Properties

Label 637.2.u.a.30.1
Level $637$
Weight $2$
Character 637.30
Analytic conductor $5.086$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 637 = 7^{2} \cdot 13 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 637.u (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(5.08647060876\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 30.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 637.30
Dual form 637.2.u.a.361.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 + 0.866025i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.73205i q^{8} -2.00000 q^{9} +O(q^{10})\) \(q+(-1.50000 + 0.866025i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(1.50000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.73205i q^{8} -2.00000 q^{9} -3.00000 q^{10} -5.19615i q^{11} +(0.500000 - 0.866025i) q^{12} +(1.00000 - 3.46410i) q^{13} +(1.50000 + 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{16} +(3.00000 - 5.19615i) q^{17} +(3.00000 - 1.73205i) q^{18} -1.73205i q^{19} +(1.50000 - 0.866025i) q^{20} +(4.50000 + 7.79423i) q^{22} -1.73205i q^{24} +(-1.00000 - 1.73205i) q^{25} +(1.50000 + 6.06218i) q^{26} -5.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} -3.00000 q^{30} +(-1.50000 + 0.866025i) q^{31} +(-4.50000 - 2.59808i) q^{32} -5.19615i q^{33} +10.3923i q^{34} +(-1.00000 + 1.73205i) q^{36} +(1.50000 + 2.59808i) q^{38} +(1.00000 - 3.46410i) q^{39} +(1.50000 - 2.59808i) q^{40} +(4.50000 + 2.59808i) q^{41} +(-5.50000 - 9.52628i) q^{43} +(-4.50000 - 2.59808i) q^{44} +(-3.00000 - 1.73205i) q^{45} +(7.50000 + 4.33013i) q^{47} +(2.50000 + 4.33013i) q^{48} +(3.00000 + 1.73205i) q^{50} +(3.00000 - 5.19615i) q^{51} +(-2.50000 - 2.59808i) q^{52} +(4.50000 + 7.79423i) q^{53} +(7.50000 - 4.33013i) q^{54} +(4.50000 - 7.79423i) q^{55} -1.73205i q^{57} -5.19615i q^{58} +(3.00000 + 1.73205i) q^{59} +(1.50000 - 0.866025i) q^{60} -7.00000 q^{61} +(1.50000 - 2.59808i) q^{62} -1.00000 q^{64} +(4.50000 - 4.33013i) q^{65} +(4.50000 + 7.79423i) q^{66} +8.66025i q^{67} +(-3.00000 - 5.19615i) q^{68} +(1.50000 - 0.866025i) q^{71} +3.46410i q^{72} +(7.50000 - 4.33013i) q^{73} +(-1.00000 - 1.73205i) q^{75} +(-1.50000 - 0.866025i) q^{76} +(1.50000 + 6.06218i) q^{78} +(2.50000 - 4.33013i) q^{79} +8.66025i q^{80} +1.00000 q^{81} -9.00000 q^{82} +3.46410i q^{83} +(9.00000 - 5.19615i) q^{85} +(16.5000 + 9.52628i) q^{86} +(-1.50000 + 2.59808i) q^{87} -9.00000 q^{88} +(6.00000 - 3.46410i) q^{89} +6.00000 q^{90} +(-1.50000 + 0.866025i) q^{93} -15.0000 q^{94} +(1.50000 - 2.59808i) q^{95} +(-4.50000 - 2.59808i) q^{96} +(4.50000 - 2.59808i) q^{97} +10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{2} + 2q^{3} + q^{4} + 3q^{5} - 3q^{6} - 4q^{9} + O(q^{10}) \) \( 2q - 3q^{2} + 2q^{3} + q^{4} + 3q^{5} - 3q^{6} - 4q^{9} - 6q^{10} + q^{12} + 2q^{13} + 3q^{15} + 5q^{16} + 6q^{17} + 6q^{18} + 3q^{20} + 9q^{22} - 2q^{25} + 3q^{26} - 10q^{27} - 3q^{29} - 6q^{30} - 3q^{31} - 9q^{32} - 2q^{36} + 3q^{38} + 2q^{39} + 3q^{40} + 9q^{41} - 11q^{43} - 9q^{44} - 6q^{45} + 15q^{47} + 5q^{48} + 6q^{50} + 6q^{51} - 5q^{52} + 9q^{53} + 15q^{54} + 9q^{55} + 6q^{59} + 3q^{60} - 14q^{61} + 3q^{62} - 2q^{64} + 9q^{65} + 9q^{66} - 6q^{68} + 3q^{71} + 15q^{73} - 2q^{75} - 3q^{76} + 3q^{78} + 5q^{79} + 2q^{81} - 18q^{82} + 18q^{85} + 33q^{86} - 3q^{87} - 18q^{88} + 12q^{89} + 12q^{90} - 3q^{93} - 30q^{94} + 3q^{95} - 9q^{96} + 9q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 + 0.866025i −1.06066 + 0.612372i −0.925615 0.378467i \(-0.876451\pi\)
−0.135045 + 0.990839i \(0.543118\pi\)
\(3\) 1.00000 0.577350 0.288675 0.957427i \(-0.406785\pi\)
0.288675 + 0.957427i \(0.406785\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.50000 + 0.866025i 0.670820 + 0.387298i 0.796387 0.604787i \(-0.206742\pi\)
−0.125567 + 0.992085i \(0.540075\pi\)
\(6\) −1.50000 + 0.866025i −0.612372 + 0.353553i
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) −2.00000 −0.666667
\(10\) −3.00000 −0.948683
\(11\) 5.19615i 1.56670i −0.621582 0.783349i \(-0.713510\pi\)
0.621582 0.783349i \(-0.286490\pi\)
\(12\) 0.500000 0.866025i 0.144338 0.250000i
\(13\) 1.00000 3.46410i 0.277350 0.960769i
\(14\) 0 0
\(15\) 1.50000 + 0.866025i 0.387298 + 0.223607i
\(16\) 2.50000 + 4.33013i 0.625000 + 1.08253i
\(17\) 3.00000 5.19615i 0.727607 1.26025i −0.230285 0.973123i \(-0.573966\pi\)
0.957892 0.287129i \(-0.0927008\pi\)
\(18\) 3.00000 1.73205i 0.707107 0.408248i
\(19\) 1.73205i 0.397360i −0.980064 0.198680i \(-0.936335\pi\)
0.980064 0.198680i \(-0.0636654\pi\)
\(20\) 1.50000 0.866025i 0.335410 0.193649i
\(21\) 0 0
\(22\) 4.50000 + 7.79423i 0.959403 + 1.66174i
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 1.73205i 0.353553i
\(25\) −1.00000 1.73205i −0.200000 0.346410i
\(26\) 1.50000 + 6.06218i 0.294174 + 1.18889i
\(27\) −5.00000 −0.962250
\(28\) 0 0
\(29\) −1.50000 + 2.59808i −0.278543 + 0.482451i −0.971023 0.238987i \(-0.923185\pi\)
0.692480 + 0.721437i \(0.256518\pi\)
\(30\) −3.00000 −0.547723
