Properties

Label 1600.2.l.f.401.3
Level $1600$
Weight $2$
Character 1600.401
Analytic conductor $12.776$
Analytic rank $0$
Dimension $12$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.l (of order \(4\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(12.7760643234\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(6\) over \(\Q(i)\)
Coefficient field: 12.0.4767670494822400.1
Defining polynomial: \(x^{12} - 4 x^{11} + 7 x^{10} - 4 x^{9} - 8 x^{8} + 24 x^{7} - 38 x^{6} + 48 x^{5} - 32 x^{4} - 32 x^{3} + 112 x^{2} - 128 x + 64\)
Coefficient ring: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 2^{7} \)
Twist minimal: no (minimal twist has level 400)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 401.3
Root \(-1.41313 + 0.0554252i\) of defining polynomial
Character \(\chi\) \(=\) 1600.401
Dual form 1600.2.l.f.1201.3

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.488516 - 0.488516i) q^{3} -4.71540i q^{7} -2.52270i q^{9} +O(q^{10})\) \(q+(-0.488516 - 0.488516i) q^{3} -4.71540i q^{7} -2.52270i q^{9} +(3.91360 - 3.91360i) q^{11} +(0.0878822 + 0.0878822i) q^{13} -4.67442 q^{17} +(-1.81249 - 1.81249i) q^{19} +(-2.30355 + 2.30355i) q^{21} +1.63007i q^{23} +(-2.69793 + 2.69793i) q^{27} +(3.26362 + 3.26362i) q^{29} +2.12875 q^{31} -3.82371 q^{33} +(-3.97797 + 3.97797i) q^{37} -0.0858637i q^{39} +8.25504i q^{41} +(2.27336 - 2.27336i) q^{43} -4.06129 q^{47} -15.2350 q^{49} +(2.28353 + 2.28353i) q^{51} +(5.03938 - 5.03938i) q^{53} +1.77086i q^{57} +(5.16453 - 5.16453i) q^{59} +(7.12726 + 7.12726i) q^{61} -11.8956 q^{63} +(-7.49920 - 7.49920i) q^{67} +(0.796314 - 0.796314i) q^{69} +4.54072i q^{71} -8.30557i q^{73} +(-18.4542 - 18.4542i) q^{77} -11.5317 q^{79} -4.93215 q^{81} +(-1.16919 - 1.16919i) q^{83} -3.18866i q^{87} -3.24572i q^{89} +(0.414400 - 0.414400i) q^{91} +(-1.03993 - 1.03993i) q^{93} +13.9581 q^{97} +(-9.87285 - 9.87285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q - 2q^{3} + O(q^{10}) \) \( 12q - 2q^{3} + 2q^{11} - 4q^{13} - 8q^{17} + 14q^{19} - 20q^{21} + 10q^{27} + 4q^{31} + 28q^{33} + 8q^{37} - 8q^{47} + 4q^{49} - 10q^{51} - 16q^{53} - 20q^{59} + 4q^{61} + 8q^{63} - 50q^{67} - 8q^{77} - 12q^{79} - 8q^{81} + 2q^{83} - 44q^{93} - 12q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).

\(n\) \(577\) \(901\) \(1151\)
\(\chi(n)\) \(1\) \(e\left(\frac{3}{4}\right)\) \(1\)

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
\(3\) −0.488516 0.488516i −0.282045 0.282045i 0.551879 0.833924i \(-0.313911\pi\)
−0.833924 + 0.551879i \(0.813911\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) 4.71540i 1.78226i −0.453753 0.891128i \(-0.649915\pi\)
0.453753 0.891128i \(-0.350085\pi\)
\(8\) 0 0
\(9\) 2.52270i 0.840901i
\(10\) 0 0
\(11\) 3.91360 3.91360i 1.17999 1.17999i 0.200249 0.979745i \(-0.435825\pi\)
0.979745 0.200249i \(-0.0641750\pi\)
\(12\) 0 0
\(13\) 0.0878822 + 0.0878822i 0.0243741 + 0.0243741i 0.719189 0.694815i \(-0.244514\pi\)
−0.694815 + 0.719189i \(0.744514\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.67442 −1.13371 −0.566857 0.823816i \(-0.691841\pi\)
−0.566857 + 0.823816i \(0.691841\pi\)
\(18\) 0 0
\(19\) −1.81249 1.81249i −0.415813 0.415813i 0.467945 0.883758i \(-0.344995\pi\)
−0.883758 + 0.467945i \(0.844995\pi\)
\(20\) 0 0
\(21\) −2.30355 + 2.30355i −0.502676 + 0.502676i
\(22\) 0 0
\(23\) 1.63007i 0.339893i 0.985453 + 0.169946i \(0.0543594\pi\)
−0.985453 + 0.169946i \(0.945641\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) −2.69793 + 2.69793i −0.519217 + 0.519217i
\(28\) 0 0
\(29\) 3.26362 + 3.26362i 0.606039 + 0.606039i 0.941909 0.335869i \(-0.109030\pi\)
−0.335869 + 0.941909i \(0.609030\pi\)
\(30\) 0 0
\(31\) 2.12875 0.382334 0.191167 0.981557i \(-0.438773\pi\)
0.191167 + 0.981557i \(0.438773\pi\)
\(32\) 0 0
\(33\) −3.82371 −0.665622
