Properties

Label 2940.2.bb.d.949.2
Level $2940$
Weight $2$
Character 2940.949
Analytic conductor $23.476$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 2940 = 2^{2} \cdot 3 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2940.bb (of order \(6\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.4760181943\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 949.2
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 2940.949
Dual form 2940.2.bb.d.1549.2

$q$-expansion

\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{3} +(-2.23205 + 0.133975i) q^{5} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{3} +(-2.23205 + 0.133975i) q^{5} +(0.500000 + 0.866025i) q^{9} +(2.00000 - 3.46410i) q^{11} +(-2.00000 - 1.00000i) q^{15} +(-3.46410 - 2.00000i) q^{17} +(-3.46410 + 2.00000i) q^{23} +(4.96410 - 0.598076i) q^{25} +1.00000i q^{27} +6.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(3.46410 - 2.00000i) q^{33} +(-6.92820 + 4.00000i) q^{37} -10.0000 q^{41} -4.00000i q^{43} +(-1.23205 - 1.86603i) q^{45} +(-3.46410 + 2.00000i) q^{47} +(-2.00000 - 3.46410i) q^{51} +(-10.3923 - 6.00000i) q^{53} +(-4.00000 + 8.00000i) q^{55} +(2.00000 - 3.46410i) q^{59} +(-1.00000 - 1.73205i) q^{61} +(3.46410 + 2.00000i) q^{67} -4.00000 q^{69} +(-6.92820 - 4.00000i) q^{73} +(4.59808 + 1.96410i) q^{75} +(-6.00000 - 10.3923i) q^{79} +(-0.500000 + 0.866025i) q^{81} -4.00000i q^{83} +(8.00000 + 4.00000i) q^{85} +(5.19615 + 3.00000i) q^{87} +(-5.00000 - 8.66025i) q^{89} +(-3.46410 + 2.00000i) q^{93} +8.00000i q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{5} + 2q^{9} + O(q^{10}) \) \( 4q - 2q^{5} + 2q^{9} + 8q^{11} - 8q^{15} + 6q^{25} + 24q^{29} - 8q^{31} - 40q^{41} + 2q^{45} - 8q^{51} - 16q^{55} + 8q^{59} - 4q^{61} - 16q^{69} + 8q^{75} - 24q^{79} - 2q^{81} + 32q^{85} - 20q^{89} + 16q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2940\mathbb{Z}\right)^\times\).

\(n\) \(1081\) \(1177\) \(1471\) \(1961\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0.866025 + 0.500000i 0.500000 + 0.288675i
\(4\) 0 0
\(5\) −2.23205 + 0.133975i −0.998203 + 0.0599153i
\(6\) 0 0
\(7\) 0 0
\(8\) 0 0
\(9\) 0.500000 + 0.866025i 0.166667 + 0.288675i
\(10\) 0 0
\(11\) 2.00000 3.46410i 0.603023 1.04447i −0.389338 0.921095i \(-0.627296\pi\)
0.992361 0.123371i \(-0.0393705\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) −2.00000 1.00000i −0.516398 0.258199i
\(16\) 0 0
\(17\) −3.46410 2.00000i −0.840168 0.485071i 0.0171533 0.999853i \(-0.494540\pi\)
−0.857321 + 0.514782i \(0.827873\pi\)
\(18\) 0 0
\(19\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −3.46410 + 2.00000i −0.722315 + 0.417029i −0.815604 0.578610i \(-0.803595\pi\)
0.0932891 + 0.995639i \(0.470262\pi\)
\(24\) 0 0
\(25\) 4.96410 0.598076i 0.992820 0.119615i
\(26\) 0 0
\(27\) 1.00000i 0.192450i
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −2.00000 + 3.46410i −0.359211 + 0.622171i −0.987829 0.155543i \(-0.950287\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 0 0
\(33\) 3.46410 2.00000i 0.603023 0.348155i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −6.92820 + 4.00000i −1.13899 + 0.657596i −0.946180 0.323640i \(-0.895093\pi\)
−0.192809 + 0.981236i \(0.561760\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −10.0000 −1.56174 −0.780869 0.624695i \(-0.785223\pi\)
−0.780869 + 0.624695i \(0.785223\pi\)
\(42\) 0 0
\(43\) 4.00000i 0.609994i −0.952353 0.304997i \(-0.901344\pi\)
0.952353 0.304997i \(-0.0986555\pi\)
\(44\) 0 0
\(45\) −1.23205 1.86603i −0.183663 0.278171i
\(46\) 0 0
\(47\) −3.46410 + 2.00000i −0.505291 + 0.291730i −0.730896 0.682489i \(-0.760898\pi\)
0.225605 + 0.974219i \(0.427564\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 0 0