\(31\) −1.50000 + 0.866025i −0.269408 + 0.155543i −0.628619 0.777714i \(-0.716379\pi\)
0.359211 + 0.933257i \(0.383046\pi\)
\(32\) −4.50000 2.59808i −0.795495 0.459279i
\(33\) 5.19615i 0.904534i
\(34\) 10.3923i 1.78227i
\(35\) 0 0
\(36\) −1.00000 + 1.73205i −0.166667 + 0.288675i
\(37\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 1.50000 + 2.59808i 0.243332 + 0.421464i
\(39\) 1.00000 3.46410i 0.160128 0.554700i
\(40\) 1.50000 2.59808i 0.237171 0.410792i
\(41\) 4.50000 + 2.59808i 0.702782 + 0.405751i 0.808383 0.588657i \(-0.200343\pi\)
−0.105601 + 0.994409i \(0.533677\pi\)
\(42\) 0 0
\(43\) −5.50000 9.52628i −0.838742 1.45274i −0.890947 0.454108i \(-0.849958\pi\)
0.0522047 0.998636i \(-0.483375\pi\)
\(44\) −4.50000 2.59808i −0.678401 0.391675i
\(45\) −3.00000 1.73205i −0.447214 0.258199i
\(46\) 0 0
\(47\) 7.50000 + 4.33013i 1.09399 + 0.631614i 0.934635 0.355608i \(-0.115726\pi\)
0.159352 + 0.987222i \(0.449059\pi\)
\(48\) 2.50000 + 4.33013i 0.360844 + 0.625000i
\(49\) 0 0
\(50\) 3.00000 + 1.73205i 0.424264 + 0.244949i
\(51\) 3.00000 5.19615i 0.420084 0.727607i
\(52\) −2.50000 2.59808i −0.346688 0.360288i
\(53\) 4.50000 + 7.79423i 0.618123 + 1.07062i 0.989828 + 0.142269i \(0.0454398\pi\)
−0.371706 + 0.928351i \(0.621227\pi\)
\(54\) 7.50000 4.33013i 1.02062 0.589256i
\(55\) 4.50000 7.79423i 0.606780 1.05097i
\(56\) 0 0
\(57\) 1.73205i 0.229416i
\(58\) 5.19615i 0.682288i
\(59\) 3.00000 + 1.73205i 0.390567 + 0.225494i 0.682406 0.730974i \(-0.260934\pi\)
−0.291839 + 0.956467i \(0.594267\pi\)
\(60\) 1.50000 0.866025i 0.193649 0.111803i
\(61\) −7.00000 −0.896258 −0.448129 0.893969i \(-0.647910\pi\)
−0.448129 + 0.893969i \(0.647910\pi\)
\(62\) 1.50000 2.59808i 0.190500 0.329956i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 4.50000 4.33013i 0.558156 0.537086i
\(66\) 4.50000 + 7.79423i 0.553912 + 0.959403i
\(67\) 8.66025i 1.05802i 0.848616 + 0.529009i \(0.177436\pi\)
−0.848616 + 0.529009i \(0.822564\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.50000 0.866025i 0.178017 0.102778i −0.408344 0.912828i \(-0.633893\pi\)
0.586361 + 0.810050i \(0.300560\pi\)
\(72\) 3.46410i 0.408248i
\(73\) 7.50000 4.33013i 0.877809 0.506803i 0.00787336 0.999969i \(-0.497494\pi\)
0.869935 + 0.493166i \(0.164160\pi\)
\(74\) 0 0
\(75\) −1.00000 1.73205i −0.115470 0.200000i
\(76\) −1.50000 0.866025i −0.172062 0.0993399i
\(77\) 0 0
\(78\) 1.50000 + 6.06218i 0.169842 + 0.686406i
\(79\) 2.50000 4.33013i 0.281272 0.487177i −0.690426 0.723403i \(-0.742577\pi\)
0.971698 + 0.236225i \(0.0759104\pi\)
\(80\) 8.66025i 0.968246i
\(81\) 1.00000 0.111111
\(82\) −9.00000 −0.993884
\(83\) 3.46410i 0.380235i 0.981761 + 0.190117i \(0.0608868\pi\)
−0.981761 + 0.190117i \(0.939113\pi\)
\(84\) 0 0
\(85\) 9.00000 5.19615i 0.976187 0.563602i
\(86\) 16.5000 + 9.52628i 1.77924 + 1.02725i
\(87\) −1.50000 + 2.59808i −0.160817 + 0.278543i
\(88\) −9.00000 −0.959403
\(89\) 6.00000 3.46410i 0.635999 0.367194i −0.147073 0.989126i \(-0.546985\pi\)
0.783072 + 0.621932i \(0.213652\pi\)
\(90\) 6.00000 0.632456
\(91\) 0 0
\(92\) 0 0
\(93\) −1.50000 + 0.866025i −0.155543 + 0.0898027i
\(94\) −15.0000 −1.54713
\(95\) 1.50000 2.59808i 0.153897 0.266557i
\(96\) −4.50000 2.59808i −0.459279 0.265165i
\(97\) 4.50000 2.59808i 0.456906 0.263795i −0.253837 0.967247i \(-0.581693\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) 10.3923i 1.04447i
\(100\) −2.00000 −0.200000
\(101\) 9.00000 0.895533 0.447767 0.894150i \(-0.352219\pi\)
0.447767 + 0.894150i \(0.352219\pi\)
\(102\) 10.3923i 1.02899i
\(103\) −6.50000 + 11.2583i −0.640464 + 1.10932i 0.344865 + 0.938652i \(0.387925\pi\)
−0.985329 + 0.170664i \(0.945409\pi\)
\(104\) −6.00000 1.73205i −0.588348 0.169842i
\(105\) 0 0
\(106\) −13.5000 7.79423i −1.31124 0.757042i
\(107\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(108\) −2.50000 + 4.33013i −0.240563 + 0.416667i
\(109\) 4.50000 2.59808i 0.431022 0.248851i −0.268760 0.963207i \(-0.586614\pi\)
0.699782 + 0.714357i \(0.253281\pi\)
\(110\) 15.5885i 1.48630i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.50000 12.9904i −0.705541 1.22203i −0.966496 0.256681i \(-0.917371\pi\)
0.260955 0.965351i \(-0.415962\pi\)
\(114\) 1.50000 + 2.59808i 0.140488 + 0.243332i
\(115\) 0 0
\(116\) 1.50000 + 2.59808i 0.139272 + 0.241225i
\(117\) −2.00000 + 6.92820i −0.184900 + 0.640513i
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) 1.50000 2.59808i 0.136931 0.237171i
\(121\) −16.0000 −1.45455
\(122\) 10.5000 6.06218i 0.950625 0.548844i
\(123\) 4.50000 + 2.59808i 0.405751 + 0.234261i
\(124\) 1.73205i 0.155543i
\(125\) 12.1244i 1.08444i
\(126\) 0 0
\(127\) −6.50000 + 11.2583i −0.576782 + 0.999015i 0.419064 + 0.907957i \(0.362358\pi\)
−0.995846 + 0.0910585i \(0.970975\pi\)
\(128\) 10.5000 6.06218i 0.928078 0.535826i
\(129\) −5.50000 9.52628i −0.484248 0.838742i
\(130\) −3.00000 + 10.3923i −0.263117 + 0.911465i
\(131\) 7.50000 12.9904i 0.655278 1.13497i −0.326546 0.945181i \(-0.605885\pi\)
0.981824 0.189794i \(-0.0607819\pi\)
\(132\) −4.50000 2.59808i −0.391675 0.226134i
\(133\) 0 0