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) −3.97797 + 3.97797i −0.653974 + 0.653974i −0.953948 0.299973i \(-0.903022\pi\)
0.299973 + 0.953948i \(0.403022\pi\)
\(38\) 0 0
\(39\) 0.0858637i 0.0137492i
\(40\) 0 0
\(41\) 8.25504i 1.28922i 0.764511 + 0.644611i \(0.222980\pi\)
−0.764511 + 0.644611i \(0.777020\pi\)
\(42\) 0 0
\(43\) 2.27336 2.27336i 0.346685 0.346685i −0.512188 0.858873i \(-0.671165\pi\)
0.858873 + 0.512188i \(0.171165\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −4.06129 −0.592400 −0.296200 0.955126i \(-0.595719\pi\)
−0.296200 + 0.955126i \(0.595719\pi\)
\(48\) 0 0
\(49\) −15.2350 −2.17643
\(50\) 0 0
\(51\) 2.28353 + 2.28353i 0.319758 + 0.319758i
\(52\) 0 0
\(53\) 5.03938 5.03938i 0.692211 0.692211i −0.270507 0.962718i \(-0.587191\pi\)
0.962718 + 0.270507i \(0.0871912\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 1.77086i 0.234556i
\(58\) 0 0
\(59\) 5.16453 5.16453i 0.672365 0.672365i −0.285896 0.958261i \(-0.592291\pi\)
0.958261 + 0.285896i \(0.0922911\pi\)
\(60\) 0 0
\(61\) 7.12726 + 7.12726i 0.912552 + 0.912552i 0.996472 0.0839206i \(-0.0267442\pi\)
−0.0839206 + 0.996472i \(0.526744\pi\)
\(62\) 0 0
\(63\) −11.8956 −1.49870
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −7.49920 7.49920i −0.916173 0.916173i 0.0805758 0.996748i \(-0.474324\pi\)
−0.996748 + 0.0805758i \(0.974324\pi\)
\(68\) 0 0
\(69\) 0.796314 0.796314i 0.0958649 0.0958649i
\(70\) 0 0
\(71\) 4.54072i 0.538884i 0.963017 + 0.269442i \(0.0868393\pi\)
−0.963017 + 0.269442i \(0.913161\pi\)
\(72\) 0 0
\(73\) 8.30557i 0.972093i −0.873933 0.486047i \(-0.838439\pi\)
0.873933 0.486047i \(-0.161561\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −18.4542 18.4542i −2.10305 2.10305i
\(78\) 0 0
\(79\) −11.5317 −1.29742 −0.648709 0.761037i \(-0.724691\pi\)
−0.648709 + 0.761037i \(0.724691\pi\)
\(80\) 0 0
\(81\) −4.93215 −0.548017
\(82\) 0 0
\(83\) −1.16919 1.16919i −0.128335 0.128335i 0.640022 0.768357i \(-0.278925\pi\)
−0.768357 + 0.640022i \(0.778925\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 3.18866i 0.341861i
\(88\) 0 0
\(89\) 3.24572i 0.344046i −0.985093 0.172023i \(-0.944970\pi\)
0.985093 0.172023i \(-0.0550304\pi\)
\(90\) 0 0
\(91\) 0.414400 0.414400i 0.0434409 0.0434409i
\(92\) 0 0
\(93\) −1.03993 1.03993i −0.107835 0.107835i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 13.9581 1.41723 0.708613 0.705598i \(-0.249321\pi\)
0.708613 + 0.705598i \(0.249321\pi\)
\(98\) 0 0
\(99\) −9.87285 9.87285i −0.992258 0.992258i
\(100\) 0 0
\(101\) 13.4088 13.4088i 1.33422 1.33422i 0.432672 0.901552i \(-0.357571\pi\)
0.901552 0.432672i \(-0.142429\pi\)
\(102\) 0 0
\(103\) 13.7638i 1.35618i 0.734977 + 0.678092i \(0.237193\pi\)
−0.734977 + 0.678092i \(0.762807\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −0.327996 + 0.327996i −0.0317086 + 0.0317086i −0.722783 0.691075i \(-0.757138\pi\)
0.691075 + 0.722783i \(0.257138\pi\)
\(108\) 0 0
\(109\) −0.149698 0.149698i −0.0143385 0.0143385i 0.699901 0.714240i \(-0.253227\pi\)
−0.714240 + 0.699901i \(0.753227\pi\)
\(110\) 0 0
\(111\) 3.88660 0.368900
\(112\) 0 0
\(113\) −5.97999 −0.562550 −0.281275 0.959627i \(-0.590757\pi\)
−0.281275 + 0.959627i \(0.590757\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.221701 0.221701i 0.0204962 0.0204962i
\(118\) 0 0
\(119\) 22.0418i 2.02057i
\(120\) 0 0
\(121\) 19.6325i 1.78477i
\(122\) 0 0
\(123\) 4.03272 4.03272i 0.363618 0.363618i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) −2.73076 −0.242315 −0.121158 0.992633i \(-0.538661\pi\)
−0.121158 + 0.992633i \(0.538661\pi\)
\(128\) 0 0
\(129\) −2.22115 −0.195561
\(130\) 0 0
\(131\) 0.813555 + 0.813555i 0.0710806 + 0.0710806i 0.741753 0.670673i \(-0.233994\pi\)
−0.670673 + 0.741753i \(0.733994\pi\)
\(132\) 0 0
\(133\) −8.54661 + 8.54661i −0.741085 + 0.741085i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.199812i 0.0170711i 0.999964 + 0.00853557i \(0.00271699\pi\)
