Properties

Label 585.2.i.a.196.1
Level $585$
Weight $2$
Character 585.196
Analytic conductor $4.671$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(4.67124851824\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 196.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 585.196
Dual form 585.2.i.a.391.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 3.46410i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{3} +(1.00000 + 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(2.00000 - 3.46410i) q^{7} +(1.50000 - 2.59808i) q^{9} +(3.00000 + 1.73205i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.50000 - 0.866025i) q^{15} +(-2.00000 + 3.46410i) q^{16} -3.00000 q^{17} +2.00000 q^{19} +(1.00000 - 1.73205i) q^{20} -6.92820i q^{21} +(-1.50000 - 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +8.00000 q^{28} +(-3.00000 + 5.19615i) q^{29} +(2.00000 + 3.46410i) q^{31} -4.00000 q^{35} +6.00000 q^{36} +8.00000 q^{37} +(-1.50000 - 0.866025i) q^{39} +(6.00000 + 10.3923i) q^{41} +(0.500000 - 0.866025i) q^{43} -3.00000 q^{45} +6.92820i q^{48} +(-4.50000 - 7.79423i) q^{49} +(-4.50000 + 2.59808i) q^{51} +(1.00000 - 1.73205i) q^{52} -3.00000 q^{53} +(3.00000 - 1.73205i) q^{57} +(-3.00000 - 5.19615i) q^{59} -3.46410i q^{60} +(-5.50000 + 9.52628i) q^{61} +(-6.00000 - 10.3923i) q^{63} -8.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-4.50000 - 2.59808i) q^{69} +6.00000 q^{71} +8.00000 q^{73} +1.73205i q^{75} +(2.00000 + 3.46410i) q^{76} +(3.50000 - 6.06218i) q^{79} +4.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} +(-3.00000 + 5.19615i) q^{83} +(12.0000 - 6.92820i) q^{84} +(1.50000 + 2.59808i) q^{85} +10.3923i q^{87} -18.0000 q^{89} -4.00000 q^{91} +(3.00000 - 5.19615i) q^{92} +(6.00000 + 3.46410i) q^{93} +(-1.00000 - 1.73205i) q^{95} +(-7.00000 + 12.1244i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 3 q^{3} + 2 q^{4} - q^{5} + 4 q^{7} + 3 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 3 q^{3} + 2 q^{4} - q^{5} + 4 q^{7} + 3 q^{9} + 6 q^{12} - q^{13} - 3 q^{15} - 4 q^{16} - 6 q^{17} + 4 q^{19} + 2 q^{20} - 3 q^{23} - q^{25} + 16 q^{28} - 6 q^{29} + 4 q^{31} - 8 q^{35} + 12 q^{36} + 16 q^{37} - 3 q^{39} + 12 q^{41} + q^{43} - 6 q^{45} - 9 q^{49} - 9 q^{51} + 2 q^{52} - 6 q^{53} + 6 q^{57} - 6 q^{59} - 11 q^{61} - 12 q^{63} - 16 q^{64} - q^{65} + 4 q^{67} - 6 q^{68} - 9 q^{69} + 12 q^{71} + 16 q^{73} + 4 q^{76} + 7 q^{79} + 8 q^{80} - 9 q^{81} - 6 q^{83} + 24 q^{84} + 3 q^{85} - 36 q^{89} - 8 q^{91} + 6 q^{92} + 12 q^{93} - 2 q^{95} - 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(326\) \(352\) \(496\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(3\) 1.50000 0.866025i 0.866025 0.500000i
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 2.00000 3.46410i 0.755929 1.30931i −0.188982 0.981981i \(-0.560519\pi\)
0.944911 0.327327i \(-0.106148\pi\)
\(8\) 0 0
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) 0 0
\(11\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(12\) 3.00000 + 1.73205i 0.866025 + 0.500000i
\(13\) −0.500000 0.866025i −0.138675 0.240192i
\(14\) 0 0
\(15\) −1.50000 0.866025i −0.387298 0.223607i
\(16\) −2.00000 + 3.46410i −0.500000 + 0.866025i
\(17\) −3.00000 −0.727607 −0.363803 0.931476i \(-0.618522\pi\)
−0.363803 + 0.931476i \(0.618522\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) 6.92820i 1.51186i
\(22\) 0 0
\(23\) −1.50000 2.59808i −0.312772 0.541736i 0.666190 0.745782i \(-0.267924\pi\)
−0.978961 + 0.204046i \(0.934591\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 8.00000 1.51186
\(29\) −3.00000 + 5.19615i −0.557086 + 0.964901i 0.440652 + 0.897678i \(0.354747\pi\)
−0.997738 + 0.0672232i \(0.978586\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.00000 −0.676123
\(36\) 6.00000 1.00000
\(37\) 8.00000 1.31519 0.657596 0.753371i \(-0.271573\pi\)
0.657596 + 0.753371i \(0.271573\pi\)
\(38\) 0 0
\(39\) −1.50000 0.866025i −0.240192 0.138675i
\(40\) 0 0
\(41\) 6.00000 + 10.3923i 0.937043 + 1.62301i 0.770950 + 0.636895i \(0.219782\pi\)
0.166092 + 0.986110i \(0.446885\pi\)
\(42\) 0 0
\(43\) 0.500000 0.866025i 0.0762493 0.132068i −0.825380 0.564578i \(-0.809039\pi\)
0.901629 + 0.432511i \(0.142372\pi\)
\(44\) 0 0
\(45\) −3.00000 −0.447214
\(46\) 0 0
