Properties

Label 882.2.h.l.67.1
Level $882$
Weight $2$
Character 882.67
Analytic conductor $7.043$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 882.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(7.04280545828\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} - 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 67.1
Root \(-1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.67
Dual form 882.2.h.l.79.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.44949 q^{5} +(1.72474 + 0.158919i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})\) \(q+(-0.500000 + 0.866025i) q^{2} +(-0.724745 - 1.57313i) q^{3} +(-0.500000 - 0.866025i) q^{4} +1.44949 q^{5} +(1.72474 + 0.158919i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +(-0.724745 + 1.25529i) q^{10} +2.00000 q^{11} +(-1.00000 + 1.41421i) q^{12} +(2.44949 - 4.24264i) q^{13} +(-1.05051 - 2.28024i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.00000 - 1.73205i) q^{17} +(-1.00000 - 2.82843i) q^{18} +(1.27526 + 2.20881i) q^{19} +(-0.724745 - 1.25529i) q^{20} +(-1.00000 + 1.73205i) q^{22} -1.00000 q^{23} +(-0.724745 - 1.57313i) q^{24} -2.89898 q^{25} +(2.44949 + 4.24264i) q^{26} +(5.00000 + 1.41421i) q^{27} +(3.44949 + 5.97469i) q^{29} +(2.50000 + 0.230351i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.44949 - 3.14626i) q^{33} +(1.00000 + 1.73205i) q^{34} +(2.94949 + 0.548188i) q^{36} +(-5.89898 - 10.2173i) q^{37} -2.55051 q^{38} +(-8.44949 - 0.778539i) q^{39} +1.44949 q^{40} +(4.89898 - 8.48528i) q^{41} +(-3.44949 - 5.97469i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(-2.82577 + 3.30518i) q^{45} +(0.500000 - 0.866025i) q^{46} +(4.89898 - 8.48528i) q^{47} +(1.72474 + 0.158919i) q^{48} +(1.44949 - 2.51059i) q^{50} +(-3.44949 - 0.317837i) q^{51} -4.89898 q^{52} +(5.44949 - 9.43879i) q^{53} +(-3.72474 + 3.62302i) q^{54} +2.89898 q^{55} +(2.55051 - 3.60697i) q^{57} -6.89898 q^{58} +(-1.00000 - 1.73205i) q^{59} +(-1.44949 + 2.04989i) q^{60} +(3.27526 - 5.67291i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(3.55051 - 6.14966i) q^{65} +(3.44949 + 0.317837i) q^{66} +(6.44949 + 11.1708i) q^{67} -2.00000 q^{68} +(0.724745 + 1.57313i) q^{69} +0.101021 q^{71} +(-1.94949 + 2.28024i) q^{72} +(-3.44949 + 5.97469i) q^{73} +11.7980 q^{74} +(2.10102 + 4.56048i) q^{75} +(1.27526 - 2.20881i) q^{76} +(4.89898 - 6.92820i) q^{78} +(0.949490 - 1.64456i) q^{79} +(-0.724745 + 1.25529i) q^{80} +(-1.39898 - 8.89060i) q^{81} +(4.89898 + 8.48528i) q^{82} +(1.00000 + 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +6.89898 q^{86} +(6.89898 - 9.75663i) q^{87} +2.00000 q^{88} +(-8.44949 - 14.6349i) q^{89} +(-1.44949 - 4.09978i) q^{90} +(0.500000 + 0.866025i) q^{92} +(6.00000 - 8.48528i) q^{93} +(4.89898 + 8.48528i) q^{94} +(1.84847 + 3.20164i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(1.44949 + 2.51059i) q^{97} +(-3.89898 + 4.56048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 4q^{5} + 2q^{6} + 4q^{8} + 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 4q^{5} + 2q^{6} + 4q^{8} + 2q^{9} + 2q^{10} + 8q^{11} - 4q^{12} - 14q^{15} - 2q^{16} + 4q^{17} - 4q^{18} + 10q^{19} + 2q^{20} - 4q^{22} - 4q^{23} + 2q^{24} + 8q^{25} + 20q^{27} + 4q^{29} + 10q^{30} + 12q^{31} - 2q^{32} + 4q^{33} + 4q^{34} + 2q^{36} - 4q^{37} - 20q^{38} - 24q^{39} - 4q^{40} - 4q^{43} - 4q^{44} - 26q^{45} + 2q^{46} + 2q^{48} - 4q^{50} - 4q^{51} + 12q^{53} - 10q^{54} - 8q^{55} + 20q^{57} - 8q^{58} - 4q^{59} + 4q^{60} + 18q^{61} - 24q^{62} + 4q^{64} + 24q^{65} + 4q^{66} + 16q^{67} - 8q^{68} - 2q^{69} + 20q^{71} + 2q^{72} - 4q^{73} + 8q^{74} + 28q^{75} + 10q^{76} - 6q^{79} + 2q^{80} + 14q^{81} + 4q^{83} - 4q^{85} + 8q^{86} + 8q^{87} + 8q^{88} - 24q^{89} + 4q^{90} + 2q^{92} + 24q^{93} - 22q^{95} - 4q^{96} - 4q^{97} + 4q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
<
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.500000 + 0.866025i −0.353553 + 0.612372i
\(3\) −0.724745 1.57313i −0.418432 0.908248i
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.44949 0.648232 0.324116 0.946017i \(-0.394933\pi\)
0.324116 + 0.946017i \(0.394933\pi\)
\(6\) 1.72474 + 0.158919i 0.704124 + 0.0648783i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) −1.94949 + 2.28024i −0.649830 + 0.760080i
\(10\) −0.724745 + 1.25529i −0.229184 + 0.396959i
\(11\) 2.00000 0.603023 0.301511 0.953463i \(-0.402509\pi\)
0.301511 + 0.953463i \(0.402509\pi\)
\(12\) −1.00000 + 1.41421i −0.288675 + 0.408248i
\(13\) 2.44949 4.24264i 0.679366 1.17670i −0.295806 0.955248i \(-0.595588\pi\)
0.975172 0.221449i \(-0.0710785\pi\)
\(14\) 0 0
\(15\) −1.05051 2.28024i −0.271241 0.588755i
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) 1.00000 1.73205i 0.242536 0.420084i −0.718900 0.695113i \(-0.755354\pi\)
0.961436 + 0.275029i \(0.0886875\pi\)
\(18\) −1.00000 2.82843i −0.235702 0.666667i
\(19\) 1.27526 + 2.20881i 0.292564 + 0.506735i 0.974415 0.224756i \(-0.0721584\pi\)
−0.681852 + 0.731491i \(0.738825\pi\)
\(20\) −0.724745 1.25529i −0.162058 0.280692i
\(21\) 0 0
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) −1.00000 −0.208514 −0.104257 0.994550i \(-0.533247\pi\)
−0.104257 + 0.994550i \(0.533247\pi\)
\(24\) −0.724745 1.57313i −0.147938 0.321114i
\(25\) −2.89898 −0.579796
\(26\) 2.44949 + 4.24264i 0.480384 + 0.832050i
\(27\) 5.00000 + 1.41421i 0.962250 + 0.272166i
\(28\) 0 0
\(29\) 3.44949 + 5.97469i 0.640554 + 1.10947i 0.985309 + 0.170780i \(0.0546286\pi\)
−0.344755 + 0.938693i \(0.612038\pi\)
