Properties

Label 1728.2.bc.a.721.1
Level $1728$
Weight $2$
Character 1728.721
Analytic conductor $13.798$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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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 721.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 1728.721
Dual form 1728.2.bc.a.1009.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.00000 - 0.267949i) q^{5} +(-2.36603 - 1.36603i) q^{7} +O(q^{10})\) \(q+(-1.00000 - 0.267949i) q^{5} +(-2.36603 - 1.36603i) q^{7} +(1.13397 + 4.23205i) q^{11} +(0.901924 - 3.36603i) q^{13} +5.73205 q^{17} +(2.36603 + 2.36603i) q^{19} +(-4.09808 + 2.36603i) q^{23} +(-3.40192 - 1.96410i) q^{25} +(-2.36603 + 0.633975i) q^{29} +(0.267949 + 0.464102i) q^{31} +(2.00000 + 2.00000i) q^{35} +(4.73205 - 4.73205i) q^{37} +(2.59808 - 1.50000i) q^{41} +(-2.23205 - 8.33013i) q^{43} +(3.83013 - 6.63397i) q^{47} +(0.232051 + 0.401924i) q^{49} +(7.46410 - 7.46410i) q^{53} -4.53590i q^{55} +(7.33013 + 1.96410i) q^{59} +(11.1962 - 3.00000i) q^{61} +(-1.80385 + 3.12436i) q^{65} +(1.76795 - 6.59808i) q^{67} +2.92820i q^{71} -6.26795i q^{73} +(3.09808 - 11.5622i) q^{77} +(6.00000 - 10.3923i) q^{79} +(-1.36603 + 0.366025i) q^{83} +(-5.73205 - 1.53590i) q^{85} +2.00000i q^{89} +(-6.73205 + 6.73205i) q^{91} +(-1.73205 - 3.00000i) q^{95} +(-5.86603 + 10.1603i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 4q^{5} - 6q^{7} + O(q^{10}) \) \( 4q - 4q^{5} - 6q^{7} + 8q^{11} + 14q^{13} + 16q^{17} + 6q^{19} - 6q^{23} - 24q^{25} - 6q^{29} + 8q^{31} + 8q^{35} + 12q^{37} - 2q^{43} - 2q^{47} - 6q^{49} + 16q^{53} + 12q^{59} + 24q^{61} - 28q^{65} + 14q^{67} + 2q^{77} + 24q^{79} - 2q^{83} - 16q^{85} - 20q^{91} - 20q^{97} + O(q^{100}) \)

Character values

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

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

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
\(5\) −1.00000 0.267949i −0.447214 0.119831i 0.0281817 0.999603i \(-0.491028\pi\)
−0.475395 + 0.879772i \(0.657695\pi\)
\(6\) 0 0
\(7\) −2.36603 1.36603i −0.894274 0.516309i −0.0189356 0.999821i \(-0.506028\pi\)
−0.875338 + 0.483512i \(0.839361\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) 1.13397 + 4.23205i 0.341906 + 1.27601i 0.896185 + 0.443680i \(0.146327\pi\)
−0.554279 + 0.832331i \(0.687006\pi\)
\(12\) 0 0
\(13\) 0.901924 3.36603i 0.250149 0.933567i −0.720577 0.693375i \(-0.756123\pi\)
0.970725 0.240192i \(-0.0772105\pi\)
\(14\) 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 0.924350 0.381546i \(-0.124608\pi\)
−0.381546 + 0.924350i \(0.624608\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) −4.09808 + 2.36603i −0.854508 + 0.493350i −0.862169 0.506620i \(-0.830895\pi\)
0.00766135 + 0.999971i \(0.497561\pi\)
\(24\) 0 0
\(25\) −3.40192 1.96410i −0.680385 0.392820i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) −2.36603 + 0.633975i −0.439360 + 0.117726i −0.471717 0.881750i \(-0.656365\pi\)
0.0323566 + 0.999476i \(0.489699\pi\)
\(30\) 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 −0.201537 0.979481i \(-0.564594\pi\)
0.979481 + 0.201537i \(0.0645935\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 2.59808 1.50000i 0.405751 0.234261i −0.283211 0.959058i \(-0.591400\pi\)