\(47\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) 6.92820i 1.00000i
\(49\) −4.50000 7.79423i −0.642857 1.11346i
\(50\) 0 0
\(51\) −4.50000 + 2.59808i −0.630126 + 0.363803i
\(52\) 1.00000 1.73205i 0.138675 0.240192i
\(53\) −3.00000 −0.412082 −0.206041 0.978543i \(-0.566058\pi\)
−0.206041 + 0.978543i \(0.566058\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 3.00000 1.73205i 0.397360 0.229416i
\(58\) 0 0
\(59\) −3.00000 5.19615i −0.390567 0.676481i 0.601958 0.798528i \(-0.294388\pi\)
−0.992524 + 0.122047i \(0.961054\pi\)
\(60\) 3.46410i 0.447214i
\(61\) −5.50000 + 9.52628i −0.704203 + 1.21972i 0.262776 + 0.964857i \(0.415362\pi\)
−0.966978 + 0.254858i \(0.917971\pi\)
\(62\) 0 0
\(63\) −6.00000 10.3923i −0.755929 1.30931i
\(64\) −8.00000 −1.00000
\(65\) −0.500000 + 0.866025i −0.0620174 + 0.107417i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) −4.50000 2.59808i −0.541736 0.312772i
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 8.00000 0.936329 0.468165 0.883641i \(-0.344915\pi\)
0.468165 + 0.883641i \(0.344915\pi\)
\(74\) 0 0
\(75\) 1.73205i 0.200000i
\(76\) 2.00000 + 3.46410i 0.229416 + 0.397360i
\(77\) 0 0
\(78\) 0 0
\(79\) 3.50000 6.06218i 0.393781 0.682048i −0.599164 0.800626i \(-0.704500\pi\)
0.992945 + 0.118578i \(0.0378336\pi\)
\(80\) 4.00000 0.447214
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) 0 0
\(83\) −3.00000 + 5.19615i −0.329293 + 0.570352i −0.982372 0.186938i \(-0.940144\pi\)
0.653079 + 0.757290i \(0.273477\pi\)
\(84\) 12.0000 6.92820i 1.30931 0.755929i
\(85\) 1.50000 + 2.59808i 0.162698 + 0.281801i
\(86\) 0 0
\(87\) 10.3923i 1.11417i
\(88\) 0 0
\(89\) −18.0000 −1.90800 −0.953998 0.299813i \(-0.903076\pi\)
−0.953998 + 0.299813i \(0.903076\pi\)
\(90\) 0 0
\(91\) −4.00000 −0.419314
\(92\) 3.00000 5.19615i 0.312772 0.541736i
\(93\) 6.00000 + 3.46410i 0.622171 + 0.359211i
\(94\) 0 0
\(95\) −1.00000 1.73205i −0.102598 0.177705i
\(96\) 0 0
\(97\) −7.00000 + 12.1244i −0.710742 + 1.23104i 0.253837 + 0.967247i \(0.418307\pi\)
−0.964579 + 0.263795i \(0.915026\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −2.00000 −0.200000
\(101\) 7.50000 12.9904i 0.746278 1.29259i −0.203317 0.979113i \(-0.565172\pi\)
0.949595 0.313478i \(-0.101494\pi\)
\(102\) 0 0
\(103\) 2.00000 + 3.46410i 0.197066 + 0.341328i 0.947576 0.319531i \(-0.103525\pi\)
−0.750510 + 0.660859i \(0.770192\pi\)
\(104\) 0 0
\(105\) −6.00000 + 3.46410i −0.585540 + 0.338062i
\(106\) 0 0
\(107\) −3.00000 −0.290021 −0.145010 0.989430i \(-0.546322\pi\)
−0.145010 + 0.989430i \(0.546322\pi\)
\(108\) 9.00000 5.19615i 0.866025 0.500000i
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 0 0
\(111\) 12.0000 6.92820i 1.13899 0.657596i
\(112\) 8.00000 + 13.8564i 0.755929 + 1.30931i
\(113\) −1.50000 2.59808i −0.141108 0.244406i 0.786806 0.617200i \(-0.211733\pi\)
−0.927914 + 0.372794i \(0.878400\pi\)
\(114\) 0 0
\(115\) −1.50000 + 2.59808i −0.139876 + 0.242272i
\(116\) −12.0000 −1.11417
\(117\) −3.00000 −0.277350
\(118\) 0 0
\(119\) −6.00000 + 10.3923i −0.550019 + 0.952661i
\(120\) 0 0
\(121\) 5.50000 + 9.52628i 0.500000 + 0.866025i
\(122\) 0 0
\(123\) 18.0000 + 10.3923i 1.62301 + 0.937043i
\(124\) −4.00000 + 6.92820i −0.359211 + 0.622171i
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0 0
\(129\) 1.73205i 0.152499i
\(130\) 0 0
\(131\) 10.5000 + 18.1865i 0.917389 + 1.58896i 0.803365 + 0.595487i \(0.203041\pi\)
0.114024 + 0.993478i \(0.463626\pi\)
\(132\) 0 0
\(133\) 4.00000 6.92820i 0.346844 0.600751i
\(134\) 0 0
\(135\) −4.50000 + 2.59808i −0.387298 + 0.223607i
\(136\) 0 0
\(137\) −3.00000 + 5.19615i −0.256307 + 0.443937i −0.965250 0.261329i \(-0.915839\pi\)
0.708942 + 0.705266i \(0.249173\pi\)
\(138\) 0 0
\(139\) −2.50000 4.33013i −0.212047 0.367277i 0.740308 0.672268i \(-0.234680\pi\)
−0.952355 + 0.304991i \(0.901346\pi\)
\(140\) −4.00000 6.92820i −0.338062 0.585540i
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) 6.00000 + 10.3923i 0.500000 + 0.866025i
\(145\) 6.00000 0.498273
\(146\) 0 0
\(147\) −13.5000 7.79423i −1.11346 0.642857i
\(148\) 8.00000 + 13.8564i 0.657596 + 1.13899i
\(149\) −9.00000 15.5885i −0.737309 1.27706i −0.953703 0.300750i \(-0.902763\pi\)
0.216394 0.976306i \(-0.430570\pi\)
\(150\) 0 0