−0.999964 + 0.00853557i \(0.997283\pi\)
\(138\) 0 0
\(139\) 11.6301 11.6301i 0.986448 0.986448i −0.0134610 0.999909i \(-0.504285\pi\)
0.999909 + 0.0134610i \(0.00428488\pi\)
\(140\) 0 0
\(141\) 1.98400 + 1.98400i 0.167083 + 0.167083i
\(142\) 0 0
\(143\) 0.687871 0.0575227
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 7.44256 + 7.44256i 0.613852 + 0.613852i
\(148\) 0 0
\(149\) −1.13384 + 1.13384i −0.0928880 + 0.0928880i −0.752024 0.659136i \(-0.770922\pi\)
0.659136 + 0.752024i \(0.270922\pi\)
\(150\) 0 0
\(151\) 7.12216i 0.579593i 0.957088 + 0.289797i \(0.0935877\pi\)
−0.957088 + 0.289797i \(0.906412\pi\)
\(152\) 0 0
\(153\) 11.7922i 0.953341i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 5.32145 + 5.32145i 0.424698 + 0.424698i 0.886818 0.462120i \(-0.152911\pi\)
−0.462120 + 0.886818i \(0.652911\pi\)
\(158\) 0 0
\(159\) −4.92363 −0.390469
\(160\) 0 0
\(161\) 7.68643 0.605775
\(162\) 0 0
\(163\) −12.3010 12.3010i −0.963488 0.963488i 0.0358685 0.999357i \(-0.488580\pi\)
−0.999357 + 0.0358685i \(0.988580\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 9.86820i 0.763624i −0.924240 0.381812i \(-0.875300\pi\)
0.924240 0.381812i \(-0.124700\pi\)
\(168\) 0 0
\(169\) 12.9846i 0.998812i
\(170\) 0 0
\(171\) −4.57237 + 4.57237i −0.349658 + 0.349658i
\(172\) 0 0
\(173\) 13.4089 + 13.4089i 1.01946 + 1.01946i 0.999807 + 0.0196525i \(0.00625599\pi\)
0.0196525 + 0.999807i \(0.493744\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −5.04591 −0.379274
\(178\) 0 0
\(179\) −0.419587 0.419587i −0.0313614 0.0313614i 0.691252 0.722614i \(-0.257059\pi\)
−0.722614 + 0.691252i \(0.757059\pi\)
\(180\) 0 0
\(181\) −14.2605 + 14.2605i −1.05998 + 1.05998i −0.0618956 + 0.998083i \(0.519715\pi\)
−0.998083 + 0.0618956i \(0.980285\pi\)
\(182\) 0 0
\(183\) 6.96356i 0.514761i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −18.2938 + 18.2938i −1.33777 + 1.33777i
\(188\) 0 0
\(189\) 12.7218 + 12.7218i 0.925377 + 0.925377i
\(190\) 0 0
\(191\) −17.3304 −1.25399 −0.626993 0.779025i \(-0.715715\pi\)
−0.626993 + 0.779025i \(0.715715\pi\)
\(192\) 0 0
\(193\) −16.8667 −1.21409 −0.607045 0.794667i \(-0.707645\pi\)
−0.607045 + 0.794667i \(0.707645\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 3.58908 3.58908i 0.255712 0.255712i −0.567596 0.823307i \(-0.692126\pi\)
0.823307 + 0.567596i \(0.192126\pi\)
\(198\) 0 0
\(199\) 6.64501i 0.471052i 0.971868 + 0.235526i \(0.0756813\pi\)
−0.971868 + 0.235526i \(0.924319\pi\)
\(200\) 0 0
\(201\) 7.32695i 0.516803i
\(202\) 0 0
\(203\) 15.3893 15.3893i 1.08012 1.08012i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 4.11218 0.285816
\(208\) 0 0
\(209\) −14.1867 −0.981314
\(210\) 0 0
\(211\) −1.90906 1.90906i −0.131425 0.131425i 0.638334 0.769759i \(-0.279624\pi\)
−0.769759 + 0.638334i \(0.779624\pi\)
\(212\) 0 0
\(213\) 2.21821 2.21821i 0.151989 0.151989i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 10.0379i 0.681418i
\(218\) 0 0
\(219\) −4.05740 + 4.05740i −0.274174 + 0.274174i
\(220\) 0 0
\(221\) −0.410798 0.410798i −0.0276333 0.0276333i
\(222\) 0 0
\(223\) 24.1071 1.61433 0.807165 0.590326i \(-0.201001\pi\)
0.807165 + 0.590326i \(0.201001\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 6.67411 + 6.67411i 0.442977 + 0.442977i 0.893011 0.450035i \(-0.148588\pi\)
−0.450035 + 0.893011i \(0.648588\pi\)
\(228\) 0 0
\(229\) 16.0807 16.0807i 1.06264 1.06264i 0.0647388 0.997902i \(-0.479379\pi\)
0.997902 0.0647388i \(-0.0206214\pi\)
\(230\) 0 0
\(231\) 18.0303i 1.18631i
\(232\) 0 0
\(233\) 16.4976i 1.08079i −0.841411 0.540396i \(-0.818274\pi\)
0.841411 0.540396i \(-0.181726\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 5.63342 + 5.63342i 0.365930 + 0.365930i
\(238\) 0 0
\(239\) −5.25917 −0.340188 −0.170094 0.985428i \(-0.554407\pi\)
−0.170094 + 0.985428i \(0.554407\pi\)
\(240\) 0 0
\(241\) −14.1126 −0.909075 −0.454538 0.890728i \(-0.650196\pi\)
