Properties

Label 735.2.s.b.521.1
Level 735
Weight 2
Character 735.521
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 521.1
Root \(0.500000 + 0.866025i\) of \(x^{2} - x + 1\)
Character \(\chi\) \(=\) 735.521
Dual form 735.2.s.b.656.1

$q$-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 \(\left(\mathbb{Z}/735\mathbb{Z}\right)^\times\).

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

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 −0.925615 0.378467i \(-0.876451\pi\)
−0.135045 + 0.990839i \(0.543118\pi\)
\(3\) 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 −0.0258656 0.999665i \(-0.508234\pi\)
−0.878668 + 0.477432i \(0.841568\pi\)
\(12\) 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 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) −4.50000 2.59808i −1.06066 0.612372i
\(19\) −3.00000 + 1.73205i −0.688247 + 0.397360i −0.802955 0.596040i \(-0.796740\pi\)
0.114708 + 0.993399i \(0.463407\pi\)
\(20\) 1.00000 0.223607
\(21\) 0 0
\(22\) 6.00000 1.27920
\(23\) −3.00000 + 1.73205i −0.625543 + 0.361158i −0.779024 0.626994i \(-0.784285\pi\)
0.153481 + 0.988152i \(0.450952\pi\)
\(24\) 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 \(0.222422\pi\)
−0.765641 + 0.643268i \(0.777578\pi\)
\(30\) −1.50000 2.59808i −0.273861 0.474342i
\(31\) −3.00000 1.73205i −0.538816 0.311086i 0.205783 0.978598i \(-0.434026\pi\)
−0.744599 + 0.667512i \(0.767359\pi\)
\(32\) −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 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 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 0.856560 + 0.516047i \(0.172597\pi\)
0.0186297 + 0.999826i \(0.494070\pi\)
\(48\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(54\) −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 −0.150148 0.988663i \(-0.547975\pi\)
0.931282 0.364299i \(-0.118692\pi\)
\(60\) 1.50000 + 0.866025i 0.193649 + 0.111803i
\(61\) 6.00000 3.46410i 0.768221 0.443533i −0.0640184 0.997949i \(-0.520392\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) 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 −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 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 \(-0.934100\pi\)
0.978645 0.205557i \(-0.0659005\pi\)
\(72\) 4.50000 2.59808i 0.530330 0.306186i
\(73\) 6.00000 + 3.46410i 0.702247 + 0.405442i 0.808184 0.588930i \(-0.200451\pi\)
−0.105937 + 0.994373i \(0.533784\pi\)
\(74\) −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 0.548352 0.836247i \(-0.315255\pi\)
−0.998388 + 0.0567635i \(0.981922\pi\)
\(80\) −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 0.662071 0.749441i \(-0.269678\pi\)
−0.980071 + 0.198650i \(0.936344\pi\)
\(90\) 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 \(-0.885595\pi\)
0.936103 0.351726i \(-0.114405\pi\)
\(98\) 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 −0.677284 0.735721i \(-0.736843\pi\)
0.975796 + 0.218685i \(0.0701767\pi\)
\(102\) 9.00000 15.5885i 0.891133 1.54349i
\(103\) 3.00000 1.73205i 0.295599 0.170664i −0.344865 0.938652i \(-0.612075\pi\)
0.640464 + 0.767988i \(0.278742\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −9.00000 + 5.19615i −0.870063 + 0.502331i −0.867369 0.497665i \(-0.834191\pi\)
−0.00269372 + 0.999996i \(0.500857\pi\)
\(108\) 4.50000 + 2.59808i 0.433013 + 0.250000i
\(109\) 1.00000 1.73205i 0.0957826 0.165900i −0.814152 0.580651i \(-0.802798\pi\)
0.909935 + 0.414751i \(0.136131\pi\)
\(110\) 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 \(0.105659\pi\)
−0.945413 + 0.325875i \(0.894341\pi\)
\(114\) 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 0.999602 + 0.0281993i \(0.00897729\pi\)
−0.475380 + 0.879781i \(0.657689\pi\)
\(132\) −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 0.998965 + 0.0454914i \(0.0144854\pi\)
0.538879 + 0.842383i \(0.318848\pi\)
\(138\) 9.00000 5.19615i 0.766131 0.442326i
\(139\) 17.3205i 1.46911i −0.678551 0.734553i \(-0.737392\pi\)
0.678551 0.734553i \(-0.262608\pi\)
