Properties

Label 1600.2.n.i.1343.1
Level $1600$
Weight $2$
Character 1600.1343
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 1343.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1600.1343
Dual form 1600.2.n.i.1407.1

$q$-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 \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).

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

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 −0.356822 0.934172i \(-0.616140\pi\)
0.934172 + 0.356822i \(0.116140\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) 0 0
\(7\) −1.00000 1.00000i −0.377964 0.377964i 0.492403 0.870367i \(-0.336119\pi\)
−0.870367 + 0.492403i \(0.836119\pi\)
\(8\) 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 −0.993229 0.116171i \(-0.962938\pi\)
−0.116171 0.993229i \(-0.537062\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) −4.00000 + 4.00000i −0.970143 + 0.970143i −0.999567 0.0294245i \(-0.990633\pi\)
0.0294245 + 0.999567i \(0.490633\pi\)
\(18\) 0 0
\(19\) −4.00000 −0.917663 −0.458831 0.888523i \(-0.651732\pi\)
−0.458831 + 0.888523i \(0.651732\pi\)
\(20\) 0 0
\(21\) −2.00000 −0.436436
\(22\) 0 0
\(23\) −5.00000 + 5.00000i −1.04257 + 1.04257i −0.0435195 + 0.999053i \(0.513857\pi\)
−0.999053 + 0.0435195i \(0.986143\pi\)
\(24\) 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 \(-0.940546\pi\)
0.982607 0.185695i \(-0.0594537\pi\)
\(30\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(38\) 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 0.0699387 0.997551i \(-0.477720\pi\)
0.997551 0.0699387i \(-0.0222804\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −3.00000 3.00000i −0.437595 0.437595i 0.453607 0.891202i \(-0.350137\pi\)
−0.891202 + 0.453607i \(0.850137\pi\)
\(48\) 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 \(-0.377012\pi\)
−0.926279 + 0.376837i \(0.877012\pi\)
\(54\) 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 \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 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 0.499694 0.866202i \(-0.333446\pi\)
−0.866202 + 0.499694i \(0.833446\pi\)
\(68\) 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 \(-0.142600\pi\)
−0.433155 + 0.901319i \(0.642600\pi\)
\(74\) 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 \(-0.648589\pi\)
−0.450035 + 0.893011i \(0.648589\pi\)
\(80\) 0 0
\(81\) 5.00000 0.555556
\(82\) 0 0
\(83\) −5.00000 + 5.00000i −0.548821 + 0.548821i −0.926100 0.377279i \(-0.876860\pi\)
0.377279 + 0.926100i \(0.376860\pi\)
\(84\) 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 \(0.177808\pi\)
−0.847998 + 0.529999i \(0.822192\pi\)
\(90\) 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 0.250229 0.968187i \(-0.419494\pi\)
0.968187 0.250229i \(-0.0805058\pi\)
\(98\) 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 −0.839287 0.543688i \(-0.817027\pi\)
0.543688 + 0.839287i \(0.317027\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 3.00000 + 3.00000i 0.290021 + 0.290021i 0.837088 0.547068i \(-0.184256\pi\)
−0.547068 + 0.837088i \(0.684256\pi\)
\(108\) 0 0
\(109\) 16.0000i 1.53252i −0.642529 0.766261i \(-0.722115\pi\)
0.642529 0.766261i \(-0.277885\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −8.00000 8.00000i −0.752577 0.752577i 0.222383 0.974959i \(-0.428617\pi\)
−0.974959 + 0.222383i \(0.928617\pi\)
\(114\) 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 0.904445 + 0.426589i \(0.140285\pi\)
0.426589 + 0.904445i \(0.359715\pi\)
\(128\) 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 \(-0.589439\pi\)
0.960784 + 0.277298i \(0.0894389\pi\)
\(138\) 0 0
\(139\) −12.0000 −1.01783 −0.508913 0.860818i \(-0.669953\pi\)
−0.508913 + 0.860818i \(0.669953\pi\)
\(140\) 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 \(0.106271\pi\)
−0.944784 + 0.327693i \(0.893729\pi\)
\(150\) 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 \(-0.899099\pi\)
0.311708 + 0.950178i \(0.399099\pi\)
\(158\) 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 −0.965465 0.260531i \(-0.916102\pi\)
0.260531 + 0.965465i \(0.416102\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −5.00000 5.00000i −0.386912 0.386912i 0.486673 0.873584i \(-0.338210\pi\)
−0.873584 + 0.486673i \(0.838210\pi\)
\(168\) 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 \(-0.108484\pi\)
−0.334254 + 0.942483i \(0.608484\pi\)
\(174\) 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 \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 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 \(-0.315262\pi\)