0.688963 + 0.724797i \(0.258066\pi\)
\(42\) 0 0
\(43\) −2.23205 8.33013i −0.340385 1.27033i −0.897912 0.440174i \(-0.854917\pi\)
0.557528 0.830158i \(-0.311750\pi\)
\(44\) 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 0.0256010 0.999672i \(-0.491850\pi\)
0.999672 0.0256010i \(-0.00814993\pi\)
\(54\) 0 0
\(55\) 4.53590i 0.611620i
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 7.33013 + 1.96410i 0.954301 + 0.255704i 0.702186 0.711993i \(-0.252207\pi\)
0.252115 + 0.967697i \(0.418874\pi\)
\(60\) 0 0
\(61\) 11.1962 3.00000i 1.43352 0.384111i 0.543261 0.839564i \(-0.317189\pi\)
0.890260 + 0.455453i \(0.150523\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) −1.80385 + 3.12436i −0.223740 + 0.387529i
\(66\) 0 0
\(67\) 1.76795 6.59808i 0.215989 0.806083i −0.769827 0.638253i \(-0.779657\pi\)
0.985816 0.167830i \(-0.0536760\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 2.92820i 0.347514i 0.984789 + 0.173757i \(0.0555907\pi\)
−0.984789 + 0.173757i \(0.944409\pi\)
\(72\) 0 0
\(73\) 6.26795i 0.733608i −0.930298 0.366804i \(-0.880452\pi\)
0.930298 0.366804i \(-0.119548\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 3.09808 11.5622i 0.353059 1.31763i
\(78\) 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
\(83\) −1.36603 + 0.366025i −0.149941 + 0.0401765i −0.333009 0.942924i \(-0.608064\pi\)
0.183068 + 0.983100i \(0.441397\pi\)
\(84\) 0 0
\(85\) −5.73205 1.53590i −0.621728 0.166592i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 2.00000i 0.212000i 0.994366 + 0.106000i \(0.0338043\pi\)
−0.994366 + 0.106000i \(0.966196\pi\)
\(90\) 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
\(101\) −0.535898 2.00000i −0.0533239 0.199007i 0.934125 0.356946i \(-0.116182\pi\)
−0.987449 + 0.157938i \(0.949515\pi\)
\(102\) 0 0
\(103\) −13.0981 + 7.56218i −1.29059 + 0.745124i −0.978759 0.205014i \(-0.934276\pi\)
−0.311833 + 0.950137i \(0.600943\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 12.4904 12.4904i 1.20749 1.20749i 0.235654 0.971837i \(-0.424277\pi\)
0.971837 0.235654i \(-0.0757231\pi\)
\(108\) 0 0
\(109\) 10.7321 + 10.7321i 1.02794 + 1.02794i 0.999598 + 0.0283459i \(0.00902398\pi\)
0.0283459 + 0.999598i \(0.490976\pi\)
\(110\) 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
\(115\) 4.73205 1.26795i 0.441266 0.118237i
\(116\) 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
\(131\) 2.09808 7.83013i 0.183310 0.684121i −0.811676 0.584108i \(-0.801445\pi\)
0.994986 0.100014i \(-0.0318887\pi\)
\(132\) 0 0
\(133\) −2.36603 8.83013i −0.205160 0.765669i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.25833 4.76795i −0.705557 0.407353i 0.103857 0.994592i \(-0.466882\pi\)
−0.809414 + 0.587239i \(0.800215\pi\)
\(138\) 0 0
\(139\) 11.4282 + 3.06218i 0.969328 + 0.259731i 0.708544 0.705667i \(-0.249352\pi\)
0.260784 + 0.965397i \(0.416019\pi\)
\(140\) 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
\(149\) −7.83013 2.09808i −0.641469 0.171881i −0.0766003 0.997062i \(-0.524407\pi\)
−0.564869 + 0.825181i \(0.691073\pi\)
\(150\) 0 0
\(151\) −0.633975 0.366025i −0.0515921 0.0297867i 0.473982 0.880534i \(-0.342816\pi\)