−0.454538 + 0.890728i \(0.650196\pi\)
\(242\) 0 0
\(243\) 10.5032 + 10.5032i 0.673782 + 0.673782i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0.318571i 0.0202702i
\(248\) 0 0
\(249\) 1.14234i 0.0723927i
\(250\) 0 0
\(251\) 9.98825 9.98825i 0.630453 0.630453i −0.317729 0.948182i \(-0.602920\pi\)
0.948182 + 0.317729i \(0.102920\pi\)
\(252\) 0 0
\(253\) 6.37943 + 6.37943i 0.401071 + 0.401071i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.44760 0.526947 0.263474 0.964667i \(-0.415132\pi\)
0.263474 + 0.964667i \(0.415132\pi\)
\(258\) 0 0
\(259\) 18.7577 + 18.7577i 1.16555 + 1.16555i
\(260\) 0 0
\(261\) 8.23315 8.23315i 0.509619 0.509619i
\(262\) 0 0
\(263\) 18.3064i 1.12882i −0.825494 0.564410i \(-0.809104\pi\)
0.825494 0.564410i \(-0.190896\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −1.58559 + 1.58559i −0.0970364 + 0.0970364i
\(268\) 0 0
\(269\) 13.5631 + 13.5631i 0.826955 + 0.826955i 0.987094 0.160140i \(-0.0511945\pi\)
−0.160140 + 0.987094i \(0.551194\pi\)
\(270\) 0 0
\(271\) 2.24520 0.136386 0.0681930 0.997672i \(-0.478277\pi\)
0.0681930 + 0.997672i \(0.478277\pi\)
\(272\) 0 0
\(273\) −0.404882 −0.0245046
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) −7.28255 + 7.28255i −0.437566 + 0.437566i −0.891192 0.453626i \(-0.850130\pi\)
0.453626 + 0.891192i \(0.350130\pi\)
\(278\) 0 0
\(279\) 5.37020i 0.321506i
\(280\) 0 0
\(281\) 6.04084i 0.360367i −0.983633 0.180183i \(-0.942331\pi\)
0.983633 0.180183i \(-0.0576691\pi\)
\(282\) 0 0
\(283\) −15.1350 + 15.1350i −0.899682 + 0.899682i −0.995408 0.0957259i \(-0.969483\pi\)
0.0957259 + 0.995408i \(0.469483\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 38.9259 2.29772
\(288\) 0 0
\(289\) 4.85021 0.285306
\(290\) 0 0
\(291\) −6.81873 6.81873i −0.399721 0.399721i
\(292\) 0 0
\(293\) 10.7777 10.7777i 0.629637 0.629637i −0.318339 0.947977i \(-0.603125\pi\)
0.947977 + 0.318339i \(0.103125\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 21.1172i 1.22534i
\(298\) 0 0
\(299\) −0.143254 + 0.143254i −0.00828459 + 0.00828459i
\(300\) 0 0
\(301\) −10.7198 10.7198i −0.617881 0.617881i
\(302\) 0 0
\(303\) −13.1008 −0.752621
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 7.94378 + 7.94378i 0.453376 + 0.453376i 0.896473 0.443098i \(-0.146120\pi\)
−0.443098 + 0.896473i \(0.646120\pi\)
\(308\) 0 0
\(309\) 6.72382 6.72382i 0.382505 0.382505i
\(310\) 0 0
\(311\) 31.1649i 1.76720i −0.468244 0.883599i \(-0.655113\pi\)
0.468244 0.883599i \(-0.344887\pi\)
\(312\) 0 0
\(313\) 5.35842i 0.302876i 0.988467 + 0.151438i \(0.0483903\pi\)
−0.988467 + 0.151438i \(0.951610\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 8.88165 + 8.88165i 0.498843 + 0.498843i 0.911078 0.412235i \(-0.135252\pi\)
−0.412235 + 0.911078i \(0.635252\pi\)
\(318\) 0 0
\(319\) 25.5450 1.43025
\(320\) 0 0
\(321\) 0.320463 0.0178865
\(322\) 0 0
\(323\) 8.47233 + 8.47233i 0.471413 + 0.471413i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0.146260i 0.00808817i
\(328\) 0 0
\(329\) 19.1506i 1.05581i
\(330\) 0 0
\(331\) −6.07281 + 6.07281i −0.333792 + 0.333792i −0.854025 0.520233i \(-0.825845\pi\)
0.520233 + 0.854025i \(0.325845\pi\)
\(332\) 0 0
\(333\) 10.0352 + 10.0352i 0.549928 + 0.549928i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 22.0227 1.19965 0.599827 0.800130i \(-0.295236\pi\)
0.599827 + 0.800130i \(0.295236\pi\)
\(338\) 0 0
\(339\) 2.92132 + 2.92132i 0.158664 + 0.158664i
\(340\) 0 0
\(341\) 8.33106 8.33106i 0.451152 0.451152i
\(342\) 0 0
\(343\) 38.8315i 2.09670i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 11.8920 11.8920i 0.638395 0.638395i −0.311765 0.950159i \(-0.600920\pi\)
0.950159 + 0.311765i \(0.100920\pi\)
\(348\) 0 0
\(349\) −8.65696 8.65696i −0.463396 0.463396i 0.436371 0.899767i \(-0.356264\pi\)
−0.899767 + 0.436371i \(0.856264\pi\)
\(350\) 0 0
\(351\) −0.474200 −0.0253109
\(352\) 0 0
