Properties

Label 1176.2.q.e.961.1
Level $1176$
Weight $2$
Character 1176.961
Analytic conductor $9.390$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1176.q (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(9.39040727770\)
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 168)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 961.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1176.961
Dual form 1176.2.q.e.361.1

$q$-expansion

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

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).

\(n\) \(295\) \(589\) \(785\) \(1081\)
\(\chi(n)\) \(1\) \(1\) \(1\) \(e\left(\frac{1}{3}\right)\)

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 −0.550990 0.834512i \(-0.685750\pi\)
0.998203 + 0.0599153i \(0.0190830\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 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 \(0.193114\pi\)
0.0829925 + 0.996550i \(0.473552\pi\)
\(12\) 0 0
\(13\) 3.00000 0.832050 0.416025 0.909353i \(-0.363423\pi\)
0.416025 + 0.909353i \(0.363423\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) 0 0
\(17\) 2.00000 + 3.46410i 0.485071 + 0.840168i 0.999853 0.0171533i \(-0.00546033\pi\)
−0.514782 + 0.857321i \(0.672127\pi\)
\(18\) 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
\(21\) 0 0
\(22\) 0 0
\(23\) 2.00000 3.46410i 0.417029 0.722315i −0.578610 0.815604i \(-0.696405\pi\)
0.995639 + 0.0932891i \(0.0297381\pi\)
\(24\) 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
\(35\) 0 0
\(36\) 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 \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 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
\(49\) 0 0
\(50\) 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 \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 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 \(0.202149\pi\)
0.111241 + 0.993793i \(0.464517\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) −6.00000 −0.712069 −0.356034 0.934473i \(-0.615871\pi\)
−0.356034 + 0.934473i \(0.615871\pi\)
\(72\) 0 0
\(73\) −5.50000 9.52628i −0.643726 1.11497i −0.984594 0.174855i \(-0.944054\pi\)
0.340868 0.940111i \(-0.389279\pi\)
\(74\) 0 0
\(75\) 0.500000 0.866025i 0.0577350 0.100000i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −0.500000 + 0.866025i −0.0562544 + 0.0974355i −0.892781 0.450490i \(-0.851249\pi\)
0.836527 + 0.547926i \(0.184582\pi\)
\(80\) 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 −0.996326 0.0856373i \(-0.972707\pi\)
0.572327 + 0.820025i \(0.306041\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 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 \(-0.248359\pi\)
0.710742 + 0.703452i \(0.248359\pi\)
\(98\) 0 0
\(99\) −6.00000 −0.603023
\(100\) 0 0
\(101\) −3.00000 5.19615i −0.298511 0.517036i 0.677284 0.735721i \(-0.263157\pi\)
−0.975796 + 0.218685i \(0.929823\pi\)
\(102\) 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
\(105\) 0 0
\(106\) 0 0
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 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
\(119\) 0 0
\(120\) 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 \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 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
\(133\) 0 0
\(134\) 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
\(147\) 0 0
\(148\) 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 0.981617 0.190864i \(-0.0611289\pi\)
−0.656101 + 0.754673i \(0.727796\pi\)
\(152\) 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 \(0.0884028\pi\)
−0.243403 + 0.969925i \(0.578264\pi\)
\(158\) 0 0
\(159\) −4.00000 + 6.92820i −0.317221 + 0.549442i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −2.00000 + 3.46410i −0.156652 + 0.271329i −0.933659 0.358162i \(-0.883403\pi\)
0.777007 + 0.629492i \(0.216737\pi\)
\(164\) 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 \(-0.558392\pi\)
0.942703 0.333633i \(-0.108275\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −13.0000 22.5167i −0.971666 1.68297i −0.690526 0.723307i \(-0.742621\pi\)
−0.281139 0.959667i \(-0.590712\pi\)
\(180\) 0 0
\(181\) 7.00000 0.520306 0.260153 0.965567i \(-0.416227\pi\)
0.260153 + 0.965567i \(0.416227\pi\)
\(182\) 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
\(189\) 0 0
\(190\) 0 0
\(191\) −5.00000 + 8.66025i −0.361787 + 0.626634i −0.988255 0.152813i \(-0.951167\pi\)
