.77851i\) of defining polynomial
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.f.373.5

$q$-expansion

\(f(q)\) \(=\) \(q+2.05365 q^{2} +(1.70867 + 0.283604i) q^{3} +2.21746 q^{4} +(-0.0731228 + 0.126652i) q^{5} +(3.50901 + 0.582422i) q^{6} +0.446582 q^{8} +(2.83914 + 0.969173i) q^{9} +O(q^{10})\) \(q+2.05365 q^{2} +(1.70867 + 0.283604i) q^{3} +2.21746 q^{4} +(-0.0731228 + 0.126652i) q^{5} +(3.50901 + 0.582422i) q^{6} +0.446582 q^{8} +(2.83914 + 0.969173i) q^{9} +(-0.150168 + 0.260099i) q^{10} +(-0.832020 - 1.44110i) q^{11} +(3.78891 + 0.628880i) q^{12} +(-0.0999454 - 0.173111i) q^{13} +(-0.160862 + 0.195670i) q^{15} -3.51780 q^{16} +(-3.13555 + 5.43093i) q^{17} +(5.83058 + 1.99034i) q^{18} +(-3.45879 - 5.99080i) q^{19} +(-0.162147 + 0.280847i) q^{20} +(-1.70867 - 2.95951i) q^{22} +(3.09092 - 5.35363i) q^{23} +(0.763064 + 0.126652i) q^{24} +(2.48931 + 4.31160i) q^{25} +(-0.205252 - 0.355508i) q^{26} +(4.57630 + 2.46119i) q^{27} +(-2.46757 + 4.27396i) q^{29} +(-0.330354 + 0.401837i) q^{30} +2.51780 q^{31} -8.11747 q^{32} +(-1.01295 - 2.69834i) q^{33} +(-6.43931 + 11.1532i) q^{34} +(6.29567 + 2.14910i) q^{36} +(-3.50023 - 6.06257i) q^{37} +(-7.10312 - 12.3030i) q^{38} +(-0.121679 - 0.324134i) q^{39} +(-0.0326554 + 0.0565608i) q^{40} +(-1.15895 - 2.00736i) q^{41} +(-0.940993 + 1.62985i) q^{43} +(-1.84497 - 3.19558i) q^{44} +(-0.330354 + 0.288715i) q^{45} +(6.34765 - 10.9944i) q^{46} +1.81177 q^{47} +(-6.01077 - 0.997660i) q^{48} +(5.11215 + 8.85451i) q^{50} +(-6.89787 + 8.39045i) q^{51} +(-0.221625 - 0.383865i) q^{52} +(-2.67307 + 4.62989i) q^{53} +(9.39810 + 5.05442i) q^{54} +0.243359 q^{55} +(-4.21093 - 11.2172i) q^{57} +(-5.06752 + 8.77720i) q^{58} +4.57099 q^{59} +(-0.356705 + 0.433890i) q^{60} +0.678276 q^{61} +5.17066 q^{62} -9.63481 q^{64} +0.0292332 q^{65} +(-2.08024 - 5.54143i) q^{66} -6.18684 q^{67} +(-6.95296 + 12.0429i) q^{68} +(6.79968 - 8.27101i) q^{69} +1.27749 q^{71} +(1.26791 + 0.432816i) q^{72} +(0.778603 - 1.34858i) q^{73} +(-7.18823 - 12.4504i) q^{74} +(3.03063 + 8.07311i) q^{75} +(-7.66972 - 13.2843i) q^{76} +(-0.249886 - 0.665657i) q^{78} +12.7957 q^{79} +(0.257231 - 0.445537i) q^{80} +(7.12141 + 5.50323i) q^{81} +(-2.38008 - 4.12241i) q^{82} +(-3.75687 + 6.50709i) q^{83} +(-0.458561 - 0.794251i) q^{85} +(-1.93247 + 3.34713i) q^{86} +(-5.42839 + 6.60299i) q^{87} +(-0.371566 - 0.643571i) q^{88} +(-4.53394 - 7.85301i) q^{89} +(-0.678430 + 0.592918i) q^{90} +(6.85398 - 11.8714i) q^{92} +(4.30209 + 0.714056i) q^{93} +3.72074 q^{94} +1.01167 q^{95} +(-13.8701 - 2.30214i) q^{96} +(3.98514 - 6.90246i) q^{97} +(-0.965543 - 4.89786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 10q - 4q^{2} + q^{3} + 8q^{4} - 4q^{5} + 2q^{6} - 6q^{8} + 11q^{9} + O(q^{10}) \) \( 10q - 4q^{2} + q^{3} + 8q^{4} - 4q^{5} + 2q^{6} - 6q^{8} + 11q^{9} + 7q^{10} + 4q^{11} + 20q^{12} + 8q^{13} - 19q^{15} - 4q^{16} - 12q^{17} + 4q^{18} - q^{19} - 5q^{20} - q^{22} + 3q^{23} - 6q^{24} - q^{25} - 11q^{26} + 7q^{27} + 7q^{29} + 16q^{30} - 6q^{31} + 4q^{32} - 14q^{33} - 3q^{34} + 34q^{36} - 20q^{38} + 2q^{39} + 3q^{40} - 5q^{41} - 7q^{43} - 10q^{44} + 16q^{45} + 3q^{46} + 54q^{47} + 5q^{48} + 19q^{50} - 9q^{51} + 10q^{52} - 21q^{53} - q^{54} - 4q^{55} - 4q^{57} - 10q^{58} + 60q^{59} + 10q^{60} - 28q^{61} + 12q^{62} - 50q^{64} + 22q^{65} - 19q^{66} + 4q^{67} - 27q^{68} - 15q^{69} - 6q^{71} - 36q^{72} - 15q^{73} - 36q^{74} + 14q^{75} - 5q^{76} - 20q^{78} + 8q^{79} - 20q^{80} + 23q^{81} + 5q^{82} - 9q^{83} - 6q^{85} - 8q^{86} - 2q^{87} - 18q^{88} - 28q^{89} - 28q^{90} + 27q^{92} - 6q^{93} - 6q^{94} + 28q^{95} - 59q^{96} + 12q^{97} + 35q^{99} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.05365 1.45215 0.726073 0.687617i \(-0.241343\pi\)
0.726073 + 0.687617i \(0.241343\pi\)
\(3\) 1.70867 + 0.283604i 0.986504 + 0.163739i
\(4\) 2.21746 1.10873
\(5\) −0.0731228 + 0.126652i −0.0327015 + 0.0566407i −0.881913 0.471412i \(-0.843744\pi\)
0.849211 + 0.528053i \(0.177078\pi\)
\(6\) 3.50901 + 0.582422i 1.43255 + 0.237773i
\(7\) 0 0
\(8\) 0.446582 0.157891
\(9\) 2.83914 + 0.969173i 0.946379 + 0.323058i
\(10\) −0.150168 + 0.260099i −0.0474874 + 0.0822506i
\(11\) −0.832020 1.44110i −0.250864 0.434508i 0.712900 0.701265i \(-0.247381\pi\)
−0.963764 + 0.266757i \(0.914048\pi\)
\(12\) 3.78891 + 0.628880i 1.09377 + 0.181542i
\(13\) −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
\(16\) −3.51780 −0.879449
\(17\) −3.13555 + 5.43093i −0.760483 + 1.31720i 0.182119 + 0.983277i \(0.441704\pi\)
−0.942602 + 0.333919i \(0.891629\pi\)
\(18\) 5.83058 + 1.99034i 1.37428 + 0.469127i
\(19\) −3.45879 5.99080i −0.793500 1.37438i −0.923787 0.382907i \(-0.874923\pi\)