\(30\) 2.50000 + 0.230351i 0.456435 + 0.0420561i
\(31\) 3.00000 + 5.19615i 0.538816 + 0.933257i 0.998968 + 0.0454165i \(0.0144615\pi\)
−0.460152 + 0.887840i \(0.652205\pi\)
\(32\) −0.500000 0.866025i −0.0883883 0.153093i
\(33\) −1.44949 3.14626i −0.252324 0.547694i
\(34\) 1.00000 + 1.73205i 0.171499 + 0.297044i
\(35\) 0 0
\(36\) 2.94949 + 0.548188i 0.491582 + 0.0913647i
\(37\) −5.89898 10.2173i −0.969786 1.67972i −0.696165 0.717881i \(-0.745112\pi\)
−0.273621 0.961838i \(-0.588221\pi\)
\(38\) −2.55051 −0.413747
\(39\) −8.44949 0.778539i −1.35300 0.124666i
\(40\) 1.44949 0.229184
\(41\) 4.89898 8.48528i 0.765092 1.32518i −0.175106 0.984550i \(-0.556027\pi\)
0.940198 0.340629i \(-0.110640\pi\)
\(42\) 0 0
\(43\) −3.44949 5.97469i −0.526042 0.911132i −0.999540 0.0303367i \(-0.990342\pi\)
0.473497 0.880795i \(-0.342991\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) −2.82577 + 3.30518i −0.421240 + 0.492708i
\(46\) 0.500000 0.866025i 0.0737210 0.127688i
\(47\) 4.89898 8.48528i 0.714590 1.23771i −0.248528 0.968625i \(-0.579947\pi\)
0.963118 0.269081i \(-0.0867199\pi\)
\(48\) 1.72474 + 0.158919i 0.248945 + 0.0229379i
\(49\) 0 0
\(50\) 1.44949 2.51059i 0.204989 0.355051i
\(51\) −3.44949 0.317837i −0.483025 0.0445061i
\(52\) −4.89898 −0.679366
\(53\) 5.44949 9.43879i 0.748545 1.29652i −0.199975 0.979801i \(-0.564086\pi\)
0.948520 0.316717i \(-0.102581\pi\)
\(54\) −3.72474 + 3.62302i −0.506874 + 0.493031i
\(55\) 2.89898 0.390898
\(56\) 0 0
\(57\) 2.55051 3.60697i 0.337823 0.477754i
\(58\) −6.89898 −0.905880
\(59\) −1.00000 1.73205i −0.130189 0.225494i 0.793560 0.608492i \(-0.208225\pi\)
−0.923749 + 0.382998i \(0.874892\pi\)
\(60\) −1.44949 + 2.04989i −0.187128 + 0.264639i
\(61\) 3.27526 5.67291i 0.419353 0.726341i −0.576521 0.817082i \(-0.695590\pi\)
0.995875 + 0.0907408i \(0.0289235\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 3.55051 6.14966i 0.440387 0.762772i
\(66\) 3.44949 + 0.317837i 0.424603 + 0.0391231i
\(67\) 6.44949 + 11.1708i 0.787931 + 1.36474i 0.927233 + 0.374486i \(0.122181\pi\)
−0.139302 + 0.990250i \(0.544486\pi\)
\(68\) −2.00000 −0.242536
\(69\) 0.724745 + 1.57313i 0.0872490 + 0.189383i
\(70\) 0 0
\(71\) 0.101021 0.0119889 0.00599446 0.999982i \(-0.498092\pi\)
0.00599446 + 0.999982i \(0.498092\pi\)
\(72\) −1.94949 + 2.28024i −0.229750 + 0.268729i
\(73\) −3.44949 + 5.97469i −0.403732 + 0.699285i −0.994173 0.107796i \(-0.965621\pi\)
0.590441 + 0.807081i \(0.298954\pi\)
\(74\) 11.7980 1.37148
\(75\) 2.10102 + 4.56048i 0.242605 + 0.526599i
\(76\) 1.27526 2.20881i 0.146282 0.253368i
\(77\) 0 0
\(78\) 4.89898 6.92820i 0.554700 0.784465i
\(79\) 0.949490 1.64456i 0.106826 0.185028i −0.807657 0.589653i \(-0.799265\pi\)
0.914483 + 0.404625i \(0.132598\pi\)
\(80\) −0.724745 + 1.25529i −0.0810289 + 0.140346i
\(81\) −1.39898 8.89060i −0.155442 0.987845i
\(82\) 4.89898 + 8.48528i 0.541002 + 0.937043i
\(83\) 1.00000 + 1.73205i 0.109764 + 0.190117i 0.915675 0.401920i \(-0.131657\pi\)
−0.805910 + 0.592037i \(0.798324\pi\)
\(84\) 0 0
\(85\) 1.44949 2.51059i 0.157219 0.272312i
\(86\) 6.89898 0.743936
\(87\) 6.89898 9.75663i 0.739648 1.04602i
\(88\) 2.00000 0.213201
\(89\) −8.44949 14.6349i −0.895644 1.55130i −0.833005 0.553265i \(-0.813382\pi\)
−0.0626387 0.998036i \(-0.519952\pi\)
\(90\) −1.44949 4.09978i −0.152790 0.432154i
\(91\) 0 0
\(92\) 0.500000 + 0.866025i 0.0521286 + 0.0902894i
\(93\) 6.00000 8.48528i 0.622171 0.879883i
\(94\) 4.89898 + 8.48528i 0.505291 + 0.875190i
\(95\) 1.84847 + 3.20164i 0.189649 + 0.328482i
\(96\) −1.00000 + 1.41421i −0.102062 + 0.144338i
\(97\) 1.44949 + 2.51059i 0.147173 + 0.254912i 0.930182 0.367099i \(-0.119649\pi\)
−0.783008 + 0.622011i \(0.786316\pi\)
\(98\) 0 0
\(99\) −3.89898 + 4.56048i −0.391862 + 0.458345i
\(100\) 1.44949 + 2.51059i 0.144949 + 0.251059i
\(101\) 17.2474 1.71619 0.858093 0.513495i \(-0.171649\pi\)
0.858093 + 0.513495i \(0.171649\pi\)
\(102\) 2.00000 2.82843i 0.198030 0.280056i
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) 2.44949 4.24264i 0.240192 0.416025i
\(105\) 0 0
\(106\) 5.44949 + 9.43879i 0.529301 + 0.916777i
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) −1.27526 5.03723i −0.122711 0.484708i
\(109\) −6.34847 + 10.9959i −0.608073 + 1.05321i 0.383485 + 0.923547i \(0.374724\pi\)
−0.991558 + 0.129666i \(0.958609\pi\)
\(110\) −1.44949 + 2.51059i −0.138203 + 0.239375i
\(111\) −11.7980 + 16.6848i −1.11981 + 1.58365i
\(112\) 0 0
\(113\) 3.05051 5.28364i 0.286968 0.497043i −0.686117 0.727492i \(-0.740686\pi\)
0.973084 + 0.230449i \(0.0740194\pi\)
\(114\) 1.84847 + 4.01229i 0.173125 + 0.375785i
\(115\) −1.44949 −0.135166
\(116\) 3.44949 5.97469i 0.320277 0.554736i
\(117\) 4.89898 + 13.8564i 0.452911 + 1.28103i
\(118\) 2.00000 0.184115
\(119\) 0 0
\(120\) −1.05051 2.28024i −0.0958980 0.208156i
\(121\) −7.00000 −0.636364
\(122\) 3.27526 + 5.67291i 0.296528 + 0.513601i
\(123\) −16.8990 1.55708i −1.52373 0.140397i
\(124\) 3.00000 5.19615i 0.269408 0.466628i
\(125\) −11.4495 −1.02407
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) −0.500000 + 0.866025i −0.0441942 + 0.0765466i
\(129\) −6.89898 + 9.75663i −0.607421 + 0.859023i
\(130\) 3.55051 + 6.14966i 0.311400 + 0.539361i
\(131\) 8.55051 0.747062 0.373531 0.927618i \(-0.378147\pi\)
0.373531 + 0.927618i \(0.378147\pi\)
\(132\) −2.00000 + 2.82843i −0.174078 + 0.246183i
\(133\) 0 0
\(134\) −12.8990 −1.11430
\(135\) 7.24745 + 2.04989i 0.623761 + 0.176426i
