Properties

Label 1600.2.q.f.49.4
Level $1600$
Weight $2$
Character 1600.49
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.q (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 49.4
Root \(-1.41313 + 0.0554252i\) of defining polynomial
Character \(\chi\) \(=\) 1600.49
Dual form 1600.2.q.f.849.4

$q$-expansion

\(f(q)\) \(=\) \(q+(0.488516 + 0.488516i) q^{3} -4.71540 q^{7} -2.52270i q^{9} +O(q^{10})\) \(q+(0.488516 + 0.488516i) q^{3} -4.71540 q^{7} -2.52270i q^{9} +(3.91360 + 3.91360i) q^{11} +(-0.0878822 - 0.0878822i) q^{13} -4.67442i q^{17} +(1.81249 - 1.81249i) q^{19} +(-2.30355 - 2.30355i) q^{21} -1.63007 q^{23} +(2.69793 - 2.69793i) q^{27} +(-3.26362 + 3.26362i) q^{29} +2.12875 q^{31} +3.82371i q^{33} +(3.97797 - 3.97797i) q^{37} -0.0858637i q^{39} -8.25504i q^{41} +(2.27336 - 2.27336i) q^{43} -4.06129i q^{47} +15.2350 q^{49} +(2.28353 - 2.28353i) q^{51} +(5.03938 - 5.03938i) q^{53} +1.77086 q^{57} +(-5.16453 - 5.16453i) q^{59} +(7.12726 - 7.12726i) q^{61} +11.8956i q^{63} +(-7.49920 - 7.49920i) q^{67} +(-0.796314 - 0.796314i) q^{69} -4.54072i q^{71} +8.30557 q^{73} +(-18.4542 - 18.4542i) q^{77} +11.5317 q^{79} -4.93215 q^{81} +(1.16919 + 1.16919i) q^{83} -3.18866 q^{87} -3.24572i q^{89} +(0.414400 + 0.414400i) q^{91} +(1.03993 + 1.03993i) q^{93} +13.9581i q^{97} +(9.87285 - 9.87285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12q + 2q^{3} - 12q^{7} + O(q^{10}) \) \( 12q + 2q^{3} - 12q^{7} + 2q^{11} + 4q^{13} - 14q^{19} - 20q^{21} - 12q^{23} - 10q^{27} + 4q^{31} - 8q^{37} - 4q^{49} - 10q^{51} - 16q^{53} - 16q^{57} + 20q^{59} + 4q^{61} - 50q^{67} + 40q^{73} - 8q^{77} + 12q^{79} - 8q^{81} - 2q^{83} + 64q^{87} + 44q^{93} + 12q^{99} + O(q^{100}) \)

Character values

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

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

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 0.833924 0.551879i \(-0.186089\pi\)
−0.551879 + 0.833924i \(0.686089\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −4.71540 −1.78226 −0.891128 0.453753i \(-0.850085\pi\)
−0.891128 + 0.453753i \(0.850085\pi\)
\(8\) 0 0
\(9\) 2.52270i 0.840901i
\(10\) 0 0
\(11\) 3.91360 + 3.91360i 1.17999 + 1.17999i 0.979745 + 0.200249i \(0.0641750\pi\)
0.200249 + 0.979745i \(0.435825\pi\)
\(12\) 0 0
\(13\) −0.0878822 0.0878822i −0.0243741 0.0243741i 0.694815 0.719189i \(-0.255486\pi\)
−0.719189 + 0.694815i \(0.755486\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.67442i 1.13371i −0.823816 0.566857i \(-0.808159\pi\)
0.823816 0.566857i \(-0.191841\pi\)
\(18\) 0 0
\(19\) 1.81249 1.81249i 0.415813 0.415813i −0.467945 0.883758i \(-0.655005\pi\)
0.883758 + 0.467945i \(0.155005\pi\)
\(20\) 0 0
\(21\) −2.30355 2.30355i −0.502676 0.502676i
\(22\) 0 0
\(23\) −1.63007 −0.339893 −0.169946 0.985453i \(-0.554359\pi\)
−0.169946 + 0.985453i \(0.554359\pi\)
\(24\) 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 \(-0.890970\pi\)
0.335869 + 0.941909i \(0.390970\pi\)
\(30\) 0 0
\(31\) 2.12875 0.382334 0.191167 0.981557i \(-0.438773\pi\)
0.191167 + 0.981557i \(0.438773\pi\)
\(32\) 0 0
\(33\) 3.82371i 0.665622i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 3.97797 3.97797i 0.653974 0.653974i −0.299973 0.953948i \(-0.596978\pi\)
0.953948 + 0.299973i \(0.0969778\pi\)
\(38\) 0 0
\(39\) 0.0858637i 0.0137492i
\(40\) 0 0
\(41\) 8.25504i 1.28922i −0.764511 0.644611i \(-0.777020\pi\)
0.764511 0.644611i \(-0.222980\pi\)
\(42\) 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
