Properties

Label 1728.2.bc.d.1585.1
Level $1728$
Weight $2$
Character 1728.1585
Analytic conductor $13.798$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Newspace parameters

Level: \( N \) \(=\) \( 1728 = 2^{6} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1728.bc (of order \(12\), degree \(4\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.7981494693\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{12})\)
Defining polynomial: \(x^{4} - x^{2} + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 144)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 1585.1
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1728.1585
Dual form 1728.2.bc.d.145.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.267949 - 1.00000i) q^{5} +(2.36603 + 1.36603i) q^{7} +O(q^{10})\) \(q+(0.267949 - 1.00000i) q^{5} +(2.36603 + 1.36603i) q^{7} +(-4.23205 + 1.13397i) q^{11} +(-3.36603 - 0.901924i) q^{13} +5.73205 q^{17} +(2.36603 - 2.36603i) q^{19} +(4.09808 - 2.36603i) q^{23} +(3.40192 + 1.96410i) q^{25} +(0.633975 + 2.36603i) q^{29} +(0.267949 + 0.464102i) q^{31} +(2.00000 - 2.00000i) q^{35} +(4.73205 + 4.73205i) q^{37} +(-2.59808 + 1.50000i) q^{41} +(8.33013 - 2.23205i) q^{43} +(3.83013 - 6.63397i) q^{47} +(0.232051 + 0.401924i) q^{49} +(7.46410 + 7.46410i) q^{53} +4.53590i q^{55} +(-1.96410 + 7.33013i) q^{59} +(-3.00000 - 11.1962i) q^{61} +(-1.80385 + 3.12436i) q^{65} +(-6.59808 - 1.76795i) q^{67} -2.92820i q^{71} +6.26795i q^{73} +(-11.5622 - 3.09808i) q^{77} +(6.00000 - 10.3923i) q^{79} +(0.366025 + 1.36603i) q^{83} +(1.53590 - 5.73205i) q^{85} -2.00000i q^{89} +(-6.73205 - 6.73205i) q^{91} +(-1.73205 - 3.00000i) q^{95} +(-5.86603 + 10.1603i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 8q^{5} + 6q^{7} + O(q^{10}) \) \( 4q + 8q^{5} + 6q^{7} - 10q^{11} - 10q^{13} + 16q^{17} + 6q^{19} + 6q^{23} + 24q^{25} + 6q^{29} + 8q^{31} + 8q^{35} + 12q^{37} + 16q^{43} - 2q^{47} - 6q^{49} + 16q^{53} + 6q^{59} - 12q^{61} - 28q^{65} - 16q^{67} - 22q^{77} + 24q^{79} - 2q^{83} + 20q^{85} - 20q^{91} - 20q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).

\(n\) \(325\) \(703\) \(1217\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) 0.267949 1.00000i 0.119831 0.447214i −0.879772 0.475395i \(-0.842305\pi\)
0.999603 + 0.0281817i \(0.00897171\pi\)
\(6\) 0 0
\(7\) 2.36603 + 1.36603i 0.894274 + 0.516309i 0.875338 0.483512i \(-0.160639\pi\)
0.0189356 + 0.999821i \(0.493972\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −4.23205 + 1.13397i −1.27601 + 0.341906i −0.832331 0.554279i \(-0.812994\pi\)
−0.443680 + 0.896185i \(0.646327\pi\)
\(12\) 0 0
\(13\) −3.36603 0.901924i −0.933567 0.250149i −0.240192 0.970725i \(-0.577210\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 5.73205 1.39023 0.695113 0.718900i \(-0.255354\pi\)
0.695113 + 0.718900i \(0.255354\pi\)
\(18\) 0 0
\(19\) 2.36603 2.36603i 0.542803 0.542803i −0.381546 0.924350i \(-0.624608\pi\)
0.924350 + 0.381546i \(0.124608\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 4.09808 2.36603i 0.854508 0.493350i −0.00766135 0.999971i \(-0.502439\pi\)
0.862169 + 0.506620i \(0.169105\pi\)
\(24\) 0 0
\(25\) 3.40192 + 1.96410i 0.680385 + 0.392820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 0.633975 + 2.36603i 0.117726 + 0.439360i 0.999476 0.0323566i \(-0.0103012\pi\)
−0.881750 + 0.471717i \(0.843635\pi\)
\(30\) 0 0
\(31\) 0.267949 + 0.464102i 0.0481251 + 0.0833551i 0.889085 0.457743i \(-0.151342\pi\)
−0.840959 + 0.541098i \(0.818009\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 2.00000 2.00000i 0.338062 0.338062i
\(36\) 0 0
\(37\) 4.73205 + 4.73205i 0.777944 + 0.777944i 0.979481 0.201537i \(-0.0645935\pi\)
−0.201537 + 0.979481i \(0.564594\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) −2.59808 + 1.50000i −0.405751 + 0.234261i −0.688963 0.724797i \(-0.741934\pi\)
0.283211 + 0.959058i \(0.408600\pi\)
\(42\) 0 0
