Properties

Label 637.2.q.c.491.1
Level $637$
Weight $2$
Character 637.491
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.q (of order \(6\), degree \(2\), 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 491.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 637.491
Dual form 637.2.q.c.589.1

$q$-expansion

\(f(q)\) \(=\) \(q+(1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\) \(q+(1.50000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.73205i q^{5} +(1.50000 + 0.866025i) q^{6} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(4.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(-1.00000 - 3.46410i) q^{13} +(1.50000 - 0.866025i) q^{15} +(2.50000 + 4.33013i) q^{16} +(-3.00000 + 5.19615i) q^{17} -3.46410i q^{18} +(1.50000 + 0.866025i) q^{19} +(-1.50000 - 0.866025i) q^{20} +(4.50000 - 7.79423i) q^{22} +(-1.50000 + 0.866025i) q^{24} +2.00000 q^{25} +(-4.50000 - 4.33013i) q^{26} +5.00000 q^{27} +(-1.50000 - 2.59808i) q^{29} +(1.50000 - 2.59808i) q^{30} -1.73205i q^{31} +(4.50000 + 2.59808i) q^{32} +(4.50000 + 2.59808i) q^{33} +10.3923i q^{34} +(-1.00000 - 1.73205i) q^{36} +3.00000 q^{38} +(2.50000 - 2.59808i) q^{39} +3.00000 q^{40} +(-4.50000 + 2.59808i) q^{41} +(-5.50000 + 9.52628i) q^{43} -5.19615i q^{44} +(-3.00000 - 1.73205i) q^{45} -8.66025i q^{47} +(-2.50000 + 4.33013i) q^{48} +(3.00000 - 1.73205i) q^{50} -6.00000 q^{51} +(-3.50000 - 0.866025i) q^{52} -9.00000 q^{53} +(7.50000 - 4.33013i) q^{54} +(-4.50000 - 7.79423i) q^{55} +1.73205i q^{57} +(-4.50000 - 2.59808i) q^{58} +(3.00000 + 1.73205i) q^{59} -1.73205i q^{60} +(-3.50000 + 6.06218i) q^{61} +(-1.50000 - 2.59808i) q^{62} -1.00000 q^{64} +(-6.00000 + 1.73205i) q^{65} +9.00000 q^{66} +(-7.50000 + 4.33013i) q^{67} +(3.00000 + 5.19615i) q^{68} +(1.50000 + 0.866025i) q^{71} +(3.00000 + 1.73205i) q^{72} +8.66025i q^{73} +(1.00000 + 1.73205i) q^{75} +(1.50000 - 0.866025i) q^{76} +(1.50000 - 6.06218i) q^{78} -5.00000 q^{79} +(7.50000 - 4.33013i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-4.50000 + 7.79423i) q^{82} +3.46410i q^{83} +(9.00000 + 5.19615i) q^{85} +19.0526i q^{86} +(1.50000 - 2.59808i) q^{87} +(4.50000 + 7.79423i) q^{88} +(6.00000 - 3.46410i) q^{89} -6.00000 q^{90} +(1.50000 - 0.866025i) q^{93} +(-7.50000 - 12.9904i) q^{94} +(1.50000 - 2.59808i) q^{95} +5.19615i q^{96} +(-4.50000 - 2.59808i) q^{97} -10.3923i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + 3q^{2} + q^{3} + q^{4} + 3q^{6} + 2q^{9} + O(q^{10}) \) \( 2q + 3q^{2} + q^{3} + q^{4} + 3q^{6} + 2q^{9} - 3q^{10} + 9q^{11} + 2q^{12} - 2q^{13} + 3q^{15} + 5q^{16} - 6q^{17} + 3q^{19} - 3q^{20} + 9q^{22} - 3q^{24} + 4q^{25} - 9q^{26} + 10q^{27} - 3q^{29} + 3q^{30} + 9q^{32} + 9q^{33} - 2q^{36} + 6q^{38} + 5q^{39} + 6q^{40} - 9q^{41} - 11q^{43} - 6q^{45} - 5q^{48} + 6q^{50} - 12q^{51} - 7q^{52} - 18q^{53} + 15q^{54} - 9q^{55} - 9q^{58} + 6q^{59} - 7q^{61} - 3q^{62} - 2q^{64} - 12q^{65} + 18q^{66} - 15q^{67} + 6q^{68} + 3q^{71} + 6q^{72} + 2q^{75} + 3q^{76} + 3q^{78} - 10q^{79} + 15q^{80} - q^{81} - 9q^{82} + 18q^{85} + 3q^{87} + 9q^{88} + 12q^{89} - 12q^{90} + 3q^{93} - 15q^{94} + 3q^{95} - 9q^{97} + O(q^{100}) \)

Character values

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

\(n\) \(197\) \(248\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(1\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.50000 0.866025i 1.06066 0.612372i 0.135045 0.990839i \(-0.456882\pi\)
0.925615 + 0.378467i \(0.123549\pi\)
\(3\) 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i \(-0.0734519\pi\)
−0.684819 + 0.728714i \(0.740119\pi\)
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.73205i 0.774597i −0.921954 0.387298i \(-0.873408\pi\)
0.921954 0.387298i \(-0.126592\pi\)
\(6\) 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 0.367610 0.929980i \(-0.380176\pi\)
0.989191 + 0.146631i \(0.0468429\pi\)
\(12\) 1.00000 0.288675
