Properties

Label 637.2.k.b.459.1
Level $637$
Weight $2$
Character 637.459
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.k (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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 459.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 637.459
Dual form 637.2.k.b.569.1

$q$-expansion

\(f(q)\) \(=\) \(q-1.73205i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q-1.73205i q^{2} +(-0.500000 - 0.866025i) q^{3} -1.00000 q^{4} +(-1.50000 + 0.866025i) q^{5} +(-1.50000 + 0.866025i) q^{6} -1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{10} +(-4.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} +(1.00000 - 3.46410i) q^{13} +(1.50000 + 0.866025i) q^{15} -5.00000 q^{16} -6.00000 q^{17} +(-3.00000 - 1.73205i) q^{18} +(1.50000 + 0.866025i) q^{19} +(1.50000 - 0.866025i) q^{20} +(4.50000 + 7.79423i) q^{22} +(-1.50000 + 0.866025i) q^{24} +(-1.00000 + 1.73205i) q^{25} +(-6.00000 - 1.73205i) q^{26} -5.00000 q^{27} +(-1.50000 + 2.59808i) q^{29} +(1.50000 - 2.59808i) q^{30} +(1.50000 + 0.866025i) q^{31} +5.19615i q^{32} +(4.50000 + 2.59808i) q^{33} +10.3923i q^{34} +(-1.00000 + 1.73205i) q^{36} +(1.50000 - 2.59808i) q^{38} +(-3.50000 + 0.866025i) 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} +3.46410i 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} +(-1.00000 + 3.46410i) q^{52} +(4.50000 - 7.79423i) q^{53} +8.66025i q^{54} +(4.50000 - 7.79423i) q^{55} -1.73205i q^{57} +(4.50000 + 2.59808i) q^{58} -3.46410i q^{59} +(-1.50000 - 0.866025i) q^{60} +(3.50000 - 6.06218i) q^{61} +(1.50000 - 2.59808i) q^{62} -1.00000 q^{64} +(1.50000 + 6.06218i) q^{65} +(4.50000 - 7.79423i) q^{66} +(7.50000 - 4.33013i) q^{67} +6.00000 q^{68} +(1.50000 - 0.866025i) q^{71} +(-3.00000 - 1.73205i) q^{72} +(-7.50000 - 4.33013i) q^{73} +2.00000 q^{75} +(-1.50000 - 0.866025i) q^{76} +(1.50000 + 6.06218i) q^{78} +(2.50000 + 4.33013i) q^{79} +(7.50000 - 4.33013i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(4.50000 - 7.79423i) q^{82} +3.46410i q^{83} +(9.00000 - 5.19615i) q^{85} +(-16.5000 + 9.52628i) q^{86} +3.00000 q^{87} +(4.50000 + 7.79423i) q^{88} +6.92820i q^{89} +6.00000 q^{90} -1.73205i q^{93} +(7.50000 + 12.9904i) q^{94} -3.00000 q^{95} +(4.50000 - 2.59808i) q^{96} +(4.50000 - 2.59808i) q^{97} +10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - 2q^{4} - 3q^{5} - 3q^{6} + 2q^{9} + O(q^{10}) \) \( 2q - q^{3} - 2q^{4} - 3q^{5} - 3q^{6} + 2q^{9} + 3q^{10} - 9q^{11} + q^{12} + 2q^{13} + 3q^{15} - 10q^{16} - 12q^{17} - 6q^{18} + 3q^{19} + 3q^{20} + 9q^{22} - 3q^{24} - 2q^{25} - 12q^{26} - 10q^{27} - 3q^{29} + 3q^{30} + 3q^{31} + 9q^{33} - 2q^{36} + 3q^{38} - 7q^{39} + 3q^{40} + 9q^{41} - 11q^{43} + 9q^{44} - 15q^{47} + 5q^{48} + 6q^{50} + 6q^{51} - 2q^{52} + 9q^{53} + 9q^{55} + 9q^{58} - 3q^{60} + 7q^{61} + 3q^{62} - 2q^{64} + 3q^{65} + 9q^{66} + 15q^{67} + 12q^{68} + 3q^{71} - 6q^{72} - 15q^{73} + 4q^{75} - 3q^{76} + 3q^{78} + 5q^{79} + 15q^{80} - q^{81} + 9q^{82} + 18q^{85} - 33q^{86} + 6q^{87} + 9q^{88} + 12q^{90} + 15q^{94} - 6q^{95} + 9q^{96} + 9q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.73205i 1.22474i −0.790569 0.612372i \(-0.790215\pi\)
0.790569 0.612372i \(-0.209785\pi\)
\(3\) −0.500000 0.866025i −0.288675 0.500000i 0.684819 0.728714i \(-0.259881\pi\)
−0.973494 + 0.228714i \(0.926548\pi\)
\(4\) −1.00000 −0.500000
\(5\) −1.50000 + 0.866025i −0.670820 + 0.387298i −0.796387 0.604787i \(-0.793258\pi\)
0.125567 + 0.992085i \(0.459925\pi\)
\(6\) −1.50000 + 0.866025i −0.612372 + 0.353553i
\(7\) 0 0
\(8\) 1.73205i 0.612372i
\(9\) 1.00000 1.73205i 0.333333 0.577350i
\(10\) 1.50000 + 2.59808i 0.474342 + 0.821584i
\(11\) −4.50000 + 2.59808i −1.35680 + 0.783349i −0.989191 0.146631i \(-0.953157\pi\)
−0.367610 + 0.929980i \(0.619824\pi\)
\(12\) 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
\(16\) −5.00000 −1.25000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) −3.00000 1.73205i −0.707107 0.408248i
