Properties

Label 882.2.e.n.373.2
Level $882$
Weight $2$
Character 882.373
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.e (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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 126)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 373.2
Root \(1.22474 + 0.707107i\) of defining polynomial
Character \(\chi\) \(=\) 882.373
Dual form 882.2.e.n.655.2

$q$-expansion

\(f(q)\) \(=\) \(q+1.00000 q^{2} +(1.72474 + 0.158919i) q^{3} +1.00000 q^{4} +(-0.724745 - 1.25529i) q^{5} +(1.72474 + 0.158919i) q^{6} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})\) \(q+1.00000 q^{2} +(1.72474 + 0.158919i) q^{3} +1.00000 q^{4} +(-0.724745 - 1.25529i) q^{5} +(1.72474 + 0.158919i) q^{6} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +(-0.724745 - 1.25529i) q^{10} +(-1.00000 + 1.73205i) q^{11} +(1.72474 + 0.158919i) q^{12} +(2.44949 - 4.24264i) q^{13} +(-1.05051 - 2.28024i) q^{15} +1.00000 q^{16} +(1.00000 + 1.73205i) q^{17} +(2.94949 + 0.548188i) q^{18} +(1.27526 - 2.20881i) q^{19} +(-0.724745 - 1.25529i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(0.500000 + 0.866025i) q^{23} +(1.72474 + 0.158919i) q^{24} +(1.44949 - 2.51059i) q^{25} +(2.44949 - 4.24264i) q^{26} +(5.00000 + 1.41421i) q^{27} +(3.44949 + 5.97469i) q^{29} +(-1.05051 - 2.28024i) q^{30} -6.00000 q^{31} +1.00000 q^{32} +(-2.00000 + 2.82843i) q^{33} +(1.00000 + 1.73205i) q^{34} +(2.94949 + 0.548188i) q^{36} +(-5.89898 + 10.2173i) q^{37} +(1.27526 - 2.20881i) q^{38} +(4.89898 - 6.92820i) q^{39} +(-0.724745 - 1.25529i) q^{40} +(4.89898 - 8.48528i) q^{41} +(-3.44949 - 5.97469i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-1.44949 - 4.09978i) q^{45} +(0.500000 + 0.866025i) q^{46} -9.79796 q^{47} +(1.72474 + 0.158919i) q^{48} +(1.44949 - 2.51059i) q^{50} +(1.44949 + 3.14626i) q^{51} +(2.44949 - 4.24264i) q^{52} +(5.44949 + 9.43879i) q^{53} +(5.00000 + 1.41421i) q^{54} +2.89898 q^{55} +(2.55051 - 3.60697i) q^{57} +(3.44949 + 5.97469i) q^{58} +2.00000 q^{59} +(-1.05051 - 2.28024i) q^{60} -6.55051 q^{61} -6.00000 q^{62} +1.00000 q^{64} -7.10102 q^{65} +(-2.00000 + 2.82843i) q^{66} -12.8990 q^{67} +(1.00000 + 1.73205i) q^{68} +(0.724745 + 1.57313i) q^{69} +0.101021 q^{71} +(2.94949 + 0.548188i) q^{72} +(-3.44949 - 5.97469i) q^{73} +(-5.89898 + 10.2173i) q^{74} +(2.89898 - 4.09978i) q^{75} +(1.27526 - 2.20881i) q^{76} +(4.89898 - 6.92820i) q^{78} -1.89898 q^{79} +(-0.724745 - 1.25529i) q^{80} +(8.39898 + 3.23375i) q^{81} +(4.89898 - 8.48528i) q^{82} +(1.00000 + 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +(-3.44949 - 5.97469i) q^{86} +(5.00000 + 10.8530i) q^{87} +(-1.00000 + 1.73205i) q^{88} +(-8.44949 + 14.6349i) q^{89} +(-1.44949 - 4.09978i) q^{90} +(0.500000 + 0.866025i) q^{92} +(-10.3485 - 0.953512i) q^{93} -9.79796 q^{94} -3.69694 q^{95} +(1.72474 + 0.158919i) q^{96} +(1.44949 + 2.51059i) q^{97} +(-3.89898 + 4.56048i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9} + O(q^{10}) \) \( 4 q + 4 q^{2} + 2 q^{3} + 4 q^{4} + 2 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 14 q^{15} + 4 q^{16} + 4 q^{17} + 2 q^{18} + 10 q^{19} + 2 q^{20} - 4 q^{22} + 2 q^{23} + 2 q^{24} - 4 q^{25} + 20 q^{27} + 4 q^{29} - 14 q^{30} - 24 q^{31} + 4 q^{32} - 8 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} + 10 q^{38} + 2 q^{40} - 4 q^{43} - 4 q^{44} + 4 q^{45} + 2 q^{46} + 2 q^{48} - 4 q^{50} - 4 q^{51} + 12 q^{53} + 20 q^{54} - 8 q^{55} + 20 q^{57} + 4 q^{58} + 8 q^{59} - 14 q^{60} - 36 q^{61} - 24 q^{62} + 4 q^{64} - 48 q^{65} - 8 q^{66} - 32 q^{67} + 4 q^{68} - 2 q^{69} + 20 q^{71} + 2 q^{72} - 4 q^{73} - 4 q^{74} - 8 q^{75} + 10 q^{76} + 12 q^{79} + 2 q^{80} + 14 q^{81} + 4 q^{83} - 4 q^{85} - 4 q^{86} + 20 q^{87} - 4 q^{88} - 24 q^{89} + 4 q^{90} + 2 q^{92} - 12 q^{93} + 44 q^{95} + 2 q^{96} - 4 q^{97} + 4 q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 1.72474 + 0.158919i 0.995782 + 0.0917517i
\(4\) 1.00000 0.500000
\(5\) −0.724745 1.25529i −0.324116 0.561385i 0.657217 0.753701i \(-0.271733\pi\)
−0.981333 + 0.192316i \(0.938400\pi\)
\(6\) 1.72474 + 0.158919i 0.704124 + 0.0648783i
\(7\) 0 0
\(8\) 1.00000 0.353553
\(9\) 2.94949 + 0.548188i 0.983163 + 0.182729i
\(10\) −0.724745 1.25529i −0.229184 0.396959i
\(11\) −1.00000 + 1.73205i −0.301511 + 0.522233i −0.976478 0.215615i \(-0.930824\pi\)
0.674967 + 0.737848i \(0.264158\pi\)
\(12\) 1.72474 + 0.158919i 0.497891 + 0.0458759i
\(13\) 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
\(16\) 1.00000 0.250000
\(17\) 1.00000 + 1.73205i 0.242536 + 0.420084i 0.961436 0.275029i \(-0.0886875\pi\)
