Properties

Label 336.2.q.a.289.1
Level $336$
Weight $2$
Character 336.289
Analytic conductor $2.683$
Analytic rank $1$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 336.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(2.68297350792\)
Analytic rank: \(1\)
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 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 289.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 336.289
Dual form 336.2.q.a.193.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{5} +(-2.50000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} -3.00000 q^{13} +2.00000 q^{15} +(-2.00000 - 3.46410i) q^{17} +(-2.50000 + 4.33013i) q^{19} +(2.00000 + 1.73205i) q^{21} +(-2.00000 + 3.46410i) q^{23} +(0.500000 + 0.866025i) q^{25} +1.00000 q^{27} -4.00000 q^{29} +(3.50000 + 6.06218i) q^{31} +(-3.00000 + 5.19615i) q^{33} +(1.00000 - 5.19615i) q^{35} +(4.50000 - 7.79423i) q^{37} +(1.50000 + 2.59808i) q^{39} -2.00000 q^{41} +1.00000 q^{43} +(-1.00000 - 1.73205i) q^{45} +(1.00000 - 1.73205i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-2.00000 + 3.46410i) q^{51} +(-4.00000 - 6.92820i) q^{53} +12.0000 q^{55} +5.00000 q^{57} +(-5.00000 + 8.66025i) q^{61} +(0.500000 - 2.59808i) q^{63} +(3.00000 - 5.19615i) q^{65} +(-7.50000 - 12.9904i) q^{67} +4.00000 q^{69} +6.00000 q^{71} +(5.50000 + 9.52628i) q^{73} +(0.500000 - 0.866025i) q^{75} +(12.0000 + 10.3923i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} -6.00000 q^{83} +8.00000 q^{85} +(2.00000 + 3.46410i) q^{87} +(4.00000 - 6.92820i) q^{89} +(7.50000 - 2.59808i) q^{91} +(3.50000 - 6.06218i) q^{93} +(-5.00000 - 8.66025i) q^{95} -14.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - q^{3} - 2q^{5} - 5q^{7} - q^{9} + O(q^{10}) \) \( 2q - q^{3} - 2q^{5} - 5q^{7} - q^{9} - 6q^{11} - 6q^{13} + 4q^{15} - 4q^{17} - 5q^{19} + 4q^{21} - 4q^{23} + q^{25} + 2q^{27} - 8q^{29} + 7q^{31} - 6q^{33} + 2q^{35} + 9q^{37} + 3q^{39} - 4q^{41} + 2q^{43} - 2q^{45} + 2q^{47} + 11q^{49} - 4q^{51} - 8q^{53} + 24q^{55} + 10q^{57} - 10q^{61} + q^{63} + 6q^{65} - 15q^{67} + 8q^{69} + 12q^{71} + 11q^{73} + q^{75} + 24q^{77} + q^{79} - q^{81} - 12q^{83} + 16q^{85} + 4q^{87} + 8q^{89} + 15q^{91} + 7q^{93} - 10q^{95} - 28q^{97} + 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).

\(n\) \(85\) \(113\) \(127\) \(241\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −0.500000 0.866025i −0.288675 0.500000i
\(4\) 0 0
\(5\) −1.00000 + 1.73205i −0.447214 + 0.774597i −0.998203 0.0599153i \(-0.980917\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(6\) 0 0
\(7\) −2.50000 + 0.866025i −0.944911 + 0.327327i
\(8\) 0 0
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) −3.00000 5.19615i −0.904534 1.56670i −0.821541 0.570149i \(-0.806886\pi\)
−0.0829925 0.996550i \(-0.526448\pi\)
\(12\) 0 0
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) 0 0
\(15\) 2.00000 0.516398
\(16\) 0 0
\(17\) −2.00000 3.46410i −0.485071 0.840168i 0.514782 0.857321i \(-0.327873\pi\)
−0.999853 + 0.0171533i \(0.994540\pi\)
\(18\) 0 0
\(19\) −2.50000 + 4.33013i −0.573539 + 0.993399i 0.422659 + 0.906289i \(0.361097\pi\)
−0.996199 + 0.0871106i \(0.972237\pi\)
\(20\) 0 0
\(21\) 2.00000 + 1.73205i 0.436436 + 0.377964i
\(22\) 0 0
\(23\) −2.00000 + 3.46410i −0.417029 + 0.722315i −0.995639 0.0932891i \(-0.970262\pi\)
0.578610 + 0.815604i \(0.303595\pi\)
\(24\) 0 0
\(25\) 0.500000 + 0.866025i 0.100000 + 0.173205i
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −4.00000 −0.742781 −0.371391 0.928477i \(-0.621119\pi\)
−0.371391 + 0.928477i \(0.621119\pi\)
\(30\) 0 0
\(31\) 3.50000 + 6.06218i 0.628619 + 1.08880i 0.987829 + 0.155543i \(0.0497126\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 0 0
\(33\) −3.00000 + 5.19615i −0.522233 + 0.904534i
\(34\) 0 0
\(35\) 1.00000 5.19615i 0.169031 0.878310i
\(36\) 0 0
\(37\) 4.50000 7.79423i 0.739795 1.28136i −0.212792 0.977098i \(-0.568256\pi\)
0.952587 0.304266i \(-0.0984111\pi\)
\(38\) 0 0
