Properties

Label 585.2.bt.a.571.2
Level $585$
Weight $2$
Character 585.571
Analytic conductor $4.671$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 585.bt (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 571.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 585.571
Dual form 585.2.bt.a.376.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.73205 - 1.00000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.866025 + 0.500000i) q^{5} +3.46410 q^{6} +(1.73205 - 1.00000i) q^{7} +(1.50000 + 2.59808i) q^{9} +O(q^{10})\) \(q+(1.73205 - 1.00000i) q^{2} +(1.50000 + 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(0.866025 + 0.500000i) q^{5} +3.46410 q^{6} +(1.73205 - 1.00000i) q^{7} +(1.50000 + 2.59808i) q^{9} +2.00000 q^{10} +(-5.19615 + 3.00000i) q^{11} +(3.00000 - 1.73205i) q^{12} +(-0.232051 - 3.59808i) q^{13} +(2.00000 - 3.46410i) q^{14} +(0.866025 + 1.50000i) q^{15} +(2.00000 + 3.46410i) q^{16} -1.00000 q^{17} +(5.19615 + 3.00000i) q^{18} -8.00000i q^{19} +(1.73205 - 1.00000i) q^{20} +3.46410 q^{21} +(-6.00000 + 10.3923i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{25} +(-4.00000 - 6.00000i) q^{26} +5.19615i q^{27} -4.00000i q^{28} +(-1.00000 - 1.73205i) q^{29} +(3.00000 + 1.73205i) q^{30} +(-6.92820 - 4.00000i) q^{31} +(6.92820 + 4.00000i) q^{32} -10.3923 q^{33} +(-1.73205 + 1.00000i) q^{34} +2.00000 q^{35} +6.00000 q^{36} +2.00000i q^{37} +(-8.00000 - 13.8564i) q^{38} +(2.76795 - 5.59808i) q^{39} +(-1.73205 - 1.00000i) q^{41} +(6.00000 - 3.46410i) q^{42} +(-2.50000 - 4.33013i) q^{43} +12.0000i q^{44} +3.00000i q^{45} +2.00000i q^{46} +(8.66025 - 5.00000i) q^{47} +6.92820i q^{48} +(-1.50000 + 2.59808i) q^{49} +(1.73205 + 1.00000i) q^{50} +(-1.50000 - 0.866025i) q^{51} +(-6.46410 - 3.19615i) q^{52} +9.00000 q^{53} +(5.19615 + 9.00000i) q^{54} -6.00000 q^{55} +(6.92820 - 12.0000i) q^{57} +(-3.46410 - 2.00000i) q^{58} +(-5.19615 - 3.00000i) q^{59} +3.46410 q^{60} +(2.50000 + 4.33013i) q^{61} -16.0000 q^{62} +(5.19615 + 3.00000i) q^{63} +8.00000 q^{64} +(1.59808 - 3.23205i) q^{65} +(-18.0000 + 10.3923i) q^{66} +(-1.00000 + 1.73205i) q^{68} +(-1.50000 + 0.866025i) q^{69} +(3.46410 - 2.00000i) q^{70} +10.0000i q^{71} -4.00000i q^{73} +(2.00000 + 3.46410i) q^{74} +1.73205i q^{75} +(-13.8564 - 8.00000i) q^{76} +(-6.00000 + 10.3923i) q^{77} +(-0.803848 - 12.4641i) q^{78} +(-0.500000 - 0.866025i) q^{79} +4.00000i q^{80} +(-4.50000 + 7.79423i) q^{81} -4.00000 q^{82} +(3.46410 - 6.00000i) q^{84} +(-0.866025 - 0.500000i) q^{85} +(-8.66025 - 5.00000i) q^{86} -3.46410i q^{87} +(3.00000 + 5.19615i) q^{90} +(-4.00000 - 6.00000i) q^{91} +(1.00000 + 1.73205i) q^{92} +(-6.92820 - 12.0000i) q^{93} +(10.0000 - 17.3205i) q^{94} +(4.00000 - 6.92820i) q^{95} +(6.92820 + 12.0000i) q^{96} +(-8.66025 + 5.00000i) q^{97} +6.00000i q^{98} +(-15.5885 - 9.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 6 q^{3} + 4 q^{4} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 6 q^{3} + 4 q^{4} + 6 q^{9} + 8 q^{10} + 12 q^{12} + 6 q^{13} + 8 q^{14} + 8 q^{16} - 4 q^{17} - 24 q^{22} - 2 q^{23} + 2 q^{25} - 16 q^{26} - 4 q^{29} + 12 q^{30} + 8 q^{35} + 24 q^{36} - 32 q^{38} + 18 q^{39} + 24 q^{42} - 10 q^{43} - 6 q^{49} - 6 q^{51} - 12 q^{52} + 36 q^{53} - 24 q^{55} + 10 q^{61} - 64 q^{62} + 32 q^{64} - 4 q^{65} - 72 q^{66} - 4 q^{68} - 6 q^{69} + 8 q^{74} - 24 q^{77} - 24 q^{78} - 2 q^{79} - 18 q^{81} - 16 q^{82} + 12 q^{90} - 16 q^{91} + 4 q^{92} + 40 q^{94} + 16 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/585\mathbb{Z}\right)^\times\).

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205 1.00000i 1.22474 0.707107i 0.258819 0.965926i \(-0.416667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(3\) 1.50000 + 0.866025i 0.866025 + 0.500000i
\(4\) 1.00000 1.73205i 0.500000 0.866025i
\(5\) 0.866025 + 0.500000i 0.387298 + 0.223607i
\(6\) 3.46410 1.41421
\(7\) 1.73205 1.00000i 0.654654 0.377964i −0.135583 0.990766i \(-0.543291\pi\)
0.790237 + 0.612801i \(0.209957\pi\)
\(8\) 0 0
\(9\) 1.50000 + 2.59808i 0.500000 + 0.866025i
\(10\) 2.00000 0.632456
\(11\) −5.19615 + 3.00000i −1.56670 + 0.904534i −0.570149 + 0.821541i \(0.693114\pi\)
−0.996550 + 0.0829925i \(0.973552\pi\)
\(12\) 3.00000 1.73205i 0.866025 0.500000i
\(13\) −0.232051 3.59808i −0.0643593 0.997927i
\(14\) 2.00000 3.46410i 0.534522 0.925820i
\(15\) 0.866025 + 1.50000i 0.223607 + 0.387298i
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −1.00000 −0.242536 −0.121268 0.992620i \(-0.538696\pi\)
−0.121268 + 0.992620i \(0.538696\pi\)
\(18\) 5.19615 + 3.00000i 1.22474 + 0.707107i
\(19\) 8.00000i 1.83533i −0.397360 0.917663i \(-0.630073\pi\)
0.397360 0.917663i \(-0.369927\pi\)
\(20\) 1.73205 1.00000i 0.387298 0.223607i
\(21\) 3.46410 0.755929
\(22\) −6.00000 + 10.3923i −1.27920 + 2.21565i
\(23\) −0.500000 + 0.866025i −0.104257 + 0.180579i −0.913434 0.406986i \(-0.866580\pi\)
0.809177 + 0.587565i \(0.199913\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) −4.00000 6.00000i −0.784465 1.17670i
\(27\) 5.19615i 1.00000i
\(28\) 4.00000i 0.755929i
\(29\) −1.00000 1.73205i −0.185695 0.321634i 0.758115 0.652121i \(-0.226120\pi\)
−0.943811 + 0.330487i \(0.892787\pi\)
\(30\) 3.00000 + 1.73205i 0.547723 + 0.316228i
\(31\) −6.92820 4.00000i −1.24434 0.718421i −0.274367 0.961625i \(-0.588468\pi\)