−0.718900 + 0.695113i \(0.755354\pi\)
\(18\) 2.94949 + 0.548188i 0.695201 + 0.129209i
\(19\) 1.27526 2.20881i 0.292564 0.506735i −0.681852 0.731491i \(-0.738825\pi\)
0.974415 + 0.224756i \(0.0721584\pi\)
\(20\) −0.724745 1.25529i −0.162058 0.280692i
\(21\) 0 0
\(22\) −1.00000 + 1.73205i −0.213201 + 0.369274i
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 1.72474 + 0.158919i 0.352062 + 0.0324391i
\(25\) 1.44949 2.51059i 0.289898 0.502118i
\(26\) 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 \(0.612038\pi\)
\(30\) −1.05051 2.28024i −0.191796 0.416313i
\(31\) −6.00000 −1.07763 −0.538816 0.842424i \(-0.681128\pi\)
−0.538816 + 0.842424i \(0.681128\pi\)
\(32\) 1.00000 0.176777
\(33\) −2.00000 + 2.82843i −0.348155 + 0.492366i
\(34\) 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 −0.273621 + 0.961838i \(0.588221\pi\)
−0.696165 + 0.717881i \(0.745112\pi\)
\(38\) 1.27526 2.20881i 0.206874 0.358316i
\(39\) 4.89898 6.92820i 0.784465 1.10940i
\(40\) −0.724745 1.25529i −0.114592 0.198480i
\(41\) 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
\(45\) −1.44949 4.09978i −0.216077 0.611159i
\(46\) 0.500000 + 0.866025i 0.0737210 + 0.127688i
\(47\) −9.79796 −1.42918 −0.714590 0.699544i \(-0.753387\pi\)
−0.714590 + 0.699544i \(0.753387\pi\)
\(48\) 1.72474 + 0.158919i 0.248945 + 0.0229379i
\(49\) 0 0
\(50\) 1.44949 2.51059i 0.204989 0.355051i
\(51\) 1.44949 + 3.14626i 0.202969 + 0.440565i
\(52\) 2.44949 4.24264i 0.339683 0.588348i
\(53\) 5.44949 + 9.43879i 0.748545 + 1.29652i 0.948520 + 0.316717i \(0.102581\pi\)
−0.199975 + 0.979801i \(0.564086\pi\)
\(54\) 5.00000 + 1.41421i 0.680414 + 0.192450i
\(55\) 2.89898 0.390898
\(56\) 0 0
\(57\) 2.55051 3.60697i 0.337823 0.477754i
\(58\) 3.44949 + 5.97469i 0.452940 + 0.784515i
\(59\) 2.00000 0.260378 0.130189 0.991489i \(-0.458442\pi\)
0.130189 + 0.991489i \(0.458442\pi\)
\(60\) −1.05051 2.28024i −0.135620 0.294378i
\(61\) −6.55051 −0.838707 −0.419353 0.907823i \(-0.637743\pi\)
−0.419353 + 0.907823i \(0.637743\pi\)
\(62\) −6.00000 −0.762001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −7.10102 −0.880773
\(66\) −2.00000 + 2.82843i −0.246183 + 0.348155i
\(67\) −12.8990 −1.57586 −0.787931 0.615764i \(-0.788847\pi\)
−0.787931 + 0.615764i \(0.788847\pi\)
\(68\) 1.00000 + 1.73205i 0.121268 + 0.210042i
\(69\) 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 \(0.498092\pi\)
\(72\) 2.94949 + 0.548188i 0.347601 + 0.0646046i
\(73\) −3.44949 5.97469i −0.403732 0.699285i 0.590441 0.807081i \(-0.298954\pi\)
−0.994173 + 0.107796i \(0.965621\pi\)
\(74\) −5.89898 + 10.2173i −0.685742 + 1.18774i
\(75\) 2.89898 4.09978i 0.334745 0.473401i
\(76\) 1.27526 2.20881i 0.146282 0.253368i
\(77\) 0 0
\(78\) 4.89898 6.92820i 0.554700 0.784465i
\(79\) −1.89898 −0.213652 −0.106826 0.994278i \(-0.534069\pi\)
−0.106826 + 0.994278i \(0.534069\pi\)
\(80\) −0.724745 1.25529i −0.0810289 0.140346i
\(81\) 8.39898 + 3.23375i 0.933220 + 0.359306i
\(82\) 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
\(86\) −3.44949 5.97469i −0.371968 0.644268i
\(87\) 5.00000 + 10.8530i 0.536056 + 1.16356i
\(88\) −1.00000 + 1.73205i −0.106600 + 0.184637i
\(89\) −8.44949 + 14.6349i −0.895644 + 1.55130i −0.0626387 + 0.998036i \(0.519952\pi\)
−0.833005 + 0.553265i \(0.813382\pi\)
\(90\) −1.44949 4.09978i −0.152790 0.432154i
\(91\) 0 0
\(92\) 0.500000 + 0.866025i 0.0521286 + 0.0902894i
\(93\) −10.3485 0.953512i −1.07309 0.0988746i
\(94\) −9.79796 −1.01058
\(95\) −3.69694 −0.379298
\(96\) 1.72474 + 0.158919i 0.176031 + 0.0162196i
\(97\) 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
\(101\) −8.62372 + 14.9367i −0.858093 + 1.48626i 0.0156533 + 0.999877i \(0.495017\pi\)
−0.873746 + 0.486383i \(0.838316\pi\)
\(102\) 1.44949 + 3.14626i 0.143521 + 0.311527i
\(103\) 7.00000 + 12.1244i 0.689730 + 1.19465i 0.971925 + 0.235291i \(0.0756043\pi\)
−0.282194 + 0.959357i \(0.591062\pi\)
\(104\) 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 −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 5.00000 + 1.41421i 0.481125 + 0.136083i
\(109\) −6.34847 10.9959i −0.608073 1.05321i −0.991558 0.129666i \(-0.958609\pi\)
0.383485 0.923547i \(-0.374724\pi\)
\(110\) 2.89898 0.276407
\(111\) −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 \(0.0740194\pi\)
\(114\) 2.55051 3.60697i 0.238877 0.337823i
\(115\) 0.724745 1.25529i 0.0675828 0.117057i
\(116\) 3.44949 + 5.97469i 0.320277 + 0.554736i
\(117\) 9.55051 11.1708i 0.882945 1.03274i
\(118\) 2.00000 0.184115
\(119\) 0 0
\(120\) −1.05051 2.28024i −0.0958980 0.208156i