\(140\) 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 −0.725213 0.688525i \(-0.758259\pi\)
0.233674 + 0.972315i \(0.424925\pi\)
\(150\) 1.50000 2.59808i 0.122474 0.212132i
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) 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 0.895466 0.445130i \(-0.146843\pi\)
0.0622385 + 0.998061i \(0.480176\pi\)
\(158\) 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 0.988227 + 0.152992i \(0.0488907\pi\)
−0.361619 + 0.932326i \(0.617776\pi\)
\(164\) 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 −0.973670 0.227964i \(-0.926793\pi\)
0.289412 0.957205i \(-0.406540\pi\)
\(174\) 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 0.797096 0.603853i \(-0.206369\pi\)
−0.124404 + 0.992232i \(0.539702\pi\)
\(180\) 1.50000 + 2.59808i 0.111803 + 0.193649i
\(181\) 20.7846i 1.54491i 0.635071 + 0.772454i \(0.280971\pi\)
−0.635071 + 0.772454i \(0.719029\pi\)
\(182\) 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 −0.137705 0.990473i \(-0.543973\pi\)
0.788922 + 0.614493i \(0.210639\pi\)
\(192\) −1.50000 0.866025i −0.108253 0.0625000i
\(193\) 7.00000 12.1244i 0.503871 0.872730i −0.496119 0.868255i \(-0.665242\pi\)
0.999990 0.00447566i \(-0.00142465\pi\)
\(194\) 6.00000 + 10.3923i 0.430775 + 0.746124i
\(195\) 0 0
\(196\) 0 0
\(197\) 13.8564i 0.987228i 0.869681 + 0.493614i \(0.164324\pi\)
−0.869681 + 0.493614i \(0.835676\pi\)
\(198\) 9.00000 + 15.5885i 0.639602 + 1.10782i
\(199\) 9.00000 + 5.19615i 0.637993 + 0.368345i 0.783841 0.620962i \(-0.213258\pi\)
−0.145848 + 0.989307i \(0.546591\pi\)
\(200\) 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 \(0.196921\pi\)
−0.814664 + 0.579934i \(0.803079\pi\)
\(224\) 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 −0.125435 0.992102i \(-0.540033\pi\)
0.921903 0.387421i \(-0.126634\pi\)
\(228\) −3.00000 + 5.19615i −0.198680 + 0.344124i
\(229\) 6.00000 3.46410i 0.396491 0.228914i −0.288478 0.957487i \(-0.593149\pi\)
0.684969 + 0.728572i \(0.259816\pi\)
\(230\) 6.00000 0.395628
\(231\) 0 0
\(232\) 12.0000 0.787839
\(233\) −6.00000 + 3.46410i −0.393073 + 0.226941i −0.683491 0.729959i \(-0.739539\pi\)
0.290418 + 0.956900i \(0.406206\pi\)
\(234\) 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 \(0.109112\pi\)
−0.941822 + 0.336111i \(0.890888\pi\)
\(240\) −7.50000 + 4.33013i −0.484123 + 0.279508i
\(241\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(242\) −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 0.757159 0.653231i \(-0.226587\pi\)
−0.944294 + 0.329104i \(0.893253\pi\)
\(258\) 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 −0.315394 0.948961i \(-0.602137\pi\)
−0.979521 + 0.201341i \(0.935470\pi\)
\(264\) −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 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) 4.50000 7.79423i 0.273861 0.474342i
\(271\) −21.0000 + 12.1244i −1.27566 + 0.736502i −0.976047 0.217559i \(-0.930191\pi\)
−0.299612 + 0.954061i \(0.596857\pi\)
\(272\) −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 −0.995997 0.0893846i \(-0.971510\pi\)
0.575408 + 0.817867i \(0.304843\pi\)
\(278\) 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 \(-0.864375\pi\)
0.910594 0.413302i \(-0.135625\pi\)
\(282\) −18.0000 31.1769i −1.07188 1.85656i
\(283\) 15.0000 + 8.66025i 0.891657 + 0.514799i 0.874484 0.485054i \(-0.161200\pi\)
0.0171732 + 0.999853i \(0.494533\pi\)
\(284\) −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 \(0.243259\pi\)
−0.721923 + 0.691974i \(0.756741\pi\)
\(308\) 0 0
\(309\) 6.00000 0.341328
\(310\) 3.00000 + 5.19615i 0.170389 + 0.295122i
\(311\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(312\) 0 0
\(313\) 18.0000 10.3923i 1.01742 0.587408i 0.104065 0.994571i \(-0.466815\pi\)
0.913356 + 0.407163i \(0.133482\pi\)
\(314\) −24.0000 −1.35440
\(315\) 0 0
\(316\) −8.00000 −0.450035
\(317\) −24.0000 + 13.8564i −1.34797 + 0.778253i −0.987962 0.154694i \(-0.950561\pi\)
−0.360012 + 0.932948i \(0.617227\pi\)
\(318\) 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 −0.937829 0.347097i \(-0.887167\pi\)