0.130287 0.991476i \(-0.458410\pi\)
\(20\) −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 −0.339916 0.940456i \(-0.610399\pi\)
0.984417 0.175852i \(-0.0562682\pi\)
\(24\) 0.763064 + 0.126652i 0.155760 + 0.0258528i
\(25\) 2.48931 + 4.31160i 0.497861 + 0.862321i
\(26\) −0.205252 0.355508i −0.0402533 0.0697208i
\(27\) 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 \(0.318178\pi\)
\(30\) −0.330354 + 0.401837i −0.0603141 + 0.0733650i
\(31\) 2.51780 0.452209 0.226105 0.974103i \(-0.427401\pi\)
0.226105 + 0.974103i \(0.427401\pi\)
\(32\) −8.11747 −1.43498
\(33\) −1.01295 2.69834i −0.176332 0.469720i
\(34\) −6.43931 + 11.1532i −1.10433 + 1.91276i
\(35\) 0 0
\(36\) 6.29567 + 2.14910i 1.04928 + 0.358184i
\(37\) −3.50023 6.06257i −0.575434 0.996681i −0.995994 0.0894162i \(-0.971500\pi\)
0.420560 0.907264i \(-0.361833\pi\)
\(38\) −7.10312 12.3030i −1.15228 1.99581i
\(39\) −0.121679 0.324134i −0.0194843 0.0519030i
\(40\) −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 \(0.212502\pi\)
\(44\) −1.84497 3.19558i −0.278140 0.481752i
\(45\) −0.330354 + 0.288715i −0.0492463 + 0.0430391i
\(46\) 6.34765 10.9944i 0.935910 1.62104i
\(47\) 1.81177 0.264275 0.132137 0.991231i \(-0.457816\pi\)
0.132137 + 0.991231i \(0.457816\pi\)
\(48\) −6.01077 0.997660i −0.867579 0.144000i
\(49\) 0 0
\(50\) 5.11215 + 8.85451i 0.722967 + 1.25222i
\(51\) −6.89787 + 8.39045i −0.965895 + 1.17490i
\(52\) −0.221625 0.383865i −0.0307338 0.0532325i
\(53\) −2.67307 + 4.62989i −0.367174 + 0.635964i −0.989123 0.147094i \(-0.953008\pi\)
0.621948 + 0.783058i \(0.286341\pi\)
\(54\) 9.39810 + 5.05442i 1.27892 + 0.687819i
\(55\) 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
\(59\) 4.57099 0.595092 0.297546 0.954708i \(-0.403832\pi\)
0.297546 + 0.954708i \(0.403832\pi\)
\(60\) −0.356705 + 0.433890i −0.0460505 + 0.0560149i
\(61\) 0.678276 0.0868443 0.0434221 0.999057i \(-0.486174\pi\)
0.0434221 + 0.999057i \(0.486174\pi\)
\(62\) 5.17066 0.656674
\(63\) 0 0
\(64\) −9.63481 −1.20435
\(65\) 0.0292332 0.00362593
\(66\) −2.08024 5.54143i −0.256060 0.682103i
\(67\) −6.18684 −0.755842 −0.377921 0.925838i \(-0.623361\pi\)
−0.377921 + 0.925838i \(0.623361\pi\)
\(68\) −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 \(0.475847\pi\)
\(72\) 1.26791 + 0.432816i 0.149424 + 0.0510078i
\(73\) 0.778603 1.34858i 0.0911286 0.157839i −0.816858 0.576839i \(-0.804286\pi\)
0.907986 + 0.419000i \(0.137619\pi\)
\(74\) −7.18823 12.4504i −0.835614 1.44733i
\(75\) 3.03063 + 8.07311i 0.349947 + 0.932202i
\(76\) −7.66972 13.2843i −0.879777 1.52382i
\(77\) 0 0
\(78\) −0.249886 0.665657i −0.0282940 0.0753708i
\(79\) 12.7957 1.43963 0.719817 0.694164i \(-0.244226\pi\)
0.719817 + 0.694164i \(0.244226\pi\)
\(80\) 0.257231 0.445537i 0.0287593 0.0498126i
\(81\) 7.12141 + 5.50323i 0.791267 + 0.611470i
\(82\) −2.38008 4.12241i −0.262835 0.455244i
\(83\) −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
\(87\) −5.42839 + 6.60299i −0.581984 + 0.707915i
\(88\) −0.371566 0.643571i −0.0396090 0.0686048i
\(89\) −4.53394 7.85301i −0.480597 0.832418i 0.519155 0.854680i \(-0.326247\pi\)
−0.999752 + 0.0222619i \(0.992913\pi\)
\(90\) −0.678430 + 0.592918i −0.0715128 + 0.0624991i
\(91\) 0 0
\(92\) 6.85398 11.8714i 0.714577 1.23768i
\(93\) 4.30209 + 0.714056i 0.446106 + 0.0740442i
\(94\) 3.72074 0.383765
\(95\) 1.01167 0.103795
\(96\) −13.8701 2.30214i −1.41561 0.234962i
\(97\) 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
\(100\) 5.51993 + 9.56080i 0.551993 + 0.956080i
\(101\) 7.42150 + 12.8544i 0.738467 + 1.27906i 0.953186 + 0.302386i \(0.0977832\pi\)
−0.214719 + 0.976676i \(0.568883\pi\)
\(102\) −14.1658 + 17.2310i −1.40262 + 1.70612i
\(103\) −0.101974 + 0.176624i −0.0100478 + 0.0174033i −0.871006 0.491273i \(-0.836532\pi\)
0.860958 + 0.508676i \(0.169865\pi\)
\(104\) −0.0446339 0.0773081i −0.00437671 0.00758068i
\(105\) 0 0
\(106\) −5.48953 + 9.50815i −0.533191 + 0.923513i
\(107\) 3.48444 + 6.03524i 0.336854 + 0.583448i 0.983839 0.179054i \(-0.0573038\pi\)
−0.646985 + 0.762503i \(0.723970\pi\)
\(108\) 10.1478 + 5.45759i 0.976468 + 0.525157i
\(109\) 3.33058 5.76874i 0.319012 0.552545i −0.661270 0.750148i \(-0.729982\pi\)
0.980282 + 0.197603i \(0.0633157\pi\)
\(110\) 0.499772 0.0476514
\(111\) −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 \(0.833912\pi\)
\(114\) −8.64776 23.0362i −0.809937 2.15754i
\(115\) 0.452033 + 0.782945i 0.0421523 + 0.0730100i
\(116\) −5.47174 + 9.47733i −0.508038 + 0.879948i
\(117\) −0.115985 0.588349i −0.0107228 0.0543929i
\(118\) 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
\(122\) 1.39294 0.126111
\(123\) −1.41098 3.75862i −0.127223 0.338903i
\(124\) 5.58311 0.501378
