Properties

Label 1600.2.n.k.1407.1
Level $1600$
Weight $2$
Character 1600.1407
Analytic conductor $12.776$
Analytic rank $0$
Dimension $2$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1600,2,Mod(1343,1600)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1600.1343");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1600 = 2^{6} \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1600.n (of order \(4\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(12.7760643234\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(i)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 800)
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 1407.1
Root \(1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1600.1407
Dual form 1600.2.n.k.1343.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(1.00000 + 1.00000i) q^{3} +(-1.00000 + 1.00000i) q^{7} -1.00000i q^{9} +O(q^{10})\) \(q+(1.00000 + 1.00000i) q^{3} +(-1.00000 + 1.00000i) q^{7} -1.00000i q^{9} +4.00000i q^{11} +(4.00000 - 4.00000i) q^{13} +(4.00000 + 4.00000i) q^{17} +4.00000 q^{19} -2.00000 q^{21} +(-5.00000 - 5.00000i) q^{23} +(4.00000 - 4.00000i) q^{27} +2.00000i q^{29} +8.00000i q^{31} +(-4.00000 + 4.00000i) q^{33} +8.00000 q^{39} -4.00000 q^{41} +(7.00000 + 7.00000i) q^{43} +(-3.00000 + 3.00000i) q^{47} +5.00000i q^{49} +8.00000i q^{51} +(4.00000 - 4.00000i) q^{53} +(4.00000 + 4.00000i) q^{57} +4.00000 q^{59} +8.00000 q^{61} +(1.00000 + 1.00000i) q^{63} +(-3.00000 + 3.00000i) q^{67} -10.0000i q^{69} +16.0000i q^{71} +(-4.00000 + 4.00000i) q^{73} +(-4.00000 - 4.00000i) q^{77} +8.00000 q^{79} +5.00000 q^{81} +(-5.00000 - 5.00000i) q^{83} +(-2.00000 + 2.00000i) q^{87} -10.0000i q^{89} +8.00000i q^{91} +(-8.00000 + 8.00000i) q^{93} +(-12.0000 - 12.0000i) q^{97} +4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{3} - 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{3} - 2 q^{7} + 8 q^{13} + 8 q^{17} + 8 q^{19} - 4 q^{21} - 10 q^{23} + 8 q^{27} - 8 q^{33} + 16 q^{39} - 8 q^{41} + 14 q^{43} - 6 q^{47} + 8 q^{53} + 8 q^{57} + 8 q^{59} + 16 q^{61} + 2 q^{63} - 6 q^{67} - 8 q^{73} - 8 q^{77} + 16 q^{79} + 10 q^{81} - 10 q^{83} - 4 q^{87} - 16 q^{93} - 24 q^{97} + 8 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 1.00000 + 1.00000i 0.577350 + 0.577350i 0.934172 0.356822i \(-0.116140\pi\)
−0.356822 + 0.934172i \(0.616140\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 + 1.00000i −0.377964 + 0.377964i −0.870367 0.492403i \(-0.836119\pi\)
0.492403 + 0.870367i \(0.336119\pi\)
\(8\) 0 0
\(9\) 1.00000i 0.333333i
\(10\) 0 0
\(11\) 4.00000i 1.20605i 0.797724 + 0.603023i \(0.206037\pi\)
−0.797724 + 0.603023i \(0.793963\pi\)
\(12\) 0 0
\(13\) 4.00000 4.00000i 1.10940 1.10940i 0.116171 0.993229i \(-0.462938\pi\)
0.993229 0.116171i \(-0.0370621\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 4.00000 + 4.00000i 0.970143 + 0.970143i 0.999567 0.0294245i \(-0.00936746\pi\)
−0.0294245 + 0.999567i \(0.509367\pi\)
\(18\) 0 0
\(19\) 4.00000 0.917663 0.458831 0.888523i \(-0.348268\pi\)
0.458831 + 0.888523i \(0.348268\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) −5.00000 5.00000i −1.04257 1.04257i −0.999053 0.0435195i \(-0.986143\pi\)
−0.0435195 0.999053i \(-0.513857\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) 0 0
\(27\) 4.00000 4.00000i 0.769800 0.769800i
\(28\) 0 0
\(29\) 2.00000i 0.371391i 0.982607 + 0.185695i \(0.0594537\pi\)
−0.982607 + 0.185695i \(0.940546\pi\)
\(30\) 0 0
\(31\) 8.00000i 1.43684i 0.695608 + 0.718421i \(0.255135\pi\)
−0.695608 + 0.718421i \(0.744865\pi\)
\(32\) 0 0