−0.525574 + 0.850748i \(0.676149\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.143594 0.535898i −0.0115337 0.0430444i
\(156\) 0 0
\(157\) 1.26795 4.73205i 0.101193 0.377659i −0.896692 0.442655i \(-0.854037\pi\)
0.997886 + 0.0649959i \(0.0207034\pi\)
\(158\) 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 0.925944 0.377661i \(-0.123272\pi\)
−0.377661 + 0.925944i \(0.623272\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 6.46410 3.73205i 0.500207 0.288795i −0.228592 0.973522i \(-0.573412\pi\)
0.728799 + 0.684728i \(0.240079\pi\)
\(168\) 0 0
\(169\) 0.741670 + 0.428203i 0.0570515 + 0.0329387i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) −1.63397 + 0.437822i −0.124229 + 0.0332870i −0.320398 0.947283i \(-0.603817\pi\)
0.196169 + 0.980570i \(0.437150\pi\)
\(174\) 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 0.631365 0.775486i \(-0.282495\pi\)
−0.775486 + 0.631365i \(0.782495\pi\)
\(180\) 0 0
\(181\) −7.39230 + 7.39230i −0.549466 + 0.549466i −0.926286 0.376821i \(-0.877017\pi\)
0.376821 + 0.926286i \(0.377017\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −6.00000 + 3.46410i −0.441129 + 0.254686i
\(186\) 0 0
\(187\) 6.50000 + 24.2583i 0.475327 + 1.77394i
\(188\) 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 −0.999651 0.0263987i \(-0.991596\pi\)
0.0263987 + 0.999651i \(0.491596\pi\)
\(198\) 0 0
\(199\) 25.1244i 1.78102i −0.454965 0.890509i \(-0.650348\pi\)
0.454965 0.890509i \(-0.349652\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.46410 + 1.73205i 0.453691 + 0.121566i
\(204\) 0 0
\(205\) −3.00000 + 0.803848i −0.209529 + 0.0561432i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7.33013 + 12.6962i −0.507035 + 0.878211i
\(210\) 0 0
\(211\) 1.09808 4.09808i 0.0755947 0.282123i −0.917773 0.397106i \(-0.870015\pi\)
0.993367 + 0.114983i \(0.0366812\pi\)
\(212\) 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
\(221\) 5.16987 19.2942i 0.347763 1.29787i
\(222\) 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
\(227\) 2.13397 0.571797i 0.141637 0.0379515i −0.187304 0.982302i \(-0.559975\pi\)
0.328941 + 0.944351i \(0.393308\pi\)
\(228\) 0 0
\(229\) 6.83013 + 1.83013i 0.451347 + 0.120938i 0.477330 0.878724i \(-0.341605\pi\)
−0.0259823 + 0.999662i \(0.508271\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 3.19615i 0.209387i 0.994505 + 0.104693i \(0.0333861\pi\)
−0.994505 + 0.104693i \(0.966614\pi\)
\(234\) 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
\(245\) −0.124356 0.464102i −0.00794479 0.0296504i
\(246\) 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 −0.866745 0.498751i \(-0.833792\pi\)
0.498751 + 0.866745i \(0.333792\pi\)
\(252\) 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
\(259\) −17.6603 + 4.73205i −1.09735 + 0.294035i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −2.49038 1.43782i −0.153563 0.0886599i 0.421249 0.906945i \(-0.361592\pi\)
−0.574813 + 0.818285i \(0.694925\pi\)
\(264\) 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 0.667395 0.744704i \(-0.267409\pi\)
−0.744704 + 0.667395i \(0.767409\pi\)
\(270\) 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
\(275\) 4.45448 16.6244i 0.268615 1.00249i
\(276\) 0 0