\(121\) 3.50000 + 6.06218i 0.318182 + 0.551107i
\(122\) −6.55051 −0.593055
\(123\) 9.79796 13.8564i 0.883452 1.24939i
\(124\) −6.00000 −0.538816
\(125\) −11.4495 −1.02407
\(126\) 0 0
\(127\) −3.00000 −0.266207 −0.133103 0.991102i \(-0.542494\pi\)
−0.133103 + 0.991102i \(0.542494\pi\)
\(128\) 1.00000 0.0883883
\(129\) −5.00000 10.8530i −0.440225 0.955554i
\(130\) −7.10102 −0.622801
\(131\) −4.27526 7.40496i −0.373531 0.646974i 0.616575 0.787296i \(-0.288520\pi\)
−0.990106 + 0.140322i \(0.955186\pi\)
\(132\) −2.00000 + 2.82843i −0.174078 + 0.246183i
\(133\) 0 0
\(134\) −12.8990 −1.11430
\(135\) −1.84847 7.30142i −0.159091 0.628406i
\(136\) 1.00000 + 1.73205i 0.0857493 + 0.148522i
\(137\) −3.89898 + 6.75323i −0.333112 + 0.576967i −0.983120 0.182960i \(-0.941432\pi\)
0.650008 + 0.759927i \(0.274765\pi\)
\(138\) 0.724745 + 1.57313i 0.0616944 + 0.133914i
\(139\) 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
\(142\) 0.101021 0.00847745
\(143\) 4.89898 + 8.48528i 0.409673 + 0.709575i
\(144\) 2.94949 + 0.548188i 0.245791 + 0.0456823i
\(145\) 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
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 2.89898 4.09978i 0.236701 0.334745i
\(151\) 2.50000 4.33013i 0.203447 0.352381i −0.746190 0.665733i \(-0.768119\pi\)
0.949637 + 0.313353i \(0.101452\pi\)
\(152\) 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
\(156\) 4.89898 6.92820i 0.392232 0.554700i
\(157\) 8.34847 0.666280 0.333140 0.942877i \(-0.391892\pi\)
0.333140 + 0.942877i \(0.391892\pi\)
\(158\) −1.89898 −0.151075
\(159\) 7.89898 + 17.1455i 0.626430 + 1.35973i
\(160\) −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 −0.159251 0.987238i \(-0.550908\pi\)
0.934599 0.355704i \(-0.115759\pi\)
\(164\) 4.89898 8.48528i 0.382546 0.662589i
\(165\) 5.00000 + 0.460702i 0.389249 + 0.0358656i
\(166\) 1.00000 + 1.73205i 0.0776151 + 0.134433i
\(167\) −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
\(171\) 4.97219 5.81577i 0.380233 0.444743i
\(172\) −3.44949 5.97469i −0.263021 0.455566i
\(173\) 3.10102 0.235766 0.117883 0.993027i \(-0.462389\pi\)
0.117883 + 0.993027i \(0.462389\pi\)
\(174\) 5.00000 + 10.8530i 0.379049 + 0.822764i
\(175\) 0 0
\(176\) −1.00000 + 1.73205i −0.0753778 + 0.130558i
\(177\) 3.44949 + 0.317837i 0.259280 + 0.0238901i
\(178\) −8.44949 + 14.6349i −0.633316 + 1.09694i
\(179\) −10.3485 17.9241i −0.773481 1.33971i −0.935644 0.352944i \(-0.885181\pi\)
0.162163 0.986764i \(-0.448153\pi\)
\(180\) −1.44949 4.09978i −0.108039 0.305579i
\(181\) 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
\(184\) 0.500000 + 0.866025i 0.0368605 + 0.0638442i
\(185\) 17.1010 1.25729
\(186\) −10.3485 0.953512i −0.758787 0.0699149i
\(187\) −4.00000 −0.292509
\(188\) −9.79796 −0.714590
\(189\) 0 0
\(190\) −3.69694 −0.268204
\(191\) 4.10102 0.296739 0.148370 0.988932i \(-0.452597\pi\)
0.148370 + 0.988932i \(0.452597\pi\)
\(192\) 1.72474 + 0.158919i 0.124473 + 0.0114690i
\(193\) −17.8990 −1.28840 −0.644198 0.764858i \(-0.722809\pi\)
−0.644198 + 0.764858i \(0.722809\pi\)
\(194\) 1.44949 + 2.51059i 0.104067 + 0.180250i
\(195\) −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 \(0.297230\pi\)
\(198\) −3.89898 + 4.56048i −0.277088 + 0.324099i
\(199\) −1.44949 2.51059i −0.102752 0.177971i 0.810066 0.586339i \(-0.199431\pi\)
−0.912817 + 0.408368i \(0.866098\pi\)
\(200\) 1.44949 2.51059i 0.102494 0.177526i
\(201\) −22.2474 2.04989i −1.56921 0.144588i
\(202\) −8.62372 + 14.9367i −0.606763 + 1.05094i
\(203\) 0 0
\(204\) 1.44949 + 3.14626i 0.101485 + 0.220283i
\(205\) −14.2020 −0.991914
\(206\) 7.00000 + 12.1244i 0.487713 + 0.844744i
\(207\) 1.00000 + 2.82843i 0.0695048 + 0.196589i
\(208\) 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 \(0.313108\pi\)
\(212\) 5.44949 + 9.43879i 0.374272 + 0.648259i
\(213\) 0.174235 + 0.0160540i 0.0119384 + 0.00110000i
\(214\) 6.00000 10.3923i 0.410152 0.710403i
\(215\) −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
\(219\) −5.00000 10.8530i −0.337869 0.733378i
\(220\) 2.89898 0.195449
\(221\) 9.79796 0.659082
\(222\) −11.7980 + 16.6848i −0.791827 + 1.11981i
\(223\) −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
\(227\) −2.72474 + 4.71940i −0.180848 + 0.313237i −0.942169 0.335137i \(-0.891217\pi\)
0.761322 + 0.648374i \(0.224551\pi\)
\(228\) 2.55051 3.60697i 0.168912 0.238877i
\(229\) 0.623724 + 1.08032i 0.0412169 + 0.0713897i 0.885898 0.463880i \(-0.153543\pi\)
−0.844681 + 0.535270i \(0.820210\pi\)
\(230\) 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 −0.728306 0.685252i \(-0.759692\pi\)
