Properties

Label 1620.2.i.e.541.1
Level $1620$
Weight $2$
Character 1620.541
Analytic conductor $12.936$
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] = [1620,2,Mod(541,1620)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1620, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1620.541");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1620 = 2^{2} \cdot 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1620.i (of order \(3\), 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: \(12.9357651274\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 541.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 1620.541
Dual form 1620.2.i.e.1081.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.500000 - 0.866025i) q^{5} +(2.00000 - 3.46410i) q^{7} +O(q^{10})\) \(q+(-0.500000 - 0.866025i) q^{5} +(2.00000 - 3.46410i) q^{7} +(-1.50000 + 2.59808i) q^{11} +(2.00000 + 3.46410i) q^{13} +5.00000 q^{19} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(4.50000 - 7.79423i) q^{29} +(-2.50000 - 4.33013i) q^{31} -4.00000 q^{35} +2.00000 q^{37} +(4.50000 + 7.79423i) q^{41} +(5.00000 - 8.66025i) q^{43} +(3.00000 - 5.19615i) q^{47} +(-4.50000 - 7.79423i) q^{49} -12.0000 q^{53} +3.00000 q^{55} +(-4.50000 - 7.79423i) q^{59} +(5.00000 - 8.66025i) q^{61} +(2.00000 - 3.46410i) q^{65} +(-1.00000 - 1.73205i) q^{67} +3.00000 q^{71} -4.00000 q^{73} +(6.00000 + 10.3923i) q^{77} +(2.00000 - 3.46410i) q^{79} +(-3.00000 + 5.19615i) q^{83} -9.00000 q^{89} +16.0000 q^{91} +(-2.50000 - 4.33013i) q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - q^{5} + 4 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - q^{5} + 4 q^{7} - 3 q^{11} + 4 q^{13} + 10 q^{19} + 6 q^{23} - q^{25} + 9 q^{29} - 5 q^{31} - 8 q^{35} + 4 q^{37} + 9 q^{41} + 10 q^{43} + 6 q^{47} - 9 q^{49} - 24 q^{53} + 6 q^{55} - 9 q^{59} + 10 q^{61} + 4 q^{65} - 2 q^{67} + 6 q^{71} - 8 q^{73} + 12 q^{77} + 4 q^{79} - 6 q^{83} - 18 q^{89} + 32 q^{91} - 5 q^{95} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1620\mathbb{Z}\right)^\times\).

\(n\) \(811\) \(1297\) \(1541\)
\(\chi(n)\) \(1\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 0 0
\(4\) 0 0
\(5\) −0.500000 0.866025i −0.223607 0.387298i
\(6\) 0 0
\(7\) 2.00000 3.46410i 0.755929 1.30931i −0.188982 0.981981i \(-0.560519\pi\)
0.944911 0.327327i \(-0.106148\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) 0 0
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) 0 0
\(13\) 2.00000 + 3.46410i 0.554700 + 0.960769i 0.997927 + 0.0643593i \(0.0205004\pi\)
−0.443227 + 0.896410i \(0.646166\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) 5.00000 1.14708 0.573539 0.819178i \(-0.305570\pi\)
0.573539 + 0.819178i \(0.305570\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 3.00000 + 5.19615i 0.625543 + 1.08347i 0.988436 + 0.151642i \(0.0484560\pi\)
−0.362892 + 0.931831i \(0.618211\pi\)
\(24\) 0 0
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 4.50000 7.79423i 0.835629 1.44735i −0.0578882 0.998323i \(-0.518437\pi\)
0.893517 0.449029i \(-0.148230\pi\)
\(30\) 0 0
\(31\) −2.50000 4.33013i −0.449013 0.777714i 0.549309 0.835619i \(-0.314891\pi\)
−0.998322 + 0.0579057i \(0.981558\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) −4.00000 −0.676123
\(36\) 0 0
\(37\) 2.00000 0.328798 0.164399 0.986394i \(-0.447432\pi\)
0.164399 + 0.986394i \(0.447432\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 4.50000 + 7.79423i 0.702782 + 1.21725i 0.967486 + 0.252924i \(0.0813924\pi\)
−0.264704 + 0.964330i \(0.585274\pi\)
\(42\) 0 0
\(43\) 5.00000 8.66025i 0.762493 1.32068i −0.179069 0.983836i \(-0.557309\pi\)