\(51\) −2.00000 3.46410i −0.280056 0.485071i
\(52\) 0 0
\(53\) −10.3923 6.00000i −1.42749 0.824163i −0.430570 0.902557i \(-0.641688\pi\)
−0.996922 + 0.0783936i \(0.975021\pi\)
\(54\) 0 0
\(55\) −4.00000 + 8.00000i −0.539360 + 1.07872i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 2.00000 3.46410i 0.260378 0.450988i −0.705965 0.708247i \(-0.749486\pi\)
0.966342 + 0.257260i \(0.0828195\pi\)
\(60\) 0 0
\(61\) −1.00000 1.73205i −0.128037 0.221766i 0.794879 0.606768i \(-0.207534\pi\)
−0.922916 + 0.385002i \(0.874201\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) 3.46410 + 2.00000i 0.423207 + 0.244339i 0.696449 0.717607i \(-0.254762\pi\)
−0.273241 + 0.961946i \(0.588096\pi\)
\(68\) 0 0
\(69\) −4.00000 −0.481543
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0 0
\(73\) −6.92820 4.00000i −0.810885 0.468165i 0.0363782 0.999338i \(-0.488418\pi\)
−0.847263 + 0.531174i \(0.821751\pi\)
\(74\) 0 0
\(75\) 4.59808 + 1.96410i 0.530940 + 0.226795i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −6.00000 10.3923i −0.675053 1.16923i −0.976453 0.215728i \(-0.930788\pi\)
0.301401 0.953498i \(-0.402546\pi\)
\(80\) 0 0
\(81\) −0.500000 + 0.866025i −0.0555556 + 0.0962250i
\(82\) 0 0
\(83\) 4.00000i 0.439057i −0.975606 0.219529i \(-0.929548\pi\)
0.975606 0.219529i \(-0.0704519\pi\)
\(84\) 0 0
\(85\) 8.00000 + 4.00000i 0.867722 + 0.433861i
\(86\) 0 0
\(87\) 5.19615 + 3.00000i 0.557086 + 0.321634i
\(88\) 0 0
\(89\) −5.00000 8.66025i −0.529999 0.917985i −0.999388 0.0349934i \(-0.988859\pi\)
0.469389 0.882992i \(-0.344474\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −3.46410 + 2.00000i −0.359211 + 0.207390i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 8.00000i 0.812277i 0.913812 + 0.406138i \(0.133125\pi\)
−0.913812 + 0.406138i \(0.866875\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) 1.00000 1.73205i 0.0995037 0.172345i −0.811976 0.583691i \(-0.801608\pi\)
0.911479 + 0.411346i \(0.134941\pi\)
\(102\) 0 0
\(103\) 3.46410 2.00000i 0.341328 0.197066i −0.319531 0.947576i \(-0.603525\pi\)
0.660859 + 0.750510i \(0.270192\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 10.3923 6.00000i 1.00466 0.580042i 0.0950377 0.995474i \(-0.469703\pi\)
0.909624 + 0.415432i \(0.136370\pi\)
\(108\) 0 0
\(109\) −1.00000 + 1.73205i −0.0957826 + 0.165900i −0.909935 0.414751i \(-0.863869\pi\)
0.814152 + 0.580651i \(0.197202\pi\)
\(110\) 0 0
\(111\) −8.00000 −0.759326
\(112\) 0 0
\(113\) 12.0000i 1.12887i −0.825479 0.564433i \(-0.809095\pi\)
0.825479 0.564433i \(-0.190905\pi\)
\(114\) 0 0
\(115\) 7.46410 4.92820i 0.696031 0.459557i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −2.50000 4.33013i −0.227273 0.393648i
\(122\) 0 0
\(123\) −8.66025 5.00000i −0.780869 0.450835i
\(124\) 0 0
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 0 0
\(127\) 4.00000i 0.354943i 0.984126 + 0.177471i \(0.0567917\pi\)
−0.984126 + 0.177471i \(0.943208\pi\)
\(128\) 0 0
\(129\) 2.00000 3.46410i 0.176090 0.304997i
\(130\) 0 0
\(131\) −6.00000 10.3923i −0.524222 0.907980i −0.999602 0.0281993i \(-0.991023\pi\)
0.475380 0.879781i \(-0.342311\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.133975 2.23205i −0.0115307 0.192104i
\(136\) 0 0
\(137\) −10.3923 6.00000i −0.887875 0.512615i −0.0146279 0.999893i \(-0.504656\pi\)
−0.873247 + 0.487278i \(0.837990\pi\)
\(138\) 0 0
\(139\) −16.0000 −1.35710 −0.678551 0.734553i \(-0.737392\pi\)
−0.678551 + 0.734553i \(0.737392\pi\)
\(140\) 0 0
\(141\) −4.00000 −0.336861
\(142\) 0 0
\(143\) 0 0
\(144\) 0 0
\(145\) −13.3923 + 0.803848i −1.11217 + 0.0667559i
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) −1.00000 1.73205i −0.0819232 0.141895i 0.822153 0.569267i \(-0.192773\pi\)