0.957599 + 0.288106i \(0.0930254\pi\)
\(234\) 9.55051 11.1708i 0.624336 0.730261i
\(235\) 7.10102 + 12.2993i 0.463220 + 0.802320i
\(236\) 2.00000 0.130189
\(237\) −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 \(0.237227\pi\)
\(240\) −1.05051 2.28024i −0.0678101 0.147189i
\(241\) 0.449490 0.778539i 0.0289542 0.0501501i −0.851185 0.524865i \(-0.824116\pi\)
0.880139 + 0.474715i \(0.157449\pi\)
\(242\) 3.50000 + 6.06218i 0.224989 + 0.389692i
\(243\) 13.9722 + 6.91215i 0.896317 + 0.443415i
\(244\) −6.55051 −0.419353
\(245\) 0 0
\(246\) 9.79796 13.8564i 0.624695 0.883452i
\(247\) −6.24745 10.8209i −0.397516 0.688517i
\(248\) −6.00000 −0.381000
\(249\) 1.44949 + 3.14626i 0.0918577 + 0.199386i
\(250\) −11.4495 −0.724129
\(251\) −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
\(254\) −3.00000 −0.188237
\(255\) 2.89898 4.09978i 0.181541 0.256738i
\(256\) 1.00000 0.0625000
\(257\) 4.10102 + 7.10318i 0.255815 + 0.443084i 0.965116 0.261821i \(-0.0843230\pi\)
−0.709302 + 0.704905i \(0.750990\pi\)
\(258\) −5.00000 10.8530i −0.311286 0.675679i
\(259\) 0 0
\(260\) −7.10102 −0.440387
\(261\) 6.89898 + 19.5133i 0.427036 + 1.20784i
\(262\) −4.27526 7.40496i −0.264126 0.457480i
\(263\) −12.9495 + 22.4292i −0.798500 + 1.38304i 0.122093 + 0.992519i \(0.461039\pi\)
−0.920593 + 0.390523i \(0.872294\pi\)
\(264\) −2.00000 + 2.82843i −0.123091 + 0.174078i
\(265\) 7.89898 13.6814i 0.485230 0.840444i
\(266\) 0 0
\(267\) −16.8990 + 23.8988i −1.03420 + 1.46258i
\(268\) −12.8990 −0.787931
\(269\) −9.17423 15.8902i −0.559363 0.968845i −0.997550 0.0699611i \(-0.977712\pi\)
0.438187 0.898884i \(-0.355621\pi\)
\(270\) −1.84847 7.30142i −0.112494 0.444350i
\(271\) 3.55051 6.14966i 0.215678 0.373565i −0.737804 0.675015i \(-0.764137\pi\)
0.953482 + 0.301450i \(0.0974705\pi\)
\(272\) 1.00000 + 1.73205i 0.0606339 + 0.105021i
\(273\) 0 0
\(274\) −3.89898 + 6.75323i −0.235546 + 0.407978i
\(275\) 2.89898 + 5.02118i 0.174815 + 0.302789i
\(276\) 0.724745 + 1.57313i 0.0436245 + 0.0946914i
\(277\) 9.34847 16.1920i 0.561695 0.972884i −0.435654 0.900114i \(-0.643483\pi\)
0.997349 0.0727700i \(-0.0231839\pi\)
\(278\) 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 \(0.641545\pi\)
\(282\) −16.8990 1.55708i −1.00632 0.0927227i
\(283\) 25.4495 1.51282 0.756408 0.654101i \(-0.226953\pi\)
0.756408 + 0.654101i \(0.226953\pi\)
\(284\) 0.101021 0.00599446
\(285\) −6.37628 0.587512i −0.377698 0.0348012i
\(286\) 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
\(290\) 5.00000 8.66025i 0.293610 0.508548i
\(291\) 2.10102 + 4.56048i 0.123164 + 0.267340i
\(292\) −3.44949 5.97469i −0.201866 0.349642i
\(293\) 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
\(297\) −7.44949 + 7.24604i −0.432263 + 0.420458i
\(298\) 3.00000 + 5.19615i 0.173785 + 0.301005i
\(299\) 4.89898 0.283315
\(300\) 2.89898 4.09978i 0.167373 0.236701i
\(301\) 0 0
\(302\) 2.50000 4.33013i 0.143859 0.249171i
\(303\) −17.2474 + 24.3916i −0.990840 + 1.40126i
\(304\) 1.27526 2.20881i 0.0731409 0.126684i
\(305\) 4.74745 + 8.22282i 0.271838 + 0.470837i
\(306\) 2.00000 + 5.65685i 0.114332 + 0.323381i
\(307\) −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
\(310\) 4.34847 + 7.53177i 0.246976 + 0.427776i
\(311\) −30.6969 −1.74066 −0.870332 0.492466i \(-0.836096\pi\)
−0.870332 + 0.492466i \(0.836096\pi\)
\(312\) 4.89898 6.92820i 0.277350 0.392232i
\(313\) 4.69694 0.265487 0.132743 0.991150i \(-0.457621\pi\)
0.132743 + 0.991150i \(0.457621\pi\)
\(314\) 8.34847 0.471131
\(315\) 0 0
\(316\) −1.89898 −0.106826
\(317\) 20.6969 1.16246 0.581228 0.813741i \(-0.302572\pi\)
0.581228 + 0.813741i \(0.302572\pi\)
\(318\) 7.89898 + 17.1455i 0.442953 + 0.961474i
\(319\) −13.7980 −0.772537
\(320\) −0.724745 1.25529i −0.0405145 0.0701731i
\(321\) 12.0000 16.9706i 0.669775 0.947204i
\(322\) 0 0
\(323\) 5.10102 0.283828
\(324\) 8.39898 + 3.23375i 0.466610 + 0.179653i
\(325\) −7.10102 12.2993i −0.393894 0.682244i
\(326\) 9.89898 17.1455i 0.548254 0.949603i
\(327\) −9.20204 19.9740i −0.508874 1.10456i
\(328\) 4.89898 8.48528i 0.270501 0.468521i
\(329\) 0 0
\(330\) 5.00000 + 0.460702i 0.275241 + 0.0253608i
\(331\) 4.69694 0.258167 0.129084 0.991634i \(-0.458796\pi\)
0.129084 + 0.991634i \(0.458796\pi\)
\(332\) 1.00000 + 1.73205i 0.0548821 + 0.0950586i
\(333\) −23.0000 + 26.9022i −1.26039 + 1.47423i
\(334\) −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 \(-0.0532296\pi\)
\(338\) −5.50000 9.52628i −0.299161 0.518161i
\(339\) 6.10102 8.62815i 0.331362 0.468617i
\(340\) 1.44949 2.51059i 0.0786096 0.136156i