0.941562 0.336840i \(-0.109358\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 3.00000 5.19615i 0.437595 0.757937i −0.559908 0.828554i \(-0.689164\pi\)
0.997503 + 0.0706177i \(0.0224970\pi\)
\(48\) 0 0
\(49\) −4.50000 7.79423i −0.642857 1.11346i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −12.0000 −1.64833 −0.824163 0.566352i \(-0.808354\pi\)
−0.824163 + 0.566352i \(0.808354\pi\)
\(54\) 0 0
\(55\) 3.00000 0.404520
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) −4.50000 7.79423i −0.585850 1.01472i −0.994769 0.102151i \(-0.967427\pi\)
0.408919 0.912571i \(-0.365906\pi\)
\(60\) 0 0
\(61\) 5.00000 8.66025i 0.640184 1.10883i −0.345207 0.938527i \(-0.612191\pi\)
0.985391 0.170305i \(-0.0544754\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0 0
\(65\) 2.00000 3.46410i 0.248069 0.429669i
\(66\) 0 0
\(67\) −1.00000 1.73205i −0.122169 0.211604i 0.798454 0.602056i \(-0.205652\pi\)
−0.920623 + 0.390453i \(0.872318\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 3.00000 0.356034 0.178017 0.984027i \(-0.443032\pi\)
0.178017 + 0.984027i \(0.443032\pi\)
\(72\) 0 0
\(73\) −4.00000 −0.468165 −0.234082 0.972217i \(-0.575209\pi\)
−0.234082 + 0.972217i \(0.575209\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 6.00000 + 10.3923i 0.683763 + 1.18431i
\(78\) 0 0
\(79\) 2.00000 3.46410i 0.225018 0.389742i −0.731307 0.682048i \(-0.761089\pi\)
0.956325 + 0.292306i \(0.0944227\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) 0 0
\(83\) −3.00000 + 5.19615i −0.329293 + 0.570352i −0.982372 0.186938i \(-0.940144\pi\)
0.653079 + 0.757290i \(0.273477\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) 0 0
\(91\) 16.0000 1.67726
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) −2.50000 4.33013i −0.256495 0.444262i
\(96\) 0 0
\(97\) −1.00000 + 1.73205i −0.101535 + 0.175863i −0.912317 0.409484i \(-0.865709\pi\)
0.810782 + 0.585348i \(0.199042\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 7.50000 12.9904i 0.746278 1.29259i −0.203317 0.979113i \(-0.565172\pi\)
0.949595 0.313478i \(-0.101494\pi\)
\(102\) 0 0
\(103\) 5.00000 + 8.66025i 0.492665 + 0.853320i 0.999964 0.00844953i \(-0.00268960\pi\)
−0.507300 + 0.861770i \(0.669356\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 6.00000 0.580042 0.290021 0.957020i \(-0.406338\pi\)
0.290021 + 0.957020i \(0.406338\pi\)
\(108\) 0 0
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) −6.00000 10.3923i −0.564433 0.977626i −0.997102 0.0760733i \(-0.975762\pi\)
0.432670 0.901553i \(-0.357572\pi\)
\(114\) 0 0
\(115\) 3.00000 5.19615i 0.279751 0.484544i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 20.0000 1.77471 0.887357 0.461084i \(-0.152539\pi\)
0.887357 + 0.461084i \(0.152539\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 7.50000 + 12.9904i 0.655278 + 1.13497i 0.981824 + 0.189794i \(0.0607819\pi\)
−0.326546 + 0.945181i \(0.605885\pi\)
\(132\) 0 0
\(133\) 10.0000 17.3205i 0.867110 1.50188i
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 0 0
\(139\) 6.50000 + 11.2583i 0.551323 + 0.954919i 0.998179 + 0.0603135i \(0.0192101\pi\)
−0.446857 + 0.894606i \(0.647457\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) −12.0000 −1.00349
\(144\) 0 0
\(145\) −9.00000 −0.747409
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 9.00000 + 15.5885i 0.737309 + 1.27706i 0.953703 + 0.300750i \(0.0972370\pi\)
−0.216394 + 0.976306i \(0.569430\pi\)
\(150\) 0 0
\(151\) −8.50000 + 14.7224i −0.691720 + 1.19809i 0.279554 + 0.960130i \(0.409814\pi\)
−0.971274 + 0.237964i \(0.923520\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −2.50000 + 4.33013i −0.200805 + 0.347804i