\(19\) 1.50000 + 0.866025i 0.344124 + 0.198680i 0.662094 0.749421i \(-0.269668\pi\)
−0.317970 + 0.948101i \(0.603001\pi\)
\(20\) 1.50000 0.866025i 0.335410 0.193649i
\(21\) 0 0
\(22\) 4.50000 + 7.79423i 0.959403 + 1.66174i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −1.50000 + 0.866025i −0.306186 + 0.176777i
\(25\) −1.00000 + 1.73205i −0.200000 + 0.346410i
\(26\) −6.00000 1.73205i −1.17670 0.339683i
\(27\) −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 \(0.256518\pi\)
\(30\) 1.50000 2.59808i 0.273861 0.474342i
\(31\) 1.50000 + 0.866025i 0.269408 + 0.155543i 0.628619 0.777714i \(-0.283621\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 5.19615i 0.918559i
\(33\) 4.50000 + 2.59808i 0.783349 + 0.452267i
\(34\) 10.3923i 1.78227i
\(35\) 0 0
\(36\) −1.00000 + 1.73205i −0.166667 + 0.288675i
\(37\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(38\) 1.50000 2.59808i 0.243332 0.421464i
\(39\) −3.50000 + 0.866025i −0.560449 + 0.138675i
\(40\) 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
\(45\) 3.46410i 0.516398i
\(46\) 0 0
\(47\) −7.50000 + 4.33013i −1.09399 + 0.631614i −0.934635 0.355608i \(-0.884274\pi\)
−0.159352 + 0.987222i \(0.550941\pi\)
\(48\) 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
\(52\) −1.00000 + 3.46410i −0.138675 + 0.480384i
\(53\) 4.50000 7.79423i 0.618123 1.07062i −0.371706 0.928351i \(-0.621227\pi\)
0.989828 0.142269i \(-0.0454398\pi\)
\(54\) 8.66025i 1.17851i
\(55\) 4.50000 7.79423i 0.606780 1.05097i
\(56\) 0 0
\(57\) 1.73205i 0.229416i
\(58\) 4.50000 + 2.59808i 0.590879 + 0.341144i
\(59\) 3.46410i 0.450988i −0.974245 0.225494i \(-0.927600\pi\)
0.974245 0.225494i \(-0.0723995\pi\)
\(60\) −1.50000 0.866025i −0.193649 0.111803i
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) 1.50000 2.59808i 0.190500 0.329956i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 1.50000 + 6.06218i 0.186052 + 0.751921i
\(66\) 4.50000 7.79423i 0.553912 0.959403i
\(67\) 7.50000 4.33013i 0.916271 0.529009i 0.0338274 0.999428i \(-0.489230\pi\)
0.882443 + 0.470418i \(0.155897\pi\)
\(68\) 6.00000 0.727607
\(69\) 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 \(0.300560\pi\)
\(72\) −3.00000 1.73205i −0.353553 0.204124i
\(73\) −7.50000 4.33013i −0.877809 0.506803i −0.00787336 0.999969i \(-0.502506\pi\)
−0.869935 + 0.493166i \(0.835840\pi\)
\(74\) 0 0
\(75\) 2.00000 0.230940
\(76\) −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 0.971698 0.236225i \(-0.0759104\pi\)
−0.690426 + 0.723403i \(0.742577\pi\)
\(80\) 7.50000 4.33013i 0.838525 0.484123i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 4.50000 7.79423i 0.496942 0.860729i
\(83\) 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
\(87\) 3.00000 0.321634
\(88\) 4.50000 + 7.79423i 0.479702 + 0.830868i
\(89\) 6.92820i 0.734388i 0.930144 + 0.367194i \(0.119682\pi\)
−0.930144 + 0.367194i \(0.880318\pi\)
\(90\) 6.00000 0.632456
\(91\) 0 0
\(92\) 0 0
\(93\) 1.73205i 0.179605i
\(94\) 7.50000 + 12.9904i 0.773566 + 1.33986i
\(95\) −3.00000 −0.307794
\(96\) 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
\(100\) 1.00000 1.73205i 0.100000 0.173205i
\(101\) −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i \(-0.314447\pi\)
−0.998240 + 0.0592978i \(0.981114\pi\)
\(102\) 9.00000 5.19615i 0.891133 0.514496i
\(103\) −6.50000 11.2583i −0.640464 1.10932i −0.985329 0.170664i \(-0.945409\pi\)
0.344865 0.938652i \(-0.387925\pi\)
\(104\) −6.00000 1.73205i −0.588348 0.169842i
\(105\) 0 0
\(106\) −13.5000 7.79423i −1.31124 0.757042i
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 5.00000 0.481125
\(109\) −4.50000 2.59808i −0.431022 0.248851i 0.268760 0.963207i \(-0.413386\pi\)
−0.699782 + 0.714357i \(0.746719\pi\)
\(110\) −13.5000 7.79423i −1.28717 0.743151i
\(111\) 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 \(-0.415962\pi\)
\(114\) −3.00000 −0.280976
\(115\) 0 0
\(116\) 1.50000 2.59808i 0.139272 0.241225i
\(117\) −5.00000 5.19615i −0.462250 0.480384i
\(118\) −6.00000 −0.552345
\(119\) 0 0
\(120\) 1.50000 2.59808i 0.136931 0.237171i