\(151\) 11.0000 19.0526i 0.895167 1.55048i 0.0615699 0.998103i \(-0.480389\pi\)
0.833597 0.552372i \(-0.186277\pi\)
\(152\) 0 0
\(153\) −4.50000 + 7.79423i −0.363803 + 0.630126i
\(154\) 0 0
\(155\) 2.00000 3.46410i 0.160644 0.278243i
\(156\) 3.46410i 0.277350i
\(157\) 6.50000 + 11.2583i 0.518756 + 0.898513i 0.999762 + 0.0217953i \(0.00693820\pi\)
−0.481006 + 0.876717i \(0.659728\pi\)
\(158\) 0 0
\(159\) −4.50000 + 2.59808i −0.356873 + 0.206041i
\(160\) 0 0
\(161\) −12.0000 −0.945732
\(162\) 0 0
\(163\) −16.0000 −1.25322 −0.626608 0.779334i \(-0.715557\pi\)
−0.626608 + 0.779334i \(0.715557\pi\)
\(164\) −12.0000 + 20.7846i −0.937043 + 1.62301i
\(165\) 0 0
\(166\) 0 0
\(167\) −6.00000 10.3923i −0.464294 0.804181i 0.534875 0.844931i \(-0.320359\pi\)
−0.999169 + 0.0407502i \(0.987025\pi\)
\(168\) 0 0
\(169\) −0.500000 + 0.866025i −0.0384615 + 0.0666173i
\(170\) 0 0
\(171\) 3.00000 5.19615i 0.229416 0.397360i
\(172\) 2.00000 0.152499
\(173\) −7.50000 + 12.9904i −0.570214 + 0.987640i 0.426329 + 0.904568i \(0.359807\pi\)
−0.996544 + 0.0830722i \(0.973527\pi\)
\(174\) 0 0
\(175\) 2.00000 + 3.46410i 0.151186 + 0.261861i
\(176\) 0 0
\(177\) −9.00000 5.19615i −0.676481 0.390567i
\(178\) 0 0
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) −3.00000 5.19615i −0.223607 0.387298i
\(181\) −25.0000 −1.85824 −0.929118 0.369784i \(-0.879432\pi\)
−0.929118 + 0.369784i \(0.879432\pi\)
\(182\) 0 0
\(183\) 19.0526i 1.40841i
\(184\) 0 0
\(185\) −4.00000 6.92820i −0.294086 0.509372i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −18.0000 10.3923i −1.30931 0.755929i
\(190\) 0 0
\(191\) −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i \(-0.867950\pi\)
0.806641 + 0.591041i \(0.201283\pi\)
\(192\) −12.0000 + 6.92820i −0.866025 + 0.500000i
\(193\) 2.00000 + 3.46410i 0.143963 + 0.249351i 0.928986 0.370116i \(-0.120682\pi\)
−0.785022 + 0.619467i \(0.787349\pi\)
\(194\) 0 0
\(195\) 1.73205i 0.124035i
\(196\) 9.00000 15.5885i 0.642857 1.11346i
\(197\) 12.0000 0.854965 0.427482 0.904024i \(-0.359401\pi\)
0.427482 + 0.904024i \(0.359401\pi\)
\(198\) 0 0
\(199\) −7.00000 −0.496217 −0.248108 0.968732i \(-0.579809\pi\)
−0.248108 + 0.968732i \(0.579809\pi\)
\(200\) 0 0
\(201\) 6.00000 + 3.46410i 0.423207 + 0.244339i
\(202\) 0 0
\(203\) 12.0000 + 20.7846i 0.842235 + 1.45879i
\(204\) −9.00000 5.19615i −0.630126 0.363803i
\(205\) 6.00000 10.3923i 0.419058 0.725830i
\(206\) 0 0
\(207\) −9.00000 −0.625543
\(208\) 4.00000 0.277350
\(209\) 0 0
\(210\) 0 0
\(211\) −2.50000 4.33013i −0.172107 0.298098i 0.767049 0.641588i \(-0.221724\pi\)
−0.939156 + 0.343490i \(0.888391\pi\)
\(212\) −3.00000 5.19615i −0.206041 0.356873i
\(213\) 9.00000 5.19615i 0.616670 0.356034i
\(214\) 0 0
\(215\) −1.00000 −0.0681994
\(216\) 0 0
\(217\) 16.0000 1.08615
\(218\) 0 0
\(219\) 12.0000 6.92820i 0.810885 0.468165i
\(220\) 0 0
\(221\) 1.50000 + 2.59808i 0.100901 + 0.174766i
\(222\) 0 0
\(223\) 11.0000 19.0526i 0.736614 1.27585i −0.217397 0.976083i \(-0.569757\pi\)
0.954011 0.299770i \(-0.0969101\pi\)
\(224\) 0 0
\(225\) 1.50000 + 2.59808i 0.100000 + 0.173205i
\(226\) 0 0
\(227\) 6.00000 10.3923i 0.398234 0.689761i −0.595274 0.803523i \(-0.702957\pi\)
0.993508 + 0.113761i \(0.0362899\pi\)
\(228\) 6.00000 + 3.46410i 0.397360 + 0.229416i
\(229\) −1.00000 1.73205i −0.0660819 0.114457i 0.831092 0.556136i \(-0.187717\pi\)
−0.897173 + 0.441679i \(0.854383\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 27.0000 1.76883 0.884414 0.466702i \(-0.154558\pi\)
0.884414 + 0.466702i \(0.154558\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 6.00000 10.3923i 0.390567 0.676481i
\(237\) 12.1244i 0.787562i
\(238\) 0 0
\(239\) 9.00000 + 15.5885i 0.582162 + 1.00833i 0.995223 + 0.0976302i \(0.0311262\pi\)
−0.413061 + 0.910703i \(0.635540\pi\)
\(240\) 6.00000 3.46410i 0.387298 0.223607i
\(241\) 5.00000 8.66025i 0.322078 0.557856i −0.658838 0.752285i \(-0.728952\pi\)
0.980917 + 0.194429i \(0.0622852\pi\)
\(242\) 0 0
\(243\) −13.5000 7.79423i −0.866025 0.500000i
\(244\) −22.0000 −1.40841
\(245\) −4.50000 + 7.79423i −0.287494 + 0.497955i
\(246\) 0 0
\(247\) −1.00000 1.73205i −0.0636285 0.110208i
\(248\) 0 0
\(249\) 10.3923i 0.658586i
\(250\) 0 0
\(251\) −27.0000 −1.70422 −0.852112 0.523359i \(-0.824679\pi\)
−0.852112 + 0.523359i \(0.824679\pi\)