−0.904076 + 0.427372i \(0.859440\pi\)
\(150\) 0 0
\(151\) 10.0000 17.3205i 0.813788 1.40952i −0.0964061 0.995342i \(-0.530735\pi\)
0.910195 0.414181i \(-0.135932\pi\)
\(152\) 0 0
\(153\) 4.00000i 0.323381i
\(154\) 0 0
\(155\) 4.00000 8.00000i 0.321288 0.642575i
\(156\) 0 0
\(157\) −6.92820 4.00000i −0.552931 0.319235i 0.197372 0.980329i \(-0.436759\pi\)
−0.750303 + 0.661094i \(0.770093\pi\)
\(158\) 0 0
\(159\) −6.00000 10.3923i −0.475831 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −17.3205 + 10.0000i −1.35665 + 0.783260i −0.989170 0.146772i \(-0.953112\pi\)
−0.367477 + 0.930033i \(0.619778\pi\)
\(164\) 0 0
\(165\) −7.46410 + 4.92820i −0.581080 + 0.383660i
\(166\) 0 0
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.46410 2.00000i 0.263371 0.152057i −0.362500 0.931984i \(-0.618077\pi\)
0.625871 + 0.779926i \(0.284744\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 3.46410 2.00000i 0.260378 0.150329i
\(178\) 0 0
\(179\) 2.00000 3.46410i 0.149487 0.258919i −0.781551 0.623841i \(-0.785571\pi\)
0.931038 + 0.364922i \(0.118904\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 2.00000i 0.147844i
\(184\) 0 0
\(185\) 14.9282 9.85641i 1.09754 0.724657i
\(186\) 0 0
\(187\) −13.8564 + 8.00000i −1.01328 + 0.585018i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −12.0000 20.7846i −0.868290 1.50392i −0.863743 0.503932i \(-0.831886\pi\)
−0.00454614 0.999990i \(-0.501447\pi\)
\(192\) 0 0
\(193\) 13.8564 + 8.00000i 0.997406 + 0.575853i 0.907480 0.420096i \(-0.138004\pi\)
0.0899262 + 0.995948i \(0.471337\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.00000i 0.284988i −0.989796 0.142494i \(-0.954488\pi\)
0.989796 0.142494i \(-0.0455122\pi\)
\(198\) 0 0
\(199\) −6.00000 + 10.3923i −0.425329 + 0.736691i −0.996451 0.0841740i \(-0.973175\pi\)
0.571122 + 0.820865i \(0.306508\pi\)
\(200\) 0 0
\(201\) 2.00000 + 3.46410i 0.141069 + 0.244339i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 22.3205 1.33975i 1.55893 0.0935719i
\(206\) 0 0
\(207\) −3.46410 2.00000i −0.240772 0.139010i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 0.535898 + 8.92820i 0.0365480 + 0.608898i
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) −4.00000 6.92820i −0.270295 0.468165i
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 20.0000i 1.33930i 0.742677 + 0.669650i \(0.233556\pi\)
−0.742677 + 0.669650i \(0.766444\pi\)
\(224\) 0 0
\(225\) 3.00000 + 4.00000i 0.200000 + 0.266667i
\(226\) 0 0
\(227\) 17.3205 + 10.0000i 1.14960 + 0.663723i 0.948790 0.315906i \(-0.102309\pi\)
0.200812 + 0.979630i \(0.435642\pi\)
\(228\) 0 0
\(229\) 13.0000 + 22.5167i 0.859064 + 1.48794i 0.872823 + 0.488037i \(0.162287\pi\)
−0.0137585 + 0.999905i \(0.504380\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −17.3205 + 10.0000i −1.13470 + 0.655122i −0.945114 0.326741i \(-0.894049\pi\)
−0.189590 + 0.981863i \(0.560716\pi\)
\(234\) 0 0
\(235\) 7.46410 4.92820i 0.486904 0.321481i
\(236\) 0 0
\(237\) 12.0000i 0.779484i
\(238\) 0 0
\(239\) −8.00000 −0.517477 −0.258738 0.965947i \(-0.583307\pi\)
−0.258738 + 0.965947i \(0.583307\pi\)
\(240\) 0 0
\(241\) 1.00000 1.73205i 0.0644157 0.111571i −0.832019 0.554747i \(-0.812815\pi\)
0.896435 + 0.443176i \(0.146148\pi\)
\(242\) 0 0
\(243\) −0.866025 + 0.500000i −0.0555556 + 0.0320750i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 2.00000 3.46410i 0.126745 0.219529i
\(250\) 0 0
\(251\) −12.0000 −0.757433 −0.378717 0.925513i \(-0.623635\pi\)
−0.378717 + 0.925513i \(0.623635\pi\)
\(252\) 0 0
\(253\) 16.0000i 1.00591i
\(254\) 0 0
\(255\) 4.92820 + 7.46410i 0.308616 + 0.467420i
\(256\) 0 0
\(257\) 10.3923 6.00000i 0.648254 0.374270i −0.139533 0.990217i \(-0.544560\pi\)