\(121\) 8.00000 13.8564i 0.727273 1.25967i
\(122\) −10.5000 6.06218i −0.950625 0.548844i
\(123\) 5.19615i 0.468521i
\(124\) −1.50000 0.866025i −0.134704 0.0777714i
\(125\) 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 \(0.970975\pi\)
\(128\) 12.1244i 1.07165i
\(129\) −5.50000 + 9.52628i −0.484248 + 0.838742i
\(130\) 10.5000 2.59808i 0.920911 0.227866i
\(131\) 7.50000 + 12.9904i 0.655278 + 1.13497i 0.981824 + 0.189794i \(0.0607819\pi\)
−0.326546 + 0.945181i \(0.605885\pi\)
\(132\) −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
\(136\) 10.3923i 0.891133i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 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
\(143\) 4.50000 + 18.1865i 0.376309 + 1.52083i
\(144\) −5.00000 + 8.66025i −0.416667 + 0.721688i
\(145\) 5.19615i 0.431517i
\(146\) −7.50000 + 12.9904i −0.620704 + 1.07509i
\(147\) 0 0
\(148\) 0 0
\(149\) −16.5000 9.52628i −1.35173 0.780423i −0.363241 0.931695i \(-0.618330\pi\)
−0.988492 + 0.151272i \(0.951663\pi\)
\(150\) 3.46410i 0.282843i
\(151\) 10.5000 + 6.06218i 0.854478 + 0.493333i 0.862159 0.506637i \(-0.169112\pi\)
−0.00768132 + 0.999970i \(0.502445\pi\)
\(152\) 1.50000 2.59808i 0.121666 0.210732i
\(153\) −6.00000 + 10.3923i −0.485071 + 0.840168i
\(154\) 0 0
\(155\) −3.00000 −0.240966
\(156\) 3.50000 0.866025i 0.280224 0.0693375i
\(157\) 11.5000 19.9186i 0.917800 1.58968i 0.115050 0.993360i \(-0.463297\pi\)
0.802749 0.596316i \(-0.203370\pi\)
\(158\) 7.50000 4.33013i 0.596668 0.344486i
\(159\) −9.00000 −0.713746
\(160\) −4.50000 7.79423i −0.355756 0.616188i
\(161\) 0 0
\(162\) −1.50000 + 0.866025i −0.117851 + 0.0680414i
\(163\) 10.5000 + 6.06218i 0.822423 + 0.474826i 0.851251 0.524758i \(-0.175844\pi\)
−0.0288280 + 0.999584i \(0.509178\pi\)
\(164\) −4.50000 2.59808i −0.351391 0.202876i
\(165\) −9.00000 −0.700649
\(166\) 6.00000 0.465690
\(167\) 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
\(171\) 3.00000 1.73205i 0.229416 0.132453i
\(172\) 5.50000 + 9.52628i 0.419371 + 0.726372i
\(173\) 7.50000 12.9904i 0.570214 0.987640i −0.426329 0.904568i \(-0.640193\pi\)
0.996544 0.0830722i \(-0.0264732\pi\)
\(174\) 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
\(178\) 12.0000 0.899438
\(179\) −1.50000 2.59808i −0.112115 0.194189i 0.804508 0.593942i \(-0.202429\pi\)
−0.916623 + 0.399753i \(0.869096\pi\)
\(180\) 3.46410i 0.258199i
\(181\) −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
\(186\) −3.00000 −0.219971
\(187\) 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
\(191\) 7.50000 12.9904i 0.542681 0.939951i −0.456068 0.889945i \(-0.650743\pi\)
0.998749 0.0500060i \(-0.0159241\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 1.50000 0.866025i 0.107972 0.0623379i −0.445041 0.895510i \(-0.646811\pi\)
0.553014 + 0.833172i \(0.313478\pi\)
\(194\) −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 \(0.370371\pi\)
\(198\) 18.0000 1.27920
\(199\) −4.00000 −0.283552 −0.141776 0.989899i \(-0.545281\pi\)
−0.141776 + 0.989899i \(0.545281\pi\)
\(200\) 3.00000 + 1.73205i 0.212132 + 0.122474i
\(201\) −7.50000 4.33013i −0.529009 0.305424i
\(202\) −13.5000 + 7.79423i −0.949857 + 0.548400i
\(203\) 0 0
\(204\) −3.00000 5.19615i −0.210042 0.363803i
\(205\) −9.00000 −0.628587
\(206\) −19.5000 + 11.2583i −1.35863 + 0.784405i
\(207\) 0 0
\(208\) −5.00000 + 17.3205i −0.346688 + 1.20096i
\(209\) −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 \(0.314345\pi\)
\(212\) −4.50000 + 7.79423i −0.309061 + 0.535310i
\(213\) −1.50000 0.866025i −0.102778 0.0593391i
\(214\) 0 0
\(215\) 16.5000 + 9.52628i 1.12529 + 0.649687i
\(216\) 8.66025i 0.589256i
\(217\) 0 0
\(218\) −4.50000 + 7.79423i −0.304778 + 0.527892i
\(219\) 8.66025i 0.585206i
\(220\) −4.50000 + 7.79423i −0.303390 + 0.525487i
\(221\) −6.00000 + 20.7846i −0.403604 + 1.39812i
\(222\) 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
\(227\) 17.3205i 1.14960i −0.818293 0.574801i \(-0.805079\pi\)
0.818293 0.574801i \(-0.194921\pi\)
\(228\) 1.73205i 0.114708i