\(13\) −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 \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) 3.46410i 0.816497i
\(19\) 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 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) −1.50000 + 0.866025i −0.306186 + 0.176777i
\(25\) 2.00000 0.400000
\(26\) −4.50000 4.33013i −0.882523 0.849208i
\(27\) 5.00000 0.962250
\(28\) 0 0
\(29\) −1.50000 2.59808i −0.278543 0.482451i 0.692480 0.721437i \(-0.256518\pi\)
−0.971023 + 0.238987i \(0.923185\pi\)
\(30\) 1.50000 2.59808i 0.273861 0.474342i
\(31\) 1.73205i 0.311086i −0.987829 0.155543i \(-0.950287\pi\)
0.987829 0.155543i \(-0.0497126\pi\)
\(32\) 4.50000 + 2.59808i 0.795495 + 0.459279i
\(33\) 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 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(38\) 3.00000 0.486664
\(39\) 2.50000 2.59808i 0.400320 0.416025i
\(40\) 3.00000 0.474342
\(41\) −4.50000 + 2.59808i −0.702782 + 0.405751i −0.808383 0.588657i \(-0.799657\pi\)
0.105601 + 0.994409i \(0.466323\pi\)
\(42\) 0 0
\(43\) −5.50000 + 9.52628i −0.838742 + 1.45274i 0.0522047 + 0.998636i \(0.483375\pi\)
−0.890947 + 0.454108i \(0.849958\pi\)
\(44\) 5.19615i 0.783349i
\(45\) −3.00000 1.73205i −0.447214 0.258199i
\(46\) 0 0
\(47\) 8.66025i 1.26323i −0.775283 0.631614i \(-0.782393\pi\)
0.775283 0.631614i \(-0.217607\pi\)
\(48\) −2.50000 + 4.33013i −0.360844 + 0.625000i
\(49\) 0 0
\(50\) 3.00000 1.73205i 0.424264 0.244949i
\(51\) −6.00000 −0.840168
\(52\) −3.50000 0.866025i −0.485363 0.120096i
\(53\) −9.00000 −1.23625 −0.618123 0.786082i \(-0.712106\pi\)
−0.618123 + 0.786082i \(0.712106\pi\)
\(54\) 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
\(58\) −4.50000 2.59808i −0.590879 0.341144i
\(59\) 3.00000 + 1.73205i 0.390567 + 0.225494i 0.682406 0.730974i \(-0.260934\pi\)
−0.291839 + 0.956467i \(0.594267\pi\)
\(60\) 1.73205i 0.223607i
\(61\) −3.50000 + 6.06218i −0.448129 + 0.776182i −0.998264 0.0588933i \(-0.981243\pi\)
0.550135 + 0.835076i \(0.314576\pi\)
\(62\) −1.50000 2.59808i −0.190500 0.329956i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −6.00000 + 1.73205i −0.744208 + 0.214834i
\(66\) 9.00000 1.10782
\(67\) −7.50000 + 4.33013i −0.916271 + 0.529009i −0.882443 0.470418i \(-0.844103\pi\)
−0.0338274 + 0.999428i \(0.510770\pi\)
\(68\) 3.00000 + 5.19615i 0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 1.50000 + 0.866025i 0.178017 + 0.102778i 0.586361 0.810050i \(-0.300560\pi\)
−0.408344 + 0.912828i \(0.633893\pi\)
\(72\) 3.00000 + 1.73205i 0.353553 + 0.204124i
\(73\) 8.66025i 1.01361i 0.862062 + 0.506803i \(0.169173\pi\)
−0.862062 + 0.506803i \(0.830827\pi\)
\(74\) 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
\(79\) −5.00000 −0.562544 −0.281272 0.959628i \(-0.590756\pi\)
−0.281272 + 0.959628i \(0.590756\pi\)
\(80\) 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
\(86\) 19.0526i 2.05449i
\(87\) 1.50000 2.59808i 0.160817 0.278543i
\(88\) 4.50000 + 7.79423i 0.479702 + 0.830868i
\(89\) 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
\(94\) −7.50000 12.9904i −0.773566 1.33986i
\(95\) 1.50000 2.59808i 0.153897 0.266557i
\(96\) 5.19615i 0.530330i
\(97\) −4.50000 2.59808i −0.456906 0.263795i 0.253837 0.967247i \(-0.418307\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 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 0.998240 0.0592978i \(-0.0188862\pi\)
−0.550474 + 0.834853i \(0.685553\pi\)
\(102\) −9.00000 + 5.19615i −0.891133 + 0.514496i
\(103\) −13.0000 −1.28093 −0.640464 0.767988i \(-0.721258\pi\)
−0.640464 + 0.767988i \(0.721258\pi\)
\(104\) 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
\(109\) 5.19615i 0.497701i −0.968542 0.248851i \(-0.919947\pi\)
0.968542 0.248851i \(-0.0800528\pi\)
\(110\) −13.5000 7.79423i −1.28717 0.743151i
\(111\) 0 0
\(112\) 0 0
\(113\) −7.50000 + 12.9904i −0.705541 + 1.22203i 0.260955 + 0.965351i \(0.415962\pi\)
−0.966496 + 0.256681i \(0.917371\pi\)
\(114\) 1.50000 + 2.59808i 0.140488 + 0.243332i