\(136\) 1.00000 1.73205i 0.0857493 0.148522i
\(137\) 7.79796 0.666225 0.333112 0.942887i \(-0.391901\pi\)
0.333112 + 0.942887i \(0.391901\pi\)
\(138\) −1.72474 0.158919i −0.146820 0.0135281i
\(139\) 2.27526 3.94086i 0.192985 0.334259i −0.753253 0.657730i \(-0.771517\pi\)
0.946238 + 0.323471i \(0.104850\pi\)
\(140\) 0 0
\(141\) −16.8990 1.55708i −1.42315 0.131130i
\(142\) −0.0505103 + 0.0874863i −0.00423873 + 0.00734169i
\(143\) 4.89898 8.48528i 0.409673 0.709575i
\(144\) −1.00000 2.82843i −0.0833333 0.235702i
\(145\) 5.00000 + 8.66025i 0.415227 + 0.719195i
\(146\) −3.44949 5.97469i −0.285482 0.494469i
\(147\) 0 0
\(148\) −5.89898 + 10.2173i −0.484893 + 0.839860i
\(149\) −6.00000 −0.491539 −0.245770 0.969328i \(-0.579041\pi\)
−0.245770 + 0.969328i \(0.579041\pi\)
\(150\) −5.00000 0.460702i −0.408248 0.0376161i
\(151\) −5.00000 −0.406894 −0.203447 0.979086i \(-0.565214\pi\)
−0.203447 + 0.979086i \(0.565214\pi\)
\(152\) 1.27526 + 2.20881i 0.103437 + 0.179158i
\(153\) 2.00000 + 5.65685i 0.161690 + 0.457330i
\(154\) 0 0
\(155\) 4.34847 + 7.53177i 0.349277 + 0.604966i
\(156\) 3.55051 + 7.70674i 0.284268 + 0.617033i
\(157\) −4.17423 7.22999i −0.333140 0.577016i 0.649986 0.759947i \(-0.274775\pi\)
−0.983126 + 0.182931i \(0.941442\pi\)
\(158\) 0.949490 + 1.64456i 0.0755373 + 0.130835i
\(159\) −18.7980 1.73205i −1.49078 0.137361i
\(160\) −0.724745 1.25529i −0.0572961 0.0992398i
\(161\) 0 0
\(162\) 8.39898 + 3.23375i 0.659886 + 0.254067i
\(163\) 9.89898 + 17.1455i 0.775348 + 1.34294i 0.934599 + 0.355704i \(0.115759\pi\)
−0.159251 + 0.987238i \(0.550908\pi\)
\(164\) −9.79796 −0.765092
\(165\) −2.10102 4.56048i −0.163564 0.355033i
\(166\) −2.00000 −0.155230
\(167\) −5.34847 + 9.26382i −0.413877 + 0.716856i −0.995310 0.0967384i \(-0.969159\pi\)
0.581433 + 0.813594i \(0.302492\pi\)
\(168\) 0 0
\(169\) −5.50000 9.52628i −0.423077 0.732791i
\(170\) 1.44949 + 2.51059i 0.111171 + 0.192553i
\(171\) −7.52270 1.39816i −0.575276 0.106920i
\(172\) −3.44949 + 5.97469i −0.263021 + 0.455566i
\(173\) −1.55051 + 2.68556i −0.117883 + 0.204180i −0.918929 0.394424i \(-0.870944\pi\)
0.801045 + 0.598604i \(0.204277\pi\)
\(174\) 5.00000 + 10.8530i 0.379049 + 0.822764i
\(175\) 0 0
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) −2.00000 + 2.82843i −0.150329 + 0.212598i
\(178\) 16.8990 1.26663
\(179\) −10.3485 + 17.9241i −0.773481 + 1.33971i 0.162163 + 0.986764i \(0.448153\pi\)
−0.935644 + 0.352944i \(0.885181\pi\)
\(180\) 4.27526 + 0.794593i 0.318659 + 0.0592255i
\(181\) 10.3485 0.769196 0.384598 0.923084i \(-0.374340\pi\)
0.384598 + 0.923084i \(0.374340\pi\)
\(182\) 0 0
\(183\) −11.2980 1.04100i −0.835169 0.0769528i
\(184\) −1.00000 −0.0737210
\(185\) −8.55051 14.8099i −0.628646 1.08885i
\(186\) 4.34847 + 9.43879i 0.318845 + 0.692086i
\(187\) 2.00000 3.46410i 0.146254 0.253320i
\(188\) −9.79796 −0.714590
\(189\) 0 0
\(190\) −3.69694 −0.268204
\(191\) −2.05051 + 3.55159i −0.148370 + 0.256984i −0.930625 0.365974i \(-0.880736\pi\)
0.782255 + 0.622958i \(0.214069\pi\)
\(192\) −0.724745 1.57313i −0.0523040 0.113531i
\(193\) 8.94949 + 15.5010i 0.644198 + 1.11578i 0.984486 + 0.175463i \(0.0561422\pi\)
−0.340288 + 0.940321i \(0.610524\pi\)
\(194\) −2.89898 −0.208135
\(195\) −12.2474 1.12848i −0.877058 0.0808124i
\(196\) 0 0
\(197\) 16.6969 1.18961 0.594804 0.803871i \(-0.297230\pi\)
0.594804 + 0.803871i \(0.297230\pi\)
\(198\) −2.00000 5.65685i −0.142134 0.402015i
\(199\) −1.44949 + 2.51059i −0.102752 + 0.177971i −0.912817 0.408368i \(-0.866098\pi\)
0.810066 + 0.586339i \(0.199431\pi\)
\(200\) −2.89898 −0.204989
\(201\) 12.8990 18.2419i 0.909824 1.28669i
\(202\) −8.62372 + 14.9367i −0.606763 + 1.05094i
\(203\) 0 0
\(204\) 1.44949 + 3.14626i 0.101485 + 0.220283i
\(205\) 7.10102 12.2993i 0.495957 0.859022i
\(206\) 7.00000 12.1244i 0.487713 0.844744i
\(207\) 1.94949 2.28024i 0.135499 0.158488i
\(208\) 2.44949 + 4.24264i 0.169842 + 0.294174i
\(209\) 2.55051 + 4.41761i 0.176422 + 0.305573i
\(210\) 0 0
\(211\) −6.44949 + 11.1708i −0.444001 + 0.769033i −0.997982 0.0634968i \(-0.979775\pi\)
0.553981 + 0.832529i \(0.313108\pi\)
\(212\) −10.8990 −0.748545
\(213\) −0.0732141 0.158919i −0.00501655 0.0108889i
\(214\) −12.0000 −0.820303
\(215\) −5.00000 8.66025i −0.340997 0.590624i
\(216\) 5.00000 + 1.41421i 0.340207 + 0.0962250i
\(217\) 0 0
\(218\) −6.34847 10.9959i −0.429973 0.744734i
\(219\) 11.8990 + 1.09638i 0.804059 + 0.0740862i
\(220\) −1.44949 2.51059i −0.0977246 0.169264i
\(221\) −4.89898 8.48528i −0.329541 0.570782i
\(222\) −8.55051 18.5597i −0.573873 1.24565i
\(223\) −5.55051 9.61377i −0.371690 0.643785i 0.618136 0.786071i \(-0.287888\pi\)
−0.989826 + 0.142286i \(0.954555\pi\)
\(224\) 0 0
\(225\) 5.65153 6.61037i 0.376769 0.440691i
\(226\) 3.05051 + 5.28364i 0.202917 + 0.351462i
\(227\) 5.44949 0.361695 0.180848 0.983511i \(-0.442116\pi\)
0.180848 + 0.983511i \(0.442116\pi\)
\(228\) −4.39898 0.405324i −0.291330 0.0268432i
\(229\) −1.24745 −0.0824337 −0.0412169 0.999150i \(-0.513123\pi\)
−0.0412169 + 0.999150i \(0.513123\pi\)
\(230\) 0.724745 1.25529i 0.0477883 0.0827717i
\(231\) 0 0
\(232\) 3.44949 + 5.97469i 0.226470 + 0.392258i
\(233\) 3.50000 + 6.06218i 0.229293 + 0.397146i 0.957599 0.288106i \(-0.0930254\pi\)
−0.728306 + 0.685252i \(0.759692\pi\)
\(234\) −14.4495 2.68556i −0.944593 0.175561i
\(235\) 7.10102 12.2993i 0.463220 0.802320i
\(236\) −1.00000 + 1.73205i −0.0650945 + 0.112747i
\(237\) −3.27526 0.301783i −0.212751 0.0196029i
\(238\) 0 0