\(252\) 12.0000 20.7846i 0.755929 1.30931i
\(253\) 0 0
\(254\) 0 0
\(255\) 4.50000 + 2.59808i 0.281801 + 0.162698i
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −1.50000 2.59808i −0.0935674 0.162064i 0.815442 0.578838i \(-0.196494\pi\)
−0.909010 + 0.416775i \(0.863160\pi\)
\(258\) 0 0
\(259\) 16.0000 27.7128i 0.994192 1.72199i
\(260\) −2.00000 −0.124035
\(261\) 9.00000 + 15.5885i 0.557086 + 0.964901i
\(262\) 0 0
\(263\) 1.50000 2.59808i 0.0924940 0.160204i −0.816066 0.577959i \(-0.803849\pi\)
0.908560 + 0.417755i \(0.137183\pi\)
\(264\) 0 0
\(265\) 1.50000 + 2.59808i 0.0921443 + 0.159599i
\(266\) 0 0
\(267\) −27.0000 + 15.5885i −1.65237 + 0.953998i
\(268\) −4.00000 + 6.92820i −0.244339 + 0.423207i
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) 20.0000 1.21491 0.607457 0.794353i \(-0.292190\pi\)
0.607457 + 0.794353i \(0.292190\pi\)
\(272\) 6.00000 10.3923i 0.363803 0.630126i
\(273\) −6.00000 + 3.46410i −0.363137 + 0.209657i
\(274\) 0 0
\(275\) 0 0
\(276\) 10.3923i 0.625543i
\(277\) 11.0000 19.0526i 0.660926 1.14476i −0.319447 0.947604i \(-0.603497\pi\)
0.980373 0.197153i \(-0.0631696\pi\)
\(278\) 0 0
\(279\) 12.0000 0.718421
\(280\) 0 0
\(281\) 6.00000 10.3923i 0.357930 0.619953i −0.629685 0.776851i \(-0.716816\pi\)
0.987615 + 0.156898i \(0.0501493\pi\)
\(282\) 0 0
\(283\) 6.50000 + 11.2583i 0.386385 + 0.669238i 0.991960 0.126550i \(-0.0403903\pi\)
−0.605575 + 0.795788i \(0.707057\pi\)
\(284\) 6.00000 + 10.3923i 0.356034 + 0.616670i
\(285\) −3.00000 1.73205i −0.177705 0.102598i
\(286\) 0 0
\(287\) 48.0000 2.83335
\(288\) 0 0
\(289\) −8.00000 −0.470588
\(290\) 0 0
\(291\) 24.2487i 1.42148i
\(292\) 8.00000 + 13.8564i 0.468165 + 0.810885i
\(293\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(294\) 0 0
\(295\) −3.00000 + 5.19615i −0.174667 + 0.302532i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −1.50000 + 2.59808i −0.0867472 + 0.150251i
\(300\) −3.00000 + 1.73205i −0.173205 + 0.100000i
\(301\) −2.00000 3.46410i −0.115278 0.199667i
\(302\) 0 0
\(303\) 25.9808i 1.49256i
\(304\) −4.00000 + 6.92820i −0.229416 + 0.397360i
\(305\) 11.0000 0.629858
\(306\) 0 0
\(307\) −4.00000 −0.228292 −0.114146 0.993464i \(-0.536413\pi\)
−0.114146 + 0.993464i \(0.536413\pi\)
\(308\) 0 0
\(309\) 6.00000 + 3.46410i 0.341328 + 0.197066i
\(310\) 0 0
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 0 0
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) 0 0
\(315\) −6.00000 + 10.3923i −0.338062 + 0.585540i
\(316\) 14.0000 0.787562
\(317\) 15.0000 25.9808i 0.842484 1.45922i −0.0453045 0.998973i \(-0.514426\pi\)
0.887788 0.460252i \(-0.152241\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 4.00000 + 6.92820i 0.223607 + 0.387298i
\(321\) −4.50000 + 2.59808i −0.251166 + 0.145010i
\(322\) 0 0
\(323\) −6.00000 −0.333849
\(324\) 9.00000 15.5885i 0.500000 0.866025i
\(325\) 1.00000 0.0554700
\(326\) 0 0
\(327\) −15.0000 + 8.66025i −0.829502 + 0.478913i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −10.0000 + 17.3205i −0.549650 + 0.952021i 0.448649 + 0.893708i \(0.351905\pi\)
−0.998298 + 0.0583130i \(0.981428\pi\)
\(332\) −12.0000 −0.658586
\(333\) 12.0000 20.7846i 0.657596 1.13899i
\(334\) 0 0
\(335\) 2.00000 3.46410i 0.109272 0.189264i
\(336\) 24.0000 + 13.8564i 1.30931 + 0.755929i
\(337\) −2.50000 4.33013i −0.136184 0.235877i 0.789865 0.613280i \(-0.210150\pi\)
−0.926049 + 0.377403i \(0.876817\pi\)
\(338\) 0 0
\(339\) −4.50000 2.59808i −0.244406 0.141108i
\(340\) −3.00000 + 5.19615i −0.162698 + 0.281801i
\(341\) 0 0
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 5.19615i 0.279751i
\(346\) 0 0
\(347\) −7.50000 12.9904i −0.402621 0.697360i 0.591420 0.806363i \(-0.298567\pi\)
−0.994041 + 0.109003i \(0.965234\pi\)
\(348\) −18.0000 + 10.3923i −0.964901 + 0.557086i
\(349\) 5.00000 8.66025i 0.267644 0.463573i −0.700609 0.713545i \(-0.747088\pi\)
0.968253 + 0.249973i \(0.0804216\pi\)
\(350\) 0 0
\(351\) −4.50000 + 2.59808i −0.240192 + 0.138675i
\(352\) 0 0
\(353\) 12.0000 20.7846i 0.638696 1.10625i −0.347024 0.937856i \(-0.612808\pi\)
0.985719 0.168397i \(-0.0538590\pi\)
\(354\) 0 0
\(355\) −3.00000 5.19615i −0.159223 0.275783i
\(356\) −18.0000 31.1769i −0.953998 1.65237i
\(357\) 20.7846i 1.10004i
\(358\) 0 0
\(359\) 18.0000 0.950004 0.475002 0.879985i \(-0.342447\pi\)