\(341\) 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
\(345\) 1.44949 2.04989i 0.0780379 0.110362i
\(346\) 3.10102 0.166712
\(347\) 19.5959 1.05196 0.525982 0.850496i \(-0.323698\pi\)
0.525982 + 0.850496i \(0.323698\pi\)
\(348\) 5.00000 + 10.8530i 0.268028 + 0.581782i
\(349\) 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
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 3.44949 + 0.317837i 0.183338 + 0.0168929i
\(355\) −0.0732141 0.126811i −0.00388580 0.00673040i
\(356\) −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 −0.726277 0.687402i \(-0.758751\pi\)
0.958446 + 0.285273i \(0.0920843\pi\)
\(360\) −1.44949 4.09978i −0.0763948 0.216077i
\(361\) 6.24745 + 10.8209i 0.328813 + 0.569521i
\(362\) 10.3485 0.543903
\(363\) 5.07321 + 11.0119i 0.266275 + 0.577976i
\(364\) 0 0
\(365\) −5.00000 + 8.66025i −0.261712 + 0.453298i
\(366\) −11.2980 1.04100i −0.590554 0.0544138i
\(367\) −6.89898 + 11.9494i −0.360124 + 0.623753i −0.987981 0.154576i \(-0.950599\pi\)
0.627857 + 0.778329i \(0.283932\pi\)
\(368\) 0.500000 + 0.866025i 0.0260643 + 0.0451447i
\(369\) 19.1010 22.3417i 0.994359 1.16306i
\(370\) 17.1010 0.889040
\(371\) 0 0
\(372\) −10.3485 0.953512i −0.536543 0.0494373i
\(373\) 3.44949 + 5.97469i 0.178608 + 0.309358i 0.941404 0.337281i \(-0.109507\pi\)
−0.762796 + 0.646639i \(0.776174\pi\)
\(374\) −4.00000 −0.206835
\(375\) −19.7474 1.81954i −1.01975 0.0939605i
\(376\) −9.79796 −0.505291
\(377\) 33.7980 1.74068
\(378\) 0 0
\(379\) 22.4949 1.15549 0.577743 0.816219i \(-0.303934\pi\)
0.577743 + 0.816219i \(0.303934\pi\)
\(380\) −3.69694 −0.189649
\(381\) −5.17423 0.476756i −0.265084 0.0244249i
\(382\) 4.10102 0.209826
\(383\) −1.44949 2.51059i −0.0740655 0.128285i 0.826614 0.562769i \(-0.190264\pi\)
−0.900679 + 0.434484i \(0.856931\pi\)
\(384\) 1.72474 + 0.158919i 0.0880155 + 0.00810978i
\(385\) 0 0
\(386\) −17.8990 −0.911034
\(387\) −6.89898 19.5133i −0.350695 0.991915i
\(388\) 1.44949 + 2.51059i 0.0735867 + 0.127456i
\(389\) 12.4495 21.5631i 0.631214 1.09330i −0.356090 0.934452i \(-0.615890\pi\)
0.987304 0.158843i \(-0.0507764\pi\)
\(390\) −12.2474 1.12848i −0.620174 0.0571430i
\(391\) −1.00000 + 1.73205i −0.0505722 + 0.0875936i
\(392\) 0 0
\(393\) −6.19694 13.4511i −0.312594 0.678517i
\(394\) 16.6969 0.841180
\(395\) 1.37628 + 2.38378i 0.0692479 + 0.119941i
\(396\) −3.89898 + 4.56048i −0.195931 + 0.229173i
\(397\) 19.3485 33.5125i 0.971072 1.68195i 0.278740 0.960367i \(-0.410083\pi\)
0.692332 0.721579i \(-0.256583\pi\)
\(398\) −1.44949 2.51059i −0.0726564 0.125844i
\(399\) 0 0
\(400\) 1.44949 2.51059i 0.0724745 0.125529i
\(401\) 9.94949 + 17.2330i 0.496854 + 0.860576i 0.999993 0.00362911i \(-0.00115518\pi\)
−0.503140 + 0.864205i \(0.667822\pi\)
\(402\) −22.2474 2.04989i −1.10960 0.102239i
\(403\) −14.6969 + 25.4558i −0.732107 + 1.26805i
\(404\) −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
\(408\) 1.44949 + 3.14626i 0.0717604 + 0.155763i
\(409\) 13.7980 0.682265 0.341133 0.940015i \(-0.389189\pi\)
0.341133 + 0.940015i \(0.389189\pi\)
\(410\) −14.2020 −0.701389
\(411\) −7.79796 + 11.0280i −0.384645 + 0.543970i
\(412\) 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
\(416\) 2.44949 4.24264i 0.120096 0.208013i
\(417\) 4.55051 6.43539i 0.222839 0.315143i
\(418\) 2.55051 + 4.41761i 0.124750 + 0.216073i
\(419\) 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
\(423\) −28.8990 5.37113i −1.40512 0.261153i
\(424\) 5.44949 + 9.43879i 0.264651 + 0.458388i
\(425\) 5.79796 0.281242
\(426\) 0.174235 + 0.0160540i 0.00844169 + 0.000777821i
\(427\) 0 0
\(428\) 6.00000 10.3923i 0.290021 0.502331i
\(429\) 7.10102 + 15.4135i 0.342841 + 0.744170i
\(430\) −5.00000 + 8.66025i −0.241121 + 0.417635i
\(431\) −15.7980 27.3629i −0.760961 1.31802i −0.942356 0.334613i \(-0.891395\pi\)
0.181395 0.983410i \(-0.441939\pi\)
\(432\) 5.00000 + 1.41421i 0.240563 + 0.0680414i
\(433\) 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
\(436\) −6.34847 10.9959i −0.304037 0.526607i
\(437\) 2.55051 0.122007
\(438\) −5.00000 10.8530i −0.238909 0.518577i
\(439\) −2.20204 −0.105098 −0.0525488 0.998618i \(-0.516735\pi\)
−0.0525488 + 0.998618i \(0.516735\pi\)
\(440\) 2.89898 0.138203
\(441\) 0 0
\(442\) 9.79796 0.466041
\(443\) −14.8990 −0.707872 −0.353936 0.935270i \(-0.615157\pi\)
−0.353936 + 0.935270i \(0.615157\pi\)
\(444\) −11.7980 + 16.6848i −0.559906 + 0.791827i
\(445\) 24.4949 1.16117
\(446\) −5.55051 9.61377i −0.262824 0.455225i
\(447\) 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 \(0.338459\pi\)