\(39\) 1.50000 + 2.59808i 0.240192 + 0.416025i
\(40\) 0 0
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 1.00000 0.152499 0.0762493 0.997089i \(-0.475706\pi\)
0.0762493 + 0.997089i \(0.475706\pi\)
\(44\) 0 0
\(45\) −1.00000 1.73205i −0.149071 0.258199i
\(46\) 0 0
\(47\) 1.00000 1.73205i 0.145865 0.252646i −0.783830 0.620975i \(-0.786737\pi\)
0.929695 + 0.368329i \(0.120070\pi\)
\(48\) 0 0
\(49\) 5.50000 4.33013i 0.785714 0.618590i
\(50\) 0 0
\(51\) −2.00000 + 3.46410i −0.280056 + 0.485071i
\(52\) 0 0
\(53\) −4.00000 6.92820i −0.549442 0.951662i −0.998313 0.0580651i \(-0.981507\pi\)
0.448871 0.893597i \(-0.351826\pi\)
\(54\) 0 0
\(55\) 12.0000 1.61808
\(56\) 0 0
\(57\) 5.00000 0.662266
\(58\) 0 0
\(59\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) −5.00000 + 8.66025i −0.640184 + 1.10883i 0.345207 + 0.938527i \(0.387809\pi\)
−0.985391 + 0.170305i \(0.945525\pi\)
\(62\) 0 0
\(63\) 0.500000 2.59808i 0.0629941 0.327327i
\(64\) 0 0
\(65\) 3.00000 5.19615i 0.372104 0.644503i
\(66\) 0 0
\(67\) −7.50000 12.9904i −0.916271 1.58703i −0.805030 0.593234i \(-0.797851\pi\)
−0.111241 0.993793i \(-0.535483\pi\)
\(68\) 0 0
\(69\) 4.00000 0.481543
\(70\) 0 0
\(71\) 6.00000 0.712069 0.356034 0.934473i \(-0.384129\pi\)
0.356034 + 0.934473i \(0.384129\pi\)
\(72\) 0 0
\(73\) 5.50000 + 9.52628i 0.643726 + 1.11497i 0.984594 + 0.174855i \(0.0559458\pi\)
−0.340868 + 0.940111i \(0.610721\pi\)
\(74\) 0 0
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 0 0
\(77\) 12.0000 + 10.3923i 1.36753 + 1.18431i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 0 0
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 0 0
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 8.00000 0.867722
\(86\) 0 0
\(87\) 2.00000 + 3.46410i 0.214423 + 0.371391i
\(88\) 0 0
\(89\) 4.00000 6.92820i 0.423999 0.734388i −0.572327 0.820025i \(-0.693959\pi\)
0.996326 + 0.0856373i \(0.0272926\pi\)
\(90\) 0 0
\(91\) 7.50000 2.59808i 0.786214 0.272352i
\(92\) 0 0
\(93\) 3.50000 6.06218i 0.362933 0.628619i
\(94\) 0 0
\(95\) −5.00000 8.66025i −0.512989 0.888523i
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 0 0
\(99\) 6.00000 0.603023
\(100\) 0 0
\(101\) 3.00000 + 5.19615i 0.298511 + 0.517036i 0.975796 0.218685i \(-0.0701767\pi\)
−0.677284 + 0.735721i \(0.736843\pi\)
\(102\) 0 0
\(103\) −4.50000 + 7.79423i −0.443398 + 0.767988i −0.997939 0.0641683i \(-0.979561\pi\)
0.554541 + 0.832156i \(0.312894\pi\)
\(104\) 0 0
\(105\) −5.00000 + 1.73205i −0.487950 + 0.169031i
\(106\) 0 0
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) 0 0
\(109\) 5.50000 + 9.52628i 0.526804 + 0.912452i 0.999512 + 0.0312328i \(0.00994332\pi\)
−0.472708 + 0.881219i \(0.656723\pi\)
\(110\) 0 0
\(111\) −9.00000 −0.854242
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) 0 0
\(115\) −4.00000 6.92820i −0.373002 0.646058i
\(116\) 0 0
\(117\) 1.50000 2.59808i 0.138675 0.240192i
\(118\) 0 0
\(119\) 8.00000 + 6.92820i 0.733359 + 0.635107i
\(120\) 0 0
\(121\) −12.5000 + 21.6506i −1.13636 + 1.96824i
\(122\) 0 0
\(123\) 1.00000 + 1.73205i 0.0901670 + 0.156174i
\(124\) 0 0
\(125\) −12.0000 −1.07331
\(126\) 0 0
\(127\) 1.00000 0.0887357 0.0443678 0.999015i \(-0.485873\pi\)
0.0443678 + 0.999015i \(0.485873\pi\)
\(128\) 0 0
\(129\) −0.500000 0.866025i −0.0440225 0.0762493i
\(130\) 0 0
\(131\) 7.00000 12.1244i 0.611593 1.05931i −0.379379 0.925241i \(-0.623862\pi\)
0.990972 0.134069i \(-0.0428042\pi\)
\(132\) 0 0
\(133\) 2.50000 12.9904i 0.216777 1.12641i
\(134\) 0 0
\(135\) −1.00000 + 1.73205i −0.0860663 + 0.149071i
\(136\) 0 0
\(137\) −10.0000 17.3205i −0.854358 1.47979i −0.877240 0.480053i \(-0.840618\pi\)
0.0228820 0.999738i \(-0.492716\pi\)
\(138\) 0 0
\(139\) 9.00000 0.763370 0.381685 0.924292i \(-0.375344\pi\)
0.381685 + 0.924292i \(0.375344\pi\)
\(140\) 0 0
\(141\) −2.00000 −0.168430
\(142\) 0 0
\(143\) 9.00000 + 15.5885i 0.752618 + 1.30357i
\(144\) 0 0
\(145\) 4.00000 6.92820i 0.332182 0.575356i
\(146\) 0 0
\(147\) −6.50000 2.59808i −0.536111 0.214286i
\(148\) 0 0