\(239\) −3.39898 + 5.88721i −0.219862 + 0.380812i −0.954766 0.297360i \(-0.903894\pi\)
0.734904 + 0.678171i \(0.237227\pi\)
\(240\) 2.50000 + 0.230351i 0.161374 + 0.0148691i
\(241\) −0.898979 −0.0579084 −0.0289542 0.999581i \(-0.509218\pi\)
−0.0289542 + 0.999581i \(0.509218\pi\)
\(242\) 3.50000 6.06218i 0.224989 0.389692i
\(243\) −12.9722 + 8.64420i −0.832167 + 0.554526i
\(244\) −6.55051 −0.419353
\(245\) 0 0
\(246\) 9.79796 13.8564i 0.624695 0.883452i
\(247\) 12.4949 0.795031
\(248\) 3.00000 + 5.19615i 0.190500 + 0.329956i
\(249\) 2.00000 2.82843i 0.126745 0.179244i
\(250\) 5.72474 9.91555i 0.362065 0.627114i
\(251\) −17.4495 −1.10140 −0.550701 0.834703i \(-0.685640\pi\)
−0.550701 + 0.834703i \(0.685640\pi\)
\(252\) 0 0
\(253\) −2.00000 −0.125739
\(254\) 1.50000 2.59808i 0.0941184 0.163018i
\(255\) −5.00000 0.460702i −0.313112 0.0288503i
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −8.20204 −0.511629 −0.255815 0.966726i \(-0.582344\pi\)
−0.255815 + 0.966726i \(0.582344\pi\)
\(258\) −5.00000 10.8530i −0.311286 0.675679i
\(259\) 0 0
\(260\) −7.10102 −0.440387
\(261\) −20.3485 3.78194i −1.25954 0.234096i
\(262\) −4.27526 + 7.40496i −0.264126 + 0.457480i
\(263\) 25.8990 1.59700 0.798500 0.601995i \(-0.205627\pi\)
0.798500 + 0.601995i \(0.205627\pi\)
\(264\) −1.44949 3.14626i −0.0892099 0.193639i
\(265\) 7.89898 13.6814i 0.485230 0.840444i
\(266\) 0 0
\(267\) −16.8990 + 23.8988i −1.03420 + 1.46258i
\(268\) 6.44949 11.1708i 0.393965 0.682368i
\(269\) −9.17423 + 15.8902i −0.559363 + 0.968845i 0.438187 + 0.898884i \(0.355621\pi\)
−0.997550 + 0.0699611i \(0.977712\pi\)
\(270\) −5.39898 + 5.25153i −0.328571 + 0.319598i
\(271\) 3.55051 + 6.14966i 0.215678 + 0.373565i 0.953482 0.301450i \(-0.0974705\pi\)
−0.737804 + 0.675015i \(0.764137\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 0 0
\(274\) −3.89898 + 6.75323i −0.235546 + 0.407978i
\(275\) −5.79796 −0.349630
\(276\) 1.00000 1.41421i 0.0601929 0.0851257i
\(277\) −18.6969 −1.12339 −0.561695 0.827344i \(-0.689851\pi\)
−0.561695 + 0.827344i \(0.689851\pi\)
\(278\) 2.27526 + 3.94086i 0.136461 + 0.236357i
\(279\) −17.6969 3.28913i −1.05949 0.196915i
\(280\) 0 0
\(281\) 9.50000 + 16.4545i 0.566722 + 0.981592i 0.996887 + 0.0788417i \(0.0251222\pi\)
−0.430165 + 0.902750i \(0.641545\pi\)
\(282\) 9.79796 13.8564i 0.583460 0.825137i
\(283\) −12.7247 22.0399i −0.756408 1.31014i −0.944672 0.328018i \(-0.893619\pi\)
0.188264 0.982118i \(-0.439714\pi\)
\(284\) −0.0505103 0.0874863i −0.00299723 0.00519136i
\(285\) 3.69694 5.22826i 0.218988 0.309695i
\(286\) 4.89898 + 8.48528i 0.289683 + 0.501745i
\(287\) 0 0
\(288\) 2.94949 + 0.548188i 0.173800 + 0.0323023i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −10.0000 −0.587220
\(291\) 2.89898 4.09978i 0.169941 0.240333i
\(292\) 6.89898 0.403732
\(293\) 1.37628 2.38378i 0.0804029 0.139262i −0.823020 0.568012i \(-0.807713\pi\)
0.903423 + 0.428750i \(0.141046\pi\)
\(294\) 0 0
\(295\) −1.44949 2.51059i −0.0843926 0.146172i
\(296\) −5.89898 10.2173i −0.342871 0.593870i
\(297\) 10.0000 + 2.82843i 0.580259 + 0.164122i
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) −2.44949 + 4.24264i −0.141658 + 0.245358i
\(300\) 2.89898 4.09978i 0.167373 0.236701i
\(301\) 0 0
\(302\) 2.50000 4.33013i 0.143859 0.249171i
\(303\) −12.5000 27.1325i −0.718106 1.55872i
\(304\) −2.55051 −0.146282
\(305\) 4.74745 8.22282i 0.271838 0.470837i
\(306\) −5.89898 1.09638i −0.337222 0.0626757i
\(307\) −25.2474 −1.44095 −0.720474 0.693482i \(-0.756076\pi\)
−0.720474 + 0.693482i \(0.756076\pi\)
\(308\) 0 0
\(309\) 10.1464 + 22.0239i 0.577210 + 1.25289i
\(310\) −8.69694 −0.493953
\(311\) 15.3485 + 26.5843i 0.870332 + 1.50746i 0.861654 + 0.507497i \(0.169429\pi\)
0.00867810 + 0.999962i \(0.497238\pi\)
\(312\) −8.44949 0.778539i −0.478358 0.0440761i
\(313\) −2.34847 + 4.06767i −0.132743 + 0.229918i −0.924733 0.380616i \(-0.875712\pi\)
0.791990 + 0.610534i \(0.209045\pi\)
\(314\) 8.34847 0.471131
\(315\) 0 0
\(316\) −1.89898 −0.106826
\(317\) −10.3485 + 17.9241i −0.581228 + 1.00672i 0.414106 + 0.910229i \(0.364094\pi\)
−0.995334 + 0.0964878i \(0.969239\pi\)
\(318\) 10.8990 15.4135i 0.611184 0.864345i
\(319\) 6.89898 + 11.9494i 0.386269 + 0.669037i
\(320\) 1.44949 0.0810289
\(321\) 12.0000 16.9706i 0.669775 0.947204i
\(322\) 0 0
\(323\) 5.10102 0.283828
\(324\) −7.00000 + 5.65685i −0.388889 + 0.314270i
\(325\) −7.10102 + 12.2993i −0.393894 + 0.682244i
\(326\) −19.7980 −1.09651
\(327\) 21.8990 + 2.01778i 1.21102 + 0.111583i
\(328\) 4.89898 8.48528i 0.270501 0.468521i
\(329\) 0 0
\(330\) 5.00000 + 0.460702i 0.275241 + 0.0253608i
\(331\) −2.34847 + 4.06767i −0.129084 + 0.223579i −0.923322 0.384027i \(-0.874537\pi\)
0.794238 + 0.607606i \(0.207870\pi\)
\(332\) 1.00000 1.73205i 0.0548821 0.0950586i
\(333\) 34.7980 + 6.46750i 1.90692 + 0.354417i
\(334\) −5.34847 9.26382i −0.292655 0.506894i
\(335\) 9.34847 + 16.1920i 0.510761 + 0.884665i
\(336\) 0 0
\(337\) 11.6969 20.2597i 0.637173 1.10362i −0.348877 0.937168i \(-0.613437\pi\)
0.986050 0.166447i \(-0.0532296\pi\)
\(338\) 11.0000 0.598321
\(339\) −10.5227 0.969566i −0.571515 0.0526596i
\(340\) −2.89898 −0.157219
\(341\) 6.00000 + 10.3923i 0.324918 + 0.562775i
\(342\) 4.97219 5.81577i 0.268865 0.314481i
\(343\) 0 0
\(344\) −3.44949 5.97469i −0.185984 0.322134i
\(345\) 1.05051 + 2.28024i 0.0565576 + 0.122764i
\(346\) −1.55051 2.68556i −0.0833559 0.144377i
\(347\) −9.79796 16.9706i −0.525982 0.911028i −0.999542 0.0302659i \(-0.990365\pi\)
