Properties

Label 735.2.s.b.656.1
Level 735
Weight 2
Character 735.656
Analytic conductor 5.869
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 735.s (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.86900454856\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 105)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 656.1
Root \(0.500000 - 0.866025i\) of \(x^{2} - x + 1\)
Character \(\chi\) \(=\) 735.656
Dual form 735.2.s.b.521.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -3.00000 q^{6} +1.73205i q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.50000 - 0.866025i) q^{2} +(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -3.00000 q^{6} +1.73205i q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.50000 + 0.866025i) q^{10} +(-3.00000 + 1.73205i) q^{11} +(1.50000 + 0.866025i) q^{12} -1.73205i q^{15} +(2.50000 - 4.33013i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(-4.50000 + 2.59808i) q^{18} +(-3.00000 - 1.73205i) q^{19} +1.00000 q^{20} +6.00000 q^{22} +(-3.00000 - 1.73205i) q^{23} +(1.50000 + 2.59808i) q^{24} +(-0.500000 - 0.866025i) q^{25} -5.19615i q^{27} -6.92820i q^{29} +(-1.50000 + 2.59808i) q^{30} +(-3.00000 + 1.73205i) q^{31} +(-4.50000 + 2.59808i) q^{32} +(-3.00000 + 5.19615i) q^{33} +10.3923i q^{34} +3.00000 q^{36} +(1.00000 - 1.73205i) q^{37} +(3.00000 + 5.19615i) q^{38} +(1.50000 + 0.866025i) q^{40} +6.00000 q^{41} -8.00000 q^{43} +(-3.00000 - 1.73205i) q^{44} +(-1.50000 - 2.59808i) q^{45} +(3.00000 + 5.19615i) q^{46} +(6.00000 - 10.3923i) q^{47} -8.66025i q^{48} +1.73205i q^{50} +(-9.00000 - 5.19615i) q^{51} +(-4.50000 + 7.79423i) q^{54} +3.46410i q^{55} -6.00000 q^{57} +(-6.00000 + 10.3923i) q^{58} +(6.00000 + 10.3923i) q^{59} +(1.50000 - 0.866025i) q^{60} +(6.00000 + 3.46410i) q^{61} +6.00000 q^{62} -1.00000 q^{64} +(9.00000 - 5.19615i) q^{66} +(-4.00000 - 6.92820i) q^{67} +(3.00000 - 5.19615i) q^{68} -6.00000 q^{69} +3.46410i q^{71} +(4.50000 + 2.59808i) q^{72} +(6.00000 - 3.46410i) q^{73} +(-3.00000 + 1.73205i) q^{74} +(-1.50000 - 0.866025i) q^{75} -3.46410i q^{76} +(-4.00000 + 6.92820i) q^{79} +(-2.50000 - 4.33013i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-9.00000 - 5.19615i) q^{82} -6.00000 q^{85} +(12.0000 + 6.92820i) q^{86} +(-6.00000 - 10.3923i) q^{87} +(-3.00000 - 5.19615i) q^{88} +(-3.00000 + 5.19615i) q^{89} +5.19615i q^{90} -3.46410i q^{92} +(-3.00000 + 5.19615i) q^{93} +(-18.0000 + 10.3923i) q^{94} +(-3.00000 + 1.73205i) q^{95} +(-4.50000 + 7.79423i) q^{96} +6.92820i q^{97} +10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{2} + 3q^{3} + q^{4} + q^{5} - 6q^{6} + 3q^{9} + O(q^{10}) \) \( 2q - 3q^{2} + 3q^{3} + q^{4} + q^{5} - 6q^{6} + 3q^{9} - 3q^{10} - 6q^{11} + 3q^{12} + 5q^{16} - 6q^{17} - 9q^{18} - 6q^{19} + 2q^{20} + 12q^{22} - 6q^{23} + 3q^{24} - q^{25} - 3q^{30} - 6q^{31} - 9q^{32} - 6q^{33} + 6q^{36} + 2q^{37} + 6q^{38} + 3q^{40} + 12q^{41} - 16q^{43} - 6q^{44} - 3q^{45} + 6q^{46} + 12q^{47} - 18q^{51} - 9q^{54} - 12q^{57} - 12q^{58} + 12q^{59} + 3q^{60} + 12q^{61} + 12q^{62} - 2q^{64} + 18q^{66} - 8q^{67} + 6q^{68} - 12q^{69} + 9q^{72} + 12q^{73} - 6q^{74} - 3q^{75} - 8q^{79} - 5q^{80} - 9q^{81} - 18q^{82} - 12q^{85} + 24q^{86} - 12q^{87} - 6q^{88} - 6q^{89} - 6q^{93} - 36q^{94} - 6q^{95} - 9q^{96} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

\(n\) \(346\) \(442\) \(491\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 0.866025i −1.06066 0.612372i −0.135045 0.990839i \(-0.543118\pi\)
−0.925615 + 0.378467i \(0.876451\pi\)
\(3\) 1.50000 0.866025i 0.866025 0.500000i
\(4\) 0.500000 + 0.866025i 0.250000 + 0.433013i
\(5\) 0.500000 0.866025i 0.223607 0.387298i
\(6\) −3.00000 −1.22474
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −1.50000 + 0.866025i −0.474342 + 0.273861i
\(11\) −3.00000 + 1.73205i −0.904534 + 0.522233i −0.878668 0.477432i \(-0.841568\pi\)
−0.0258656 + 0.999665i \(0.508234\pi\)
\(12\) 1.50000 + 0.866025i 0.433013 + 0.250000i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 1.73205i 0.447214i
\(16\) 2.50000 4.33013i 0.625000 1.08253i
\(17\) −3.00000 5.19615i −0.727607 1.26025i −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) −4.50000 + 2.59808i −1.06066 + 0.612372i
\(19\) −3.00000 1.73205i −0.688247 0.397360i 0.114708 0.993399i \(-0.463407\pi\)
−0.802955 + 0.596040i \(0.796740\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 6.00000 1.27920
\(23\) −3.00000 1.73205i −0.625543 0.361158i 0.153481 0.988152i \(-0.450952\pi\)
−0.779024 + 0.626994i \(0.784285\pi\)
\(24\) 1.50000 + 2.59808i 0.306186 + 0.530330i
\(25\) −0.500000 0.866025i −0.100000 0.173205i
\(26\) 0 0
\(27\) 5.19615i 1.00000i
\(28\) 0 0
\(29\) 6.92820i 1.28654i −0.765641 0.643268i \(-0.777578\pi\)
0.765641 0.643268i \(-0.222422\pi\)
\(30\) −1.50000 + 2.59808i −0.273861 + 0.474342i