\(47\) 4.06129i 0.592400i −0.955126 0.296200i \(-0.904281\pi\)
0.955126 0.296200i \(-0.0957195\pi\)
\(48\) 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
\(57\) 1.77086 0.234556
\(58\) 0 0
\(59\) −5.16453 5.16453i −0.672365 0.672365i 0.285896 0.958261i \(-0.407709\pi\)
−0.958261 + 0.285896i \(0.907709\pi\)
\(60\) 0 0
\(61\) 7.12726 7.12726i 0.912552 0.912552i −0.0839206 0.996472i \(-0.526744\pi\)
0.996472 + 0.0839206i \(0.0267442\pi\)
\(62\) 0 0
\(63\) 11.8956i 1.49870i
\(64\) 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 \(-0.913161\pi\)
0.963017 0.269442i \(-0.0868393\pi\)
\(72\) 0 0
\(73\) 8.30557 0.972093 0.486047 0.873933i \(-0.338439\pi\)
0.486047 + 0.873933i \(0.338439\pi\)
\(74\) 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 \(-0.275309\pi\)
0.648709 + 0.761037i \(0.275309\pi\)
\(80\) 0 0
\(81\) −4.93215 −0.548017
\(82\) 0 0
\(83\) 1.16919 + 1.16919i 0.128335 + 0.128335i 0.768357 0.640022i \(-0.221075\pi\)
−0.640022 + 0.768357i \(0.721075\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −3.18866 −0.341861
\(88\) 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
\(97\) 13.9581i 1.41723i 0.705598 + 0.708613i \(0.250679\pi\)
−0.705598 + 0.708613i \(0.749321\pi\)
\(98\) 0 0
\(99\) 9.87285 9.87285i 0.992258 0.992258i
\(100\) 0 0
\(101\) 13.4088 + 13.4088i 1.33422 + 1.33422i 0.901552 + 0.432672i \(0.142429\pi\)
0.432672 + 0.901552i \(0.357571\pi\)
\(102\) 0 0
\(103\) −13.7638 −1.35618 −0.678092 0.734977i \(-0.737193\pi\)
−0.678092 + 0.734977i \(0.737193\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0.327996 0.327996i 0.0317086 0.0317086i −0.691075 0.722783i \(-0.742862\pi\)
0.722783 + 0.691075i \(0.242862\pi\)
\(108\) 0 0
\(109\) 0.149698 0.149698i 0.0143385 0.0143385i −0.699901 0.714240i \(-0.746773\pi\)
0.714240 + 0.699901i \(0.246773\pi\)
\(110\) 0 0
\(111\) 3.88660 0.368900
\(112\) 0 0
\(113\) 5.97999i 0.562550i 0.959627 + 0.281275i \(0.0907573\pi\)
−0.959627 + 0.281275i \(0.909243\pi\)
\(114\) 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
\(127\) 2.73076i 0.242315i −0.992633 0.121158i \(-0.961339\pi\)
0.992633 0.121158i \(-0.0386607\pi\)
\(128\) 0 0
\(129\) 2.22115 0.195561
\(130\) 0 0
\(131\) 0.813555 0.813555i 0.0710806 0.0710806i −0.670673 0.741753i \(-0.733994\pi\)
0.741753 + 0.670673i \(0.233994\pi\)
\(132\) 0 0
\(133\) −8.54661 + 8.54661i −0.741085 + 0.741085i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0.199812 0.0170711 0.00853557 0.999964i \(-0.497283\pi\)
0.00853557 + 0.999964i \(0.497283\pi\)
\(138\) 0 0
\(139\) −11.6301 11.6301i −0.986448 0.986448i 0.0134610 0.999909i \(-0.495715\pi\)
−0.999909 + 0.0134610i \(0.995715\pi\)
\(140\) 0 0
\(141\) 1.98400 1.98400i 0.167083 0.167083i
\(142\) 0 0
\(143\) 0.687871i 0.0575227i
\(144\) 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 \(-0.229078\pi\)
−0.659136 + 0.752024i \(0.729078\pi\)
\(150\) 0 0
\(151\) 7.12216i 0.579593i −0.957088 0.289797i \(-0.906412\pi\)
0.957088 0.289797i \(-0.0935877\pi\)
\(152\) 0 0
\(153\) −11.7922 −0.953341
\(154\) 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 0.999357 0.0358685i \(-0.0114197\pi\)
−0.0358685 + 0.999357i \(0.511420\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −9.86820 −0.763624 −0.381812 0.924240i \(-0.624700\pi\)
−0.381812 + 0.924240i \(0.624700\pi\)
\(168\) 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 \(-0.993744\pi\)
−0.0196525 0.999807i \(-0.506256\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 5.04591i 0.379274i