−0.969975 + 0.243204i \(0.921802\pi\)
\(32\) 6.92820 + 4.00000i 1.22474 + 0.707107i
\(33\) −10.3923 −1.80907
\(34\) −1.73205 + 1.00000i −0.297044 + 0.171499i
\(35\) 2.00000 0.338062
\(36\) 6.00000 1.00000
\(37\) 2.00000i 0.328798i 0.986394 + 0.164399i \(0.0525685\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) −8.00000 13.8564i −1.29777 2.24781i
\(39\) 2.76795 5.59808i 0.443227 0.896410i
\(40\) 0 0
\(41\) −1.73205 1.00000i −0.270501 0.156174i 0.358614 0.933486i \(-0.383249\pi\)
−0.629115 + 0.777312i \(0.716583\pi\)
\(42\) 6.00000 3.46410i 0.925820 0.534522i
\(43\) −2.50000 4.33013i −0.381246 0.660338i 0.609994 0.792406i \(-0.291172\pi\)
−0.991241 + 0.132068i \(0.957838\pi\)
\(44\) 12.0000i 1.80907i
\(45\) 3.00000i 0.447214i
\(46\) 2.00000i 0.294884i
\(47\) 8.66025 5.00000i 1.26323 0.729325i 0.289530 0.957169i \(-0.406501\pi\)
0.973698 + 0.227844i \(0.0731676\pi\)
\(48\) 6.92820i 1.00000i
\(49\) −1.50000 + 2.59808i −0.214286 + 0.371154i
\(50\) 1.73205 + 1.00000i 0.244949 + 0.141421i
\(51\) −1.50000 0.866025i −0.210042 0.121268i
\(52\) −6.46410 3.19615i −0.896410 0.443227i
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) 5.19615 + 9.00000i 0.707107 + 1.22474i
\(55\) −6.00000 −0.809040
\(56\) 0 0
\(57\) 6.92820 12.0000i 0.917663 1.58944i
\(58\) −3.46410 2.00000i −0.454859 0.262613i
\(59\) −5.19615 3.00000i −0.676481 0.390567i 0.122047 0.992524i \(-0.461054\pi\)
−0.798528 + 0.601958i \(0.794388\pi\)
\(60\) 3.46410 0.447214
\(61\) 2.50000 + 4.33013i 0.320092 + 0.554416i 0.980507 0.196485i \(-0.0629528\pi\)
−0.660415 + 0.750901i \(0.729619\pi\)
\(62\) −16.0000 −2.03200
\(63\) 5.19615 + 3.00000i 0.654654 + 0.377964i
\(64\) 8.00000 1.00000
\(65\) 1.59808 3.23205i 0.198217 0.400887i
\(66\) −18.0000 + 10.3923i −2.21565 + 1.27920i
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) −1.00000 + 1.73205i −0.121268 + 0.210042i
\(69\) −1.50000 + 0.866025i −0.180579 + 0.104257i
\(70\) 3.46410 2.00000i 0.414039 0.239046i
\(71\) 10.0000i 1.18678i 0.804914 + 0.593391i \(0.202211\pi\)
−0.804914 + 0.593391i \(0.797789\pi\)
\(72\) 0 0
\(73\) 4.00000i 0.468165i −0.972217 0.234082i \(-0.924791\pi\)
0.972217 0.234082i \(-0.0752085\pi\)
\(74\) 2.00000 + 3.46410i 0.232495 + 0.402694i
\(75\) 1.73205i 0.200000i
\(76\) −13.8564 8.00000i −1.58944 0.917663i
\(77\) −6.00000 + 10.3923i −0.683763 + 1.18431i
\(78\) −0.803848 12.4641i −0.0910178 1.41128i
\(79\) −0.500000 0.866025i −0.0562544 0.0974355i 0.836527 0.547926i \(-0.184582\pi\)
−0.892781 + 0.450490i \(0.851249\pi\)
\(80\) 4.00000i 0.447214i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) −4.00000 −0.441726
\(83\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(84\) 3.46410 6.00000i 0.377964 0.654654i
\(85\) −0.866025 0.500000i −0.0939336 0.0542326i
\(86\) −8.66025 5.00000i −0.933859 0.539164i
\(87\) 3.46410i 0.371391i
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 3.00000 + 5.19615i 0.316228 + 0.547723i
\(91\) −4.00000 6.00000i −0.419314 0.628971i
\(92\) 1.00000 + 1.73205i 0.104257 + 0.180579i
\(93\) −6.92820 12.0000i −0.718421 1.24434i
\(94\) 10.0000 17.3205i 1.03142 1.78647i
\(95\) 4.00000 6.92820i 0.410391 0.710819i
\(96\) 6.92820 + 12.0000i 0.707107 + 1.22474i
\(97\) −8.66025 + 5.00000i −0.879316 + 0.507673i −0.870433 0.492287i \(-0.836161\pi\)
−0.00888289 + 0.999961i \(0.502828\pi\)
\(98\) 6.00000i 0.606092i
\(99\) −15.5885 9.00000i −1.56670 0.904534i
\(100\) 2.00000 0.200000
\(101\) −3.50000 6.06218i −0.348263 0.603209i 0.637678 0.770303i \(-0.279895\pi\)
−0.985941 + 0.167094i \(0.946562\pi\)
\(102\) −3.46410 −0.342997
\(103\) −8.00000 + 13.8564i −0.788263 + 1.36531i 0.138767 + 0.990325i \(0.455686\pi\)
−0.927030 + 0.374987i \(0.877647\pi\)
\(104\) 0 0
\(105\) 3.00000 + 1.73205i 0.292770 + 0.169031i
\(106\) 15.5885 9.00000i 1.51408 0.874157i
\(107\) 17.0000 1.64345 0.821726 0.569883i \(-0.193011\pi\)
0.821726 + 0.569883i \(0.193011\pi\)
\(108\) 9.00000 + 5.19615i 0.866025 + 0.500000i
\(109\) 20.0000i 1.91565i 0.287348 + 0.957826i \(0.407226\pi\)
−0.287348 + 0.957826i \(0.592774\pi\)
\(110\) −10.3923 + 6.00000i −0.990867 + 0.572078i
\(111\) −1.73205 + 3.00000i −0.164399 + 0.284747i
\(112\) 6.92820 + 4.00000i 0.654654 + 0.377964i
\(113\) −9.50000 + 16.4545i −0.893685 + 1.54791i −0.0582609 + 0.998301i \(0.518556\pi\)
−0.835424 + 0.549606i \(0.814778\pi\)
\(114\) 27.7128i 2.59554i
\(115\) −0.866025 + 0.500000i −0.0807573 + 0.0466252i
\(116\) −4.00000 −0.371391
\(117\) 9.00000 6.00000i 0.832050 0.554700i
\(118\) −12.0000 −1.10469
\(119\) −1.73205 + 1.00000i −0.158777 + 0.0916698i
\(120\) 0 0
\(121\) 12.5000 21.6506i 1.13636 1.96824i
\(122\) 8.66025 + 5.00000i 0.784063 + 0.452679i
\(123\) −1.73205 3.00000i −0.156174 0.270501i
\(124\) −13.8564 + 8.00000i −1.24434 + 0.718421i
\(125\) 1.00000i 0.0894427i
\(126\) 12.0000 1.06904
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0 0
\(129\) 8.66025i 0.762493i
\(130\) −0.464102 7.19615i −0.0407044 0.631144i
\(131\) −7.50000 + 12.9904i −0.655278 + 1.13497i 0.326546 + 0.945181i \(0.394115\pi\)
−0.981824 + 0.189794i \(0.939218\pi\)
\(132\) −10.3923 + 18.0000i −0.904534 + 1.56670i
\(133\) −8.00000 13.8564i −0.693688 1.20150i
\(134\) 0 0
\(135\) −2.59808 + 4.50000i −0.223607 + 0.387298i
\(136\) 0 0