\(33\) −4.00000 + 4.00000i −0.696311 + 0.696311i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(38\) 0 0
\(39\) 8.00000 1.28103
\(40\) 0 0
\(41\) −4.00000 −0.624695 −0.312348 0.949968i \(-0.601115\pi\)
−0.312348 + 0.949968i \(0.601115\pi\)
\(42\) 0 0
\(43\) 7.00000 + 7.00000i 1.06749 + 1.06749i 0.997551 + 0.0699387i \(0.0222804\pi\)
0.0699387 + 0.997551i \(0.477720\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 + 3.00000i −0.437595 + 0.437595i −0.891202 0.453607i \(-0.850137\pi\)
0.453607 + 0.891202i \(0.350137\pi\)
\(48\) 0 0
\(49\) 5.00000i 0.714286i
\(50\) 0 0
\(51\) 8.00000i 1.12022i
\(52\) 0 0
\(53\) 4.00000 4.00000i 0.549442 0.549442i −0.376837 0.926279i \(-0.622988\pi\)
0.926279 + 0.376837i \(0.122988\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 4.00000 + 4.00000i 0.529813 + 0.529813i
\(58\) 0 0
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 8.00000 1.02430 0.512148 0.858898i \(-0.328850\pi\)
0.512148 + 0.858898i \(0.328850\pi\)
\(62\) 0 0
\(63\) 1.00000 + 1.00000i 0.125988 + 0.125988i
\(64\) 0 0
\(65\) 0 0
\(66\) 0 0
\(67\) −3.00000 + 3.00000i −0.366508 + 0.366508i −0.866202 0.499694i \(-0.833446\pi\)
0.499694 + 0.866202i \(0.333446\pi\)
\(68\) 0 0
\(69\) 10.0000i 1.20386i
\(70\) 0 0
\(71\) 16.0000i 1.89885i 0.313993 + 0.949425i \(0.398333\pi\)
−0.313993 + 0.949425i \(0.601667\pi\)
\(72\) 0 0
\(73\) −4.00000 + 4.00000i −0.468165 + 0.468165i −0.901319 0.433155i \(-0.857400\pi\)
0.433155 + 0.901319i \(0.357400\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) −4.00000 4.00000i −0.455842 0.455842i
\(78\) 0 0
\(79\) 8.00000 0.900070 0.450035 0.893011i \(-0.351411\pi\)
0.450035 + 0.893011i \(0.351411\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) −5.00000 5.00000i −0.548821 0.548821i 0.377279 0.926100i \(-0.376860\pi\)
−0.926100 + 0.377279i \(0.876860\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −2.00000 + 2.00000i −0.214423 + 0.214423i
\(88\) 0 0
\(89\) 10.0000i 1.06000i −0.847998 0.529999i \(-0.822192\pi\)
0.847998 0.529999i \(-0.177808\pi\)
\(90\) 0 0
\(91\) 8.00000i 0.838628i
\(92\) 0 0
\(93\) −8.00000 + 8.00000i −0.829561 + 0.829561i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −12.0000 12.0000i −1.21842 1.21842i −0.968187 0.250229i \(-0.919494\pi\)
−0.250229 0.968187i \(-0.580506\pi\)
\(98\) 0 0
\(99\) 4.00000 0.402015
\(100\) 0 0
\(101\) −6.00000 −0.597022 −0.298511 0.954406i \(-0.596490\pi\)
−0.298511 + 0.954406i \(0.596490\pi\)
\(102\) 0 0
\(103\) −3.00000 3.00000i −0.295599 0.295599i 0.543688 0.839287i \(-0.317027\pi\)
−0.839287 + 0.543688i \(0.817027\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.00000 3.00000i 0.290021 0.290021i −0.547068 0.837088i \(-0.684256\pi\)
0.837088 + 0.547068i \(0.184256\pi\)
\(108\) 0 0
\(109\) 16.0000i 1.53252i 0.642529 + 0.766261i \(0.277885\pi\)
−0.642529 + 0.766261i \(0.722115\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 8.00000 8.00000i 0.752577 0.752577i −0.222383 0.974959i \(-0.571383\pi\)
0.974959 + 0.222383i \(0.0713835\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −4.00000 4.00000i −0.369800 0.369800i
\(118\) 0 0
\(119\) −8.00000 −0.733359
\(120\) 0 0
\(121\) −5.00000 −0.454545
\(122\) 0 0
\(123\) −4.00000 4.00000i −0.360668 0.360668i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 15.0000 15.0000i 1.33103 1.33103i 0.426589 0.904445i \(-0.359715\pi\)
0.904445 0.426589i \(-0.140285\pi\)
\(128\) 0 0
\(129\) 14.0000i 1.23263i
\(130\) 0 0
\(131\) 12.0000i 1.04844i 0.851581 + 0.524222i \(0.175644\pi\)
−0.851581 + 0.524222i \(0.824356\pi\)
\(132\) 0 0