0.787787 + 0.615948i \(0.211227\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 3.00000 + 5.19615i 0.185695 + 0.321634i
\(262\) 0 0
\(263\) 3.46410 + 2.00000i 0.213606 + 0.123325i 0.602986 0.797752i \(-0.293977\pi\)
−0.389380 + 0.921077i \(0.627311\pi\)
\(264\) 0 0
\(265\) 24.0000 + 12.0000i 1.47431 + 0.737154i
\(266\) 0 0
\(267\) 10.0000i 0.611990i
\(268\) 0 0
\(269\) 3.00000 5.19615i 0.182913 0.316815i −0.759958 0.649972i \(-0.774781\pi\)
0.942871 + 0.333157i \(0.108114\pi\)
\(270\) 0 0
\(271\) −2.00000 3.46410i −0.121491 0.210429i 0.798865 0.601511i \(-0.205434\pi\)
−0.920356 + 0.391082i \(0.872101\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 7.85641 18.3923i 0.473759 1.10910i
\(276\) 0 0
\(277\) 27.7128 + 16.0000i 1.66510 + 0.961347i 0.970221 + 0.242222i \(0.0778761\pi\)
0.694881 + 0.719125i \(0.255457\pi\)
\(278\) 0 0
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −24.2487 14.0000i −1.44144 0.832214i −0.443491 0.896279i \(-0.646260\pi\)
−0.997946 + 0.0640654i \(0.979593\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.500000 0.866025i −0.0294118 0.0509427i
\(290\) 0 0
\(291\) −4.00000 + 6.92820i −0.234484 + 0.406138i
\(292\) 0 0
\(293\) 12.0000i 0.701047i −0.936554 0.350524i \(-0.886004\pi\)
0.936554 0.350524i \(-0.113996\pi\)
\(294\) 0 0
\(295\) −4.00000 + 8.00000i −0.232889 + 0.465778i
\(296\) 0 0
\(297\) 3.46410 + 2.00000i 0.201008 + 0.116052i
\(298\) 0 0
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 1.73205 1.00000i 0.0995037 0.0574485i
\(304\) 0 0
\(305\) 2.46410 + 3.73205i 0.141094 + 0.213697i
\(306\) 0 0
\(307\) 12.0000i 0.684876i 0.939540 + 0.342438i \(0.111253\pi\)
−0.939540 + 0.342438i \(0.888747\pi\)
\(308\) 0 0
\(309\) 4.00000 0.227552
\(310\) 0 0
\(311\) −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 0 0
\(313\) −13.8564 + 8.00000i −0.783210 + 0.452187i −0.837567 0.546335i \(-0.816023\pi\)
0.0543564 + 0.998522i \(0.482689\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 3.46410 2.00000i 0.194563 0.112331i −0.399554 0.916710i \(-0.630835\pi\)
0.594117 + 0.804379i \(0.297502\pi\)
\(318\) 0 0
\(319\) 12.0000 20.7846i 0.671871 1.16371i
\(320\) 0 0
\(321\) 12.0000 0.669775
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −1.73205 + 1.00000i −0.0957826 + 0.0553001i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) 0 0
\(333\) −6.92820 4.00000i −0.379663 0.219199i
\(334\) 0 0
\(335\) −8.00000 4.00000i −0.437087 0.218543i
\(336\) 0 0
\(337\) 8.00000i 0.435788i −0.975972 0.217894i \(-0.930081\pi\)
0.975972 0.217894i \(-0.0699187\pi\)
\(338\) 0 0
\(339\) 6.00000 10.3923i 0.325875 0.564433i
\(340\) 0 0
\(341\) 8.00000 + 13.8564i 0.433224 + 0.750366i
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 8.92820 0.535898i 0.480678 0.0288518i
\(346\) 0 0
\(347\) −10.3923 6.00000i −0.557888 0.322097i 0.194409 0.980921i \(-0.437721\pi\)
−0.752297 + 0.658824i \(0.771054\pi\)
\(348\) 0 0
\(349\) 14.0000 0.749403 0.374701 0.927146i \(-0.377745\pi\)
0.374701 + 0.927146i \(0.377745\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −24.2487 14.0000i −1.29063 0.745145i −0.311863 0.950127i \(-0.600953\pi\)
−0.978766 + 0.204982i \(0.934286\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 12.0000 + 20.7846i 0.633336 + 1.09697i 0.986865 + 0.161546i \(0.0516481\pi\)
−0.353529 + 0.935423i \(0.615019\pi\)
\(360\) 0 0
\(361\) 9.50000 16.4545i 0.500000 0.866025i
\(362\) 0 0
\(363\) 5.00000i 0.262432i
\(364\) 0 0
\(365\) 16.0000 + 8.00000i 0.837478 + 0.418739i
\(366\) 0 0
\(367\) −3.46410 2.00000i −0.180825 0.104399i 0.406855 0.913493i \(-0.366625\pi\)
−0.587680 + 0.809093i \(0.699959\pi\)
\(368\) 0 0