0.475002 + 0.879985i \(0.342447\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) 0 0
\(363\) 16.5000 + 9.52628i 0.866025 + 0.500000i
\(364\) −4.00000 6.92820i −0.209657 0.363137i
\(365\) −4.00000 6.92820i −0.209370 0.362639i
\(366\) 0 0
\(367\) −8.50000 + 14.7224i −0.443696 + 0.768505i −0.997960 0.0638362i \(-0.979666\pi\)
0.554264 + 0.832341i \(0.313000\pi\)
\(368\) 12.0000 0.625543
\(369\) 36.0000 1.87409
\(370\) 0 0
\(371\) −6.00000 + 10.3923i −0.311504 + 0.539542i
\(372\) 13.8564i 0.718421i
\(373\) −17.5000 30.3109i −0.906116 1.56944i −0.819413 0.573204i \(-0.805700\pi\)
−0.0867031 0.996234i \(-0.527633\pi\)
\(374\) 0 0
\(375\) 1.50000 0.866025i 0.0774597 0.0447214i
\(376\) 0 0
\(377\) 6.00000 0.309016
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 2.00000 3.46410i 0.102598 0.177705i
\(381\) −24.0000 + 13.8564i −1.22956 + 0.709885i
\(382\) 0 0
\(383\) 12.0000 + 20.7846i 0.613171 + 1.06204i 0.990702 + 0.136047i \(0.0434398\pi\)
−0.377531 + 0.925997i \(0.623227\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −1.50000 2.59808i −0.0762493 0.132068i
\(388\) −28.0000 −1.42148
\(389\) 4.50000 7.79423i 0.228159 0.395183i −0.729103 0.684403i \(-0.760063\pi\)
0.957263 + 0.289220i \(0.0933960\pi\)
\(390\) 0 0
\(391\) 4.50000 + 7.79423i 0.227575 + 0.394171i
\(392\) 0 0
\(393\) 31.5000 + 18.1865i 1.58896 + 0.917389i
\(394\) 0 0
\(395\) −7.00000 −0.352208
\(396\) 0 0
\(397\) −4.00000 −0.200754 −0.100377 0.994949i \(-0.532005\pi\)
−0.100377 + 0.994949i \(0.532005\pi\)
\(398\) 0 0
\(399\) 13.8564i 0.693688i
\(400\) −2.00000 3.46410i −0.100000 0.173205i
\(401\) −9.00000 15.5885i −0.449439 0.778450i 0.548911 0.835881i \(-0.315043\pi\)
−0.998350 + 0.0574304i \(0.981709\pi\)
\(402\) 0 0
\(403\) 2.00000 3.46410i 0.0996271 0.172559i
\(404\) 30.0000 1.49256
\(405\) −4.50000 + 7.79423i −0.223607 + 0.387298i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −16.0000 27.7128i −0.791149 1.37031i −0.925256 0.379344i \(-0.876150\pi\)
0.134107 0.990967i \(-0.457183\pi\)
\(410\) 0 0
\(411\) 10.3923i 0.512615i
\(412\) −4.00000 + 6.92820i −0.197066 + 0.341328i
\(413\) −24.0000 −1.18096
\(414\) 0 0
\(415\) 6.00000 0.294528
\(416\) 0 0
\(417\) −7.50000 4.33013i −0.367277 0.212047i
\(418\) 0 0
\(419\) −7.50000 12.9904i −0.366399 0.634622i 0.622601 0.782540i \(-0.286076\pi\)
−0.989000 + 0.147918i \(0.952743\pi\)
\(420\) −12.0000 6.92820i −0.585540 0.338062i
\(421\) −1.00000 + 1.73205i −0.0487370 + 0.0844150i −0.889365 0.457198i \(-0.848853\pi\)
0.840628 + 0.541613i \(0.182186\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 1.50000 2.59808i 0.0727607 0.126025i
\(426\) 0 0
\(427\) 22.0000 + 38.1051i 1.06465 + 1.84404i
\(428\) −3.00000 5.19615i −0.145010 0.251166i
\(429\) 0 0
\(430\) 0 0
\(431\) 24.0000 1.15604 0.578020 0.816023i \(-0.303826\pi\)
0.578020 + 0.816023i \(0.303826\pi\)
\(432\) 18.0000 + 10.3923i 0.866025 + 0.500000i
\(433\) −37.0000 −1.77811 −0.889053 0.457804i \(-0.848636\pi\)
−0.889053 + 0.457804i \(0.848636\pi\)
\(434\) 0 0
\(435\) 9.00000 5.19615i 0.431517 0.249136i
\(436\) −10.0000 17.3205i −0.478913 0.829502i
\(437\) −3.00000 5.19615i −0.143509 0.248566i
\(438\) 0 0
\(439\) 6.50000 11.2583i 0.310228 0.537331i −0.668184 0.743996i \(-0.732928\pi\)
0.978412 + 0.206666i \(0.0662612\pi\)
\(440\) 0 0
\(441\) −27.0000 −1.28571
\(442\) 0 0
\(443\) −4.50000 + 7.79423i −0.213801 + 0.370315i −0.952901 0.303281i \(-0.901918\pi\)
0.739100 + 0.673596i \(0.235251\pi\)
\(444\) 24.0000 + 13.8564i 1.13899 + 0.657596i
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) 0 0
\(447\) −27.0000 15.5885i −1.27706 0.737309i
\(448\) −16.0000 + 27.7128i −0.755929 + 1.30931i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 3.00000 5.19615i 0.141108 0.244406i
\(453\) 38.1051i 1.79033i
\(454\) 0 0
\(455\) 2.00000 + 3.46410i 0.0937614 + 0.162400i
\(456\) 0 0
\(457\) −4.00000 + 6.92820i −0.187112 + 0.324088i −0.944286 0.329125i \(-0.893246\pi\)
0.757174 + 0.653213i \(0.226579\pi\)
\(458\) 0 0
\(459\) 15.5885i 0.727607i
\(460\) −6.00000 −0.279751
\(461\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(462\) 0 0
\(463\) −13.0000 22.5167i −0.604161 1.04644i −0.992183 0.124788i \(-0.960175\pi\)
0.388022 0.921650i \(-0.373158\pi\)