0.473560 0.880762i \(-0.342969\pi\)
\(348\) −11.8990 1.09638i −0.637852 0.0587719i
\(349\) 5.55051 + 9.61377i 0.297112 + 0.514613i 0.975474 0.220115i \(-0.0706432\pi\)
−0.678362 + 0.734728i \(0.737310\pi\)
\(350\) 0 0
\(351\) 18.2474 17.7491i 0.973977 0.947377i
\(352\) −1.00000 1.73205i −0.0533002 0.0923186i
\(353\) 6.00000 0.319348 0.159674 0.987170i \(-0.448956\pi\)
0.159674 + 0.987170i \(0.448956\pi\)
\(354\) −1.44949 3.14626i −0.0770395 0.167222i
\(355\) 0.146428 0.00777160
\(356\) −8.44949 + 14.6349i −0.447822 + 0.775651i
\(357\) 0 0
\(358\) −10.3485 17.9241i −0.546934 0.947317i
\(359\) 4.39898 + 7.61926i 0.232169 + 0.402129i 0.958446 0.285273i \(-0.0920843\pi\)
−0.726277 + 0.687402i \(0.758751\pi\)
\(360\) −2.82577 + 3.30518i −0.148931 + 0.174198i
\(361\) 6.24745 10.8209i 0.328813 0.569521i
\(362\) −5.17423 + 8.96204i −0.271952 + 0.471034i
\(363\) 5.07321 + 11.0119i 0.266275 + 0.577976i
\(364\) 0 0
\(365\) −5.00000 + 8.66025i −0.261712 + 0.453298i
\(366\) 6.55051 9.26382i 0.342401 0.484228i
\(367\) 13.7980 0.720248 0.360124 0.932905i \(-0.382734\pi\)
0.360124 + 0.932905i \(0.382734\pi\)
\(368\) 0.500000 0.866025i 0.0260643 0.0451447i
\(369\) 9.79796 + 27.7128i 0.510061 + 1.44267i
\(370\) 17.1010 0.889040
\(371\) 0 0
\(372\) −10.3485 0.953512i −0.536543 0.0494373i
\(373\) −6.89898 −0.357216 −0.178608 0.983920i \(-0.557159\pi\)
−0.178608 + 0.983920i \(0.557159\pi\)
\(374\) 2.00000 + 3.46410i 0.103418 + 0.179124i
\(375\) 8.29796 + 18.0116i 0.428505 + 0.930113i
\(376\) 4.89898 8.48528i 0.252646 0.437595i
\(377\) 33.7980 1.74068
\(378\) 0 0
\(379\) 22.4949 1.15549 0.577743 0.816219i \(-0.303934\pi\)
0.577743 + 0.816219i \(0.303934\pi\)
\(380\) 1.84847 3.20164i 0.0948245 0.164241i
\(381\) 2.17423 + 4.71940i 0.111389 + 0.241782i
\(382\) −2.05051 3.55159i −0.104913 0.181715i
\(383\) 2.89898 0.148131 0.0740655 0.997253i \(-0.476403\pi\)
0.0740655 + 0.997253i \(0.476403\pi\)
\(384\) 1.72474 + 0.158919i 0.0880155 + 0.00810978i
\(385\) 0 0
\(386\) −17.8990 −0.911034
\(387\) 20.3485 + 3.78194i 1.03437 + 0.192247i
\(388\) 1.44949 2.51059i 0.0735867 0.127456i
\(389\) −24.8990 −1.26243 −0.631214 0.775609i \(-0.717443\pi\)
−0.631214 + 0.775609i \(0.717443\pi\)
\(390\) 7.10102 10.0424i 0.359574 0.508515i
\(391\) −1.00000 + 1.73205i −0.0505722 + 0.0875936i
\(392\) 0 0
\(393\) −6.19694 13.4511i −0.312594 0.678517i
\(394\) −8.34847 + 14.4600i −0.420590 + 0.728483i
\(395\) 1.37628 2.38378i 0.0692479 0.119941i
\(396\) 5.89898 + 1.09638i 0.296435 + 0.0550950i
\(397\) 19.3485 + 33.5125i 0.971072 + 1.68195i 0.692332 + 0.721579i \(0.256583\pi\)
0.278740 + 0.960367i \(0.410083\pi\)
\(398\) −1.44949 2.51059i −0.0726564 0.125844i
\(399\) 0 0
\(400\) 1.44949 2.51059i 0.0724745 0.125529i
\(401\) −19.8990 −0.993708 −0.496854 0.867834i \(-0.665511\pi\)
−0.496854 + 0.867834i \(0.665511\pi\)
\(402\) 9.34847 + 20.2918i 0.466259 + 1.01206i
\(403\) 29.3939 1.46421
\(404\) −8.62372 14.9367i −0.429046 0.743130i
\(405\) −2.02781 12.8868i −0.100763 0.640352i
\(406\) 0 0
\(407\) −11.7980 20.4347i −0.584803 1.01291i
\(408\) −3.44949 0.317837i −0.170775 0.0157353i
\(409\) −6.89898 11.9494i −0.341133 0.590859i 0.643511 0.765437i \(-0.277477\pi\)
−0.984643 + 0.174578i \(0.944144\pi\)
\(410\) 7.10102 + 12.2993i 0.350694 + 0.607421i
\(411\) −5.65153 12.2672i −0.278769 0.605097i
\(412\) 7.00000 + 12.1244i 0.344865 + 0.597324i
\(413\) 0 0
\(414\) 1.00000 + 2.82843i 0.0491473 + 0.139010i
\(415\) 1.44949 + 2.51059i 0.0711527 + 0.123240i
\(416\) −4.89898 −0.240192
\(417\) −7.84847 0.723161i −0.384341 0.0354133i
\(418\) −5.10102 −0.249499
\(419\) 14.7247 25.5040i 0.719351 1.24595i −0.241906 0.970300i \(-0.577773\pi\)
0.961257 0.275653i \(-0.0888940\pi\)
\(420\) 0 0
\(421\) −11.4495 19.8311i −0.558014 0.966509i −0.997662 0.0683385i \(-0.978230\pi\)
0.439648 0.898170i \(-0.355103\pi\)
\(422\) −6.44949 11.1708i −0.313956 0.543788i
\(423\) 9.79796 + 27.7128i 0.476393 + 1.34744i
\(424\) 5.44949 9.43879i 0.264651 0.458388i
\(425\) −2.89898 + 5.02118i −0.140621 + 0.243563i
\(426\) 0.174235 + 0.0160540i 0.00844169 + 0.000777821i
\(427\) 0 0
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) −16.8990 1.55708i −0.815890 0.0751764i
\(430\) 10.0000 0.482243
\(431\) −15.7980 + 27.3629i −0.760961 + 1.31802i 0.181395 + 0.983410i \(0.441939\pi\)
−0.942356 + 0.334613i \(0.891395\pi\)
\(432\) −3.72474 + 3.62302i −0.179207 + 0.174313i
\(433\) 7.79796 0.374746 0.187373 0.982289i \(-0.440003\pi\)
0.187373 + 0.982289i \(0.440003\pi\)
\(434\) 0 0
\(435\) 10.0000 14.1421i 0.479463 0.678064i
\(436\) 12.6969 0.608073
\(437\) −1.27526 2.20881i −0.0610037 0.105662i
\(438\) −6.89898 + 9.75663i −0.329646 + 0.466190i
\(439\) 1.10102 1.90702i 0.0525488 0.0910173i −0.838554 0.544818i \(-0.816599\pi\)
0.891103 + 0.453801i \(0.149932\pi\)
\(440\) 2.89898 0.138203
\(441\) 0 0
\(442\) 9.79796 0.466041
\(443\) 7.44949 12.9029i 0.353936 0.613035i −0.632999 0.774152i \(-0.718176\pi\)
0.986935 + 0.161117i \(0.0515098\pi\)
\(444\) 20.3485 + 1.87492i 0.965696 + 0.0889795i
\(445\) −12.2474 21.2132i −0.580585 1.00560i
\(446\) 11.1010 0.525649
\(447\) 4.34847 + 9.43879i 0.205676 + 0.446440i
\(448\) 0 0
\(449\) 20.5959 0.971981 0.485991 0.873964i \(-0.338459\pi\)
0.485991 + 0.873964i \(0.338459\pi\)
\(450\) 2.89898 + 8.19955i 0.136659 + 0.386531i
\(451\) 9.79796 16.9706i 0.461368 0.799113i
\(452\) −6.10102 −0.286968
\(453\) 3.62372 + 7.86566i 0.170257 + 0.369561i
\(454\) −2.72474 + 4.71940i −0.127879 + 0.221492i