\(156\) 0 0
\(157\) −7.00000 12.1244i −0.558661 0.967629i −0.997609 0.0691164i \(-0.977982\pi\)
0.438948 0.898513i \(-0.355351\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 24.0000 1.89146
\(162\) 0 0
\(163\) −4.00000 −0.313304 −0.156652 0.987654i \(-0.550070\pi\)
−0.156652 + 0.987654i \(0.550070\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 0 0
\(169\) −1.50000 + 2.59808i −0.115385 + 0.199852i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 3.00000 5.19615i 0.228086 0.395056i −0.729155 0.684349i \(-0.760087\pi\)
0.957241 + 0.289292i \(0.0934200\pi\)
\(174\) 0 0
\(175\) 2.00000 + 3.46410i 0.151186 + 0.261861i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 9.00000 0.672692 0.336346 0.941739i \(-0.390809\pi\)
0.336346 + 0.941739i \(0.390809\pi\)
\(180\) 0 0
\(181\) −13.0000 −0.966282 −0.483141 0.875542i \(-0.660504\pi\)
−0.483141 + 0.875542i \(0.660504\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −1.00000 1.73205i −0.0735215 0.127343i
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i \(-0.867950\pi\)
0.806641 + 0.591041i \(0.201283\pi\)
\(192\) 0 0
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) −12.0000 −0.854965 −0.427482 0.904024i \(-0.640599\pi\)
−0.427482 + 0.904024i \(0.640599\pi\)
\(198\) 0 0
\(199\) −16.0000 −1.13421 −0.567105 0.823646i \(-0.691937\pi\)
−0.567105 + 0.823646i \(0.691937\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) −18.0000 31.1769i −1.26335 2.18819i
\(204\) 0 0
\(205\) 4.50000 7.79423i 0.314294 0.544373i
\(206\) 0 0
\(207\) 0 0
\(208\) 0 0
\(209\) −7.50000 + 12.9904i −0.518786 + 0.898563i
\(210\) 0 0
\(211\) −2.50000 4.33013i −0.172107 0.298098i 0.767049 0.641588i \(-0.221724\pi\)
−0.939156 + 0.343490i \(0.888391\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) 0 0
\(215\) −10.0000 −0.681994
\(216\) 0 0
\(217\) −20.0000 −1.35769
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −4.00000 + 6.92820i −0.267860 + 0.463947i −0.968309 0.249756i \(-0.919650\pi\)
0.700449 + 0.713702i \(0.252983\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 12.0000 20.7846i 0.796468 1.37952i −0.125435 0.992102i \(-0.540033\pi\)
0.921903 0.387421i \(-0.126634\pi\)
\(228\) 0 0
\(229\) −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i \(-0.319740\pi\)
−0.999088 + 0.0426906i \(0.986407\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −30.0000 −1.96537 −0.982683 0.185296i \(-0.940675\pi\)
−0.982683 + 0.185296i \(0.940675\pi\)
\(234\) 0 0
\(235\) −6.00000 −0.391397
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 12.0000 + 20.7846i 0.776215 + 1.34444i 0.934109 + 0.356988i \(0.116196\pi\)
−0.157893 + 0.987456i \(0.550470\pi\)
\(240\) 0 0
\(241\) −14.5000 + 25.1147i −0.934027 + 1.61778i −0.157667 + 0.987492i \(0.550397\pi\)
−0.776360 + 0.630290i \(0.782936\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) −4.50000 + 7.79423i −0.287494 + 0.497955i
\(246\) 0 0
\(247\) 10.0000 + 17.3205i 0.636285 + 1.10208i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) −18.0000 −1.13165
\(254\) 0 0
\(255\) 0 0
\(256\) 0 0
\(257\) 3.00000 + 5.19615i 0.187135 + 0.324127i 0.944294 0.329104i \(-0.106747\pi\)
−0.757159 + 0.653231i \(0.773413\pi\)
\(258\) 0 0
\(259\) 4.00000 6.92820i 0.248548 0.430498i
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) −3.00000 + 5.19615i −0.184988 + 0.320408i −0.943572 0.331166i \(-0.892558\pi\)
0.758585 + 0.651575i \(0.225891\pi\)
\(264\) 0 0
\(265\) 6.00000 + 10.3923i 0.368577 + 0.638394i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 21.0000 1.28039 0.640196 0.768211i \(-0.278853\pi\)