\(134\) −7.50000 12.9904i −0.647901 1.12220i
\(135\) −7.50000 4.33013i −0.645497 0.372678i
\(136\) −9.00000 5.19615i −0.771744 0.445566i
\(137\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0 0
\(139\) −6.50000 11.2583i −0.551323 0.954919i −0.998179 0.0603135i \(-0.980790\pi\)
0.446857 0.894606i \(-0.352543\pi\)
\(140\) 0 0
\(141\) 7.50000 + 4.33013i 0.631614 + 0.364662i
\(142\) −1.50000 + 2.59808i −0.125877 + 0.218026i
\(143\) −18.0000 5.19615i −1.50524 0.434524i
\(144\) −5.00000 8.66025i −0.416667 0.721688i
\(145\) −4.50000 + 2.59808i −0.373705 + 0.215758i
\(146\) −7.50000 + 12.9904i −0.620704 + 1.07509i
\(147\) 0 0
\(148\) 0 0
\(149\) 19.0526i 1.56085i 0.625252 + 0.780423i \(0.284996\pi\)
−0.625252 + 0.780423i \(0.715004\pi\)
\(150\) 3.00000 + 1.73205i 0.244949 + 0.141421i
\(151\) −10.5000 + 6.06218i −0.854478 + 0.493333i −0.862159 0.506637i \(-0.830888\pi\)
0.00768132 + 0.999970i \(0.497555\pi\)
\(152\) −3.00000 −0.243332
\(153\) −6.00000 + 10.3923i −0.485071 + 0.840168i
\(154\) 0 0
\(155\) −3.00000 −0.240966
\(156\) −2.50000 2.59808i −0.200160 0.208013i
\(157\) 11.5000 + 19.9186i 0.917800 + 1.58968i 0.802749 + 0.596316i \(0.203370\pi\)
0.115050 + 0.993360i \(0.463297\pi\)
\(158\) 8.66025i 0.688973i
\(159\) 4.50000 + 7.79423i 0.356873 + 0.618123i
\(160\) −4.50000 7.79423i −0.355756 0.616188i
\(161\) 0 0
\(162\) −1.50000 + 0.866025i −0.117851 + 0.0680414i
\(163\) 12.1244i 0.949653i −0.880079 0.474826i \(-0.842511\pi\)
0.880079 0.474826i \(-0.157489\pi\)
\(164\) 4.50000 2.59808i 0.351391 0.202876i
\(165\) 4.50000 7.79423i 0.350325 0.606780i
\(166\) −3.00000 5.19615i −0.232845 0.403300i
\(167\) 1.50000 + 0.866025i 0.116073 + 0.0670151i 0.556913 0.830571i \(-0.311986\pi\)
−0.440839 + 0.897586i \(0.645319\pi\)
\(168\) 0 0
\(169\) −11.0000 6.92820i −0.846154 0.532939i
\(170\) −9.00000 + 15.5885i −0.690268 + 1.19558i
\(171\) 3.46410i 0.264906i
\(172\) −11.0000 −0.838742
\(173\) −15.0000 −1.14043 −0.570214 0.821496i \(-0.693140\pi\)
−0.570214 + 0.821496i \(0.693140\pi\)
\(174\) 5.19615i 0.393919i
\(175\) 0 0
\(176\) 22.5000 12.9904i 1.69600 0.979187i
\(177\) 3.00000 + 1.73205i 0.225494 + 0.130189i
\(178\) −6.00000 + 10.3923i −0.449719 + 0.778936i
\(179\) 3.00000 0.224231 0.112115 0.993695i \(-0.464237\pi\)
0.112115 + 0.993695i \(0.464237\pi\)
\(180\) −3.00000 + 1.73205i −0.223607 + 0.129099i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −7.00000 −0.517455
\(184\) 0 0
\(185\) 0 0
\(186\) 1.50000 2.59808i 0.109985 0.190500i
\(187\) −27.0000 15.5885i −1.97444 1.13994i
\(188\) 7.50000 4.33013i 0.546994 0.315807i
\(189\) 0 0
\(190\) 5.19615i 0.376969i
\(191\) −15.0000 −1.08536 −0.542681 0.839939i \(-0.682591\pi\)
−0.542681 + 0.839939i \(0.682591\pi\)
\(192\) −1.00000 −0.0721688
\(193\) 1.73205i 0.124676i 0.998055 + 0.0623379i \(0.0198556\pi\)
−0.998055 + 0.0623379i \(0.980144\pi\)
\(194\) −4.50000 + 7.79423i −0.323081 + 0.559593i
\(195\) 4.50000 4.33013i 0.322252 0.310087i
\(196\) 0 0
\(197\) 19.5000 + 11.2583i 1.38932 + 0.802123i 0.993238 0.116094i \(-0.0370372\pi\)
0.396079 + 0.918216i \(0.370371\pi\)
\(198\) −9.00000 15.5885i −0.639602 1.10782i
\(199\) 2.00000 3.46410i 0.141776 0.245564i −0.786389 0.617731i \(-0.788052\pi\)
0.928166 + 0.372168i \(0.121385\pi\)
\(200\) −3.00000 + 1.73205i −0.212132 + 0.122474i
\(201\) 8.66025i 0.610847i
\(202\) −13.5000 + 7.79423i −0.949857 + 0.548400i
\(203\) 0 0
\(204\) −3.00000 5.19615i −0.210042 0.363803i
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) 22.5167i 1.56881i
\(207\) 0 0
\(208\) 17.5000 4.33013i 1.21341 0.300240i
\(209\) −9.00000 −0.622543
\(210\) 0 0
\(211\) −6.50000 + 11.2583i −0.447478 + 0.775055i −0.998221 0.0596196i \(-0.981011\pi\)
0.550743 + 0.834675i \(0.314345\pi\)
\(212\) 9.00000 0.618123
\(213\) 1.50000 0.866025i 0.102778 0.0593391i
\(214\) 0 0
\(215\) 19.0526i 1.29937i
\(216\) 8.66025i 0.589256i
\(217\) 0 0
\(218\) −4.50000 + 7.79423i −0.304778 + 0.527892i
\(219\) 7.50000 4.33013i 0.506803 0.292603i
\(220\) −4.50000 7.79423i −0.303390 0.525487i
\(221\) −15.0000 15.5885i −1.00901 1.04859i
\(222\) 0 0
\(223\) −4.50000 2.59808i −0.301342 0.173980i 0.341703 0.939808i \(-0.388996\pi\)
−0.643046 + 0.765828i \(0.722329\pi\)
\(224\) 0 0
\(225\) 2.00000 + 3.46410i 0.133333 + 0.230940i
\(226\) 22.5000 + 12.9904i 1.49668 + 0.864107i
\(227\) 15.0000 + 8.66025i 0.995585 + 0.574801i 0.906939 0.421262i \(-0.138413\pi\)
0.0886460 + 0.996063i \(0.471746\pi\)
\(228\) −1.50000 0.866025i −0.0993399 0.0573539i
\(229\) −10.5000 6.06218i −0.693860 0.400600i 0.111197 0.993798i \(-0.464532\pi\)
−0.805056 + 0.593198i \(0.797865\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.50000 + 2.59808i 0.295439 + 0.170572i
\(233\) −1.50000 + 2.59808i −0.0982683 + 0.170206i −0.910968 0.412477i \(-0.864664\pi\)
0.812700 + 0.582683i \(0.197997\pi\)
\(234\) −3.00000 12.1244i −0.196116 0.792594i
\(235\) 7.50000 + 12.9904i 0.489246 + 0.847399i
\(236\) 3.00000 1.73205i 0.195283 0.112747i
\(237\) 2.50000 4.33013i 0.162392 0.281272i
\(238\) 0 0