\(115\) 0 0
\(116\) −3.00000 −0.278543
\(117\) −7.00000 1.73205i −0.647150 0.160128i
\(118\) 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
\(122\) 12.1244i 1.09769i
\(123\) −4.50000 2.59808i −0.405751 0.234261i
\(124\) −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 −0.995846 0.0910585i \(-0.970975\pi\)
0.419064 0.907957i \(-0.362358\pi\)
\(128\) −10.5000 + 6.06218i −0.928078 + 0.535826i
\(129\) −11.0000 −0.968496
\(130\) −7.50000 + 7.79423i −0.657794 + 0.683599i
\(131\) 15.0000 1.31056 0.655278 0.755388i \(-0.272551\pi\)
0.655278 + 0.755388i \(0.272551\pi\)
\(132\) 4.50000 2.59808i 0.391675 0.226134i
\(133\) 0 0
\(134\) −7.50000 + 12.9904i −0.647901 + 1.12220i
\(135\) 8.66025i 0.745356i
\(136\) −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 −0.446857 0.894606i \(-0.647457\pi\)
0.998179 0.0603135i \(-0.0192101\pi\)
\(140\) 0 0
\(141\) 7.50000 4.33013i 0.631614 0.364662i
\(142\) 3.00000 0.251754
\(143\) −13.5000 12.9904i −1.12893 1.08631i
\(144\) 10.0000 0.833333
\(145\) −4.50000 + 2.59808i −0.373705 + 0.215758i
\(146\) 7.50000 + 12.9904i 0.620704 + 1.07509i
\(147\) 0 0
\(148\) 0 0
\(149\) 16.5000 + 9.52628i 1.35173 + 0.780423i 0.988492 0.151272i \(-0.0483370\pi\)
0.363241 + 0.931695i \(0.381670\pi\)
\(150\) 3.00000 + 1.73205i 0.244949 + 0.141421i
\(151\) 12.1244i 0.986666i 0.869841 + 0.493333i \(0.164222\pi\)
−0.869841 + 0.493333i \(0.835778\pi\)
\(152\) −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
\(156\) −1.00000 3.46410i −0.0800641 0.277350i
\(157\) 23.0000 1.83560 0.917800 0.397043i \(-0.129964\pi\)
0.917800 + 0.397043i \(0.129964\pi\)
\(158\) −7.50000 + 4.33013i −0.596668 + 0.344486i
\(159\) −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
\(163\) −10.5000 6.06218i −0.822423 0.474826i 0.0288280 0.999584i \(-0.490822\pi\)
−0.851251 + 0.524758i \(0.824156\pi\)
\(164\) 5.19615i 0.405751i
\(165\) 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 \(-0.688014\pi\)
0.440839 + 0.897586i \(0.354681\pi\)
\(168\) 0 0
\(169\) −11.0000 + 6.92820i −0.846154 + 0.532939i
\(170\) 18.0000 1.38054
\(171\) 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 \(0.359807\pi\)
−0.996544 + 0.0830722i \(0.973527\pi\)
\(174\) 5.19615i 0.393919i
\(175\) 0 0
\(176\) 22.5000 + 12.9904i 1.69600 + 0.979187i
\(177\) 3.46410i 0.260378i
\(178\) 6.00000 10.3923i 0.449719 0.778936i
\(179\) −1.50000 2.59808i −0.112115 0.194189i 0.804508 0.593942i \(-0.202429\pi\)
−0.916623 + 0.399753i \(0.869096\pi\)
\(180\) −3.00000 + 1.73205i −0.223607 + 0.129099i
\(181\) 2.00000 0.148659 0.0743294 0.997234i \(-0.476318\pi\)
0.0743294 + 0.997234i \(0.476318\pi\)
\(182\) 0 0
\(183\) −7.00000 −0.517455
\(184\) 0 0
\(185\) 0 0
\(186\) 1.50000 2.59808i 0.109985 0.190500i
\(187\) 31.1769i 2.27988i
\(188\) −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 −0.553014 0.833172i \(-0.686522\pi\)
0.445041 + 0.895510i \(0.353189\pi\)
\(194\) −9.00000 −0.646162
\(195\) −4.50000 4.33013i −0.322252 0.310087i
\(196\) 0 0
\(197\) 19.5000 11.2583i 1.38932 0.802123i 0.396079 0.918216i \(-0.370371\pi\)
0.993238 + 0.116094i \(0.0370372\pi\)
\(198\) −9.00000 15.5885i −0.639602 1.10782i
\(199\) −2.00000 + 3.46410i −0.141776 + 0.245564i −0.928166 0.372168i \(-0.878615\pi\)
0.786389 + 0.617731i \(0.211948\pi\)
\(200\) 3.46410i 0.244949i
\(201\) −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
\(205\) 4.50000 + 7.79423i 0.314294 + 0.544373i
\(206\) −19.5000 + 11.2583i −1.35863 + 0.784405i
\(207\) 0 0
\(208\) 12.5000 12.9904i 0.866719 0.900721i
\(209\) 9.00000 0.622543
\(210\) 0 0
\(211\) −6.50000 11.2583i −0.447478 0.775055i 0.550743 0.834675i \(-0.314345\pi\)
−0.998221 + 0.0596196i \(0.981011\pi\)
\(212\) −4.50000 + 7.79423i −0.309061 + 0.535310i
\(213\) 1.73205i 0.118678i
\(214\) 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
\(219\) −7.50000 + 4.33013i −0.506803 + 0.292603i
\(220\) −9.00000 −0.606780