\(149\) −2.00000 + 3.46410i −0.163846 + 0.283790i −0.936245 0.351348i \(-0.885723\pi\)
0.772399 + 0.635138i \(0.219057\pi\)
\(150\) 0 0
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) −14.0000 −1.12451
\(156\) 0 0
\(157\) −9.00000 15.5885i −0.718278 1.24409i −0.961681 0.274169i \(-0.911597\pi\)
0.243403 0.969925i \(-0.421736\pi\)
\(158\) 0 0
\(159\) −4.00000 + 6.92820i −0.317221 + 0.549442i
\(160\) 0 0
\(161\) 2.00000 10.3923i 0.157622 0.819028i
\(162\) 0 0
\(163\) 2.00000 3.46410i 0.156652 0.271329i −0.777007 0.629492i \(-0.783263\pi\)
0.933659 + 0.358162i \(0.116597\pi\)
\(164\) 0 0
\(165\) −6.00000 10.3923i −0.467099 0.809040i
\(166\) 0 0
\(167\) −18.0000 −1.39288 −0.696441 0.717614i \(-0.745234\pi\)
−0.696441 + 0.717614i \(0.745234\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) −2.50000 4.33013i −0.191180 0.331133i
\(172\) 0 0
\(173\) −10.0000 + 17.3205i −0.760286 + 1.31685i 0.182417 + 0.983221i \(0.441608\pi\)
−0.942703 + 0.333633i \(0.891725\pi\)
\(174\) 0 0
\(175\) −2.00000 1.73205i −0.151186 0.130931i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 13.0000 + 22.5167i 0.971666 + 1.68297i 0.690526 + 0.723307i \(0.257379\pi\)
0.281139 + 0.959667i \(0.409288\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) 0 0
\(183\) 10.0000 0.739221
\(184\) 0 0
\(185\) 9.00000 + 15.5885i 0.661693 + 1.14609i
\(186\) 0 0
\(187\) −12.0000 + 20.7846i −0.877527 + 1.51992i
\(188\) 0 0
\(189\) −2.50000 + 0.866025i −0.181848 + 0.0629941i
\(190\) 0 0
\(191\) 5.00000 8.66025i 0.361787 0.626634i −0.626468 0.779447i \(-0.715500\pi\)
0.988255 + 0.152813i \(0.0488333\pi\)
\(192\) 0 0
\(193\) −1.50000 2.59808i −0.107972 0.187014i 0.806976 0.590584i \(-0.201102\pi\)
−0.914949 + 0.403570i \(0.867769\pi\)
\(194\) 0 0
\(195\) −6.00000 −0.429669
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) −8.00000 13.8564i −0.567105 0.982255i −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 0 0
\(201\) −7.50000 + 12.9904i −0.529009 + 0.916271i
\(202\) 0 0
\(203\) 10.0000 3.46410i 0.701862 0.243132i
\(204\) 0 0
\(205\) 2.00000 3.46410i 0.139686 0.241943i
\(206\) 0 0
\(207\) −2.00000 3.46410i −0.139010 0.240772i
\(208\) 0 0
\(209\) 30.0000 2.07514
\(210\) 0 0
\(211\) 4.00000 0.275371 0.137686 0.990476i \(-0.456034\pi\)
0.137686 + 0.990476i \(0.456034\pi\)
\(212\) 0 0
\(213\) −3.00000 5.19615i −0.205557 0.356034i
\(214\) 0 0
\(215\) −1.00000 + 1.73205i −0.0681994 + 0.118125i
\(216\) 0 0
\(217\) −14.0000 12.1244i −0.950382 0.823055i
\(218\) 0 0
\(219\) 5.50000 9.52628i 0.371656 0.643726i
\(220\) 0 0
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) 0 0
\(223\) −24.0000 −1.60716 −0.803579 0.595198i \(-0.797074\pi\)
−0.803579 + 0.595198i \(0.797074\pi\)
\(224\) 0 0
\(225\) −1.00000 −0.0666667
\(226\) 0 0
\(227\) 7.00000 + 12.1244i 0.464606 + 0.804722i 0.999184 0.0403978i \(-0.0128625\pi\)
−0.534577 + 0.845120i \(0.679529\pi\)
\(228\) 0 0
\(229\) 3.50000 6.06218i 0.231287 0.400600i −0.726900 0.686743i \(-0.759040\pi\)
0.958187 + 0.286143i \(0.0923732\pi\)
\(230\) 0 0
\(231\) 3.00000 15.5885i 0.197386 1.02565i
\(232\) 0 0
\(233\) −13.0000 + 22.5167i −0.851658 + 1.47512i 0.0280525 + 0.999606i \(0.491069\pi\)
−0.879711 + 0.475509i \(0.842264\pi\)
\(234\) 0 0
\(235\) 2.00000 + 3.46410i 0.130466 + 0.225973i
\(236\) 0 0
\(237\) −1.00000 −0.0649570
\(238\) 0 0
\(239\) −2.00000 −0.129369 −0.0646846 0.997906i \(-0.520604\pi\)
−0.0646846 + 0.997906i \(0.520604\pi\)
\(240\) 0 0
\(241\) 1.00000 + 1.73205i 0.0644157 + 0.111571i 0.896435 0.443176i \(-0.146148\pi\)
−0.832019 + 0.554747i \(0.812815\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 2.00000 + 13.8564i 0.127775 + 0.885253i
\(246\) 0 0
\(247\) 7.50000 12.9904i 0.477214 0.826558i
\(248\) 0 0
\(249\) 3.00000 + 5.19615i 0.190117 + 0.329293i
\(250\) 0 0
\(251\) −4.00000 −0.252478 −0.126239 0.992000i \(-0.540291\pi\)
−0.126239 + 0.992000i \(0.540291\pi\)
\(252\) 0 0
\(253\) 24.0000 1.50887
\(254\) 0 0
\(255\) −4.00000 6.92820i −0.250490 0.433861i