\(239\) 10.3923i 0.672222i −0.941822 0.336111i \(-0.890888\pi\)
0.941822 0.336111i \(-0.109112\pi\)
\(240\) 8.66025i 0.559017i
\(241\) 6.00000 + 3.46410i 0.386494 + 0.223142i 0.680640 0.732618i \(-0.261702\pi\)
−0.294146 + 0.955761i \(0.595035\pi\)
\(242\) 24.0000 13.8564i 1.54278 0.890724i
\(243\) 16.0000 1.02640
\(244\) −3.50000 + 6.06218i −0.224065 + 0.388091i
\(245\) 0 0
\(246\) −9.00000 −0.573819
\(247\) −6.00000 1.73205i −0.381771 0.110208i
\(248\) 1.50000 + 2.59808i 0.0952501 + 0.164978i
\(249\) 3.46410i 0.219529i
\(250\) 10.5000 + 18.1865i 0.664078 + 1.15022i
\(251\) 1.50000 + 2.59808i 0.0946792 + 0.163989i 0.909475 0.415759i \(-0.136484\pi\)
−0.814795 + 0.579748i \(0.803151\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 22.5167i 1.41282i
\(255\) 9.00000 5.19615i 0.563602 0.325396i
\(256\) −9.50000 + 16.4545i −0.593750 + 1.02841i
\(257\) 15.0000 + 25.9808i 0.935674 + 1.62064i 0.773427 + 0.633885i \(0.218541\pi\)
0.162247 + 0.986750i \(0.448126\pi\)
\(258\) 16.5000 + 9.52628i 1.02725 + 0.593080i
\(259\) 0 0
\(260\) −1.50000 6.06218i −0.0930261 0.375960i
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) 25.9808i 1.60510i
\(263\) 3.00000 0.184988 0.0924940 0.995713i \(-0.470516\pi\)
0.0924940 + 0.995713i \(0.470516\pi\)
\(264\) −9.00000 −0.553912
\(265\) 15.5885i 0.957591i
\(266\) 0 0
\(267\) 6.00000 3.46410i 0.367194 0.212000i
\(268\) 7.50000 + 4.33013i 0.458135 + 0.264505i
\(269\) −3.00000 + 5.19615i −0.182913 + 0.316815i −0.942871 0.333157i \(-0.891886\pi\)
0.759958 + 0.649972i \(0.225219\pi\)
\(270\) 15.0000 0.912871
\(271\) 15.0000 8.66025i 0.911185 0.526073i 0.0303728 0.999539i \(-0.490331\pi\)
0.880812 + 0.473466i \(0.156997\pi\)
\(272\) 30.0000 1.81902
\(273\) 0 0
\(274\) 0 0
\(275\) −9.00000 + 5.19615i −0.542720 + 0.313340i
\(276\) 0 0
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) 19.5000 + 11.2583i 1.16953 + 0.675230i
\(279\) 3.00000 1.73205i 0.179605 0.103695i
\(280\) 0 0
\(281\) 6.92820i 0.413302i 0.978415 + 0.206651i \(0.0662565\pi\)
−0.978415 + 0.206651i \(0.933744\pi\)
\(282\) −15.0000 −0.893237
\(283\) −19.0000 −1.12943 −0.564716 0.825285i \(-0.691014\pi\)
−0.564716 + 0.825285i \(0.691014\pi\)
\(284\) 1.73205i 0.102778i
\(285\) 1.50000 2.59808i 0.0888523 0.153897i
\(286\) 31.5000 7.79423i 1.86263 0.460882i
\(287\) 0 0
\(288\) 9.00000 + 5.19615i 0.530330 + 0.306186i
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) 4.50000 7.79423i 0.264249 0.457693i
\(291\) 4.50000 2.59808i 0.263795 0.152302i
\(292\) 8.66025i 0.506803i
\(293\) 22.5000 12.9904i 1.31446 0.758906i 0.331632 0.943409i \(-0.392401\pi\)
0.982832 + 0.184503i \(0.0590674\pi\)
\(294\) 0 0
\(295\) 3.00000 + 5.19615i 0.174667 + 0.302532i
\(296\) 0 0
\(297\) 25.9808i 1.50756i
\(298\) −16.5000 28.5788i −0.955819 1.65553i
\(299\) 0 0
\(300\) −2.00000 −0.115470
\(301\) 0 0
\(302\) 10.5000 18.1865i 0.604207 1.04652i
\(303\) 9.00000 0.517036
\(304\) 7.50000 4.33013i 0.430155 0.248350i
\(305\) −10.5000 6.06218i −0.601228 0.347119i
\(306\) 20.7846i 1.18818i
\(307\) 24.2487i 1.38395i 0.721923 + 0.691974i \(0.243259\pi\)
−0.721923 + 0.691974i \(0.756741\pi\)
\(308\) 0 0
\(309\) −6.50000 + 11.2583i −0.369772 + 0.640464i
\(310\) 4.50000 2.59808i 0.255583 0.147561i
\(311\) −7.50000 12.9904i −0.425286 0.736617i 0.571161 0.820838i \(-0.306493\pi\)
−0.996447 + 0.0842210i \(0.973160\pi\)
\(312\) −6.00000 1.73205i −0.339683 0.0980581i
\(313\) 9.50000 16.4545i 0.536972 0.930062i −0.462093 0.886831i \(-0.652902\pi\)
0.999065 0.0432311i \(-0.0137652\pi\)
\(314\) −34.5000 19.9186i −1.94695 1.12407i
\(315\) 0 0
\(316\) −2.50000 4.33013i −0.140636 0.243589i
\(317\) 4.50000 + 2.59808i 0.252745 + 0.145922i 0.621021 0.783794i \(-0.286718\pi\)
−0.368275 + 0.929717i \(0.620052\pi\)
\(318\) −13.5000 7.79423i −0.757042 0.437079i
\(319\) 13.5000 + 7.79423i 0.755855 + 0.436393i
\(320\) −1.50000 0.866025i −0.0838525 0.0484123i
\(321\) 0 0
\(322\) 0 0
\(323\) −9.00000 5.19615i −0.500773 0.289122i
\(324\) 0.500000 0.866025i 0.0277778 0.0481125i
\(325\) −7.00000 + 1.73205i −0.388290 + 0.0960769i
\(326\) 10.5000 + 18.1865i 0.581541 + 1.00726i
\(327\) 4.50000 2.59808i 0.248851 0.143674i
\(328\) 4.50000 7.79423i 0.248471 0.430364i
\(329\) 0 0
\(330\) 15.5885i 0.858116i
\(331\) 32.9090i 1.80884i −0.426643 0.904420i \(-0.640304\pi\)
0.426643 0.904420i \(-0.359696\pi\)
\(332\) 3.00000 + 1.73205i 0.164646 + 0.0950586i
\(333\) 0 0
\(334\) −3.00000 −0.164153
\(335\) −7.50000 + 12.9904i −0.409769 + 0.709740i
\(336\) 0 0
\(337\) 22.0000 1.19842 0.599208 0.800593i \(-0.295482\pi\)
0.599208 + 0.800593i \(0.295482\pi\)
\(338\) 22.5000 + 0.866025i 1.22384 + 0.0471056i
\(339\) −7.50000 12.9904i −0.407344 0.705541i
\(340\) 10.3923i 0.563602i
\(341\) 4.50000 + 7.79423i 0.243689 + 0.422081i
\(342\) −3.00000 5.19615i −0.162221 0.280976i
\(343\) 0 0
\(344\) −16.5000 + 9.52628i −0.889620 + 0.513623i
\(345\) 0 0
\(346\) 22.5000 12.9904i 1.20961 0.698367i
\(347\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(348\) 1.50000 + 2.59808i 0.0804084 + 0.139272i