\(229\) 10.5000 6.06218i 0.693860 0.400600i −0.111197 0.993798i \(-0.535468\pi\)
0.805056 + 0.593198i \(0.202135\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.50000 + 2.59808i 0.295439 + 0.170572i
\(233\) −1.50000 2.59808i −0.0982683 0.170206i 0.812700 0.582683i \(-0.197997\pi\)
−0.910968 + 0.412477i \(0.864664\pi\)
\(234\) −9.00000 + 8.66025i −0.588348 + 0.566139i
\(235\) 7.50000 12.9904i 0.489246 0.847399i
\(236\) 3.46410i 0.225494i
\(237\) 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 \(-0.109112\pi\)
\(240\) −7.50000 4.33013i −0.484123 0.279508i
\(241\) 6.92820i 0.446285i −0.974786 0.223142i \(-0.928369\pi\)
0.974786 0.223142i \(-0.0716315\pi\)
\(242\) −24.0000 13.8564i −1.54278 0.890724i
\(243\) −8.00000 + 13.8564i −0.513200 + 0.888889i
\(244\) −3.50000 + 6.06218i −0.224065 + 0.388091i
\(245\) 0 0
\(246\) −9.00000 −0.573819
\(247\) 4.50000 4.33013i 0.286328 0.275519i
\(248\) 1.50000 2.59808i 0.0952501 0.164978i
\(249\) 3.00000 1.73205i 0.190117 0.109764i
\(250\) −21.0000 −1.32816
\(251\) 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
\(254\) 19.5000 + 11.2583i 1.22354 + 0.706410i
\(255\) −9.00000 5.19615i −0.563602 0.325396i
\(256\) 19.0000 1.18750
\(257\) −30.0000 −1.87135 −0.935674 0.352865i \(-0.885208\pi\)
−0.935674 + 0.352865i \(0.885208\pi\)
\(258\) 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
\(262\) 22.5000 12.9904i 1.39005 0.802548i
\(263\) −1.50000 2.59808i −0.0924940 0.160204i 0.816066 0.577959i \(-0.196151\pi\)
−0.908560 + 0.417755i \(0.862817\pi\)
\(264\) 4.50000 7.79423i 0.276956 0.479702i
\(265\) 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
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) −7.50000 12.9904i −0.456435 0.790569i
\(271\) 17.3205i 1.05215i 0.850439 + 0.526073i \(0.176336\pi\)
−0.850439 + 0.526073i \(0.823664\pi\)
\(272\) 30.0000 1.81902
\(273\) 0 0
\(274\) 0 0
\(275\) 10.3923i 0.626680i
\(276\) 0 0
\(277\) −10.0000 −0.600842 −0.300421 0.953807i \(-0.597127\pi\)
−0.300421 + 0.953807i \(0.597127\pi\)
\(278\) −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 \(0.933744\pi\)
\(282\) 7.50000 12.9904i 0.446619 0.773566i
\(283\) 9.50000 + 16.4545i 0.564716 + 0.978117i 0.997076 + 0.0764162i \(0.0243478\pi\)
−0.432360 + 0.901701i \(0.642319\pi\)
\(284\) −1.50000 + 0.866025i −0.0890086 + 0.0513892i
\(285\) 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
\(289\) 19.0000 1.11765
\(290\) −9.00000 −0.528498
\(291\) −4.50000 2.59808i −0.263795 0.152302i
\(292\) 7.50000 + 4.33013i 0.438904 + 0.253402i
\(293\) 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
\(297\) 22.5000 12.9904i 1.30558 0.753778i
\(298\) −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
\(303\) −4.50000 + 7.79423i −0.258518 + 0.447767i
\(304\) −7.50000 4.33013i −0.430155 0.248350i
\(305\) 12.1244i 0.694239i
\(306\) 18.0000 + 10.3923i 1.02899 + 0.594089i
\(307\) 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
\(310\) 5.19615i 0.295122i
\(311\) −7.50000 + 12.9904i −0.425286 + 0.736617i −0.996447 0.0842210i \(-0.973160\pi\)
0.571161 + 0.820838i \(0.306493\pi\)
\(312\) 1.50000 + 6.06218i 0.0849208 + 0.343203i
\(313\) 9.50000 + 16.4545i 0.536972 + 0.930062i 0.999065 + 0.0432311i \(0.0137652\pi\)
−0.462093 + 0.886831i \(0.652902\pi\)
\(314\) −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 \(-0.713282\pi\)
0.368275 + 0.929717i \(0.379948\pi\)
\(318\) 15.5885i 0.874157i
\(319\) 15.5885i 0.872786i
\(320\) 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
\(325\) 5.00000 + 5.19615i 0.277350 + 0.288231i
\(326\) 10.5000 18.1865i 0.581541 1.00726i
\(327\) 5.19615i 0.287348i
\(328\) 4.50000 7.79423i 0.248471 0.430364i
\(329\) 0 0
\(330\) 15.5885i 0.858116i
\(331\) 28.5000 + 16.4545i 1.56650 + 0.904420i 0.996572 + 0.0827265i \(0.0263628\pi\)
0.569929 + 0.821694i \(0.306971\pi\)
\(332\) 3.46410i 0.190117i
\(333\) 0 0
\(334\) 1.50000 2.59808i 0.0820763 0.142160i
\(335\) −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 \(0.295482\pi\)
\(338\) −12.0000 + 19.0526i −0.652714 + 1.03632i