\(353\) 26.6153 1.41659 0.708296 0.705916i \(-0.249464\pi\)
0.708296 + 0.705916i \(0.249464\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 10.7678 10.7678i 0.569890 0.569890i
\(358\) 0 0
\(359\) 4.85032i 0.255990i −0.991775 0.127995i \(-0.959146\pi\)
0.991775 0.127995i \(-0.0408542\pi\)
\(360\) 0 0
\(361\) 12.4298i 0.654199i
\(362\) 0 0
\(363\) −9.59078 + 9.59078i −0.503385 + 0.503385i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −15.6741 −0.818182 −0.409091 0.912494i \(-0.634154\pi\)
−0.409091 + 0.912494i \(0.634154\pi\)
\(368\) 0 0
\(369\) 20.8250 1.08411
\(370\) 0 0
\(371\) −23.7627 23.7627i −1.23370 1.23370i
\(372\) 0 0
\(373\) −5.44481 + 5.44481i −0.281922 + 0.281922i −0.833875 0.551953i \(-0.813883\pi\)
0.551953 + 0.833875i \(0.313883\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0.573629i 0.0295434i
\(378\) 0 0
\(379\) 17.4103 17.4103i 0.894309 0.894309i −0.100616 0.994925i \(-0.532081\pi\)
0.994925 + 0.100616i \(0.0320814\pi\)
\(380\) 0 0
\(381\) 1.33402 + 1.33402i 0.0683438 + 0.0683438i
\(382\) 0 0
\(383\) −9.04928 −0.462396 −0.231198 0.972907i \(-0.574265\pi\)
−0.231198 + 0.972907i \(0.574265\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) −5.73503 5.73503i −0.291528 0.291528i
\(388\) 0 0
\(389\) −15.3617 + 15.3617i −0.778871 + 0.778871i −0.979639 0.200768i \(-0.935656\pi\)
0.200768 + 0.979639i \(0.435656\pi\)
\(390\) 0 0
\(391\) 7.61962i 0.385341i
\(392\) 0 0
\(393\) 0.794869i 0.0400959i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 9.44519 + 9.44519i 0.474041 + 0.474041i 0.903220 0.429179i \(-0.141197\pi\)
−0.429179 + 0.903220i \(0.641197\pi\)
\(398\) 0 0
\(399\) 8.35031 0.418038
\(400\) 0 0
\(401\) −21.5765 −1.07748 −0.538739 0.842473i \(-0.681099\pi\)
−0.538739 + 0.842473i \(0.681099\pi\)
\(402\) 0 0
\(403\) 0.187079 + 0.187079i 0.00931907 + 0.00931907i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 31.1363i 1.54337i
\(408\) 0 0
\(409\) 4.17336i 0.206359i 0.994663 + 0.103180i \(0.0329017\pi\)
−0.994663 + 0.103180i \(0.967098\pi\)
\(410\) 0 0
\(411\) 0.0976116 0.0976116i 0.00481482 0.00481482i
\(412\) 0 0
\(413\) −24.3529 24.3529i −1.19833 1.19833i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −11.3629 −0.556445
\(418\) 0 0
\(419\) −27.1191 27.1191i −1.32485 1.32485i −0.909794 0.415060i \(-0.863761\pi\)
−0.415060 0.909794i \(-0.636239\pi\)
\(420\) 0 0
\(421\) −26.9594 + 26.9594i −1.31392 + 1.31392i −0.395421 + 0.918500i \(0.629401\pi\)
−0.918500 + 0.395421i \(0.870599\pi\)
\(422\) 0 0
\(423\) 10.2454i 0.498150i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 33.6079 33.6079i 1.62640 1.62640i
\(428\) 0 0
\(429\) −0.336036 0.336036i −0.0162240 0.0162240i
\(430\) 0 0
\(431\) 22.4059 1.07925 0.539626 0.841905i \(-0.318566\pi\)
0.539626 + 0.841905i \(0.318566\pi\)
\(432\) 0 0
\(433\) 16.8061 0.807649 0.403824 0.914837i \(-0.367681\pi\)
0.403824 + 0.914837i \(0.367681\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 2.95448 2.95448i 0.141332 0.141332i
\(438\) 0 0
\(439\) 9.08322i 0.433519i 0.976225 + 0.216759i \(0.0695487\pi\)
−0.976225 + 0.216759i \(0.930451\pi\)
\(440\) 0 0
\(441\) 38.4335i 1.83017i
\(442\) 0 0
\(443\) 12.5397 12.5397i 0.595781 0.595781i −0.343406 0.939187i \(-0.611581\pi\)
0.939187 + 0.343406i \(0.111581\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 1.10780 0.0523972
\(448\) 0 0
\(449\) 18.0707 0.852811 0.426406 0.904532i \(-0.359780\pi\)
0.426406 + 0.904532i \(0.359780\pi\)
\(450\) 0 0
\(451\) 32.3069 + 32.3069i 1.52127 + 1.52127i
\(452\) 0 0
\(453\) 3.47929 3.47929i 0.163471 0.163471i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 18.6637i 0.873052i 0.899692 + 0.436526i \(0.143791\pi\)
−0.899692 + 0.436526i \(0.856209\pi\)
\(458\) 0 0
\(459\) 12.6113 12.6113i 0.588643 0.588643i
\(460\) 0 0
\(461\) −0.831229 0.831229i −0.0387142 0.0387142i 0.687485 0.726199i \(-0.258715\pi\)