\(221\) 21.0000 + 5.19615i 1.41261 + 0.349531i
\(222\) 0 0
\(223\) 4.50000 2.59808i 0.301342 0.173980i −0.341703 0.939808i \(-0.611004\pi\)
0.643046 + 0.765828i \(0.277671\pi\)
\(224\) 0 0
\(225\) 2.00000 3.46410i 0.133333 0.230940i
\(226\) 25.9808i 1.72821i
\(227\) 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
\(229\) 12.1244i 0.801200i 0.916253 + 0.400600i \(0.131198\pi\)
−0.916253 + 0.400600i \(0.868802\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 4.50000 2.59808i 0.295439 0.170572i
\(233\) 3.00000 0.196537 0.0982683 0.995160i \(-0.468670\pi\)
0.0982683 + 0.995160i \(0.468670\pi\)
\(234\) −12.0000 + 3.46410i −0.784465 + 0.226455i
\(235\) −15.0000 −0.978492
\(236\) 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 \(0.109112\pi\)
−0.941822 + 0.336111i \(0.890888\pi\)
\(240\) 7.50000 + 4.33013i 0.484123 + 0.279508i
\(241\) 6.00000 + 3.46410i 0.386494 + 0.223142i 0.680640 0.732618i \(-0.261702\pi\)
−0.294146 + 0.955761i \(0.595035\pi\)
\(242\) 27.7128i 1.78145i
\(243\) 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
\(247\) 1.50000 6.06218i 0.0954427 0.385727i
\(248\) 3.00000 0.190500
\(249\) −3.00000 + 1.73205i −0.190117 + 0.109764i
\(250\) −10.5000 18.1865i −0.664078 1.15022i
\(251\) −1.50000 + 2.59808i −0.0946792 + 0.163989i −0.909475 0.415759i \(-0.863516\pi\)
0.814795 + 0.579748i \(0.196849\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −19.5000 11.2583i −1.22354 0.706410i
\(255\) 10.3923i 0.650791i
\(256\) −9.50000 + 16.4545i −0.593750 + 1.02841i
\(257\) −15.0000 25.9808i −0.935674 1.62064i −0.773427 0.633885i \(-0.781459\pi\)
−0.162247 0.986750i \(-0.551874\pi\)
\(258\) −16.5000 + 9.52628i −1.02725 + 0.593080i
\(259\) 0 0
\(260\) −1.50000 + 6.06218i −0.0930261 + 0.375960i
\(261\) −6.00000 −0.371391
\(262\) 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
\(268\) 8.66025i 0.529009i
\(269\) 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) −7.50000 12.9904i −0.456435 0.790569i
\(271\) 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 \(0.0695395\pi\)
\(278\) 22.5167i 1.35046i
\(279\) −3.00000 1.73205i −0.179605 0.103695i
\(280\) 0 0
\(281\) 6.92820i 0.413302i −0.978415 0.206651i \(-0.933744\pi\)
0.978415 0.206651i \(-0.0662565\pi\)
\(282\) 7.50000 12.9904i 0.446619 0.773566i
\(283\) −9.50000 16.4545i −0.564716 0.978117i −0.997076 0.0764162i \(-0.975652\pi\)
0.432360 0.901701i \(-0.357681\pi\)
\(284\) 1.50000 0.866025i 0.0890086 0.0513892i
\(285\) 3.00000 0.177705
\(286\) −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
\(291\) 5.19615i 0.304604i
\(292\) 7.50000 + 4.33013i 0.438904 + 0.253402i
\(293\) −22.5000 12.9904i −1.31446 0.758906i −0.331632 0.943409i \(-0.607599\pi\)
−0.982832 + 0.184503i \(0.940933\pi\)
\(294\) 0 0
\(295\) 3.00000 5.19615i 0.174667 0.302532i
\(296\) 0 0
\(297\) 22.5000 12.9904i 1.30558 0.753778i
\(298\) 33.0000 1.91164
\(299\) 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
\(304\) 8.66025i 0.496700i
\(305\) 10.5000 + 6.06218i 0.601228 + 0.347119i
\(306\) 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
\(310\) −4.50000 + 2.59808i −0.255583 + 0.147561i
\(311\) −15.0000 −0.850572 −0.425286 0.905059i \(-0.639826\pi\)
−0.425286 + 0.905059i \(0.639826\pi\)
\(312\) 4.50000 + 4.33013i 0.254762 + 0.245145i
\(313\) 19.0000 1.07394 0.536972 0.843600i \(-0.319568\pi\)
0.536972 + 0.843600i \(0.319568\pi\)
\(314\) 34.5000 19.9186i 1.94695 1.12407i
\(315\) 0 0
\(316\) −2.50000 + 4.33013i −0.140636 + 0.243589i
\(317\) 5.19615i 0.291845i 0.989296 + 0.145922i \(0.0466150\pi\)
−0.989296 + 0.145922i \(0.953385\pi\)
\(318\) −13.5000 7.79423i −0.757042 0.437079i
\(319\) −13.5000 7.79423i −0.755855 0.436393i
\(320\) 1.73205i 0.0968246i
\(321\) 0 0
\(322\) 0 0
\(323\) −9.00000 + 5.19615i −0.500773 + 0.289122i
\(324\) −1.00000 −0.0555556
\(325\) −2.00000 6.92820i −0.110940 0.384308i
\(326\) −21.0000 −1.16308
\(327\) 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