\(369\) −5.00000 8.66025i −0.260290 0.450835i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −20.7846 + 12.0000i −1.07619 + 0.621336i −0.929865 0.367901i \(-0.880077\pi\)
−0.146321 + 0.989237i \(0.546743\pi\)
\(374\) 0 0
\(375\) −10.5263 3.76795i −0.543575 0.194576i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −8.00000 −0.410932 −0.205466 0.978664i \(-0.565871\pi\)
−0.205466 + 0.978664i \(0.565871\pi\)
\(380\) 0 0
\(381\) −2.00000 + 3.46410i −0.102463 + 0.177471i
\(382\) 0 0
\(383\) 24.2487 14.0000i 1.23905 0.715367i 0.270151 0.962818i \(-0.412926\pi\)
0.968900 + 0.247451i \(0.0795931\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 3.46410 2.00000i 0.176090 0.101666i
\(388\) 0 0
\(389\) −17.0000 + 29.4449i −0.861934 + 1.49291i 0.00812520 + 0.999967i \(0.497414\pi\)
−0.870059 + 0.492947i \(0.835920\pi\)
\(390\) 0 0
\(391\) 16.0000 0.809155
\(392\) 0 0
\(393\) 12.0000i 0.605320i
\(394\) 0 0
\(395\) 14.7846 + 22.3923i 0.743894 + 1.12668i
\(396\) 0 0
\(397\) −6.92820 + 4.00000i −0.347717 + 0.200754i −0.663679 0.748017i \(-0.731006\pi\)
0.315963 + 0.948772i \(0.397673\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 7.00000 + 12.1244i 0.349563 + 0.605461i 0.986172 0.165726i \(-0.0529966\pi\)
−0.636609 + 0.771187i \(0.719663\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 1.00000 2.00000i 0.0496904 0.0993808i
\(406\) 0 0
\(407\) 32.0000i 1.58618i
\(408\) 0 0
\(409\) 13.0000 22.5167i 0.642809 1.11338i −0.341994 0.939702i \(-0.611102\pi\)
0.984803 0.173675i \(-0.0555643\pi\)
\(410\) 0 0
\(411\) −6.00000 10.3923i −0.295958 0.512615i
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0.535898 + 8.92820i 0.0263062 + 0.438268i
\(416\) 0 0
\(417\) −13.8564 8.00000i −0.678551 0.391762i
\(418\) 0 0
\(419\) 28.0000 1.36789 0.683945 0.729534i \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 0 0
\(421\) 10.0000 0.487370 0.243685 0.969854i \(-0.421644\pi\)
0.243685 + 0.969854i \(0.421644\pi\)
\(422\) 0 0
\(423\) −3.46410 2.00000i −0.168430 0.0972433i
\(424\) 0 0
\(425\) −18.3923 7.85641i −0.892158 0.381092i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −4.00000 + 6.92820i −0.192673 + 0.333720i −0.946135 0.323772i \(-0.895049\pi\)
0.753462 + 0.657491i \(0.228382\pi\)
\(432\) 0 0
\(433\) 16.0000i 0.768911i −0.923144 0.384455i \(-0.874389\pi\)
0.923144 0.384455i \(-0.125611\pi\)
\(434\) 0 0
\(435\) −12.0000 6.00000i −0.575356 0.287678i
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −6.00000 10.3923i −0.286364 0.495998i 0.686575 0.727059i \(-0.259113\pi\)
−0.972939 + 0.231062i \(0.925780\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −31.1769 + 18.0000i −1.48126 + 0.855206i −0.999774 0.0212481i \(-0.993236\pi\)
−0.481486 + 0.876454i \(0.659903\pi\)
\(444\) 0 0
\(445\) 12.3205 + 18.6603i 0.584048 + 0.884581i
\(446\) 0 0
\(447\) 2.00000i 0.0945968i
\(448\) 0 0
\(449\) −18.0000 −0.849473 −0.424736 0.905317i \(-0.639633\pi\)
−0.424736 + 0.905317i \(0.639633\pi\)
\(450\) 0 0
\(451\) −20.0000 + 34.6410i −0.941763 + 1.63118i
\(452\) 0 0
\(453\) 17.3205 10.0000i 0.813788 0.469841i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 34.6410 20.0000i 1.62044 0.935561i 0.633636 0.773631i \(-0.281562\pi\)
0.986802 0.161929i \(-0.0517716\pi\)
\(458\) 0 0
\(459\) 2.00000 3.46410i 0.0933520 0.161690i
\(460\) 0 0
\(461\) 6.00000 0.279448 0.139724 0.990190i \(-0.455378\pi\)
0.139724 + 0.990190i \(0.455378\pi\)
\(462\) 0 0
\(463\) 12.0000i 0.557687i −0.960337 0.278844i \(-0.910049\pi\)
0.960337 0.278844i \(-0.0899511\pi\)
\(464\) 0 0
\(465\) 7.46410 4.92820i 0.346139 0.228540i
\(466\) 0 0
\(467\) 10.3923 6.00000i 0.480899 0.277647i −0.239892 0.970799i \(-0.577112\pi\)
0.720791 + 0.693153i \(0.243779\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −4.00000 6.92820i −0.184310 0.319235i