\(133\) −4.00000 + 4.00000i −0.346844 + 0.346844i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −8.00000 8.00000i −0.683486 0.683486i 0.277298 0.960784i \(-0.410561\pi\)
−0.960784 + 0.277298i \(0.910561\pi\)
\(138\) 0 0
\(139\) 12.0000 1.01783 0.508913 0.860818i \(-0.330047\pi\)
0.508913 + 0.860818i \(0.330047\pi\)
\(140\) 0 0
\(141\) −6.00000 −0.505291
\(142\) 0 0
\(143\) 16.0000 + 16.0000i 1.33799 + 1.33799i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −5.00000 + 5.00000i −0.412393 + 0.412393i
\(148\) 0 0
\(149\) 8.00000i 0.655386i −0.944784 0.327693i \(-0.893729\pi\)
0.944784 0.327693i \(-0.106271\pi\)
\(150\) 0 0
\(151\) 8.00000i 0.651031i −0.945537 0.325515i \(-0.894462\pi\)
0.945537 0.325515i \(-0.105538\pi\)
\(152\) 0 0
\(153\) 4.00000 4.00000i 0.323381 0.323381i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 8.00000 + 8.00000i 0.638470 + 0.638470i 0.950178 0.311708i \(-0.100901\pi\)
−0.311708 + 0.950178i \(0.600901\pi\)
\(158\) 0 0
\(159\) 8.00000 0.634441
\(160\) 0 0
\(161\) 10.0000 0.788110
\(162\) 0 0
\(163\) −9.00000 9.00000i −0.704934 0.704934i 0.260531 0.965465i \(-0.416102\pi\)
−0.965465 + 0.260531i \(0.916102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.00000 + 5.00000i −0.386912 + 0.386912i −0.873584 0.486673i \(-0.838210\pi\)
0.486673 + 0.873584i \(0.338210\pi\)
\(168\) 0 0
\(169\) 19.0000i 1.46154i
\(170\) 0 0
\(171\) 4.00000i 0.305888i
\(172\) 0 0
\(173\) −8.00000 + 8.00000i −0.608229 + 0.608229i −0.942483 0.334254i \(-0.891516\pi\)
0.334254 + 0.942483i \(0.391516\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 4.00000 + 4.00000i 0.300658 + 0.300658i
\(178\) 0 0
\(179\) −12.0000 −0.896922 −0.448461 0.893802i \(-0.648028\pi\)
−0.448461 + 0.893802i \(0.648028\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) 0 0
\(183\) 8.00000 + 8.00000i 0.591377 + 0.591377i
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) −16.0000 + 16.0000i −1.17004 + 1.17004i
\(188\) 0 0
\(189\) 8.00000i 0.581914i
\(190\) 0 0
\(191\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(192\) 0 0
\(193\) 4.00000 4.00000i 0.287926 0.287926i −0.548333 0.836260i \(-0.684738\pi\)
0.836260 + 0.548333i \(0.184738\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 4.00000 + 4.00000i 0.284988 + 0.284988i 0.835095 0.550106i \(-0.185413\pi\)
−0.550106 + 0.835095i \(0.685413\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) −6.00000 −0.423207
\(202\) 0 0
\(203\) −2.00000 2.00000i −0.140372 0.140372i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −5.00000 + 5.00000i −0.347524 + 0.347524i
\(208\) 0 0
\(209\) 16.0000i 1.10674i
\(210\) 0 0
\(211\) 20.0000i 1.37686i −0.725304 0.688428i \(-0.758301\pi\)
0.725304 0.688428i \(-0.241699\pi\)
\(212\) 0 0
\(213\) −16.0000 + 16.0000i −1.09630 + 1.09630i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) −8.00000 8.00000i −0.543075 0.543075i
\(218\) 0 0
\(219\) −8.00000 −0.540590
\(220\) 0 0
\(221\) 32.0000 2.15255
\(222\) 0 0
\(223\) −9.00000 9.00000i −0.602685 0.602685i 0.338340 0.941024i \(-0.390135\pi\)
−0.941024 + 0.338340i \(0.890135\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.00000 7.00000i 0.464606 0.464606i −0.435556 0.900162i \(-0.643448\pi\)
0.900162 + 0.435556i \(0.143448\pi\)
\(228\) 0 0
\(229\) 26.0000i 1.71813i −0.511868 0.859064i \(-0.671046\pi\)
0.511868 0.859064i \(-0.328954\pi\)
\(230\) 0 0
\(231\) 8.00000i 0.526361i
\(232\) 0 0
\(233\) 12.0000 12.0000i 0.786146 0.786146i −0.194714 0.980860i \(-0.562378\pi\)
0.980860 + 0.194714i \(0.0623778\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 8.00000 + 8.00000i 0.519656 + 0.519656i
\(238\) 0 0
\(239\) −24.0000 −1.55243 −0.776215 0.630468i \(-0.782863\pi\)