−0.726199 + 0.687485i \(0.758715\pi\)
\(462\) 0 0
\(463\) 7.82533 0.363674 0.181837 0.983329i \(-0.441796\pi\)
0.181837 + 0.983329i \(0.441796\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 8.75068 + 8.75068i 0.404933 + 0.404933i 0.879967 0.475034i \(-0.157564\pi\)
−0.475034 + 0.879967i \(0.657564\pi\)
\(468\) 0 0
\(469\) −35.3617 + 35.3617i −1.63285 + 1.63285i
\(470\) 0 0
\(471\) 5.19922i 0.239568i
\(472\) 0 0
\(473\) 17.7941i 0.818172i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −12.7129 12.7129i −0.582082 0.582082i
\(478\) 0 0
\(479\) −2.10417 −0.0961421 −0.0480710 0.998844i \(-0.515307\pi\)
−0.0480710 + 0.998844i \(0.515307\pi\)
\(480\) 0 0
\(481\) −0.699186 −0.0318801
\(482\) 0 0
\(483\) −3.75494 3.75494i −0.170856 0.170856i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 4.87183i 0.220764i −0.993889 0.110382i \(-0.964793\pi\)
0.993889 0.110382i \(-0.0352074\pi\)
\(488\) 0 0
\(489\) 12.0185i 0.543494i
\(490\) 0 0
\(491\) −14.3582 + 14.3582i −0.647975 + 0.647975i −0.952503 0.304528i \(-0.901501\pi\)
0.304528 + 0.952503i \(0.401501\pi\)
\(492\) 0 0
\(493\) −15.2555 15.2555i −0.687075 0.687075i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 21.4113 0.960429
\(498\) 0 0
\(499\) 25.1060 + 25.1060i 1.12390 + 1.12390i 0.991150 + 0.132748i \(0.0423801\pi\)
0.132748 + 0.991150i \(0.457620\pi\)
\(500\) 0 0
\(501\) −4.82077 + 4.82077i −0.215376 + 0.215376i
\(502\) 0 0
\(503\) 18.8868i 0.842120i −0.907033 0.421060i \(-0.861658\pi\)
0.907033 0.421060i \(-0.138342\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −6.34316 + 6.34316i −0.281710 + 0.281710i
\(508\) 0 0
\(509\) −22.9756 22.9756i −1.01837 1.01837i −0.999828 0.0185459i \(-0.994096\pi\)
−0.0185459 0.999828i \(-0.505904\pi\)
\(510\) 0 0
\(511\) −39.1641 −1.73252
\(512\) 0 0
\(513\) 9.77993 0.431794
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −15.8942 + 15.8942i −0.699028 + 0.699028i
\(518\) 0 0
\(519\) 13.1009i 0.575066i
\(520\) 0 0
\(521\) 20.2089i 0.885367i −0.896678 0.442683i \(-0.854027\pi\)
0.896678 0.442683i \(-0.145973\pi\)
\(522\) 0 0
\(523\) −3.93445 + 3.93445i −0.172042 + 0.172042i −0.787876 0.615834i \(-0.788819\pi\)
0.615834 + 0.787876i \(0.288819\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −9.95066 −0.433458
\(528\) 0 0
\(529\) 20.3429 0.884473
\(530\) 0 0
\(531\) −13.0286 13.0286i −0.565393 0.565393i
\(532\) 0 0
\(533\) −0.725471 + 0.725471i −0.0314237 + 0.0314237i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.409950i 0.0176906i
\(538\) 0 0
\(539\) −59.6238 + 59.6238i −2.56818 + 2.56818i
\(540\) 0 0
\(541\) −3.17895 3.17895i −0.136674 0.136674i 0.635460 0.772134i \(-0.280811\pi\)
−0.772134 + 0.635460i \(0.780811\pi\)
\(542\) 0 0
\(543\) 13.9330 0.597923
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.32918 1.32918i −0.0568317 0.0568317i 0.678120 0.734951i \(-0.262795\pi\)
−0.734951 + 0.678120i \(0.762795\pi\)
\(548\) 0 0
\(549\) 17.9800 17.9800i 0.767366 0.767366i
\(550\) 0 0
\(551\) 11.8306i 0.503998i
\(552\) 0 0
\(553\) 54.3766i 2.31233i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 24.9082 + 24.9082i 1.05539 + 1.05539i 0.998373 + 0.0570196i \(0.0181598\pi\)
0.0570196 + 0.998373i \(0.481840\pi\)
\(558\) 0 0
\(559\) 0.399576 0.0169003
\(560\) 0 0
\(561\) 17.8736 0.754625
\(562\) 0 0
\(563\) −3.80804 3.80804i −0.160490 0.160490i 0.622294 0.782784i \(-0.286201\pi\)
−0.782784 + 0.622294i \(0.786201\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 23.2571i 0.976706i
\(568\) 0 0
\(569\) 8.43971i 0.353811i 0.984228 + 0.176905i \(0.0566087\pi\)
−0.984228 + 0.176905i \(0.943391\pi\)
\(570\) 0 0
\(571\) 21.2821 21.2821i 0.890629 0.890629i −0.103953 0.994582i \(-0.533149\pi\)
0.994582 + 0.103953i \(0.0331491\pi\)
\(572\) 0 0
\(573\) 8.46619 + 8.46619i 0.353680 + 0.353680i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) −36.3491 −1.51323 −0.756615 0.653860i \(-0.773148\pi\)