\(137\) 5.19615 3.00000i 0.443937 0.256307i −0.261329 0.965250i \(-0.584161\pi\)
0.705266 + 0.708942i \(0.250827\pi\)
\(138\) −1.73205 + 3.00000i −0.147442 + 0.255377i
\(139\) 5.50000 9.52628i 0.466504 0.808008i −0.532764 0.846264i \(-0.678847\pi\)
0.999268 + 0.0382553i \(0.0121800\pi\)
\(140\) 2.00000 3.46410i 0.169031 0.292770i
\(141\) 17.3205 1.45865
\(142\) 10.0000 + 17.3205i 0.839181 + 1.45350i
\(143\) 12.0000 + 18.0000i 1.00349 + 1.50524i
\(144\) −6.00000 + 10.3923i −0.500000 + 0.866025i
\(145\) 2.00000i 0.166091i
\(146\) −4.00000 6.92820i −0.331042 0.573382i
\(147\) −4.50000 + 2.59808i −0.371154 + 0.214286i
\(148\) 3.46410 + 2.00000i 0.284747 + 0.164399i
\(149\) −1.73205 1.00000i −0.141895 0.0819232i 0.427372 0.904076i \(-0.359440\pi\)
−0.569267 + 0.822153i \(0.692773\pi\)
\(150\) 1.73205 + 3.00000i 0.141421 + 0.244949i
\(151\) 3.46410 2.00000i 0.281905 0.162758i −0.352381 0.935857i \(-0.614628\pi\)
0.634285 + 0.773099i \(0.281294\pi\)
\(152\) 0 0
\(153\) −1.50000 2.59808i −0.121268 0.210042i
\(154\) 24.0000i 1.93398i
\(155\) −4.00000 6.92820i −0.321288 0.556487i
\(156\) −6.92820 10.3923i −0.554700 0.832050i
\(157\) 6.50000 11.2583i 0.518756 0.898513i −0.481006 0.876717i \(-0.659728\pi\)
0.999762 0.0217953i \(-0.00693820\pi\)
\(158\) −1.73205 1.00000i −0.137795 0.0795557i
\(159\) 13.5000 + 7.79423i 1.07062 + 0.618123i
\(160\) 4.00000 + 6.92820i 0.316228 + 0.547723i
\(161\) 2.00000i 0.157622i
\(162\) 18.0000i 1.41421i
\(163\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(164\) −3.46410 + 2.00000i −0.270501 + 0.156174i
\(165\) −9.00000 5.19615i −0.700649 0.404520i
\(166\) 0 0
\(167\) −1.73205 1.00000i −0.134030 0.0773823i 0.431486 0.902120i \(-0.357990\pi\)
−0.565516 + 0.824737i \(0.691323\pi\)
\(168\) 0 0
\(169\) −12.8923 + 1.66987i −0.991716 + 0.128452i
\(170\) −2.00000 −0.153393
\(171\) 20.7846 12.0000i 1.58944 0.917663i
\(172\) −10.0000 −0.762493
\(173\) −6.50000 11.2583i −0.494186 0.855955i 0.505792 0.862656i \(-0.331200\pi\)
−0.999978 + 0.00670064i \(0.997867\pi\)
\(174\) −3.46410 6.00000i −0.262613 0.454859i
\(175\) 1.73205 + 1.00000i 0.130931 + 0.0755929i
\(176\) −20.7846 12.0000i −1.56670 0.904534i
\(177\) −5.19615 9.00000i −0.390567 0.676481i
\(178\) 0 0
\(179\) 15.0000 1.12115 0.560576 0.828103i \(-0.310580\pi\)
0.560576 + 0.828103i \(0.310580\pi\)
\(180\) 5.19615 + 3.00000i 0.387298 + 0.223607i
\(181\) 21.0000 1.56092 0.780459 0.625207i \(-0.214986\pi\)
0.780459 + 0.625207i \(0.214986\pi\)
\(182\) −12.9282 6.39230i −0.958302 0.473829i
\(183\) 8.66025i 0.640184i
\(184\) 0 0
\(185\) −1.00000 + 1.73205i −0.0735215 + 0.127343i
\(186\) −24.0000 13.8564i −1.75977 1.01600i
\(187\) 5.19615 3.00000i 0.379980 0.219382i
\(188\) 20.0000i 1.45865i
\(189\) 5.19615 + 9.00000i 0.377964 + 0.654654i
\(190\) 16.0000i 1.16076i
\(191\) −9.50000 16.4545i −0.687396 1.19060i −0.972677 0.232161i \(-0.925420\pi\)
0.285282 0.958444i \(-0.407913\pi\)
\(192\) 12.0000 + 6.92820i 0.866025 + 0.500000i
\(193\) 3.46410 + 2.00000i 0.249351 + 0.143963i 0.619467 0.785022i \(-0.287349\pi\)
−0.370116 + 0.928986i \(0.620682\pi\)
\(194\) −10.0000 + 17.3205i −0.717958 + 1.24354i
\(195\) 5.19615 3.46410i 0.372104 0.248069i
\(196\) 3.00000 + 5.19615i 0.214286 + 0.371154i
\(197\) 20.0000i 1.42494i 0.701702 + 0.712470i \(0.252424\pi\)
−0.701702 + 0.712470i \(0.747576\pi\)
\(198\) −36.0000 −2.55841
\(199\) 3.00000 0.212664 0.106332 0.994331i \(-0.466089\pi\)
0.106332 + 0.994331i \(0.466089\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) −12.1244 7.00000i −0.853067 0.492518i
\(203\) −3.46410 2.00000i −0.243132 0.140372i
\(204\) −3.00000 + 1.73205i −0.210042 + 0.121268i
\(205\) −1.00000 1.73205i −0.0698430 0.120972i
\(206\) 32.0000i 2.22955i
\(207\) −3.00000 −0.208514
\(208\) 12.0000 8.00000i 0.832050 0.554700i
\(209\) 24.0000 + 41.5692i 1.66011 + 2.87540i
\(210\) 6.92820 0.478091
\(211\) 7.50000 12.9904i 0.516321 0.894295i −0.483499 0.875345i \(-0.660634\pi\)
0.999820 0.0189499i \(-0.00603229\pi\)
\(212\) 9.00000 15.5885i 0.618123 1.07062i
\(213\) −8.66025 + 15.0000i −0.593391 + 1.02778i
\(214\) 29.4449 17.0000i 2.01281 1.16210i
\(215\) 5.00000i 0.340997i
\(216\) 0 0
\(217\) −16.0000 −1.08615
\(218\) 20.0000 + 34.6410i 1.35457 + 2.34619i
\(219\) 3.46410 6.00000i 0.234082 0.405442i
\(220\) −6.00000 + 10.3923i −0.404520 + 0.700649i
\(221\) 0.232051 + 3.59808i 0.0156094 + 0.242033i
\(222\) 6.92820i 0.464991i
\(223\) −12.1244 + 7.00000i −0.811907 + 0.468755i −0.847618 0.530607i \(-0.821964\pi\)
0.0357107 + 0.999362i \(0.488630\pi\)
\(224\) 16.0000 1.06904
\(225\) −1.50000 + 2.59808i −0.100000 + 0.173205i
\(226\) 38.0000i 2.52772i
\(227\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(228\) −13.8564 24.0000i −0.917663 1.58944i
\(229\) 22.5167 + 13.0000i 1.48794 + 0.859064i 0.999905 0.0137585i \(-0.00437961\pi\)
0.488037 + 0.872823i \(0.337713\pi\)
\(230\) −1.00000 + 1.73205i −0.0659380 + 0.114208i
\(231\) −18.0000 + 10.3923i −1.18431 + 0.683763i
\(232\) 0 0
\(233\) −19.0000 −1.24473 −0.622366 0.782727i \(-0.713828\pi\)
−0.622366 + 0.782727i \(0.713828\pi\)
\(234\) 9.58846 19.3923i 0.626817 1.26771i
\(235\) 10.0000 0.652328
\(236\) −10.3923 + 6.00000i −0.676481 + 0.390567i
\(237\) 1.73205i 0.112509i
\(238\) −2.00000 + 3.46410i −0.129641 + 0.224544i