\(256\) 0 0
\(257\) 9.00000 15.5885i 0.561405 0.972381i −0.435970 0.899961i \(-0.643595\pi\)
0.997374 0.0724199i \(-0.0230722\pi\)
\(258\) 0 0
\(259\) −4.50000 + 23.3827i −0.279616 + 1.45293i
\(260\) 0 0
\(261\) 2.00000 3.46410i 0.123797 0.214423i
\(262\) 0 0
\(263\) −6.00000 10.3923i −0.369976 0.640817i 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) 0 0
\(265\) 16.0000 0.982872
\(266\) 0 0
\(267\) −8.00000 −0.489592
\(268\) 0 0
\(269\) 9.00000 + 15.5885i 0.548740 + 0.950445i 0.998361 + 0.0572259i \(0.0182255\pi\)
−0.449622 + 0.893219i \(0.648441\pi\)
\(270\) 0 0
\(271\) 4.00000 6.92820i 0.242983 0.420858i −0.718580 0.695444i \(-0.755208\pi\)
0.961563 + 0.274586i \(0.0885408\pi\)
\(272\) 0 0
\(273\) −6.00000 5.19615i −0.363137 0.314485i
\(274\) 0 0
\(275\) 3.00000 5.19615i 0.180907 0.313340i
\(276\) 0 0
\(277\) −0.500000 0.866025i −0.0300421 0.0520344i 0.850613 0.525792i \(-0.176231\pi\)
−0.880656 + 0.473757i \(0.842897\pi\)
\(278\) 0 0
\(279\) −7.00000 −0.419079
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) −0.500000 0.866025i −0.0297219 0.0514799i 0.850782 0.525519i \(-0.176129\pi\)
−0.880504 + 0.474039i \(0.842796\pi\)
\(284\) 0 0
\(285\) −5.00000 + 8.66025i −0.296174 + 0.512989i
\(286\) 0 0
\(287\) 5.00000 1.73205i 0.295141 0.102240i
\(288\) 0 0
\(289\) 0.500000 0.866025i 0.0294118 0.0509427i
\(290\) 0 0
\(291\) 7.00000 + 12.1244i 0.410347 + 0.710742i
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) −3.00000 5.19615i −0.174078 0.301511i
\(298\) 0 0
\(299\) 6.00000 10.3923i 0.346989 0.601003i
\(300\) 0 0
\(301\) −2.50000 + 0.866025i −0.144098 + 0.0499169i
\(302\) 0 0
\(303\) 3.00000 5.19615i 0.172345 0.298511i
\(304\) 0 0
\(305\) −10.0000 17.3205i −0.572598 0.991769i
\(306\) 0 0
\(307\) 11.0000 0.627803 0.313902 0.949456i \(-0.398364\pi\)
0.313902 + 0.949456i \(0.398364\pi\)
\(308\) 0 0
\(309\) 9.00000 0.511992
\(310\) 0 0
\(311\) −9.00000 15.5885i −0.510343 0.883940i −0.999928 0.0119847i \(-0.996185\pi\)
0.489585 0.871956i \(-0.337148\pi\)
\(312\) 0 0
\(313\) 0.500000 0.866025i 0.0282617 0.0489506i −0.851549 0.524276i \(-0.824336\pi\)
0.879810 + 0.475325i \(0.157669\pi\)
\(314\) 0 0
\(315\) 4.00000 + 3.46410i 0.225374 + 0.195180i
\(316\) 0 0
\(317\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(318\) 0 0
\(319\) 12.0000 + 20.7846i 0.671871 + 1.16371i
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 20.0000 1.11283
\(324\) 0 0
\(325\) −1.50000 2.59808i −0.0832050 0.144115i
\(326\) 0 0
\(327\) 5.50000 9.52628i 0.304151 0.526804i
\(328\) 0 0
\(329\) −1.00000 + 5.19615i −0.0551318 + 0.286473i
\(330\) 0 0
\(331\) 2.50000 4.33013i 0.137412 0.238005i −0.789104 0.614260i \(-0.789455\pi\)
0.926516 + 0.376254i \(0.122788\pi\)
\(332\) 0 0
\(333\) 4.50000 + 7.79423i 0.246598 + 0.427121i
\(334\) 0 0
\(335\) 30.0000 1.63908
\(336\) 0 0
\(337\) 29.0000 1.57973 0.789865 0.613280i \(-0.210150\pi\)
0.789865 + 0.613280i \(0.210150\pi\)
\(338\) 0 0
\(339\) −3.00000 5.19615i −0.162938 0.282216i
\(340\) 0 0
\(341\) 21.0000 36.3731i 1.13721 1.96971i
\(342\) 0 0
\(343\) −10.0000 + 15.5885i −0.539949 + 0.841698i
\(344\) 0 0
\(345\) −4.00000 + 6.92820i −0.215353 + 0.373002i
\(346\) 0 0
\(347\) 6.00000 + 10.3923i 0.322097 + 0.557888i 0.980921 0.194409i \(-0.0622790\pi\)
−0.658824 + 0.752297i \(0.728946\pi\)
\(348\) 0 0
\(349\) −22.0000 −1.17763 −0.588817 0.808267i \(-0.700406\pi\)
−0.588817 + 0.808267i \(0.700406\pi\)
\(350\) 0 0
\(351\) −3.00000 −0.160128
\(352\) 0 0
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) 0 0
\(355\) −6.00000 + 10.3923i −0.318447 + 0.551566i
\(356\) 0 0
\(357\) 2.00000 10.3923i 0.105851 0.550019i
\(358\) 0 0
\(359\) −6.00000 + 10.3923i −0.316668 + 0.548485i −0.979791 0.200026i \(-0.935897\pi\)
0.663123 + 0.748511i \(0.269231\pi\)
\(360\) 0 0
\(361\) −3.00000 5.19615i −0.157895 0.273482i
\(362\) 0 0
\(363\) 25.0000 1.31216
\(364\) 0 0
\(365\) −22.0000 −1.15153
\(366\) 0 0
\(367\) −3.50000 6.06218i −0.182699 0.316443i 0.760100 0.649806i \(-0.225150\pi\)