\(455\) 0 0
\(456\) 2.55051 3.60697i 0.119439 0.168912i
\(457\) 8.74745 15.1510i 0.409188 0.708735i −0.585611 0.810593i \(-0.699145\pi\)
0.994799 + 0.101857i \(0.0324785\pi\)
\(458\) 0.623724 1.08032i 0.0291447 0.0504801i
\(459\) 7.44949 7.24604i 0.347712 0.338216i
\(460\) 0.724745 + 1.25529i 0.0337914 + 0.0585284i
\(461\) 2.82577 + 4.89437i 0.131609 + 0.227954i 0.924297 0.381674i \(-0.124652\pi\)
−0.792688 + 0.609628i \(0.791319\pi\)
\(462\) 0 0
\(463\) −1.84847 + 3.20164i −0.0859057 + 0.148793i −0.905777 0.423755i \(-0.860712\pi\)
0.819871 + 0.572548i \(0.194045\pi\)
\(464\) −6.89898 −0.320277
\(465\) 8.69694 12.2993i 0.403311 0.570368i
\(466\) −7.00000 −0.324269
\(467\) 5.00000 + 8.66025i 0.231372 + 0.400749i 0.958212 0.286058i \(-0.0923451\pi\)
−0.726840 + 0.686807i \(0.759012\pi\)
\(468\) 9.55051 11.1708i 0.441472 0.516372i
\(469\) 0 0
\(470\) 7.10102 + 12.2993i 0.327546 + 0.567326i
\(471\) −8.34847 + 11.8065i −0.384677 + 0.544016i
\(472\) −1.00000 1.73205i −0.0460287 0.0797241i
\(473\) −6.89898 11.9494i −0.317215 0.549433i
\(474\) 1.89898 2.68556i 0.0872230 0.123352i
\(475\) −3.69694 6.40329i −0.169627 0.293803i
\(476\) 0 0
\(477\) 10.8990 + 30.8270i 0.499030 + 1.41147i
\(478\) −3.39898 5.88721i −0.155466 0.269274i
\(479\) −9.59592 −0.438449 −0.219224 0.975674i \(-0.570353\pi\)
−0.219224 + 0.975674i \(0.570353\pi\)
\(480\) −1.44949 + 2.04989i −0.0661599 + 0.0935642i
\(481\) −57.7980 −2.63536
\(482\) 0.449490 0.778539i 0.0204737 0.0354615i
\(483\) 0 0
\(484\) 3.50000 + 6.06218i 0.159091 + 0.275554i
\(485\) 2.10102 + 3.63907i 0.0954024 + 0.165242i
\(486\) −1.00000 15.5563i −0.0453609 0.705650i
\(487\) 18.1969 31.5180i 0.824582 1.42822i −0.0776564 0.996980i \(-0.524744\pi\)
0.902238 0.431238i \(-0.141923\pi\)
\(488\) 3.27526 5.67291i 0.148264 0.256800i
\(489\) 19.7980 27.9985i 0.895295 1.26614i
\(490\) 0 0
\(491\) −7.89898 + 13.6814i −0.356476 + 0.617434i −0.987369 0.158435i \(-0.949355\pi\)
0.630893 + 0.775869i \(0.282688\pi\)
\(492\) 7.10102 + 15.4135i 0.320139 + 0.694894i
\(493\) 13.7980 0.621429
\(494\) −6.24745 + 10.8209i −0.281086 + 0.486855i
\(495\) −5.65153 + 6.61037i −0.254017 + 0.297114i
\(496\) −6.00000 −0.269408
\(497\) 0 0
\(498\) 1.44949 + 3.14626i 0.0649532 + 0.140987i
\(499\) −25.3939 −1.13679 −0.568393 0.822757i \(-0.692435\pi\)
−0.568393 + 0.822757i \(0.692435\pi\)
\(500\) 5.72474 + 9.91555i 0.256018 + 0.443437i
\(501\) 18.4495 + 1.69994i 0.824262 + 0.0759478i
\(502\) 8.72474 15.1117i 0.389404 0.674468i
\(503\) 24.4949 1.09217 0.546087 0.837729i \(-0.316117\pi\)
0.546087 + 0.837729i \(0.316117\pi\)
\(504\) 0 0
\(505\) 25.0000 1.11249
\(506\) 1.00000 1.73205i 0.0444554 0.0769991i
\(507\) −11.0000 + 15.5563i −0.488527 + 0.690882i
\(508\) 1.50000 + 2.59808i 0.0665517 + 0.115271i
\(509\) 7.10102 0.314747 0.157374 0.987539i \(-0.449697\pi\)
0.157374 + 0.987539i \(0.449697\pi\)
\(510\) 2.89898 4.09978i 0.128369 0.181541i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 3.25255 + 12.8475i 0.143604 + 0.567232i
\(514\) 4.10102 7.10318i 0.180888 0.313308i
\(515\) −20.2929 −0.894210
\(516\) 11.8990 + 1.09638i 0.523823 + 0.0482653i
\(517\) 9.79796 16.9706i 0.430914 0.746364i
\(518\) 0 0
\(519\) 5.34847 + 0.492810i 0.234772 + 0.0216320i
\(520\) 3.55051 6.14966i 0.155700 0.269681i
\(521\) −4.65153 + 8.05669i −0.203787 + 0.352970i −0.949746 0.313023i \(-0.898658\pi\)
0.745958 + 0.665993i \(0.231992\pi\)
\(522\) 13.4495 15.7313i 0.588668 0.688541i
\(523\) −7.17423 12.4261i −0.313707 0.543357i 0.665455 0.746438i \(-0.268238\pi\)
−0.979162 + 0.203081i \(0.934904\pi\)
\(524\) −4.27526 7.40496i −0.186765 0.323487i
\(525\) 0 0
\(526\) −12.9495 + 22.4292i −0.564625 + 0.977958i
\(527\) 12.0000 0.522728
\(528\) 3.44949 + 0.317837i 0.150120 + 0.0138321i
\(529\) −22.0000 −0.956522
\(530\) 7.89898 + 13.6814i 0.343110 + 0.594284i
\(531\) 5.89898 + 1.09638i 0.255994 + 0.0475787i
\(532\) 0 0
\(533\) −24.0000 41.5692i −1.03956 1.80056i
\(534\) −12.2474 26.5843i −0.529999 1.15042i
\(535\) 8.69694 + 15.0635i 0.376001 + 0.651254i
\(536\) 6.44949 + 11.1708i 0.278576 + 0.482507i
\(537\) 35.6969 + 3.28913i 1.54044 + 0.141936i
\(538\) −9.17423 15.8902i −0.395529 0.685077i
\(539\) 0 0
\(540\) −1.84847 7.30142i −0.0795455 0.314203i
\(541\) 9.24745 + 16.0171i 0.397579 + 0.688627i 0.993427 0.114471i \(-0.0365172\pi\)
−0.595848 + 0.803097i \(0.703184\pi\)
\(542\) −7.10102 −0.305015
\(543\) −7.50000 16.2795i −0.321856 0.698621i
\(544\) −2.00000 −0.0857493
\(545\) −9.20204 + 15.9384i −0.394172 + 0.682726i
\(546\) 0 0
\(547\) 3.79796 + 6.57826i 0.162389 + 0.281266i 0.935725 0.352730i \(-0.114747\pi\)
−0.773336 + 0.633996i \(0.781413\pi\)
\(548\) −3.89898 6.75323i −0.166556 0.288484i
\(549\) 6.55051 + 18.5276i 0.279569 + 0.790740i
\(550\) 2.89898 5.02118i 0.123613 0.214104i
\(551\) −8.79796 + 15.2385i −0.374806 + 0.649182i
\(552\) 0.724745 + 1.57313i 0.0308472 + 0.0669570i
\(553\) 0 0
\(554\) 9.34847 16.1920i 0.397178 0.687933i
\(555\) −17.1010 + 24.1845i −0.725898 + 1.02657i
\(556\) −4.55051 −0.192985
\(557\) 6.44949 11.1708i 0.273274 0.473324i −0.696424 0.717630i \(-0.745227\pi\)
0.969698 + 0.244306i \(0.0785602\pi\)
\(558\) 11.6969 13.6814i 0.495171 0.579181i
\(559\) −33.7980 −1.42950
\(560\) 0 0
\(561\) −6.89898 0.635674i −0.291275 0.0268382i
\(562\) −19.0000 −0.801467
\(563\) −19.9722 34.5929i −0.841728 1.45791i −0.888433 0.459006i \(-0.848206\pi\)
0.0467054 0.998909i \(-0.485128\pi\)
\(564\) 7.10102 + 15.4135i 0.299007 + 0.649025i