\(239\) 17.3205 + 10.0000i 1.12037 + 0.646846i 0.941495 0.337026i \(-0.109421\pi\)
0.178875 + 0.983872i \(0.442754\pi\)
\(240\) −3.46410 + 6.00000i −0.223607 + 0.387298i
\(241\) 25.9808 15.0000i 1.67357 0.966235i 0.707953 0.706260i \(-0.249619\pi\)
0.965615 0.259975i \(-0.0837143\pi\)
\(242\) 50.0000i 3.21412i
\(243\) −13.5000 + 7.79423i −0.866025 + 0.500000i
\(244\) 10.0000 0.640184
\(245\) −2.59808 + 1.50000i −0.165985 + 0.0958315i
\(246\) −6.00000 3.46410i −0.382546 0.220863i
\(247\) −28.7846 + 1.85641i −1.83152 + 0.118120i
\(248\) 0 0
\(249\) 0 0
\(250\) 1.00000 + 1.73205i 0.0632456 + 0.109545i
\(251\) 3.00000 0.189358 0.0946792 0.995508i \(-0.469817\pi\)
0.0946792 + 0.995508i \(0.469817\pi\)
\(252\) 10.3923 6.00000i 0.654654 0.377964i
\(253\) 6.00000i 0.377217i
\(254\) 0 0
\(255\) −0.866025 1.50000i −0.0542326 0.0939336i
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) 1.50000 2.59808i 0.0935674 0.162064i −0.815442 0.578838i \(-0.803506\pi\)
0.909010 + 0.416775i \(0.136840\pi\)
\(258\) −8.66025 15.0000i −0.539164 0.933859i
\(259\) 2.00000 + 3.46410i 0.124274 + 0.215249i
\(260\) −4.00000 6.00000i −0.248069 0.372104i
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) 30.0000i 1.85341i
\(263\) −4.50000 7.79423i −0.277482 0.480613i 0.693276 0.720672i \(-0.256167\pi\)
−0.970758 + 0.240059i \(0.922833\pi\)
\(264\) 0 0
\(265\) 7.79423 + 4.50000i 0.478796 + 0.276433i
\(266\) −27.7128 16.0000i −1.69918 0.981023i
\(267\) 0 0
\(268\) 0 0
\(269\) −14.0000 −0.853595 −0.426798 0.904347i \(-0.640358\pi\)
−0.426798 + 0.904347i \(0.640358\pi\)
\(270\) 10.3923i 0.632456i
\(271\) 28.0000i 1.70088i −0.526073 0.850439i \(-0.676336\pi\)
0.526073 0.850439i \(-0.323664\pi\)
\(272\) −2.00000 3.46410i −0.121268 0.210042i
\(273\) −0.803848 12.4641i −0.0486511 0.754362i
\(274\) 6.00000 10.3923i 0.362473 0.627822i
\(275\) −5.19615 3.00000i −0.313340 0.180907i
\(276\) 3.46410i 0.208514i
\(277\) −5.00000 8.66025i −0.300421 0.520344i 0.675810 0.737075i \(-0.263794\pi\)
−0.976231 + 0.216731i \(0.930460\pi\)
\(278\) 22.0000i 1.31947i
\(279\) 24.0000i 1.43684i
\(280\) 0 0
\(281\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(282\) 30.0000 17.3205i 1.78647 1.03142i
\(283\) 15.5000 26.8468i 0.921379 1.59588i 0.124096 0.992270i \(-0.460397\pi\)
0.797283 0.603606i \(-0.206270\pi\)
\(284\) 17.3205 + 10.0000i 1.02778 + 0.593391i
\(285\) 12.0000 6.92820i 0.710819 0.410391i
\(286\) 38.7846 + 19.1769i 2.29338 + 1.13395i
\(287\) −4.00000 −0.236113
\(288\) 24.0000i 1.41421i
\(289\) −16.0000 −0.941176
\(290\) −2.00000 3.46410i −0.117444 0.203419i
\(291\) −17.3205 −1.01535
\(292\) −6.92820 4.00000i −0.405442 0.234082i
\(293\) 5.19615 + 3.00000i 0.303562 + 0.175262i 0.644042 0.764990i \(-0.277256\pi\)
−0.340480 + 0.940252i \(0.610589\pi\)
\(294\) −5.19615 + 9.00000i −0.303046 + 0.524891i
\(295\) −3.00000 5.19615i −0.174667 0.302532i
\(296\) 0 0
\(297\) −15.5885 27.0000i −0.904534 1.56670i
\(298\) −4.00000 −0.231714
\(299\) 3.23205 + 1.59808i 0.186914 + 0.0924191i
\(300\) 3.00000 + 1.73205i 0.173205 + 0.100000i
\(301\) −8.66025 5.00000i −0.499169 0.288195i
\(302\) 4.00000 6.92820i 0.230174 0.398673i
\(303\) 12.1244i 0.696526i
\(304\) 27.7128 16.0000i 1.58944 0.917663i
\(305\) 5.00000i 0.286299i
\(306\) −5.19615 3.00000i −0.297044 0.171499i
\(307\) 4.00000i 0.228292i 0.993464 + 0.114146i \(0.0364132\pi\)
−0.993464 + 0.114146i \(0.963587\pi\)
\(308\) 12.0000 + 20.7846i 0.683763 + 1.18431i
\(309\) −24.0000 + 13.8564i −1.36531 + 0.788263i
\(310\) −13.8564 8.00000i −0.786991 0.454369i
\(311\) 4.00000 6.92820i 0.226819 0.392862i −0.730044 0.683400i \(-0.760501\pi\)
0.956864 + 0.290537i \(0.0938340\pi\)
\(312\) 0 0
\(313\) 5.00000 + 8.66025i 0.282617 + 0.489506i 0.972028 0.234863i \(-0.0754642\pi\)
−0.689412 + 0.724370i \(0.742131\pi\)
\(314\) 26.0000i 1.46726i
\(315\) 3.00000 + 5.19615i 0.169031 + 0.292770i
\(316\) −2.00000 −0.112509
\(317\) 22.5167 13.0000i 1.26466 0.730153i 0.290689 0.956818i \(-0.406116\pi\)
0.973973 + 0.226665i \(0.0727822\pi\)
\(318\) 31.1769 1.74831
\(319\) 10.3923 + 6.00000i 0.581857 + 0.335936i
\(320\) 6.92820 + 4.00000i 0.387298 + 0.223607i
\(321\) 25.5000 + 14.7224i 1.42327 + 0.821726i
\(322\) 2.00000 + 3.46410i 0.111456 + 0.193047i
\(323\) 8.00000i 0.445132i
\(324\) 9.00000 + 15.5885i 0.500000 + 0.866025i
\(325\) 3.00000 2.00000i 0.166410 0.110940i
\(326\) 0 0
\(327\) −17.3205 + 30.0000i −0.957826 + 1.65900i
\(328\) 0 0
\(329\) 10.0000 17.3205i 0.551318 0.954911i
\(330\) −20.7846 −1.14416
\(331\) 6.92820 4.00000i 0.380808 0.219860i −0.297361 0.954765i \(-0.596107\pi\)
0.678170 + 0.734905i \(0.262773\pi\)
\(332\) 0 0
\(333\) −5.19615 + 3.00000i −0.284747 + 0.164399i
\(334\) −4.00000 −0.218870
\(335\) 0 0
\(336\) 6.92820 + 12.0000i 0.377964 + 0.654654i
\(337\) −1.50000 + 2.59808i −0.0817102 + 0.141526i −0.903985 0.427565i \(-0.859372\pi\)
0.822274 + 0.569091i \(0.192705\pi\)
\(338\) −20.6603 + 15.7846i −1.12377 + 0.858570i
\(339\) −28.5000 + 16.4545i −1.54791 + 0.893685i
\(340\) −1.73205 + 1.00000i −0.0939336 + 0.0542326i
\(341\) 48.0000 2.59935
\(342\) 24.0000 41.5692i 1.29777 2.24781i
\(343\) 20.0000i 1.07990i
\(344\) 0 0
\(345\) −1.73205 −0.0932505
\(346\) −22.5167 13.0000i −1.21050 0.698884i
\(347\) 2.50000 4.33013i 0.134207 0.232453i −0.791087 0.611703i \(-0.790485\pi\)