\(349\) 4.50000 + 2.59808i 0.240879 + 0.139072i 0.615581 0.788074i \(-0.288921\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) 0 0
\(351\) −5.00000 + 17.3205i −0.266880 + 0.924500i
\(352\) −13.5000 + 23.3827i −0.719552 + 1.24630i
\(353\) 1.73205i 0.0921878i −0.998937 0.0460939i \(-0.985323\pi\)
0.998937 0.0460939i \(-0.0146773\pi\)
\(354\) −6.00000 −0.318896
\(355\) 3.00000 0.159223
\(356\) 6.92820i 0.367194i
\(357\) 0 0
\(358\) −4.50000 + 2.59808i −0.237832 + 0.137313i
\(359\) 16.5000 + 9.52628i 0.870837 + 0.502778i 0.867626 0.497217i \(-0.165645\pi\)
0.00321050 + 0.999995i \(0.498978\pi\)
\(360\) −3.00000 + 5.19615i −0.158114 + 0.273861i
\(361\) 16.0000 0.842105
\(362\) 3.00000 1.73205i 0.157676 0.0910346i
\(363\) −16.0000 −0.839782
\(364\) 0 0
\(365\) 15.0000 0.785136
\(366\) 10.5000 6.06218i 0.548844 0.316875i
\(367\) −23.0000 −1.20059 −0.600295 0.799779i \(-0.704950\pi\)
−0.600295 + 0.799779i \(0.704950\pi\)
\(368\) 0 0
\(369\) −9.00000 5.19615i −0.468521 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 1.73205i 0.0898027i
\(373\) 19.0000 0.983783 0.491891 0.870657i \(-0.336306\pi\)
0.491891 + 0.870657i \(0.336306\pi\)
\(374\) 54.0000 2.79227
\(375\) 12.1244i 0.626099i
\(376\) 7.50000 12.9904i 0.386783 0.669928i
\(377\) 7.50000 + 7.79423i 0.386270 + 0.401423i
\(378\) 0 0
\(379\) −1.50000 0.866025i −0.0770498 0.0444847i 0.460980 0.887410i \(-0.347498\pi\)
−0.538030 + 0.842926i \(0.680831\pi\)
\(380\) −1.50000 2.59808i −0.0769484 0.133278i
\(381\) −6.50000 + 11.2583i −0.333005 + 0.576782i
\(382\) 22.5000 12.9904i 1.15120 0.664646i
\(383\) 15.5885i 0.796533i −0.917270 0.398266i \(-0.869612\pi\)
0.917270 0.398266i \(-0.130388\pi\)
\(384\) 10.5000 6.06218i 0.535826 0.309359i
\(385\) 0 0
\(386\) −1.50000 2.59808i −0.0763480 0.132239i
\(387\) 11.0000 + 19.0526i 0.559161 + 0.968496i
\(388\) 5.19615i 0.263795i
\(389\) −1.50000 2.59808i −0.0760530 0.131728i 0.825491 0.564416i \(-0.190898\pi\)
−0.901544 + 0.432688i \(0.857565\pi\)
\(390\) −3.00000 + 10.3923i −0.151911 + 0.526235i
\(391\) 0 0
\(392\) 0 0
\(393\) 7.50000 12.9904i 0.378325 0.655278i
\(394\) −39.0000 −1.96479
\(395\) 7.50000 4.33013i 0.377366 0.217872i
\(396\) 9.00000 + 5.19615i 0.452267 + 0.261116i
\(397\) 36.3731i 1.82551i 0.408505 + 0.912756i \(0.366050\pi\)
−0.408505 + 0.912756i \(0.633950\pi\)
\(398\) 6.92820i 0.347279i
\(399\) 0 0
\(400\) 5.00000 8.66025i 0.250000 0.433013i
\(401\) −6.00000 + 3.46410i −0.299626 + 0.172989i −0.642275 0.766475i \(-0.722009\pi\)
0.342649 + 0.939463i \(0.388676\pi\)
\(402\) −7.50000 12.9904i −0.374066 0.647901i
\(403\) 1.50000 + 6.06218i 0.0747203 + 0.301979i
\(404\) 4.50000 7.79423i 0.223883 0.387777i
\(405\) 1.50000 + 0.866025i 0.0745356 + 0.0430331i
\(406\) 0 0
\(407\) 0 0
\(408\) −9.00000 5.19615i −0.445566 0.257248i
\(409\) −6.00000 3.46410i −0.296681 0.171289i 0.344270 0.938871i \(-0.388126\pi\)
−0.640951 + 0.767582i \(0.721460\pi\)
\(410\) −13.5000 7.79423i −0.666717 0.384930i
\(411\) 0 0
\(412\) 6.50000 + 11.2583i 0.320232 + 0.554658i
\(413\) 0 0
\(414\) 0 0
\(415\) −3.00000 + 5.19615i −0.147264 + 0.255069i
\(416\) −13.5000 + 12.9904i −0.661892 + 0.636906i
\(417\) −6.50000 11.2583i −0.318306 0.551323i
\(418\) 13.5000 7.79423i 0.660307 0.381228i
\(419\) 10.5000 18.1865i 0.512959 0.888470i −0.486928 0.873442i \(-0.661883\pi\)
0.999887 0.0150285i \(-0.00478389\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 22.5167i 1.09609i
\(423\) −15.0000 8.66025i −0.729325 0.421076i
\(424\) 13.5000 7.79423i 0.655618 0.378521i
\(425\) −12.0000 −0.582086
\(426\) −1.50000 + 2.59808i −0.0726752 + 0.125877i
\(427\) 0 0
\(428\) 0 0
\(429\) −18.0000 5.19615i −0.869048 0.250873i
\(430\) 16.5000 + 28.5788i 0.795701 + 1.37819i
\(431\) 32.9090i 1.58517i −0.609762 0.792585i \(-0.708735\pi\)
0.609762 0.792585i \(-0.291265\pi\)
\(432\) −12.5000 21.6506i −0.601407 1.04167i
\(433\) 9.50000 + 16.4545i 0.456541 + 0.790752i 0.998775 0.0494752i \(-0.0157549\pi\)
−0.542234 + 0.840227i \(0.682422\pi\)
\(434\) 0 0
\(435\) −4.50000 + 2.59808i −0.215758 + 0.124568i
\(436\) 5.19615i 0.248851i
\(437\) 0 0
\(438\) −7.50000 + 12.9904i −0.358364 + 0.620704i
\(439\) 4.00000 + 6.92820i 0.190910 + 0.330665i 0.945552 0.325471i \(-0.105523\pi\)
−0.754642 + 0.656136i \(0.772190\pi\)
\(440\) −13.5000 7.79423i −0.643587 0.371575i
\(441\) 0 0
\(442\) 36.0000 + 10.3923i 1.71235 + 0.494312i
\(443\) −7.50000 + 12.9904i −0.356336 + 0.617192i −0.987346 0.158583i \(-0.949307\pi\)
0.631010 + 0.775775i \(0.282641\pi\)
\(444\) 0 0
\(445\) 12.0000 0.568855
\(446\) 9.00000 0.426162
\(447\) 19.0526i 0.901155i
\(448\) 0 0
\(449\) 1.50000 0.866025i 0.0707894 0.0408703i −0.464188 0.885737i \(-0.653654\pi\)
0.534977 + 0.844867i \(0.320320\pi\)
\(450\) −6.00000 3.46410i −0.282843 0.163299i
\(451\) 13.5000 23.3827i 0.635690 1.10105i
\(452\) −15.0000 −0.705541
\(453\) −10.5000 + 6.06218i −0.493333 + 0.284826i
\(454\) −30.0000 −1.40797
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) −30.0000 + 17.3205i −1.40334 + 0.810219i −0.994734 0.102491i \(-0.967319\pi\)