\(31\) −3.00000 + 1.73205i −0.538816 + 0.311086i −0.744599 0.667512i \(-0.767359\pi\)
0.205783 + 0.978598i \(0.434026\pi\)
\(32\) −4.50000 + 2.59808i −0.795495 + 0.459279i
\(33\) −3.00000 + 5.19615i −0.522233 + 0.904534i
\(34\) 10.3923i 1.78227i
\(35\) 0 0
\(36\) 3.00000 0.500000
\(37\) 1.00000 1.73205i 0.164399 0.284747i −0.772043 0.635571i \(-0.780765\pi\)
0.936442 + 0.350823i \(0.114098\pi\)
\(38\) 3.00000 + 5.19615i 0.486664 + 0.842927i
\(39\) 0 0
\(40\) 1.50000 + 0.866025i 0.237171 + 0.136931i
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) −8.00000 −1.21999 −0.609994 0.792406i \(-0.708828\pi\)
−0.609994 + 0.792406i \(0.708828\pi\)
\(44\) −3.00000 1.73205i −0.452267 0.261116i
\(45\) −1.50000 2.59808i −0.223607 0.387298i
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) 6.00000 10.3923i 0.875190 1.51587i 0.0186297 0.999826i \(-0.494070\pi\)
0.856560 0.516047i \(-0.172597\pi\)
\(48\) 8.66025i 1.25000i
\(49\) 0 0
\(50\) 1.73205i 0.244949i
\(51\) −9.00000 5.19615i −1.26025 0.727607i
\(52\) 0 0
\(53\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(54\) −4.50000 + 7.79423i −0.612372 + 1.06066i
\(55\) 3.46410i 0.467099i
\(56\) 0 0
\(57\) −6.00000 −0.794719
\(58\) −6.00000 + 10.3923i −0.787839 + 1.36458i
\(59\) 6.00000 + 10.3923i 0.781133 + 1.35296i 0.931282 + 0.364299i \(0.118692\pi\)
−0.150148 + 0.988663i \(0.547975\pi\)
\(60\) 1.50000 0.866025i 0.193649 0.111803i
\(61\) 6.00000 + 3.46410i 0.768221 + 0.443533i 0.832240 0.554416i \(-0.187058\pi\)
−0.0640184 + 0.997949i \(0.520392\pi\)
\(62\) 6.00000 0.762001
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 9.00000 5.19615i 1.10782 0.639602i
\(67\) −4.00000 6.92820i −0.488678 0.846415i 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) 3.00000 5.19615i 0.363803 0.630126i
\(69\) −6.00000 −0.722315
\(70\) 0 0
\(71\) 3.46410i 0.411113i 0.978645 + 0.205557i \(0.0659005\pi\)
−0.978645 + 0.205557i \(0.934100\pi\)
\(72\) 4.50000 + 2.59808i 0.530330 + 0.306186i
\(73\) 6.00000 3.46410i 0.702247 0.405442i −0.105937 0.994373i \(-0.533784\pi\)
0.808184 + 0.588930i \(0.200451\pi\)
\(74\) −3.00000 + 1.73205i −0.348743 + 0.201347i
\(75\) −1.50000 0.866025i −0.173205 0.100000i
\(76\) 3.46410i 0.397360i
\(77\) 0 0
\(78\) 0 0
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) −2.50000 4.33013i −0.279508 0.484123i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −9.00000 5.19615i −0.993884 0.573819i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) 12.0000 + 6.92820i 1.29399 + 0.747087i
\(87\) −6.00000 10.3923i −0.643268 1.11417i
\(88\) −3.00000 5.19615i −0.319801 0.553912i
\(89\) −3.00000 + 5.19615i −0.317999 + 0.550791i −0.980071 0.198650i \(-0.936344\pi\)
0.662071 + 0.749441i \(0.269678\pi\)
\(90\) 5.19615i 0.547723i
\(91\) 0 0
\(92\) 3.46410i 0.361158i
\(93\) −3.00000 + 5.19615i −0.311086 + 0.538816i
\(94\) −18.0000 + 10.3923i −1.85656 + 1.07188i
\(95\) −3.00000 + 1.73205i −0.307794 + 0.177705i
\(96\) −4.50000 + 7.79423i −0.459279 + 0.795495i
\(97\) 6.92820i 0.703452i 0.936103 + 0.351726i \(0.114405\pi\)
−0.936103 + 0.351726i \(0.885595\pi\)
\(98\) 0 0
\(99\) 10.3923i 1.04447i
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 9.00000 + 15.5885i 0.891133 + 1.54349i
\(103\) 3.00000 + 1.73205i 0.295599 + 0.170664i 0.640464 0.767988i \(-0.278742\pi\)
−0.344865 + 0.938652i \(0.612075\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.00000 5.19615i −0.870063 0.502331i −0.00269372 0.999996i \(-0.500857\pi\)
−0.867369 + 0.497665i \(0.834191\pi\)
\(108\) 4.50000 2.59808i 0.433013 0.250000i
\(109\) 1.00000 + 1.73205i 0.0957826 + 0.165900i 0.909935 0.414751i \(-0.136131\pi\)
−0.814152 + 0.580651i \(0.802798\pi\)
\(110\) 3.00000 5.19615i 0.286039 0.495434i
\(111\) 3.46410i 0.328798i
\(112\) 0 0
\(113\) 6.92820i 0.651751i −0.945413 0.325875i \(-0.894341\pi\)
0.945413 0.325875i \(-0.105659\pi\)
\(114\) 9.00000 + 5.19615i 0.842927 + 0.486664i
\(115\) −3.00000 + 1.73205i −0.279751 + 0.161515i
\(116\) 6.00000 3.46410i 0.557086 0.321634i
\(117\) 0 0
\(118\) 20.7846i 1.91338i
\(119\) 0 0
\(120\) 3.00000 0.273861
\(121\) 0.500000 0.866025i 0.0454545 0.0787296i
\(122\) −6.00000 10.3923i −0.543214 0.940875i
\(123\) 9.00000 5.19615i 0.811503 0.468521i
\(124\) −3.00000 1.73205i −0.269408 0.155543i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −4.00000 −0.354943 −0.177471 0.984126i \(-0.556792\pi\)
−0.177471 + 0.984126i \(0.556792\pi\)
\(128\) 10.5000 + 6.06218i 0.928078 + 0.535826i
\(129\) −12.0000 + 6.92820i −1.05654 + 0.609994i
\(130\) 0 0
\(131\) 6.00000 10.3923i 0.524222 0.907980i −0.475380 0.879781i \(-0.657689\pi\)
0.999602 0.0281993i \(-0.00897729\pi\)
\(132\) −6.00000 −0.522233
\(133\) 0 0
\(134\) 13.8564i 1.19701i
\(135\) −4.50000 2.59808i −0.387298 0.223607i