−0.942799 + 0.333363i \(0.891817\pi\)
\(368\) 0 0
\(369\) 1.00000 1.73205i 0.0520579 0.0901670i
\(370\) 0 0
\(371\) 16.0000 + 13.8564i 0.830679 + 0.719389i
\(372\) 0 0
\(373\) 6.50000 11.2583i 0.336557 0.582934i −0.647225 0.762299i \(-0.724071\pi\)
0.983783 + 0.179364i \(0.0574041\pi\)
\(374\) 0 0
\(375\) 6.00000 + 10.3923i 0.309839 + 0.536656i
\(376\) 0 0
\(377\) 12.0000 0.618031
\(378\) 0 0
\(379\) 15.0000 0.770498 0.385249 0.922813i \(-0.374116\pi\)
0.385249 + 0.922813i \(0.374116\pi\)
\(380\) 0 0
\(381\) −0.500000 0.866025i −0.0256158 0.0443678i
\(382\) 0 0
\(383\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(384\) 0 0
\(385\) −30.0000 + 10.3923i −1.52894 + 0.529641i
\(386\) 0 0
\(387\) −0.500000 + 0.866025i −0.0254164 + 0.0440225i
\(388\) 0 0
\(389\) 13.0000 + 22.5167i 0.659126 + 1.14164i 0.980842 + 0.194804i \(0.0624070\pi\)
−0.321716 + 0.946836i \(0.604260\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) −14.0000 −0.706207
\(394\) 0 0
\(395\) 1.00000 + 1.73205i 0.0503155 + 0.0871489i
\(396\) 0 0
\(397\) 2.50000 4.33013i 0.125471 0.217323i −0.796446 0.604710i \(-0.793289\pi\)
0.921917 + 0.387387i \(0.126622\pi\)
\(398\) 0 0
\(399\) −12.5000 + 4.33013i −0.625783 + 0.216777i
\(400\) 0 0
\(401\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(402\) 0 0
\(403\) −10.5000 18.1865i −0.523042 0.905936i
\(404\) 0 0
\(405\) 2.00000 0.0993808
\(406\) 0 0
\(407\) −54.0000 −2.67668
\(408\) 0 0
\(409\) 1.50000 + 2.59808i 0.0741702 + 0.128467i 0.900725 0.434389i \(-0.143036\pi\)
−0.826555 + 0.562856i \(0.809703\pi\)
\(410\) 0 0
\(411\) −10.0000 + 17.3205i −0.493264 + 0.854358i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 6.00000 10.3923i 0.294528 0.510138i
\(416\) 0 0
\(417\) −4.50000 7.79423i −0.220366 0.381685i
\(418\) 0 0
\(419\) −26.0000 −1.27018 −0.635092 0.772437i \(-0.719038\pi\)
−0.635092 + 0.772437i \(0.719038\pi\)
\(420\) 0 0
\(421\) −35.0000 −1.70580 −0.852898 0.522078i \(-0.825157\pi\)
−0.852898 + 0.522078i \(0.825157\pi\)
\(422\) 0 0
\(423\) 1.00000 + 1.73205i 0.0486217 + 0.0842152i
\(424\) 0 0
\(425\) 2.00000 3.46410i 0.0970143 0.168034i
\(426\) 0 0
\(427\) 5.00000 25.9808i 0.241967 1.25730i
\(428\) 0 0
\(429\) 9.00000 15.5885i 0.434524 0.752618i
\(430\) 0 0
\(431\) −9.00000 15.5885i −0.433515 0.750870i 0.563658 0.826008i \(-0.309393\pi\)
−0.997173 + 0.0751385i \(0.976060\pi\)
\(432\) 0 0
\(433\) 31.0000 1.48976 0.744882 0.667196i \(-0.232506\pi\)
0.744882 + 0.667196i \(0.232506\pi\)
\(434\) 0 0
\(435\) −8.00000 −0.383571
\(436\) 0 0
\(437\) −10.0000 17.3205i −0.478365 0.828552i
\(438\) 0 0
\(439\) 12.0000 20.7846i 0.572729 0.991995i −0.423556 0.905870i \(-0.639218\pi\)
0.996284 0.0861252i \(-0.0274485\pi\)
\(440\) 0 0
\(441\) 1.00000 + 6.92820i 0.0476190 + 0.329914i
\(442\) 0 0
\(443\) −8.00000 + 13.8564i −0.380091 + 0.658338i −0.991075 0.133306i \(-0.957441\pi\)
0.610984 + 0.791643i \(0.290774\pi\)
\(444\) 0 0
\(445\) 8.00000 + 13.8564i 0.379236 + 0.656857i
\(446\) 0 0
\(447\) 4.00000 0.189194
\(448\) 0 0
\(449\) −38.0000 −1.79333 −0.896665 0.442709i \(-0.854018\pi\)
−0.896665 + 0.442709i \(0.854018\pi\)
\(450\) 0 0
\(451\) 6.00000 + 10.3923i 0.282529 + 0.489355i
\(452\) 0 0
\(453\) −4.00000 + 6.92820i −0.187936 + 0.325515i
\(454\) 0 0
\(455\) −3.00000 + 15.5885i −0.140642 + 0.730798i
\(456\) 0 0
\(457\) −6.50000 + 11.2583i −0.304057 + 0.526642i −0.977051 0.213006i \(-0.931675\pi\)
0.672994 + 0.739648i \(0.265008\pi\)
\(458\) 0 0
\(459\) −2.00000 3.46410i −0.0933520 0.161690i
\(460\) 0 0
\(461\) −12.0000 −0.558896 −0.279448 0.960161i \(-0.590151\pi\)
−0.279448 + 0.960161i \(0.590151\pi\)
\(462\) 0 0
\(463\) −17.0000 −0.790057 −0.395029 0.918669i \(-0.629265\pi\)
−0.395029 + 0.918669i \(0.629265\pi\)
\(464\) 0 0
\(465\) 7.00000 + 12.1244i 0.324617 + 0.562254i
\(466\) 0 0
\(467\) 15.0000 25.9808i 0.694117 1.20225i −0.276360 0.961054i \(-0.589128\pi\)
0.970477 0.241192i \(-0.0775384\pi\)
\(468\) 0 0
\(469\) 30.0000 + 25.9808i 1.38527 + 1.19968i