\(43\) 8.33013 2.23205i 1.27033 0.340385i 0.440174 0.897912i \(-0.354917\pi\)
0.830158 + 0.557528i \(0.188250\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.83013 6.63397i 0.558681 0.967665i −0.438925 0.898523i \(-0.644641\pi\)
0.997607 0.0691412i \(-0.0220259\pi\)
\(48\) 0 0
\(49\) 0.232051 + 0.401924i 0.0331501 + 0.0574177i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) 7.46410 + 7.46410i 1.02527 + 1.02527i 0.999672 + 0.0256010i \(0.00814993\pi\)
0.0256010 + 0.999672i \(0.491850\pi\)
\(54\) 0 0
\(55\) 4.53590i 0.611620i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −1.96410 + 7.33013i −0.255704 + 0.954301i 0.711993 + 0.702186i \(0.247793\pi\)
−0.967697 + 0.252115i \(0.918874\pi\)
\(60\) 0 0
\(61\) −3.00000 11.1962i −0.384111 1.43352i −0.839564 0.543261i \(-0.817189\pi\)
0.455453 0.890260i \(-0.349477\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.80385 + 3.12436i −0.223740 + 0.387529i
\(66\) 0 0
\(67\) −6.59808 1.76795i −0.806083 0.215989i −0.167830 0.985816i \(-0.553676\pi\)
−0.638253 + 0.769827i \(0.720343\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.92820i 0.347514i −0.984789 0.173757i \(-0.944409\pi\)
0.984789 0.173757i \(-0.0555907\pi\)
\(72\) 0 0
\(73\) 6.26795i 0.733608i 0.930298 + 0.366804i \(0.119548\pi\)
−0.930298 + 0.366804i \(0.880452\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −11.5622 3.09808i −1.31763 0.353059i
\(78\) 0 0
\(79\) 6.00000 10.3923i 0.675053 1.16923i −0.301401 0.953498i \(-0.597454\pi\)
0.976453 0.215728i \(-0.0692125\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) 0.366025 + 1.36603i 0.0401765 + 0.149941i 0.983100 0.183068i \(-0.0586028\pi\)
−0.942924 + 0.333009i \(0.891936\pi\)
\(84\) 0 0
\(85\) 1.53590 5.73205i 0.166592 0.621728i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.00000i 0.212000i −0.994366 0.106000i \(-0.966196\pi\)
0.994366 0.106000i \(-0.0338043\pi\)
\(90\) 0 0
\(91\) −6.73205 6.73205i −0.705711 0.705711i
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −1.73205 3.00000i −0.177705 0.307794i
\(96\) 0 0
\(97\) −5.86603 + 10.1603i −0.595605 + 1.03162i 0.397857 + 0.917448i \(0.369754\pi\)
−0.993461 + 0.114170i \(0.963579\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 2.00000 0.535898i 0.199007 0.0533239i −0.157938 0.987449i \(-0.550485\pi\)
0.356946 + 0.934125i \(0.383818\pi\)
\(102\) 0 0
\(103\) 13.0981 7.56218i 1.29059 0.745124i 0.311833 0.950137i \(-0.399057\pi\)
0.978759 + 0.205014i \(0.0657238\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.4904 + 12.4904i 1.20749 + 1.20749i 0.971837 + 0.235654i \(0.0757231\pi\)
0.235654 + 0.971837i \(0.424277\pi\)
\(108\) 0 0
\(109\) 10.7321 10.7321i 1.02794 1.02794i 0.0283459 0.999598i \(-0.490976\pi\)
0.999598 0.0283459i \(-0.00902398\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 6.92820 + 12.0000i 0.651751 + 1.12887i 0.982698 + 0.185216i \(0.0592984\pi\)
−0.330947 + 0.943649i \(0.607368\pi\)
\(114\) 0 0
\(115\) −1.26795 4.73205i −0.118237 0.441266i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 13.5622 + 7.83013i 1.24324 + 0.717787i
\(120\) 0 0
\(121\) 7.09808 4.09808i 0.645280 0.372552i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 6.53590 6.53590i 0.584589 0.584589i
\(126\) 0 0
\(127\) −4.19615 −0.372348 −0.186174 0.982517i \(-0.559609\pi\)
−0.186174 + 0.982517i \(0.559609\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) −7.83013 2.09808i −0.684121 0.183310i −0.100014 0.994986i \(-0.531889\pi\)
−0.584108 + 0.811676i \(0.698555\pi\)
\(132\) 0 0
\(133\) 8.83013 2.36603i 0.765669 0.205160i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 8.25833 + 4.76795i 0.705557 + 0.407353i 0.809414 0.587239i \(-0.199785\pi\)
−0.103857 + 0.994592i \(0.533118\pi\)
\(138\) 0 0
\(139\) −3.06218 + 11.4282i −0.259731 + 0.969328i 0.705667 + 0.708544i \(0.250648\pi\)
−0.965397 + 0.260784i \(0.916019\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 15.2679 1.27677
