Properties

Label 441.2.h.f.373.5
Level $441$
Weight $2$
Character 441.373
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 373.5
Root \(-1.02682 - 1.77851i\) of defining polynomial
Character \(\chi\) \(=\) 441.373
Dual form 441.2.h.f.214.5

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 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 0.849211 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
\(9\) 2.83914 0.969173i 0.946379 0.323058i
\(10\) −0.150168 0.260099i −0.0474874 0.0822506i
\(11\) −0.832020 + 1.44110i −0.250864 + 0.434508i −0.963764 0.266757i \(-0.914048\pi\)
0.712900 + 0.701265i \(0.247381\pi\)
\(12\) 3.78891 0.628880i 1.09377 0.181542i
\(13\) −0.0999454 + 0.173111i −0.0277199 + 0.0480122i −0.879553 0.475802i \(-0.842158\pi\)
0.851833 + 0.523814i \(0.175491\pi\)
\(14\) 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 −0.942602 0.333919i \(-0.891629\pi\)
0.182119 0.983277i \(-0.441704\pi\)
\(18\) 5.83058 1.99034i 1.37428 0.469127i
\(19\) −3.45879 + 5.99080i −0.793500 + 1.37438i 0.130287 + 0.991476i \(0.458410\pi\)
−0.923787 + 0.382907i \(0.874923\pi\)
\(20\) −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 \(0.610399\pi\)
\(24\) 0.763064 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 0.540650 0.841248i \(-0.318178\pi\)
−0.998867 + 0.0475930i \(0.984845\pi\)
\(30\) −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 0.420560 + 0.907264i \(0.361833\pi\)
−0.995994 + 0.0894162i \(0.971500\pi\)
\(38\) −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 −0.942221 0.334993i \(-0.891266\pi\)
0.761223 + 0.648491i \(0.224599\pi\)
\(42\) 0 0
\(43\) −0.940993 1.62985i −0.143500 0.248550i 0.785312 0.619100i \(-0.212502\pi\)
−0.928812 + 0.370550i \(0.879169\pi\)
\(44\) −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 0.621948 0.783058i \(-0.286341\pi\)
−0.989123 + 0.147094i \(0.953008\pi\)
\(54\) 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 0.907986 0.419000i \(-0.137619\pi\)
−0.816858 + 0.576839i \(0.804286\pi\)
\(74\) −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 0.582778 0.812631i \(-0.301966\pi\)
−0.995148 + 0.0983854i \(0.968632\pi\)
\(84\) 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 −0.999752 0.0222619i \(-0.992913\pi\)
0.519155 + 0.854680i \(0.326247\pi\)
\(90\) −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 0.994278 0.106821i \(-0.0340671\pi\)
−0.589649 + 0.807660i \(0.700734\pi\)
\(98\) 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 −0.214719 0.976676i \(-0.568883\pi\)
0.953186 0.302386i \(-0.0977832\pi\)
\(102\) −14.1658 17.2310i −1.40262 1.70612i
\(103\) −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
\(107\) 3.48444 6.03524i 0.336854 0.583448i −0.646985 0.762503i \(-0.723970\pi\)
0.983839 + 0.179054i \(0.0573038\pi\)
\(108\) 10.1478 5.45759i 0.976468 0.525157i
\(109\) 3.33058 + 5.76874i 0.319012 + 0.552545i 0.980282 0.197603i \(-0.0633157\pi\)
−0.661270 + 0.750148i \(0.729982\pi\)
\(110\) 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 −0.866933 0.498425i \(-0.833912\pi\)
0.865115 + 0.501573i \(0.167245\pi\)
\(114\) −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 −0.865628 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
\(135\) −0.646348 0.399630i −0.0556288 0.0343947i
\(136\) −1.40028 2.42536i −0.120073 0.207973i
\(137\) 3.22255 5.58162i 0.275321 0.476870i −0.694895 0.719111i \(-0.744549\pi\)
0.970216 + 0.242241i \(0.0778826\pi\)
\(138\) 13.9641 + 16.9857i 1.18871 + 1.44592i
\(139\) −6.26527 + 10.8518i −0.531413 + 0.920435i 0.467914 + 0.883774i \(0.345006\pi\)
−0.999328 + 0.0366611i \(0.988328\pi\)
\(140\) 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 −0.957821 0.287365i \(-0.907221\pi\)
0.230045 0.973180i \(-0.426113\pi\)
\(150\) 6.22383 16.5793i 0.508174 1.35369i
\(151\) −4.23300 + 7.33177i −0.344476 + 0.596651i −0.985259 0.171072i \(-0.945277\pi\)
0.640782 + 0.767723i \(0.278610\pi\)
\(152\) −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 −0.904638 0.426181i \(-0.859859\pi\)
0.821403 + 0.570349i \(0.193192\pi\)
\(164\) −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 −0.550415 0.834891i \(-0.685530\pi\)
0.998244 + 0.0592278i \(0.0188638\pi\)
\(168\) 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 0.973751 0.227615i \(-0.0730929\pi\)
−0.683996 + 0.729485i \(0.739760\pi\)
\(180\) −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 0.966001 + 0.258540i \(0.0832413\pi\)
−0.259098 + 0.965851i \(0.583425\pi\)