\(339\) −7.50000 + 12.9904i −0.407344 + 0.705541i
\(340\) −9.00000 + 5.19615i −0.488094 + 0.281801i
\(341\) −9.00000 −0.487377
\(342\) −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 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) −3.00000 −0.160817
\(349\) 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
\(353\) −1.50000 + 0.866025i −0.0798369 + 0.0460939i −0.539387 0.842058i \(-0.681344\pi\)
0.459550 + 0.888152i \(0.348011\pi\)
\(354\) 3.00000 + 5.19615i 0.159448 + 0.276172i
\(355\) −1.50000 + 2.59808i −0.0796117 + 0.137892i
\(356\) 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 \(-0.834355\pi\)
−0.00321050 + 0.999995i \(0.501022\pi\)
\(360\) 6.00000 0.316228
\(361\) −8.00000 13.8564i −0.421053 0.729285i
\(362\) 3.46410i 0.182069i
\(363\) −16.0000 −0.839782
\(364\) 0 0
\(365\) 15.0000 0.785136
\(366\) 12.1244i 0.633750i
\(367\) 11.5000 + 19.9186i 0.600295 + 1.03974i 0.992776 + 0.119982i \(0.0382835\pi\)
−0.392481 + 0.919760i \(0.628383\pi\)
\(368\) 0 0
\(369\) 9.00000 5.19615i 0.468521 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 1.73205i 0.0898027i
\(373\) −9.50000 + 16.4545i −0.491891 + 0.851981i −0.999956 0.00933789i \(-0.997028\pi\)
0.508065 + 0.861319i \(0.330361\pi\)
\(374\) −27.0000 46.7654i −1.39614 2.41818i
\(375\) −10.5000 + 6.06218i −0.542218 + 0.313050i
\(376\) 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 \(0.680831\pi\)
\(380\) 3.00000 0.153897
\(381\) 13.0000 0.666010
\(382\) −22.5000 12.9904i −1.15120 0.664646i
\(383\) 13.5000 + 7.79423i 0.689818 + 0.398266i 0.803544 0.595246i \(-0.202945\pi\)
−0.113726 + 0.993512i \(0.536279\pi\)
\(384\) 10.5000 6.06218i 0.535826 0.309359i
\(385\) 0 0
\(386\) −1.50000 2.59808i −0.0763480 0.132239i
\(387\) −22.0000 −1.11832
\(388\) −4.50000 + 2.59808i −0.228453 + 0.131897i
\(389\) −1.50000 + 2.59808i −0.0760530 + 0.131728i −0.901544 0.432688i \(-0.857565\pi\)
0.825491 + 0.564416i \(0.190898\pi\)
\(390\) −7.50000 7.79423i −0.379777 0.394676i
\(391\) 0 0
\(392\) 0 0
\(393\) 7.50000 12.9904i 0.378325 0.655278i
\(394\) 19.5000 33.7750i 0.982396 1.70156i
\(395\) −7.50000 4.33013i −0.377366 0.217872i
\(396\) 10.3923i 0.522233i
\(397\) −31.5000 18.1865i −1.58094 0.912756i −0.994722 0.102602i \(-0.967283\pi\)
−0.586217 0.810154i \(-0.699383\pi\)
\(398\) 6.92820i 0.347279i
\(399\) 0 0
\(400\) 5.00000 8.66025i 0.250000 0.433013i
\(401\) 6.92820i 0.345978i −0.984924 0.172989i \(-0.944657\pi\)
0.984924 0.172989i \(-0.0553425\pi\)
\(402\) −7.50000 + 12.9904i −0.374066 + 0.647901i
\(403\) 4.50000 4.33013i 0.224161 0.215699i
\(404\) 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
\(409\) 6.92820i 0.342578i 0.985221 + 0.171289i \(0.0547931\pi\)
−0.985221 + 0.171289i \(0.945207\pi\)
\(410\) 15.5885i 0.769859i
\(411\) 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
\(416\) 18.0000 + 5.19615i 0.882523 + 0.254762i
\(417\) −6.50000 + 11.2583i −0.318306 + 0.551323i
\(418\) 15.5885i 0.762456i
\(419\) 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 \(\pi\)
\(422\) 19.5000 + 11.2583i 0.949245 + 0.548047i
\(423\) 17.3205i 0.842152i
\(424\) −13.5000 7.79423i −0.655618 0.378521i
\(425\) 6.00000 10.3923i 0.291043 0.504101i
\(426\) −1.50000 + 2.59808i −0.0726752 + 0.125877i
\(427\) 0 0
\(428\) 0 0
\(429\) 13.5000 12.9904i 0.651786 0.627182i
\(430\) 16.5000 28.5788i 0.795701 1.37819i
\(431\) −28.5000 + 16.4545i −1.37280 + 0.792585i −0.991279 0.131777i \(-0.957932\pi\)
−0.381517 + 0.924362i \(0.624598\pi\)
\(432\) 25.0000 1.20281
\(433\) 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
\(436\) 4.50000 + 2.59808i 0.215511 + 0.124425i
\(437\) 0 0
\(438\) 15.0000 0.716728
\(439\) −8.00000 −0.381819 −0.190910 0.981608i \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) −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 0.631010 0.775775i \(-0.282641\pi\)
−0.987346 + 0.158583i \(0.949307\pi\)
\(444\) 0 0
\(445\) −6.00000 10.3923i −0.284427 0.492642i
\(446\) −4.50000 + 7.79423i −0.213081 + 0.369067i