\(125\) −1.45933 −0.130526
\(126\) 0 0
\(127\) 13.4788 1.19605 0.598027 0.801476i \(-0.295952\pi\)
0.598027 + 0.801476i \(0.295952\pi\)
\(128\) −3.55154 −0.313915
\(129\) −2.07008 + 2.51801i −0.182261 + 0.221698i
\(130\) 0.0600345 0.00526538
\(131\) −9.91665 + 17.1761i −0.866422 + 1.50069i −0.000793988 1.00000i \(0.500253\pi\)
−0.865628 + 0.500687i \(0.833081\pi\)
\(132\) −2.24617 5.98345i −0.195504 0.520793i
\(133\) 0 0
\(134\) −12.7056 −1.09759
\(135\) −0.646348 + 0.399630i −0.0556288 + 0.0343947i
\(136\) −1.40028 + 2.42536i −0.120073 + 0.207973i
\(137\) 3.22255 + 5.58162i 0.275321 + 0.476870i 0.970216 0.242241i \(-0.0778826\pi\)
−0.694895 + 0.719111i \(0.744549\pi\)
\(138\) 13.9641 16.9857i 1.18871 1.44592i
\(139\) −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
\(142\) 2.62352 0.220161
\(143\) −0.166313 + 0.288063i −0.0139078 + 0.0240890i
\(144\) −9.98750 3.40935i −0.832292 0.284113i
\(145\) −0.360872 0.625048i −0.0299688 0.0519074i
\(146\) 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 0.230045 + 0.973180i \(0.426113\pi\)
−0.957821 + 0.287365i \(0.907221\pi\)
\(150\) 6.22383 + 16.5793i 0.508174 + 1.35369i
\(151\) −4.23300 7.33177i −0.344476 0.596651i 0.640782 0.767723i \(-0.278610\pi\)
−0.985259 + 0.171072i \(0.945277\pi\)
\(152\) −1.54463 2.67538i −0.125286 0.217002i
\(153\) −14.1658 + 12.3803i −1.14524 + 1.00089i
\(154\) 0 0
\(155\) −0.184108 + 0.318885i −0.0147879 + 0.0256135i
\(156\) −0.269819 0.718755i −0.0216028 0.0575464i
\(157\) −5.69935 −0.454858 −0.227429 0.973795i \(-0.573032\pi\)
−0.227429 + 0.973795i \(0.573032\pi\)
\(158\) 26.2779 2.09056
\(159\) −5.88046 + 7.15288i −0.466351 + 0.567261i
\(160\) 0.593572 1.02810i 0.0469260 0.0812782i
\(161\) 0 0
\(162\) 14.6248 + 11.3017i 1.14904 + 0.887944i
\(163\) −1.06267 1.84060i −0.0832349 0.144167i 0.821403 0.570349i \(-0.193192\pi\)
−0.904638 + 0.426181i \(0.859859\pi\)
\(164\) −2.56993 4.45125i −0.200678 0.347584i
\(165\) 0.415821 + 0.0690175i 0.0323716 + 0.00537300i
\(166\) −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
\(170\) −0.941721 1.63111i −0.0722267 0.125100i
\(171\) −4.01386 20.3609i −0.306947 1.55703i
\(172\) −2.08661 + 3.61412i −0.159103 + 0.275574i
\(173\) 15.9109 1.20968 0.604842 0.796345i \(-0.293236\pi\)
0.604842 + 0.796345i \(0.293236\pi\)
\(174\) −11.1480 + 13.5602i −0.845127 + 1.02800i
\(175\) 0 0
\(176\) 2.92688 + 5.06950i 0.220622 + 0.382128i
\(177\) 7.81033 + 1.29635i 0.587060 + 0.0974395i
\(178\) −9.31110 16.1273i −0.697897 1.20879i
\(179\) 3.87665 6.71456i 0.289755 0.501870i −0.683996 0.729485i \(-0.739760\pi\)
0.973751 + 0.227615i \(0.0730929\pi\)
\(180\) −0.732546 + 0.640214i −0.0546008 + 0.0477187i
\(181\) 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
\(185\) 1.02379 0.0752703
\(186\) 8.83497 + 1.46642i 0.647812 + 0.107523i
\(187\) 10.4354 0.763110
\(188\) 4.01754 0.293009
\(189\) 0 0
\(190\) 2.07760 0.150725
\(191\) −4.96765 −0.359447 −0.179723 0.983717i \(-0.557520\pi\)
−0.179723 + 0.983717i \(0.557520\pi\)
\(192\) −16.4628 2.73247i −1.18810 0.197199i
\(193\) −14.9044 −1.07284 −0.536422 0.843950i \(-0.680224\pi\)
−0.536422 + 0.843950i \(0.680224\pi\)
\(194\) 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 \(0.773524\pi\)
\(198\) −1.98288 10.0585i −0.140917 0.714824i
\(199\) 9.97208 17.2722i 0.706902 1.22439i −0.259098 0.965851i \(-0.583425\pi\)
0.966001 0.258540i \(-0.0832413\pi\)
\(200\) 1.11168 + 1.92549i 0.0786077 + 0.136152i
\(201\) −10.5713 1.75461i −0.745641 0.123761i
\(202\) 15.2411 + 26.3984i 1.07236 + 1.85739i
\(203\) 0 0
\(204\) −15.2957 + 18.6055i −1.07092 + 1.30264i
\(205\) 0.338983 0.0236756
\(206\) −0.209419 + 0.362724i −0.0145909 + 0.0252722i
\(207\) 13.9641 12.2040i 0.970574 0.848240i
\(208\) 0.351587 + 0.608967i 0.0243782 + 0.0422243i
\(209\) −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
\(213\) 2.18282 + 0.362302i 0.149564 + 0.0248245i
\(214\) 7.15581 + 12.3942i 0.489161 + 0.847252i
\(215\) −0.137616 0.238358i −0.00938535 0.0162559i
\(216\) 2.04370 + 1.09912i 0.139056 + 0.0747860i
\(217\) 0 0
\(218\) 6.83983 11.8469i 0.463252 0.802376i
\(219\) 1.71284 2.08347i 0.115743 0.140788i
\(220\) 0.539638 0.0363824
\(221\) 1.25354 0.0843220
\(222\) −8.75137 23.3122i −0.587353 1.56462i
\(223\) −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
\(226\) −0.0396834 0.0687336i −0.00263970 0.00457209i
\(227\) −1.92643 3.33667i −0.127861 0.221462i 0.794986 0.606627i \(-0.207478\pi\)
−0.922848 + 0.385165i \(0.874145\pi\)
\(228\) −9.33756 24.8738i −0.618395 1.64731i
\(229\) 6.55812 11.3590i 0.433373 0.750624i −0.563788 0.825919i \(-0.690657\pi\)
0.997161 + 0.0752952i \(0.0239899\pi\)