\(136\) 9.00000 5.19615i 0.771744 0.445566i
\(137\) 18.0000 10.3923i 1.53784 0.887875i 0.538879 0.842383i \(-0.318848\pi\)
0.998965 0.0454914i \(-0.0144854\pi\)
\(138\) 9.00000 + 5.19615i 0.766131 + 0.442326i
\(139\) 17.3205i 1.46911i 0.678551 + 0.734553i \(0.262608\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) 20.7846i 1.75038i
\(142\) 3.00000 5.19615i 0.251754 0.436051i
\(143\) 0 0
\(144\) −7.50000 12.9904i −0.625000 1.08253i
\(145\) −6.00000 3.46410i −0.498273 0.287678i
\(146\) −12.0000 −0.993127
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) −6.00000 3.46410i −0.491539 0.283790i 0.233674 0.972315i \(-0.424925\pi\)
−0.725213 + 0.688525i \(0.758259\pi\)
\(150\) 1.50000 + 2.59808i 0.122474 + 0.212132i
\(151\) 4.00000 + 6.92820i 0.325515 + 0.563809i 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 3.00000 5.19615i 0.243332 0.421464i
\(153\) −18.0000 −1.45521
\(154\) 0 0
\(155\) 3.46410i 0.278243i
\(156\) 0 0
\(157\) 12.0000 6.92820i 0.957704 0.552931i 0.0622385 0.998061i \(-0.480176\pi\)
0.895466 + 0.445130i \(0.146843\pi\)
\(158\) 12.0000 6.92820i 0.954669 0.551178i
\(159\) 0 0
\(160\) 5.19615i 0.410792i
\(161\) 0 0
\(162\) 15.5885i 1.22474i
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) 3.00000 + 5.19615i 0.234261 + 0.405751i
\(165\) 3.00000 + 5.19615i 0.233550 + 0.404520i
\(166\) 0 0
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 9.00000 + 5.19615i 0.690268 + 0.398527i
\(171\) −9.00000 + 5.19615i −0.688247 + 0.397360i
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i \(0.406540\pi\)
−0.973670 + 0.227964i \(0.926793\pi\)
\(174\) 20.7846i 1.57568i
\(175\) 0 0
\(176\) 17.3205i 1.30558i
\(177\) 18.0000 + 10.3923i 1.35296 + 0.781133i
\(178\) 9.00000 5.19615i 0.674579 0.389468i
\(179\) 9.00000 5.19615i 0.672692 0.388379i −0.124404 0.992232i \(-0.539702\pi\)
0.797096 + 0.603853i \(0.206369\pi\)
\(180\) 1.50000 2.59808i 0.111803 0.193649i
\(181\) 20.7846i 1.54491i −0.635071 0.772454i \(-0.719029\pi\)
0.635071 0.772454i \(-0.280971\pi\)
\(182\) 0 0
\(183\) 12.0000 0.887066
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) −1.00000 1.73205i −0.0735215 0.127343i
\(186\) 9.00000 5.19615i 0.659912 0.381000i
\(187\) 18.0000 + 10.3923i 1.31629 + 0.759961i
\(188\) 12.0000 0.875190
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 9.00000 + 5.19615i 0.651217 + 0.375980i 0.788922 0.614493i \(-0.210639\pi\)
−0.137705 + 0.990473i \(0.543973\pi\)
\(192\) −1.50000 + 0.866025i −0.108253 + 0.0625000i
\(193\) 7.00000 + 12.1244i 0.503871 + 0.872730i 0.999990 + 0.00447566i \(0.00142465\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(194\) 6.00000 10.3923i 0.430775 0.746124i
\(195\) 0 0
\(196\) 0 0
\(197\) 13.8564i 0.987228i −0.869681 0.493614i \(-0.835676\pi\)
0.869681 0.493614i \(-0.164324\pi\)
\(198\) 9.00000 15.5885i 0.639602 1.10782i
\(199\) 9.00000 5.19615i 0.637993 0.368345i −0.145848 0.989307i \(-0.546591\pi\)
0.783841 + 0.620962i \(0.213258\pi\)
\(200\) 1.50000 0.866025i 0.106066 0.0612372i
\(201\) −12.0000 6.92820i −0.846415 0.488678i
\(202\) 10.3923i 0.731200i
\(203\) 0 0
\(204\) 10.3923i 0.727607i
\(205\) 3.00000 5.19615i 0.209529 0.362915i
\(206\) −3.00000 5.19615i −0.209020 0.362033i
\(207\) −9.00000 + 5.19615i −0.625543 + 0.361158i
\(208\) 0 0
\(209\) 12.0000 0.830057
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) 3.00000 + 5.19615i 0.205557 + 0.356034i
\(214\) 9.00000 + 15.5885i 0.615227 + 1.06561i
\(215\) −4.00000 + 6.92820i −0.272798 + 0.472500i
\(216\) 9.00000 0.612372
\(217\) 0 0
\(218\) 3.46410i 0.234619i
\(219\) 6.00000 10.3923i 0.405442 0.702247i
\(220\) −3.00000 + 1.73205i −0.202260 + 0.116775i
\(221\) 0 0
\(222\) −3.00000 + 5.19615i −0.201347 + 0.348743i
\(223\) 17.3205i 1.15987i −0.814664 0.579934i \(-0.803079\pi\)
0.814664 0.579934i \(-0.196921\pi\)
\(224\) 0 0
\(225\) −3.00000 −0.200000
\(226\) −6.00000 + 10.3923i −0.399114 + 0.691286i
\(227\) 12.0000 + 20.7846i 0.796468 + 1.37952i 0.921903 + 0.387421i \(0.126634\pi\)
−0.125435 + 0.992102i \(0.540033\pi\)
\(228\) −3.00000 5.19615i −0.198680 0.344124i
\(229\) 6.00000 + 3.46410i 0.396491 + 0.228914i 0.684969 0.728572i \(-0.259816\pi\)
−0.288478 + 0.957487i \(0.593149\pi\)
\(230\) 6.00000 0.395628
\(231\) 0 0
\(232\) 12.0000 0.787839
\(233\) −6.00000 3.46410i −0.393073 0.226941i 0.290418 0.956900i \(-0.406206\pi\)
−0.683491 + 0.729959i \(0.739539\pi\)
\(234\) 0 0
\(235\) −6.00000 10.3923i −0.391397 0.677919i
\(236\) −6.00000 + 10.3923i −0.390567 + 0.676481i
\(237\) 13.8564i 0.900070i
\(238\) 0 0
\(239\) 10.3923i 0.672222i −0.941822 0.336111i \(-0.890888\pi\)
0.941822 0.336111i \(-0.109112\pi\)
\(240\) −7.50000 4.33013i −0.484123 0.279508i
\(241\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(242\) −1.50000 + 0.866025i −0.0964237 + 0.0556702i