\(178\) 0 0
\(179\) 0.419587 0.419587i 0.0313614 0.0313614i −0.691252 0.722614i \(-0.742941\pi\)
0.722614 + 0.691252i \(0.242941\pi\)
\(180\) 0 0
\(181\) −14.2605 14.2605i −1.05998 1.05998i −0.998083 0.0618956i \(-0.980285\pi\)
−0.0618956 0.998083i \(-0.519715\pi\)
\(182\) 0 0
\(183\) 6.96356 0.514761
\(184\) 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
\(193\) 16.8667i 1.21409i 0.794667 + 0.607045i \(0.207645\pi\)
−0.794667 + 0.607045i \(0.792355\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −3.58908 + 3.58908i −0.255712 + 0.255712i −0.823307 0.567596i \(-0.807874\pi\)
0.567596 + 0.823307i \(0.307874\pi\)
\(198\) 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
\(207\) 4.11218i 0.285816i
\(208\) 0 0
\(209\) 14.1867 0.981314
\(210\) 0 0
\(211\) −1.90906 + 1.90906i −0.131425 + 0.131425i −0.769759 0.638334i \(-0.779624\pi\)
0.638334 + 0.769759i \(0.279624\pi\)
\(212\) 0 0
\(213\) 2.21821 2.21821i 0.151989 0.151989i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −10.0379 −0.681418
\(218\) 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
\(223\) 24.1071i 1.61433i −0.590326 0.807165i \(-0.701001\pi\)
0.590326 0.807165i \(-0.298999\pi\)
\(224\) 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 −0.997902 0.0647388i \(-0.979379\pi\)
−0.0647388 0.997902i \(-0.520621\pi\)
\(230\) 0 0
\(231\) 18.0303i 1.18631i
\(232\) 0 0
\(233\) 16.4976 1.08079 0.540396 0.841411i \(-0.318274\pi\)
0.540396 + 0.841411i \(0.318274\pi\)
\(234\) 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 \(-0.445593\pi\)
0.170094 + 0.985428i \(0.445593\pi\)
\(240\) 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
\(247\) −0.318571 −0.0202702
\(248\) 0 0
\(249\) 1.14234i 0.0723927i
\(250\) 0 0
\(251\) 9.98825 + 9.98825i 0.630453 + 0.630453i 0.948182 0.317729i \(-0.102920\pi\)
−0.317729 + 0.948182i \(0.602920\pi\)
\(252\) 0 0
\(253\) −6.37943 6.37943i −0.401071 0.401071i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 8.44760i 0.526947i 0.964667 + 0.263474i \(0.0848682\pi\)
−0.964667 + 0.263474i \(0.915132\pi\)
\(258\) 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
\(263\) 18.3064 1.12882 0.564410 0.825494i \(-0.309104\pi\)
0.564410 + 0.825494i \(0.309104\pi\)
\(264\) 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 \(-0.948806\pi\)
0.160140 + 0.987094i \(0.448806\pi\)
\(270\) 0 0
\(271\) 2.24520 0.136386 0.0681930 0.997672i \(-0.478277\pi\)
0.0681930 + 0.997672i \(0.478277\pi\)
\(272\) 0 0
\(273\) 0.404882i 0.0245046i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 7.28255 7.28255i 0.437566 0.437566i −0.453626 0.891192i \(-0.649870\pi\)
0.891192 + 0.453626i \(0.149870\pi\)
\(278\) 0 0
\(279\) 5.37020i 0.321506i
\(280\) 0 0
\(281\) 6.04084i 0.360367i 0.983633 + 0.180183i \(0.0576691\pi\)
−0.983633 + 0.180183i \(0.942331\pi\)
\(282\) 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
\(287\) 38.9259i 2.29772i
\(288\) 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
\(297\) 21.1172 1.22534
\(298\) 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
\(303\) 13.1008i 0.752621i
\(304\) 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 \(0.344887\pi\)
−0.468244 + 0.883599i \(0.655113\pi\)
\(312\) 0 0
\(313\) −5.35842 −0.302876 −0.151438 0.988467i \(-0.548390\pi\)
−0.151438 + 0.988467i \(0.548390\pi\)
\(314\) 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
\(327\) 0.146260 0.00808817
\(328\) 0 0
\(329\) 19.1506i 1.05581i