−0.756615 + 0.653860i \(0.773148\pi\)
\(578\) 0 0
\(579\) 8.23964 + 8.23964i 0.342428 + 0.342428i
\(580\) 0 0
\(581\) −5.51321 + 5.51321i −0.228726 + 0.228726i
\(582\) 0 0
\(583\) 39.4442i 1.63361i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 6.55994 6.55994i 0.270758 0.270758i −0.558647 0.829405i \(-0.688679\pi\)
0.829405 + 0.558647i \(0.188679\pi\)
\(588\) 0 0
\(589\) −3.85833 3.85833i −0.158980 0.158980i
\(590\) 0 0
\(591\) −3.50665 −0.144244
\(592\) 0 0
\(593\) −1.40974 −0.0578911 −0.0289455 0.999581i \(-0.509215\pi\)
−0.0289455 + 0.999581i \(0.509215\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 3.24619 3.24619i 0.132858 0.132858i
\(598\) 0 0
\(599\) 23.3593i 0.954435i −0.878785 0.477218i \(-0.841645\pi\)
0.878785 0.477218i \(-0.158355\pi\)
\(600\) 0 0
\(601\) 20.4138i 0.832695i 0.909206 + 0.416347i \(0.136690\pi\)
−0.909206 + 0.416347i \(0.863310\pi\)
\(602\) 0 0
\(603\) −18.9183 + 18.9183i −0.770411 + 0.770411i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) −0.758240 −0.0307760 −0.0153880 0.999882i \(-0.504898\pi\)
−0.0153880 + 0.999882i \(0.504898\pi\)
\(608\) 0 0
\(609\) −15.0358 −0.609283
\(610\) 0 0
\(611\) −0.356915 0.356915i −0.0144392 0.0144392i
\(612\) 0 0
\(613\) 12.0341 12.0341i 0.486052 0.486052i −0.421006 0.907058i \(-0.638323\pi\)
0.907058 + 0.421006i \(0.138323\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 32.6899i 1.31605i −0.752998 0.658023i \(-0.771393\pi\)
0.752998 0.658023i \(-0.228607\pi\)
\(618\) 0 0
\(619\) −26.3836 + 26.3836i −1.06045 + 1.06045i −0.0623934 + 0.998052i \(0.519873\pi\)
−0.998052 + 0.0623934i \(0.980127\pi\)
\(620\) 0 0
\(621\) −4.39781 4.39781i −0.176478 0.176478i
\(622\) 0 0
\(623\) −15.3049 −0.613178
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) 6.93042 + 6.93042i 0.276774 + 0.276774i
\(628\) 0 0
\(629\) 18.5947 18.5947i 0.741420 0.741420i
\(630\) 0 0
\(631\) 6.08765i 0.242345i −0.992631 0.121173i \(-0.961335\pi\)
0.992631 0.121173i \(-0.0386655\pi\)
\(632\) 0 0
\(633\) 1.86521i 0.0741354i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) −1.33889 1.33889i −0.0530487 0.0530487i
\(638\) 0 0
\(639\) 11.4549 0.453149
\(640\) 0 0
\(641\) 11.1680 0.441111 0.220555 0.975374i \(-0.429213\pi\)
0.220555 + 0.975374i \(0.429213\pi\)
\(642\) 0 0
\(643\) 21.9585 + 21.9585i 0.865957 + 0.865957i 0.992022 0.126065i \(-0.0402348\pi\)
−0.126065 + 0.992022i \(0.540235\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 36.9848i 1.45402i −0.686625 0.727011i \(-0.740909\pi\)
0.686625 0.727011i \(-0.259091\pi\)
\(648\) 0 0
\(649\) 40.4238i 1.58677i
\(650\) 0 0
\(651\) −4.90368 + 4.90368i −0.192190 + 0.192190i
\(652\) 0 0
\(653\) −18.4157 18.4157i −0.720663 0.720663i 0.248077 0.968740i \(-0.420201\pi\)
−0.968740 + 0.248077i \(0.920201\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) −20.9525 −0.817435
\(658\) 0 0
\(659\) 15.5421 + 15.5421i 0.605434 + 0.605434i 0.941749 0.336316i \(-0.109181\pi\)
−0.336316 + 0.941749i \(0.609181\pi\)
\(660\) 0 0
\(661\) 29.6677 29.6677i 1.15394 1.15394i 0.168185 0.985755i \(-0.446209\pi\)
0.985755 0.168185i \(-0.0537906\pi\)
\(662\) 0 0
\(663\) 0.401363i 0.0155877i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −5.31992 + 5.31992i −0.205988 + 0.205988i
\(668\) 0 0
\(669\) −11.7767 11.7767i −0.455313 0.455313i
\(670\) 0 0
\(671\) 55.7864 2.15361
\(672\) 0 0
\(673\) −29.2198 −1.12634 −0.563171 0.826340i \(-0.690419\pi\)
−0.563171 + 0.826340i \(0.690419\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 17.2591 17.2591i 0.663320 0.663320i −0.292841 0.956161i \(-0.594601\pi\)
0.956161 + 0.292841i \(0.0946006\pi\)
\(678\) 0 0
\(679\) 65.8179i 2.52586i
\(680\) 0 0
\(681\) 6.52082i 0.249878i
\(682\) 0 0
\(683\) −1.10407 + 1.10407i −0.0422459 + 0.0422459i −0.727914 0.685668i \(-0.759510\pi\)