0.925294 + 0.379250i \(0.123818\pi\)
\(348\) −6.00000 3.46410i −0.321634 0.185695i
\(349\) 1.73205 1.00000i 0.0927146 0.0535288i −0.452926 0.891548i \(-0.649620\pi\)
0.545640 + 0.838019i \(0.316286\pi\)
\(350\) 4.00000 0.213809
\(351\) 18.6962 1.20577i 0.997927 0.0643593i
\(352\) −48.0000 −2.55841
\(353\) 5.19615 3.00000i 0.276563 0.159674i −0.355303 0.934751i \(-0.615622\pi\)
0.631867 + 0.775077i \(0.282289\pi\)
\(354\) −18.0000 10.3923i −0.956689 0.552345i
\(355\) −5.00000 + 8.66025i −0.265372 + 0.459639i
\(356\) 0 0
\(357\) −3.46410 −0.183340
\(358\) 25.9808 15.0000i 1.37313 0.792775i
\(359\) 10.0000i 0.527780i −0.964553 0.263890i \(-0.914994\pi\)
0.964553 0.263890i \(-0.0850056\pi\)
\(360\) 0 0
\(361\) −45.0000 −2.36842
\(362\) 36.3731 21.0000i 1.91173 1.10374i
\(363\) 37.5000 21.6506i 1.96824 1.13636i
\(364\) −14.3923 + 0.928203i −0.754362 + 0.0486511i
\(365\) 2.00000 3.46410i 0.104685 0.181319i
\(366\) 8.66025 + 15.0000i 0.452679 + 0.784063i
\(367\) −10.5000 18.1865i −0.548096 0.949329i −0.998405 0.0564568i \(-0.982020\pi\)
0.450310 0.892873i \(-0.351314\pi\)
\(368\) −4.00000 −0.208514
\(369\) 6.00000i 0.312348i
\(370\) 4.00000i 0.207950i
\(371\) 15.5885 9.00000i 0.809312 0.467257i
\(372\) −27.7128 −1.43684
\(373\) −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i \(-0.997028\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(374\) 6.00000 10.3923i 0.310253 0.537373i
\(375\) −0.866025 + 1.50000i −0.0447214 + 0.0774597i
\(376\) 0 0
\(377\) −6.00000 + 4.00000i −0.309016 + 0.206010i
\(378\) 18.0000 + 10.3923i 0.925820 + 0.534522i
\(379\) 18.0000i 0.924598i 0.886724 + 0.462299i \(0.152975\pi\)
−0.886724 + 0.462299i \(0.847025\pi\)
\(380\) −8.00000 13.8564i −0.410391 0.710819i
\(381\) 0 0
\(382\) −32.9090 19.0000i −1.68377 0.972125i
\(383\) −22.5167 13.0000i −1.15055 0.664269i −0.201527 0.979483i \(-0.564590\pi\)
−0.949021 + 0.315214i \(0.897924\pi\)
\(384\) 0 0
\(385\) −10.3923 + 6.00000i −0.529641 + 0.305788i
\(386\) 8.00000 0.407189
\(387\) 7.50000 12.9904i 0.381246 0.660338i
\(388\) 20.0000i 1.01535i
\(389\) 11.5000 + 19.9186i 0.583073 + 1.00991i 0.995113 + 0.0987463i \(0.0314832\pi\)
−0.412039 + 0.911166i \(0.635183\pi\)
\(390\) 5.53590 11.1962i 0.280321 0.566939i
\(391\) 0.500000 0.866025i 0.0252861 0.0437968i
\(392\) 0 0
\(393\) −22.5000 + 12.9904i −1.13497 + 0.655278i
\(394\) 20.0000 + 34.6410i 1.00759 + 1.74519i
\(395\) 1.00000i 0.0503155i
\(396\) −31.1769 + 18.0000i −1.56670 + 0.904534i
\(397\) 28.0000i 1.40528i 0.711546 + 0.702640i \(0.247995\pi\)
−0.711546 + 0.702640i \(0.752005\pi\)
\(398\) 5.19615 3.00000i 0.260460 0.150376i
\(399\) 27.7128i 1.38738i
\(400\) −2.00000 + 3.46410i −0.100000 + 0.173205i
\(401\) 27.7128 + 16.0000i 1.38391 + 0.799002i 0.992620 0.121265i \(-0.0386950\pi\)
0.391292 + 0.920267i \(0.372028\pi\)
\(402\) 0 0
\(403\) −12.7846 + 25.8564i −0.636847 + 1.28800i
\(404\) −14.0000 −0.696526
\(405\) −7.79423 + 4.50000i −0.387298 + 0.223607i
\(406\) −8.00000 −0.397033
\(407\) −6.00000 10.3923i −0.297409 0.515127i
\(408\) 0 0
\(409\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) −3.46410 2.00000i −0.171080 0.0987730i
\(411\) 10.3923 0.512615
\(412\) 16.0000 + 27.7128i 0.788263 + 1.36531i
\(413\) −12.0000 −0.590481
\(414\) −5.19615 + 3.00000i −0.255377 + 0.147442i
\(415\) 0 0
\(416\) 12.7846 25.8564i 0.626817 1.26771i
\(417\) 16.5000 9.52628i 0.808008 0.466504i
\(418\) 83.1384 + 48.0000i 4.06643 + 2.34776i
\(419\) −7.50000 + 12.9904i −0.366399 + 0.634622i −0.989000 0.147918i \(-0.952743\pi\)
0.622601 + 0.782540i \(0.286076\pi\)
\(420\) 6.00000 3.46410i 0.292770 0.169031i
\(421\) −6.92820 + 4.00000i −0.337660 + 0.194948i −0.659237 0.751935i \(-0.729121\pi\)
0.321577 + 0.946883i \(0.395787\pi\)
\(422\) 30.0000i 1.46038i
\(423\) 25.9808 + 15.0000i 1.26323 + 0.729325i
\(424\) 0 0
\(425\) −0.500000 0.866025i −0.0242536 0.0420084i
\(426\) 34.6410i 1.67836i
\(427\) 8.66025 + 5.00000i 0.419099 + 0.241967i
\(428\) 17.0000 29.4449i 0.821726 1.42327i
\(429\) 2.41154 + 37.3923i 0.116430 + 1.80532i
\(430\) −5.00000 8.66025i −0.241121 0.417635i
\(431\) 24.0000i 1.15604i 0.816023 + 0.578020i \(0.196174\pi\)
−0.816023 + 0.578020i \(0.803826\pi\)
\(432\) −18.0000 + 10.3923i −0.866025 + 0.500000i
\(433\) 5.00000 0.240285 0.120142 0.992757i \(-0.461665\pi\)
0.120142 + 0.992757i \(0.461665\pi\)
\(434\) −27.7128 + 16.0000i −1.33026 + 0.768025i
\(435\) 1.73205 3.00000i 0.0830455 0.143839i
\(436\) 34.6410 + 20.0000i 1.65900 + 0.957826i
\(437\) 6.92820 + 4.00000i 0.331421 + 0.191346i
\(438\) 13.8564i 0.662085i
\(439\) −12.5000 21.6506i −0.596592 1.03333i −0.993320 0.115392i \(-0.963188\pi\)
0.396728 0.917936i \(-0.370146\pi\)
\(440\) 0 0
\(441\) −9.00000 −0.428571
\(442\) 4.00000 + 6.00000i 0.190261 + 0.285391i
\(443\) −10.5000 18.1865i −0.498870 0.864068i 0.501129 0.865373i \(-0.332918\pi\)
−0.999999 + 0.00130426i \(0.999585\pi\)
\(444\) 3.46410 + 6.00000i 0.164399 + 0.284747i
\(445\) 0 0
\(446\) −14.0000 + 24.2487i −0.662919 + 1.14821i
\(447\) −1.73205 3.00000i −0.0819232 0.141895i
\(448\) 13.8564 8.00000i 0.654654 0.377964i
\(449\) 36.0000i 1.69895i −0.527633 0.849473i \(-0.676920\pi\)
0.527633 0.849473i \(-0.323080\pi\)
\(450\) 6.00000i 0.282843i
\(451\) 12.0000 0.565058
\(452\) 19.0000 + 32.9090i 0.893685 + 1.54791i