\(230\) 0.928316 + 1.60789i 0.0612113 + 0.106021i
\(231\) 0 0
\(232\) −1.10197 + 1.90868i −0.0723481 + 0.125311i
\(233\) −8.75115 15.1574i −0.573307 0.992997i −0.996223 0.0868284i \(-0.972327\pi\)
0.422916 0.906169i \(-0.361007\pi\)
\(234\) −0.238191 1.20826i −0.0155711 0.0789864i
\(235\) −0.132482 + 0.229466i −0.00864218 + 0.0149687i
\(236\) 10.1360 0.659795
\(237\) 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 \(0.757283\pi\)
\(240\) 0.565880 0.688327i 0.0365274 0.0444313i
\(241\) 3.11553 + 5.39626i 0.200689 + 0.347604i 0.948751 0.316026i \(-0.102349\pi\)
−0.748062 + 0.663629i \(0.769015\pi\)
\(242\) 8.45174 14.6389i 0.543299 0.941021i
\(243\) 10.6074 + 11.4229i 0.680467 + 0.732779i
\(244\) 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
\(248\) 1.12440 0.0713997
\(249\) −8.26470 + 10.0530i −0.523754 + 0.637085i
\(250\) −2.99694 −0.189543
\(251\) −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
\(254\) 27.6808 1.73684
\(255\) −0.558279 1.48717i −0.0349608 0.0931299i
\(256\) 11.9760 0.748501
\(257\) 5.90082 10.2205i 0.368083 0.637539i −0.621183 0.783666i \(-0.713347\pi\)
0.989266 + 0.146127i \(0.0466808\pi\)
\(258\) −4.25121 + 5.17110i −0.264669 + 0.321939i
\(259\) 0 0
\(260\) 0.0648233 0.00402017
\(261\) −11.1480 + 9.74286i −0.690043 + 0.603068i
\(262\) −20.3653 + 35.2737i −1.25817 + 2.17922i
\(263\) 11.1200 + 19.2605i 0.685691 + 1.18765i 0.973219 + 0.229879i \(0.0738331\pi\)
−0.287528 + 0.957772i \(0.592834\pi\)
\(264\) −0.452366 1.20503i −0.0278412 0.0741645i
\(265\) −0.390925 0.677101i −0.0240143 0.0415940i
\(266\) 0 0
\(267\) −5.51988 14.7041i −0.337811 0.899876i
\(268\) −13.7191 −0.838024
\(269\) 1.19442 2.06880i 0.0728251 0.126137i −0.827313 0.561741i \(-0.810132\pi\)
0.900138 + 0.435604i \(0.143465\pi\)
\(270\) −1.32737 + 0.820699i −0.0807811 + 0.0499462i
\(271\) 11.6129 + 20.1142i 0.705435 + 1.22185i 0.966534 + 0.256537i \(0.0825815\pi\)
−0.261100 + 0.965312i \(0.584085\pi\)
\(272\) 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
\(276\) 15.0780 18.3406i 0.907590 1.10398i
\(277\) 2.30900 + 3.99931i 0.138734 + 0.240295i 0.927018 0.375017i \(-0.122363\pi\)
−0.788283 + 0.615312i \(0.789030\pi\)
\(278\) −12.8666 22.2857i −0.771690 1.33661i
\(279\) 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 \(0.0520098\pi\)
\(282\) 6.35754 + 1.05522i 0.378586 + 0.0628372i
\(283\) −15.8497 −0.942165 −0.471082 0.882089i \(-0.656137\pi\)
−0.471082 + 0.882089i \(0.656137\pi\)
\(284\) 2.83279 0.168095
\(285\) 1.72861 + 0.286912i 0.102394 + 0.0169952i
\(286\) −0.341548 + 0.591579i −0.0201962 + 0.0349808i
\(287\) 0 0
\(288\) −23.0466 7.86723i −1.35803 0.463581i
\(289\) −11.1634 19.3355i −0.656669 1.13738i
\(290\) −0.741102 1.28363i −0.0435190 0.0753772i
\(291\) 8.76687 10.6639i 0.513923 0.625127i
\(292\) 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
\(296\) −1.56314 2.70744i −0.0908557 0.157367i
\(297\) −0.260748 8.64268i −0.0151302 0.501499i
\(298\) −18.2438 + 31.5993i −1.05684 + 1.83050i
\(299\) −1.23569 −0.0714619
\(300\) 6.72029 + 17.9018i 0.387996 + 1.03356i
\(301\) 0 0
\(302\) −8.69307 15.0568i −0.500230 0.866424i
\(303\) 9.03537 + 24.0688i 0.519068 + 1.38272i
\(304\) 12.1673 + 21.0744i 0.697843 + 1.20870i
\(305\) −0.0495974 + 0.0859053i −0.00283994 + 0.00491892i
\(306\) −29.0915 + 25.4247i −1.66305 + 1.45343i
\(307\) −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
\(311\) 14.0557 0.797026 0.398513 0.917163i \(-0.369526\pi\)
0.398513 + 0.917163i \(0.369526\pi\)
\(312\) −0.0543399 0.144753i −0.00307639 0.00819501i
\(313\) −21.7446 −1.22908 −0.614540 0.788886i \(-0.710658\pi\)
−0.614540 + 0.788886i \(0.710658\pi\)
\(314\) −11.7045 −0.660520
\(315\) 0 0
\(316\) 28.3740 1.59616
\(317\) 8.56297 0.480944 0.240472 0.970656i \(-0.422698\pi\)
0.240472 + 0.970656i \(0.422698\pi\)
\(318\) −12.0764 + 14.6895i −0.677209 + 0.823745i
\(319\) 8.21228 0.459799
\(320\) 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
\(324\) 15.7914 + 12.2032i 0.877301 + 0.677955i
\(325\) 0.497589 0.861850i 0.0276013 0.0478068i
\(326\) −2.18235 3.77995i −0.120869 0.209352i
\(327\) 7.32692 8.91233i 0.405179 0.492853i
\(328\) −0.517568 0.896453i −0.0285779 0.0494984i
\(329\) 0 0
\(330\) 0.853949 + 0.141737i 0.0470083 + 0.00780239i
\(331\) 10.8472 0.596216 0.298108 0.954532i \(-0.403644\pi\)
0.298108 + 0.954532i \(0.403644\pi\)
\(332\) −8.33070 + 14.4292i −0.457207 + 0.791905i
\(333\) −4.06195 20.6048i −0.222593 1.12914i
\(334\) 11.8849 + 20.5853i 0.650314 + 1.12638i
\(335\) 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
\(339\) −0.0235254 0.0626679i −0.00127772 0.00340365i
\(340\) −1.01684 1.76122i −0.0551459 0.0955154i