\(243\) −13.5000 7.79423i −0.866025 0.500000i
\(244\) 6.92820i 0.443533i
\(245\) 0 0
\(246\) −18.0000 −1.14764
\(247\) 0 0
\(248\) −3.00000 5.19615i −0.190500 0.329956i
\(249\) 0 0
\(250\) 1.50000 + 0.866025i 0.0948683 + 0.0547723i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 12.0000 0.754434
\(254\) 6.00000 + 3.46410i 0.376473 + 0.217357i
\(255\) −9.00000 + 5.19615i −0.563602 + 0.325396i
\(256\) −9.50000 16.4545i −0.593750 1.02841i
\(257\) −3.00000 + 5.19615i −0.187135 + 0.324127i −0.944294 0.329104i \(-0.893253\pi\)
0.757159 + 0.653231i \(0.226587\pi\)
\(258\) 24.0000 1.49417
\(259\) 0 0
\(260\) 0 0
\(261\) −18.0000 10.3923i −1.11417 0.643268i
\(262\) −18.0000 + 10.3923i −1.11204 + 0.642039i
\(263\) −21.0000 + 12.1244i −1.29492 + 0.747620i −0.979521 0.201341i \(-0.935470\pi\)
−0.315394 + 0.948961i \(0.602137\pi\)
\(264\) −9.00000 5.19615i −0.553912 0.319801i
\(265\) 0 0
\(266\) 0 0
\(267\) 10.3923i 0.635999i
\(268\) 4.00000 6.92820i 0.244339 0.423207i
\(269\) −9.00000 15.5885i −0.548740 0.950445i −0.998361 0.0572259i \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) 4.50000 + 7.79423i 0.273861 + 0.474342i
\(271\) −21.0000 12.1244i −1.27566 0.736502i −0.299612 0.954061i \(-0.596857\pi\)
−0.976047 + 0.217559i \(0.930191\pi\)
\(272\) −30.0000 −1.81902
\(273\) 0 0
\(274\) −36.0000 −2.17484
\(275\) 3.00000 + 1.73205i 0.180907 + 0.104447i
\(276\) −3.00000 5.19615i −0.180579 0.312772i
\(277\) −7.00000 12.1244i −0.420589 0.728482i 0.575408 0.817867i \(-0.304843\pi\)
−0.995997 + 0.0893846i \(0.971510\pi\)
\(278\) 15.0000 25.9808i 0.899640 1.55822i
\(279\) 10.3923i 0.622171i
\(280\) 0 0
\(281\) 13.8564i 0.826604i 0.910594 + 0.413302i \(0.135625\pi\)
−0.910594 + 0.413302i \(0.864375\pi\)
\(282\) −18.0000 + 31.1769i −1.07188 + 1.85656i
\(283\) 15.0000 8.66025i 0.891657 0.514799i 0.0171732 0.999853i \(-0.494533\pi\)
0.874484 + 0.485054i \(0.161200\pi\)
\(284\) −3.00000 + 1.73205i −0.178017 + 0.102778i
\(285\) −3.00000 + 5.19615i −0.177705 + 0.307794i
\(286\) 0 0
\(287\) 0 0
\(288\) 15.5885i 0.918559i
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 6.00000 + 10.3923i 0.352332 + 0.610257i
\(291\) 6.00000 + 10.3923i 0.351726 + 0.609208i
\(292\) 6.00000 + 3.46410i 0.351123 + 0.202721i
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 0 0
\(295\) 12.0000 0.698667
\(296\) 3.00000 + 1.73205i 0.174371 + 0.100673i
\(297\) 9.00000 + 15.5885i 0.522233 + 0.904534i
\(298\) 6.00000 + 10.3923i 0.347571 + 0.602010i
\(299\) 0 0
\(300\) 1.73205i 0.100000i
\(301\) 0 0
\(302\) 13.8564i 0.797347i
\(303\) 9.00000 + 5.19615i 0.517036 + 0.298511i
\(304\) −15.0000 + 8.66025i −0.860309 + 0.496700i
\(305\) 6.00000 3.46410i 0.343559 0.198354i
\(306\) 27.0000 + 15.5885i 1.54349 + 0.891133i
\(307\) 24.2487i 1.38395i −0.721923 0.691974i \(-0.756741\pi\)
0.721923 0.691974i \(-0.243259\pi\)
\(308\) 0 0
\(309\) 6.00000 0.341328
\(310\) 3.00000 5.19615i 0.170389 0.295122i
\(311\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(312\) 0 0
\(313\) 18.0000 + 10.3923i 1.01742 + 0.587408i 0.913356 0.407163i \(-0.133482\pi\)
0.104065 + 0.994571i \(0.466815\pi\)
\(314\) −24.0000 −1.35440
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −24.0000 13.8564i −1.34797 0.778253i −0.360012 0.932948i \(-0.617227\pi\)
−0.987962 + 0.154694i \(0.950561\pi\)
\(318\) 0 0
\(319\) 12.0000 + 20.7846i 0.671871 + 1.16371i
\(320\) −0.500000 + 0.866025i −0.0279508 + 0.0484123i
\(321\) −18.0000 −1.00466
\(322\) 0 0
\(323\) 20.7846i 1.15649i
\(324\) 4.50000 7.79423i 0.250000 0.433013i
\(325\) 0 0
\(326\) −24.0000 + 13.8564i −1.32924 + 0.767435i
\(327\) 3.00000 + 1.73205i 0.165900 + 0.0957826i
\(328\) 10.3923i 0.573819i
\(329\) 0 0
\(330\) 10.3923i 0.572078i
\(331\) −14.0000 + 24.2487i −0.769510 + 1.33283i 0.168320 + 0.985732i \(0.446166\pi\)
−0.937829 + 0.347097i \(0.887167\pi\)
\(332\) 0 0
\(333\) −3.00000 5.19615i −0.164399 0.284747i
\(334\) −18.0000 10.3923i −0.984916 0.568642i
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) −14.0000 −0.762629 −0.381314 0.924445i \(-0.624528\pi\)
−0.381314 + 0.924445i \(0.624528\pi\)
\(338\) −19.5000 11.2583i −1.06066 0.612372i
\(339\) −6.00000 10.3923i −0.325875 0.564433i
\(340\) −3.00000 5.19615i −0.162698 0.281801i
\(341\) 6.00000 10.3923i 0.324918 0.562775i
\(342\) 18.0000 0.973329
\(343\) 0 0
\(344\) 13.8564i 0.747087i
\(345\) −3.00000 + 5.19615i −0.161515 + 0.279751i
\(346\) 27.0000 15.5885i 1.45153 0.838041i
\(347\) −15.0000 + 8.66025i −0.805242 + 0.464907i −0.845301 0.534291i \(-0.820579\pi\)
0.0400587 + 0.999197i \(0.487246\pi\)
\(348\) 6.00000 10.3923i 0.321634 0.557086i
\(349\) 6.92820i 0.370858i 0.982658 + 0.185429i \(0.0593675\pi\)
−0.982658 + 0.185429i \(0.940632\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 9.00000 15.5885i 0.479702 0.830868i