−0.836260 + 0.548333i \(0.815262\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −4.00000 + 4.00000i −0.284988 + 0.284988i −0.835095 0.550106i \(-0.814587\pi\)
0.550106 + 0.835095i \(0.314587\pi\)
\(198\) 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 −0.941024 0.338340i \(-0.890135\pi\)
0.338340 + 0.941024i \(0.390135\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 7.00000 + 7.00000i 0.464606 + 0.464606i 0.900162 0.435556i \(-0.143448\pi\)
−0.435556 + 0.900162i \(0.643448\pi\)
\(228\) 0 0
\(229\) 26.0000i 1.71813i 0.511868 + 0.859064i \(0.328954\pi\)
−0.511868 + 0.859064i \(0.671046\pi\)
\(230\) 0 0
\(231\) 8.00000i 0.526361i
\(232\) 0 0
\(233\) −12.0000 12.0000i −0.786146 0.786146i 0.194714 0.980860i \(-0.437622\pi\)
−0.980860 + 0.194714i \(0.937622\pi\)
\(234\) 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 \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 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 \(-0.999381\pi\)
0.00194553 + 0.999998i \(0.499381\pi\)
\(258\) 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 −0.372906 0.927869i \(-0.621638\pi\)
0.927869 + 0.372906i \(0.121638\pi\)
\(264\) 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 \(-0.738749\pi\)
0.681677 0.731653i \(-0.261251\pi\)
\(270\) 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 \(-0.987923\pi\)
0.0379334 + 0.999280i \(0.487923\pi\)
\(278\) 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 −0.542705 0.839924i \(-0.682600\pi\)
0.839924 + 0.542705i \(0.182600\pi\)
\(284\) 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 \(-0.357210\pi\)
−0.901060 + 0.433695i \(0.857210\pi\)
\(294\) 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 0.616296 0.787515i \(-0.288633\pi\)
−0.787515 + 0.616296i \(0.788633\pi\)
\(308\) 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 \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 20.0000 20.0000i 1.12331 1.12331i 0.132072 0.991240i \(-0.457837\pi\)
0.991240 0.132072i \(-0.0421629\pi\)
\(318\) 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 \(-0.538632\pi\)
0.992644 + 0.121069i \(0.0386321\pi\)
\(338\) 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 0.733439 0.679756i \(-0.237914\pi\)
−0.679756 + 0.733439i \(0.737914\pi\)
\(348\) 0 0
\(349\) 2.00000i 0.107058i 0.998566 + 0.0535288i \(0.0170469\pi\)
−0.998566 + 0.0535288i \(0.982953\pi\)
\(350\) 0 0
\(351\) 32.0000i 1.70803i
\(352\) 0 0
\(353\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(354\) 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 \(-0.281685\pi\)
0.633336 + 0.773877i \(0.281685\pi\)
\(360\) 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 −0.973987 0.226603i \(-0.927238\pi\)
−0.226603 0.973987i \(-0.572762\pi\)
\(368\) 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 −0.958888 0.283785i \(-0.908410\pi\)
−0.283785 0.958888i \(-0.591590\pi\)
\(374\) 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 \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) 30.0000 1.53695
\(382\) 0 0
\(383\) −17.0000 + 17.0000i −0.868659 + 0.868659i −0.992324 0.123665i \(-0.960535\pi\)
0.123665 + 0.992324i \(0.460535\pi\)
\(384\) 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 \(0.0650067\pi\)
−0.979219 + 0.202808i \(0.934993\pi\)
\(390\) 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 \(-0.795339\pi\)
0.599569 + 0.800323i \(0.295339\pi\)
\(398\) 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 \(0.164637\pi\)
−0.869196 + 0.494468i \(0.835363\pi\)
\(410\) 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 \(-0.260263\pi\)
0.683945 + 0.729534i \(0.260263\pi\)
\(420\) 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 \(-0.0121414\pi\)
−0.0381340 + 0.999273i \(0.512141\pi\)
\(434\) 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 \(-0.561144\pi\)
−0.190910 + 0.981608i \(0.561144\pi\)
\(440\) 0 0
\(441\) 5.00000 0.238095
\(442\) 0 0
\(443\) −13.0000 + 13.0000i −0.617649 + 0.617649i −0.944928 0.327279i \(-0.893868\pi\)
0.327279 + 0.944928i \(0.393868\pi\)
\(444\) 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 \(-0.969911\pi\)
0.995536 0.0943858i \(-0.0300887\pi\)
\(450\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(458\) 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 −0.773373 0.633951i \(-0.781432\pi\)
0.633951 + 0.773373i \(0.281432\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 25.0000 + 25.0000i 1.15686 + 1.15686i 0.985147 + 0.171715i \(0.0549310\pi\)
0.171715 + 0.985147i \(0.445069\pi\)
\(468\) 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 \(-0.380888\pi\)
0.365529 + 0.930800i \(0.380888\pi\)