−0.776215 + 0.630468i \(0.782863\pi\)
\(240\) 0 0
\(241\) 4.00000 0.257663 0.128831 0.991667i \(-0.458877\pi\)
0.128831 + 0.991667i \(0.458877\pi\)
\(242\) 0 0
\(243\) −7.00000 7.00000i −0.449050 0.449050i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 16.0000 16.0000i 1.01806 1.01806i
\(248\) 0 0
\(249\) 10.0000i 0.633724i
\(250\) 0 0
\(251\) 12.0000i 0.757433i −0.925513 0.378717i \(-0.876365\pi\)
0.925513 0.378717i \(-0.123635\pi\)
\(252\) 0 0
\(253\) 20.0000 20.0000i 1.25739 1.25739i
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 16.0000 + 16.0000i 0.998053 + 0.998053i 0.999998 0.00194553i \(-0.000619281\pi\)
−0.00194553 + 0.999998i \(0.500619\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 2.00000 0.123797
\(262\) 0 0
\(263\) 9.00000 + 9.00000i 0.554964 + 0.554964i 0.927869 0.372906i \(-0.121638\pi\)
−0.372906 + 0.927869i \(0.621638\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 10.0000 10.0000i 0.611990 0.611990i
\(268\) 0 0
\(269\) 24.0000i 1.46331i 0.681677 + 0.731653i \(0.261251\pi\)
−0.681677 + 0.731653i \(0.738749\pi\)
\(270\) 0 0
\(271\) 8.00000i 0.485965i −0.970031 0.242983i \(-0.921874\pi\)
0.970031 0.242983i \(-0.0781258\pi\)
\(272\) 0 0
\(273\) −8.00000 + 8.00000i −0.484182 + 0.484182i
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 16.0000 + 16.0000i 0.961347 + 0.961347i 0.999280 0.0379334i \(-0.0120775\pi\)
−0.0379334 + 0.999280i \(0.512077\pi\)
\(278\) 0 0
\(279\) 8.00000 0.478947
\(280\) 0 0
\(281\) −20.0000 −1.19310 −0.596550 0.802576i \(-0.703462\pi\)
−0.596550 + 0.802576i \(0.703462\pi\)
\(282\) 0 0
\(283\) 5.00000 + 5.00000i 0.297219 + 0.297219i 0.839924 0.542705i \(-0.182600\pi\)
−0.542705 + 0.839924i \(0.682600\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 4.00000 4.00000i 0.236113 0.236113i
\(288\) 0 0
\(289\) 15.0000i 0.882353i
\(290\) 0 0
\(291\) 24.0000i 1.40690i
\(292\) 0 0
\(293\) 8.00000 8.00000i 0.467365 0.467365i −0.433695 0.901060i \(-0.642790\pi\)
0.901060 + 0.433695i \(0.142790\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0 0
\(297\) 16.0000 + 16.0000i 0.928414 + 0.928414i
\(298\) 0 0
\(299\) −40.0000 −2.31326
\(300\) 0 0
\(301\) −14.0000 −0.806947
\(302\) 0 0
\(303\) −6.00000 6.00000i −0.344691 0.344691i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −3.00000 + 3.00000i −0.171219 + 0.171219i −0.787515 0.616296i \(-0.788633\pi\)
0.616296 + 0.787515i \(0.288633\pi\)
\(308\) 0 0
\(309\) 6.00000i 0.341328i
\(310\) 0 0
\(311\) 8.00000i 0.453638i −0.973937 0.226819i \(-0.927167\pi\)
0.973937 0.226819i \(-0.0728326\pi\)
\(312\) 0 0
\(313\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −20.0000 20.0000i −1.12331 1.12331i −0.991240 0.132072i \(-0.957837\pi\)
−0.132072 0.991240i \(-0.542163\pi\)
\(318\) 0 0
\(319\) −8.00000 −0.447914
\(320\) 0 0
\(321\) 6.00000 0.334887
\(322\) 0 0
\(323\) 16.0000 + 16.0000i 0.890264 + 0.890264i
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) −16.0000 + 16.0000i −0.884802 + 0.884802i
\(328\) 0 0
\(329\) 6.00000i 0.330791i
\(330\) 0 0
\(331\) 12.0000i 0.659580i −0.944054 0.329790i \(-0.893022\pi\)
0.944054 0.329790i \(-0.106978\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −16.0000 16.0000i −0.871576 0.871576i 0.121069 0.992644i \(-0.461368\pi\)
−0.992644 + 0.121069i \(0.961368\pi\)
\(338\) 0 0
\(339\) 16.0000 0.869001
\(340\) 0 0
\(341\) −32.0000 −1.73290
\(342\) 0 0
\(343\) −12.0000 12.0000i −0.647939 0.647939i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 1.00000 1.00000i 0.0536828 0.0536828i −0.679756 0.733439i \(-0.737914\pi\)
0.733439 + 0.679756i \(0.237914\pi\)
\(348\) 0 0