\(331\) −28.5000 16.4545i −1.56650 0.904420i −0.996572 0.0827265i \(-0.973637\pi\)
−0.569929 0.821694i \(-0.693029\pi\)
\(332\) 3.00000 + 1.73205i 0.164646 + 0.0950586i
\(333\) 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 \(0.295482\pi\)
\(338\) −10.5000 + 19.9186i −0.571125 + 1.08343i
\(339\) −15.0000 −0.814688
\(340\) 9.00000 5.19615i 0.488094 0.281801i
\(341\) −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
\(346\) 25.9808i 1.39673i
\(347\) 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 \(-0.711079\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) −5.00000 17.3205i −0.266880 0.924500i
\(352\) 27.0000 1.43910
\(353\) −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
\(359\) 19.0526i 1.00556i 0.864416 + 0.502778i \(0.167689\pi\)
−0.864416 + 0.502778i \(0.832311\pi\)
\(360\) 3.00000 5.19615i 0.158114 0.273861i
\(361\) −8.00000 13.8564i −0.421053 0.729285i
\(362\) 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
\(367\) −11.5000 19.9186i −0.600295 1.03974i −0.992776 0.119982i \(-0.961716\pi\)
0.392481 0.919760i \(-0.371617\pi\)
\(368\) 0 0
\(369\) 10.3923i 0.541002i
\(370\) 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
\(376\) 15.0000 0.773566
\(377\) −7.50000 + 7.79423i −0.386270 + 0.401423i
\(378\) 0 0
\(379\) −1.50000 + 0.866025i −0.0770498 + 0.0444847i −0.538030 0.842926i \(-0.680831\pi\)
0.460980 + 0.887410i \(0.347498\pi\)
\(380\) −1.50000 2.59808i −0.0769484 0.133278i
\(381\) 6.50000 11.2583i 0.333005 0.576782i
\(382\) 25.9808i 1.32929i
\(383\) 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
\(387\) 11.0000 + 19.0526i 0.559161 + 0.968496i
\(388\) −4.50000 + 2.59808i −0.228453 + 0.131897i
\(389\) 3.00000 0.152106 0.0760530 0.997104i \(-0.475768\pi\)
0.0760530 + 0.997104i \(0.475768\pi\)
\(390\) −10.5000 2.59808i −0.531688 0.131559i
\(391\) 0 0
\(392\) 0 0
\(393\) 7.50000 + 12.9904i 0.378325 + 0.655278i
\(394\) 19.5000 33.7750i 0.982396 1.70156i
\(395\) 8.66025i 0.435745i
\(396\) −9.00000 5.19615i −0.452267 0.261116i
\(397\) −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
\(401\) 6.00000 3.46410i 0.299626 0.172989i −0.342649 0.939463i \(-0.611324\pi\)
0.642275 + 0.766475i \(0.277991\pi\)
\(402\) −15.0000 −0.748132
\(403\) −6.00000 + 1.73205i −0.298881 + 0.0862796i
\(404\) 9.00000 0.447767
\(405\) −1.50000 + 0.866025i −0.0745356 + 0.0430331i
\(406\) 0 0
\(407\) 0 0
\(408\) 10.3923i 0.514496i
\(409\) −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
\(415\) 6.00000 0.294528
\(416\) 4.50000 18.1865i 0.220631 0.891668i
\(417\) 13.0000 0.636613
\(418\) 13.5000 7.79423i 0.660307 0.381228i
\(419\) −10.5000 18.1865i −0.512959 0.888470i −0.999887 0.0150285i \(-0.995216\pi\)
0.486928 0.873442i \(-0.338117\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) −19.5000 11.2583i −0.949245 0.548047i
\(423\) −15.0000 8.66025i −0.729325 0.421076i
\(424\) 15.5885i 0.757042i
\(425\) −6.00000 + 10.3923i −0.291043 + 0.504101i
\(426\) 1.50000 + 2.59808i 0.0726752 + 0.125877i
\(427\) 0 0
\(428\) 0 0
\(429\) 4.50000 18.1865i 0.217262 0.878054i
\(430\) 33.0000 1.59140
\(431\) 28.5000 16.4545i 1.37280 0.792585i 0.381517 0.924362i \(-0.375402\pi\)
0.991279 + 0.131777i \(0.0420683\pi\)
\(432\) 12.5000 + 21.6506i 0.601407 + 1.04167i
\(433\) −9.50000 + 16.4545i −0.456541 + 0.790752i −0.998775 0.0494752i \(-0.984245\pi\)
0.542234 + 0.840227i \(0.317578\pi\)
\(434\) 0 0
\(435\) −4.50000 2.59808i −0.215758 0.124568i
\(436\) −4.50000 2.59808i −0.215511 0.124425i
\(437\) 0 0
\(438\) −7.50000 + 12.9904i −0.358364 + 0.620704i
\(439\) −4.00000 6.92820i −0.190910 0.330665i 0.754642 0.656136i \(-0.227810\pi\)
−0.945552 + 0.325471i \(0.894477\pi\)
\(440\) 13.5000 7.79423i 0.643587 0.371575i
\(441\) 0 0
\(442\) 36.0000 10.3923i 1.71235 0.494312i
\(443\) 15.0000 0.712672 0.356336 0.934358i \(-0.384026\pi\)
0.356336 + 0.934358i \(0.384026\pi\)
\(444\) 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 0.534977 0.844867i \(-0.320320\pi\)