\(470\) 0 0
\(471\) −9.00000 + 15.5885i −0.414698 + 0.718278i
\(472\) 0 0
\(473\) −3.00000 5.19615i −0.137940 0.238919i
\(474\) 0 0
\(475\) −5.00000 −0.229416
\(476\) 0 0
\(477\) 8.00000 0.366295
\(478\) 0 0
\(479\) 8.00000 + 13.8564i 0.365529 + 0.633115i 0.988861 0.148842i \(-0.0475547\pi\)
−0.623332 + 0.781958i \(0.714221\pi\)
\(480\) 0 0
\(481\) −13.5000 + 23.3827i −0.615547 + 1.06616i
\(482\) 0 0
\(483\) −10.0000 + 3.46410i −0.455016 + 0.157622i
\(484\) 0 0
\(485\) 14.0000 24.2487i 0.635707 1.10108i
\(486\) 0 0
\(487\) 12.5000 + 21.6506i 0.566429 + 0.981084i 0.996915 + 0.0784867i \(0.0250088\pi\)
−0.430486 + 0.902597i \(0.641658\pi\)
\(488\) 0 0
\(489\) −4.00000 −0.180886
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 0 0
\(493\) 8.00000 + 13.8564i 0.360302 + 0.624061i
\(494\) 0 0
\(495\) −6.00000 + 10.3923i −0.269680 + 0.467099i
\(496\) 0 0
\(497\) −15.0000 + 5.19615i −0.672842 + 0.233079i
\(498\) 0 0
\(499\) −8.50000 + 14.7224i −0.380512 + 0.659067i −0.991136 0.132855i \(-0.957586\pi\)
0.610623 + 0.791921i \(0.290919\pi\)
\(500\) 0 0
\(501\) 9.00000 + 15.5885i 0.402090 + 0.696441i
\(502\) 0 0
\(503\) 14.0000 0.624229 0.312115 0.950044i \(-0.398963\pi\)
0.312115 + 0.950044i \(0.398963\pi\)
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 0 0
\(507\) 2.00000 + 3.46410i 0.0888231 + 0.153846i
\(508\) 0 0
\(509\) −3.00000 + 5.19615i −0.132973 + 0.230315i −0.924821 0.380402i \(-0.875786\pi\)
0.791849 + 0.610718i \(0.209119\pi\)
\(510\) 0 0
\(511\) −22.0000 19.0526i −0.973223 0.842836i
\(512\) 0 0
\(513\) −2.50000 + 4.33013i −0.110378 + 0.191180i
\(514\) 0 0
\(515\) −9.00000 15.5885i −0.396587 0.686909i
\(516\) 0 0
\(517\) −12.0000 −0.527759
\(518\) 0 0
\(519\) 20.0000 0.877903
\(520\) 0 0
\(521\) 6.00000 + 10.3923i 0.262865 + 0.455295i 0.967002 0.254769i \(-0.0819994\pi\)
−0.704137 + 0.710064i \(0.748666\pi\)
\(522\) 0 0
\(523\) 14.5000 25.1147i 0.634041 1.09819i −0.352677 0.935745i \(-0.614728\pi\)
0.986718 0.162446i \(-0.0519382\pi\)
\(524\) 0 0
\(525\) −0.500000 + 2.59808i −0.0218218 + 0.113389i
\(526\) 0 0
\(527\) 14.0000 24.2487i 0.609850 1.05629i
\(528\) 0 0
\(529\) 3.50000 + 6.06218i 0.152174 + 0.263573i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 6.00000 0.259889
\(534\) 0 0
\(535\) −12.0000 20.7846i −0.518805 0.898597i
\(536\) 0 0
\(537\) 13.0000 22.5167i 0.560991 0.971666i
\(538\) 0 0
\(539\) −39.0000 15.5885i −1.67985 0.671442i
\(540\) 0 0
\(541\) −0.500000 + 0.866025i −0.0214967 + 0.0372333i −0.876574 0.481268i \(-0.840176\pi\)
0.855077 + 0.518501i \(0.173510\pi\)
\(542\) 0 0
\(543\) 3.50000 + 6.06218i 0.150199 + 0.260153i
\(544\) 0 0
\(545\) −22.0000 −0.942376
\(546\) 0 0
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) 0 0
\(549\) −5.00000 8.66025i −0.213395 0.369611i
\(550\) 0 0
\(551\) 10.0000 17.3205i 0.426014 0.737878i
\(552\) 0 0
\(553\) −0.500000 + 2.59808i −0.0212622 + 0.110481i
\(554\) 0 0
\(555\) 9.00000 15.5885i 0.382029 0.661693i
\(556\) 0 0
\(557\) 1.00000 + 1.73205i 0.0423714 + 0.0733893i 0.886433 0.462856i \(-0.153175\pi\)
−0.844062 + 0.536246i \(0.819842\pi\)
\(558\) 0 0
\(559\) −3.00000 −0.126886
\(560\) 0 0
\(561\) 24.0000 1.01328
\(562\) 0 0
\(563\) −1.00000 1.73205i −0.0421450 0.0729972i 0.844183 0.536054i \(-0.180086\pi\)
−0.886328 + 0.463057i \(0.846752\pi\)
\(564\) 0 0
\(565\) −6.00000 + 10.3923i −0.252422 + 0.437208i
\(566\) 0 0
\(567\) 2.00000 + 1.73205i 0.0839921 + 0.0727393i
\(568\) 0 0
\(569\) 9.00000 15.5885i 0.377300 0.653502i −0.613369 0.789797i \(-0.710186\pi\)
0.990668 + 0.136295i \(0.0435194\pi\)
\(570\) 0 0
\(571\) 11.5000 + 19.9186i 0.481260 + 0.833567i 0.999769 0.0215055i \(-0.00684595\pi\)
−0.518509 + 0.855072i \(0.673513\pi\)
\(572\) 0 0
\(573\) −10.0000 −0.417756
\(574\) 0 0
\(575\) −4.00000 −0.166812
\(576\) 0 0
\(577\) −19.5000 33.7750i −0.811796 1.40607i −0.911606 0.411065i \(-0.865157\pi\)
0.0998105 0.995006i \(-0.468176\pi\)
\(578\) 0 0
\(579\) −1.50000 + 2.59808i −0.0623379 + 0.107972i
\(580\) 0 0