\(277\) −6.75833 25.2224i −0.406069 1.51547i −0.802076 0.597222i \(-0.796271\pi\)
0.396007 0.918247i \(-0.370395\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 8.66025 + 5.00000i 0.516627 + 0.298275i 0.735554 0.677466i \(-0.236922\pi\)
−0.218926 + 0.975741i \(0.570255\pi\)
\(282\) 0 0
\(283\) 19.5622 + 5.24167i 1.16285 + 0.311585i 0.788104 0.615542i \(-0.211063\pi\)
0.374747 + 0.927127i \(0.377730\pi\)
\(284\) 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
\(293\) 5.36603 + 1.43782i 0.313487 + 0.0839985i 0.412132 0.911124i \(-0.364784\pi\)
−0.0986454 + 0.995123i \(0.531451\pi\)
\(294\) 0 0
\(295\) −6.80385 3.92820i −0.396135 0.228709i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 4.26795 + 15.9282i 0.246822 + 0.921152i
\(300\) 0 0
\(301\) −6.09808 + 22.7583i −0.351487 + 1.31177i
\(302\) 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 0.615454 0.788173i \(-0.288973\pi\)
−0.788173 + 0.615454i \(0.788973\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) −19.0981 + 11.0263i −1.08295 + 0.625243i −0.931691 0.363251i \(-0.881667\pi\)
−0.151261 + 0.988494i \(0.548333\pi\)
\(312\) 0 0
\(313\) 18.6506 + 10.7679i 1.05420 + 0.608640i 0.923821 0.382824i \(-0.125049\pi\)
0.130375 + 0.991465i \(0.458382\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.5622 5.50962i 1.15489 0.309451i 0.369965 0.929046i \(-0.379370\pi\)
0.784922 + 0.619595i \(0.212703\pi\)
\(318\) 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
\(331\) −0.0262794 0.0980762i −0.00144445 0.00539076i 0.965200 0.261513i \(-0.0842216\pi\)
−0.966644 + 0.256123i \(0.917555\pi\)
\(332\) 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
\(347\) −17.6244 4.72243i −0.946125 0.253513i −0.247408 0.968911i \(-0.579579\pi\)
−0.698717 + 0.715398i \(0.746245\pi\)
\(348\) 0 0
\(349\) 15.9282 4.26795i 0.852617 0.228458i 0.194061 0.980989i \(-0.437834\pi\)
0.658556 + 0.752531i \(0.271167\pi\)
\(350\) 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
\(355\) 0.784610 2.92820i 0.0416428 0.155413i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 11.2679i 0.594700i 0.954769 + 0.297350i \(0.0961028\pi\)
−0.954769 + 0.297350i \(0.903897\pi\)
\(360\) 0 0
\(361\) 7.80385i 0.410729i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) −1.67949 + 6.26795i −0.0879086 + 0.328079i
\(366\) 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
\(371\) −27.8564 + 7.46410i −1.44623 + 0.387517i
\(372\) 0 0
\(373\) 27.4904 + 7.36603i 1.42340 + 0.381398i 0.886688 0.462368i \(-0.153000\pi\)
0.536710 + 0.843767i \(0.319667\pi\)
\(374\) 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 −0.797014 0.603961i \(-0.793588\pi\)
0.603961 + 0.797014i \(0.293588\pi\)
\(380\) 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
\(389\) 5.29423 + 19.7583i 0.268428 + 1.00179i 0.960119 + 0.279593i \(0.0901996\pi\)
−0.691691 + 0.722194i \(0.743134\pi\)
\(390\) 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 0.435192 0.900337i \(-0.356680\pi\)
−0.900337 + 0.435192i \(0.856680\pi\)
\(398\) 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
\(403\) 1.80385 0.483340i 0.0898560 0.0240769i
\(404\) 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 0.385981 0.922507i \(-0.373863\pi\)