\(330\) 0 0
\(331\) −6.07281 6.07281i −0.333792 0.333792i 0.520233 0.854025i \(-0.325845\pi\)
−0.854025 + 0.520233i \(0.825845\pi\)
\(332\) 0 0
\(333\) −10.0352 10.0352i −0.549928 0.549928i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 22.0227i 1.19965i 0.800130 + 0.599827i \(0.204764\pi\)
−0.800130 + 0.599827i \(0.795236\pi\)
\(338\) 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
\(343\) −38.8315 −2.09670
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −11.8920 + 11.8920i −0.638395 + 0.638395i −0.950159 0.311765i \(-0.899080\pi\)
0.311765 + 0.950159i \(0.399080\pi\)
\(348\) 0 0
\(349\) 8.65696 8.65696i 0.463396 0.463396i −0.436371 0.899767i \(-0.643736\pi\)
0.899767 + 0.436371i \(0.143736\pi\)
\(350\) 0 0
\(351\) −0.474200 −0.0253109
\(352\) 0 0
\(353\) 26.6153i 1.41659i −0.705916 0.708296i \(-0.749464\pi\)
0.705916 0.708296i \(-0.250536\pi\)
\(354\) 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
\(367\) 15.6741i 0.818182i −0.912494 0.409091i \(-0.865846\pi\)
0.912494 0.409091i \(-0.134154\pi\)
\(368\) 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
\(377\) 0.573629 0.0295434
\(378\) 0 0
\(379\) −17.4103 17.4103i −0.894309 0.894309i 0.100616 0.994925i \(-0.467919\pi\)
−0.994925 + 0.100616i \(0.967919\pi\)
\(380\) 0 0
\(381\) 1.33402 1.33402i 0.0683438 0.0683438i
\(382\) 0 0
\(383\) 9.04928i 0.462396i 0.972907 + 0.231198i \(0.0742646\pi\)
−0.972907 + 0.231198i \(0.925735\pi\)
\(384\) 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 \(-0.0643437\pi\)
−0.200768 + 0.979639i \(0.564344\pi\)
\(390\) 0 0
\(391\) 7.61962i 0.385341i
\(392\) 0 0
\(393\) 0.794869 0.0400959
\(394\) 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
\(407\) 31.1363 1.54337
\(408\) 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
\(417\) 11.3629i 0.556445i
\(418\) 0 0
\(419\) 27.1191 27.1191i 1.32485 1.32485i 0.415060 0.909794i \(-0.363761\pi\)
0.909794 0.415060i \(-0.136239\pi\)
\(420\) 0 0
\(421\) −26.9594 26.9594i −1.31392 1.31392i −0.918500 0.395421i \(-0.870599\pi\)
−0.395421 0.918500i \(-0.629401\pi\)
\(422\) 0 0
\(423\) −10.2454 −0.498150
\(424\) 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
\(433\) 16.8061i 0.807649i −0.914837 0.403824i \(-0.867681\pi\)
0.914837 0.403824i \(-0.132319\pi\)
\(434\) 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
\(447\) 1.10780i 0.0523972i
\(448\) 0 0
\(449\) −18.0707 −0.852811 −0.426406 0.904532i \(-0.640220\pi\)
−0.426406 + 0.904532i \(0.640220\pi\)
\(450\) 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
\(457\) 18.6637 0.873052 0.436526 0.899692i \(-0.356209\pi\)
0.436526 + 0.899692i \(0.356209\pi\)
\(458\) 0 0
\(459\) −12.6113 12.6113i −0.588643 0.588643i
\(460\) 0 0
\(461\) −0.831229 + 0.831229i −0.0387142 + 0.0387142i −0.726199 0.687485i \(-0.758715\pi\)
0.687485 + 0.726199i \(0.258715\pi\)
\(462\) 0 0
\(463\) 7.82533i 0.363674i −0.983329 0.181837i \(-0.941796\pi\)
0.983329 0.181837i \(-0.0582043\pi\)
\(464\) 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
\(473\) 17.7941 0.818172
\(474\) 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 \(-0.484693\pi\)
0.0480710 + 0.998844i \(0.484693\pi\)
\(480\) 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
\(487\) −4.87183 −0.220764 −0.110382 0.993889i \(-0.535207\pi\)
−0.110382 + 0.993889i \(0.535207\pi\)
\(488\) 0 0
\(489\) 12.0185i 0.543494i
\(490\) 0 0
\(491\) −14.3582 14.3582i −0.647975 0.647975i 0.304528 0.952503i \(-0.401501\pi\)