\(349\) 2.00000i 0.107058i −0.998566 0.0535288i \(-0.982953\pi\)
0.998566 0.0535288i \(-0.0170469\pi\)
\(350\) 0 0
\(351\) 32.0000i 1.70803i
\(352\) 0 0
\(353\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) −8.00000 8.00000i −0.423405 0.423405i
\(358\) 0 0
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) 0 0
\(361\) −3.00000 −0.157895
\(362\) 0 0
\(363\) −5.00000 5.00000i −0.262432 0.262432i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −23.0000 + 23.0000i −1.20059 + 1.20059i −0.226603 + 0.973987i \(0.572762\pi\)
−0.973987 + 0.226603i \(0.927238\pi\)
\(368\) 0 0
\(369\) 4.00000i 0.208232i
\(370\) 0 0
\(371\) 8.00000i 0.415339i
\(372\) 0 0
\(373\) 24.0000 24.0000i 1.24267 1.24267i 0.283785 0.958888i \(-0.408410\pi\)
0.958888 0.283785i \(-0.0915902\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 8.00000 + 8.00000i 0.412021 + 0.412021i
\(378\) 0 0
\(379\) 4.00000 0.205466 0.102733 0.994709i \(-0.467241\pi\)
0.102733 + 0.994709i \(0.467241\pi\)
\(380\) 0 0
\(381\) 30.0000 1.53695
\(382\) 0 0
\(383\) −17.0000 17.0000i −0.868659 0.868659i 0.123665 0.992324i \(-0.460535\pi\)
−0.992324 + 0.123665i \(0.960535\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 7.00000 7.00000i 0.355830 0.355830i
\(388\) 0 0
\(389\) 8.00000i 0.405616i −0.979219 0.202808i \(-0.934993\pi\)
0.979219 0.202808i \(-0.0650067\pi\)
\(390\) 0 0
\(391\) 40.0000i 2.02289i
\(392\) 0 0
\(393\) −12.0000 + 12.0000i −0.605320 + 0.605320i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 4.00000 + 4.00000i 0.200754 + 0.200754i 0.800323 0.599569i \(-0.204661\pi\)
−0.599569 + 0.800323i \(0.704661\pi\)
\(398\) 0 0
\(399\) −8.00000 −0.400501
\(400\) 0 0
\(401\) 30.0000 1.49813 0.749064 0.662497i \(-0.230503\pi\)
0.749064 + 0.662497i \(0.230503\pi\)
\(402\) 0 0
\(403\) 32.0000 + 32.0000i 1.59403 + 1.59403i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 20.0000i 0.988936i −0.869196 0.494468i \(-0.835363\pi\)
0.869196 0.494468i \(-0.164637\pi\)
\(410\) 0 0
\(411\) 16.0000i 0.789222i
\(412\) 0 0
\(413\) −4.00000 + 4.00000i −0.196827 + 0.196827i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 12.0000 + 12.0000i 0.587643 + 0.587643i
\(418\) 0 0
\(419\) −28.0000 −1.36789 −0.683945 0.729534i \(-0.739737\pi\)
−0.683945 + 0.729534i \(0.739737\pi\)
\(420\) 0 0
\(421\) 8.00000 0.389896 0.194948 0.980814i \(-0.437546\pi\)
0.194948 + 0.980814i \(0.437546\pi\)
\(422\) 0 0
\(423\) 3.00000 + 3.00000i 0.145865 + 0.145865i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −8.00000 + 8.00000i −0.387147 + 0.387147i
\(428\) 0 0
\(429\) 32.0000i 1.54497i
\(430\) 0 0
\(431\) 8.00000i 0.385346i 0.981263 + 0.192673i \(0.0617157\pi\)
−0.981263 + 0.192673i \(0.938284\pi\)
\(432\) 0 0
\(433\) −20.0000 + 20.0000i −0.961139 + 0.961139i −0.999273 0.0381340i \(-0.987859\pi\)
0.0381340 + 0.999273i \(0.487859\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −20.0000 20.0000i −0.956730 0.956730i
\(438\) 0 0
\(439\) 8.00000 0.381819 0.190910 0.981608i \(-0.438856\pi\)
0.190910 + 0.981608i \(0.438856\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) 0 0
\(443\) −13.0000 13.0000i −0.617649 0.617649i 0.327279 0.944928i \(-0.393868\pi\)
−0.944928 + 0.327279i \(0.893868\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 8.00000 8.00000i 0.378387 0.378387i
\(448\) 0 0
\(449\) 4.00000i 0.188772i 0.995536 + 0.0943858i \(0.0300887\pi\)
−0.995536 + 0.0943858i \(0.969911\pi\)
\(450\) 0 0
\(451\) 16.0000i 0.753411i
\(452\) 0 0
\(453\) 8.00000 8.00000i 0.375873 0.375873i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(458\) 0 0
\(459\) 32.0000 1.49363
\(460\) 0 0