\(144\) 0 0
\(145\) 2.53590 0.210595
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 2.09808 7.83013i 0.171881 0.641469i −0.825181 0.564869i \(-0.808927\pi\)
0.997062 0.0766003i \(-0.0244065\pi\)
\(150\) 0 0
\(151\) 0.633975 + 0.366025i 0.0515921 + 0.0297867i 0.525574 0.850748i \(-0.323851\pi\)
−0.473982 + 0.880534i \(0.657184\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0.535898 0.143594i 0.0430444 0.0115337i
\(156\) 0 0
\(157\) −4.73205 1.26795i −0.377659 0.101193i 0.0649959 0.997886i \(-0.479297\pi\)
−0.442655 + 0.896692i \(0.645963\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 12.9282 1.01889
\(162\) 0 0
\(163\) 7.00000 7.00000i 0.548282 0.548282i −0.377661 0.925944i \(-0.623272\pi\)
0.925944 + 0.377661i \(0.123272\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −6.46410 + 3.73205i −0.500207 + 0.288795i −0.728799 0.684728i \(-0.759921\pi\)
0.228592 + 0.973522i \(0.426588\pi\)
\(168\) 0 0
\(169\) −0.741670 0.428203i −0.0570515 0.0329387i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.437822 + 1.63397i 0.0332870 + 0.124229i 0.980570 0.196169i \(-0.0628501\pi\)
−0.947283 + 0.320398i \(0.896183\pi\)
\(174\) 0 0
\(175\) 5.36603 + 9.29423i 0.405633 + 0.702578i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) −1.92820 + 1.92820i −0.144121 + 0.144121i −0.775486 0.631365i \(-0.782495\pi\)
0.631365 + 0.775486i \(0.282495\pi\)
\(180\) 0 0
\(181\) −7.39230 7.39230i −0.549466 0.549466i 0.376821 0.926286i \(-0.377017\pi\)
−0.926286 + 0.376821i \(0.877017\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 6.00000 3.46410i 0.441129 0.254686i
\(186\) 0 0
\(187\) −24.2583 + 6.50000i −1.77394 + 0.475327i
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −12.0263 + 20.8301i −0.870191 + 1.50722i −0.00839227 + 0.999965i \(0.502671\pi\)
−0.861799 + 0.507250i \(0.830662\pi\)
\(192\) 0 0
\(193\) −10.8660 18.8205i −0.782154 1.35473i −0.930685 0.365822i \(-0.880788\pi\)
0.148531 0.988908i \(-0.452545\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −13.6603 13.6603i −0.973253 0.973253i 0.0263987 0.999651i \(-0.491596\pi\)
−0.999651 + 0.0263987i \(0.991596\pi\)
\(198\) 0 0
\(199\) 25.1244i 1.78102i 0.454965 + 0.890509i \(0.349652\pi\)
−0.454965 + 0.890509i \(0.650348\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −1.73205 + 6.46410i −0.121566 + 0.453691i
\(204\) 0 0
\(205\) 0.803848 + 3.00000i 0.0561432 + 0.209529i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7.33013 + 12.6962i −0.507035 + 0.878211i
\(210\) 0 0
\(211\) −4.09808 1.09808i −0.282123 0.0755947i 0.114983 0.993367i \(-0.463319\pi\)
−0.397106 + 0.917773i \(0.629985\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) 8.92820i 0.608898i
\(216\) 0 0
\(217\) 1.46410i 0.0993897i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) −19.2942 5.16987i −1.29787 0.347763i
\(222\) 0 0
\(223\) 8.02628 13.9019i 0.537479 0.930942i −0.461559 0.887109i \(-0.652710\pi\)
0.999039 0.0438324i \(-0.0139568\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) −0.571797 2.13397i −0.0379515 0.141637i 0.944351 0.328941i \(-0.106692\pi\)
−0.982302 + 0.187304i \(0.940025\pi\)
\(228\) 0 0
\(229\) −1.83013 + 6.83013i −0.120938 + 0.451347i −0.999662 0.0259823i \(-0.991729\pi\)
0.878724 + 0.477330i \(0.158395\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.19615i 0.209387i −0.994505 0.104693i \(-0.966614\pi\)
0.994505 0.104693i \(-0.0333861\pi\)
\(234\) 0 0
\(235\) −5.60770 5.60770i −0.365806 0.365806i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −7.90192 13.6865i −0.511133 0.885308i −0.999917 0.0129033i \(-0.995893\pi\)
0.488784 0.872405i \(-0.337441\pi\)
\(240\) 0 0
\(241\) −11.5981 + 20.0885i −0.747098 + 1.29401i 0.202110 + 0.979363i \(0.435220\pi\)
−0.949208 + 0.314649i \(0.898113\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.464102 0.124356i 0.0296504 0.00794479i
\(246\) 0 0