\(472\) 0 0
\(473\) −13.8564 8.00000i −0.637118 0.367840i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 12.0000i 0.549442i
\(478\) 0 0
\(479\) −8.00000 + 13.8564i −0.365529 + 0.633115i −0.988861 0.148842i \(-0.952445\pi\)
0.623332 + 0.781958i \(0.285779\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −1.07180 17.8564i −0.0486678 0.810818i
\(486\) 0 0
\(487\) 10.3923 + 6.00000i 0.470920 + 0.271886i 0.716625 0.697459i \(-0.245686\pi\)
−0.245705 + 0.969345i \(0.579019\pi\)
\(488\) 0 0
\(489\) −20.0000 −0.904431
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 0 0
\(493\) −20.7846 12.0000i −0.936092 0.540453i
\(494\) 0 0
\(495\) −8.92820 + 0.535898i −0.401293 + 0.0240868i
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 12.0000 + 20.7846i 0.537194 + 0.930447i 0.999054 + 0.0434940i \(0.0138489\pi\)
−0.461860 + 0.886953i \(0.652818\pi\)
\(500\) 0 0
\(501\) −6.00000 + 10.3923i −0.268060 + 0.464294i
\(502\) 0 0
\(503\) 36.0000i 1.60516i −0.596544 0.802580i \(-0.703460\pi\)
0.596544 0.802580i \(-0.296540\pi\)
\(504\) 0 0
\(505\) −2.00000 + 4.00000i −0.0889988 + 0.177998i
\(506\) 0 0
\(507\) 11.2583 + 6.50000i 0.500000 + 0.288675i
\(508\) 0 0
\(509\) 21.0000 + 36.3731i 0.930809 + 1.61221i 0.781943 + 0.623350i \(0.214229\pi\)
0.148866 + 0.988857i \(0.452438\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −7.46410 + 4.92820i −0.328908 + 0.217163i
\(516\) 0 0
\(517\) 16.0000i 0.703679i
\(518\) 0 0
\(519\) 4.00000 0.175581
\(520\) 0 0
\(521\) 19.0000 32.9090i 0.832405 1.44177i −0.0637207 0.997968i \(-0.520297\pi\)
0.896126 0.443800i \(-0.146370\pi\)
\(522\) 0 0
\(523\) 24.2487 14.0000i 1.06032 0.612177i 0.134801 0.990873i \(-0.456961\pi\)
0.925521 + 0.378695i \(0.123627\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 13.8564 8.00000i 0.603595 0.348485i
\(528\) 0 0
\(529\) −3.50000 + 6.06218i −0.152174 + 0.263573i
\(530\) 0 0
\(531\) 4.00000 0.173585
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −22.3923 + 14.7846i −0.968104 + 0.639194i
\(536\) 0 0
\(537\) 3.46410 2.00000i 0.149487 0.0863064i
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) 1.00000 + 1.73205i 0.0429934 + 0.0744667i 0.886721 0.462304i \(-0.152977\pi\)
−0.843728 + 0.536771i \(0.819644\pi\)
\(542\) 0 0
\(543\) −8.66025 5.00000i −0.371647 0.214571i
\(544\) 0 0
\(545\) 2.00000 4.00000i 0.0856706 0.171341i
\(546\) 0 0
\(547\) 28.0000i 1.19719i 0.801050 + 0.598597i \(0.204275\pi\)
−0.801050 + 0.598597i \(0.795725\pi\)
\(548\) 0 0
\(549\) 1.00000 1.73205i 0.0426790 0.0739221i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 17.8564 1.07180i 0.757962 0.0454952i
\(556\) 0 0
\(557\) 10.3923 + 6.00000i 0.440336 + 0.254228i 0.703740 0.710457i \(-0.251512\pi\)
−0.263404 + 0.964686i \(0.584845\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) −16.0000 −0.675521
\(562\) 0 0
\(563\) 17.3205 + 10.0000i 0.729972 + 0.421450i 0.818412 0.574632i \(-0.194855\pi\)
−0.0884397 + 0.996082i \(0.528188\pi\)
\(564\) 0 0
\(565\) 1.60770 + 26.7846i 0.0676362 + 1.12684i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13.0000 + 22.5167i 0.544988 + 0.943948i 0.998608 + 0.0527519i \(0.0167993\pi\)
−0.453619 + 0.891196i \(0.649867\pi\)
\(570\) 0 0
\(571\) −20.0000 + 34.6410i −0.836974 + 1.44968i 0.0554391 + 0.998462i \(0.482344\pi\)
−0.892413 + 0.451219i \(0.850989\pi\)
\(572\) 0 0
\(573\) 24.0000i 1.00261i
\(574\) 0 0
\(575\) −16.0000 + 12.0000i −0.667246 + 0.500435i
\(576\) 0 0
\(577\) 27.7128 + 16.0000i 1.15370 + 0.666089i 0.949786 0.312900i \(-0.101301\pi\)
0.203913 + 0.978989i \(0.434634\pi\)
\(578\) 0 0