0.991905 + 0.126984i \(0.0405295\pi\)
\(410\) 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
\(419\) 1.77757 6.63397i 0.0868399 0.324091i −0.908816 0.417196i \(-0.863013\pi\)
0.995656 + 0.0931055i \(0.0296794\pi\)
\(420\) 0 0
\(421\) 8.19615 + 30.5885i 0.399456 + 1.49079i 0.814056 + 0.580786i \(0.197255\pi\)
−0.414600 + 0.910004i \(0.636078\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) −19.5000 11.2583i −0.945889 0.546109i
\(426\) 0 0
\(427\) −30.5885 8.19615i −1.48028 0.396640i
\(428\) 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
\(437\) −15.2942 4.09808i −0.731622 0.196038i
\(438\) 0 0
\(439\) 22.8564 + 13.1962i 1.09088 + 0.629818i 0.933810 0.357770i \(-0.116463\pi\)
0.157067 + 0.987588i \(0.449796\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −4.62436 17.2583i −0.219710 0.819968i −0.984455 0.175636i \(-0.943802\pi\)
0.764745 0.644332i \(-0.222865\pi\)
\(444\) 0 0
\(445\) 0.535898 2.00000i 0.0254040 0.0948091i
\(446\) 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 0.551889 0.833917i \(-0.313907\pi\)
−0.446249 + 0.894909i \(0.647240\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) −35.6865 + 9.56218i −1.66209 + 0.445355i −0.962961 0.269642i \(-0.913094\pi\)
−0.699127 + 0.714997i \(0.746428\pi\)
\(462\) 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 0.765419 0.643533i \(-0.222532\pi\)
−0.643533 + 0.765419i \(0.722532\pi\)
\(468\) 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
\(475\) −3.40192 12.6962i −0.156091 0.582539i
\(476\) 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 \(-0.958021\pi\)
0.991316 0.131499i \(-0.0419789\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −13.8923 3.72243i −0.626951 0.167991i −0.0686652 0.997640i \(-0.521874\pi\)
−0.558286 + 0.829649i \(0.688541\pi\)
\(492\) 0 0
\(493\) −13.5622 + 3.63397i −0.610810 + 0.163666i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 4.00000 6.92820i 0.179425 0.310772i
\(498\) 0 0
\(499\) 2.33013 8.69615i 0.104311 0.389293i −0.893955 0.448156i \(-0.852081\pi\)
0.998266 + 0.0588630i \(0.0187475\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 27.7128i 1.23565i −0.786314 0.617827i \(-0.788013\pi\)
0.786314 0.617827i \(-0.211987\pi\)
\(504\) 0 0
\(505\) 2.14359i 0.0953887i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −3.07180 + 11.4641i −0.136155 + 0.508137i 0.863835 + 0.503774i \(0.168056\pi\)
−0.999990 + 0.00436335i \(0.998611\pi\)
\(510\) 0 0
\(511\) −8.56218 + 14.8301i −0.378768 + 0.656046i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 15.1244 4.05256i 0.666459 0.178577i
\(516\) 0 0
\(517\) 32.4186 + 8.68653i 1.42577 + 0.382033i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 13.0000i 0.569540i −0.958596 0.284770i \(-0.908083\pi\)
0.958596 0.284770i \(-0.0919173\pi\)
\(522\) 0 0
\(523\) 7.53590 7.53590i 0.329522 0.329522i −0.522883 0.852405i \(-0.675143\pi\)
0.852405 + 0.522883i \(0.175143\pi\)
\(524\) 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
\(533\) −2.70577 10.0981i −0.117200 0.437396i
\(534\) 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 0.752739 0.658319i \(-0.228732\pi\)
−0.658319 + 0.752739i \(0.728732\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −7.85641 13.6077i −0.336531 0.582890i