\(247\) −10.0981 + 5.83013i −0.642525 + 0.370962i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −5.83013 5.83013i −0.367994 0.367994i 0.498751 0.866745i \(-0.333792\pi\)
−0.866745 + 0.498751i \(0.833792\pi\)
\(252\) 0 0
\(253\) −14.6603 + 14.6603i −0.921682 + 0.921682i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) −9.42820 16.3301i −0.588115 1.01865i −0.994479 0.104934i \(-0.966537\pi\)
0.406364 0.913711i \(-0.366796\pi\)
\(258\) 0 0
\(259\) 4.73205 + 17.6603i 0.294035 + 1.09735i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 2.49038 + 1.43782i 0.153563 + 0.0886599i 0.574813 0.818285i \(-0.305075\pi\)
−0.421249 + 0.906945i \(0.638408\pi\)
\(264\) 0 0
\(265\) 9.46410 5.46410i 0.581375 0.335657i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.26795 + 1.26795i −0.0773082 + 0.0773082i −0.744704 0.667395i \(-0.767409\pi\)
0.667395 + 0.744704i \(0.267409\pi\)
\(270\) 0 0
\(271\) 0.392305 0.0238308 0.0119154 0.999929i \(-0.496207\pi\)
0.0119154 + 0.999929i \(0.496207\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −16.6244 4.45448i −1.00249 0.268615i
\(276\) 0 0
\(277\) 25.2224 6.75833i 1.51547 0.406069i 0.597222 0.802076i \(-0.296271\pi\)
0.918247 + 0.396007i \(0.129605\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −8.66025 5.00000i −0.516627 0.298275i 0.218926 0.975741i \(-0.429745\pi\)
−0.735554 + 0.677466i \(0.763078\pi\)
\(282\) 0 0
\(283\) −5.24167 + 19.5622i −0.311585 + 1.16285i 0.615542 + 0.788104i \(0.288937\pi\)
−0.927127 + 0.374747i \(0.877730\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −8.19615 −0.483804
\(288\) 0 0
\(289\) 15.8564 0.932730
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.43782 + 5.36603i −0.0839985 + 0.313487i −0.995123 0.0986454i \(-0.968549\pi\)
0.911124 + 0.412132i \(0.135216\pi\)
\(294\) 0 0
\(295\) 6.80385 + 3.92820i 0.396135 + 0.228709i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −15.9282 + 4.26795i −0.921152 + 0.246822i
\(300\) 0 0
\(301\) 22.7583 + 6.09808i 1.31177 + 0.351487i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −12.0000 −0.687118
\(306\) 0 0
\(307\) −3.02628 + 3.02628i −0.172719 + 0.172719i −0.788173 0.615454i \(-0.788973\pi\)
0.615454 + 0.788173i \(0.288973\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 19.0981 11.0263i 1.08295 0.625243i 0.151261 0.988494i \(-0.451667\pi\)
0.931691 + 0.363251i \(0.118333\pi\)
\(312\) 0 0
\(313\) −18.6506 10.7679i −1.05420 0.608640i −0.130375 0.991465i \(-0.541618\pi\)
−0.923821 + 0.382824i \(0.874951\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −5.50962 20.5622i −0.309451 1.15489i −0.929046 0.369965i \(-0.879370\pi\)
0.619595 0.784922i \(-0.287297\pi\)
\(318\) 0 0
\(319\) −5.36603 9.29423i −0.300440 0.520377i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 13.5622 13.5622i 0.754620 0.754620i
\(324\) 0 0
\(325\) −9.67949 9.67949i −0.536922 0.536922i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 18.1244 10.4641i 0.999228 0.576905i
\(330\) 0 0
\(331\) 0.0980762 0.0262794i 0.00539076 0.00144445i −0.256123 0.966644i \(-0.582445\pi\)
0.261513 + 0.965200i \(0.415778\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −3.53590 + 6.12436i −0.193187 + 0.334609i
\(336\) 0 0
\(337\) 8.89230 + 15.4019i 0.484395 + 0.838996i 0.999839 0.0179267i \(-0.00570654\pi\)
−0.515445 + 0.856923i \(0.672373\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) −1.66025 1.66025i −0.0899078 0.0899078i
\(342\) 0 0
\(343\) 17.8564i 0.964155i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 4.72243 17.6244i 0.253513 0.946125i −0.715398 0.698717i \(-0.753755\pi\)
0.968911 0.247408i \(-0.0795787\pi\)
\(348\) 0 0
\(349\) −4.26795 15.9282i −0.228458 0.852617i −0.980989 0.194061i \(-0.937834\pi\)
0.752531 0.658556i \(-0.228833\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) −7.16025 + 12.4019i −0.381102 + 0.660088i −0.991220 0.132223i \(-0.957789\pi\)
0.610118 + 0.792310i \(0.291122\pi\)
\(354\) 0 0