\(450\) 5.65153 6.61037i 0.266416 0.311616i
\(451\) 9.79796 + 16.9706i 0.461368 + 0.799113i
\(452\) 3.05051 5.28364i 0.143484 0.248521i
\(453\) 5.00000 7.07107i 0.234920 0.332228i
\(454\) −2.72474 + 4.71940i −0.127879 + 0.221492i
\(455\) 0 0
\(456\) 2.55051 3.60697i 0.119439 0.168912i
\(457\) −17.4949 −0.818377 −0.409188 0.912450i \(-0.634188\pi\)
−0.409188 + 0.912450i \(0.634188\pi\)
\(458\) 0.623724 + 1.08032i 0.0291447 + 0.0504801i
\(459\) 2.55051 + 10.0745i 0.119048 + 0.470236i
\(460\) 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 \(0.194045\pi\)
\(464\) 3.44949 + 5.97469i 0.160139 + 0.277368i
\(465\) 6.30306 + 13.6814i 0.292297 + 0.634461i
\(466\) 3.50000 6.06218i 0.162134 0.280825i
\(467\) 5.00000 8.66025i 0.231372 0.400749i −0.726840 0.686807i \(-0.759012\pi\)
0.958212 + 0.286058i \(0.0923451\pi\)
\(468\) 9.55051 11.1708i 0.441472 0.516372i
\(469\) 0 0
\(470\) 7.10102 + 12.2993i 0.327546 + 0.567326i
\(471\) 14.3990 + 1.32673i 0.663470 + 0.0611324i
\(472\) 2.00000 0.0920575
\(473\) 13.7980 0.634431
\(474\) −3.27526 0.301783i −0.150437 0.0138614i
\(475\) −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
\(479\) 4.79796 8.31031i 0.219224 0.379708i −0.735347 0.677691i \(-0.762981\pi\)
0.954571 + 0.297983i \(0.0963140\pi\)
\(480\) −1.05051 2.28024i −0.0479490 0.104078i
\(481\) 28.8990 + 50.0545i 1.31768 + 2.28229i
\(482\) 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
\(486\) 13.9722 + 6.91215i 0.633792 + 0.313541i
\(487\) 18.1969 + 31.5180i 0.824582 + 1.42822i 0.902238 + 0.431238i \(0.141923\pi\)
−0.0776564 + 0.996980i \(0.524744\pi\)
\(488\) −6.55051 −0.296528
\(489\) 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 \(0.282688\pi\)
\(492\) 9.79796 13.8564i 0.441726 0.624695i
\(493\) −6.89898 + 11.9494i −0.310714 + 0.538173i
\(494\) −6.24745 10.8209i −0.281086 0.486855i
\(495\) 8.55051 + 1.58919i 0.384317 + 0.0714286i
\(496\) −6.00000 −0.269408
\(497\) 0 0
\(498\) 1.44949 + 3.14626i 0.0649532 + 0.140987i
\(499\) 12.6969 + 21.9917i 0.568393 + 0.984486i 0.996725 + 0.0808642i \(0.0257680\pi\)
−0.428332 + 0.903621i \(0.640899\pi\)
\(500\) −11.4495 −0.512037
\(501\) −10.6969 + 15.1278i −0.477904 + 0.675858i
\(502\) −17.4495 −0.778809
\(503\) 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
\(506\) −2.00000 −0.0889108
\(507\) −7.97219 17.3045i −0.354058 0.768518i
\(508\) −3.00000 −0.133103
\(509\) −3.55051 6.14966i −0.157374 0.272579i 0.776547 0.630059i \(-0.216969\pi\)
−0.933921 + 0.357480i \(0.883636\pi\)
\(510\) 2.89898 4.09978i 0.128369 0.181541i
\(511\) 0 0
\(512\) 1.00000 0.0441942
\(513\) 9.50000 9.24055i 0.419435 0.407980i
\(514\) 4.10102 + 7.10318i 0.180888 + 0.313308i
\(515\) 10.1464 17.5741i 0.447105 0.774409i
\(516\) −5.00000 10.8530i −0.220113 0.477777i
\(517\) 9.79796 16.9706i 0.430914 0.746364i
\(518\) 0 0
\(519\) 5.34847 + 0.492810i 0.234772 + 0.0216320i
\(520\) −7.10102 −0.311400
\(521\) −4.65153 8.05669i −0.203787 0.352970i 0.745958 0.665993i \(-0.231992\pi\)
−0.949746 + 0.313023i \(0.898658\pi\)
\(522\) 6.89898 + 19.5133i 0.301960 + 0.854072i
\(523\) −7.17423 + 12.4261i −0.313707 + 0.543357i −0.979162 0.203081i \(-0.934904\pi\)
0.665455 + 0.746438i \(0.268238\pi\)
\(524\) −4.27526 7.40496i −0.186765 0.323487i
\(525\) 0 0
\(526\) −12.9495 + 22.4292i −0.564625 + 0.977958i
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) −2.00000 + 2.82843i −0.0870388 + 0.123091i
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) 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
\(534\) −16.8990 + 23.8988i −0.731290 + 1.03420i
\(535\) −17.3939 −0.752003
\(536\) −12.8990 −0.557151
\(537\) −15.0000 32.5590i −0.647298 1.40503i
\(538\) −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 −0.595848 0.803097i \(-0.703184\pi\)
0.993427 + 0.114471i \(0.0365172\pi\)
\(542\) 3.55051 6.14966i 0.152507 0.264151i
\(543\) 17.8485 + 1.64456i 0.765951 + 0.0705750i
\(544\) 1.00000 + 1.73205i 0.0428746 + 0.0742611i
\(545\) −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
\(549\) −19.3207 3.59091i −0.824586 0.153256i
\(550\) 2.89898 + 5.02118i 0.123613 + 0.214104i
\(551\) 17.5959 0.749611
\(552\) 0.724745 + 1.57313i 0.0308472 + 0.0669570i
\(553\) 0 0
\(554\) 9.34847 16.1920i 0.397178 0.687933i
\(555\) 29.4949 + 2.71767i 1.25199 + 0.115359i
\(556\) 2.27526 3.94086i 0.0964923 0.167130i
\(557\) 6.44949 + 11.1708i 0.273274 + 0.473324i 0.969698 0.244306i \(-0.0785602\pi\)
−0.696424 + 0.717630i \(0.745227\pi\)
\(558\) −17.6969 3.28913i −0.749171 0.139240i
\(559\) −33.7980 −1.42950
\(560\) 0 0
\(561\) −6.89898 0.635674i −0.291275 0.0268382i