\(200\) 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 −0.103912 0.994587i \(-0.533136\pi\)
0.913293 0.407303i \(-0.133531\pi\)
\(212\) −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 0.789995 0.613113i \(-0.210083\pi\)
−0.925969 + 0.377600i \(0.876750\pi\)
\(224\) 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 −0.922848 0.385165i \(-0.874145\pi\)
0.794986 + 0.606627i \(0.207478\pi\)
\(228\) −9.33756 + 24.8738i −0.618395 + 1.64731i
\(229\) 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
\(233\) −8.75115 + 15.1574i −0.573307 + 0.992997i 0.422916 + 0.906169i \(0.361007\pi\)
−0.996223 + 0.0868284i \(0.972327\pi\)
\(234\) −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 −0.723099 0.690745i \(-0.757283\pi\)
0.959752 + 0.280849i \(0.0906161\pi\)
\(240\) 0.565880 + 0.688327i 0.0365274 + 0.0444313i
\(241\) 3.11553 5.39626i 0.200689 0.347604i −0.748062 0.663629i \(-0.769015\pi\)
0.948751 + 0.316026i \(0.102349\pi\)
\(242\) 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 0.989266 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
\(261\) −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 −0.287528 0.957772i \(-0.592834\pi\)
0.973219 0.229879i \(-0.0738331\pi\)
\(264\) −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 0.900138 0.435604i \(-0.143465\pi\)
−0.827313 + 0.561741i \(0.810132\pi\)
\(270\) −1.32737 0.820699i −0.0807811 0.0499462i
\(271\) 11.6129 20.1142i 0.705435 1.22185i −0.261100 0.965312i \(-0.584085\pi\)
0.966534 0.256537i \(-0.0825815\pi\)
\(272\) 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 −0.788283 0.615312i \(-0.789030\pi\)
0.927018 + 0.375017i \(0.122363\pi\)
\(278\) −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 0.986681 0.162668i \(-0.0520098\pi\)
−0.634215 + 0.773157i \(0.718676\pi\)
\(282\) 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 −0.995081 0.0990615i \(-0.968416\pi\)
0.583330 + 0.812235i \(0.301749\pi\)
\(294\) 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 −0.816819 0.576893i \(-0.804265\pi\)
0.908014 + 0.418940i \(0.137598\pi\)
\(338\) 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 0.960186 0.279362i \(-0.0901228\pi\)
−0.722027 + 0.691865i \(0.756789\pi\)
\(350\) 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 −0.899095 0.437753i \(-0.855774\pi\)
0.828653 + 0.559763i \(0.189108\pi\)
\(354\) 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 0.288114 + 0.957596i \(0.406972\pi\)
−0.973360 + 0.229284i \(0.926362\pi\)
\(360\) −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 −0.539882 0.841741i \(-0.681531\pi\)
0.998910 + 0.0466808i \(0.0148644\pi\)
\(368\) −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 0.855282 0.518163i \(-0.173384\pi\)
−0.876383 + 0.481614i \(0.840051\pi\)
\(374\) 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 0.998808 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
\(387\) −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 −0.993251 0.115983i \(-0.962998\pi\)
0.597070 + 0.802189i \(0.296331\pi\)
\(390\) 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 −0.999817 0.0191225i \(-0.993913\pi\)
0.516469 + 0.856306i \(0.327246\pi\)
\(398\) 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 \(0.949563\pi\)
\(402\) −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 0.411339 + 0.911482i \(0.365061\pi\)
−0.995036 + 0.0995110i \(0.968272\pi\)
\(420\) 0 0
\(421\) −1.22251 2.11744i −0.0595813 0.103198i 0.834696 0.550711i \(-0.185643\pi\)
−0.894278 + 0.447513i \(0.852310\pi\)
\(422\) 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 0.919244 0.393688i \(-0.128801\pi\)
−0.800566 + 0.599244i \(0.795468\pi\)
\(432\) −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 −0.974768 0.223220i \(-0.928343\pi\)
0.294070 0.955784i \(-0.404990\pi\)
\(462\) 0 0
\(463\) −8.21031 + 14.2207i −0.381565 + 0.660891i −0.991286 0.131726i \(-0.957948\pi\)
0.609721 + 0.792616i \(0.291282\pi\)
\(464\) 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 −0.987234 0.159276i \(-0.949084\pi\)
0.631554 + 0.775332i \(0.282418\pi\)
\(468\) −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 −0.000975329 1.00000i \(0.500310\pi\)
−0.865537 + 0.500844i \(0.833023\pi\)
\(480\) 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 0.913466 0.406914i \(-0.133395\pi\)
−0.809131 + 0.587628i \(0.800062\pi\)
\(488\) 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 0.287904 + 0.957659i \(0.407042\pi\)
−0.973309 + 0.229497i \(0.926292\pi\)