\(453\) 6.92820 0.325515
\(454\) 0 0
\(455\) −0.464102 7.19615i −0.0217574 0.337361i
\(456\) 0 0
\(457\) −6.92820 + 4.00000i −0.324088 + 0.187112i −0.653213 0.757174i \(-0.726579\pi\)
0.329125 + 0.944286i \(0.393246\pi\)
\(458\) 52.0000 2.42980
\(459\) 5.19615i 0.242536i
\(460\) 2.00000i 0.0932505i
\(461\) −1.73205 + 1.00000i −0.0806696 + 0.0465746i −0.539792 0.841798i \(-0.681497\pi\)
0.459123 + 0.888373i \(0.348164\pi\)
\(462\) −20.7846 + 36.0000i −0.966988 + 1.67487i
\(463\) −19.0526 11.0000i −0.885448 0.511213i −0.0129968 0.999916i \(-0.504137\pi\)
−0.872451 + 0.488702i \(0.837470\pi\)
\(464\) 4.00000 6.92820i 0.185695 0.321634i
\(465\) 13.8564i 0.642575i
\(466\) −32.9090 + 19.0000i −1.52448 + 0.880158i
\(467\) −21.0000 −0.971764 −0.485882 0.874024i \(-0.661502\pi\)
−0.485882 + 0.874024i \(0.661502\pi\)
\(468\) −1.39230 21.5885i −0.0643593 0.997927i
\(469\) 0 0
\(470\) 17.3205 10.0000i 0.798935 0.461266i
\(471\) 19.5000 11.2583i 0.898513 0.518756i
\(472\) 0 0
\(473\) 25.9808 + 15.0000i 1.19460 + 0.689701i
\(474\) −1.73205 3.00000i −0.0795557 0.137795i
\(475\) 6.92820 4.00000i 0.317888 0.183533i
\(476\) 4.00000i 0.183340i
\(477\) 13.5000 + 23.3827i 0.618123 + 1.07062i
\(478\) 40.0000 1.82956
\(479\) −15.5885 + 9.00000i −0.712255 + 0.411220i −0.811895 0.583803i \(-0.801564\pi\)
0.0996406 + 0.995023i \(0.468231\pi\)
\(480\) 13.8564i 0.632456i
\(481\) 7.19615 0.464102i 0.328116 0.0211612i
\(482\) 30.0000 51.9615i 1.36646 2.36678i
\(483\) −1.73205 + 3.00000i −0.0788110 + 0.136505i
\(484\) −25.0000 43.3013i −1.13636 1.96824i
\(485\) −10.0000 −0.454077
\(486\) −15.5885 + 27.0000i −0.707107 + 1.22474i
\(487\) 24.0000i 1.08754i −0.839233 0.543772i \(-0.816996\pi\)
0.839233 0.543772i \(-0.183004\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) −3.00000 + 5.19615i −0.135526 + 0.234738i
\(491\) 8.00000 13.8564i 0.361035 0.625331i −0.627096 0.778942i \(-0.715757\pi\)
0.988131 + 0.153611i \(0.0490902\pi\)
\(492\) −6.92820 −0.312348
\(493\) 1.00000 + 1.73205i 0.0450377 + 0.0780076i
\(494\) −48.0000 + 32.0000i −2.15962 + 1.43975i
\(495\) −9.00000 15.5885i −0.404520 0.700649i
\(496\) 32.0000i 1.43684i
\(497\) 10.0000 + 17.3205i 0.448561 + 0.776931i
\(498\) 0 0
\(499\) −24.2487 14.0000i −1.08552 0.626726i −0.153141 0.988204i \(-0.548939\pi\)
−0.932381 + 0.361478i \(0.882272\pi\)
\(500\) 1.73205 + 1.00000i 0.0774597 + 0.0447214i
\(501\) −1.73205 3.00000i −0.0773823 0.134030i
\(502\) 5.19615 3.00000i 0.231916 0.133897i
\(503\) −25.0000 −1.11469 −0.557347 0.830279i \(-0.688181\pi\)
−0.557347 + 0.830279i \(0.688181\pi\)
\(504\) 0 0
\(505\) 7.00000i 0.311496i
\(506\) −6.00000 10.3923i −0.266733 0.461994i
\(507\) −20.7846 8.66025i −0.923077 0.384615i
\(508\) 0 0
\(509\) 5.19615 + 3.00000i 0.230315 + 0.132973i 0.610718 0.791849i \(-0.290881\pi\)
−0.380402 + 0.924821i \(0.624214\pi\)
\(510\) −3.00000 1.73205i −0.132842 0.0766965i
\(511\) −4.00000 6.92820i −0.176950 0.306486i
\(512\) 32.0000i 1.41421i
\(513\) 41.5692 1.83533
\(514\) 6.00000i 0.264649i
\(515\) −13.8564 + 8.00000i −0.610586 + 0.352522i
\(516\) −15.0000 8.66025i −0.660338 0.381246i
\(517\) −30.0000 + 51.9615i −1.31940 + 2.28527i
\(518\) 6.92820 + 4.00000i 0.304408 + 0.175750i
\(519\) 22.5167i 0.988372i
\(520\) 0 0
\(521\) 10.0000 0.438108 0.219054 0.975713i \(-0.429703\pi\)
0.219054 + 0.975713i \(0.429703\pi\)
\(522\) 12.0000i 0.525226i
\(523\) 20.0000 0.874539 0.437269 0.899331i \(-0.355946\pi\)
0.437269 + 0.899331i \(0.355946\pi\)
\(524\) 15.0000 + 25.9808i 0.655278 + 1.13497i
\(525\) 1.73205 + 3.00000i 0.0755929 + 0.130931i
\(526\) −15.5885 9.00000i −0.679689 0.392419i
\(527\) 6.92820 + 4.00000i 0.301797 + 0.174243i
\(528\) −20.7846 36.0000i −0.904534 1.56670i
\(529\) 11.0000 + 19.0526i 0.478261 + 0.828372i
\(530\) 18.0000 0.781870
\(531\) 18.0000i 0.781133i
\(532\) −32.0000 −1.38738
\(533\) −3.19615 + 6.46410i −0.138441 + 0.279991i
\(534\) 0 0
\(535\) 14.7224 + 8.50000i 0.636506 + 0.367487i
\(536\) 0 0
\(537\) 22.5000 + 12.9904i 0.970947 + 0.560576i
\(538\) −24.2487 + 14.0000i −1.04544 + 0.603583i
\(539\) 18.0000i 0.775315i
\(540\) 5.19615 + 9.00000i 0.223607 + 0.387298i
\(541\) 32.0000i 1.37579i 0.725811 + 0.687894i \(0.241464\pi\)
−0.725811 + 0.687894i \(0.758536\pi\)
\(542\) −28.0000 48.4974i −1.20270 2.08314i
\(543\) 31.5000 + 18.1865i 1.35179 + 0.780459i
\(544\) −6.92820 4.00000i −0.297044 0.171499i
\(545\) −10.0000 + 17.3205i −0.428353 + 0.741929i
\(546\) −13.8564 20.7846i −0.592999 0.889499i
\(547\) 2.00000 + 3.46410i 0.0855138 + 0.148114i 0.905610 0.424111i \(-0.139413\pi\)
−0.820096 + 0.572226i \(0.806080\pi\)
\(548\) 12.0000i 0.512615i
\(549\) −7.50000 + 12.9904i −0.320092 + 0.554416i
\(550\) −12.0000 −0.511682
\(551\) −13.8564 + 8.00000i −0.590303 + 0.340811i
\(552\) 0 0
\(553\) −1.73205 1.00000i −0.0736543 0.0425243i
\(554\) −17.3205 10.0000i −0.735878 0.424859i
\(555\) −3.00000 + 1.73205i −0.127343 + 0.0735215i
\(556\) −11.0000 19.0526i −0.466504 0.808008i
\(557\) 12.0000i 0.508456i −0.967144 0.254228i \(-0.918179\pi\)
0.967144 0.254228i \(-0.0818214\pi\)
\(558\) −24.0000 41.5692i −1.01600 1.75977i
\(559\) −15.0000 + 10.0000i −0.634432 + 0.422955i
\(560\) 4.00000 + 6.92820i 0.169031 + 0.292770i
\(561\) 10.3923 0.438763
\(562\) 0 0