\(447\) 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
\(451\) −27.0000 −1.27138
\(452\) 7.50000 + 12.9904i 0.352770 + 0.611016i
\(453\) 12.1244i 0.569652i
\(454\) −30.0000 −1.40797
\(455\) 0 0
\(456\) −3.00000 −0.140488
\(457\) 34.6410i 1.62044i −0.586127 0.810219i \(-0.699348\pi\)
0.586127 0.810219i \(-0.300652\pi\)
\(458\) −10.5000 18.1865i −0.490633 0.849801i
\(459\) 30.0000 1.40028
\(460\) 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 \(0.809467\pi\)
\(464\) 7.50000 12.9904i 0.348179 0.603063i
\(465\) 1.50000 + 2.59808i 0.0695608 + 0.120483i
\(466\) −4.50000 + 2.59808i −0.208458 + 0.120354i
\(467\) −10.5000 18.1865i −0.485882 0.841572i 0.513986 0.857798i \(-0.328168\pi\)
−0.999868 + 0.0162260i \(0.994835\pi\)
\(468\) 5.00000 + 5.19615i 0.231125 + 0.240192i
\(469\) 0 0
\(470\) −22.5000 12.9904i −1.03785 0.599202i
\(471\) −23.0000 −1.05978
\(472\) −6.00000 −0.276172
\(473\) 49.5000 + 28.5788i 2.27601 + 1.31406i
\(474\) −7.50000 4.33013i −0.344486 0.198889i
\(475\) −3.00000 + 1.73205i −0.137649 + 0.0794719i
\(476\) 0 0
\(477\) −9.00000 15.5885i −0.412082 0.713746i
\(478\) −18.0000 −0.823301
\(479\) −25.5000 + 14.7224i −1.16512 + 0.672685i −0.952527 0.304455i \(-0.901526\pi\)
−0.212598 + 0.977140i \(0.568192\pi\)
\(480\) −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
\(485\) −4.50000 + 7.79423i −0.204334 + 0.353918i
\(486\) 24.0000 + 13.8564i 1.08866 + 0.628539i
\(487\) 24.2487i 1.09881i 0.835555 + 0.549407i \(0.185146\pi\)
−0.835555 + 0.549407i \(0.814854\pi\)
\(488\) −10.5000 6.06218i −0.475313 0.274422i
\(489\) 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 \(-0.0418613\pi\)
\(492\) 5.19615i 0.234261i
\(493\) 9.00000 15.5885i 0.405340 0.702069i
\(494\) −7.50000 7.79423i −0.337441 0.350679i
\(495\) −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 \(-0.654323\pi\)
0.533199 + 0.845990i \(0.320990\pi\)
\(500\) 12.1244i 0.542218i
\(501\) 1.73205i 0.0773823i
\(502\) 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
\(507\) −0.500000 + 12.9904i −0.0222058 + 0.576923i
\(508\) 6.50000 11.2583i 0.288391 0.499508i
\(509\) 6.92820i 0.307087i 0.988142 + 0.153544i \(0.0490686\pi\)
−0.988142 + 0.153544i \(0.950931\pi\)
\(510\) −9.00000 + 15.5885i −0.398527 + 0.690268i
\(511\) 0 0
\(512\) 8.66025i 0.382733i
\(513\) −7.50000 4.33013i −0.331133 0.191180i
\(514\) 51.9615i 2.29192i
\(515\) 19.5000 + 11.2583i 0.859273 + 0.496101i
\(516\) 5.50000 9.52628i 0.242124 0.419371i
\(517\) 22.5000 38.9711i 0.989549 1.71395i
\(518\) 0 0
\(519\) −15.0000 −0.658427
\(520\) 10.5000 2.59808i 0.460455 0.113933i
\(521\) 19.5000 33.7750i 0.854311 1.47971i −0.0229727 0.999736i \(-0.507313\pi\)
0.877283 0.479973i \(-0.159354\pi\)
\(522\) 9.00000 5.19615i 0.393919 0.227429i
\(523\) 4.00000 0.174908 0.0874539 0.996169i \(-0.472127\pi\)
0.0874539 + 0.996169i \(0.472127\pi\)
\(524\) −7.50000 12.9904i −0.327639 0.567487i
\(525\) 0 0
\(526\) −4.50000 + 2.59808i −0.196209 + 0.113282i
\(527\) −9.00000 5.19615i −0.392046 0.226348i
\(528\) −22.5000 12.9904i −0.979187 0.565334i
\(529\) −23.0000 −1.00000
\(530\) 27.0000 1.17281
\(531\) −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
\(536\) −7.50000 12.9904i −0.323951 0.561099i
\(537\) −1.50000 + 2.59808i −0.0647298 + 0.112115i
\(538\) 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 \(-0.750598\pi\)
0.257004 + 0.966410i \(0.417265\pi\)
\(542\) 30.0000 1.28861
\(543\) 1.00000 + 1.73205i 0.0429141 + 0.0743294i
\(544\) 31.1769i 1.33670i
\(545\) 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
\(549\) −7.00000 12.1244i −0.298753 0.517455i
\(550\) −18.0000 −0.767523
\(551\) −4.50000 + 2.59808i −0.191706 + 0.110682i
\(552\) 0 0
\(553\) 0 0
\(554\) 17.3205i 0.735878i
\(555\) 0 0
\(556\) 6.50000 + 11.2583i 0.275661 + 0.477460i
\(557\) 13.5000 7.79423i 0.572013 0.330252i −0.185940 0.982561i \(-0.559533\pi\)
0.757953 + 0.652309i \(0.226200\pi\)
\(558\) −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
\(562\) 12.0000 0.506189