\(355\) −2.92820 0.784610i −0.155413 0.0416428i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.2679i 0.594700i −0.954769 0.297350i \(-0.903897\pi\)
0.954769 0.297350i \(-0.0961028\pi\)
\(360\) 0 0
\(361\) 7.80385i 0.410729i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 6.26795 + 1.67949i 0.328079 + 0.0879086i
\(366\) 0 0
\(367\) −14.1244 + 24.4641i −0.737285 + 1.27702i 0.216428 + 0.976299i \(0.430559\pi\)
−0.953713 + 0.300717i \(0.902774\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 7.46410 + 27.8564i 0.387517 + 1.44623i
\(372\) 0 0
\(373\) −7.36603 + 27.4904i −0.381398 + 1.42340i 0.462368 + 0.886688i \(0.347000\pi\)
−0.843767 + 0.536710i \(0.819667\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.53590i 0.439621i
\(378\) 0 0
\(379\) −3.75833 3.75833i −0.193052 0.193052i 0.603961 0.797014i \(-0.293588\pi\)
−0.797014 + 0.603961i \(0.793588\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −6.73205 11.6603i −0.343992 0.595811i 0.641178 0.767392i \(-0.278446\pi\)
−0.985170 + 0.171581i \(0.945113\pi\)
\(384\) 0 0
\(385\) −6.19615 + 10.7321i −0.315785 + 0.546956i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −19.7583 + 5.29423i −1.00179 + 0.268428i −0.722194 0.691691i \(-0.756866\pi\)
−0.279593 + 0.960119i \(0.590200\pi\)
\(390\) 0 0
\(391\) 23.4904 13.5622i 1.18796 0.685869i
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −8.78461 8.78461i −0.442002 0.442002i
\(396\) 0 0
\(397\) −9.26795 + 9.26795i −0.465145 + 0.465145i −0.900337 0.435192i \(-0.856680\pi\)
0.435192 + 0.900337i \(0.356680\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 1.79423 + 3.10770i 0.0895995 + 0.155191i 0.907342 0.420393i \(-0.138108\pi\)
−0.817742 + 0.575584i \(0.804775\pi\)
\(402\) 0 0
\(403\) −0.483340 1.80385i −0.0240769 0.0898560i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −25.3923 14.6603i −1.25865 0.726682i
\(408\) 0 0
\(409\) −27.8660 + 16.0885i −1.37789 + 0.795523i −0.991905 0.126984i \(-0.959470\pi\)
−0.385981 + 0.922507i \(0.626137\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −14.6603 + 14.6603i −0.721384 + 0.721384i
\(414\) 0 0
\(415\) 1.46410 0.0718699
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −6.63397 1.77757i −0.324091 0.0868399i 0.0931055 0.995656i \(-0.470321\pi\)
−0.417196 + 0.908816i \(0.636987\pi\)
\(420\) 0 0
\(421\) −30.5885 + 8.19615i −1.49079 + 0.399456i −0.910004 0.414600i \(-0.863922\pi\)
−0.580786 + 0.814056i \(0.697255\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 19.5000 + 11.2583i 0.945889 + 0.546109i
\(426\) 0 0
\(427\) 8.19615 30.5885i 0.396640 1.48028i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −16.1962 −0.780141 −0.390071 0.920785i \(-0.627549\pi\)
−0.390071 + 0.920785i \(0.627549\pi\)
\(432\) 0 0
\(433\) −5.73205 −0.275465 −0.137732 0.990469i \(-0.543981\pi\)
−0.137732 + 0.990469i \(0.543981\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 4.09808 15.2942i 0.196038 0.731622i
\(438\) 0 0
\(439\) −22.8564 13.1962i −1.09088 0.629818i −0.157067 0.987588i \(-0.550204\pi\)
−0.933810 + 0.357770i \(0.883537\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 17.2583 4.62436i 0.819968 0.219710i 0.175636 0.984455i \(-0.443802\pi\)
0.644332 + 0.764745i \(0.277135\pi\)
\(444\) 0 0
\(445\) −2.00000 0.535898i −0.0948091 0.0254040i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 3.33975 0.157612 0.0788062 0.996890i \(-0.474889\pi\)
0.0788062 + 0.996890i \(0.474889\pi\)
\(450\) 0 0
\(451\) 9.29423 9.29423i 0.437648 0.437648i
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8.53590 + 4.92820i −0.400169 + 0.231038i
\(456\) 0 0
\(457\) −2.25833 1.30385i −0.105640 0.0609914i 0.446249 0.894909i \(-0.352760\pi\)
−0.551889 + 0.833917i \(0.686093\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 9.56218 + 35.6865i 0.445355 + 1.66209i 0.714997 + 0.699127i \(0.246428\pi\)
−0.269642 + 0.962961i \(0.586906\pi\)
\(462\) 0 0