0.626468 + 0.779447i \(0.284500\pi\)
\(192\) 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
\(203\) 0 0
\(204\) 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 \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) 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
\(217\) 0 0
\(218\) 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 −0.958187 0.286143i \(-0.907627\pi\)
0.726900 + 0.686743i \(0.240960\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 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 \(-0.479396\pi\)
0.0646846 + 0.997906i \(0.479396\pi\)
\(240\) 0 0
\(241\) −1.00000 1.73205i −0.0644157 0.111571i 0.832019 0.554747i \(-0.187185\pi\)
−0.896435 + 0.443176i \(0.853852\pi\)
\(242\) 0 0
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 0 0
\(245\) 0 0
\(246\) 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 \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 2.00000 3.46410i 0.123797 0.214423i
\(262\) 0 0
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 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 \(-0.981774\pi\)
0.449622 0.893219i \(-0.351559\pi\)
\(270\) 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
\(273\) 0 0
\(274\) 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
\(287\) 0 0
\(288\) 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
\(301\) 0 0
\(302\) 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 −0.879810 0.475325i \(-0.842331\pi\)
0.851549 + 0.524276i \(0.175664\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 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
\(329\) 0 0
\(330\) 0 0
\(331\) −2.50000 + 4.33013i −0.137412 + 0.238005i −0.926516 0.376254i \(-0.877212\pi\)
0.789104 + 0.614260i \(0.210545\pi\)
\(332\) 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
\(343\) 0 0
\(344\) 0 0
\(345\) −4.00000 + 6.92820i −0.215353 + 0.373002i
\(346\) 0 0
\(347\) −6.00000 10.3923i −0.322097 0.557888i 0.658824 0.752297i \(-0.271054\pi\)
−0.980921 + 0.194409i \(0.937721\pi\)
\(348\) 0 0
\(349\) 22.0000 1.17763 0.588817 0.808267i \(-0.299594\pi\)
0.588817 + 0.808267i \(0.299594\pi\)
\(350\) 0 0
\(351\) 3.00000 0.160128
\(352\) 0 0
\(353\) 3.00000 + 5.19615i 0.159674 + 0.276563i 0.934751 0.355303i \(-0.115622\pi\)
−0.775077 + 0.631867i \(0.782289\pi\)
\(354\) 0 0
\(355\) −6.00000 + 10.3923i −0.318447 + 0.551566i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 6.00000 10.3923i 0.316668 0.548485i −0.663123 0.748511i \(-0.730769\pi\)
0.979791 + 0.200026i \(0.0641026\pi\)
\(360\) 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
\(371\) 0 0
\(372\) 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 \(-0.625884\pi\)
−0.385249 + 0.922813i \(0.625884\pi\)
\(380\) 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
\(385\) 0 0
\(386\) 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 −0.921917 0.387387i \(-0.873378\pi\)
0.796446 + 0.604710i \(0.206711\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 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 0.826555 0.562856i \(-0.190297\pi\)
−0.900725 + 0.434389i \(0.856964\pi\)
\(410\) 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
\(427\) 0 0
\(428\) 0 0
\(429\) 9.00000 15.5885i 0.434524 0.752618i
\(430\) 0 0
\(431\) 9.00000 + 15.5885i 0.433515 + 0.750870i 0.997173 0.0751385i \(-0.0239399\pi\)
−0.563658 + 0.826008i \(0.690607\pi\)
\(432\) 0 0
\(433\) −31.0000 −1.48976 −0.744882 0.667196i \(-0.767494\pi\)
−0.744882 + 0.667196i \(0.767494\pi\)
\(434\) 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
\(441\) 0 0
\(442\) 0 0
\(443\) 8.00000 13.8564i 0.380091 0.658338i −0.610984 0.791643i \(-0.709226\pi\)
0.991075 + 0.133306i \(0.0425592\pi\)
\(444\) 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
\(455\) 0 0
\(456\) 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 \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 17.0000 0.790057 0.395029 0.918669i \(-0.370735\pi\)
0.395029 + 0.918669i \(0.370735\pi\)
\(464\) 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
\(469\) 0 0
\(470\) 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
\(483\) 0 0
\(484\) 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 \(-0.974991\pi\)
0.430486 0.902597i \(-0.358342\pi\)
\(488\) 0 0
\(489\) 4.00000 0.180886