−0.408607 + 0.912710i \(0.633985\pi\)
\(458\) 21.0000 0.981266
\(459\) −15.0000 + 25.9808i −0.700140 + 1.21268i
\(460\) 0 0
\(461\) −25.5000 + 14.7224i −1.18765 + 0.685692i −0.957773 0.287527i \(-0.907167\pi\)
−0.229881 + 0.973219i \(0.573834\pi\)
\(462\) 0 0
\(463\) 24.2487i 1.12693i 0.826139 + 0.563467i \(0.190533\pi\)
−0.826139 + 0.563467i \(0.809467\pi\)
\(464\) −15.0000 −0.696358
\(465\) −3.00000 −0.139122
\(466\) 5.19615i 0.240707i
\(467\) −10.5000 + 18.1865i −0.485882 + 0.841572i −0.999868 0.0162260i \(-0.994835\pi\)
0.513986 + 0.857798i \(0.328168\pi\)
\(468\) 5.00000 + 5.19615i 0.231125 + 0.240192i
\(469\) 0 0
\(470\) −22.5000 12.9904i −1.03785 0.599202i
\(471\) 11.5000 + 19.9186i 0.529892 + 0.917800i
\(472\) 3.00000 5.19615i 0.138086 0.239172i
\(473\) −49.5000 + 28.5788i −2.27601 + 1.31406i
\(474\) 8.66025i 0.397779i
\(475\) −3.00000 + 1.73205i −0.137649 + 0.0794719i
\(476\) 0 0
\(477\) −9.00000 15.5885i −0.412082 0.713746i
\(478\) 9.00000 + 15.5885i 0.411650 + 0.712999i
\(479\) 29.4449i 1.34537i −0.739929 0.672685i \(-0.765141\pi\)
0.739929 0.672685i \(-0.234859\pi\)
\(480\) −4.50000 7.79423i −0.205396 0.355756i
\(481\) 0 0
\(482\) −12.0000 −0.546585
\(483\) 0 0
\(484\) −8.00000 + 13.8564i −0.363636 + 0.629837i
\(485\) 9.00000 0.408669
\(486\) −24.0000 + 13.8564i −1.08866 + 0.628539i
\(487\) −21.0000 12.1244i −0.951601 0.549407i −0.0580230 0.998315i \(-0.518480\pi\)
−0.893578 + 0.448908i \(0.851813\pi\)
\(488\) 12.1244i 0.548844i
\(489\) 12.1244i 0.548282i
\(490\) 0 0
\(491\) 13.5000 23.3827i 0.609246 1.05525i −0.382118 0.924113i \(-0.624805\pi\)
0.991365 0.131132i \(-0.0418613\pi\)
\(492\) 4.50000 2.59808i 0.202876 0.117130i
\(493\) 9.00000 + 15.5885i 0.405340 + 0.702069i
\(494\) 10.5000 2.59808i 0.472417 0.116893i
\(495\) −9.00000 + 15.5885i −0.404520 + 0.700649i
\(496\) −7.50000 4.33013i −0.336760 0.194428i
\(497\) 0 0
\(498\) −3.00000 5.19615i −0.134433 0.232845i
\(499\) −1.50000 0.866025i −0.0671492 0.0387686i 0.466049 0.884759i \(-0.345677\pi\)
−0.533199 + 0.845990i \(0.679010\pi\)
\(500\) −10.5000 6.06218i −0.469574 0.271109i
\(501\) 1.50000 + 0.866025i 0.0670151 + 0.0386912i
\(502\) −4.50000 2.59808i −0.200845 0.115958i
\(503\) −4.50000 7.79423i −0.200645 0.347527i 0.748091 0.663596i \(-0.230970\pi\)
−0.948736 + 0.316068i \(0.897637\pi\)
\(504\) 0 0
\(505\) 13.5000 + 7.79423i 0.600742 + 0.346839i
\(506\) 0 0
\(507\) −11.0000 6.92820i −0.488527 0.307692i
\(508\) 6.50000 + 11.2583i 0.288391 + 0.499508i
\(509\) 6.00000 3.46410i 0.265945 0.153544i −0.361098 0.932528i \(-0.617598\pi\)
0.627044 + 0.778984i \(0.284265\pi\)
\(510\) −9.00000 + 15.5885i −0.398527 + 0.690268i
\(511\) 0 0
\(512\) 8.66025i 0.382733i
\(513\) 8.66025i 0.382360i
\(514\) −45.0000 25.9808i −1.98486 1.14596i
\(515\) −19.5000 + 11.2583i −0.859273 + 0.496101i
\(516\) −11.0000 −0.484248
\(517\) 22.5000 38.9711i 0.989549 1.71395i
\(518\) 0 0
\(519\) −15.0000 −0.658427
\(520\) −7.50000 7.79423i −0.328897 0.341800i
\(521\) 19.5000 + 33.7750i 0.854311 + 1.47971i 0.877283 + 0.479973i \(0.159354\pi\)
−0.0229727 + 0.999736i \(0.507313\pi\)
\(522\) 10.3923i 0.454859i
\(523\) −2.00000 3.46410i −0.0874539 0.151475i 0.818980 0.573822i \(-0.194540\pi\)
−0.906434 + 0.422347i \(0.861206\pi\)
\(524\) −7.50000 12.9904i −0.327639 0.567487i
\(525\) 0 0
\(526\) −4.50000 + 2.59808i −0.196209 + 0.113282i
\(527\) 10.3923i 0.452696i
\(528\) 22.5000 12.9904i 0.979187 0.565334i
\(529\) 11.5000 19.9186i 0.500000 0.866025i
\(530\) −13.5000 23.3827i −0.586403 1.01568i
\(531\) −6.00000 3.46410i −0.260378 0.150329i
\(532\) 0 0
\(533\) 13.5000 12.9904i 0.584750 0.562676i
\(534\) −6.00000 + 10.3923i −0.259645 + 0.449719i
\(535\) 0 0
\(536\) 15.0000 0.647901
\(537\) 3.00000 0.129460
\(538\) 10.3923i 0.448044i
\(539\) 0 0
\(540\) −7.50000 + 4.33013i −0.322749 + 0.186339i
\(541\) 10.5000 + 6.06218i 0.451430 + 0.260633i 0.708434 0.705777i \(-0.249402\pi\)
−0.257004 + 0.966410i \(0.582735\pi\)
\(542\) −15.0000 + 25.9808i −0.644305 + 1.11597i
\(543\) −2.00000 −0.0858282
\(544\) −27.0000 + 15.5885i −1.15762 + 0.668350i
\(545\) 9.00000 0.385518
\(546\) 0 0
\(547\) −28.0000 −1.19719 −0.598597 0.801050i \(-0.704275\pi\)
−0.598597 + 0.801050i \(0.704275\pi\)
\(548\) 0 0
\(549\) 14.0000 0.597505
\(550\) 9.00000 15.5885i 0.383761 0.664694i
\(551\) 4.50000 + 2.59808i 0.191706 + 0.110682i
\(552\) 0 0
\(553\) 0 0
\(554\) 17.3205i 0.735878i
\(555\) 0 0
\(556\) −13.0000 −0.551323
\(557\) 15.5885i 0.660504i 0.943893 + 0.330252i \(0.107134\pi\)
−0.943893 + 0.330252i \(0.892866\pi\)
\(558\) −3.00000 + 5.19615i −0.127000 + 0.219971i
\(559\) −38.5000 + 9.52628i −1.62838 + 0.402919i
\(560\) 0 0
\(561\) −27.0000 15.5885i −1.13994 0.658145i
\(562\) −6.00000 10.3923i −0.253095 0.438373i
\(563\) −18.0000 + 31.1769i −0.758610 + 1.31395i 0.184950 + 0.982748i \(0.440788\pi\)
−0.943560 + 0.331202i \(0.892546\pi\)
\(564\) 7.50000 4.33013i 0.315807 0.182331i
\(565\) 25.9808i 1.09302i
\(566\) 28.5000 16.4545i 1.19794 0.691633i