\(464\) −12.0000 20.7846i −0.557086 0.964901i
\(465\) 6.92820i 0.321288i
\(466\) 0 0
\(467\) −3.00000 −0.138823 −0.0694117 0.997588i \(-0.522112\pi\)
−0.0694117 + 0.997588i \(0.522112\pi\)
\(468\) −3.00000 5.19615i −0.138675 0.240192i
\(469\) 16.0000 0.738811
\(470\) 0 0
\(471\) 19.5000 + 11.2583i 0.898513 + 0.518756i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) −1.00000 + 1.73205i −0.0458831 + 0.0794719i
\(476\) −24.0000 −1.10004
\(477\) −4.50000 + 7.79423i −0.206041 + 0.356873i
\(478\) 0 0
\(479\) −3.00000 + 5.19615i −0.137073 + 0.237418i −0.926388 0.376571i \(-0.877103\pi\)
0.789314 + 0.613990i \(0.210436\pi\)
\(480\) 0 0
\(481\) −4.00000 6.92820i −0.182384 0.315899i
\(482\) 0 0
\(483\) −18.0000 + 10.3923i −0.819028 + 0.472866i
\(484\) −11.0000 + 19.0526i −0.500000 + 0.866025i
\(485\) 14.0000 0.635707
\(486\) 0 0
\(487\) 38.0000 1.72194 0.860972 0.508652i \(-0.169856\pi\)
0.860972 + 0.508652i \(0.169856\pi\)
\(488\) 0 0
\(489\) −24.0000 + 13.8564i −1.08532 + 0.626608i
\(490\) 0 0
\(491\) 18.0000 + 31.1769i 0.812329 + 1.40699i 0.911230 + 0.411897i \(0.135134\pi\)
−0.0989017 + 0.995097i \(0.531533\pi\)
\(492\) 41.5692i 1.87409i
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) 0 0
\(495\) 0 0
\(496\) −16.0000 −0.718421
\(497\) 12.0000 20.7846i 0.538274 0.932317i
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 1.00000 + 1.73205i 0.0447214 + 0.0774597i
\(501\) −18.0000 10.3923i −0.804181 0.464294i
\(502\) 0 0
\(503\) −33.0000 −1.47140 −0.735699 0.677309i \(-0.763146\pi\)
−0.735699 + 0.677309i \(0.763146\pi\)
\(504\) 0 0
\(505\) −15.0000 −0.667491
\(506\) 0 0
\(507\) 1.73205i 0.0769231i
\(508\) −16.0000 27.7128i −0.709885 1.22956i
\(509\) 15.0000 + 25.9808i 0.664863 + 1.15158i 0.979322 + 0.202306i \(0.0648436\pi\)
−0.314459 + 0.949271i \(0.601823\pi\)
\(510\) 0 0
\(511\) 16.0000 27.7128i 0.707798 1.22594i
\(512\) 0 0
\(513\) 10.3923i 0.458831i
\(514\) 0 0
\(515\) 2.00000 3.46410i 0.0881305 0.152647i
\(516\) 3.00000 1.73205i 0.132068 0.0762493i
\(517\) 0 0
\(518\) 0 0
\(519\) 25.9808i 1.14043i
\(520\) 0 0
\(521\) 6.00000 0.262865 0.131432 0.991325i \(-0.458042\pi\)
0.131432 + 0.991325i \(0.458042\pi\)
\(522\) 0 0
\(523\) −28.0000 −1.22435 −0.612177 0.790721i \(-0.709706\pi\)
−0.612177 + 0.790721i \(0.709706\pi\)
\(524\) −21.0000 + 36.3731i −0.917389 + 1.58896i
\(525\) 6.00000 + 3.46410i 0.261861 + 0.151186i
\(526\) 0 0
\(527\) −6.00000 10.3923i −0.261364 0.452696i
\(528\) 0 0
\(529\) 7.00000 12.1244i 0.304348 0.527146i
\(530\) 0 0
\(531\) −18.0000 −0.781133
\(532\) 16.0000 0.693688
\(533\) 6.00000 10.3923i 0.259889 0.450141i
\(534\) 0 0
\(535\) 1.50000 + 2.59808i 0.0648507 + 0.112325i
\(536\) 0 0
\(537\) 13.5000 7.79423i 0.582568 0.336346i
\(538\) 0 0
\(539\) 0 0
\(540\) −9.00000 5.19615i −0.387298 0.223607i
\(541\) 20.0000 0.859867 0.429934 0.902861i \(-0.358537\pi\)
0.429934 + 0.902861i \(0.358537\pi\)
\(542\) 0 0
\(543\) −37.5000 + 21.6506i −1.60928 + 0.929118i
\(544\) 0 0
\(545\) 5.00000 + 8.66025i 0.214176 + 0.370965i
\(546\) 0 0
\(547\) 20.0000 34.6410i 0.855138 1.48114i −0.0213785 0.999771i \(-0.506805\pi\)
0.876517 0.481371i \(-0.159861\pi\)
\(548\) −12.0000 −0.512615
\(549\) 16.5000 + 28.5788i 0.704203 + 1.21972i
\(550\) 0 0
\(551\) −6.00000 + 10.3923i −0.255609 + 0.442727i
\(552\) 0 0
\(553\) −14.0000 24.2487i −0.595341 1.03116i
\(554\) 0 0
\(555\) −12.0000 6.92820i −0.509372 0.294086i
\(556\) 5.00000 8.66025i 0.212047 0.367277i
\(557\) 6.00000 0.254228 0.127114 0.991888i \(-0.459429\pi\)
0.127114 + 0.991888i \(0.459429\pi\)
\(558\) 0 0
\(559\) −1.00000 −0.0422955
\(560\) 8.00000 13.8564i 0.338062 0.585540i
\(561\) 0 0
\(562\) 0 0
\(563\) 19.5000 + 33.7750i 0.821827 + 1.42345i 0.904320 + 0.426855i \(0.140378\pi\)
−0.0824933 + 0.996592i \(0.526288\pi\)
\(564\) 0 0
\(565\) −1.50000 + 2.59808i −0.0631055 + 0.109302i
\(566\) 0 0
\(567\) −36.0000 −1.51186
\(568\) 0 0
\(569\) −21.0000 + 36.3731i −0.880366 + 1.52484i −0.0294311 + 0.999567i \(0.509370\pi\)
−0.850935 + 0.525271i \(0.823964\pi\)
\(570\) 0 0
\(571\) 14.0000 + 24.2487i 0.585882 + 1.01478i 0.994765 + 0.102190i \(0.0325850\pi\)
−0.408883 + 0.912587i \(0.634082\pi\)
\(572\) 0 0
\(573\) 5.19615i 0.217072i
\(574\) 0 0
\(575\) 3.00000 0.125109
\(576\) −12.0000 + 20.7846i −0.500000 + 0.866025i