\(461\) −18.0000 −0.838344 −0.419172 0.907907i \(-0.637680\pi\)
−0.419172 + 0.907907i \(0.637680\pi\)
\(462\) 0 0
\(463\) −3.00000 3.00000i −0.139422 0.139422i 0.633951 0.773373i \(-0.281432\pi\)
−0.773373 + 0.633951i \(0.781432\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 25.0000 25.0000i 1.15686 1.15686i 0.171715 0.985147i \(-0.445069\pi\)
0.985147 0.171715i \(-0.0549310\pi\)
\(468\) 0 0
\(469\) 6.00000i 0.277054i
\(470\) 0 0
\(471\) 16.0000i 0.737241i
\(472\) 0 0
\(473\) −28.0000 + 28.0000i −1.28744 + 1.28744i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −4.00000 4.00000i −0.183147 0.183147i
\(478\) 0 0
\(479\) −16.0000 −0.731059 −0.365529 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 10.0000 + 10.0000i 0.455016 + 0.455016i
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 25.0000 25.0000i 1.13286 1.13286i 0.143158 0.989700i \(-0.454274\pi\)
0.989700 0.143158i \(-0.0457258\pi\)
\(488\) 0 0
\(489\) 18.0000i 0.813988i
\(490\) 0 0
\(491\) 12.0000i 0.541552i 0.962642 + 0.270776i \(0.0872803\pi\)
−0.962642 + 0.270776i \(0.912720\pi\)
\(492\) 0 0
\(493\) −8.00000 + 8.00000i −0.360302 + 0.360302i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −16.0000 16.0000i −0.717698 0.717698i
\(498\) 0 0
\(499\) −20.0000 −0.895323 −0.447661 0.894203i \(-0.647743\pi\)
−0.447661 + 0.894203i \(0.647743\pi\)
\(500\) 0 0
\(501\) −10.0000 −0.446767
\(502\) 0 0
\(503\) −11.0000 11.0000i −0.490466 0.490466i 0.417987 0.908453i \(-0.362736\pi\)
−0.908453 + 0.417987i \(0.862736\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 19.0000 19.0000i 0.843820 0.843820i
\(508\) 0 0
\(509\) 30.0000i 1.32973i −0.746965 0.664863i \(-0.768490\pi\)
0.746965 0.664863i \(-0.231510\pi\)
\(510\) 0 0
\(511\) 8.00000i 0.353899i
\(512\) 0 0
\(513\) 16.0000 16.0000i 0.706417 0.706417i
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) −12.0000 12.0000i −0.527759 0.527759i
\(518\) 0 0
\(519\) −16.0000 −0.702322
\(520\) 0 0
\(521\) −22.0000 −0.963837 −0.481919 0.876216i \(-0.660060\pi\)
−0.481919 + 0.876216i \(0.660060\pi\)
\(522\) 0 0
\(523\) 5.00000 + 5.00000i 0.218635 + 0.218635i 0.807923 0.589288i \(-0.200592\pi\)
−0.589288 + 0.807923i \(0.700592\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) −32.0000 + 32.0000i −1.39394 + 1.39394i
\(528\) 0 0
\(529\) 27.0000i 1.17391i
\(530\) 0 0
\(531\) 4.00000i 0.173585i
\(532\) 0 0
\(533\) −16.0000 + 16.0000i −0.693037 + 0.693037i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −12.0000 12.0000i −0.517838 0.517838i
\(538\) 0 0
\(539\) −20.0000 −0.861461
\(540\) 0 0
\(541\) 30.0000 1.28980 0.644900 0.764267i \(-0.276899\pi\)
0.644900 + 0.764267i \(0.276899\pi\)
\(542\) 0 0
\(543\) −10.0000 10.0000i −0.429141 0.429141i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −17.0000 + 17.0000i −0.726868 + 0.726868i −0.969994 0.243127i \(-0.921827\pi\)
0.243127 + 0.969994i \(0.421827\pi\)
\(548\) 0 0
\(549\) 8.00000i 0.341432i
\(550\) 0 0
\(551\) 8.00000i 0.340811i
\(552\) 0 0
\(553\) −8.00000 + 8.00000i −0.340195 + 0.340195i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(558\) 0 0
\(559\) 56.0000 2.36855
\(560\) 0 0
\(561\) −32.0000 −1.35104
\(562\) 0 0
\(563\) −15.0000 15.0000i −0.632175 0.632175i 0.316438 0.948613i \(-0.397513\pi\)
−0.948613 + 0.316438i \(0.897513\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −5.00000 + 5.00000i −0.209980 + 0.209980i
\(568\) 0 0
\(569\) 20.0000i 0.838444i 0.907884 + 0.419222i \(0.137697\pi\)
−0.907884 + 0.419222i \(0.862303\pi\)
\(570\) 0 0
\(571\) 4.00000i 0.167395i −0.996491 0.0836974i \(-0.973327\pi\)