0.640196 + 0.768211i \(0.278853\pi\)
\(270\) 0 0
\(271\) 32.0000 1.94386 0.971931 0.235267i \(-0.0755965\pi\)
0.971931 + 0.235267i \(0.0755965\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) −1.50000 2.59808i −0.0904534 0.156670i
\(276\) 0 0
\(277\) −13.0000 + 22.5167i −0.781094 + 1.35290i 0.150210 + 0.988654i \(0.452005\pi\)
−0.931305 + 0.364241i \(0.881328\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 9.00000 15.5885i 0.536895 0.929929i −0.462174 0.886789i \(-0.652930\pi\)
0.999069 0.0431402i \(-0.0137362\pi\)
\(282\) 0 0
\(283\) 11.0000 + 19.0526i 0.653882 + 1.13256i 0.982173 + 0.187980i \(0.0601941\pi\)
−0.328291 + 0.944577i \(0.606473\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 36.0000 2.12501
\(288\) 0 0
\(289\) −17.0000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −15.0000 25.9808i −0.876309 1.51781i −0.855361 0.518032i \(-0.826665\pi\)
−0.0209480 0.999781i \(-0.506668\pi\)
\(294\) 0 0
\(295\) −4.50000 + 7.79423i −0.262000 + 0.453798i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) −12.0000 + 20.7846i −0.693978 + 1.20201i
\(300\) 0 0
\(301\) −20.0000 34.6410i −1.15278 1.99667i
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) −10.0000 −0.572598
\(306\) 0 0
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 1.50000 + 2.59808i 0.0850572 + 0.147323i 0.905416 0.424526i \(-0.139559\pi\)
−0.820358 + 0.571850i \(0.806226\pi\)
\(312\) 0 0
\(313\) −10.0000 + 17.3205i −0.565233 + 0.979013i 0.431795 + 0.901972i \(0.357881\pi\)
−0.997028 + 0.0770410i \(0.975453\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) −9.00000 + 15.5885i −0.505490 + 0.875535i 0.494489 + 0.869184i \(0.335355\pi\)
−0.999980 + 0.00635137i \(0.997978\pi\)
\(318\) 0 0
\(319\) 13.5000 + 23.3827i 0.755855 + 1.30918i
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) −4.00000 −0.221880
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −12.0000 20.7846i −0.661581 1.14589i
\(330\) 0 0
\(331\) −2.50000 + 4.33013i −0.137412 + 0.238005i −0.926516 0.376254i \(-0.877212\pi\)
0.789104 + 0.614260i \(0.210545\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) −1.00000 + 1.73205i −0.0546358 + 0.0946320i
\(336\) 0 0
\(337\) −4.00000 6.92820i −0.217894 0.377403i 0.736270 0.676688i \(-0.236585\pi\)
−0.954164 + 0.299285i \(0.903252\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 15.0000 0.812296
\(342\) 0 0
\(343\) −8.00000 −0.431959
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −12.0000 20.7846i −0.644194 1.11578i −0.984487 0.175457i \(-0.943860\pi\)
0.340293 0.940319i \(-0.389474\pi\)
\(348\) 0 0
\(349\) −8.50000 + 14.7224i −0.454995 + 0.788074i −0.998688 0.0512103i \(-0.983692\pi\)
0.543693 + 0.839284i \(0.317025\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 3.00000 5.19615i 0.159674 0.276563i −0.775077 0.631867i \(-0.782289\pi\)
0.934751 + 0.355303i \(0.115622\pi\)
\(354\) 0 0
\(355\) −1.50000 2.59808i −0.0796117 0.137892i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 15.0000 0.791670 0.395835 0.918322i \(-0.370455\pi\)
0.395835 + 0.918322i \(0.370455\pi\)
\(360\) 0 0
\(361\) 6.00000 0.315789
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 2.00000 + 3.46410i 0.104685 + 0.181319i
\(366\) 0 0
\(367\) −7.00000 + 12.1244i −0.365397 + 0.632886i −0.988840 0.148983i \(-0.952400\pi\)
0.623443 + 0.781869i \(0.285733\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) −24.0000 + 41.5692i −1.24602 + 2.15817i
\(372\) 0 0
\(373\) 14.0000 + 24.2487i 0.724893 + 1.25555i 0.959018 + 0.283344i \(0.0914439\pi\)
−0.234126 + 0.972206i \(0.575223\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 36.0000 1.85409