\(567\) 0 0
\(568\) −1.50000 2.59808i −0.0629386 0.109013i
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 5.19615i 0.217643i
\(571\) 11.5000 + 19.9186i 0.481260 + 0.833567i 0.999769 0.0215055i \(-0.00684595\pi\)
−0.518509 + 0.855072i \(0.673513\pi\)
\(572\) −13.5000 + 12.9904i −0.564463 + 0.543155i
\(573\) −15.0000 −0.626634
\(574\) 0 0
\(575\) 0 0
\(576\) 2.00000 0.0833333
\(577\) 13.5000 7.79423i 0.562012 0.324478i −0.191940 0.981407i \(-0.561478\pi\)
0.753953 + 0.656929i \(0.228145\pi\)
\(578\) 28.5000 + 16.4545i 1.18544 + 0.684416i
\(579\) 1.73205i 0.0719816i
\(580\) 5.19615i 0.215758i
\(581\) 0 0
\(582\) −4.50000 + 7.79423i −0.186531 + 0.323081i
\(583\) 40.5000 23.3827i 1.67734 0.968412i
\(584\) −7.50000 12.9904i −0.310352 0.537546i
\(585\) −9.00000 + 8.66025i −0.372104 + 0.358057i
\(586\) −22.5000 + 38.9711i −0.929466 + 1.60988i
\(587\) 13.5000 + 7.79423i 0.557205 + 0.321702i 0.752023 0.659137i \(-0.229078\pi\)
−0.194818 + 0.980839i \(0.562412\pi\)
\(588\) 0 0
\(589\) 1.50000 + 2.59808i 0.0618064 + 0.107052i
\(590\) −9.00000 5.19615i −0.370524 0.213922i
\(591\) 19.5000 + 11.2583i 0.802123 + 0.463106i
\(592\) 0 0
\(593\) −4.50000 2.59808i −0.184793 0.106690i 0.404750 0.914428i \(-0.367359\pi\)
−0.589543 + 0.807737i \(0.700692\pi\)
\(594\) −22.5000 38.9711i −0.923186 1.59901i
\(595\) 0 0
\(596\) 16.5000 + 9.52628i 0.675866 + 0.390212i
\(597\) 2.00000 3.46410i 0.0818546 0.141776i
\(598\) 0 0
\(599\) −4.50000 7.79423i −0.183865 0.318464i 0.759328 0.650708i \(-0.225528\pi\)
−0.943193 + 0.332244i \(0.892194\pi\)
\(600\) −3.00000 + 1.73205i −0.122474 + 0.0707107i
\(601\) 9.50000 16.4545i 0.387513 0.671192i −0.604601 0.796528i \(-0.706668\pi\)
0.992114 + 0.125336i \(0.0400009\pi\)
\(602\) 0 0
\(603\) 17.3205i 0.705346i
\(604\) 12.1244i 0.493333i
\(605\) −24.0000 13.8564i −0.975739 0.563343i
\(606\) −13.5000 + 7.79423i −0.548400 + 0.316619i
\(607\) 43.0000 1.74532 0.872658 0.488332i \(-0.162394\pi\)
0.872658 + 0.488332i \(0.162394\pi\)
\(608\) −4.50000 + 7.79423i −0.182499 + 0.316098i
\(609\) 0 0
\(610\) 21.0000 0.850265
\(611\) 22.5000 21.6506i 0.910253 0.875891i
\(612\) 6.00000 + 10.3923i 0.242536 + 0.420084i
\(613\) 36.3731i 1.46909i 0.678558 + 0.734547i \(0.262605\pi\)
−0.678558 + 0.734547i \(0.737395\pi\)
\(614\) −21.0000 36.3731i −0.847491 1.46790i
\(615\) 4.50000 + 7.79423i 0.181458 + 0.314294i
\(616\) 0 0
\(617\) 37.5000 21.6506i 1.50969 0.871622i 0.509757 0.860318i \(-0.329735\pi\)
0.999936 0.0113033i \(-0.00359804\pi\)
\(618\) 22.5167i 0.905753i
\(619\) 16.5000 9.52628i 0.663191 0.382893i −0.130301 0.991475i \(-0.541594\pi\)
0.793492 + 0.608581i \(0.208261\pi\)
\(620\) −1.50000 + 2.59808i −0.0602414 + 0.104341i
\(621\) 0 0
\(622\) 22.5000 + 12.9904i 0.902168 + 0.520867i
\(623\) 0 0
\(624\) 17.5000 4.33013i 0.700561 0.173344i
\(625\) 5.50000 9.52628i 0.220000 0.381051i
\(626\) 32.9090i 1.31531i
\(627\) −9.00000 −0.359425
\(628\) 23.0000 0.917800
\(629\) 0 0
\(630\) 0 0
\(631\) −40.5000 + 23.3827i −1.61228 + 0.930850i −0.623439 + 0.781872i \(0.714265\pi\)
−0.988841 + 0.148978i \(0.952402\pi\)
\(632\) −7.50000 4.33013i −0.298334 0.172243i
\(633\) −6.50000 + 11.2583i −0.258352 + 0.447478i
\(634\) −9.00000 −0.357436
\(635\) −19.5000 + 11.2583i −0.773834 + 0.446773i
\(636\) 9.00000 0.356873
\(637\) 0 0
\(638\) −27.0000 −1.06894
\(639\) −3.00000 + 1.73205i −0.118678 + 0.0685189i
\(640\) 21.0000 0.830098
\(641\) −15.0000 + 25.9808i −0.592464 + 1.02618i 0.401435 + 0.915888i \(0.368512\pi\)
−0.993899 + 0.110291i \(0.964822\pi\)
\(642\) 0 0
\(643\) 4.50000 2.59808i 0.177463 0.102458i −0.408637 0.912697i \(-0.633996\pi\)
0.586100 + 0.810239i \(0.300663\pi\)
\(644\) 0 0
\(645\) 19.0526i 0.750194i
\(646\) 18.0000 0.708201
\(647\) 9.00000 0.353827 0.176913 0.984226i \(-0.443389\pi\)
0.176913 + 0.984226i \(0.443389\pi\)
\(648\) 1.73205i 0.0680414i
\(649\) 9.00000 15.5885i 0.353281 0.611900i
\(650\) 9.00000 8.66025i 0.353009 0.339683i
\(651\) 0 0
\(652\) −10.5000 6.06218i −0.411212 0.237413i
\(653\) 15.0000 + 25.9808i 0.586995 + 1.01671i 0.994623 + 0.103558i \(0.0330227\pi\)
−0.407628 + 0.913148i \(0.633644\pi\)
\(654\) −4.50000 + 7.79423i −0.175964 + 0.304778i
\(655\) 22.5000 12.9904i 0.879148 0.507576i
\(656\) 25.9808i 1.01438i
\(657\) −15.0000 + 8.66025i −0.585206 + 0.337869i
\(658\) 0 0
\(659\) −7.50000 12.9904i −0.292159 0.506033i 0.682161 0.731202i \(-0.261040\pi\)
−0.974320 + 0.225168i \(0.927707\pi\)
\(660\) −4.50000 7.79423i −0.175162 0.303390i
\(661\) 36.3731i 1.41475i −0.706839 0.707374i \(-0.749880\pi\)
0.706839 0.707374i \(-0.250120\pi\)
\(662\) 28.5000 + 49.3634i 1.10768 + 1.91856i
\(663\) −15.0000 15.5885i −0.582552 0.605406i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.50000 0.866025i 0.0580367 0.0335075i
\(669\) −4.50000 2.59808i −0.173980 0.100447i
\(670\) 25.9808i 1.00372i
\(671\) 36.3731i 1.40417i
\(672\) 0 0
\(673\) 0.500000 0.866025i 0.0192736 0.0333828i −0.856228 0.516599i \(-0.827198\pi\)
0.875501 + 0.483216i \(0.160531\pi\)