\(579\) 8.00000 + 13.8564i 0.332469 + 0.575853i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −41.5692 + 24.0000i −1.72162 + 0.993978i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 36.0000i 1.48588i −0.669359 0.742940i \(-0.733431\pi\)
0.669359 0.742940i \(-0.266569\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 2.00000 3.46410i 0.0822690 0.142494i
\(592\) 0 0
\(593\) 31.1769 18.0000i 1.28028 0.739171i 0.303383 0.952869i \(-0.401884\pi\)
0.976900 + 0.213697i \(0.0685507\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −10.3923 + 6.00000i −0.425329 + 0.245564i
\(598\) 0 0
\(599\) −12.0000 + 20.7846i −0.490307 + 0.849236i −0.999938 0.0111569i \(-0.996449\pi\)
0.509631 + 0.860393i \(0.329782\pi\)
\(600\) 0 0
\(601\) 38.0000 1.55005 0.775026 0.631929i \(-0.217737\pi\)
0.775026 + 0.631929i \(0.217737\pi\)
\(602\) 0 0
\(603\) 4.00000i 0.162893i
\(604\) 0 0
\(605\) 6.16025 + 9.33013i 0.250450 + 0.379324i
\(606\) 0 0
\(607\) −24.2487 + 14.0000i −0.984225 + 0.568242i −0.903543 0.428497i \(-0.859043\pi\)
−0.0806818 + 0.996740i \(0.525710\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −6.92820 4.00000i −0.279827 0.161558i 0.353518 0.935428i \(-0.384985\pi\)
−0.633345 + 0.773869i \(0.718319\pi\)
\(614\) 0 0
\(615\) 20.0000 + 10.0000i 0.806478 + 0.403239i
\(616\) 0 0
\(617\) 44.0000i 1.77137i −0.464283 0.885687i \(-0.653688\pi\)
0.464283 0.885687i \(-0.346312\pi\)
\(618\) 0 0
\(619\) −8.00000 + 13.8564i −0.321547 + 0.556936i −0.980807 0.194979i \(-0.937536\pi\)
0.659260 + 0.751915i \(0.270870\pi\)
\(620\) 0 0
\(621\) −2.00000 3.46410i −0.0802572 0.139010i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 24.2846 5.93782i 0.971384 0.237513i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 32.0000 1.27592
\(630\) 0 0
\(631\) −28.0000 −1.11466 −0.557331 0.830290i \(-0.688175\pi\)
−0.557331 + 0.830290i \(0.688175\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.535898 8.92820i −0.0212665 0.354305i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −7.00000 + 12.1244i −0.276483 + 0.478883i −0.970508 0.241068i \(-0.922502\pi\)
0.694025 + 0.719951i \(0.255836\pi\)
\(642\) 0 0
\(643\) 36.0000i 1.41970i −0.704352 0.709851i \(-0.748762\pi\)
0.704352 0.709851i \(-0.251238\pi\)
\(644\) 0 0
\(645\) −4.00000 + 8.00000i −0.157500 + 0.315000i
\(646\) 0 0
\(647\) −10.3923 6.00000i −0.408564 0.235884i 0.281609 0.959529i \(-0.409132\pi\)
−0.690172 + 0.723645i \(0.742465\pi\)
\(648\) 0 0
\(649\) −8.00000 13.8564i −0.314027 0.543912i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −3.46410 + 2.00000i −0.135561 + 0.0782660i −0.566247 0.824236i \(-0.691605\pi\)
0.430686 + 0.902502i \(0.358272\pi\)
\(654\) 0 0
\(655\) 14.7846 + 22.3923i 0.577683 + 0.874940i
\(656\) 0 0
\(657\) 8.00000i 0.312110i
\(658\) 0 0
\(659\) −28.0000 −1.09073 −0.545363 0.838200i \(-0.683608\pi\)
−0.545363 + 0.838200i \(0.683608\pi\)
\(660\) 0 0
\(661\) 11.0000 19.0526i 0.427850 0.741059i −0.568831 0.822454i \(-0.692604\pi\)
0.996682 + 0.0813955i \(0.0259377\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −20.7846 + 12.0000i −0.804783 + 0.464642i
\(668\) 0 0
\(669\) −10.0000 + 17.3205i −0.386622 + 0.669650i
\(670\) 0 0
\(671\) −8.00000 −0.308837
\(672\) 0 0
\(673\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(674\) 0 0
\(675\) 0.598076 + 4.96410i 0.0230200 + 0.191068i
\(676\) 0 0
\(677\) 3.46410 2.00000i 0.133136 0.0768662i −0.431953 0.901896i \(-0.642175\pi\)
0.565089 + 0.825030i \(0.308842\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 10.0000 + 17.3205i 0.383201 + 0.663723i
\(682\) 0 0
\(683\) −38.1051 22.0000i −1.45805 0.841807i −0.459136 0.888366i \(-0.651841\pi\)
−0.998916 + 0.0465592i \(0.985174\pi\)
\(684\) 0 0
\(685\) 24.0000 + 12.0000i 0.916993 + 0.458496i
\(686\) 0 0