\(581\) 15.0000 5.19615i 0.622305 0.215573i
\(582\) 0 0
\(583\) −24.0000 + 41.5692i −0.993978 + 1.72162i
\(584\) 0 0
\(585\) 3.00000 + 5.19615i 0.124035 + 0.214834i
\(586\) 0 0
\(587\) −16.0000 −0.660391 −0.330195 0.943913i \(-0.607115\pi\)
−0.330195 + 0.943913i \(0.607115\pi\)
\(588\) 0 0
\(589\) −35.0000 −1.44215
\(590\) 0 0
\(591\) 6.00000 + 10.3923i 0.246807 + 0.427482i
\(592\) 0 0
\(593\) 15.0000 25.9808i 0.615976 1.06690i −0.374236 0.927333i \(-0.622095\pi\)
0.990212 0.139569i \(-0.0445716\pi\)
\(594\) 0 0
\(595\) −20.0000 + 6.92820i −0.819920 + 0.284029i
\(596\) 0 0
\(597\) −8.00000 + 13.8564i −0.327418 + 0.567105i
\(598\) 0 0
\(599\) 2.00000 + 3.46410i 0.0817178 + 0.141539i 0.903988 0.427558i \(-0.140626\pi\)
−0.822270 + 0.569097i \(0.807293\pi\)
\(600\) 0 0
\(601\) 31.0000 1.26452 0.632258 0.774758i \(-0.282128\pi\)
0.632258 + 0.774758i \(0.282128\pi\)
\(602\) 0 0
\(603\) 15.0000 0.610847
\(604\) 0 0
\(605\) −25.0000 43.3013i −1.01639 1.76045i
\(606\) 0 0
\(607\) 0.500000 0.866025i 0.0202944 0.0351509i −0.855700 0.517472i \(-0.826873\pi\)
0.875994 + 0.482322i \(0.160206\pi\)
\(608\) 0 0
\(609\) −8.00000 6.92820i −0.324176 0.280745i
\(610\) 0 0
\(611\) −3.00000 + 5.19615i −0.121367 + 0.210214i
\(612\) 0 0
\(613\) 19.0000 + 32.9090i 0.767403 + 1.32918i 0.938967 + 0.344008i \(0.111785\pi\)
−0.171564 + 0.985173i \(0.554882\pi\)
\(614\) 0 0
\(615\) −4.00000 −0.161296
\(616\) 0 0
\(617\) −6.00000 −0.241551 −0.120775 0.992680i \(-0.538538\pi\)
−0.120775 + 0.992680i \(0.538538\pi\)
\(618\) 0 0
\(619\) 4.50000 + 7.79423i 0.180870 + 0.313276i 0.942177 0.335115i \(-0.108775\pi\)
−0.761307 + 0.648392i \(0.775442\pi\)
\(620\) 0 0
\(621\) −2.00000 + 3.46410i −0.0802572 + 0.139010i
\(622\) 0 0
\(623\) −4.00000 + 20.7846i −0.160257 + 0.832718i
\(624\) 0 0
\(625\) 9.50000 16.4545i 0.380000 0.658179i
\(626\) 0 0
\(627\) −15.0000 25.9808i −0.599042 1.03757i
\(628\) 0 0
\(629\) −36.0000 −1.43541
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 0 0
\(633\) −2.00000 3.46410i −0.0794929 0.137686i
\(634\) 0 0
\(635\) −1.00000 + 1.73205i −0.0396838 + 0.0687343i
\(636\) 0 0
\(637\) −16.5000 + 12.9904i −0.653754 + 0.514698i
\(638\) 0 0
\(639\) −3.00000 + 5.19615i −0.118678 + 0.205557i
\(640\) 0 0
\(641\) 10.0000 + 17.3205i 0.394976 + 0.684119i 0.993098 0.117286i \(-0.0374195\pi\)
−0.598122 + 0.801405i \(0.704086\pi\)
\(642\) 0 0
\(643\) 17.0000 0.670415 0.335207 0.942144i \(-0.391194\pi\)
0.335207 + 0.942144i \(0.391194\pi\)
\(644\) 0 0
\(645\) 2.00000 0.0787499
\(646\) 0 0
\(647\) −9.00000 15.5885i −0.353827 0.612845i 0.633090 0.774078i \(-0.281786\pi\)
−0.986916 + 0.161233i \(0.948453\pi\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) −3.50000 + 18.1865i −0.137176 + 0.712786i
\(652\) 0 0
\(653\) 11.0000 19.0526i 0.430463 0.745584i −0.566450 0.824096i \(-0.691684\pi\)
0.996913 + 0.0785119i \(0.0250169\pi\)
\(654\) 0 0
\(655\) 14.0000 + 24.2487i 0.547025 + 0.947476i
\(656\) 0 0
\(657\) −11.0000 −0.429151
\(658\) 0 0
\(659\) 40.0000 1.55818 0.779089 0.626913i \(-0.215682\pi\)
0.779089 + 0.626913i \(0.215682\pi\)
\(660\) 0 0
\(661\) −17.5000 30.3109i −0.680671 1.17896i −0.974776 0.223184i \(-0.928355\pi\)
0.294105 0.955773i \(-0.404978\pi\)
\(662\) 0 0
\(663\) 6.00000 10.3923i 0.233021 0.403604i
\(664\) 0 0
\(665\) 20.0000 + 17.3205i 0.775567 + 0.671660i
\(666\) 0 0
\(667\) 8.00000 13.8564i 0.309761 0.536522i
\(668\) 0 0
\(669\) 12.0000 + 20.7846i 0.463947 + 0.803579i
\(670\) 0 0
\(671\) 60.0000 2.31627
\(672\) 0 0
\(673\) 7.00000 0.269830 0.134915 0.990857i \(-0.456924\pi\)
0.134915 + 0.990857i \(0.456924\pi\)
\(674\) 0 0
\(675\) 0.500000 + 0.866025i 0.0192450 + 0.0333333i
\(676\) 0 0
\(677\) −6.00000 + 10.3923i −0.230599 + 0.399409i −0.957984 0.286820i \(-0.907402\pi\)
0.727386 + 0.686229i \(0.240735\pi\)
\(678\) 0 0
\(679\) 35.0000 12.1244i 1.34318 0.465290i
\(680\) 0 0
\(681\) 7.00000 12.1244i 0.268241 0.464606i
\(682\) 0 0
\(683\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(684\) 0 0