\(674\) −33.0000 + 19.0526i −1.27111 + 0.733877i
\(675\) 5.00000 + 8.66025i 0.192450 + 0.333333i
\(676\) −11.5000 + 6.06218i −0.442308 + 0.233161i
\(677\) 13.5000 23.3827i 0.518847 0.898670i −0.480913 0.876768i \(-0.659695\pi\)
0.999760 0.0219013i \(-0.00697196\pi\)
\(678\) 22.5000 + 12.9904i 0.864107 + 0.498893i
\(679\) 0 0
\(680\) −9.00000 15.5885i −0.345134 0.597790i
\(681\) 15.0000 + 8.66025i 0.574801 + 0.331862i
\(682\) −13.5000 7.79423i −0.516942 0.298456i
\(683\) 21.0000 + 12.1244i 0.803543 + 0.463926i 0.844708 0.535227i \(-0.179774\pi\)
−0.0411658 + 0.999152i \(0.513107\pi\)
\(684\) 3.00000 + 1.73205i 0.114708 + 0.0662266i
\(685\) 0 0
\(686\) 0 0
\(687\) −10.5000 6.06218i −0.400600 0.231287i
\(688\) 27.5000 47.6314i 1.04843 1.81593i
\(689\) 31.5000 7.79423i 1.20005 0.296936i
\(690\) 0 0
\(691\) −27.0000 + 15.5885i −1.02713 + 0.593013i −0.916161 0.400811i \(-0.868728\pi\)
−0.110968 + 0.993824i \(0.535395\pi\)
\(692\) −7.50000 + 12.9904i −0.285107 + 0.493820i
\(693\) 0 0
\(694\) 0 0
\(695\) 22.5167i 0.854106i
\(696\) 4.50000 + 2.59808i 0.170572 + 0.0984798i
\(697\) 27.0000 15.5885i 1.02270 0.590455i
\(698\) −9.00000 −0.340655
\(699\) −1.50000 + 2.59808i −0.0567352 + 0.0982683i
\(700\) 0 0
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) −7.50000 30.3109i −0.283069 1.14401i
\(703\) 0 0
\(704\) 5.19615i 0.195837i
\(705\) 7.50000 + 12.9904i 0.282466 + 0.489246i
\(706\) 1.50000 + 2.59808i 0.0564532 + 0.0977799i
\(707\) 0 0
\(708\) 3.00000 1.73205i 0.112747 0.0650945i
\(709\) 12.1244i 0.455340i 0.973738 + 0.227670i \(0.0731107\pi\)
−0.973738 + 0.227670i \(0.926889\pi\)
\(710\) −4.50000 + 2.59808i −0.168882 + 0.0975041i
\(711\) −5.00000 + 8.66025i −0.187515 + 0.324785i
\(712\) −6.00000 10.3923i −0.224860 0.389468i
\(713\) 0 0
\(714\) 0 0
\(715\) −22.5000 23.3827i −0.841452 0.874463i
\(716\) 1.50000 2.59808i 0.0560576 0.0970947i
\(717\) 10.3923i 0.388108i
\(718\) −33.0000 −1.23155
\(719\) 15.0000 0.559406 0.279703 0.960087i \(-0.409764\pi\)
0.279703 + 0.960087i \(0.409764\pi\)
\(720\) 17.3205i 0.645497i
\(721\) 0 0
\(722\) −24.0000 + 13.8564i −0.893188 + 0.515682i
\(723\) 6.00000 + 3.46410i 0.223142 + 0.128831i
\(724\) −1.00000 + 1.73205i −0.0371647 + 0.0643712i
\(725\) 6.00000 0.222834
\(726\) 24.0000 13.8564i 0.890724 0.514259i
\(727\) 32.0000 1.18681 0.593407 0.804902i \(-0.297782\pi\)
0.593407 + 0.804902i \(0.297782\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −22.5000 + 12.9904i −0.832762 + 0.480796i
\(731\) −66.0000 −2.44110
\(732\) −3.50000 + 6.06218i −0.129364 + 0.224065i
\(733\) 43.5000 + 25.1147i 1.60671 + 0.927634i 0.990100 + 0.140365i \(0.0448275\pi\)
0.616609 + 0.787269i \(0.288506\pi\)
\(734\) 34.5000 19.9186i 1.27342 0.735208i
\(735\) 0 0
\(736\) 0 0
\(737\) 45.0000 1.65760
\(738\) 18.0000 0.662589
\(739\) 39.8372i 1.46543i −0.680534 0.732717i \(-0.738252\pi\)
0.680534 0.732717i \(-0.261748\pi\)
\(740\) 0 0
\(741\) −6.00000 1.73205i −0.220416 0.0636285i
\(742\) 0 0
\(743\) −1.50000 0.866025i −0.0550297 0.0317714i 0.472233 0.881474i \(-0.343448\pi\)
−0.527262 + 0.849703i \(0.676782\pi\)
\(744\) 1.50000 + 2.59808i 0.0549927 + 0.0952501i
\(745\) −16.5000 + 28.5788i −0.604513 + 1.04705i
\(746\) −28.5000 + 16.4545i −1.04346 + 0.602441i
\(747\) 6.92820i 0.253490i
\(748\) −27.0000 + 15.5885i −0.987218 + 0.569970i
\(749\) 0 0
\(750\) 10.5000 + 18.1865i 0.383406 + 0.664078i
\(751\) −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i \(-0.285565\pi\)
−0.988761 + 0.149505i \(0.952232\pi\)
\(752\) 43.3013i 1.57903i
\(753\) 1.50000 + 2.59808i 0.0546630 + 0.0946792i
\(754\) −18.0000 5.19615i −0.655521 0.189233i
\(755\) −21.0000 −0.764268
\(756\) 0 0
\(757\) 8.50000 14.7224i 0.308938 0.535096i −0.669193 0.743089i \(-0.733360\pi\)
0.978130 + 0.207993i \(0.0666932\pi\)
\(758\) 3.00000 0.108965
\(759\) 0 0
\(760\) −4.50000 2.59808i −0.163232 0.0942421i
\(761\) 29.4449i 1.06738i 0.845682 + 0.533688i \(0.179194\pi\)
−0.845682 + 0.533688i \(0.820806\pi\)
\(762\) 22.5167i 0.815693i
\(763\) 0 0
\(764\) −7.50000 + 12.9904i −0.271340 + 0.469975i
\(765\) −18.0000 + 10.3923i −0.650791 + 0.375735i
\(766\) 13.5000 + 23.3827i 0.487775 + 0.844851i
\(767\) 9.00000 8.66025i 0.324971 0.312704i
\(768\) −9.50000 + 16.4545i −0.342802 + 0.593750i
\(769\) 16.5000 + 9.52628i 0.595005 + 0.343526i 0.767074 0.641558i \(-0.221712\pi\)
−0.172069 + 0.985085i \(0.555045\pi\)
\(770\) 0 0
\(771\) 15.0000 + 25.9808i 0.540212 + 0.935674i
\(772\) 1.50000 + 0.866025i 0.0539862 + 0.0311689i
\(773\) 12.0000 + 6.92820i 0.431610 + 0.249190i 0.700032 0.714111i \(-0.253169\pi\)
−0.268422 + 0.963301i \(0.586502\pi\)
\(774\) −33.0000 19.0526i −1.18616 0.684830i
\(775\) 3.00000 + 1.73205i 0.107763 + 0.0622171i
\(776\) −4.50000 7.79423i −0.161541 0.279797i
\(777\) 0 0
\(778\) 4.50000 + 2.59808i 0.161333 + 0.0931455i
\(779\) 4.50000 7.79423i 0.161229 0.279257i
\(780\) −1.50000 6.06218i −0.0537086 0.217061i
\(781\) −4.50000 7.79423i −0.161023 0.278899i
\(782\) 0 0
\(783\) 7.50000 12.9904i 0.268028 0.464238i
\(784\) 0 0