−0.464188 + 0.885737i \(0.653654\pi\)
\(450\) 6.92820i 0.326599i
\(451\) −13.5000 + 23.3827i −0.635690 + 1.10105i
\(452\) 7.50000 + 12.9904i 0.352770 + 0.611016i
\(453\) −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 0.408607 0.912710i \(-0.366015\pi\)
0.994734 + 0.102491i \(0.0326814\pi\)
\(458\) 10.5000 + 18.1865i 0.490633 + 0.849801i
\(459\) −15.0000 + 25.9808i −0.700140 + 1.21268i
\(460\) 0 0
\(461\) 25.5000 + 14.7224i 1.18765 + 0.685692i 0.957773 0.287527i \(-0.0928330\pi\)
0.229881 + 0.973219i \(0.426166\pi\)
\(462\) 0 0
\(463\) 24.2487i 1.12693i −0.826139 0.563467i \(-0.809467\pi\)
0.826139 0.563467i \(-0.190533\pi\)
\(464\) 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
\(467\) −21.0000 −0.971764 −0.485882 0.874024i \(-0.661502\pi\)
−0.485882 + 0.874024i \(0.661502\pi\)
\(468\) −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
\(473\) 57.1577i 2.62811i
\(474\) −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
\(478\) 9.00000 + 15.5885i 0.411650 + 0.712999i
\(479\) −25.5000 + 14.7224i −1.16512 + 0.672685i −0.952527 0.304455i \(-0.901526\pi\)
−0.212598 + 0.977140i \(0.568192\pi\)
\(480\) 9.00000 0.410792
\(481\) 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
\(486\) 27.7128i 1.25708i
\(487\) 21.0000 + 12.1244i 0.951601 + 0.549407i 0.893578 0.448908i \(-0.148187\pi\)
0.0580230 + 0.998315i \(0.481520\pi\)
\(488\) −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 0.991365 + 0.131132i \(0.0418613\pi\)
−0.382118 + 0.924113i \(0.624805\pi\)
\(492\) −4.50000 + 2.59808i −0.202876 + 0.117130i
\(493\) 18.0000 0.810679
\(494\) −3.00000 10.3923i −0.134976 0.467572i
\(495\) −18.0000 −0.809040
\(496\) 7.50000 4.33013i 0.336760 0.194428i
\(497\) 0 0
\(498\) −3.00000 + 5.19615i −0.134433 + 0.232845i
\(499\) 1.73205i 0.0775372i −0.999248 0.0387686i \(-0.987656\pi\)
0.999248 0.0387686i \(-0.0123435\pi\)
\(500\) −10.5000 6.06218i −0.469574 0.271109i
\(501\) −1.50000 0.866025i −0.0670151 0.0386912i
\(502\) 5.19615i 0.231916i
\(503\) 4.50000 7.79423i 0.200645 0.347527i −0.748091 0.663596i \(-0.769030\pi\)
0.948736 + 0.316068i \(0.102363\pi\)
\(504\) 0 0
\(505\) 13.5000 7.79423i 0.600742 0.346839i
\(506\) 0 0
\(507\) −11.5000 6.06218i −0.510733 0.269231i
\(508\) −13.0000 −0.576782
\(509\) 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
\(513\) 7.50000 + 4.33013i 0.331133 + 0.191180i
\(514\) −45.0000 25.9808i −1.98486 1.14596i
\(515\) 22.5167i 0.992203i
\(516\) −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
\(520\) −3.00000 10.3923i −0.131559 0.455733i
\(521\) 39.0000 1.70862 0.854311 0.519763i \(-0.173980\pi\)
0.854311 + 0.519763i \(0.173980\pi\)
\(522\) −9.00000 + 5.19615i −0.393919 + 0.227429i
\(523\) 2.00000 + 3.46410i 0.0874539 + 0.151475i 0.906434 0.422347i \(-0.138794\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(524\) 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
\(528\) 25.9808i 1.13067i
\(529\) 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
\(534\) 12.0000 0.519291
\(535\) 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
\(541\) 12.1244i 0.521267i 0.965438 + 0.260633i \(0.0839314\pi\)
−0.965438 + 0.260633i \(0.916069\pi\)
\(542\) 15.0000 25.9808i 0.644305 1.11597i
\(543\) 1.00000 + 1.73205i 0.0429141 + 0.0743294i
\(544\) −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
\(549\) 7.00000 + 12.1244i 0.298753 + 0.517455i
\(550\) 9.00000 15.5885i 0.383761 0.664694i
\(551\) 5.19615i 0.221364i
\(552\) 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 −0.757953 0.652309i \(-0.773800\pi\)
0.185940 + 0.982561i \(0.440467\pi\)
\(558\) −6.00000 −0.254000
\(559\) 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 \(-0.559212\pi\)
0.943560 0.331202i \(-0.107454\pi\)
\(564\) 8.66025i 0.364662i
\(565\) 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
\(569\) 3.00000 + 5.19615i 0.125767 + 0.217834i 0.922032 0.387113i \(-0.126528\pi\)