\(378\) 0 0
\(379\) −4.00000 −0.205466 −0.102733 0.994709i \(-0.532759\pi\)
−0.102733 + 0.994709i \(0.532759\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) −18.0000 31.1769i −0.919757 1.59307i −0.799783 0.600289i \(-0.795052\pi\)
−0.119974 0.992777i \(-0.538281\pi\)
\(384\) 0 0
\(385\) 6.00000 10.3923i 0.305788 0.529641i
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 9.00000 15.5885i 0.456318 0.790366i −0.542445 0.840091i \(-0.682501\pi\)
0.998763 + 0.0497253i \(0.0158346\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) −4.00000 −0.201262
\(396\) 0 0
\(397\) 2.00000 0.100377 0.0501886 0.998740i \(-0.484018\pi\)
0.0501886 + 0.998740i \(0.484018\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 9.00000 + 15.5885i 0.449439 + 0.778450i 0.998350 0.0574304i \(-0.0182907\pi\)
−0.548911 + 0.835881i \(0.684957\pi\)
\(402\) 0 0
\(403\) 10.0000 17.3205i 0.498135 0.862796i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −3.00000 + 5.19615i −0.148704 + 0.257564i
\(408\) 0 0
\(409\) 5.00000 + 8.66025i 0.247234 + 0.428222i 0.962757 0.270367i \(-0.0871450\pi\)
−0.715523 + 0.698589i \(0.753812\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) −36.0000 −1.77144
\(414\) 0 0
\(415\) 6.00000 0.294528
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(420\) 0 0
\(421\) −8.50000 + 14.7224i −0.414265 + 0.717527i −0.995351 0.0963145i \(-0.969295\pi\)
0.581086 + 0.813842i \(0.302628\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) −20.0000 34.6410i −0.967868 1.67640i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 33.0000 1.58955 0.794777 0.606902i \(-0.207588\pi\)
0.794777 + 0.606902i \(0.207588\pi\)
\(432\) 0 0
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 15.0000 + 25.9808i 0.717547 + 1.24283i
\(438\) 0 0
\(439\) −8.50000 + 14.7224i −0.405683 + 0.702663i −0.994401 0.105675i \(-0.966300\pi\)
0.588718 + 0.808339i \(0.299633\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) −3.00000 + 5.19615i −0.142534 + 0.246877i −0.928450 0.371457i \(-0.878858\pi\)
0.785916 + 0.618333i \(0.212192\pi\)
\(444\) 0 0
\(445\) 4.50000 + 7.79423i 0.213320 + 0.369482i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −39.0000 −1.84052 −0.920262 0.391303i \(-0.872024\pi\)
−0.920262 + 0.391303i \(0.872024\pi\)
\(450\) 0 0
\(451\) −27.0000 −1.27138
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) −8.00000 13.8564i −0.375046 0.649598i
\(456\) 0 0
\(457\) 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.50000 2.59808i 0.0698620 0.121004i −0.828978 0.559281i \(-0.811077\pi\)
0.898840 + 0.438276i \(0.144411\pi\)
\(462\) 0 0
\(463\) 17.0000 + 29.4449i 0.790057 + 1.36842i 0.925931 + 0.377693i \(0.123282\pi\)
−0.135874 + 0.990726i \(0.543384\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) −8.00000 −0.369406
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 15.0000 + 25.9808i 0.689701 + 1.19460i
\(474\) 0 0
\(475\) −2.50000 + 4.33013i −0.114708 + 0.198680i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −1.50000 + 2.59808i −0.0685367 + 0.118709i −0.898257 0.439470i \(-0.855166\pi\)
0.829721 + 0.558179i \(0.188500\pi\)
\(480\) 0 0
\(481\) 4.00000 + 6.92820i 0.182384 + 0.315899i
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 2.00000 0.0908153
\(486\) 0 0
\(487\) −16.0000 −0.725029 −0.362515 0.931978i \(-0.618082\pi\)
−0.362515 + 0.931978i \(0.618082\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) 1.50000 + 2.59808i 0.0676941 + 0.117250i 0.897886 0.440228i \(-0.145102\pi\)
−0.830192 + 0.557478i \(0.811769\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 6.00000 10.3923i 0.269137 0.466159i