\(341\) −2.09486 3.62840i −0.113443 0.196489i
\(342\) −8.24304 41.8140i −0.445732 2.26104i
\(343\) 0 0
\(344\) −0.420231 + 0.727861i −0.0226573 + 0.0392437i
\(345\) 0.550332 + 1.46600i 0.0296289 + 0.0789266i
\(346\) 32.6754 1.75664
\(347\) −11.5330 −0.619126 −0.309563 0.950879i \(-0.600183\pi\)
−0.309563 + 0.950879i \(0.600183\pi\)
\(348\) −12.0372 + 14.6419i −0.645263 + 0.784886i
\(349\) 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
\(352\) 6.75390 + 11.6981i 0.359984 + 0.623511i
\(353\) −1.32349 2.29236i −0.0704424 0.122010i 0.828653 0.559763i \(-0.189108\pi\)
−0.899095 + 0.437753i \(0.855774\pi\)
\(354\) 16.0396 + 2.66224i 0.852497 + 0.141496i
\(355\) −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
\(359\) −12.9835 22.4882i −0.685245 1.18688i −0.973360 0.229284i \(-0.926362\pi\)
0.288114 0.957596i \(-0.406972\pi\)
\(360\) −0.147530 + 0.128935i −0.00777553 + 0.00679547i
\(361\) −14.4264 + 24.9873i −0.759286 + 1.31512i
\(362\) 24.9761 1.31271
\(363\) 9.05362 11.0127i 0.475192 0.578014i
\(364\) 0 0
\(365\) 0.113867 + 0.197224i 0.00596009 + 0.0103232i
\(366\) 2.38008 + 0.395042i 0.124409 + 0.0206492i
\(367\) 8.79371 + 15.2312i 0.459028 + 0.795060i 0.998910 0.0466808i \(-0.0148644\pi\)
−0.539882 + 0.841741i \(0.681531\pi\)
\(368\) −10.8732 + 18.8330i −0.566806 + 0.981736i
\(369\) −1.34494 6.82241i −0.0700148 0.355160i
\(370\) 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 −0.876383 0.481614i \(-0.840051\pi\)
0.855282 + 0.518163i \(0.173384\pi\)
\(374\) 21.4306 1.10815
\(375\) −2.49352 0.413871i −0.128765 0.0213722i
\(376\) 0.809107 0.0417265
\(377\) 0.986490 0.0508068
\(378\) 0 0
\(379\) −20.4312 −1.04948 −0.524741 0.851262i \(-0.675838\pi\)
−0.524741 + 0.851262i \(0.675838\pi\)
\(380\) 2.24333 0.115080
\(381\) 23.0310 + 3.82265i 1.17991 + 0.195840i
\(382\) −10.2018 −0.521969
\(383\) 8.94638 15.4956i 0.457139 0.791788i −0.541670 0.840591i \(-0.682208\pi\)
0.998808 + 0.0488039i \(0.0155409\pi\)
\(384\) −6.06843 1.00723i −0.309678 0.0514000i
\(385\) 0 0
\(386\) −30.6084 −1.55793
\(387\) −4.25121 + 3.71538i −0.216101 + 0.188863i
\(388\) 8.83688 15.3059i 0.448625 0.777041i
\(389\) −7.81392 13.5341i −0.396181 0.686206i 0.597070 0.802189i \(-0.296331\pi\)
−0.993251 + 0.115983i \(0.962998\pi\)
\(390\) 0.102580 + 0.0170260i 0.00519431 + 0.000862146i
\(391\) 19.3835 + 33.5731i 0.980264 + 1.69787i
\(392\) 0 0
\(393\) −21.8156 + 26.5360i −1.10045 + 1.33857i
\(394\) −43.6622 −2.19967
\(395\) −0.935661 + 1.62061i −0.0470782 + 0.0815419i
\(396\) −2.14105 10.8608i −0.107592 0.545776i
\(397\) −9.63064 16.6808i −0.483348 0.837183i 0.516469 0.856306i \(-0.327246\pi\)
−0.999817 + 0.0191225i \(0.993913\pi\)
\(398\) 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 −0.987473 0.157790i \(-0.949563\pi\)
0.630387 + 0.776281i \(0.282896\pi\)
\(402\) −21.7097 3.60335i −1.08278 0.179719i
\(403\) −0.251642 0.435857i −0.0125352 0.0217116i
\(404\) 16.4569 + 28.5041i 0.818760 + 1.41813i
\(405\) −1.21774 + 0.499532i −0.0605098 + 0.0248219i
\(406\) 0 0
\(407\) −5.82452 + 10.0884i −0.288711 + 0.500062i
\(408\) −3.08047 + 3.74703i −0.152506 + 0.185505i
\(409\) −31.8610 −1.57542 −0.787712 0.616044i \(-0.788734\pi\)
−0.787712 + 0.616044i \(0.788734\pi\)
\(410\) 0.696152 0.0343805
\(411\) 3.92332 + 10.4511i 0.193523 + 0.515514i
\(412\) −0.226124 + 0.391657i −0.0111403 + 0.0192956i
\(413\) 0 0
\(414\) 28.6774 25.0628i 1.40942 1.23177i
\(415\) −0.549426 0.951633i −0.0269702 0.0467138i
\(416\) 0.811304 + 1.40522i 0.0397774 + 0.0688965i
\(417\) −7.62771 20.3190i −0.373530 0.995025i
\(418\) −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 \(0.185643\pi\)
\(422\) 24.1446 + 41.8197i 1.17534 + 2.03575i
\(423\) 5.14388 + 1.75592i 0.250104 + 0.0853759i
\(424\) −1.19375 + 2.06763i −0.0579734 + 0.100413i
\(425\) −31.2214 −1.51446
\(426\) 4.48274 + 0.744039i 0.217189 + 0.0360488i
\(427\) 0 0
\(428\) 7.72661 + 13.3829i 0.373480 + 0.646886i
\(429\) −0.365871 + 0.445039i −0.0176644 + 0.0214867i
\(430\) −0.282615 0.489503i −0.0136289 0.0236059i
\(431\) 2.46382 4.26746i 0.118678 0.205556i −0.800566 0.599244i \(-0.795468\pi\)
0.919244 + 0.393688i \(0.128801\pi\)
\(432\) −16.0985 8.65797i −0.774539 0.416557i
\(433\) −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
\(437\) −42.7633 −2.04565
\(438\) 3.51757 4.27871i 0.168076 0.204444i
\(439\) −2.44822 −0.116847 −0.0584235 0.998292i \(-0.518607\pi\)
−0.0584235 + 0.998292i \(0.518607\pi\)
\(440\) 0.108680 0.00518110
\(441\) 0 0
\(442\) 2.57432 0.122448
\(443\) −26.2950 −1.24931 −0.624657 0.780899i \(-0.714761\pi\)
−0.624657 + 0.780899i \(0.714761\pi\)
\(444\) −9.44944 25.1718i −0.448450 1.19460i
\(445\) 1.32614 0.0628650