−0.796266 + 0.604947i \(0.793194\pi\)
\(570\) 4.50000 2.59808i 0.188484 0.108821i
\(571\) −23.0000 −0.962520 −0.481260 0.876578i \(-0.659821\pi\)
−0.481260 + 0.876578i \(0.659821\pi\)
\(572\) −18.0000 + 5.19615i −0.752618 + 0.217262i
\(573\) 15.0000 0.626634
\(574\) 0 0
\(575\) 0 0
\(576\) −1.00000 + 1.73205i −0.0416667 + 0.0721688i
\(577\) 15.5885i 0.648956i 0.945893 + 0.324478i \(0.105189\pi\)
−0.945893 + 0.324478i \(0.894811\pi\)
\(578\) −28.5000 16.4545i −1.18544 0.684416i
\(579\) −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
\(583\) −40.5000 + 23.3827i −1.67734 + 0.968412i
\(584\) −15.0000 −0.620704
\(585\) −3.00000 + 12.1244i −0.124035 + 0.501280i
\(586\) −45.0000 −1.85893
\(587\) −13.5000 + 7.79423i −0.557205 + 0.321702i −0.752023 0.659137i \(-0.770922\pi\)
0.194818 + 0.980839i \(0.437588\pi\)
\(588\) 0 0
\(589\) 1.50000 2.59808i 0.0618064 0.107052i
\(590\) 10.3923i 0.427844i
\(591\) 19.5000 + 11.2583i 0.802123 + 0.463106i
\(592\) 0 0
\(593\) 5.19615i 0.213380i 0.994292 + 0.106690i \(0.0340253\pi\)
−0.994292 + 0.106690i \(0.965975\pi\)
\(594\) 22.5000 38.9711i 0.923186 1.59901i
\(595\) 0 0
\(596\) 16.5000 9.52628i 0.675866 0.390212i
\(597\) −4.00000 −0.163709
\(598\) 0 0
\(599\) 9.00000 0.367730 0.183865 0.982952i \(-0.441139\pi\)
0.183865 + 0.982952i \(0.441139\pi\)
\(600\) −3.00000 + 1.73205i −0.122474 + 0.0707107i
\(601\) −9.50000 16.4545i −0.387513 0.671192i 0.604601 0.796528i \(-0.293332\pi\)
−0.992114 + 0.125336i \(0.959999\pi\)
\(602\) 0 0
\(603\) 17.3205i 0.705346i
\(604\) 10.5000 + 6.06218i 0.427239 + 0.246667i
\(605\) −24.0000 13.8564i −0.975739 0.563343i
\(606\) 15.5885i 0.633238i
\(607\) 21.5000 37.2391i 0.872658 1.51149i 0.0134214 0.999910i \(-0.495728\pi\)
0.859237 0.511578i \(-0.170939\pi\)
\(608\) 4.50000 + 7.79423i 0.182499 + 0.316098i
\(609\) 0 0
\(610\) 21.0000 0.850265
\(611\) −30.0000 + 8.66025i −1.21367 + 0.350356i
\(612\) 12.0000 0.485071
\(613\) −31.5000 + 18.1865i −1.27227 + 0.734547i −0.975415 0.220375i \(-0.929272\pi\)
−0.296858 + 0.954922i \(0.595939\pi\)
\(614\) 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 0.999936 + 0.0113033i \(0.00359804\pi\)
0.509757 + 0.860318i \(0.329735\pi\)
\(618\) −19.5000 11.2583i −0.784405 0.452876i
\(619\) 19.0526i 0.765787i 0.923792 + 0.382893i \(0.125072\pi\)
−0.923792 + 0.382893i \(0.874928\pi\)
\(620\) −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
\(625\) −11.0000 −0.440000
\(626\) 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 −0.988841 0.148978i \(-0.952402\pi\)
−0.623439 0.781872i \(-0.714265\pi\)
\(632\) 8.66025i 0.344486i
\(633\) 6.50000 11.2583i 0.258352 0.447478i
\(634\) 4.50000 + 7.79423i 0.178718 + 0.309548i
\(635\) −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
\(640\) 10.5000 + 18.1865i 0.415049 + 0.718886i
\(641\) −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 \(-0.366004\pi\)
−0.586100 + 0.810239i \(0.699337\pi\)
\(644\) 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 0.940822 0.338902i \(-0.110055\pi\)
−0.763908 + 0.645325i \(0.776722\pi\)
\(648\) 1.50000 0.866025i 0.0589256 0.0340207i
\(649\) 18.0000 0.706562
\(650\) −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
\(655\) 25.9808i 1.01515i
\(656\) −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 −0.974320 0.225168i \(-0.927707\pi\)
0.682161 + 0.731202i \(0.261040\pi\)
\(660\) −4.50000 7.79423i −0.175162 0.303390i
\(661\) −31.5000 + 18.1865i −1.22521 + 0.707374i −0.966024 0.258454i \(-0.916787\pi\)
−0.259184 + 0.965828i \(0.583454\pi\)
\(662\) −57.0000 −2.21537
\(663\) 6.00000 + 20.7846i 0.233021 + 0.807207i
\(664\) −6.00000 −0.232845
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.73205i 0.0670151i
\(669\) 4.50000 + 2.59808i 0.173980 + 0.100447i
\(670\) 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 0.875501 0.483216i \(-0.160531\pi\)
−0.856228 + 0.516599i \(0.827198\pi\)
\(674\) 33.0000 19.0526i 1.27111 0.733877i