\(577\) −28.0000 −1.16566 −0.582828 0.812596i \(-0.698054\pi\)
−0.582828 + 0.812596i \(0.698054\pi\)
\(578\) 0 0
\(579\) 6.00000 + 3.46410i 0.249351 + 0.143963i
\(580\) 6.00000 + 10.3923i 0.249136 + 0.431517i
\(581\) 12.0000 + 20.7846i 0.497844 + 0.862291i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 1.50000 + 2.59808i 0.0620174 + 0.107417i
\(586\) 0 0
\(587\) −9.00000 + 15.5885i −0.371470 + 0.643404i −0.989792 0.142520i \(-0.954479\pi\)
0.618322 + 0.785925i \(0.287813\pi\)
\(588\) 31.1769i 1.28571i
\(589\) 4.00000 + 6.92820i 0.164817 + 0.285472i
\(590\) 0 0
\(591\) 18.0000 10.3923i 0.740421 0.427482i
\(592\) −16.0000 + 27.7128i −0.657596 + 1.13899i
\(593\) 30.0000 1.23195 0.615976 0.787765i \(-0.288762\pi\)
0.615976 + 0.787765i \(0.288762\pi\)
\(594\) 0 0
\(595\) 12.0000 0.491952
\(596\) 18.0000 31.1769i 0.737309 1.27706i
\(597\) −10.5000 + 6.06218i −0.429736 + 0.248108i
\(598\) 0 0
\(599\) 16.5000 + 28.5788i 0.674172 + 1.16770i 0.976710 + 0.214563i \(0.0688326\pi\)
−0.302539 + 0.953137i \(0.597834\pi\)
\(600\) 0 0
\(601\) −14.5000 + 25.1147i −0.591467 + 1.02445i 0.402568 + 0.915390i \(0.368118\pi\)
−0.994035 + 0.109061i \(0.965216\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 44.0000 1.79033
\(605\) 5.50000 9.52628i 0.223607 0.387298i
\(606\) 0 0
\(607\) 3.50000 + 6.06218i 0.142061 + 0.246056i 0.928272 0.371901i \(-0.121294\pi\)
−0.786212 + 0.617957i \(0.787961\pi\)
\(608\) 0 0
\(609\) 36.0000 + 20.7846i 1.45879 + 0.842235i
\(610\) 0 0
\(611\) 0 0
\(612\) −18.0000 −0.727607
\(613\) 26.0000 1.05013 0.525065 0.851062i \(-0.324041\pi\)
0.525065 + 0.851062i \(0.324041\pi\)
\(614\) 0 0
\(615\) 20.7846i 0.838116i
\(616\) 0 0
\(617\) −3.00000 5.19615i −0.120775 0.209189i 0.799298 0.600935i \(-0.205205\pi\)
−0.920074 + 0.391745i \(0.871871\pi\)
\(618\) 0 0
\(619\) 5.00000 8.66025i 0.200967 0.348085i −0.747873 0.663842i \(-0.768925\pi\)
0.948840 + 0.315757i \(0.102258\pi\)
\(620\) 8.00000 0.321288
\(621\) −13.5000 + 7.79423i −0.541736 + 0.312772i
\(622\) 0 0
\(623\) −36.0000 + 62.3538i −1.44231 + 2.49815i
\(624\) 6.00000 3.46410i 0.240192 0.138675i
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) −13.0000 + 22.5167i −0.518756 + 0.898513i
\(629\) −24.0000 −0.956943
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 0 0
\(633\) −7.50000 4.33013i −0.298098 0.172107i
\(634\) 0 0
\(635\) 8.00000 + 13.8564i 0.317470 + 0.549875i
\(636\) −9.00000 5.19615i −0.356873 0.206041i
\(637\) −4.50000 + 7.79423i −0.178296 + 0.308819i
\(638\) 0 0
\(639\) 9.00000 15.5885i 0.356034 0.616670i
\(640\) 0 0
\(641\) 21.0000 36.3731i 0.829450 1.43665i −0.0690201 0.997615i \(-0.521987\pi\)
0.898470 0.439034i \(-0.144679\pi\)
\(642\) 0 0
\(643\) 11.0000 + 19.0526i 0.433798 + 0.751360i 0.997197 0.0748254i \(-0.0238399\pi\)
−0.563399 + 0.826185i \(0.690507\pi\)
\(644\) −12.0000 20.7846i −0.472866 0.819028i
\(645\) −1.50000 + 0.866025i −0.0590624 + 0.0340997i
\(646\) 0 0
\(647\) 9.00000 0.353827 0.176913 0.984226i \(-0.443389\pi\)
0.176913 + 0.984226i \(0.443389\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 24.0000 13.8564i 0.940634 0.543075i
\(652\) −16.0000 27.7128i −0.626608 1.08532i
\(653\) −15.0000 25.9808i −0.586995 1.01671i −0.994623 0.103558i \(-0.966977\pi\)
0.407628 0.913148i \(-0.366356\pi\)
\(654\) 0 0
\(655\) 10.5000 18.1865i 0.410269 0.710607i
\(656\) −48.0000 −1.87409
\(657\) 12.0000 20.7846i 0.468165 0.810885i
\(658\) 0 0
\(659\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) 11.0000 + 19.0526i 0.427850 + 0.741059i 0.996682 0.0813955i \(-0.0259377\pi\)
−0.568831 + 0.822454i \(0.692604\pi\)
\(662\) 0 0
\(663\) 4.50000 + 2.59808i 0.174766 + 0.100901i
\(664\) 0 0
\(665\) −8.00000 −0.310227
\(666\) 0 0
\(667\) 18.0000 0.696963
\(668\) 12.0000 20.7846i 0.464294 0.804181i
\(669\) 38.1051i 1.47323i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 3.50000 6.06218i 0.134915 0.233680i −0.790650 0.612268i \(-0.790257\pi\)
0.925565 + 0.378589i \(0.123591\pi\)
\(674\) 0 0
\(675\) 4.50000 + 2.59808i 0.173205 + 0.100000i
\(676\) −2.00000 −0.0769231
\(677\) −21.0000 + 36.3731i −0.807096 + 1.39793i 0.107772 + 0.994176i \(0.465628\pi\)
−0.914867 + 0.403755i \(0.867705\pi\)
\(678\) 0 0
\(679\) 28.0000 + 48.4974i 1.07454 + 1.86116i