0.996491 0.0836974i \(-0.0266729\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 8.00000 + 8.00000i 0.333044 + 0.333044i 0.853741 0.520697i \(-0.174328\pi\)
−0.520697 + 0.853741i \(0.674328\pi\)
\(578\) 0 0
\(579\) 8.00000 0.332469
\(580\) 0 0
\(581\) 10.0000 0.414870
\(582\) 0 0
\(583\) 16.0000 + 16.0000i 0.662652 + 0.662652i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −25.0000 + 25.0000i −1.03186 + 1.03186i −0.0323850 + 0.999475i \(0.510310\pi\)
−0.999475 + 0.0323850i \(0.989690\pi\)
\(588\) 0 0
\(589\) 32.0000i 1.31854i
\(590\) 0 0
\(591\) 8.00000i 0.329076i
\(592\) 0 0
\(593\) 8.00000 8.00000i 0.328521 0.328521i −0.523503 0.852024i \(-0.675375\pi\)
0.852024 + 0.523503i \(0.175375\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) −16.0000 −0.653742 −0.326871 0.945069i \(-0.605994\pi\)
−0.326871 + 0.945069i \(0.605994\pi\)
\(600\) 0 0
\(601\) 4.00000 0.163163 0.0815817 0.996667i \(-0.474003\pi\)
0.0815817 + 0.996667i \(0.474003\pi\)
\(602\) 0 0
\(603\) 3.00000 + 3.00000i 0.122169 + 0.122169i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 5.00000 5.00000i 0.202944 0.202944i −0.598316 0.801260i \(-0.704163\pi\)
0.801260 + 0.598316i \(0.204163\pi\)
\(608\) 0 0
\(609\) 4.00000i 0.162088i
\(610\) 0 0
\(611\) 24.0000i 0.970936i
\(612\) 0 0
\(613\) −12.0000 + 12.0000i −0.484675 + 0.484675i −0.906621 0.421946i \(-0.861347\pi\)
0.421946 + 0.906621i \(0.361347\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −4.00000 4.00000i −0.161034 0.161034i 0.621991 0.783025i \(-0.286324\pi\)
−0.783025 + 0.621991i \(0.786324\pi\)
\(618\) 0 0
\(619\) 12.0000 0.482321 0.241160 0.970485i \(-0.422472\pi\)
0.241160 + 0.970485i \(0.422472\pi\)
\(620\) 0 0
\(621\) −40.0000 −1.60514
\(622\) 0 0
\(623\) 10.0000 + 10.0000i 0.400642 + 0.400642i
\(624\) 0 0
\(625\) 0 0
\(626\) 0 0
\(627\) −16.0000 + 16.0000i −0.638978 + 0.638978i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 40.0000i 1.59237i 0.605050 + 0.796187i \(0.293153\pi\)
−0.605050 + 0.796187i \(0.706847\pi\)
\(632\) 0 0
\(633\) 20.0000 20.0000i 0.794929 0.794929i
\(634\) 0 0
\(635\) 0 0
\(636\) 0 0
\(637\) 20.0000 + 20.0000i 0.792429 + 0.792429i
\(638\) 0 0
\(639\) 16.0000 0.632950
\(640\) 0 0
\(641\) 12.0000 0.473972 0.236986 0.971513i \(-0.423841\pi\)
0.236986 + 0.971513i \(0.423841\pi\)
\(642\) 0 0
\(643\) −11.0000 11.0000i −0.433798 0.433798i 0.456120 0.889918i \(-0.349239\pi\)
−0.889918 + 0.456120i \(0.849239\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.00000 1.00000i 0.0393141 0.0393141i −0.687176 0.726491i \(-0.741150\pi\)
0.726491 + 0.687176i \(0.241150\pi\)
\(648\) 0 0
\(649\) 16.0000i 0.628055i
\(650\) 0 0
\(651\) 16.0000i 0.627089i
\(652\) 0 0
\(653\) 20.0000 20.0000i 0.782660 0.782660i −0.197619 0.980279i \(-0.563321\pi\)
0.980279 + 0.197619i \(0.0633207\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 4.00000 + 4.00000i 0.156055 + 0.156055i
\(658\) 0 0
\(659\) 4.00000 0.155818 0.0779089 0.996960i \(-0.475176\pi\)
0.0779089 + 0.996960i \(0.475176\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 32.0000 + 32.0000i 1.24278 + 1.24278i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 10.0000 10.0000i 0.387202 0.387202i
\(668\) 0 0
\(669\) 18.0000i 0.695920i
\(670\) 0 0
\(671\) 32.0000i 1.23535i
\(672\) 0 0
\(673\) −4.00000 + 4.00000i −0.154189 + 0.154189i −0.779986 0.625797i \(-0.784774\pi\)
0.625797 + 0.779986i \(0.284774\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 20.0000 + 20.0000i 0.768662 + 0.768662i 0.977871 0.209209i \(-0.0670888\pi\)
−0.209209 + 0.977871i \(0.567089\pi\)
\(678\) 0 0
\(679\) 24.0000 0.921035
\(680\) 0 0
\(681\) 14.0000 0.536481