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) −18.0000 31.1769i −0.956689 1.65703i
\(355\) 3.00000 + 1.73205i 0.159223 + 0.0919277i
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) −18.0000 −0.951330
\(359\) −3.00000 1.73205i −0.158334 0.0914141i 0.418740 0.908106i \(-0.362472\pi\)
−0.577073 + 0.816692i \(0.695805\pi\)
\(360\) 4.50000 2.59808i 0.237171 0.136931i
\(361\) −3.50000 6.06218i −0.184211 0.319062i
\(362\) −18.0000 + 31.1769i −0.946059 + 1.63862i
\(363\) 1.73205i 0.0909091i
\(364\) 0 0
\(365\) 6.92820i 0.362639i
\(366\) −18.0000 10.3923i −0.940875 0.543214i
\(367\) 9.00000 5.19615i 0.469796 0.271237i −0.246358 0.969179i \(-0.579234\pi\)
0.716154 + 0.697942i \(0.245901\pi\)
\(368\) −15.0000 + 8.66025i −0.781929 + 0.451447i
\(369\) 9.00000 15.5885i 0.468521 0.811503i
\(370\) 3.46410i 0.180090i
\(371\) 0 0
\(372\) −6.00000 −0.311086
\(373\) −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) −18.0000 31.1769i −0.930758 1.61212i
\(375\) −1.50000 + 0.866025i −0.0774597 + 0.0447214i
\(376\) 18.0000 + 10.3923i 0.928279 + 0.535942i
\(377\) 0 0
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) −3.00000 1.73205i −0.153897 0.0888523i
\(381\) −6.00000 + 3.46410i −0.307389 + 0.177471i
\(382\) −9.00000 15.5885i −0.460480 0.797575i
\(383\) −6.00000 + 10.3923i −0.306586 + 0.531022i −0.977613 0.210411i \(-0.932520\pi\)
0.671027 + 0.741433i \(0.265853\pi\)
\(384\) 21.0000 1.07165
\(385\) 0 0
\(386\) 24.2487i 1.23423i
\(387\) −12.0000 + 20.7846i −0.609994 + 1.05654i
\(388\) −6.00000 + 3.46410i −0.304604 + 0.175863i
\(389\) 6.00000 3.46410i 0.304212 0.175637i −0.340121 0.940382i \(-0.610468\pi\)
0.644334 + 0.764745i \(0.277135\pi\)
\(390\) 0 0
\(391\) 20.7846i 1.05112i
\(392\) 0 0
\(393\) 20.7846i 1.04844i
\(394\) −12.0000 + 20.7846i −0.604551 + 1.04711i
\(395\) 4.00000 + 6.92820i 0.201262 + 0.348596i
\(396\) −9.00000 + 5.19615i −0.452267 + 0.261116i
\(397\) −12.0000 6.92820i −0.602263 0.347717i 0.167668 0.985843i \(-0.446376\pi\)
−0.769931 + 0.638127i \(0.779710\pi\)
\(398\) −18.0000 −0.902258
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 24.0000 + 13.8564i 1.19850 + 0.691956i 0.960221 0.279240i \(-0.0900826\pi\)
0.238282 + 0.971196i \(0.423416\pi\)
\(402\) 12.0000 + 20.7846i 0.598506 + 1.03664i
\(403\) 0 0
\(404\) −3.00000 + 5.19615i −0.149256 + 0.258518i
\(405\) −9.00000 −0.447214
\(406\) 0 0
\(407\) 6.92820i 0.343418i
\(408\) 9.00000 15.5885i 0.445566 0.771744i
\(409\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(410\) −9.00000 + 5.19615i −0.444478 + 0.256620i
\(411\) 18.0000 31.1769i 0.887875 1.53784i
\(412\) 3.46410i 0.170664i
\(413\) 0 0
\(414\) 18.0000 0.884652
\(415\) 0 0
\(416\) 0 0
\(417\) 15.0000 + 25.9808i 0.734553 + 1.27228i
\(418\) −18.0000 10.3923i −0.880409 0.508304i
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −6.00000 3.46410i −0.292075 0.168630i
\(423\) −18.0000 31.1769i −0.875190 1.51587i
\(424\) 0 0
\(425\) −3.00000 + 5.19615i −0.145521 + 0.252050i
\(426\) 10.3923i 0.503509i
\(427\) 0 0
\(428\) 10.3923i 0.502331i
\(429\) 0 0
\(430\) 12.0000 6.92820i 0.578691 0.334108i
\(431\) −9.00000 + 5.19615i −0.433515 + 0.250290i −0.700843 0.713316i \(-0.747193\pi\)
0.267328 + 0.963606i \(0.413859\pi\)
\(432\) −22.5000 12.9904i −1.08253 0.625000i
\(433\) 6.92820i 0.332948i −0.986046 0.166474i \(-0.946762\pi\)
0.986046 0.166474i \(-0.0532382\pi\)
\(434\) 0 0
\(435\) −12.0000 −0.575356
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) 6.00000 + 10.3923i 0.287019 + 0.497131i
\(438\) −18.0000 + 10.3923i −0.860073 + 0.496564i
\(439\) 15.0000 + 8.66025i 0.715911 + 0.413331i 0.813246 0.581920i \(-0.197698\pi\)
−0.0973349 + 0.995252i \(0.531032\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) 0 0
\(443\) −9.00000 5.19615i −0.427603 0.246877i 0.270722 0.962658i \(-0.412738\pi\)
−0.698325 + 0.715781i \(0.746071\pi\)
\(444\) 3.00000 1.73205i 0.142374 0.0821995i
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) −15.0000 + 25.9808i −0.710271 + 1.23022i
\(447\) −12.0000 −0.567581
\(448\) 0 0
\(449\) 13.8564i 0.653924i −0.945037 0.326962i \(-0.893975\pi\)
0.945037 0.326962i \(-0.106025\pi\)
\(450\) 4.50000 + 2.59808i 0.212132 + 0.122474i
\(451\) −18.0000 + 10.3923i −0.847587 + 0.489355i
\(452\) 6.00000 3.46410i 0.282216 0.162938i
\(453\) 12.0000 + 6.92820i 0.563809 + 0.325515i
\(454\) 41.5692i 1.95094i
\(455\) 0 0
\(456\) 10.3923i 0.486664i
\(457\) 19.0000 32.9090i 0.888783 1.53942i 0.0474665 0.998873i \(-0.484885\pi\)
0.841316 0.540544i \(-0.181781\pi\)
\(458\) −6.00000 10.3923i −0.280362 0.485601i
\(459\) −27.0000 + 15.5885i −1.26025 + 0.727607i
\(460\) −3.00000 1.73205i −0.139876 0.0807573i
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) 20.0000 0.929479 0.464739 0.885448i \(-0.346148\pi\)