\(446\) −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 \(0.866526\pi\)
\(450\) 5.93255 + 30.0937i 0.279663 + 1.41863i
\(451\) −1.92854 + 3.34034i −0.0908116 + 0.157290i
\(452\) −0.0428488 0.0742163i −0.00201544 0.00349084i
\(453\) −5.15350 13.7281i −0.242132 0.645002i
\(454\) −3.95620 6.85233i −0.185673 0.321596i
\(455\) 0 0
\(456\) −1.88053 5.00943i −0.0880638 0.234588i
\(457\) −9.15511 −0.428258 −0.214129 0.976805i \(-0.568691\pi\)
−0.214129 + 0.976805i \(0.568691\pi\)
\(458\) 13.4681 23.3274i 0.629321 1.09002i
\(459\) −27.7158 + 17.1364i −1.29366 + 0.799859i
\(460\) 1.00237 + 1.73615i 0.0467355 + 0.0809483i
\(461\) −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
\(465\) −0.405018 + 0.492657i −0.0187823 + 0.0228464i
\(466\) −17.9718 31.1280i −0.832526 1.44198i
\(467\) −7.68632 13.3131i −0.355680 0.616057i 0.631554 0.775332i \(-0.282418\pi\)
−0.987234 + 0.159276i \(0.949084\pi\)
\(468\) −0.257191 1.30464i −0.0118887 0.0603070i
\(469\) 0 0
\(470\) −0.272071 + 0.471241i −0.0125497 + 0.0217367i
\(471\) −9.73834 1.61636i −0.448719 0.0744779i
\(472\) 2.04132 0.0939594
\(473\) 3.13170 0.143996
\(474\) 44.9004 + 7.45252i 2.06234 + 0.342305i
\(475\) 17.2200 29.8259i 0.790106 1.36850i
\(476\) 0 0
\(477\) −12.0764 + 10.5542i −0.552939 + 0.483245i
\(478\) 7.51341 + 13.0136i 0.343655 + 0.595228i
\(479\) −18.9646 32.8476i −0.866513 1.50084i −0.865537 0.500844i \(-0.833023\pi\)
−0.000975329 1.00000i \(-0.500310\pi\)
\(480\) 1.30579 1.58834i 0.0596011 0.0724977i
\(481\) −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
\(485\) 0.582809 + 1.00946i 0.0264640 + 0.0458370i
\(486\) 21.7839 + 23.4586i 0.988137 + 1.06410i
\(487\) 2.30247 3.98800i 0.104335 0.180714i −0.809131 0.587628i \(-0.800062\pi\)
0.913466 + 0.406914i \(0.133395\pi\)
\(488\) 0.302906 0.0137119
\(489\) −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 \(-0.407042\pi\)
\(492\) −3.12878 8.33457i −0.141056 0.375752i
\(493\) −15.4744 26.8024i −0.696932 1.20712i
\(494\) −1.41985 + 2.45925i −0.0638820 + 0.110647i
\(495\) 0.690929 + 0.235857i 0.0310549 + 0.0106010i
\(496\) −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 −0.950914 0.309454i \(-0.899854\pi\)
0.743452 + 0.668789i \(0.233187\pi\)
\(500\) −3.23600 −0.144718
\(501\) 7.04571 + 18.7687i 0.314779 + 0.838522i
\(502\) −11.6089 −0.518131
\(503\) 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
\(506\) −21.1255 −0.939143
\(507\) 14.2553 17.3399i 0.633102 0.770094i
\(508\) 29.8888 1.32610
\(509\) −18.8207 + 32.5984i −0.834213 + 1.44490i 0.0604572 + 0.998171i \(0.480744\pi\)
−0.894670 + 0.446728i \(0.852589\pi\)
\(510\) −1.14651 3.05411i −0.0507682 0.135238i
\(511\) 0 0
\(512\) 31.6976 1.40085
\(513\) −1.08396 35.9284i −0.0478578 1.58628i
\(514\) 12.1182 20.9893i 0.534511 0.925800i
\(515\) −0.0149133 0.0258306i −0.000657158 0.00113823i
\(516\) −4.59032 + 5.58358i −0.202078 + 0.245804i
\(517\) −1.50743 2.61095i −0.0662969 0.114830i
\(518\) 0 0
\(519\) 27.1866 + 4.51240i 1.19336 + 0.198072i
\(520\) 0.0130550 0.000572500
\(521\) −17.4641 + 30.2488i −0.765117 + 1.32522i 0.175067 + 0.984556i \(0.443986\pi\)
−0.940185 + 0.340666i \(0.889348\pi\)
\(522\) −22.8940 + 20.0084i −1.00204 + 0.875743i
\(523\) 11.8735 + 20.5656i 0.519194 + 0.899270i 0.999751 + 0.0223069i \(0.00710109\pi\)
−0.480557 + 0.876963i \(0.659566\pi\)
\(524\) −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
\(528\) 3.56335 + 9.49220i 0.155075 + 0.413095i
\(529\) −7.60755 13.1767i −0.330763 0.572898i
\(530\) −0.802820 1.39053i −0.0348723 0.0604006i
\(531\) 12.9777 + 4.43008i 0.563182 + 0.192249i
\(532\) 0 0
\(533\) −0.231664 + 0.401254i −0.0100345 + 0.0173802i
\(534\) −11.3359 30.1970i −0.490552 1.30675i
\(535\) −1.01917 −0.0440626
\(536\) −2.76293 −0.119340
\(537\) 8.52822 10.3736i 0.368020 0.447652i
\(538\) 2.45292 4.24857i 0.105753 0.183169i
\(539\) 0 0
\(540\) −1.43325 + 0.886164i −0.0616773 + 0.0381344i
\(541\) 8.58542 + 14.8704i 0.369116 + 0.639328i 0.989428 0.145028i \(-0.0463271\pi\)
−0.620311 + 0.784356i \(0.712994\pi\)
\(542\) 23.8488 + 41.3074i 1.02439 + 1.77430i
\(543\) 20.7806 + 3.44914i 0.891782 + 0.148017i
\(544\) 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 \(0.307365\pi\)
\(548\) 7.14586 + 12.3770i 0.305256 + 0.528719i
\(549\) 1.92572 + 0.657366i 0.0821876 + 0.0280557i
\(550\) 8.50683 14.7343i 0.362732 0.628271i
\(551\) 34.1392 1.45438
\(552\) 3.03662 3.69369i 0.129247 0.157214i
\(553\) 0 0
\(554\) 4.74187 + 8.21316i 0.201463 + 0.348944i
\(555\) 1.74932 + 0.290350i 0.0742544 + 0.0123247i
\(556\) −13.8930 24.0633i −0.589193 1.02051i
\(557\) −0.122740 + 0.212593i −0.00520068 + 0.00900784i −0.868614 0.495489i \(-0.834989\pi\)