\(682\) 0 0
\(683\) −17.0000 17.0000i −0.650487 0.650487i 0.302623 0.953110i \(-0.402138\pi\)
−0.953110 + 0.302623i \(0.902138\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 26.0000 26.0000i 0.991962 0.991962i
\(688\) 0 0
\(689\) 32.0000i 1.21910i
\(690\) 0 0
\(691\) 20.0000i 0.760836i 0.924815 + 0.380418i \(0.124220\pi\)
−0.924815 + 0.380418i \(0.875780\pi\)
\(692\) 0 0
\(693\) −4.00000 + 4.00000i −0.151947 + 0.151947i
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) −16.0000 16.0000i −0.606043 0.606043i
\(698\) 0 0
\(699\) 24.0000 0.907763
\(700\) 0 0
\(701\) 48.0000 1.81293 0.906467 0.422276i \(-0.138769\pi\)
0.906467 + 0.422276i \(0.138769\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 6.00000 6.00000i 0.225653 0.225653i
\(708\) 0 0
\(709\) 6.00000i 0.225335i −0.993633 0.112667i \(-0.964061\pi\)
0.993633 0.112667i \(-0.0359394\pi\)
\(710\) 0 0
\(711\) 8.00000i 0.300023i
\(712\) 0 0
\(713\) 40.0000 40.0000i 1.49801 1.49801i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −24.0000 24.0000i −0.896296 0.896296i
\(718\) 0 0
\(719\) −24.0000 −0.895049 −0.447524 0.894272i \(-0.647694\pi\)
−0.447524 + 0.894272i \(0.647694\pi\)
\(720\) 0 0
\(721\) 6.00000 0.223452
\(722\) 0 0
\(723\) 4.00000 + 4.00000i 0.148762 + 0.148762i
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) 15.0000 15.0000i 0.556319 0.556319i −0.371938 0.928257i \(-0.621307\pi\)
0.928257 + 0.371938i \(0.121307\pi\)
\(728\) 0 0
\(729\) 29.0000i 1.07407i
\(730\) 0 0
\(731\) 56.0000i 2.07123i
\(732\) 0 0
\(733\) −24.0000 + 24.0000i −0.886460 + 0.886460i −0.994181 0.107721i \(-0.965645\pi\)
0.107721 + 0.994181i \(0.465645\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) −12.0000 12.0000i −0.442026 0.442026i
\(738\) 0 0
\(739\) 52.0000 1.91285 0.956425 0.291977i \(-0.0943129\pi\)
0.956425 + 0.291977i \(0.0943129\pi\)
\(740\) 0 0
\(741\) 32.0000 1.17555
\(742\) 0 0
\(743\) −1.00000 1.00000i −0.0366864 0.0366864i 0.688526 0.725212i \(-0.258258\pi\)
−0.725212 + 0.688526i \(0.758258\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) −5.00000 + 5.00000i −0.182940 + 0.182940i
\(748\) 0 0
\(749\) 6.00000i 0.219235i
\(750\) 0 0
\(751\) 16.0000i 0.583848i −0.956441 0.291924i \(-0.905705\pi\)
0.956441 0.291924i \(-0.0942955\pi\)
\(752\) 0 0
\(753\) 12.0000 12.0000i 0.437304 0.437304i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 24.0000 + 24.0000i 0.872295 + 0.872295i 0.992722 0.120427i \(-0.0384265\pi\)
−0.120427 + 0.992722i \(0.538426\pi\)
\(758\) 0 0
\(759\) 40.0000 1.45191
\(760\) 0 0
\(761\) 10.0000 0.362500 0.181250 0.983437i \(-0.441986\pi\)
0.181250 + 0.983437i \(0.441986\pi\)
\(762\) 0 0
\(763\) −16.0000 16.0000i −0.579239 0.579239i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 16.0000 16.0000i 0.577727 0.577727i
\(768\) 0 0
\(769\) 2.00000i 0.0721218i 0.999350 + 0.0360609i \(0.0114810\pi\)
−0.999350 + 0.0360609i \(0.988519\pi\)
\(770\) 0 0
\(771\) 32.0000i 1.15245i
\(772\) 0 0
\(773\) −20.0000 + 20.0000i −0.719350 + 0.719350i −0.968472 0.249122i \(-0.919858\pi\)
0.249122 + 0.968472i \(0.419858\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) −16.0000 −0.573259
\(780\) 0 0
\(781\) −64.0000 −2.29010
\(782\) 0 0
\(783\) 8.00000 + 8.00000i 0.285897 + 0.285897i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 11.0000 11.0000i 0.392108 0.392108i −0.483330 0.875438i \(-0.660573\pi\)
0.875438 + 0.483330i \(0.160573\pi\)
\(788\) 0 0
\(789\) 18.0000i 0.640817i
\(790\) 0 0
\(791\) 16.0000i 0.568895i
\(792\) 0 0
\(793\) 32.0000 32.0000i 1.13635 1.13635i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0