0.464739 + 0.885448i \(0.346148\pi\)
\(464\) −30.0000 17.3205i −1.39272 0.804084i
\(465\) 3.00000 + 5.19615i 0.139122 + 0.240966i
\(466\) 6.00000 + 10.3923i 0.277945 + 0.481414i
\(467\) −12.0000 + 20.7846i −0.555294 + 0.961797i 0.442587 + 0.896726i \(0.354061\pi\)
−0.997881 + 0.0650714i \(0.979272\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 20.7846i 0.958723i
\(471\) 12.0000 20.7846i 0.552931 0.957704i
\(472\) −18.0000 + 10.3923i −0.828517 + 0.478345i
\(473\) 24.0000 13.8564i 1.10352 0.637118i
\(474\) 12.0000 20.7846i 0.551178 0.954669i
\(475\) 3.46410i 0.158944i
\(476\) 0 0
\(477\) 0 0
\(478\) −9.00000 + 15.5885i −0.411650 + 0.712999i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 4.50000 + 7.79423i 0.205396 + 0.355756i
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 6.00000 + 3.46410i 0.272446 + 0.157297i
\(486\) 13.5000 + 23.3827i 0.612372 + 1.06066i
\(487\) −2.00000 3.46410i −0.0906287 0.156973i 0.817147 0.576429i \(-0.195554\pi\)
−0.907776 + 0.419456i \(0.862221\pi\)
\(488\) −6.00000 + 10.3923i −0.271607 + 0.470438i
\(489\) 27.7128i 1.25322i
\(490\) 0 0
\(491\) 24.2487i 1.09433i 0.837025 + 0.547165i \(0.184293\pi\)
−0.837025 + 0.547165i \(0.815707\pi\)
\(492\) 9.00000 + 5.19615i 0.405751 + 0.234261i
\(493\) −36.0000 + 20.7846i −1.62136 + 0.936092i
\(494\) 0 0
\(495\) 9.00000 + 5.19615i 0.404520 + 0.233550i
\(496\) 17.3205i 0.777714i
\(497\) 0 0
\(498\) 0 0
\(499\) 10.0000 17.3205i 0.447661 0.775372i −0.550572 0.834788i \(-0.685590\pi\)
0.998233 + 0.0594153i \(0.0189236\pi\)
\(500\) −0.500000 0.866025i −0.0223607 0.0387298i
\(501\) 18.0000 10.3923i 0.804181 0.464294i
\(502\) −18.0000 10.3923i −0.803379 0.463831i
\(503\) −12.0000 −0.535054 −0.267527 0.963550i \(-0.586206\pi\)
−0.267527 + 0.963550i \(0.586206\pi\)
\(504\) 0 0
\(505\) 6.00000 0.266996
\(506\) −18.0000 10.3923i −0.800198 0.461994i
\(507\) 19.5000 11.2583i 0.866025 0.500000i
\(508\) −2.00000 3.46410i −0.0887357 0.153695i
\(509\) 15.0000 25.9808i 0.664863 1.15158i −0.314459 0.949271i \(-0.601823\pi\)
0.979322 0.202306i \(-0.0648436\pi\)
\(510\) 18.0000 0.797053
\(511\) 0 0
\(512\) 8.66025i 0.382733i
\(513\) −9.00000 + 15.5885i −0.397360 + 0.688247i
\(514\) 9.00000 5.19615i 0.396973 0.229192i
\(515\) 3.00000 1.73205i 0.132196 0.0763233i
\(516\) −12.0000 6.92820i −0.528271 0.304997i
\(517\) 41.5692i 1.82821i
\(518\) 0 0
\(519\) 31.1769i 1.36851i
\(520\) 0 0
\(521\) −3.00000 5.19615i −0.131432 0.227648i 0.792797 0.609486i \(-0.208624\pi\)
−0.924229 + 0.381839i \(0.875291\pi\)
\(522\) 18.0000 + 31.1769i 0.787839 + 1.36458i
\(523\) −15.0000 8.66025i −0.655904 0.378686i 0.134810 0.990871i \(-0.456957\pi\)
−0.790715 + 0.612185i \(0.790291\pi\)
\(524\) 12.0000 0.524222
\(525\) 0 0
\(526\) 42.0000 1.83129
\(527\) 18.0000 + 10.3923i 0.784092 + 0.452696i
\(528\) 15.0000 + 25.9808i 0.652791 + 1.13067i
\(529\) −5.50000 9.52628i −0.239130 0.414186i
\(530\) 0 0
\(531\) 36.0000 1.56227
\(532\) 0 0
\(533\) 0 0
\(534\) 9.00000 15.5885i 0.389468 0.674579i
\(535\) −9.00000 + 5.19615i −0.389104 + 0.224649i
\(536\) 12.0000 6.92820i 0.518321 0.299253i
\(537\) 9.00000 15.5885i 0.388379 0.672692i
\(538\) 31.1769i 1.34413i
\(539\) 0 0
\(540\) 5.19615i 0.223607i
\(541\) 17.0000 29.4449i 0.730887 1.26593i −0.225617 0.974216i \(-0.572440\pi\)
0.956504 0.291718i \(-0.0942267\pi\)
\(542\) 21.0000 + 36.3731i 0.902027 + 1.56236i
\(543\) −18.0000 31.1769i −0.772454 1.33793i
\(544\) 27.0000 + 15.5885i 1.15762 + 0.668350i
\(545\) 2.00000 0.0856706
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 18.0000 + 10.3923i 0.768922 + 0.443937i
\(549\) 18.0000 10.3923i 0.768221 0.443533i
\(550\) −3.00000 5.19615i −0.127920 0.221565i
\(551\) −12.0000 + 20.7846i −0.511217 + 0.885454i
\(552\) 10.3923i 0.442326i
\(553\) 0 0
\(554\) 24.2487i 1.03023i
\(555\) −3.00000 1.73205i −0.127343 0.0735215i
\(556\) −15.0000 + 8.66025i −0.636142 + 0.367277i
\(557\) −24.0000 + 13.8564i −1.01691 + 0.587115i −0.913208 0.407493i \(-0.866403\pi\)
−0.103704 + 0.994608i \(0.533070\pi\)
\(558\) 9.00000 15.5885i 0.381000 0.659912i
\(559\) 0 0
\(560\) 0 0
\(561\) 36.0000 1.51992
\(562\) 12.0000 20.7846i 0.506189 0.876746i
\(563\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(564\) 18.0000 10.3923i 0.757937 0.437595i
\(565\) −6.00000 3.46410i −0.252422 0.145736i
\(566\) −30.0000 −1.26099
\(567\) 0 0
\(568\) −6.00000 −0.251754
\(569\) 24.0000 + 13.8564i 1.00613 + 0.580891i 0.910057 0.414483i \(-0.136038\pi\)
0.0960754 + 0.995374i \(0.469371\pi\)
\(570\) 9.00000 5.19615i 0.376969 0.217643i
\(571\) 2.00000 + 3.46410i 0.0836974 + 0.144968i 0.904835 0.425762i \(-0.139994\pi\)
−0.821138 + 0.570730i \(0.806660\pi\)
\(572\) 0 0
\(573\) 18.0000 0.751961
\(574\) 0 0
\(575\) 3.46410i 0.144463i
\(576\) −1.50000 + 2.59808i −0.0625000 + 0.108253i