0.863413 + 0.504497i \(0.168322\pi\)
\(558\) 14.6802 + 5.01126i 0.621463 + 0.212144i
\(559\) 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
\(563\) 44.2509 1.86495 0.932477 0.361230i \(-0.117643\pi\)
0.932477 + 0.361230i \(0.117643\pi\)
\(564\) 6.86466 + 1.13939i 0.289054 + 0.0479769i
\(565\) 0.00565192 0.000237778
\(566\) −32.5496 −1.36816
\(567\) 0 0
\(568\) 0.570506 0.0239379
\(569\) −5.53533 −0.232053 −0.116027 0.993246i \(-0.537016\pi\)
−0.116027 + 0.993246i \(0.537016\pi\)
\(570\) 3.54995 + 0.589216i 0.148691 + 0.0246795i
\(571\) −4.10381 −0.171739 −0.0858696 0.996306i \(-0.527367\pi\)
−0.0858696 + 0.996306i \(0.527367\pi\)
\(572\) −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
\(576\) −27.3545 9.33780i −1.13977 0.389075i
\(577\) 2.82275 4.88915i 0.117513 0.203538i −0.801269 0.598305i \(-0.795841\pi\)
0.918781 + 0.394767i \(0.129175\pi\)
\(578\) −22.9256 39.7083i −0.953579 1.65165i
\(579\) −25.4668 4.22695i −1.05836 0.175666i
\(580\) −0.800218 1.38602i −0.0332272 0.0575513i
\(581\) 0 0
\(582\) 18.0040 21.8998i 0.746292 0.907776i
\(583\) 8.89619 0.368442
\(584\) 0.347710 0.602252i 0.0143884 0.0249214i
\(585\) 0.0829970 + 0.0283320i 0.00343150 + 0.00117138i
\(586\) −14.4742 25.0700i −0.597923 1.03563i
\(587\) −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
\(591\) −36.3278 6.02965i −1.49433 0.248027i
\(592\) 12.3131 + 21.3269i 0.506065 + 0.876530i
\(593\) 9.43516 + 16.3422i 0.387456 + 0.671093i 0.992107 0.125398i \(-0.0400207\pi\)
−0.604651 + 0.796491i \(0.706687\pi\)
\(594\) −0.535484 17.7490i −0.0219712 0.728250i
\(595\) 0 0
\(596\) −19.6991 + 34.1198i −0.806906 + 1.39760i
\(597\) 21.9375 26.6844i 0.897842 1.09212i
\(598\) −2.53767 −0.103773
\(599\) 2.67451 0.109278 0.0546388 0.998506i \(-0.482599\pi\)
0.0546388 + 0.998506i \(0.482599\pi\)
\(600\) 1.35342 + 3.60531i 0.0552533 + 0.147186i
\(601\) 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
\(604\) −9.38650 16.2579i −0.381931 0.661524i
\(605\) 0.601872 + 1.04247i 0.0244696 + 0.0423825i
\(606\) 18.5554 + 49.4287i 0.753763 + 2.00790i
\(607\) 12.9026 22.3480i 0.523701 0.907076i −0.475919 0.879489i \(-0.657884\pi\)
0.999619 0.0275869i \(-0.00878231\pi\)
\(608\) 28.0766 + 48.6301i 1.13866 + 1.97221i
\(609\) 0 0
\(610\) −0.101856 + 0.176419i −0.00412401 + 0.00714299i
\(611\) −0.181079 0.313637i −0.00732565 0.0126884i
\(612\) −31.4120 + 27.4528i −1.26976 + 1.10971i
\(613\) 13.4766 23.3422i 0.544316 0.942784i −0.454333 0.890832i \(-0.650122\pi\)
0.998650 0.0519519i \(-0.0165443\pi\)
\(614\) −56.2526 −2.27017
\(615\) 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 \(0.894788\pi\)
\(618\) −0.460698 + 0.560385i −0.0185320 + 0.0225420i
\(619\) 17.3536 + 30.0573i 0.697499 + 1.20810i 0.969331 + 0.245759i \(0.0790371\pi\)
−0.271832 + 0.962345i \(0.587630\pi\)
\(620\) −0.408253 + 0.707114i −0.0163958 + 0.0283984i
\(621\) 27.3213 16.8925i 1.09637 0.677871i
\(622\) 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
\(626\) −44.6558 −1.78480
\(627\) −12.6616 + 15.4014i −0.505656 + 0.615071i
\(628\) −12.6381 −0.504314
\(629\) 43.9006 1.75043
\(630\) 0 0
\(631\) −36.7963 −1.46484 −0.732419 0.680854i \(-0.761609\pi\)
−0.732419 + 0.680854i \(0.761609\pi\)
\(632\) 5.71435 0.227305
\(633\) 14.3136 + 38.1291i 0.568914 + 1.51550i
\(634\) 17.5853 0.698401
\(635\) −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
\(639\) 3.62698 + 1.23811i 0.143481 + 0.0489790i
\(640\) 0.259699 0.449811i 0.0102655 0.0177804i
\(641\) 22.0922 + 38.2648i 0.872590 + 1.51137i 0.859308 + 0.511458i \(0.170894\pi\)
0.0132813 + 0.999912i \(0.495772\pi\)
\(642\) 8.71191 + 23.2071i 0.343831 + 0.915912i
\(643\) −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
\(646\) 89.0889 3.50515
\(647\) 16.6536 28.8448i 0.654719 1.13401i −0.327245 0.944940i \(-0.606120\pi\)
0.981964 0.189068i \(-0.0605465\pi\)
\(648\) 3.18029 + 2.45765i 0.124934 + 0.0965455i
\(649\) −3.80315 6.58725i −0.149287 0.258572i
\(650\) 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 −0.763590 0.645701i \(-0.776565\pi\)
0.940989 + 0.338438i \(0.109899\pi\)
\(654\) 15.0469 18.3028i 0.588380 0.715694i
\(655\) −1.45027 2.51194i −0.0566666 0.0981495i
\(656\) 4.07696 + 7.06150i 0.159178 + 0.275705i
\(657\) 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 \(-0.0504035\pi\)
\(660\) 0.922066 + 0.153043i 0.0358914 + 0.00595720i
\(661\) 8.65915 0.336802 0.168401 0.985719i \(-0.446140\pi\)
0.168401 + 0.985719i \(0.446140\pi\)
\(662\) 22.2763 0.865794
\(663\) 2.14189 + 0.355508i 0.0831839 + 0.0138068i
\(664\) −1.67775 + 2.90595i −0.0651094 + 0.112773i
\(665\) 0 0
\(666\) −8.34179 42.3150i −0.323238 1.63967i