\(480\) 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 0.989700 + 0.143158i \(0.0457258\pi\)
0.143158 + 0.989700i \(0.454274\pi\)
\(488\) 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 \(-0.352257\pi\)
0.447661 + 0.894203i \(0.352257\pi\)
\(500\) 0 0
\(501\) −10.0000 −0.446767
\(502\) 0 0
\(503\) −11.0000 + 11.0000i −0.490466 + 0.490466i −0.908453 0.417987i \(-0.862736\pi\)
0.417987 + 0.908453i \(0.362736\pi\)
\(504\) 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 \(0.231510\pi\)
−0.746965 + 0.664863i \(0.768490\pi\)
\(510\) 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 −0.589288 0.807923i \(-0.700592\pi\)
0.807923 + 0.589288i \(0.200592\pi\)
\(524\) 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 0.243127 0.969994i \(-0.421827\pi\)
−0.969994 + 0.243127i \(0.921827\pi\)
\(548\) 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 \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(558\) 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 −0.948613 0.316438i \(-0.897513\pi\)
0.316438 + 0.948613i \(0.397513\pi\)
\(564\) 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 \(-0.862303\pi\)
0.907884 0.419222i \(-0.137697\pi\)
\(570\) 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 \(-0.825672\pi\)
0.520697 + 0.853741i \(0.325672\pi\)
\(578\) 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 −0.999475 0.0323850i \(-0.989690\pi\)
−0.0323850 0.999475i \(-0.510310\pi\)
\(588\) 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 \(-0.324625\pi\)
−0.852024 + 0.523503i \(0.824625\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 16.0000 0.653742 0.326871 0.945069i \(-0.394006\pi\)
0.326871 + 0.945069i \(0.394006\pi\)
\(600\) 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 0.801260 0.598316i \(-0.204163\pi\)
−0.598316 + 0.801260i \(0.704163\pi\)
\(608\) 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 \(-0.138653\pi\)
−0.421946 + 0.906621i \(0.638653\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 4.00000 4.00000i 0.161034 0.161034i −0.621991 0.783025i \(-0.713676\pi\)
0.783025 + 0.621991i \(0.213676\pi\)
\(618\) 0 0
\(619\) −12.0000 −0.482321 −0.241160 0.970485i \(-0.577528\pi\)
−0.241160 + 0.970485i \(0.577528\pi\)
\(620\) 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 −0.889918 0.456120i \(-0.849239\pi\)
0.456120 + 0.889918i \(0.349239\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.00000 + 1.00000i 0.0393141 + 0.0393141i 0.726491 0.687176i \(-0.241150\pi\)
−0.687176 + 0.726491i \(0.741150\pi\)
\(648\) 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 \(-0.436679\pi\)
−0.980279 + 0.197619i \(0.936679\pi\)
\(654\) 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 \(-0.524824\pi\)
−0.0779089 + 0.996960i \(0.524824\pi\)
\(660\) 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 \(-0.215226\pi\)
−0.625797 + 0.779986i \(0.715226\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −20.0000 + 20.0000i −0.768662 + 0.768662i −0.977871 0.209209i \(-0.932911\pi\)
0.209209 + 0.977871i \(0.432911\pi\)
\(678\) 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 −0.953110 0.302623i \(-0.902138\pi\)
0.302623 + 0.953110i \(0.402138\pi\)
\(684\) 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 \(0.0359394\pi\)
−0.993633 + 0.112667i \(0.964061\pi\)
\(710\) 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 \(-0.352306\pi\)
0.447524 + 0.894272i \(0.352306\pi\)
\(720\) 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 0.928257 0.371938i \(-0.121307\pi\)
−0.371938 + 0.928257i \(0.621307\pi\)
\(728\) 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 \(-0.0343553\pi\)
−0.107721 + 0.994181i \(0.534355\pi\)
\(734\) 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 \(-0.905687\pi\)
−0.956425 + 0.291977i \(0.905687\pi\)
\(740\) 0 0
\(741\) 32.0000 1.17555
\(742\) 0 0
\(743\) −1.00000 + 1.00000i −0.0366864 + 0.0366864i −0.725212 0.688526i \(-0.758258\pi\)
0.688526 + 0.725212i \(0.258258\pi\)
\(744\) 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 \(-0.961574\pi\)
0.120427 + 0.992722i \(0.461574\pi\)
\(758\) 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 \(-0.988519\pi\)
0.999350 0.0360609i \(-0.0114810\pi\)
\(770\) 0 0
\(771\) 32.0000i 1.15245i
\(772\) 0 0
\(773\) 20.0000 + 20.0000i 0.719350 + 0.719350i 0.968472 0.249122i \(-0.0801420\pi\)
−0.249122 + 0.968472i \(0.580142\pi\)
\(774\) 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 0.875438 0.483330i \(-0.160573\pi\)
−0.483330 + 0.875438i \(0.660573\pi\)
\(788\) 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
\(797\)