−0.952503 + 0.304528i \(0.901501\pi\)
\(492\) 0 0
\(493\) 15.2555 + 15.2555i 0.687075 + 0.687075i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 21.4113i 0.960429i
\(498\) 0 0
\(499\) −25.1060 + 25.1060i −1.12390 + 1.12390i −0.132748 + 0.991150i \(0.542380\pi\)
−0.991150 + 0.132748i \(0.957620\pi\)
\(500\) 0 0
\(501\) −4.82077 4.82077i −0.215376 0.215376i
\(502\) 0 0
\(503\) 18.8868 0.842120 0.421060 0.907033i \(-0.361658\pi\)
0.421060 + 0.907033i \(0.361658\pi\)
\(504\) 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 0.0185459 0.999828i \(-0.494096\pi\)
0.999828 0.0185459i \(-0.00590369\pi\)
\(510\) 0 0
\(511\) −39.1641 −1.73252
\(512\) 0 0
\(513\) 9.77993i 0.431794i
\(514\) 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 \(0.145973\pi\)
−0.896678 + 0.442683i \(0.854027\pi\)
\(522\) 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
\(527\) 9.95066i 0.433458i
\(528\) 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
\(537\) 0.409950 0.0176906
\(538\) 0 0
\(539\) 59.6238 + 59.6238i 2.56818 + 2.56818i
\(540\) 0 0
\(541\) −3.17895 + 3.17895i −0.136674 + 0.136674i −0.772134 0.635460i \(-0.780811\pi\)
0.635460 + 0.772134i \(0.280811\pi\)
\(542\) 0 0
\(543\) 13.9330i 0.597923i
\(544\) 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
\(553\) −54.3766 −2.31233
\(554\) 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 0.782784 0.622294i \(-0.213799\pi\)
−0.622294 + 0.782784i \(0.713799\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 23.2571 0.976706
\(568\) 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 0.994582 0.103953i \(-0.0331491\pi\)
−0.103953 + 0.994582i \(0.533149\pi\)
\(572\) 0 0
\(573\) −8.46619 8.46619i −0.353680 0.353680i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 36.3491i 1.51323i −0.653860 0.756615i \(-0.726852\pi\)
0.653860 0.756615i \(-0.273148\pi\)
\(578\) 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
\(583\) 39.4442 1.63361
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −6.55994 + 6.55994i −0.270758 + 0.270758i −0.829405 0.558647i \(-0.811321\pi\)
0.558647 + 0.829405i \(0.311321\pi\)
\(588\) 0 0
\(589\) 3.85833 3.85833i 0.158980 0.158980i
\(590\) 0 0
\(591\) −3.50665 −0.144244
\(592\) 0 0
\(593\) 1.40974i 0.0578911i 0.999581 + 0.0289455i \(0.00921494\pi\)
−0.999581 + 0.0289455i \(0.990785\pi\)
\(594\) 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 \(-0.863310\pi\)
0.909206 0.416347i \(-0.136690\pi\)
\(602\) 0 0
\(603\) −18.9183 + 18.9183i −0.770411 + 0.770411i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0.758240i 0.0307760i −0.999882 0.0153880i \(-0.995102\pi\)
0.999882 0.0153880i \(-0.00489835\pi\)
\(608\) 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
\(617\) −32.6899 −1.31605 −0.658023 0.752998i \(-0.728607\pi\)
−0.658023 + 0.752998i \(0.728607\pi\)
\(618\) 0 0
\(619\) 26.3836 + 26.3836i 1.06045 + 1.06045i 0.998052 + 0.0623934i \(0.0198733\pi\)
0.0623934 + 0.998052i \(0.480127\pi\)
\(620\) 0 0
\(621\) −4.39781 + 4.39781i −0.176478 + 0.176478i
\(622\) 0 0
\(623\) 15.3049i 0.613178i
\(624\) 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 \(0.0386655\pi\)
−0.992631 + 0.121173i \(0.961335\pi\)
\(632\) 0 0
\(633\) −1.86521 −0.0741354
\(634\) 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 0.126065 0.992022i \(-0.459765\pi\)
−0.992022 + 0.126065i \(0.959765\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −36.9848 −1.45402 −0.727011 0.686625i \(-0.759091\pi\)
−0.727011 + 0.686625i \(0.759091\pi\)