0.685668 + 0.727914i \(0.259510\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) −15.7113 −0.599425
\(688\) 0 0
\(689\) 0.885743 0.0337441
\(690\) 0 0
\(691\) 28.4233 + 28.4233i 1.08127 + 1.08127i 0.996391 + 0.0848830i \(0.0270517\pi\)
0.0848830 + 0.996391i \(0.472948\pi\)
\(692\) 0 0
\(693\) −46.5545 + 46.5545i −1.76846 + 1.76846i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 38.5875i 1.46161i
\(698\) 0 0
\(699\) −8.05933 + 8.05933i −0.304832 + 0.304832i
\(700\) 0 0
\(701\) −23.7991 23.7991i −0.898880 0.898880i 0.0964573 0.995337i \(-0.469249\pi\)
−0.995337 + 0.0964573i \(0.969249\pi\)
\(702\) 0 0
\(703\) 14.4200 0.543862
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −63.2278 63.2278i −2.37793 2.37793i
\(708\) 0 0
\(709\) 1.49921 1.49921i 0.0563039 0.0563039i −0.678394 0.734698i \(-0.737324\pi\)
0.734698 + 0.678394i \(0.237324\pi\)
\(710\) 0 0
\(711\) 29.0911i 1.09100i
\(712\) 0 0
\(713\) 3.47000i 0.129953i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 2.56919 + 2.56919i 0.0959482 + 0.0959482i
\(718\) 0 0
\(719\) −7.37612 −0.275083 −0.137541 0.990496i \(-0.543920\pi\)
−0.137541 + 0.990496i \(0.543920\pi\)
\(720\) 0 0
\(721\) 64.9017 2.41707
\(722\) 0 0
\(723\) 6.89425 + 6.89425i 0.256400 + 0.256400i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 30.1470i 1.11809i 0.829137 + 0.559045i \(0.188832\pi\)
−0.829137 + 0.559045i \(0.811168\pi\)
\(728\) 0 0
\(729\) 4.53447i 0.167943i
\(730\) 0 0
\(731\) −10.6267 + 10.6267i −0.393041 + 0.393041i
\(732\) 0 0
\(733\) −1.43297 1.43297i −0.0529279 0.0529279i 0.680147 0.733075i \(-0.261916\pi\)
−0.733075 + 0.680147i \(0.761916\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −58.6977 −2.16216
\(738\) 0 0
\(739\) −31.0001 31.0001i −1.14036 1.14036i −0.988385 0.151973i \(-0.951437\pi\)
−0.151973 0.988385i \(-0.548563\pi\)
\(740\) 0 0
\(741\) −0.155627 + 0.155627i −0.00571710 + 0.00571710i
\(742\) 0 0
\(743\) 38.5395i 1.41388i −0.707276 0.706938i \(-0.750076\pi\)
0.707276 0.706938i \(-0.249924\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −2.94952 + 2.94952i −0.107917 + 0.107917i
\(748\) 0 0
\(749\) 1.54664 + 1.54664i 0.0565128 + 0.0565128i
\(750\) 0 0
\(751\) −26.9523 −0.983503 −0.491751 0.870736i \(-0.663643\pi\)
−0.491751 + 0.870736i \(0.663643\pi\)
\(752\) 0 0
\(753\) −9.75884 −0.355632
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 17.0688 17.0688i 0.620377 0.620377i −0.325251 0.945628i \(-0.605449\pi\)
0.945628 + 0.325251i \(0.105449\pi\)
\(758\) 0 0
\(759\) 6.23290i 0.226240i
\(760\) 0 0
\(761\) 6.89608i 0.249983i 0.992158 + 0.124991i \(0.0398903\pi\)
−0.992158 + 0.124991i \(0.960110\pi\)
\(762\) 0 0
\(763\) −0.705886 + 0.705886i −0.0255548 + 0.0255548i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.907741 0.0327766
\(768\) 0 0
\(769\) 11.8443 0.427117 0.213558 0.976930i \(-0.431495\pi\)
0.213558 + 0.976930i \(0.431495\pi\)
\(770\) 0 0
\(771\) −4.12679 4.12679i −0.148623 0.148623i
\(772\) 0 0
\(773\) −3.58865 + 3.58865i −0.129075 + 0.129075i −0.768693 0.639618i \(-0.779093\pi\)
0.639618 + 0.768693i \(0.279093\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 18.3269i 0.657474i
\(778\) 0 0
\(779\) 14.9622 14.9622i 0.536075 0.536075i
\(780\) 0 0
\(781\) 17.7705 + 17.7705i 0.635880 + 0.635880i
\(782\) 0 0
\(783\) −17.6100 −0.629332
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 22.4800 + 22.4800i 0.801326 + 0.801326i 0.983303 0.181977i \(-0.0582497\pi\)
−0.181977 + 0.983303i \(0.558250\pi\)
\(788\) 0 0
\(789\) −8.94296 + 8.94296i −0.318378 + 0.318378i
\(790\) 0 0
\(791\) 28.1981i 1.00261i
\(792\) 0 0
\(793\) 1.25272i 0.0444853i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) −8.67589 8.67589i −0.307316 0.307316i 0.536552 0.843867i \(-0.319727\pi\)
−0.843867 + 0.536552i \(0.819727\pi\)
\(798\) 0 0
\(799\) 18.9842 0.671612
\(800\) 0 0
\(801\) −8.18800 −0.289309
\(802\) 0 0
\(803\) −32.5046 &minu