\(492\) −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 0.743452 0.668789i \(-0.233187\pi\)
−0.950914 + 0.309454i \(0.899854\pi\)
\(500\) −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 −0.894670 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
\(513\) −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 −0.940185 0.340666i \(-0.889348\pi\)
0.175067 0.984556i \(-0.443986\pi\)
\(522\) −22.8940 20.0084i −1.00204 0.875743i
\(523\) 11.8735 20.5656i 0.519194 0.899270i −0.480557 0.876963i \(-0.659566\pi\)
0.999751 0.0223069i \(-0.00710109\pi\)
\(524\) −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 −0.620311 0.784356i \(-0.712994\pi\)
0.989428 + 0.145028i \(0.0463271\pi\)
\(542\) 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 0.568910 0.822400i \(-0.307365\pi\)
−0.996674 + 0.0814901i \(0.974032\pi\)
\(548\) 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 0.863413 0.504497i \(-0.168322\pi\)
−0.868614 + 0.495489i \(0.834989\pi\)
\(558\) 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 0.918781 0.394767i \(-0.129175\pi\)
−0.801269 + 0.598305i \(0.795841\pi\)
\(578\) −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 0.605394 0.795926i \(-0.293015\pi\)
−0.991989 + 0.126324i \(0.959682\pi\)
\(588\) 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 −0.604651 0.796491i \(-0.706687\pi\)
0.992107 + 0.125398i \(0.0400207\pi\)
\(594\) −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 0.968736 0.248095i \(-0.0798044\pi\)
−0.699224 + 0.714902i \(0.746471\pi\)
\(602\) 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 0.999619 + 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
\(611\) −0.181079 + 0.313637i −0.00732565 + 0.0126884i
\(612\) −31.4120 27.4528i −1.26976 1.10971i
\(613\) 13.4766 + 23.3422i 0.544316 + 0.942784i 0.998650 + 0.0519519i \(0.0165443\pi\)
−0.454333 + 0.890832i \(0.650122\pi\)
\(614\) −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 −0.945869 0.324549i \(-0.894788\pi\)
0.754002 + 0.656872i \(0.228121\pi\)
\(618\) −0.460698 0.560385i −0.0185320 0.0225420i
\(619\) 17.3536 30.0573i 0.697499 1.20810i −0.271832 0.962345i \(-0.587630\pi\)
0.969331 0.245759i \(-0.0790371\pi\)
\(620\) −0.408253 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 0.0132813 0.999912i \(-0.495772\pi\)
0.859308 0.511458i \(-0.170894\pi\)
\(642\) 8.71191 23.2071i 0.343831 0.915912i
\(643\) −7.24065 + 12.5412i −0.285543 + 0.494575i −0.972741 0.231895i \(-0.925507\pi\)
0.687197 + 0.726471i \(0.258841\pi\)
\(644\) 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 0.981964 + 0.189068i \(0.0605465\pi\)
−0.327245 + 0.944940i \(0.606120\pi\)
\(648\) 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 0.940989 0.338438i \(-0.109899\pi\)
−0.763590 + 0.645701i \(0.776565\pi\)
\(654\) 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 0.987489 + 0.157686i \(0.0504035\pi\)
−0.357184 + 0.934034i \(0.616263\pi\)
\(660\) 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 0.971237 0.238114i \(-0.0765291\pi\)
−0.691831 + 0.722059i \(0.743196\pi\)
\(674\) 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 0.795570 0.605861i \(-0.207171\pi\)
−0.922476 + 0.386054i \(0.873838\pi\)
\(684\) −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 −0.965810 0.259249i \(-0.916525\pi\)
0.707422 + 0.706792i \(0.249858\pi\)
\(720\) 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 −0.995208 0.0977755i \(-0.968827\pi\)
0.412928 0.910764i \(-0.364506\pi\)
\(728\) 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 0.508692 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
\(737\) 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 0.991727 + 0.128368i \(0.0409740\pi\)
−0.384693 + 0.923045i \(0.625693\pi\)
\(740\) 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 −0.257493 0.966280i \(-0.582897\pi\)
0.965570 0.260144i \(-0.0837701\pi\)
\(744\) 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 0.971351 + 0.237651i \(0.0763776\pi\)
−0.279863 + 0.960040i \(0.590289\pi\)
\(752\) −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 0.999994 + 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
\(765\) −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 −0.735412 0.677621i \(-0.763011\pi\)
0.954542 + 0.298075i \(0.0963445\pi\)
\(770\) 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 0.949071 + 0.315063i \(0.102026\pi\)
−0.201682 + 0.979451i \(0.564641\pi\)
\(774\) −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 0.018384