\(685\) 40.0000 1.52832
\(686\) 0 0
\(687\) −7.00000 −0.267067
\(688\) 0 0
\(689\) 12.0000 + 20.7846i 0.457164 + 0.791831i
\(690\) 0 0
\(691\) −3.50000 + 6.06218i −0.133146 + 0.230616i −0.924888 0.380240i \(-0.875841\pi\)
0.791742 + 0.610856i \(0.209175\pi\)
\(692\) 0 0
\(693\) −15.0000 + 5.19615i −0.569803 + 0.197386i
\(694\) 0 0
\(695\) −9.00000 + 15.5885i −0.341389 + 0.591304i
\(696\) 0 0
\(697\) 4.00000 + 6.92820i 0.151511 + 0.262424i
\(698\) 0 0
\(699\) 26.0000 0.983410
\(700\) 0 0
\(701\) 28.0000 1.05755 0.528773 0.848763i \(-0.322652\pi\)
0.528773 + 0.848763i \(0.322652\pi\)
\(702\) 0 0
\(703\) 22.5000 + 38.9711i 0.848604 + 1.46982i
\(704\) 0 0
\(705\) 2.00000 3.46410i 0.0753244 0.130466i
\(706\) 0 0
\(707\) −12.0000 10.3923i −0.451306 0.390843i
\(708\) 0 0
\(709\) 25.0000 43.3013i 0.938895 1.62621i 0.171358 0.985209i \(-0.445185\pi\)
0.767537 0.641004i \(-0.221482\pi\)
\(710\) 0 0
\(711\) 0.500000 + 0.866025i 0.0187515 + 0.0324785i
\(712\) 0 0
\(713\) −28.0000 −1.04861
\(714\) 0 0
\(715\) −36.0000 −1.34632
\(716\) 0 0
\(717\) 1.00000 + 1.73205i 0.0373457 + 0.0646846i
\(718\) 0 0
\(719\) −15.0000 + 25.9808i −0.559406 + 0.968919i 0.438141 + 0.898906i \(0.355637\pi\)
−0.997546 + 0.0700124i \(0.977696\pi\)
\(720\) 0 0
\(721\) 4.50000 23.3827i 0.167589 0.870817i
\(722\) 0 0
\(723\) 1.00000 1.73205i 0.0371904 0.0644157i
\(724\) 0 0
\(725\) −2.00000 3.46410i −0.0742781 0.128654i
\(726\) 0 0
\(727\) −5.00000 −0.185440 −0.0927199 0.995692i \(-0.529556\pi\)
−0.0927199 + 0.995692i \(0.529556\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −2.00000 3.46410i −0.0739727 0.128124i
\(732\) 0 0
\(733\) 5.50000 9.52628i 0.203147 0.351861i −0.746394 0.665505i \(-0.768216\pi\)
0.949541 + 0.313644i \(0.101550\pi\)
\(734\) 0 0
\(735\) 11.0000 8.66025i 0.405741 0.319438i
\(736\) 0 0
\(737\) −45.0000 + 77.9423i −1.65760 + 2.87104i
\(738\) 0 0
\(739\) −2.50000 4.33013i −0.0919640 0.159286i 0.816373 0.577524i \(-0.195981\pi\)
−0.908337 + 0.418238i \(0.862648\pi\)
\(740\) 0 0
\(741\) −15.0000 −0.551039
\(742\) 0 0
\(743\) 34.0000 1.24734 0.623670 0.781688i \(-0.285641\pi\)
0.623670 + 0.781688i \(0.285641\pi\)
\(744\) 0 0
\(745\) −4.00000 6.92820i −0.146549 0.253830i
\(746\) 0 0
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) 0 0
\(749\) 6.00000 31.1769i 0.219235 1.13918i
\(750\) 0 0
\(751\) −18.5000 + 32.0429i −0.675075 + 1.16926i 0.301373 + 0.953506i \(0.402555\pi\)
−0.976447 + 0.215757i \(0.930778\pi\)
\(752\) 0 0
\(753\) 2.00000 + 3.46410i 0.0728841 + 0.126239i
\(754\) 0 0
\(755\) 16.0000 0.582300
\(756\) 0 0
\(757\) 10.0000 0.363456 0.181728 0.983349i \(-0.441831\pi\)
0.181728 + 0.983349i \(0.441831\pi\)
\(758\) 0 0
\(759\) −12.0000 20.7846i −0.435572 0.754434i
\(760\) 0 0
\(761\) 6.00000 10.3923i 0.217500 0.376721i −0.736543 0.676391i \(-0.763543\pi\)
0.954043 + 0.299670i \(0.0968765\pi\)
\(762\) 0 0
\(763\) −22.0000 19.0526i −0.796453 0.689749i
\(764\) 0 0
\(765\) −4.00000 + 6.92820i −0.144620 + 0.250490i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 7.00000 0.252426 0.126213 0.992003i \(-0.459718\pi\)
0.126213 + 0.992003i \(0.459718\pi\)
\(770\) 0 0
\(771\) −18.0000 −0.648254
\(772\) 0 0
\(773\) 25.0000 + 43.3013i 0.899188 + 1.55744i 0.828535 + 0.559937i \(0.189175\pi\)
0.0706526 + 0.997501i \(0.477492\pi\)
\(774\) 0 0
\(775\) −3.50000 + 6.06218i −0.125724 + 0.217760i
\(776\) 0 0
\(777\) 22.5000 7.79423i 0.807183 0.279616i
\(778\) 0 0
\(779\) 5.00000 8.66025i 0.179144 0.310286i
\(780\) 0 0
\(781\) −18.0000 31.1769i −0.644091 1.11560i
\(782\) 0 0
\(783\) −4.00000 −0.142948
\(784\) 0 0
\(785\) 36.0000 1.28490
\(786\) 0 0
\(787\) −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i \(-0.973479\pi\)
0.426193 0.904632i \(-0.359855\pi\)
\(788\) 0 0
\(789\) −6.00000 + 10.3923i −0.213606 + 0.369976i
\(790\) 0 0
\(791\) −15.0000 + 5.19615i −0.533339 + 0.184754i
\(792\) 0 0
\(793\) 15.0000 25.9808i 0.532666 0.922604i
\(794\) 0 0
\(795\) −8.00000 13.8564i −0.283731 0.491436i
\(796\) 0 0