\(463\) −1.19615 2.07180i −0.0555899 0.0962846i 0.836891 0.547369i \(-0.184371\pi\)
−0.892481 + 0.451085i \(0.851037\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 2.63397 2.63397i 0.121886 0.121886i −0.643533 0.765419i \(-0.722532\pi\)
0.765419 + 0.643533i \(0.222532\pi\)
\(468\) 0 0
\(469\) −13.1962 13.1962i −0.609342 0.609342i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) −32.7224 + 18.8923i −1.50458 + 0.868669i
\(474\) 0 0
\(475\) 12.6962 3.40192i 0.582539 0.156091i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 4.16987 7.22243i 0.190526 0.330001i −0.754898 0.655842i \(-0.772314\pi\)
0.945425 + 0.325840i \(0.105647\pi\)
\(480\) 0 0
\(481\) −11.6603 20.1962i −0.531662 0.920865i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 8.58846 + 8.58846i 0.389982 + 0.389982i
\(486\) 0 0
\(487\) 5.80385i 0.262997i 0.991316 + 0.131499i \(0.0419789\pi\)
−0.991316 + 0.131499i \(0.958021\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 3.72243 13.8923i 0.167991 0.626951i −0.829649 0.558286i \(-0.811459\pi\)
0.997640 0.0686652i \(-0.0218740\pi\)
\(492\) 0 0
\(493\) 3.63397 + 13.5622i 0.163666 + 0.610810i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.00000 6.92820i 0.179425 0.310772i
\(498\) 0 0
\(499\) −8.69615 2.33013i −0.389293 0.104311i 0.0588630 0.998266i \(-0.481252\pi\)
−0.448156 + 0.893955i \(0.647919\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.7128i 1.23565i 0.786314 + 0.617827i \(0.211987\pi\)
−0.786314 + 0.617827i \(0.788013\pi\)
\(504\) 0 0
\(505\) 2.14359i 0.0953887i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 11.4641 + 3.07180i 0.508137 + 0.136155i 0.503774 0.863835i \(-0.331944\pi\)
0.00436335 + 0.999990i \(0.498611\pi\)
\(510\) 0 0
\(511\) −8.56218 + 14.8301i −0.378768 + 0.656046i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) −4.05256 15.1244i −0.178577 0.666459i
\(516\) 0 0
\(517\) −8.68653 + 32.4186i −0.382033 + 1.42577i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.0000i 0.569540i 0.958596 + 0.284770i \(0.0919173\pi\)
−0.958596 + 0.284770i \(0.908083\pi\)
\(522\) 0 0
\(523\) 7.53590 + 7.53590i 0.329522 + 0.329522i 0.852405 0.522883i \(-0.175143\pi\)
−0.522883 + 0.852405i \(0.675143\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 1.53590 + 2.66025i 0.0669048 + 0.115882i
\(528\) 0 0
\(529\) −0.303848 + 0.526279i −0.0132108 + 0.0228817i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 10.0981 2.70577i 0.437396 0.117200i
\(534\) 0 0
\(535\) 15.8372 9.14359i 0.684701 0.395312i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −1.43782 1.43782i −0.0619314 0.0619314i
\(540\) 0 0
\(541\) 2.19615 2.19615i 0.0944200 0.0944200i −0.658319 0.752739i \(-0.728732\pi\)
0.752739 + 0.658319i \(0.228732\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7.85641 13.6077i −0.336531 0.582890i
\(546\) 0 0
\(547\) 8.74167 + 32.6244i 0.373767 + 1.39492i 0.855138 + 0.518400i \(0.173472\pi\)
−0.481371 + 0.876517i \(0.659861\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 7.09808 + 4.09808i 0.302388 + 0.174584i
\(552\) 0 0
\(553\) 28.3923 16.3923i 1.20736 0.697072i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 14.8038 14.8038i 0.627259 0.627259i −0.320118 0.947378i \(-0.603723\pi\)
0.947378 + 0.320118i \(0.103723\pi\)
\(558\) 0 0
\(559\) −30.0526 −1.27109
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 26.9904 + 7.23205i 1.13751 + 0.304795i 0.777949 0.628327i \(-0.216260\pi\)
0.359560 + 0.933122i \(0.382927\pi\)
\(564\) 0 0
\(565\) 13.8564 3.71281i 0.582943 0.156199i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) −18.4019 10.6244i −0.771449 0.445396i 0.0619424 0.998080i \(-0.480270\pi\)
−0.833391 + 0.552684i \(0.813604\pi\)
\(570\) 0 0
\(571\) −0.892305 + 3.33013i −0.0373418 + 0.139361i −0.982080 0.188464i \(-0.939649\pi\)
0.944738 + 0.327825i \(0.106316\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 18.5885 0.775192
\(576\) 0 0
\(577\) −5.78461 −0.240816 −0.120408 0.992724i \(-0.538420\pi\)