\(565\) 4.42168 7.65858i 0.186022 0.322199i
\(566\) 25.4495 1.06972
\(567\) 0 0
\(568\) 0.101021 0.00423873
\(569\) 15.0000 25.9808i 0.628833 1.08917i −0.358954 0.933355i \(-0.616866\pi\)
0.987786 0.155815i \(-0.0498003\pi\)
\(570\) 2.67934 + 5.81577i 0.112225 + 0.243596i
\(571\) −16.8990 29.2699i −0.707200 1.22491i −0.965892 0.258947i \(-0.916625\pi\)
0.258691 0.965960i \(-0.416709\pi\)
\(572\) −9.79796 −0.409673
\(573\) 7.07321 + 0.651729i 0.295488 + 0.0272263i
\(574\) 0 0
\(575\) 2.89898 0.120896
\(576\) −1.94949 + 2.28024i −0.0812287 + 0.0950100i
\(577\) −7.79796 + 13.5065i −0.324633 + 0.562281i −0.981438 0.191779i \(-0.938574\pi\)
0.656805 + 0.754061i \(0.271908\pi\)
\(578\) −13.0000 −0.540729
\(579\) 17.8990 25.3130i 0.743856 1.05197i
\(580\) 5.00000 8.66025i 0.207614 0.359597i
\(581\) 0 0
\(582\) 2.10102 + 4.56048i 0.0870901 + 0.189038i
\(583\) 10.8990 18.8776i 0.451390 0.781830i
\(584\) −3.44949 + 5.97469i −0.142741 + 0.247234i
\(585\) 7.10102 + 20.0847i 0.293591 + 0.830401i
\(586\) 1.37628 + 2.38378i 0.0568534 + 0.0984730i
\(587\) 8.07321 + 13.9832i 0.333217 + 0.577149i 0.983141 0.182850i \(-0.0585324\pi\)
−0.649924 + 0.760000i \(0.725199\pi\)
\(588\) 0 0
\(589\) −7.65153 + 13.2528i −0.315276 + 0.546074i
\(590\) 2.89898 0.119349
\(591\) −12.1010 26.2665i −0.497769 1.08046i
\(592\) 11.7980 0.484893
\(593\) 7.34847 + 12.7279i 0.301765 + 0.522673i 0.976536 0.215355i \(-0.0690907\pi\)
−0.674770 + 0.738028i \(0.735757\pi\)
\(594\) −7.44949 + 7.24604i −0.305656 + 0.297309i
\(595\) 0 0
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) 5.00000 + 0.460702i 0.204636 + 0.0188553i
\(598\) −2.44949 4.24264i −0.100167 0.173494i
\(599\) 16.8990 + 29.2699i 0.690474 + 1.19594i 0.971683 + 0.236289i \(0.0759312\pi\)
−0.281209 + 0.959646i \(0.590736\pi\)
\(600\) 2.10102 + 4.56048i 0.0857738 + 0.186181i
\(601\) 8.34847 + 14.4600i 0.340541 + 0.589835i 0.984533 0.175198i \(-0.0560564\pi\)
−0.643992 + 0.765032i \(0.722723\pi\)
\(602\) 0 0
\(603\) −38.0454 7.07107i −1.54933 0.287956i
\(604\) 2.50000 + 4.33013i 0.101724 + 0.176190i
\(605\) −10.1464 −0.412511
\(606\) 29.7474 + 2.74094i 1.20841 + 0.111343i
\(607\) −20.6969 −0.840063 −0.420031 0.907510i \(-0.637981\pi\)
−0.420031 + 0.907510i \(0.637981\pi\)
\(608\) 1.27526 2.20881i 0.0517184 0.0895789i
\(609\) 0 0
\(610\) 4.74745 + 8.22282i 0.192219 + 0.332932i
\(611\) −24.0000 41.5692i −0.970936 1.68171i
\(612\) 3.89898 4.56048i 0.157607 0.184346i
\(613\) 7.34847 12.7279i 0.296802 0.514076i −0.678601 0.734508i \(-0.737413\pi\)
0.975402 + 0.220432i \(0.0707466\pi\)
\(614\) 12.6237 21.8649i 0.509452 0.882397i
\(615\) −24.4949 2.25697i −0.987730 0.0910098i
\(616\) 0 0
\(617\) 7.69694 13.3315i 0.309867 0.536706i −0.668466 0.743743i \(-0.733049\pi\)
0.978333 + 0.207037i \(0.0663821\pi\)
\(618\) −24.1464 2.22486i −0.971312 0.0894970i
\(619\) −30.1464 −1.21169 −0.605844 0.795584i \(-0.707164\pi\)
−0.605844 + 0.795584i \(0.707164\pi\)
\(620\) 4.34847 7.53177i 0.174639 0.302483i
\(621\) −5.00000 1.41421i −0.200643 0.0567504i
\(622\) −30.6969 −1.23084
\(623\) 0 0
\(624\) 4.89898 6.92820i 0.196116 0.277350i
\(625\) −2.10102 −0.0840408
\(626\) −2.34847 4.06767i −0.0938637 0.162577i
\(627\) 5.10102 7.21393i 0.203715 0.288097i
\(628\) −4.17423 + 7.22999i −0.166570 + 0.288508i
\(629\) −23.5959 −0.940831
\(630\) 0 0
\(631\) 27.8990 1.11064 0.555320 0.831636i \(-0.312596\pi\)
0.555320 + 0.831636i \(0.312596\pi\)
\(632\) 0.949490 1.64456i 0.0377687 0.0654173i
\(633\) 22.2474 + 2.04989i 0.884257 + 0.0814757i
\(634\) −10.3485 17.9241i −0.410990 0.711856i
\(635\) −4.34847 −0.172564
\(636\) 7.89898 + 17.1455i 0.313215 + 0.679865i
\(637\) 0 0
\(638\) −13.7980 −0.546266
\(639\) −0.196938 + 0.230351i −0.00779076 + 0.00911254i
\(640\) −0.724745 + 1.25529i −0.0286481 + 0.0496199i
\(641\) −7.49490 −0.296031 −0.148015 0.988985i \(-0.547288\pi\)
−0.148015 + 0.988985i \(0.547288\pi\)
\(642\) 8.69694 + 18.8776i 0.343241 + 0.745039i
\(643\) −19.6969 + 34.1161i −0.776771 + 1.34541i 0.157022 + 0.987595i \(0.449811\pi\)
−0.933793 + 0.357812i \(0.883523\pi\)
\(644\) 0 0
\(645\) −10.0000 + 14.1421i −0.393750 + 0.556846i
\(646\) −2.55051 + 4.41761i −0.100348 + 0.173809i
\(647\) −25.3485 + 43.9048i −0.996551 + 1.72608i −0.426412 + 0.904529i \(0.640223\pi\)
−0.570139 + 0.821548i \(0.693111\pi\)
\(648\) −1.39898 8.89060i −0.0549571 0.349256i
\(649\) −2.00000 3.46410i −0.0785069 0.135978i
\(650\) −7.10102 12.2993i −0.278525 0.482419i
\(651\) 0 0
\(652\) 9.89898 17.1455i 0.387674 0.671471i
\(653\) 9.79796 0.383424 0.191712 0.981451i \(-0.438596\pi\)
0.191712 + 0.981451i \(0.438596\pi\)
\(654\) −12.6969 + 17.9562i −0.496490 + 0.702142i
\(655\) 12.3939 0.484269
\(656\) 4.89898 + 8.48528i 0.191273 + 0.331295i
\(657\) −6.89898 19.5133i −0.269155 0.761285i
\(658\) 0 0
\(659\) 12.3485 + 21.3882i 0.481028 + 0.833165i 0.999763 0.0217701i \(-0.00693018\pi\)
−0.518735 + 0.854935i \(0.673597\pi\)
\(660\) −2.89898 + 4.09978i −0.112843 + 0.159584i
\(661\) 2.27526 + 3.94086i 0.0884972 + 0.153282i 0.906876 0.421397i \(-0.138460\pi\)
−0.818379 + 0.574679i \(0.805127\pi\)
\(662\) −2.34847 4.06767i −0.0912758 0.158094i
\(663\) −9.79796 + 13.8564i −0.380521 + 0.538138i
\(664\) 1.00000 + 1.73205i 0.0388075 + 0.0672166i
\(665\) 0 0
\(666\) −23.0000 + 26.9022i −0.891232 + 1.04244i
\(667\) −3.44949 5.97469i −0.133565 0.231341i
\(668\) 10.6969 0.413877
\(669\) −11.1010 + 15.6992i −0.429190 + 0.606967i
\(670\) −18.6969 −0.722326