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 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
\(497\) 0 0
\(498\) 0 0
\(499\) 8.50000 14.7224i 0.380512 0.659067i −0.610623 0.791921i \(-0.709081\pi\)
0.991136 + 0.132855i \(0.0424144\pi\)
\(500\) 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 −0.791849 0.610718i \(-0.790881\pi\)
0.924821 + 0.380402i \(0.124214\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 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 0.704137 0.710064i \(-0.251334\pi\)
−0.967002 + 0.254769i \(0.918001\pi\)
\(522\) 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 0
\(526\) 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
\(539\) 0 0
\(540\) 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 \(-0.472747\pi\)
0.0855138 + 0.996337i \(0.472747\pi\)
\(548\) 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 0
\(554\) 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
\(567\) 0 0
\(568\) 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 0.518509 0.855072i \(-0.326487\pi\)
−0.999769 + 0.0215055i \(0.993154\pi\)
\(572\) 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 \(0.134843\pi\)
−0.0998105 + 0.995006i \(0.531824\pi\)
\(578\) 0 0
\(579\) −1.50000 + 2.59808i −0.0623379 + 0.107972i
\(580\) 0 0
\(581\) 0 0
\(582\) 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 \(0.377905\pi\)
−0.990212 + 0.139569i \(0.955428\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −8.00000 + 13.8564i −0.327418 + 0.567105i
\(598\) 0 0
\(599\) −2.00000 3.46410i −0.0817178 0.141539i 0.822270 0.569097i \(-0.192707\pi\)
−0.903988 + 0.427558i \(0.859374\pi\)
\(600\) 0 0
\(601\) −31.0000 −1.26452 −0.632258 0.774758i \(-0.717872\pi\)
−0.632258 + 0.774758i \(0.717872\pi\)
\(602\) 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
\(609\) 0 0
\(610\) 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
\(623\) 0 0
\(624\) 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 \(-0.793153\pi\)
−0.796187 + 0.605050i \(0.793153\pi\)
\(632\) 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
\(637\) 0 0
\(638\) 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
\(651\) 0 0
\(652\) 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 \(-0.784318\pi\)
−0.779089 + 0.626913i \(0.784318\pi\)
\(660\) 0 0
\(661\) 17.5000 + 30.3109i 0.680671 + 1.17896i 0.974776 + 0.223184i \(0.0716450\pi\)
−0.294105 + 0.955773i \(0.595022\pi\)
\(662\) 0 0
\(663\) 6.00000 10.3923i 0.233021 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) 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 −0.727386 0.686229i \(-0.759265\pi\)
0.957984 + 0.286820i \(0.0925982\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 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
\(693\) 0 0
\(694\) 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
\(707\) 0 0
\(708\) 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
\(721\) 0 0
\(722\) 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 −0.949541 0.313644i \(-0.898450\pi\)
0.746394 + 0.665505i \(0.231784\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −45.0000 + 77.9423i −1.65760 + 2.87104i
\(738\) 0 0
\(739\) 2.50000 + 4.33013i 0.0919640 + 0.159286i 0.908337 0.418238i \(-0.137352\pi\)
−0.816373 + 0.577524i \(0.804019\pi\)
\(740\) 0 0
\(741\) 15.0000 0.551039
\(742\) 0 0
\(743\) −34.0000 −1.24734 −0.623670 0.781688i \(-0.714359\pi\)
−0.623670 + 0.781688i \(0.714359\pi\)
\(744\) 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
\(749\) 0 0
\(750\) 0 0
\(751\) 18.5000 32.0429i 0.675075 1.16926i −0.301373 0.953506i \(-0.597445\pi\)
0.976447 0.215757i \(-0.0692219\pi\)
\(752\) 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 −0.954043 0.299670i \(-0.903123\pi\)
0.736543 + 0.676391i \(0.236457\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 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 \(-0.540282\pi\)
−0.126213 + 0.992003i \(0.540282\pi\)
\(770\) 0 0
\(771\) 18.0000 0.648254
\(772\) 0 0
\(773\) −25.0000 43.3013i −0.899188 1.55744i −0.828535 0.559937i \(-0.810825\pi\)
−0.0706526 0.997501i \(-0.522508\pi\)
\(774\) 0 0
\(775\) −3.50000 + 6.06218i −0.125724 + 0.217760i
\(776\) 0 0
\(777\) 0 0
\(778\) 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
\(791\) 0 0
\(792\) 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
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 0 0
\(799\) 8.00000 0.283020
\(800\) 0