\(546\) 0 0
\(547\) −32.6244 + 8.74167i −1.39492 + 0.373767i −0.876517 0.481371i \(-0.840139\pi\)
−0.518400 + 0.855138i \(0.673472\pi\)
\(548\) 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 0.947378 0.320118i \(-0.103723\pi\)
−0.320118 + 0.947378i \(0.603723\pi\)
\(558\) 0 0
\(559\) −30.0526 −1.27109
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) −7.23205 + 26.9904i −0.304795 + 1.13751i 0.628327 + 0.777949i \(0.283740\pi\)
−0.933122 + 0.359560i \(0.882927\pi\)
\(564\) 0 0
\(565\) −3.71281 13.8564i −0.156199 0.582943i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 18.4019 + 10.6244i 0.771449 + 0.445396i 0.833391 0.552684i \(-0.186396\pi\)
−0.0619424 + 0.998080i \(0.519730\pi\)
\(570\) 0 0
\(571\) 3.33013 + 0.892305i 0.139361 + 0.0373418i 0.327825 0.944738i \(-0.393684\pi\)
−0.188464 + 0.982080i \(0.560351\pi\)
\(572\) 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
\(581\) 3.73205 + 1.00000i 0.154832 + 0.0414870i
\(582\) 0 0
\(583\) 40.0526 + 23.1244i 1.65881 + 0.957713i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 7.23205 + 26.9904i 0.298499 + 1.11401i 0.938399 + 0.345554i \(0.112309\pi\)
−0.639900 + 0.768458i \(0.721024\pi\)
\(588\) 0 0
\(589\) −0.464102 + 1.73205i −0.0191230 + 0.0713679i
\(590\) 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 −0.250570 0.968099i \(-0.580618\pi\)
0.713113 + 0.701049i \(0.247285\pi\)
\(600\) 0 0
\(601\) −20.5526 11.8660i −0.838356 0.484025i 0.0183488 0.999832i \(-0.494159\pi\)
−0.856705 + 0.515806i \(0.827492\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 8.19615 2.19615i 0.333221 0.0892863i
\(606\) 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 −0.948697 0.316186i \(-0.897598\pi\)
0.316186 + 0.948697i \(0.397598\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 35.0885 20.2583i 1.41261 0.815570i 0.416975 0.908918i \(-0.363090\pi\)
0.995633 + 0.0933485i \(0.0297571\pi\)
\(618\) 0 0
\(619\) −4.17949 15.5981i −0.167988 0.626940i −0.997640 0.0686590i \(-0.978128\pi\)
0.829652 0.558281i \(-0.188539\pi\)
\(620\) 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 \(-0.886020\pi\)
0.936572 0.350476i \(-0.113980\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 4.19615 + 1.12436i 0.166519 + 0.0446187i
\(636\) 0 0
\(637\) 1.56218 0.418584i 0.0618957 0.0165849i
\(638\) 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
\(643\) 2.34936 8.76795i 0.0926499 0.345774i −0.904003 0.427527i \(-0.859385\pi\)
0.996653 + 0.0817525i \(0.0260517\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 16.7321i 0.657805i 0.944364 + 0.328902i \(0.106679\pi\)
−0.944364 + 0.328902i \(0.893321\pi\)
\(648\) 0 0
\(649\) 33.2487i 1.30513i
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −7.36603 + 27.4904i −0.288255 + 1.07578i 0.658173 + 0.752867i \(0.271329\pi\)
−0.946428 + 0.322915i \(0.895337\pi\)
\(654\) 0 0
\(655\) −4.19615 + 7.26795i −0.163957 + 0.283982i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −15.0263 + 4.02628i −0.585341 + 0.156842i −0.539323 0.842099i \(-0.681320\pi\)
−0.0460178 + 0.998941i \(0.514653\pi\)
\(660\) 0 0
\(661\) −8.19615 2.19615i −0.318793 0.0854204i 0.0958740 0.995393i \(-0.469435\pi\)