\(563\) −19.5000 + 33.7750i −0.821827 + 1.42345i 0.0824933 + 0.996592i \(0.473712\pi\)
−0.904320 + 0.426855i \(0.859622\pi\)
\(564\) 17.3205 30.0000i 0.729325 1.26323i
\(565\) −16.4545 + 9.50000i −0.692245 + 0.399668i
\(566\) 62.0000i 2.60605i
\(567\) 18.0000i 0.755929i
\(568\) 0 0
\(569\) −15.0000 25.9808i −0.628833 1.08917i −0.987786 0.155815i \(-0.950200\pi\)
0.358954 0.933355i \(-0.383134\pi\)
\(570\) 13.8564 24.0000i 0.580381 1.00525i
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) 43.1769 2.78461i 1.80532 0.116430i
\(573\) 32.9090i 1.37479i
\(574\) −6.92820 + 4.00000i −0.289178 + 0.166957i
\(575\) −1.00000 −0.0417029
\(576\) 12.0000 + 20.7846i 0.500000 + 0.866025i
\(577\) 28.0000i 1.16566i −0.812596 0.582828i \(-0.801946\pi\)
0.812596 0.582828i \(-0.198054\pi\)
\(578\) −27.7128 + 16.0000i −1.15270 + 0.665512i
\(579\) 3.46410 + 6.00000i 0.143963 + 0.249351i
\(580\) −3.46410 2.00000i −0.143839 0.0830455i
\(581\) 0 0
\(582\) −30.0000 + 17.3205i −1.24354 + 0.717958i
\(583\) −46.7654 + 27.0000i −1.93682 + 1.11823i
\(584\) 0 0
\(585\) 10.7942 0.696152i 0.446286 0.0287824i
\(586\) 12.0000 0.495715
\(587\) −24.2487 + 14.0000i −1.00085 + 0.577842i −0.908500 0.417885i \(-0.862772\pi\)
−0.0923513 + 0.995726i \(0.529438\pi\)
\(588\) 10.3923i 0.428571i
\(589\) −32.0000 + 55.4256i −1.31854 + 2.28377i
\(590\) −10.3923 6.00000i −0.427844 0.247016i
\(591\) −17.3205 + 30.0000i −0.712470 + 1.23404i
\(592\) −6.92820 + 4.00000i −0.284747 + 0.164399i
\(593\) 16.0000i 0.657041i 0.944497 + 0.328521i \(0.106550\pi\)
−0.944497 + 0.328521i \(0.893450\pi\)
\(594\) −54.0000 31.1769i −2.21565 1.27920i
\(595\) −2.00000 −0.0819920
\(596\) −3.46410 + 2.00000i −0.141895 + 0.0819232i
\(597\) 4.50000 + 2.59808i 0.184173 + 0.106332i
\(598\) 7.19615 0.464102i 0.294273 0.0189785i
\(599\) −3.50000 + 6.06218i −0.143006 + 0.247694i −0.928627 0.371014i \(-0.879010\pi\)
0.785621 + 0.618708i \(0.212344\pi\)
\(600\) 0 0
\(601\) −2.50000 4.33013i −0.101977 0.176630i 0.810522 0.585708i \(-0.199184\pi\)
−0.912499 + 0.409079i \(0.865850\pi\)
\(602\) −20.0000 −0.815139
\(603\) 0 0
\(604\) 8.00000i 0.325515i
\(605\) 21.6506 12.5000i 0.880223 0.508197i
\(606\) −12.1244 21.0000i −0.492518 0.853067i
\(607\) 5.50000 9.52628i 0.223238 0.386660i −0.732551 0.680712i \(-0.761671\pi\)
0.955789 + 0.294052i \(0.0950039\pi\)
\(608\) 32.0000 55.4256i 1.29777 2.24781i
\(609\) −3.46410 6.00000i −0.140372 0.243132i
\(610\) 5.00000 + 8.66025i 0.202444 + 0.350643i
\(611\) −20.0000 30.0000i −0.809113 1.21367i
\(612\) −6.00000 −0.242536
\(613\) 28.0000i 1.13091i −0.824779 0.565455i \(-0.808701\pi\)
0.824779 0.565455i \(-0.191299\pi\)
\(614\) 4.00000 + 6.92820i 0.161427 + 0.279600i
\(615\) 3.46410i 0.139686i
\(616\) 0 0
\(617\) 1.73205 + 1.00000i 0.0697297 + 0.0402585i 0.534460 0.845194i \(-0.320515\pi\)
−0.464730 + 0.885453i \(0.653849\pi\)
\(618\) −27.7128 + 48.0000i −1.11477 + 1.93084i
\(619\) 8.66025 5.00000i 0.348085 0.200967i −0.315757 0.948840i \(-0.602258\pi\)
0.663842 + 0.747873i \(0.268925\pi\)
\(620\) −16.0000 −0.642575
\(621\) −4.50000 2.59808i −0.180579 0.104257i
\(622\) 16.0000i 0.641542i
\(623\) 0 0
\(624\) 24.9282 1.60770i 0.997927 0.0643593i
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) 17.3205 + 10.0000i 0.692267 + 0.399680i
\(627\) 83.1384i 3.32023i
\(628\) −13.0000 22.5167i −0.518756 0.898513i
\(629\) 2.00000i 0.0797452i
\(630\) 10.3923 + 6.00000i 0.414039 + 0.239046i
\(631\) 2.00000i 0.0796187i −0.999207 0.0398094i \(-0.987325\pi\)
0.999207 0.0398094i \(-0.0126751\pi\)
\(632\) 0 0
\(633\) 22.5000 12.9904i 0.894295 0.516321i
\(634\) 26.0000 45.0333i 1.03259 1.78850i
\(635\) 0 0
\(636\) 27.0000 15.5885i 1.07062 0.618123i
\(637\) 9.69615 + 4.79423i 0.384176 + 0.189954i
\(638\) 24.0000 0.950169
\(639\) −25.9808 + 15.0000i −1.02778 + 0.593391i
\(640\) 0 0
\(641\) 3.00000 + 5.19615i 0.118493 + 0.205236i 0.919171 0.393860i \(-0.128860\pi\)
−0.800678 + 0.599095i \(0.795527\pi\)
\(642\) 58.8897 2.32419
\(643\) −27.7128 16.0000i −1.09289 0.630978i −0.158543 0.987352i \(-0.550680\pi\)
−0.934344 + 0.356374i \(0.884013\pi\)
\(644\) 3.46410 + 2.00000i 0.136505 + 0.0788110i
\(645\) 4.33013 7.50000i 0.170499 0.295312i
\(646\) 8.00000 + 13.8564i 0.314756 + 0.545173i
\(647\) −17.0000 −0.668339 −0.334169 0.942513i \(-0.608456\pi\)
−0.334169 + 0.942513i \(0.608456\pi\)
\(648\) 0 0
\(649\) 36.0000 1.41312
\(650\) 3.19615 6.46410i 0.125363 0.253543i
\(651\) −24.0000 13.8564i −0.940634 0.543075i
\(652\) 0 0
\(653\) −17.0000 + 29.4449i −0.665261 + 1.15227i 0.313953 + 0.949439i \(0.398347\pi\)
−0.979214 + 0.202828i \(0.934987\pi\)
\(654\) 69.2820i 2.70914i
\(655\) −12.9904 + 7.50000i −0.507576 + 0.293049i
\(656\) 8.00000i 0.312348i
\(657\) 10.3923 6.00000i 0.405442 0.234082i
\(658\) 40.0000i 1.55936i
\(659\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(660\) −18.0000 + 10.3923i −0.700649 + 0.404520i
\(661\) 1.73205 + 1.00000i 0.0673690 + 0.0388955i 0.533306 0.845922i \(-0.320949\pi\)
−0.465937 + 0.884818i \(0.654283\pi\)
\(662\) 8.00000 13.8564i 0.310929 0.538545i
\(663\) −2.76795 + 5.59808i −0.107498 + 0.217411i
\(664\) 0 0
\(665\) 16.0000i 0.620453i
\(666\) −6.00000 + 10.3923i −0.232495 + 0.402694i
\(667\) 2.00000 0.0774403
\(668\) −3.46410 + 2.00000i −0.134030 + 0.0773823i
\(669\) −24.2487 −0.937509