\(577\) 30.0000 17.3205i 1.24892 0.721062i 0.278023 0.960574i \(-0.410321\pi\)
0.970893 + 0.239512i \(0.0769875\pi\)
\(578\) 28.5000 16.4545i 1.18544 0.684416i
\(579\) 21.0000 + 12.1244i 0.872730 + 0.503871i
\(580\) 6.92820i 0.287678i
\(581\) 0 0
\(582\) 20.7846i 0.861550i
\(583\) 0 0
\(584\) 6.00000 + 10.3923i 0.248282 + 0.430037i
\(585\) 0 0
\(586\) 9.00000 + 5.19615i 0.371787 + 0.214651i
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0 0
\(589\) 12.0000 0.494451
\(590\) −18.0000 10.3923i −0.741048 0.427844i
\(591\) −12.0000 20.7846i −0.493614 0.854965i
\(592\) −5.00000 8.66025i −0.205499 0.355934i
\(593\) −3.00000 + 5.19615i −0.123195 + 0.213380i −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 31.1769i 1.27920i
\(595\) 0 0
\(596\) 6.92820i 0.283790i
\(597\) 9.00000 15.5885i 0.368345 0.637993i
\(598\) 0 0
\(599\) −21.0000 + 12.1244i −0.858037 + 0.495388i −0.863354 0.504598i \(-0.831641\pi\)
0.00531761 + 0.999986i \(0.498307\pi\)
\(600\) 1.50000 2.59808i 0.0612372 0.106066i
\(601\) 13.8564i 0.565215i 0.959236 + 0.282607i \(0.0911993\pi\)
−0.959236 + 0.282607i \(0.908801\pi\)
\(602\) 0 0
\(603\) −24.0000 −0.977356
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) −0.500000 0.866025i −0.0203279 0.0352089i
\(606\) −9.00000 15.5885i −0.365600 0.633238i
\(607\) 15.0000 + 8.66025i 0.608831 + 0.351509i 0.772508 0.635005i \(-0.219002\pi\)
−0.163677 + 0.986514i \(0.552335\pi\)
\(608\) 18.0000 0.729996
\(609\) 0 0
\(610\) −12.0000 −0.485866
\(611\) 0 0
\(612\) −9.00000 15.5885i −0.363803 0.630126i
\(613\) 17.0000 + 29.4449i 0.686624 + 1.18927i 0.972924 + 0.231127i \(0.0742412\pi\)
−0.286300 + 0.958140i \(0.592425\pi\)
\(614\) −21.0000 + 36.3731i −0.847491 + 1.46790i
\(615\) 10.3923i 0.419058i
\(616\) 0 0
\(617\) 6.92820i 0.278919i −0.990228 0.139459i \(-0.955464\pi\)
0.990228 0.139459i \(-0.0445365\pi\)
\(618\) −9.00000 5.19615i −0.362033 0.209020i
\(619\) 15.0000 8.66025i 0.602901 0.348085i −0.167281 0.985909i \(-0.553499\pi\)
0.770182 + 0.637824i \(0.220165\pi\)
\(620\) −3.00000 + 1.73205i −0.120483 + 0.0695608i
\(621\) −9.00000 + 15.5885i −0.361158 + 0.625543i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.500000 + 0.866025i −0.0200000 + 0.0346410i
\(626\) −18.0000 31.1769i −0.719425 1.24608i
\(627\) 18.0000 10.3923i 0.718851 0.415029i
\(628\) 12.0000 + 6.92820i 0.478852 + 0.276465i
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) −40.0000 −1.59237 −0.796187 0.605050i \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) −12.0000 6.92820i −0.477334 0.275589i
\(633\) 6.00000 3.46410i 0.238479 0.137686i
\(634\) 24.0000 + 41.5692i 0.953162 + 1.65092i
\(635\) −2.00000 + 3.46410i −0.0793676 + 0.137469i
\(636\) 0 0
\(637\) 0 0
\(638\) 41.5692i 1.64574i
\(639\) 9.00000 + 5.19615i 0.356034 + 0.205557i
\(640\) 10.5000 6.06218i 0.415049 0.239629i
\(641\) 24.0000 13.8564i 0.947943 0.547295i 0.0555017 0.998459i \(-0.482324\pi\)
0.892441 + 0.451163i \(0.148991\pi\)
\(642\) 27.0000 + 15.5885i 1.06561 + 0.615227i
\(643\) 31.1769i 1.22950i 0.788723 + 0.614749i \(0.210743\pi\)
−0.788723 + 0.614749i \(0.789257\pi\)
\(644\) 0 0
\(645\) 13.8564i 0.545595i
\(646\) 18.0000 31.1769i 0.708201 1.22664i
\(647\) −6.00000 10.3923i −0.235884 0.408564i 0.723645 0.690172i \(-0.242465\pi\)
−0.959529 + 0.281609i \(0.909132\pi\)
\(648\) 13.5000 7.79423i 0.530330 0.306186i
\(649\) −36.0000 20.7846i −1.41312 0.815867i
\(650\) 0 0
\(651\) 0 0
\(652\) 16.0000 0.626608
\(653\) 36.0000 + 20.7846i 1.40879 + 0.813365i 0.995272 0.0971316i \(-0.0309668\pi\)
0.413517 + 0.910496i \(0.364300\pi\)
\(654\) −3.00000 5.19615i −0.117309 0.203186i
\(655\) −6.00000 10.3923i −0.234439 0.406061i
\(656\) 15.0000 25.9808i 0.585652 1.01438i
\(657\) 20.7846i 0.810885i
\(658\) 0 0
\(659\) 10.3923i 0.404827i 0.979300 + 0.202413i \(0.0648785\pi\)
−0.979300 + 0.202413i \(0.935122\pi\)
\(660\) −3.00000 + 5.19615i −0.116775 + 0.202260i
\(661\) −42.0000 + 24.2487i −1.63361 + 0.943166i −0.650644 + 0.759383i \(0.725501\pi\)
−0.982967 + 0.183782i \(0.941166\pi\)
\(662\) 42.0000 24.2487i 1.63238 0.942453i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 10.3923i 0.402694i
\(667\) −12.0000 + 20.7846i −0.464642 + 0.804783i
\(668\) 6.00000 + 10.3923i 0.232147 + 0.402090i
\(669\) −15.0000 25.9808i −0.579934 1.00447i
\(670\) 12.0000 + 6.92820i 0.463600 + 0.267660i
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) 21.0000 + 12.1244i 0.808890 + 0.467013i
\(675\) −4.50000 + 2.59808i −0.173205 + 0.100000i
\(676\) 6.50000 + 11.2583i 0.250000 + 0.433013i
\(677\) 3.00000 5.19615i 0.115299 0.199704i −0.802600 0.596518i \(-0.796551\pi\)
0.917899 + 0.396813i \(0.129884\pi\)
\(678\) 20.7846i 0.798228i
\(679\) 0 0
\(680\) 10.3923i 0.398527i
\(681\) 36.0000 + 20.7846i 1.37952 + 0.796468i