\(563\) 36.0000 1.51722 0.758610 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) −7.50000 4.33013i −0.315807 0.182331i
\(565\) 22.5000 + 12.9904i 0.946582 + 0.546509i
\(566\) 28.5000 16.4545i 1.19794 0.691633i
\(567\) 0 0
\(568\) −1.50000 2.59808i −0.0629386 0.109013i
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 4.50000 2.59808i 0.188484 0.108821i
\(571\) 11.5000 19.9186i 0.481260 0.833567i −0.518509 0.855072i \(-0.673513\pi\)
0.999769 + 0.0215055i \(0.00684595\pi\)
\(572\) −4.50000 18.1865i −0.188154 0.760417i
\(573\) −15.0000 −0.626634
\(574\) 0 0
\(575\) 0 0
\(576\) −1.00000 + 1.73205i −0.0416667 + 0.0721688i
\(577\) −13.5000 7.79423i −0.562012 0.324478i 0.191940 0.981407i \(-0.438522\pi\)
−0.753953 + 0.656929i \(0.771855\pi\)
\(578\) 32.9090i 1.36883i
\(579\) −1.50000 0.866025i −0.0623379 0.0359908i
\(580\) 5.19615i 0.215758i
\(581\) 0 0
\(582\) −4.50000 + 7.79423i −0.186531 + 0.323081i
\(583\) 46.7654i 1.93682i
\(584\) −7.50000 + 12.9904i −0.310352 + 0.537546i
\(585\) 12.0000 + 3.46410i 0.496139 + 0.143223i
\(586\) −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
\(591\) 22.5167i 0.926212i
\(592\) 0 0
\(593\) 4.50000 2.59808i 0.184793 0.106690i −0.404750 0.914428i \(-0.632641\pi\)
0.589543 + 0.807737i \(0.299308\pi\)
\(594\) −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 −0.943193 0.332244i \(-0.892194\pi\)
0.759328 + 0.650708i \(0.225528\pi\)
\(600\) 3.46410i 0.141421i
\(601\) 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
\(604\) −10.5000 6.06218i −0.427239 0.246667i
\(605\) 27.7128i 1.12669i
\(606\) 13.5000 + 7.79423i 0.548400 + 0.316619i
\(607\) −21.5000 + 37.2391i −0.872658 + 1.51149i −0.0134214 + 0.999910i \(0.504272\pi\)
−0.859237 + 0.511578i \(0.829061\pi\)
\(608\) −4.50000 + 7.79423i −0.182499 + 0.316098i
\(609\) 0 0
\(610\) 21.0000 0.850265
\(611\) 7.50000 + 30.3109i 0.303418 + 1.22625i
\(612\) 6.00000 10.3923i 0.242536 0.420084i
\(613\) 31.5000 18.1865i 1.27227 0.734547i 0.296858 0.954922i \(-0.404061\pi\)
0.975415 + 0.220375i \(0.0707280\pi\)
\(614\) 42.0000 1.69498
\(615\) 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 \(-0.00359804\pi\)
\(618\) 19.5000 + 11.2583i 0.784405 + 0.452876i
\(619\) −16.5000 9.52628i −0.663191 0.382893i 0.130301 0.991475i \(-0.458406\pi\)
−0.793492 + 0.608581i \(0.791739\pi\)
\(620\) 3.00000 0.120483
\(621\) 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
\(626\) 28.5000 16.4545i 1.13909 0.657653i
\(627\) 4.50000 + 7.79423i 0.179713 + 0.311272i
\(628\) −11.5000 + 19.9186i −0.458900 + 0.794838i
\(629\) 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
\(633\) 13.0000 0.516704
\(634\) 4.50000 + 7.79423i 0.178718 + 0.309548i
\(635\) 22.5167i 0.893546i
\(636\) 9.00000 0.356873
\(637\) 0 0
\(638\) −27.0000 −1.06894
\(639\) 3.46410i 0.137038i
\(640\) −10.5000 18.1865i −0.415049 0.718886i
\(641\) 30.0000 1.18493 0.592464 0.805597i \(-0.298155\pi\)
0.592464 + 0.805597i \(0.298155\pi\)
\(642\) 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
\(646\) −9.00000 + 15.5885i −0.354100 + 0.613320i
\(647\) −4.50000 7.79423i −0.176913 0.306423i 0.763908 0.645325i \(-0.223278\pi\)
−0.940822 + 0.338902i \(0.889945\pi\)
\(648\) −1.50000 + 0.866025i −0.0589256 + 0.0340207i
\(649\) 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
\(653\) −30.0000 −1.17399 −0.586995 0.809590i \(-0.699689\pi\)
−0.586995 + 0.809590i \(0.699689\pi\)
\(654\) 9.00000 0.351928
\(655\) −22.5000 12.9904i −0.879148 0.507576i
\(656\) −22.5000 12.9904i −0.878477 0.507189i
\(657\) −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 \(0.927707\pi\)
\(660\) 9.00000 0.350325
\(661\) −31.5000 + 18.1865i −1.22521 + 0.707374i −0.966024 0.258454i \(-0.916787\pi\)
−0.259184 + 0.965828i \(0.583454\pi\)
\(662\) 28.5000 49.3634i 1.10768 1.91856i
\(663\) 21.0000 5.19615i 0.815572 0.201802i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −1.50000 0.866025i −0.0580367 0.0335075i
\(669\) 5.19615i 0.200895i
\(670\) 22.5000 + 12.9904i 0.869251 + 0.501862i
\(671\) 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 \(0.160531\pi\)