−0.120408 + 0.992724i \(0.538420\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) −1.00000 + 3.73205i −0.0414870 + 0.154832i
\(582\) 0 0
\(583\) −40.0526 23.1244i −1.65881 0.957713i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −26.9904 + 7.23205i −1.11401 + 0.298499i −0.768458 0.639900i \(-0.778976\pi\)
−0.345554 + 0.938399i \(0.612309\pi\)
\(588\) 0 0
\(589\) 1.73205 + 0.464102i 0.0713679 + 0.0191230i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −17.4641 −0.717165 −0.358582 0.933498i \(-0.616740\pi\)
−0.358582 + 0.933498i \(0.616740\pi\)
\(594\) 0 0
\(595\) 11.4641 11.4641i 0.469982 0.469982i
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −11.3205 + 6.53590i −0.462543 + 0.267050i −0.713113 0.701049i \(-0.752715\pi\)
0.250570 + 0.968099i \(0.419382\pi\)
\(600\) 0 0
\(601\) 20.5526 + 11.8660i 0.838356 + 0.484025i 0.856705 0.515806i \(-0.172508\pi\)
−0.0183488 + 0.999832i \(0.505841\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −2.19615 8.19615i −0.0892863 0.333221i
\(606\) 0 0
\(607\) 8.58846 + 14.8756i 0.348595 + 0.603784i 0.986000 0.166745i \(-0.0533256\pi\)
−0.637405 + 0.770529i \(0.719992\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −18.8756 + 18.8756i −0.763627 + 0.763627i
\(612\) 0 0
\(613\) −15.6603 15.6603i −0.632512 0.632512i 0.316186 0.948697i \(-0.397598\pi\)
−0.948697 + 0.316186i \(0.897598\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −35.0885 + 20.2583i −1.41261 + 0.815570i −0.995633 0.0933485i \(-0.970243\pi\)
−0.416975 + 0.908918i \(0.636910\pi\)
\(618\) 0 0
\(619\) 15.5981 4.17949i 0.626940 0.167988i 0.0686590 0.997640i \(-0.478128\pi\)
0.558281 + 0.829652i \(0.311461\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 2.73205 4.73205i 0.109457 0.189586i
\(624\) 0 0
\(625\) 5.03590 + 8.72243i 0.201436 + 0.348897i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 27.1244 + 27.1244i 1.08152 + 1.08152i
\(630\) 0 0
\(631\) 17.6077i 0.700951i 0.936572 + 0.350476i \(0.113980\pi\)
−0.936572 + 0.350476i \(0.886020\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −1.12436 + 4.19615i −0.0446187 + 0.166519i
\(636\) 0 0
\(637\) −0.418584 1.56218i −0.0165849 0.0618957i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 19.7942 34.2846i 0.781825 1.35416i −0.149053 0.988829i \(-0.547622\pi\)
0.930878 0.365331i \(-0.119044\pi\)
\(642\) 0 0
\(643\) −8.76795 2.34936i −0.345774 0.0926499i 0.0817525 0.996653i \(-0.473948\pi\)
−0.427527 + 0.904003i \(0.640615\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16.7321i 0.657805i −0.944364 0.328902i \(-0.893321\pi\)
0.944364 0.328902i \(-0.106679\pi\)
\(648\) 0 0
\(649\) 33.2487i 1.30513i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 27.4904 + 7.36603i 1.07578 + 0.288255i 0.752867 0.658173i \(-0.228671\pi\)
0.322915 + 0.946428i \(0.395337\pi\)
\(654\) 0 0
\(655\) −4.19615 + 7.26795i −0.163957 + 0.283982i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 4.02628 + 15.0263i 0.156842 + 0.585341i 0.998941 + 0.0460178i \(0.0146531\pi\)
−0.842099 + 0.539323i \(0.818680\pi\)
\(660\) 0 0
\(661\) 2.19615 8.19615i 0.0854204 0.318793i −0.909973 0.414667i \(-0.863898\pi\)
0.995393 + 0.0958740i \(0.0305646\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 9.46410i 0.367002i
\(666\) 0 0
\(667\) 8.19615 + 8.19615i 0.317356 + 0.317356i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 25.3923 + 43.9808i 0.980259 + 1.69786i
\(672\) 0 0
\(673\) 19.1962 33.2487i 0.739957 1.28164i −0.212557 0.977149i \(-0.568179\pi\)
0.952514 0.304495i \(-0.0984877\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 4.73205 1.26795i 0.181867 0.0487312i −0.166736 0.986002i \(-0.553323\pi\)
0.348603 + 0.937270i \(0.386656\pi\)
\(678\) 0 0
\(679\) −27.7583 + 16.0263i −1.06527 + 0.615032i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −20.2942 20.2942i −0.776537 0.776537i 0.202703 0.979240i \(-0.435027\pi\)