\(682\) −18.0000 + 10.3923i −0.689256 + 0.397942i
\(683\) −15.0000 + 8.66025i −0.573959 + 0.331375i −0.758729 0.651406i \(-0.774179\pi\)
0.184770 + 0.982782i \(0.440846\pi\)
\(684\) −9.00000 5.19615i −0.344124 0.198680i
\(685\) 20.7846i 0.794139i
\(686\) 0 0
\(687\) 12.0000 0.457829
\(688\) −20.0000 + 34.6410i −0.762493 + 1.32068i
\(689\) 0 0
\(690\) 9.00000 5.19615i 0.342624 0.197814i
\(691\) −27.0000 15.5885i −1.02713 0.593013i −0.110968 0.993824i \(-0.535395\pi\)
−0.916161 + 0.400811i \(0.868728\pi\)
\(692\) −18.0000 −0.684257
\(693\) 0 0
\(694\) 30.0000 1.13878
\(695\) 15.0000 + 8.66025i 0.568982 + 0.328502i
\(696\) 18.0000 10.3923i 0.682288 0.393919i
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) 6.00000 10.3923i 0.227103 0.393355i
\(699\) −12.0000 −0.453882
\(700\) 0 0
\(701\) 20.7846i 0.785024i −0.919747 0.392512i \(-0.871606\pi\)
0.919747 0.392512i \(-0.128394\pi\)
\(702\) 0 0
\(703\) −6.00000 + 3.46410i −0.226294 + 0.130651i
\(704\) 3.00000 1.73205i 0.113067 0.0652791i
\(705\) −18.0000 10.3923i −0.677919 0.391397i
\(706\) 10.3923i 0.391120i
\(707\) 0 0
\(708\) 20.7846i 0.781133i
\(709\) −11.0000 + 19.0526i −0.413114 + 0.715534i −0.995228 0.0975728i \(-0.968892\pi\)
0.582115 + 0.813107i \(0.302225\pi\)
\(710\) −3.00000 5.19615i −0.112588 0.195008i
\(711\) 12.0000 + 20.7846i 0.450035 + 0.779484i
\(712\) −9.00000 5.19615i −0.337289 0.194734i
\(713\) 12.0000 0.449404
\(714\) 0 0
\(715\) 0 0
\(716\) 9.00000 + 5.19615i 0.336346 + 0.194189i
\(717\) −9.00000 15.5885i −0.336111 0.582162i
\(718\) 3.00000 + 5.19615i 0.111959 + 0.193919i
\(719\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) −15.0000 −0.559017
\(721\) 0 0
\(722\) 12.1244i 0.451222i
\(723\) 0 0
\(724\) 18.0000 10.3923i 0.668965 0.386227i
\(725\) −6.00000 + 3.46410i −0.222834 + 0.128654i
\(726\) −1.50000 + 2.59808i −0.0556702 + 0.0964237i
\(727\) 3.46410i 0.128476i −0.997935 0.0642382i \(-0.979538\pi\)
0.997935 0.0642382i \(-0.0204617\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) −6.00000 + 10.3923i −0.222070 + 0.384636i
\(731\) 24.0000 + 41.5692i 0.887672 + 1.53749i
\(732\) 6.00000 + 10.3923i 0.221766 + 0.384111i
\(733\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(734\) −18.0000 −0.664392
\(735\) 0 0
\(736\) 18.0000 0.663489
\(737\) 24.0000 + 13.8564i 0.884051 + 0.510407i
\(738\) −27.0000 + 15.5885i −0.993884 + 0.573819i
\(739\) 2.00000 + 3.46410i 0.0735712 + 0.127429i 0.900464 0.434930i \(-0.143227\pi\)
−0.826893 + 0.562360i \(0.809894\pi\)
\(740\) 1.00000 1.73205i 0.0367607 0.0636715i
\(741\) 0 0
\(742\) 0 0
\(743\) 31.1769i 1.14377i 0.820334 + 0.571885i \(0.193788\pi\)
−0.820334 + 0.571885i \(0.806212\pi\)
\(744\) −9.00000 5.19615i −0.329956 0.190500i
\(745\) −6.00000 + 3.46410i −0.219823 + 0.126915i
\(746\) 21.0000 12.1244i 0.768865 0.443904i
\(747\) 0 0
\(748\) 20.7846i 0.759961i
\(749\) 0 0
\(750\) 3.00000 0.109545
\(751\) −8.00000 + 13.8564i −0.291924 + 0.505627i −0.974265 0.225407i \(-0.927629\pi\)
0.682341 + 0.731034i \(0.260962\pi\)
\(752\) −30.0000 51.9615i −1.09399 1.89484i
\(753\) 18.0000 10.3923i 0.655956 0.378717i
\(754\) 0 0
\(755\) 8.00000 0.291150
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) −6.00000 3.46410i −0.217930 0.125822i
\(759\) 18.0000 10.3923i 0.653359 0.377217i
\(760\) −3.00000 5.19615i −0.108821 0.188484i
\(761\) 21.0000 36.3731i 0.761249 1.31852i −0.180957 0.983491i \(-0.557920\pi\)
0.942207 0.335032i \(-0.108747\pi\)
\(762\) 12.0000 0.434714
\(763\) 0 0
\(764\) 10.3923i 0.375980i
\(765\) −9.00000 + 15.5885i −0.325396 + 0.563602i
\(766\) 18.0000 10.3923i 0.650366 0.375489i
\(767\) 0 0
\(768\) −28.5000 16.4545i −1.02841 0.593750i
\(769\) 41.5692i 1.49902i −0.661991 0.749512i \(-0.730288\pi\)
0.661991 0.749512i \(-0.269712\pi\)
\(770\) 0 0
\(771\) 10.3923i 0.374270i
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) 3.00000 + 5.19615i 0.107903 + 0.186893i 0.914920 0.403634i \(-0.132253\pi\)
−0.807018 + 0.590527i \(0.798920\pi\)
\(774\) 36.0000 20.7846i 1.29399 0.747087i
\(775\) 3.00000 + 1.73205i 0.107763 + 0.0622171i
\(776\) −12.0000 −0.430775
\(777\) 0 0
\(778\) −12.0000 −0.430221
\(779\) −18.0000 10.3923i −0.644917 0.372343i
\(780\) 0 0
\(781\) −6.00000 10.3923i −0.214697 0.371866i
\(782\) 18.0000 31.1769i 0.643679 1.11488i
\(783\) −36.0000 −1.28654
\(784\) 0 0
\(785\) 13.8564i 0.494556i
\(786\) −18.0000 + 31.1769i −0.642039 + 1.11204i
\(787\) −21.0000 + 12.1244i −0.748569 + 0.432187i −0.825177 0.564875i \(-0.808924\pi\)
0.0766075 + 0.997061i \(0.475591\pi\)
\(788\) 12.0000 6.92820i 0.427482 0.246807i
\(789\) −21.0000 + 36.3731i −0.747620 + 1.29492i
\(790\) 13.8564i 0.492989i
\(791\) 0 0
\(792\) −18.0000 −0.639602
\(793\) 0 0
\(794\) 12.0000 + 20.7846i 0.425864 + 0.737618i
\(795\) 0 0
\(796\) 9.00000 + 5.19615i 0.318997 +