\(670\) 0 0
\(671\) −25.9808 15.0000i −1.00298 0.579069i
\(672\) 24.0000 + 13.8564i 0.925820 + 0.534522i
\(673\) −15.5000 26.8468i −0.597481 1.03487i −0.993192 0.116492i \(-0.962835\pi\)
0.395711 0.918375i \(-0.370498\pi\)
\(674\) 6.00000i 0.231111i
\(675\) −4.50000 + 2.59808i −0.173205 + 0.100000i
\(676\) −10.0000 + 24.0000i −0.384615 + 0.923077i
\(677\) 3.00000 + 5.19615i 0.115299 + 0.199704i 0.917899 0.396813i \(-0.129884\pi\)
−0.802600 + 0.596518i \(0.796551\pi\)
\(678\) −32.9090 + 57.0000i −1.26386 + 2.18907i
\(679\) −10.0000 + 17.3205i −0.383765 + 0.664700i
\(680\) 0 0
\(681\) 0 0
\(682\) 83.1384 48.0000i 3.18354 1.83801i
\(683\) 34.0000i 1.30097i 0.759517 + 0.650487i \(0.225435\pi\)
−0.759517 + 0.650487i \(0.774565\pi\)
\(684\) 48.0000i 1.83533i
\(685\) 6.00000 0.229248
\(686\) 20.0000 + 34.6410i 0.763604 + 1.32260i
\(687\) 22.5167 + 39.0000i 0.859064 + 1.48794i
\(688\) 10.0000 17.3205i 0.381246 0.660338i
\(689\) −2.08846 32.3827i −0.0795639 1.23368i
\(690\) −3.00000 + 1.73205i −0.114208 + 0.0659380i
\(691\) 8.66025 5.00000i 0.329452 0.190209i −0.326146 0.945319i \(-0.605750\pi\)
0.655598 + 0.755110i \(0.272417\pi\)
\(692\) −26.0000 −0.988372
\(693\) −36.0000 −1.36753
\(694\) 10.0000i 0.379595i
\(695\) 9.52628 5.50000i 0.361352 0.208627i
\(696\) 0 0
\(697\) 1.73205 + 1.00000i 0.0656061 + 0.0378777i
\(698\) 2.00000 3.46410i 0.0757011 0.131118i
\(699\) −28.5000 16.4545i −1.07797 0.622366i
\(700\) 3.46410 2.00000i 0.130931 0.0755929i
\(701\) −39.0000 −1.47301 −0.736505 0.676432i \(-0.763525\pi\)
−0.736505 + 0.676432i \(0.763525\pi\)
\(702\) 31.1769 20.7846i 1.17670 0.784465i
\(703\) 16.0000 0.603451
\(704\) −41.5692 + 24.0000i −1.56670 + 0.904534i
\(705\) 15.0000 + 8.66025i 0.564933 + 0.326164i
\(706\) 6.00000 10.3923i 0.225813 0.391120i
\(707\) −12.1244 7.00000i −0.455983 0.263262i
\(708\) −20.7846 −0.781133
\(709\) 6.92820 4.00000i 0.260194 0.150223i −0.364229 0.931309i \(-0.618667\pi\)
0.624423 + 0.781086i \(0.285334\pi\)
\(710\) 20.0000i 0.750587i
\(711\) 1.50000 2.59808i 0.0562544 0.0974355i
\(712\) 0 0
\(713\) 6.92820 4.00000i 0.259463 0.149801i
\(714\) −6.00000 + 3.46410i −0.224544 + 0.129641i
\(715\) 1.39230 + 21.5885i 0.0520692 + 0.807363i
\(716\) 15.0000 25.9808i 0.560576 0.970947i
\(717\) 17.3205 + 30.0000i 0.646846 + 1.12037i
\(718\) −10.0000 17.3205i −0.373197 0.646396i
\(719\) −36.0000 −1.34257 −0.671287 0.741198i \(-0.734258\pi\)
−0.671287 + 0.741198i \(0.734258\pi\)
\(720\) −10.3923 + 6.00000i −0.387298 + 0.223607i
\(721\) 32.0000i 1.19174i
\(722\) −77.9423 + 45.0000i −2.90071 + 1.67473i
\(723\) 51.9615 1.93247
\(724\) 21.0000 36.3731i 0.780459 1.35179i
\(725\) 1.00000 1.73205i 0.0371391 0.0643268i
\(726\) 43.3013 75.0000i 1.60706 2.78351i
\(727\) 18.5000 + 32.0429i 0.686127 + 1.18841i 0.973081 + 0.230463i \(0.0740239\pi\)
−0.286954 + 0.957944i \(0.592643\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 8.00000i 0.296093i
\(731\) 2.50000 + 4.33013i 0.0924658 + 0.160156i
\(732\) 15.0000 + 8.66025i 0.554416 + 0.320092i
\(733\) 20.7846 + 12.0000i 0.767697 + 0.443230i 0.832052 0.554697i \(-0.187166\pi\)
−0.0643554 + 0.997927i \(0.520499\pi\)
\(734\) −36.3731 21.0000i −1.34255 0.775124i
\(735\) −5.19615 −0.191663
\(736\) −6.92820 + 4.00000i −0.255377 + 0.147442i
\(737\) 0 0
\(738\) −6.00000 10.3923i −0.220863 0.382546i
\(739\) 12.0000i 0.441427i −0.975339 0.220714i \(-0.929161\pi\)
0.975339 0.220714i \(-0.0708386\pi\)
\(740\) 2.00000 + 3.46410i 0.0735215 + 0.127343i
\(741\) −44.7846 22.1436i −1.64520 0.813465i
\(742\) 18.0000 31.1769i 0.660801 1.14454i
\(743\) −38.1051 22.0000i −1.39794 0.807102i −0.403764 0.914863i \(-0.632298\pi\)
−0.994177 + 0.107761i \(0.965632\pi\)
\(744\) 0 0
\(745\) −1.00000 1.73205i −0.0366372 0.0634574i
\(746\) 38.0000i 1.39128i
\(747\) 0 0
\(748\) 12.0000i 0.438763i
\(749\) 29.4449 17.0000i 1.07589 0.621166i
\(750\) 3.46410i 0.126491i
\(751\) 16.0000 27.7128i 0.583848 1.01125i −0.411170 0.911559i \(-0.634880\pi\)
0.995018 0.0996961i \(-0.0317870\pi\)
\(752\) 34.6410 + 20.0000i 1.26323 + 0.729325i
\(753\) 4.50000 + 2.59808i 0.163989 + 0.0946792i
\(754\) −6.39230 + 12.9282i −0.232794 + 0.470817i
\(755\) 4.00000 0.145575
\(756\) 20.7846 0.755929
\(757\) 29.0000 1.05402 0.527011 0.849858i \(-0.323312\pi\)
0.527011 + 0.849858i \(0.323312\pi\)
\(758\) 18.0000 + 31.1769i 0.653789 + 1.13240i
\(759\) 5.19615 9.00000i 0.188608 0.326679i
\(760\) 0 0
\(761\) 39.8372 + 23.0000i 1.44410 + 0.833749i 0.998120 0.0612953i \(-0.0195231\pi\)
0.445977 + 0.895045i \(0.352856\pi\)
\(762\) 0 0
\(763\) 20.0000 + 34.6410i 0.724049 + 1.25409i
\(764\) −38.0000 −1.37479
\(765\) 3.00000i 0.108465i
\(766\) −52.0000 −1.87884
\(767\) −9.58846 + 19.3923i −0.346219 + 0.700216i
\(768\) −24.0000 + 13.8564i −0.866025 + 0.500000i
\(769\) 34.6410 + 20.0000i 1.24919 + 0.721218i 0.970947 0.239293i \(-0.0769157\pi\)
0.278240 + 0.960512i \(0.410249\pi\)
\(770\) −12.0000 + 20.7846i −0.432450 + 0.749025i
\(771\) 4.50000 2.59808i 0.162064 0.0935674i
\(772\) 6.92820 4.00000i 0.249351 0.143963i
\(773\) 18.0000i 0.647415i 0.946157 + 0.323708i \(0.104929\pi\)
−0.946157 + 0.323708i \(0.895071\pi\)
\(774\) 30.0000i 1.07833i
\(775\) 8.00000i 0.287368i
\(776\) 0 0
\(777\) 6.92820i 0.248548i
\(778\) 39.8372 + 23.0000i 1.42823 + 0.824590i