−0.979240 + 0.202703i \(0.935027\pi\)
\(684\) 0 0
\(685\) 6.98076 6.98076i 0.266721 0.266721i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −18.3923 31.8564i −0.700691 1.21363i
\(690\) 0 0
\(691\) 2.49038 + 9.29423i 0.0947386 + 0.353569i 0.996980 0.0776628i \(-0.0247457\pi\)
−0.902241 + 0.431232i \(0.858079\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 10.6077 + 6.12436i 0.402373 + 0.232310i
\(696\) 0 0
\(697\) −14.8923 + 8.59808i −0.564086 + 0.325675i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 6.66025 6.66025i 0.251554 0.251554i −0.570053 0.821608i \(-0.693077\pi\)
0.821608 + 0.570053i \(0.193077\pi\)
\(702\) 0 0
\(703\) 22.3923 0.844542
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 5.46410 + 1.46410i 0.205499 + 0.0550632i
\(708\) 0 0
\(709\) 36.5885 9.80385i 1.37411 0.368191i 0.505131 0.863043i \(-0.331444\pi\)
0.868978 + 0.494852i \(0.164778\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 2.19615 + 1.26795i 0.0822466 + 0.0474851i
\(714\) 0 0
\(715\) 4.09103 15.2679i 0.152996 0.570989i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 4.39230 0.163805 0.0819027 0.996640i \(-0.473900\pi\)
0.0819027 + 0.996640i \(0.473900\pi\)
\(720\) 0 0
\(721\) 41.3205 1.53886
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −2.49038 + 9.29423i −0.0924904 + 0.345179i
\(726\) 0 0
\(727\) −28.8109 16.6340i −1.06854 0.616920i −0.140755 0.990044i \(-0.544953\pi\)
−0.927781 + 0.373124i \(0.878286\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 47.7487 12.7942i 1.76605 0.473212i
\(732\) 0 0
\(733\) −11.0263 2.95448i −0.407265 0.109126i 0.0493698 0.998781i \(-0.484279\pi\)
−0.456635 + 0.889654i \(0.650945\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 29.9282 1.10242
\(738\) 0 0
\(739\) 8.22243 8.22243i 0.302467 0.302467i −0.539511 0.841978i \(-0.681391\pi\)
0.841978 + 0.539511i \(0.181391\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −24.7583 + 14.2942i −0.908295 + 0.524404i −0.879882 0.475192i \(-0.842379\pi\)
−0.0284129 + 0.999596i \(0.509045\pi\)
\(744\) 0 0
\(745\) −7.26795 4.19615i −0.266277 0.153735i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 12.4904 + 46.6147i 0.456389 + 1.70327i
\(750\) 0 0
\(751\) 8.85641 + 15.3397i 0.323175 + 0.559755i 0.981141 0.193292i \(-0.0619165\pi\)
−0.657966 + 0.753047i \(0.728583\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0.535898 0.535898i 0.0195033 0.0195033i
\(756\) 0 0
\(757\) −19.9282 19.9282i −0.724303 0.724303i 0.245176 0.969479i \(-0.421154\pi\)
−0.969479 + 0.245176i \(0.921154\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 45.3731 26.1962i 1.64477 0.949610i 0.665669 0.746247i \(-0.268146\pi\)
0.979104 0.203363i \(-0.0651870\pi\)
\(762\) 0 0
\(763\) 40.0526 10.7321i 1.45000 0.388526i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 13.2224 22.9019i 0.477434 0.826941i
\(768\) 0 0
\(769\) −14.1244 24.4641i −0.509337 0.882198i −0.999942 0.0108155i \(-0.996557\pi\)
0.490604 0.871383i \(-0.336776\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) −35.5885 35.5885i −1.28003 1.28003i −0.940650 0.339378i \(-0.889784\pi\)
−0.339378 0.940650i \(-0.610216\pi\)
\(774\) 0 0
\(775\) 2.10512i 0.0756181i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −2.59808 + 9.69615i −0.0930857 + 0.347401i
\(780\) 0 0
\(781\) 3.32051 + 12.3923i 0.118817 + 0.443432i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.53590 + 4.39230i −0.0905101 + 0.156768i
\(786\) 0 0
\(787\) −40.3468 10.8109i −1.43821 0.385367i −0.546302 0.837588i \(-0.683965\pi\)
−0.891906 + 0.452222i \(0.850632\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 37.8564i 1.34602i
\(792\) 0 0
\(793\) 40.3923i 1.43437i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 30.5167 + 8.17691i 1.08096 + 0.289641i 0.754987 0.655740i \(-0.227643\pi\)
0.325968 + 0.945381i \(0.394310\pi\)
\(798\) 0 0
\(799\) 21.9545 38.0263i 0.776694 1.34527i
\(800\) 0 0