\(562\) 9.50000 + 16.4545i 0.400733 + 0.694090i
\(563\) 39.9444 1.68346 0.841728 0.539902i \(-0.181539\pi\)
0.841728 + 0.539902i \(0.181539\pi\)
\(564\) −16.8990 1.55708i −0.711575 0.0655648i
\(565\) −8.84337 −0.372043
\(566\) 25.4495 1.06972
\(567\) 0 0
\(568\) 0.101021 0.00423873
\(569\) −30.0000 −1.25767 −0.628833 0.777541i \(-0.716467\pi\)
−0.628833 + 0.777541i \(0.716467\pi\)
\(570\) −6.37628 0.587512i −0.267073 0.0246082i
\(571\) 33.7980 1.41440 0.707200 0.707013i \(-0.249958\pi\)
0.707200 + 0.707013i \(0.249958\pi\)
\(572\) 4.89898 + 8.48528i 0.204837 + 0.354787i
\(573\) 7.07321 + 0.651729i 0.295488 + 0.0272263i
\(574\) 0 0
\(575\) 2.89898 0.120896
\(576\) 2.94949 + 0.548188i 0.122895 + 0.0228412i
\(577\) −7.79796 13.5065i −0.324633 0.562281i 0.656805 0.754061i \(-0.271908\pi\)
−0.981438 + 0.191779i \(0.938574\pi\)
\(578\) 6.50000 11.2583i 0.270364 0.468285i
\(579\) −30.8712 2.84448i −1.28296 0.118213i
\(580\) 5.00000 8.66025i 0.207614 0.359597i
\(581\) 0 0
\(582\) 2.10102 + 4.56048i 0.0870901 + 0.189038i
\(583\) −21.7980 −0.902779
\(584\) −3.44949 5.97469i −0.142741 0.247234i
\(585\) −20.9444 3.89270i −0.865944 0.160943i
\(586\) 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
\(590\) −1.44949 2.51059i −0.0596745 0.103359i
\(591\) 28.7980 + 2.65345i 1.18459 + 0.109149i
\(592\) −5.89898 + 10.2173i −0.242447 + 0.419930i
\(593\) 7.34847 12.7279i 0.301765 0.522673i −0.674770 0.738028i \(-0.735757\pi\)
0.976536 + 0.215355i \(0.0690907\pi\)
\(594\) −7.44949 + 7.24604i −0.305656 + 0.297309i
\(595\) 0 0
\(596\) 3.00000 + 5.19615i 0.122885 + 0.212843i
\(597\) −2.10102 4.56048i −0.0859890 0.186648i
\(598\) 4.89898 0.200334
\(599\) −33.7980 −1.38095 −0.690474 0.723358i \(-0.742598\pi\)
−0.690474 + 0.723358i \(0.742598\pi\)
\(600\) 2.89898 4.09978i 0.118350 0.167373i
\(601\) 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
\(605\) 5.07321 8.78706i 0.206255 0.357245i
\(606\) −17.2474 + 24.3916i −0.700630 + 0.990840i
\(607\) 10.3485 + 17.9241i 0.420031 + 0.727516i 0.995942 0.0899969i \(-0.0286857\pi\)
−0.575911 + 0.817513i \(0.695352\pi\)
\(608\) 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
\(612\) 2.00000 + 5.65685i 0.0808452 + 0.228665i
\(613\) 7.34847 + 12.7279i 0.296802 + 0.514076i 0.975402 0.220432i \(-0.0707466\pi\)
−0.678601 + 0.734508i \(0.737413\pi\)
\(614\) −25.2474 −1.01890
\(615\) −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 \(0.0663821\pi\)
\(618\) 10.1464 + 22.0239i 0.408149 + 0.885929i
\(619\) 15.0732 26.1076i 0.605844 1.04935i −0.386074 0.922468i \(-0.626169\pi\)
0.991918 0.126884i \(-0.0404976\pi\)
\(620\) 4.34847 + 7.53177i 0.174639 + 0.302483i
\(621\) 1.27526 + 5.03723i 0.0511742 + 0.202137i
\(622\) −30.6969 −1.23084
\(623\) 0 0
\(624\) 4.89898 6.92820i 0.196116 0.277350i
\(625\) 1.05051 + 1.81954i 0.0420204 + 0.0727815i
\(626\) 4.69694 0.187727
\(627\) 3.69694 + 8.02458i 0.147642 + 0.320471i
\(628\) 8.34847 0.333140
\(629\) −23.5959 −0.940831
\(630\) 0 0
\(631\) 27.8990 1.11064 0.555320 0.831636i \(-0.312596\pi\)
0.555320 + 0.831636i \(0.312596\pi\)
\(632\) −1.89898 −0.0755373
\(633\) −12.8990 + 18.2419i −0.512688 + 0.725051i
\(634\) 20.6969 0.821980
\(635\) 2.17423 + 3.76588i 0.0862819 + 0.149445i
\(636\) 7.89898 + 17.1455i 0.313215 + 0.679865i
\(637\) 0 0
\(638\) −13.7980 −0.546266
\(639\) 0.297959 + 0.0553782i 0.0117871 + 0.00219073i
\(640\) −0.724745 1.25529i −0.0286481 0.0496199i
\(641\) 3.74745 6.49077i 0.148015 0.256370i −0.782479 0.622678i \(-0.786045\pi\)
0.930494 + 0.366308i \(0.119378\pi\)
\(642\) 12.0000 16.9706i 0.473602 0.669775i
\(643\) −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
\(646\) 5.10102 0.200697
\(647\) −25.3485 43.9048i −0.996551 1.72608i −0.570139 0.821548i \(-0.693111\pi\)
−0.426412 0.904529i \(-0.640223\pi\)
\(648\) 8.39898 + 3.23375i 0.329943 + 0.127034i
\(649\) −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
\(653\) −4.89898 8.48528i −0.191712 0.332055i 0.754106 0.656753i \(-0.228071\pi\)
−0.945818 + 0.324698i \(0.894737\pi\)
\(654\) −9.20204 19.9740i −0.359828 0.781044i
\(655\) −6.19694 + 10.7334i −0.242134 + 0.419389i
\(656\) 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 \(0.673597\pi\)
\(660\) 5.00000 + 0.460702i 0.194625 + 0.0179328i
\(661\) −4.55051 −0.176994 −0.0884972 0.996076i \(-0.528206\pi\)
−0.0884972 + 0.996076i \(0.528206\pi\)
\(662\) 4.69694 0.182552
\(663\) 16.8990 + 1.55708i 0.656302 + 0.0604719i
\(664\) 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
\(668\) −5.34847 + 9.26382i −0.206938 + 0.358428i