0.168320 0.985732i \(-0.446166\pi\)
\(332\) 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 0.0400587 0.999197i \(-0.487246\pi\)
−0.845301 + 0.534291i \(0.820579\pi\)
\(348\) 6.00000 + 10.3923i 0.321634 + 0.557086i
\(349\) 6.92820i 0.370858i −0.982658 0.185429i \(-0.940632\pi\)
0.982658 0.185429i \(-0.0593675\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 9.00000 + 15.5885i 0.479702 + 0.830868i
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) −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 −0.577073 0.816692i \(-0.695805\pi\)
0.418740 + 0.908106i \(0.362472\pi\)
\(360\) 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 0.716154 0.697942i \(-0.245901\pi\)
−0.246358 + 0.969179i \(0.579234\pi\)
\(368\) −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 0.625917 0.779890i \(-0.284725\pi\)
−0.988363 + 0.152115i \(0.951392\pi\)
\(374\) −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 0.671027 0.741433i \(-0.265853\pi\)
−0.977613 + 0.210411i \(0.932520\pi\)
\(384\) 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 0.644334 0.764745i \(-0.277135\pi\)
−0.340121 + 0.940382i \(0.610468\pi\)
\(390\) 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 −0.769931 0.638127i \(-0.779710\pi\)
0.167668 + 0.985843i \(0.446376\pi\)
\(398\) −18.0000 −0.902258
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 24.0000 13.8564i 1.19850 0.691956i 0.238282 0.971196i \(-0.423416\pi\)
0.960221 + 0.279240i \(0.0900826\pi\)
\(402\) 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 \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) −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 0.267328 0.963606i \(-0.413859\pi\)
−0.700843 + 0.713316i \(0.747193\pi\)
\(432\) −22.5000 + 12.9904i −1.08253 + 0.625000i
\(433\) 6.92820i 0.332948i 0.986046 + 0.166474i \(0.0532382\pi\)
−0.986046 + 0.166474i \(0.946762\pi\)
\(434\) 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 −0.0973349 0.995252i \(-0.531032\pi\)
0.813246 + 0.581920i \(0.197698\pi\)
\(440\) −6.00000 −0.286039
\(441\) 0 0
\(442\) 0 0
\(443\) −9.00000 + 5.19615i −0.427603 + 0.246877i −0.698325 0.715781i \(-0.746071\pi\)
0.270722 + 0.962658i \(0.412738\pi\)
\(444\) 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 \(0.106025\pi\)
−0.945037 + 0.326962i \(0.893975\pi\)
\(450\) 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 0.841316 + 0.540544i \(0.181781\pi\)
0.0474665 + 0.998873i \(0.484885\pi\)
\(458\) −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 −0.997881 0.0650714i \(-0.979272\pi\)
0.442587 0.896726i \(-0.354061\pi\)
\(468\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) 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 −0.907776 0.419456i \(-0.862221\pi\)
0.817147 + 0.576429i \(0.195554\pi\)
\(488\) −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 \(-0.815707\pi\)
0.837025 0.547165i \(-0.184293\pi\)
\(492\) 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 0.998233 0.0594153i \(-0.0189236\pi\)
−0.550572 + 0.834788i \(0.685590\pi\)
\(500\) −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 0.979322 + 0.202306i \(0.0648436\pi\)
−0.314459 + 0.949271i \(0.601823\pi\)
\(510\) 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 −0.924229 0.381839i \(-0.875291\pi\)
0.792797 + 0.609486i \(0.208624\pi\)
\(522\) 18.0000 31.1769i 0.787839 1.36458i
\(523\) −15.0000 + 8.66025i −0.655904 + 0.378686i −0.790715 0.612185i \(-0.790291\pi\)
0.134810 + 0.990871i \(0.456957\pi\)
\(524\) 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 0.956504 + 0.291718i \(0.0942267\pi\)
−0.225617 + 0.974216i \(0.572440\pi\)
\(542\) 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 −0.103704 0.994608i \(-0.533070\pi\)
−0.913208 + 0.407493i \(0.866403\pi\)
\(558\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(564\) 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 0.0960754 0.995374i \(-0.469371\pi\)
0.910057 + 0.414483i \(0.136038\pi\)
\(570\) 9.00000 + 5.19615i 0.376969 + 0.217643i