\(671\) 6.55051 11.3458i 0.252880 0.438000i
\(672\) 0 0
\(673\) 4.29796 + 7.44428i 0.165674 + 0.286956i 0.936894 0.349612i \(-0.113687\pi\)
−0.771220 + 0.636568i \(0.780353\pi\)
\(674\) 11.6969 + 20.2597i 0.450549 + 0.780374i
\(675\) −14.4949 4.09978i −0.557909 0.157800i
\(676\) −5.50000 + 9.52628i −0.211538 + 0.366395i
\(677\) 7.34847 12.7279i 0.282425 0.489174i −0.689557 0.724232i \(-0.742195\pi\)
0.971981 + 0.235058i \(0.0755280\pi\)
\(678\) 6.10102 8.62815i 0.234308 0.331362i
\(679\) 0 0
\(680\) 1.44949 2.51059i 0.0555854 0.0962767i
\(681\) −3.94949 8.57277i −0.151345 0.328509i
\(682\) −12.0000 −0.459504
\(683\) −25.8990 + 44.8583i −0.990997 + 1.71646i −0.379551 + 0.925171i \(0.623921\pi\)
−0.611446 + 0.791286i \(0.709412\pi\)
\(684\) 2.55051 + 7.21393i 0.0975212 + 0.275832i
\(685\) 11.3031 0.431868
\(686\) 0 0
\(687\) 0.904082 + 1.96240i 0.0344929 + 0.0748703i
\(688\) 6.89898 0.263021
\(689\) −26.6969 46.2405i −1.01707 1.76162i
\(690\) −2.50000 0.230351i −0.0951734 0.00876931i
\(691\) 25.5227 44.2066i 0.970929 1.68170i 0.278168 0.960533i \(-0.410273\pi\)
0.692762 0.721167i \(-0.256394\pi\)
\(692\) 3.10102 0.117883
\(693\) 0 0
\(694\) 19.5959 0.743851
\(695\) 3.29796 5.71223i 0.125099 0.216677i
\(696\) 6.89898 9.75663i 0.261505 0.369824i
\(697\) −9.79796 16.9706i −0.371124 0.642806i
\(698\) −11.1010 −0.420180
\(699\) 7.00000 9.89949i 0.264764 0.374433i
\(700\) 0 0
\(701\) −7.39388 −0.279263 −0.139631 0.990204i \(-0.544592\pi\)
−0.139631 + 0.990204i \(0.544592\pi\)
\(702\) 6.24745 + 24.6773i 0.235795 + 0.931385i
\(703\) 15.0454 26.0594i 0.567448 0.982849i
\(704\) 2.00000 0.0753778
\(705\) −24.4949 2.25697i −0.922531 0.0850024i
\(706\) −3.00000 + 5.19615i −0.112906 + 0.195560i
\(707\) 0 0
\(708\) 3.44949 + 0.317837i 0.129640 + 0.0119451i
\(709\) −13.7980 + 23.8988i −0.518193 + 0.897537i 0.481583 + 0.876400i \(0.340062\pi\)
−0.999777 + 0.0211367i \(0.993271\pi\)
\(710\) −0.0732141 + 0.126811i −0.00274768 + 0.00475911i
\(711\) 1.89898 + 5.37113i 0.0712173 + 0.201433i
\(712\) −8.44949 14.6349i −0.316658 0.548468i
\(713\) −3.00000 5.19615i −0.112351 0.194597i
\(714\) 0 0
\(715\) 7.10102 12.2993i 0.265563 0.459969i
\(716\) 20.6969 0.773481
\(717\) 11.7247 + 1.08032i 0.437869 + 0.0403454i
\(718\) −8.79796 −0.328337
\(719\) 4.89898 + 8.48528i 0.182701 + 0.316448i 0.942799 0.333360i \(-0.108183\pi\)
−0.760098 + 0.649808i \(0.774849\pi\)
\(720\) −1.44949 4.09978i −0.0540193 0.152790i
\(721\) 0 0
\(722\) 6.24745 + 10.8209i 0.232506 + 0.402712i
\(723\) 0.651531 + 1.41421i 0.0242307 + 0.0525952i
\(724\) −5.17423 8.96204i −0.192299 0.333071i
\(725\) −10.0000 17.3205i −0.371391 0.643268i
\(726\) −12.0732 1.11243i −0.448079 0.0412862i
\(727\) −4.24745 7.35680i −0.157529 0.272848i 0.776448 0.630181i \(-0.217019\pi\)
−0.933977 + 0.357333i \(0.883686\pi\)
\(728\) 0 0
\(729\) 23.0000 + 14.1421i 0.851852 + 0.523783i
\(730\) −5.00000 8.66025i −0.185058 0.320530i
\(731\) −13.7980 −0.510336
\(732\) 4.74745 + 10.3048i 0.175471 + 0.380877i
\(733\) 17.4495 0.644512 0.322256 0.946653i \(-0.395559\pi\)
0.322256 + 0.946653i \(0.395559\pi\)
\(734\) −6.89898 + 11.9494i −0.254646 + 0.441060i
\(735\) 0 0
\(736\) 0.500000 + 0.866025i 0.0184302 + 0.0319221i
\(737\) 12.8990 + 22.3417i 0.475140 + 0.822967i
\(738\) −28.8990 5.37113i −1.06379 0.197714i
\(739\) −6.79796 + 11.7744i −0.250067 + 0.433129i −0.963544 0.267550i \(-0.913786\pi\)
0.713477 + 0.700679i \(0.247119\pi\)
\(740\) −8.55051 + 14.8099i −0.314323 + 0.544423i
\(741\) −9.05561 19.6561i −0.332666 0.722086i
\(742\) 0 0
\(743\) −18.0000 + 31.1769i −0.660356 + 1.14377i 0.320166 + 0.947361i \(0.396261\pi\)
−0.980522 + 0.196409i \(0.937072\pi\)
\(744\) 6.00000 8.48528i 0.219971 0.311086i
\(745\) −8.69694 −0.318631
\(746\) 3.44949 5.97469i 0.126295 0.218749i
\(747\) −5.89898 1.09638i −0.215832 0.0401143i
\(748\) −4.00000 −0.146254
\(749\) 0 0
\(750\) −19.7474 1.81954i −0.721075 0.0664401i
\(751\) 1.40408 0.0512357 0.0256178 0.999672i \(-0.491845\pi\)
0.0256178 + 0.999672i \(0.491845\pi\)
\(752\) 4.89898 + 8.48528i 0.178647 + 0.309426i
\(753\) 12.6464 + 27.4504i 0.460861 + 1.00035i
\(754\) −16.8990 + 29.2699i −0.615425 + 1.06595i
\(755\) −7.24745 −0.263762
\(756\) 0 0
\(757\) −35.3939 −1.28641 −0.643206 0.765693i \(-0.722396\pi\)
−0.643206 + 0.765693i \(0.722396\pi\)
\(758\) −11.2474 + 19.4812i −0.408526 + 0.707587i
\(759\) 1.44949 + 3.14626i 0.0526131 + 0.114202i
\(760\) 1.84847 + 3.20164i 0.0670510 + 0.116136i
\(761\) −2.00000 −0.0724999 −0.0362500 0.999343i \(-0.511541\pi\)
−0.0362500 + 0.999343i \(0.511541\pi\)
\(762\) −5.17423 0.476756i −0.187443 0.0172710i
\(763\) 0 0
\(764\) 4.10102 0.148370
\(765\) 2.89898 + 8.19955i 0.104813 + 0.296455i
\(766\) −1.44949 + 2.51059i −0.0523722 + 0.0907113i
\(767\) −9.79796 −0.353784
\(768\) −1.00000 + 1.41421i −0.0360844 + 0.0510310i
\(769\) −17.0454 + 29.5235i −0.614673 + 1.06465i 0.375769 + 0.926714i \(0.377379\pi\)
−0.990442 + 0.137932i \(0.955955\pi\)
\(770\) 0 0
\(771\) 5.94439 + 12.9029i 0.214082 + 0.464686i
\(772\) 8.94949 15.5010i 0.322099 0.557892i
\(773\) 16.9722 29.3967i 0.610447 1.05733i −0.380718 0.924691i \(-0.624323\pi\)
0.991165 0.132635i \(-0.0423437\pi\)
\(774\) −13.4495 + 15.7313i −0.483432 + 0.565451i
\(775\) −8.69694 15.0635i −0.312403 0.541098i
\(776\) 1.44949 + 2.51059i 0.0520336 + 0.0901249i
\(777\) 0 0
\(778\) 12.4495 21.5631i 0.446336 0.773076i
\(779\) 24.9898 0.895352
\(780\) 5.14643 + 11.1708i 0.184272 + 0.399980i
\(781\) 0.202041