\(674\) 38.1051i 1.46775i
\(675\) 5.00000 8.66025i 0.192450 0.333333i
\(676\) 11.0000 + 6.92820i 0.423077 + 0.266469i
\(677\) 13.5000 + 23.3827i 0.518847 + 0.898670i 0.999760 + 0.0219013i \(0.00697196\pi\)
−0.480913 + 0.876768i \(0.659695\pi\)
\(678\) 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
\(682\) 15.5885i 0.596913i
\(683\) 24.2487i 0.927851i −0.885874 0.463926i \(-0.846441\pi\)
0.885874 0.463926i \(-0.153559\pi\)
\(684\) −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
\(689\) −22.5000 23.3827i −0.857182 0.890809i
\(690\) 0 0
\(691\) 31.1769i 1.18603i −0.805193 0.593013i \(-0.797938\pi\)
0.805193 0.593013i \(-0.202062\pi\)
\(692\) −7.50000 + 12.9904i −0.285107 + 0.493820i
\(693\) 0 0
\(694\) 0 0
\(695\) 19.5000 + 11.2583i 0.739677 + 0.427053i
\(696\) 5.19615i 0.196960i
\(697\) −27.0000 15.5885i −1.02270 0.590455i
\(698\) 4.50000 7.79423i 0.170328 0.295016i
\(699\) −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 \(0.536145\pi\)
\(702\) 30.0000 + 8.66025i 1.13228 + 0.326860i
\(703\) 0 0
\(704\) 4.50000 2.59808i 0.169600 0.0979187i
\(705\) −15.0000 −0.564933
\(706\) 1.50000 + 2.59808i 0.0564532 + 0.0977799i
\(707\) 0 0
\(708\) 3.00000 1.73205i 0.112747 0.0650945i
\(709\) −10.5000 6.06218i −0.394336 0.227670i 0.289701 0.957117i \(-0.406444\pi\)
−0.684037 + 0.729447i \(0.739777\pi\)
\(710\) 4.50000 + 2.59808i 0.168882 + 0.0975041i
\(711\) 10.0000 0.375029
\(712\) 12.0000 0.449719
\(713\) 0 0
\(714\) 0 0
\(715\) −22.5000 23.3827i −0.841452 0.874463i
\(716\) 1.50000 + 2.59808i 0.0560576 + 0.0970947i
\(717\) −9.00000 + 5.19615i −0.336111 + 0.194054i
\(718\) 16.5000 + 28.5788i 0.615775 + 1.06655i
\(719\) −7.50000 + 12.9904i −0.279703 + 0.484459i −0.971311 0.237814i \(-0.923569\pi\)
0.691608 + 0.722273i \(0.256903\pi\)
\(720\) 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
\(724\) 2.00000 0.0743294
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 27.7128i 1.02852i
\(727\) 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
\(730\) 25.9808i 0.961591i
\(731\) 33.0000 + 57.1577i 1.22055 + 2.11405i
\(732\) 7.00000 0.258727
\(733\) −43.5000 + 25.1147i −1.60671 + 0.927634i −0.616609 + 0.787269i \(0.711494\pi\)
−0.990100 + 0.140365i \(0.955173\pi\)
\(734\) 34.5000 19.9186i 1.27342 0.735208i
\(735\) 0 0
\(736\) 0 0
\(737\) −22.5000 + 38.9711i −0.828798 + 1.43552i
\(738\) −9.00000 15.5885i −0.331295 0.573819i
\(739\) −34.5000 + 19.9186i −1.26910 + 0.732717i −0.974818 0.223001i \(-0.928415\pi\)
−0.294285 + 0.955718i \(0.595081\pi\)
\(740\) 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 \(0.676782\pi\)
\(744\) −3.00000 −0.109985
\(745\) 33.0000 1.20903
\(746\) 28.5000 + 16.4545i 1.04346 + 0.602441i
\(747\) 6.00000 + 3.46410i 0.219529 + 0.126745i
\(748\) −27.0000 + 15.5885i −0.987218 + 0.569970i
\(749\) 0 0
\(750\) 10.5000 + 18.1865i 0.383406 + 0.664078i
\(751\) 20.0000 0.729810 0.364905 0.931045i \(-0.381101\pi\)
0.364905 + 0.931045i \(0.381101\pi\)
\(752\) 37.5000 21.6506i 1.36748 0.789517i
\(753\) 1.50000 2.59808i 0.0546630 0.0946792i
\(754\) 13.5000 12.9904i 0.491641 0.473082i
\(755\) −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 \(0.0666932\pi\)
\(758\) −1.50000 + 2.59808i −0.0544825 + 0.0943664i
\(759\) 0 0
\(760\) 5.19615i 0.188484i
\(761\) −25.5000 14.7224i −0.924374 0.533688i −0.0393463 0.999226i \(-0.512528\pi\)
−0.885028 + 0.465538i \(0.845861\pi\)
\(762\) 22.5167i 0.815693i
\(763\) 0 0
\(764\) −7.50000 + 12.9904i −0.271340 + 0.469975i
\(765\) 20.7846i 0.751469i
\(766\) 13.5000 23.3827i 0.487775 0.844851i
\(767\) −12.0000 3.46410i −0.433295 0.125081i
\(768\) −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
\(773\) 13.8564i 0.498380i −0.968455 0.249190i \(-0.919836\pi\)
0.968455 0.249190i \(-0.0801644\pi\)
\(774\) 38.1051i 1.36966i
\(775\) −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
\(780\) −4.50000 + 4.33013i −0.161126 + 0.155043i
\(781\) −4.50000 + 7.79423i −0.161023 + 0.278899i
\(782\) 0 0
\(783\) 7.50000 12.9904i 0.268028 0.464238i