\(571\) 2.00000 3.46410i 0.0836974 0.144968i −0.821138 0.570730i \(-0.806660\pi\)
0.904835 + 0.425762i \(0.139994\pi\)
\(572\) 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 0.970893 0.239512i \(-0.0769875\pi\)
0.278023 + 0.960574i \(0.410321\pi\)
\(578\) 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 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 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 0.00531761 0.999986i \(-0.498307\pi\)
−0.863354 + 0.504598i \(0.831641\pi\)
\(600\) 1.50000 + 2.59808i 0.0612372 + 0.106066i
\(601\) 13.8564i 0.565215i −0.959236 0.282607i \(-0.908801\pi\)
0.959236 0.282607i \(-0.0911993\pi\)
\(602\) 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 −0.163677 0.986514i \(-0.552335\pi\)
0.772508 + 0.635005i \(0.219002\pi\)
\(608\) 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 −0.286300 0.958140i \(-0.592425\pi\)
0.972924 0.231127i \(-0.0742412\pi\)
\(614\) −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 \(0.0445365\pi\)
−0.990228 + 0.139459i \(0.955464\pi\)
\(618\) −9.00000 + 5.19615i −0.362033 + 0.209020i
\(619\) 15.0000 + 8.66025i 0.602901 + 0.348085i 0.770182 0.637824i \(-0.220165\pi\)
−0.167281 + 0.985909i \(0.553499\pi\)
\(620\) −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 0.892441 0.451163i \(-0.148991\pi\)
0.0555017 + 0.998459i \(0.482324\pi\)
\(642\) 27.0000 15.5885i 1.06561 0.615227i
\(643\) 31.1769i 1.22950i −0.788723 0.614749i \(-0.789257\pi\)
0.788723 0.614749i \(-0.210743\pi\)
\(644\) 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 −0.959529 0.281609i \(-0.909132\pi\)
0.723645 + 0.690172i \(0.242465\pi\)
\(648\) 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 0.413517 0.910496i \(-0.364300\pi\)
0.995272 + 0.0971316i \(0.0309668\pi\)
\(654\) −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 \(-0.935122\pi\)
0.979300 0.202413i \(-0.0648785\pi\)
\(660\) −3.00000 5.19615i −0.116775 0.202260i
\(661\) −42.0000 24.2487i −1.63361 0.943166i −0.982967 0.183782i \(-0.941166\pi\)
−0.650644 0.759383i \(-0.725501\pi\)
\(662\) 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 0.917899 0.396813i \(-0.129884\pi\)
−0.802600 + 0.596518i \(0.796551\pi\)
\(678\) 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 0.184770 0.982782i \(-0.440846\pi\)
−0.758729 + 0.651406i \(0.774179\pi\)
\(684\) −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 −0.916161 0.400811i \(-0.868728\pi\)
−0.110968 + 0.993824i \(0.535395\pi\)
\(692\) −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 \(0.128394\pi\)
−0.919747 + 0.392512i \(0.871606\pi\)
\(702\) 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 0.582115 0.813107i \(-0.302225\pi\)
−0.995228 + 0.0975728i \(0.968892\pi\)
\(710\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) −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 \(0.0204617\pi\)
−0.997935 + 0.0642382i \(0.979538\pi\)
\(728\) 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 \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(734\) −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 −0.826893 0.562360i \(-0.809894\pi\)
0.900464 + 0.434930i \(0.143227\pi\)
\(740\) 1.00000 + 1.73205i 0.0367607 + 0.0636715i
\(741\) 0 0
\(742\) 0 0
\(743\) 31.1769i 1.14377i −0.820334 0.571885i \(-0.806212\pi\)
0.820334 0.571885i \(-0.193788\pi\)
\(744\) −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 0.682341 0.731034i \(-0.260962\pi\)
−0.974265 + 0.225407i \(0.927629\pi\)
\(752\) −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 0.942207 + 0.335032i \(0.108747\pi\)
−0.180957 + 0.983491i \(0.557920\pi\)
\(762\) 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 \(0.269712\pi\)
−0.661991 + 0.749512i \(0.730288\pi\)
\(770\) 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 −0.807018 0.590527i \(-0.798920\pi\)
0.914920 + 0.403634i \(0.132253\pi\)
\(774\) 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 0.0766075 0.997061i \(-0.475591\pi\)
−0.825177 + 0.564875i \(0.808924\pi\)
\(788\) 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 0.184173i