\(667\) 15.2541 + 26.4209i 0.590642 + 1.02302i
\(668\) 12.8329 + 22.2273i 0.496522 + 0.860001i
\(669\) −4.46692 + 5.43348i −0.172701 + 0.210070i
\(670\) 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 \(0.0765291\pi\)
\(674\) 3.43803 + 5.95484i 0.132428 + 0.229372i
\(675\) 0.780128 + 25.8579i 0.0300271 + 0.995270i
\(676\) 14.3692 24.8881i 0.552661 0.957236i
\(677\) −38.3315 −1.47320 −0.736600 0.676329i \(-0.763570\pi\)
−0.736600 + 0.676329i \(0.763570\pi\)
\(678\) −0.0483128 0.128698i −0.00185544 0.00494260i
\(679\) 0 0
\(680\) −0.204785 0.354698i −0.00785315 0.0136021i
\(681\) −2.34534 6.24762i −0.0898738 0.239409i
\(682\) −4.30209 7.45144i −0.164736 0.285330i
\(683\) −3.31659 + 5.74450i −0.126906 + 0.219807i −0.922476 0.386054i \(-0.873838\pi\)
0.795570 + 0.605861i \(0.207171\pi\)
\(684\) −8.90056 45.1494i −0.340321 1.72633i
\(685\) −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
\(689\) 1.06864 0.0407121
\(690\) 1.13019 + 3.01064i 0.0430255 + 0.114613i
\(691\) 23.3875 0.889704 0.444852 0.895604i \(-0.353256\pi\)
0.444852 + 0.895604i \(0.353256\pi\)
\(692\) 35.2818 1.34121
\(693\) 0 0
\(694\) −23.6848 −0.899061
\(695\) 1.83254 0.0695121
\(696\) −2.42422 + 2.94878i −0.0918899 + 0.111773i
\(697\) 14.5358 0.550583
\(698\) 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 \(0.444004\pi\)
\(702\) −0.0643244 2.13208i −0.00242777 0.0804700i
\(703\) −24.2131 + 41.9383i −0.913214 + 1.58173i
\(704\) 8.01636 + 13.8847i 0.302128 + 0.523301i
\(705\) −0.291446 + 0.354510i −0.0109765 + 0.0133516i
\(706\) −2.71799 4.70769i −0.102293 0.177176i
\(707\) 0 0
\(708\) 17.3191 + 2.87460i 0.650891 + 0.108034i
\(709\) 14.2355 0.534626 0.267313 0.963610i \(-0.413864\pi\)
0.267313 + 0.963610i \(0.413864\pi\)
\(710\) −0.191839 + 0.332275i −0.00719959 + 0.0124701i
\(711\) 36.3289 + 12.4013i 1.36244 + 0.465085i
\(712\) −2.02478 3.50702i −0.0758817 0.131431i
\(713\) 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
\(717\) 4.45416 + 11.8652i 0.166344 + 0.443113i
\(718\) −26.6636 46.1827i −0.995077 1.72352i
\(719\) −6.92848 12.0005i −0.258389 0.447542i 0.707422 0.706792i \(-0.249858\pi\)
−0.965810 + 0.259249i \(0.916525\pi\)
\(720\) 1.16212 1.01564i 0.0433096 0.0378507i
\(721\) 0 0
\(722\) −29.6268 + 51.3151i −1.10259 + 1.90975i
\(723\) 3.79303 + 10.1040i 0.141064 + 0.375773i
\(724\) 26.9684 1.00227
\(725\) −24.5702 −0.912513
\(726\) 18.5929 22.6161i 0.690048 0.839362i
\(727\) −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
\(730\) 0.233843 + 0.405028i 0.00865492 + 0.0149908i
\(731\) −5.90107 10.2209i −0.218259 0.378035i
\(732\) 2.56993 + 0.426554i 0.0949873 + 0.0157659i
\(733\) −13.3003 + 23.0368i −0.491257 + 0.850883i −0.999949 0.0100658i \(-0.996796\pi\)
0.508692 + 0.860949i \(0.330129\pi\)
\(734\) 18.0592 + 31.2794i 0.666576 + 1.15454i
\(735\) 0 0
\(736\) −25.0904 + 43.4579i −0.924845 + 1.60188i
\(737\) 5.14757 + 8.91586i 0.189613 + 0.328420i
\(738\) −2.76203 14.0108i −0.101672 0.515745i
\(739\) 16.5019 28.5822i 0.607034 1.05141i −0.384693 0.923045i \(-0.625693\pi\)
0.991727 0.128368i \(-0.0409740\pi\)
\(740\) 2.27020 0.0834543
\(741\) −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 \(0.582897\pi\)
\(744\) 1.92124 + 0.318885i 0.0704360 + 0.0116909i
\(745\) −1.29919 2.25027i −0.0475988 0.0824435i
\(746\) −0.836938 + 1.44962i −0.0306425 + 0.0530743i
\(747\) −16.9728 + 14.8335i −0.621001 + 0.542728i
\(748\) 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 −0.279863 0.960040i \(-0.590289\pi\)
0.971351 0.237651i \(-0.0763776\pi\)
\(752\) −6.37345 −0.232416
\(753\) −9.65885 1.60316i −0.351988 0.0584226i
\(754\) 2.02590 0.0737789
\(755\) 1.23811 0.0450596
\(756\) 0 0
\(757\) 22.5927 0.821147 0.410573 0.911828i \(-0.365329\pi\)
0.410573 + 0.911828i \(0.365329\pi\)
\(758\) −41.9585 −1.52400
\(759\) −17.5768 2.91738i −0.637999 0.105894i
\(760\) 0.451792 0.0163882
\(761\) 13.8735 24.0296i 0.502913 0.871072i −0.497081 0.867704i \(-0.665595\pi\)
0.999994 0.00336738i \(-0.00107187\pi\)
\(762\) 47.2974 + 7.85037i 1.71340 + 0.284389i
\(763\) 0 0
\(764\) −11.0156 −0.398529
\(765\) −0.532151 2.69941i −0.0192400 0.0975974i
\(766\) 18.3727 31.8224i 0.663832 1.14979i
\(767\) −0.456849 0.791286i −0.0164959 0.0285717i
\(768\) 20.4631 + 3.39644i 0.738399 + 0.122559i
\(769\) 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
\(772\) −33.0499 −1.18949
\(773\) 20.7795 35.9912i 0.747388 1.29451i −0.201682 0.979451i \(-0.564641\pi\)
0.949071 0.315063i \(-0.102026\pi\)
\(774\) −8.73049 + 7.63007i −0.313811 + 0.274257i
\(775\) 6.26756 + 10.8557i 0.225137 + 0.389950i
\(776\) 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
\(780\) 0.110762 + 0.0183841i 0.00396591