\(498\) 0 0
\(499\) −20.5000 35.5070i −0.917706 1.58951i −0.802890 0.596127i \(-0.796706\pi\)
−0.114816 0.993387i \(-0.536628\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) −36.0000 −1.60516 −0.802580 0.596544i \(-0.796540\pi\)
−0.802580 + 0.596544i \(0.796540\pi\)
\(504\) 0 0
\(505\) −15.0000 −0.667491
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −9.00000 15.5885i −0.398918 0.690946i 0.594675 0.803966i \(-0.297281\pi\)
−0.993593 + 0.113020i \(0.963948\pi\)
\(510\) 0 0
\(511\) −8.00000 + 13.8564i −0.353899 + 0.612971i
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 5.00000 8.66025i 0.220326 0.381616i
\(516\) 0 0
\(517\) 9.00000 + 15.5885i 0.395820 + 0.685580i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 18.0000 0.788594 0.394297 0.918983i \(-0.370988\pi\)
0.394297 + 0.918983i \(0.370988\pi\)
\(522\) 0 0
\(523\) −16.0000 −0.699631 −0.349816 0.936819i \(-0.613756\pi\)
−0.349816 + 0.936819i \(0.613756\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −6.50000 + 11.2583i −0.282609 + 0.489493i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) −18.0000 + 31.1769i −0.779667 + 1.35042i
\(534\) 0 0
\(535\) −3.00000 5.19615i −0.129701 0.224649i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 27.0000 1.16297
\(540\) 0 0
\(541\) −1.00000 −0.0429934 −0.0214967 0.999769i \(-0.506843\pi\)
−0.0214967 + 0.999769i \(0.506843\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −5.50000 9.52628i −0.235594 0.408061i
\(546\) 0 0
\(547\) −10.0000 + 17.3205i −0.427569 + 0.740571i −0.996657 0.0817056i \(-0.973963\pi\)
0.569087 + 0.822277i \(0.307297\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 22.5000 38.9711i 0.958532 1.66023i
\(552\) 0 0
\(553\) −8.00000 13.8564i −0.340195 0.589234i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −24.0000 −1.01691 −0.508456 0.861088i \(-0.669784\pi\)
−0.508456 + 0.861088i \(0.669784\pi\)
\(558\) 0 0
\(559\) 40.0000 1.69182
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 9.00000 + 15.5885i 0.379305 + 0.656975i 0.990961 0.134148i \(-0.0428299\pi\)
−0.611656 + 0.791123i \(0.709497\pi\)
\(564\) 0 0
\(565\) −6.00000 + 10.3923i −0.252422 + 0.437208i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 13.5000 23.3827i 0.565949 0.980253i −0.431011 0.902347i \(-0.641843\pi\)
0.996961 0.0779066i \(-0.0248236\pi\)
\(570\) 0 0
\(571\) −5.50000 9.52628i −0.230168 0.398662i 0.727690 0.685907i \(-0.240594\pi\)
−0.957857 + 0.287244i \(0.907261\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −6.00000 −0.250217
\(576\) 0 0
\(577\) 20.0000 0.832611 0.416305 0.909225i \(-0.363325\pi\)
0.416305 + 0.909225i \(0.363325\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 12.0000 + 20.7846i 0.497844 + 0.862291i
\(582\) 0 0
\(583\) 18.0000 31.1769i 0.745484 1.29122i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −9.00000 + 15.5885i −0.371470 + 0.643404i −0.989792 0.142520i \(-0.954479\pi\)
0.618322 + 0.785925i \(0.287813\pi\)
\(588\) 0 0
\(589\) −12.5000 21.6506i −0.515054 0.892099i
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 42.0000 1.72473 0.862367 0.506284i \(-0.168981\pi\)
0.862367 + 0.506284i \(0.168981\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0 0
\(599\) 1.50000 + 2.59808i 0.0612883 + 0.106155i 0.895042 0.445983i \(-0.147146\pi\)
−0.833753 + 0.552137i \(0.813812\pi\)
\(600\) 0 0
\(601\) 9.50000 16.4545i 0.387513 0.671192i −0.604601 0.796528i \(-0.706668\pi\)
0.992114 + 0.125336i \(0.0400009\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 1.00000 1.73205i 0.0406558 0.0704179i
\(606\) 0 0