\(687\) 26.0000i 0.991962i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 16.0000 + 27.7128i 0.608669 + 1.05425i 0.991460 + 0.130410i \(0.0416295\pi\)
−0.382791 + 0.923835i \(0.625037\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 35.7128 2.14359i 1.35466 0.0813111i
\(696\) 0 0
\(697\) 34.6410 + 20.0000i 1.31212 + 0.757554i
\(698\) 0 0
\(699\) −20.0000 −0.756469
\(700\) 0 0
\(701\) 26.0000 0.982006 0.491003 0.871158i \(-0.336630\pi\)
0.491003 + 0.871158i \(0.336630\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 8.92820 0.535898i 0.336256 0.0201831i
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −3.00000 5.19615i −0.112667 0.195146i 0.804178 0.594389i \(-0.202606\pi\)
−0.916845 + 0.399244i \(0.869273\pi\)
\(710\) 0 0
\(711\) 6.00000 10.3923i 0.225018 0.389742i
\(712\) 0 0
\(713\) 16.0000i 0.599205i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −6.92820 4.00000i −0.258738 0.149383i
\(718\) 0 0
\(719\) 4.00000 + 6.92820i 0.149175 + 0.258378i 0.930923 0.365216i \(-0.119005\pi\)
−0.781748 + 0.623595i \(0.785672\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0 0
\(723\) 1.73205 1.00000i 0.0644157 0.0371904i
\(724\) 0 0
\(725\) 29.7846 3.58846i 1.10617 0.133272i
\(726\) 0 0
\(727\) 12.0000i 0.445055i −0.974926 0.222528i \(-0.928569\pi\)
0.974926 0.222528i \(-0.0714308\pi\)
\(728\) 0 0
\(729\) −1.00000 −0.0370370
\(730\) 0 0
\(731\) −8.00000 + 13.8564i −0.295891 + 0.512498i
\(732\) 0 0
\(733\) 13.8564 8.00000i 0.511798 0.295487i −0.221774 0.975098i \(-0.571185\pi\)
0.733572 + 0.679611i \(0.237852\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 13.8564 8.00000i 0.510407 0.294684i
\(738\) 0 0
\(739\) 20.0000 34.6410i 0.735712 1.27429i −0.218698 0.975793i \(-0.570181\pi\)
0.954410 0.298498i \(-0.0964856\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 36.0000i 1.32071i −0.750953 0.660356i \(-0.770405\pi\)
0.750953 0.660356i \(-0.229595\pi\)
\(744\) 0 0
\(745\) 2.46410 + 3.73205i 0.0902777 + 0.136732i
\(746\) 0 0
\(747\) 3.46410 2.00000i 0.126745 0.0731762i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 14.0000 + 24.2487i 0.510867 + 0.884848i 0.999921 + 0.0125942i \(0.00400897\pi\)
−0.489053 + 0.872254i \(0.662658\pi\)
\(752\) 0 0
\(753\) −10.3923 6.00000i −0.378717 0.218652i
\(754\) 0 0
\(755\) −20.0000 + 40.0000i −0.727875 + 1.45575i
\(756\) 0 0
\(757\) 16.0000i 0.581530i 0.956795 + 0.290765i \(0.0939098\pi\)
−0.956795 + 0.290765i \(0.906090\pi\)
\(758\) 0 0
\(759\) −8.00000 + 13.8564i −0.290382 + 0.502956i
\(760\) 0 0
\(761\) −21.0000 36.3731i −0.761249 1.31852i −0.942207 0.335032i \(-0.891253\pi\)
0.180957 0.983491i \(-0.442080\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0.535898 + 8.92820i 0.0193754 + 0.322800i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 18.0000 0.649097 0.324548 0.945869i \(-0.394788\pi\)
0.324548 + 0.945869i \(0.394788\pi\)
\(770\) 0 0
\(771\) 12.0000 0.432169
\(772\) 0 0
\(773\) −10.3923 6.00000i −0.373785 0.215805i 0.301326 0.953521i \(-0.402571\pi\)
−0.675111 + 0.737716i \(0.735904\pi\)
\(774\) 0 0
\(775\) −7.85641 + 18.3923i −0.282210 + 0.660671i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 6.00000i 0.214423i
\(784\) 0 0
\(785\) 16.0000 + 8.00000i 0.571064 + 0.285532i
\(786\) 0 0
\(787\) −24.2487 14.0000i −0.864373 0.499046i 0.00110111 0.999999i \(-0.499650\pi\)
−0.865474 + 0.500953i \(0.832983\pi\)
\(788\) 0 0
\(789\) 2.00000 + 3.46410i 0.0712019 + 0.123325i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 14.7846 + 22.3923i 0.524356 + 0.794173i
\(796\) 0 0
\(797\) 28.0000i 0.991811i 0.868377 + 0.495905i \(0.165164\pi\)
−0.868377 + 0.495905i \(0.834836\pi\)
\(798\) 0 0
\(799\) 16.0000 0.566039
\(800\) 0 0
\(801\) 5.00000