\(675\) 10.0000 0.384900
\(676\) 0.500000 + 12.9904i 0.0192308 + 0.499630i
\(677\) 27.0000 1.03769 0.518847 0.854867i \(-0.326361\pi\)
0.518847 + 0.854867i \(0.326361\pi\)
\(678\) −22.5000 + 12.9904i −0.864107 + 0.498893i
\(679\) 0 0
\(680\) −9.00000 + 15.5885i −0.345134 + 0.597790i
\(681\) 17.3205i 0.663723i
\(682\) −13.5000 7.79423i −0.516942 0.298456i
\(683\) −21.0000 12.1244i −0.803543 0.463926i 0.0411658 0.999152i \(-0.486893\pi\)
−0.844708 + 0.535227i \(0.820226\pi\)
\(684\) 3.46410i 0.132453i
\(685\) 0 0
\(686\) 0 0
\(687\) −10.5000 + 6.06218i −0.400600 + 0.231287i
\(688\) −55.0000 −2.09686
\(689\) 9.00000 + 31.1769i 0.342873 + 1.18775i
\(690\) 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
\(695\) −19.5000 11.2583i −0.739677 0.427053i
\(696\) 4.50000 + 2.59808i 0.170572 + 0.0984798i
\(697\) 31.1769i 1.18091i
\(698\) −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 \(0.536145\pi\)
\(702\) −22.5000 21.6506i −0.849208 0.817151i
\(703\) 0 0
\(704\) −4.50000 + 2.59808i −0.169600 + 0.0979187i
\(705\) −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
\(709\) 10.5000 + 6.06218i 0.394336 + 0.227670i 0.684037 0.729447i \(-0.260223\pi\)
−0.289701 + 0.957117i \(0.593556\pi\)
\(710\) 5.19615i 0.195008i
\(711\) −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
\(716\) −3.00000 −0.112115
\(717\) −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 −0.691608 0.722273i \(-0.743097\pi\)
0.971311 + 0.237814i \(0.0764307\pi\)
\(720\) 17.3205i 0.645497i
\(721\) 0 0
\(722\) −24.0000 13.8564i −0.893188 0.515682i
\(723\) 6.92820i 0.257663i
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) −3.00000 5.19615i −0.111417 0.192980i
\(726\) 24.0000 13.8564i 0.890724 0.514259i
\(727\) −32.0000 −1.18681 −0.593407 0.804902i \(-0.702218\pi\)
−0.593407 + 0.804902i \(0.702218\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 22.5000 12.9904i 0.832762 0.480796i
\(731\) −33.0000 57.1577i −1.22055 2.11405i
\(732\) −3.50000 + 6.06218i −0.129364 + 0.224065i
\(733\) 50.2295i 1.85527i −0.373491 0.927634i \(-0.621839\pi\)
0.373491 0.927634i \(-0.378161\pi\)
\(734\) −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 0.294285 0.955718i \(-0.404919\pi\)
0.974818 + 0.223001i \(0.0715853\pi\)
\(740\) 0 0
\(741\) 6.00000 1.73205i 0.220416 0.0636285i
\(742\) 0 0
\(743\) −1.50000 + 0.866025i −0.0550297 + 0.0317714i −0.527262 0.849703i \(-0.676782\pi\)
0.472233 + 0.881474i \(0.343448\pi\)
\(744\) 1.50000 + 2.59808i 0.0549927 + 0.0952501i
\(745\) 16.5000 28.5788i 0.604513 1.04705i
\(746\) 32.9090i 1.20488i
\(747\) 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
\(751\) −10.0000 17.3205i −0.364905 0.632034i 0.623856 0.781540i \(-0.285565\pi\)
−0.988761 + 0.149505i \(0.952232\pi\)
\(752\) 37.5000 21.6506i 1.36748 0.789517i
\(753\) −3.00000 −0.109326
\(754\) −4.50000 + 18.1865i −0.163880 + 0.662314i
\(755\) 21.0000 0.764268
\(756\) 0 0
\(757\) 8.50000 + 14.7224i 0.308938 + 0.535096i 0.978130 0.207993i \(-0.0666932\pi\)
−0.669193 + 0.743089i \(0.733360\pi\)
\(758\) −1.50000 + 2.59808i −0.0544825 + 0.0943664i
\(759\) 0 0
\(760\) 4.50000 + 2.59808i 0.163232 + 0.0942421i
\(761\) −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
\(765\) 18.0000 10.3923i 0.650791 0.375735i
\(766\) 27.0000 0.975550
\(767\) 3.00000 12.1244i 0.108324 0.437785i
\(768\) −19.0000 −0.685603
\(769\) −16.5000 + 9.52628i −0.595005 + 0.343526i −0.767074 0.641558i \(-0.778288\pi\)
0.172069 + 0.985085i \(0.444955\pi\)
\(770\) 0 0
\(771\) 15.0000 25.9808i 0.540212 0.935674i
\(772\) 1.73205i 0.0623379i
\(773\) 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
\(775\) 3.46410i 0.124434i
\(776\) 4.50000 7.79423i 0.161541 0.279797i
\(777\) 0 0
\(778\) 4.50000 2.59808i 0.161333 0.0931455i
\(779\) −9.00000 −0.322458
\(780\) −6.00000 + 1.73205i −0.214834 + 0.0620174i
\(781\) 9.00000 0.322045
\(782\) 0 0
\(783\) −7.50000 12.9904i −0.268028 0.464238i