−0.414667 + 0.909973i \(0.636102\pi\)
\(662\) 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
\(677\) −1.26795 4.73205i −0.0487312 0.181867i 0.937270 0.348603i \(-0.113344\pi\)
−0.986002 + 0.166736i \(0.946677\pi\)
\(678\) 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 −0.979240 0.202703i \(-0.935027\pi\)
0.202703 + 0.979240i \(0.435027\pi\)
\(684\) 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
\(691\) −9.29423 + 2.49038i −0.353569 + 0.0947386i −0.431232 0.902241i \(-0.641921\pi\)
0.0776628 + 0.996980i \(0.475254\pi\)
\(692\) 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 0.821608 0.570053i \(-0.193077\pi\)
−0.570053 + 0.821608i \(0.693077\pi\)
\(702\) 0 0
\(703\) 22.3923 0.844542
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.46410 + 5.46410i −0.0550632 + 0.205499i
\(708\) 0 0
\(709\) −9.80385 36.5885i −0.368191 1.37411i −0.863043 0.505131i \(-0.831444\pi\)
0.494852 0.868978i \(-0.335222\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −2.19615 1.26795i −0.0822466 0.0474851i
\(714\) 0 0
\(715\) −15.2679 4.09103i −0.570989 0.152996i
\(716\) 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
\(725\) 9.29423 + 2.49038i 0.345179 + 0.0924904i
\(726\) 0 0
\(727\) 28.8109 + 16.6340i 1.06854 + 0.616920i 0.927781 0.373124i \(-0.121714\pi\)
0.140755 + 0.990044i \(0.455047\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) −12.7942 47.7487i −0.473212 1.76605i
\(732\) 0 0
\(733\) 2.95448 11.0263i 0.109126 0.407265i −0.889654 0.456635i \(-0.849055\pi\)
0.998781 + 0.0493698i \(0.0157213\pi\)
\(734\) 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 0.841978 0.539511i \(-0.181391\pi\)
−0.539511 + 0.841978i \(0.681391\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.7583 14.2942i 0.908295 0.524404i 0.0284129 0.999596i \(-0.490955\pi\)
0.879882 + 0.475192i \(0.157621\pi\)
\(744\) 0 0
\(745\) 7.26795 + 4.19615i 0.266277 + 0.153735i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) −46.6147 + 12.4904i −1.70327 + 0.456389i
\(750\) 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 −0.969479 0.245176i \(-0.921154\pi\)
0.245176 + 0.969479i \(0.421154\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −45.3731 + 26.1962i −1.64477 + 0.949610i −0.665669 + 0.746247i \(0.731854\pi\)
−0.979104 + 0.203363i \(0.934813\pi\)
\(762\) 0 0
\(763\) −10.7321 40.0526i −0.388526 1.45000i
\(764\) 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 −0.339378 + 0.940650i \(0.610216\pi\)
−0.940650 + 0.339378i \(0.889784\pi\)
\(774\) 0 0
\(775\) 2.10512i 0.0756181i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 9.69615 + 2.59808i 0.347401 + 0.0930857i
\(780\) 0 0
\(781\) −12.3923 + 3.32051i −0.443432 + 0.118817i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −2.53590 + 4.39230i −0.0905101 + 0.156768i
\(786\) 0 0
\(787\) 10.8109 40.3468i 0.385367 1.43821i −0.452222 0.891906i \(-0.649368\pi\)
0.837588 0.546302i \(-0.183965\pi\)
\(788\) 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
\(797\) −8.17691 + 30.5167i −0.289641 + 1.08096i 0.655740 + 0.754987i \(0.272357\pi\)
−0.945381 + 0.325968i \(0.894310\pi\)
\(798\) 0 0
\(799\) 21.9545 38.0263i 0.776694 1.34527i
\(800\) 0 0