\(680\) 0 0
\(681\) 20.7846i 0.796468i
\(682\) 0 0
\(683\) −36.0000 −1.37750 −0.688751 0.724998i \(-0.741841\pi\)
−0.688751 + 0.724998i \(0.741841\pi\)
\(684\) 12.0000 0.458831
\(685\) 6.00000 0.229248
\(686\) 0 0
\(687\) −3.00000 1.73205i −0.114457 0.0660819i
\(688\) 2.00000 + 3.46410i 0.0762493 + 0.132068i
\(689\) 1.50000 + 2.59808i 0.0571454 + 0.0989788i
\(690\) 0 0
\(691\) −22.0000 + 38.1051i −0.836919 + 1.44959i 0.0555386 + 0.998457i \(0.482312\pi\)
−0.892458 + 0.451130i \(0.851021\pi\)
\(692\) −30.0000 −1.14043
\(693\) 0 0
\(694\) 0 0
\(695\) −2.50000 + 4.33013i −0.0948304 + 0.164251i
\(696\) 0 0
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) 0 0
\(699\) 40.5000 23.3827i 1.53185 0.884414i
\(700\) −4.00000 + 6.92820i −0.151186 + 0.261861i
\(701\) 27.0000 1.01978 0.509888 0.860241i \(-0.329687\pi\)
0.509888 + 0.860241i \(0.329687\pi\)
\(702\) 0 0
\(703\) 16.0000 0.603451
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −30.0000 51.9615i −1.12827 1.95421i
\(708\) 20.7846i 0.781133i
\(709\) −1.00000 + 1.73205i −0.0375558 + 0.0650485i −0.884192 0.467123i \(-0.845291\pi\)
0.846637 + 0.532172i \(0.178624\pi\)
\(710\) 0 0
\(711\) −10.5000 18.1865i −0.393781 0.682048i
\(712\) 0 0
\(713\) 6.00000 10.3923i 0.224702 0.389195i
\(714\) 0 0
\(715\) 0 0
\(716\) 9.00000 + 15.5885i 0.336346 + 0.582568i
\(717\) 27.0000 + 15.5885i 1.00833 + 0.582162i
\(718\) 0 0
\(719\) 24.0000 0.895049 0.447524 0.894272i \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 6.00000 10.3923i 0.223607 0.387298i
\(721\) 16.0000 0.595871
\(722\) 0 0
\(723\) 17.3205i 0.644157i
\(724\) −25.0000 43.3013i −0.929118 1.60928i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 0 0
\(727\) 15.5000 26.8468i 0.574863 0.995692i −0.421193 0.906971i \(-0.638389\pi\)
0.996056 0.0887213i \(-0.0282781\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 0 0
\(731\) −1.50000 + 2.59808i −0.0554795 + 0.0960933i
\(732\) −33.0000 + 19.0526i −1.21972 + 0.704203i
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) 0 0
\(735\) 15.5885i 0.574989i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) −34.0000 −1.25071 −0.625355 0.780340i \(-0.715046\pi\)
−0.625355 + 0.780340i \(0.715046\pi\)
\(740\) 8.00000 13.8564i 0.294086 0.509372i
\(741\) −3.00000 1.73205i −0.110208 0.0636285i
\(742\) 0 0
\(743\) −21.0000 36.3731i −0.770415 1.33440i −0.937336 0.348428i \(-0.886716\pi\)
0.166920 0.985970i \(-0.446618\pi\)
\(744\) 0 0
\(745\) −9.00000 + 15.5885i −0.329734 + 0.571117i
\(746\) 0 0
\(747\) 9.00000 + 15.5885i 0.329293 + 0.570352i
\(748\) 0 0
\(749\) −6.00000 + 10.3923i −0.219235 + 0.379727i
\(750\) 0 0
\(751\) 8.00000 + 13.8564i 0.291924 + 0.505627i 0.974265 0.225407i \(-0.0723712\pi\)
−0.682341 + 0.731034i \(0.739038\pi\)
\(752\) 0 0
\(753\) −40.5000 + 23.3827i −1.47590 + 0.852112i
\(754\) 0 0
\(755\) −22.0000 −0.800662
\(756\) 41.5692i 1.51186i
\(757\) −19.0000 −0.690567 −0.345283 0.938498i \(-0.612217\pi\)
−0.345283 + 0.938498i \(0.612217\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −6.00000 10.3923i −0.217500 0.376721i 0.736543 0.676391i \(-0.236457\pi\)
−0.954043 + 0.299670i \(0.903123\pi\)
\(762\) 0 0
\(763\) −20.0000 + 34.6410i −0.724049 + 1.25409i
\(764\) −6.00000 −0.217072
\(765\) 9.00000 0.325396
\(766\) 0 0
\(767\) −3.00000 + 5.19615i −0.108324 + 0.187622i
\(768\) −24.0000 13.8564i −0.866025 0.500000i
\(769\) −16.0000 27.7128i −0.576975 0.999350i −0.995824 0.0912938i \(-0.970900\pi\)
0.418849 0.908056i \(-0.362434\pi\)
\(770\) 0 0
\(771\) −4.50000 2.59808i −0.162064 0.0935674i
\(772\) −4.00000 + 6.92820i −0.143963 + 0.249351i
\(773\) −18.0000 −0.647415 −0.323708 0.946157i \(-0.604929\pi\)
−0.323708 + 0.946157i \(0.604929\pi\)
\(774\) 0 0
\(775\) −4.00000 −0.143684
\(776\) 0 0
\(777\) 55.4256i 1.98838i
\(778\) 0 0
\(779\) 12.0000 + 20.7846i 0.429945 + 0.744686i
\(780\) −3.00000 + 1.73205i −0.107417 + 0.0620174i
\(781\) 0 0
\(782\) 0 0
\(783\) 27.0000 + 15.5885i 0.964901 + 0.557086i
\(784\) 36.0000 1.28571
\(785\) 6.50000 11.2583i 0.231995 0.401827i
\(786\) 0 0
\(787\) 23.0000 + 39.8372i 0.819861 + 1.42004i 0.905784 + 0.423740i \(0.139283\pi\)
−0.0859225 + 0.996302i \(0.527384\pi\)
\(788\) 12.0000 + 20.7846i 0.427482 + 0.740421i
\(789\) 5.19615i 0.184988i
\(790\) 0 0