\(648\) 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 0.968740 0.248077i \(-0.0797986\pi\)
−0.248077 + 0.968740i \(0.579799\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 20.9525i 0.817435i
\(658\) 0 0
\(659\) −15.5421 + 15.5421i −0.605434 + 0.605434i −0.941749 0.336316i \(-0.890819\pi\)
0.336316 + 0.941749i \(0.390819\pi\)
\(660\) 0 0
\(661\) 29.6677 + 29.6677i 1.15394 + 1.15394i 0.985755 + 0.168185i \(0.0537906\pi\)
0.168185 + 0.985755i \(0.446209\pi\)
\(662\) 0 0
\(663\) −0.401363 −0.0155877
\(664\) 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
\(673\) 29.2198i 1.12634i 0.826340 + 0.563171i \(0.190419\pi\)
−0.826340 + 0.563171i \(0.809581\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −17.2591 + 17.2591i −0.663320 + 0.663320i −0.956161 0.292841i \(-0.905399\pi\)
0.292841 + 0.956161i \(0.405399\pi\)
\(678\) 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
\(687\) 15.7113i 0.599425i
\(688\) 0 0
\(689\) −0.885743 −0.0337441
\(690\) 0 0
\(691\) 28.4233 28.4233i 1.08127 1.08127i 0.0848830 0.996391i \(-0.472948\pi\)
0.996391 0.0848830i \(-0.0270517\pi\)
\(692\) 0 0
\(693\) −46.5545 + 46.5545i −1.76846 + 1.76846i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −38.5875 −1.46161
\(698\) 0 0
\(699\) 8.05933 + 8.05933i 0.304832 + 0.304832i
\(700\) 0 0
\(701\) −23.7991 + 23.7991i −0.898880 + 0.898880i −0.995337 0.0964573i \(-0.969249\pi\)
0.0964573 + 0.995337i \(0.469249\pi\)
\(702\) 0 0
\(703\) 14.4200i 0.543862i
\(704\) 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 \(-0.262676\pi\)
−0.734698 + 0.678394i \(0.762676\pi\)
\(710\) 0 0
\(711\) 29.0911i 1.09100i
\(712\) 0 0
\(713\) −3.47000 −0.129953
\(714\) 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 \(-0.456080\pi\)
0.137541 + 0.990496i \(0.456080\pi\)
\(720\) 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
\(727\) 30.1470 1.11809 0.559045 0.829137i \(-0.311168\pi\)
0.559045 + 0.829137i \(0.311168\pi\)
\(728\) 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 0.733075 0.680147i \(-0.238084\pi\)
−0.680147 + 0.733075i \(0.738084\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 58.6977i 2.16216i
\(738\) 0 0
\(739\) 31.0001 31.0001i 1.14036 1.14036i 0.151973 0.988385i \(-0.451437\pi\)
0.988385 0.151973i \(-0.0485626\pi\)
\(740\) 0 0
\(741\) −0.155627 0.155627i −0.00571710 0.00571710i
\(742\) 0 0
\(743\) 38.5395 1.41388 0.706938 0.707276i \(-0.250076\pi\)
0.706938 + 0.707276i \(0.250076\pi\)
\(744\) 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
\(753\) 9.75884i 0.355632i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) −17.0688 + 17.0688i −0.620377 + 0.620377i −0.945628 0.325251i \(-0.894551\pi\)
0.325251 + 0.945628i \(0.394551\pi\)
\(758\) 0 0
\(759\) 6.23290i 0.226240i
\(760\) 0 0
\(761\) 6.89608i 0.249983i −0.992158 0.124991i \(-0.960110\pi\)
0.992158 0.124991i \(-0.0398903\pi\)
\(762\) 0 0
\(763\) −0.705886 + 0.705886i −0.0255548 + 0.0255548i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0.907741i 0.0327766i
\(768\) 0 0
\(769\) −11.8443 −0.427117 −0.213558 0.976930i \(-0.568505\pi\)
−0.213558 + 0.976930i \(0.568505\pi\)
\(770\) 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
\(777\) −18.3269 −0.657474
\(778\) 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
\(783\) 17.6100i 0.629332i
\(784\) 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
\(793\) −1.25272 −0.0444853
\(794\) 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 </