\(669\) −8.04541 17.4634i −0.311053 0.675173i
\(670\) 9.34847 + 16.1920i 0.361163 + 0.625552i
\(671\) 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
\(675\) 10.7980 10.5031i 0.415614 0.404263i
\(676\) −5.50000 9.52628i −0.211538 0.366395i
\(677\) −14.6969 −0.564849 −0.282425 0.959289i \(-0.591139\pi\)
−0.282425 + 0.959289i \(0.591139\pi\)
\(678\) 6.10102 8.62815i 0.234308 0.331362i
\(679\) 0 0
\(680\) 1.44949 2.51059i 0.0555854 0.0962767i
\(681\) −5.44949 + 7.70674i −0.208825 + 0.295323i
\(682\) 6.00000 10.3923i 0.229752 0.397942i
\(683\) −25.8990 44.8583i −0.990997 1.71646i −0.611446 0.791286i \(-0.709412\pi\)
−0.379551 0.925171i \(-0.623921\pi\)
\(684\) 4.97219 5.81577i 0.190117 0.222372i
\(685\) 11.3031 0.431868
\(686\) 0 0
\(687\) 0.904082 + 1.96240i 0.0344929 + 0.0748703i
\(688\) −3.44949 5.97469i −0.131511 0.227783i
\(689\) 53.3939 2.03414
\(690\) 1.44949 2.04989i 0.0551811 0.0780379i
\(691\) −51.0454 −1.94186 −0.970929 0.239366i \(-0.923060\pi\)
−0.970929 + 0.239366i \(0.923060\pi\)
\(692\) 3.10102 0.117883
\(693\) 0 0
\(694\) 19.5959 0.743851
\(695\) −6.59592 −0.250197
\(696\) 5.00000 + 10.8530i 0.189525 + 0.411382i
\(697\) 19.5959 0.742248
\(698\) 5.55051 + 9.61377i 0.210090 + 0.363886i
\(699\) 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 \(0.544592\pi\)
\(702\) 18.2474 17.7491i 0.688706 0.669897i
\(703\) 15.0454 + 26.0594i 0.567448 + 0.982849i
\(704\) −1.00000 + 1.73205i −0.0376889 + 0.0652791i
\(705\) 10.2929 + 22.3417i 0.387651 + 0.841437i
\(706\) −3.00000 + 5.19615i −0.112906 + 0.195560i
\(707\) 0 0
\(708\) 3.44949 + 0.317837i 0.129640 + 0.0119451i
\(709\) 27.5959 1.03639 0.518193 0.855264i \(-0.326605\pi\)
0.518193 + 0.855264i \(0.326605\pi\)
\(710\) −0.0732141 0.126811i −0.00274768 0.00475911i
\(711\) −5.60102 1.04100i −0.210055 0.0390405i
\(712\) −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
\(716\) −10.3485 17.9241i −0.386740 0.669854i
\(717\) −6.79796 + 9.61377i −0.253874 + 0.359033i
\(718\) 4.39898 7.61926i 0.164168 0.284348i
\(719\) 4.89898 8.48528i 0.182701 0.316448i −0.760098 0.649808i \(-0.774849\pi\)
0.942799 + 0.333360i \(0.108183\pi\)
\(720\) −1.44949 4.09978i −0.0540193 0.152790i
\(721\) 0 0
\(722\) 6.24745 + 10.8209i 0.232506 + 0.402712i
\(723\) 0.898979 1.27135i 0.0334334 0.0472820i
\(724\) 10.3485 0.384598
\(725\) 20.0000 0.742781
\(726\) 5.07321 + 11.0119i 0.188285 + 0.408691i
\(727\) −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
\(731\) 6.89898 11.9494i 0.255168 0.441964i
\(732\) −11.2980 1.04100i −0.417585 0.0384764i
\(733\) −8.72474 15.1117i −0.322256 0.558163i 0.658697 0.752408i \(-0.271108\pi\)
−0.980953 + 0.194245i \(0.937774\pi\)
\(734\) −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
\(738\) 19.1010 22.3417i 0.703118 0.822409i
\(739\) −6.79796 11.7744i −0.250067 0.433129i 0.713477 0.700679i \(-0.247119\pi\)
−0.963544 + 0.267550i \(0.913786\pi\)
\(740\) 17.1010 0.628646
\(741\) −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 \(0.937072\pi\)
\(744\) −10.3485 0.953512i −0.379393 0.0349574i
\(745\) 4.34847 7.53177i 0.159316 0.275943i
\(746\) 3.44949 + 5.97469i 0.126295 + 0.218749i
\(747\) 2.00000 + 5.65685i 0.0731762 + 0.206973i
\(748\) −4.00000 −0.146254
\(749\) 0 0
\(750\) −19.7474 1.81954i −0.721075 0.0664401i
\(751\) −0.702041 1.21597i −0.0256178 0.0443714i 0.852932 0.522022i \(-0.174822\pi\)
−0.878550 + 0.477650i \(0.841489\pi\)
\(752\) −9.79796 −0.357295
\(753\) −30.0959 2.77305i −1.09676 0.101056i
\(754\) 33.7980 1.23085
\(755\) −7.24745 −0.263762
\(756\) 0 0
\(757\) −35.3939 −1.28641 −0.643206 0.765693i \(-0.722396\pi\)
−0.643206 + 0.765693i \(0.722396\pi\)
\(758\) 22.4949 0.817051
\(759\) −3.44949 0.317837i −0.125209 0.0115368i
\(760\) −3.69694 −0.134102
\(761\) 1.00000 + 1.73205i 0.0362500 + 0.0627868i 0.883581 0.468278i \(-0.155125\pi\)
−0.847331 + 0.531065i \(0.821792\pi\)
\(762\) −5.17423 0.476756i −0.187443 0.0172710i
\(763\) 0 0
\(764\) 4.10102 0.148370
\(765\) 5.65153 6.61037i 0.204332 0.238998i
\(766\) −1.44949 2.51059i −0.0523722 0.0907113i
\(767\) 4.89898 8.48528i 0.176892 0.306386i
\(768\) 1.72474 + 0.158919i 0.0622364 + 0.00573448i
\(769\) −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
\(772\) −17.8990 −0.644198
\(773\) 16.9722 + 29.3967i 0.610447 + 1.05733i 0.991165 + 0.132635i \(0.0423437\pi\)
−0.380718 + 0.924691i \(0.624323\pi\)
\(774\) −6.89898 19.5133i −0.247979 0.701390i
\(775\) −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
\(779\) −12.4949 21.6418i −0.447676 0.775398i
\(780\) −12.2474 1.12848i −0.438529 0.0404062i
\(781\)