\(607\) 11.0000 + 19.0526i 0.446476 + 0.773320i 0.998154 0.0607380i \(-0.0193454\pi\)
−0.551678 + 0.834058i \(0.686012\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 24.0000 0.970936
\(612\) 0 0
\(613\) −4.00000 −0.161558 −0.0807792 0.996732i \(-0.525741\pi\)
−0.0807792 + 0.996732i \(0.525741\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 24.0000 + 41.5692i 0.966204 + 1.67351i 0.706346 + 0.707867i \(0.250342\pi\)
0.259858 + 0.965647i \(0.416324\pi\)
\(618\) 0 0
\(619\) 14.0000 24.2487i 0.562708 0.974638i −0.434551 0.900647i \(-0.643093\pi\)
0.997259 0.0739910i \(-0.0235736\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) −18.0000 + 31.1769i −0.721155 + 1.24908i
\(624\) 0 0
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 5.00000 0.199047 0.0995234 0.995035i \(-0.468268\pi\)
0.0995234 + 0.995035i \(0.468268\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −10.0000 17.3205i −0.396838 0.687343i
\(636\) 0 0
\(637\) 18.0000 31.1769i 0.713186 1.23527i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) −1.50000 + 2.59808i −0.0592464 + 0.102618i −0.894127 0.447813i \(-0.852203\pi\)
0.834881 + 0.550431i \(0.185536\pi\)
\(642\) 0 0
\(643\) −7.00000 12.1244i −0.276053 0.478138i 0.694347 0.719640i \(-0.255693\pi\)
−0.970400 + 0.241502i \(0.922360\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −30.0000 −1.17942 −0.589711 0.807614i \(-0.700758\pi\)
−0.589711 + 0.807614i \(0.700758\pi\)
\(648\) 0 0
\(649\) 27.0000 1.05984
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −24.0000 41.5692i −0.939193 1.62673i −0.766982 0.641669i \(-0.778242\pi\)
−0.172211 0.985060i \(-0.555091\pi\)
\(654\) 0 0
\(655\) 7.50000 12.9904i 0.293049 0.507576i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 6.00000 10.3923i 0.233727 0.404827i −0.725175 0.688565i \(-0.758241\pi\)
0.958902 + 0.283738i \(0.0915745\pi\)
\(660\) 0 0
\(661\) 9.50000 + 16.4545i 0.369507 + 0.640005i 0.989489 0.144611i \(-0.0461932\pi\)
−0.619981 + 0.784617i \(0.712860\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −20.0000 −0.775567
\(666\) 0 0
\(667\) 54.0000 2.09089
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 15.0000 + 25.9808i 0.579069 + 1.00298i
\(672\) 0 0
\(673\) 11.0000 19.0526i 0.424019 0.734422i −0.572309 0.820038i \(-0.693952\pi\)
0.996328 + 0.0856156i \(0.0272857\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) −3.00000 + 5.19615i −0.115299 + 0.199704i −0.917899 0.396813i \(-0.870116\pi\)
0.802600 + 0.596518i \(0.203449\pi\)
\(678\) 0 0
\(679\) 4.00000 + 6.92820i 0.153506 + 0.265880i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −24.0000 −0.918334 −0.459167 0.888350i \(-0.651852\pi\)
−0.459167 + 0.888350i \(0.651852\pi\)
\(684\) 0 0
\(685\) 12.0000 0.458496
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) −24.0000 41.5692i −0.914327 1.58366i
\(690\) 0 0
\(691\) 14.0000 24.2487i 0.532585 0.922464i −0.466691 0.884420i \(-0.654554\pi\)
0.999276 0.0380440i \(-0.0121127\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 6.50000 11.2583i 0.246559 0.427053i
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) −9.00000 −0.339925 −0.169963 0.985451i \(-0.554365\pi\)
−0.169963 + 0.985451i \(0.554365\pi\)
\(702\) 0 0
\(703\) 10.0000 0.377157
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −30.0000 51.9615i −1.12827 1.95421i
\(708\) 0 0
\(709\) −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 15.0000 25.9808i 0.561754 0.972987i
\(714\) 0 0
\(715\) 6.00000 + 10.3923i 0.224387 + 0.388650i
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) −15.0000 −0.559406 −0.279703 0.960087i \(-0.590236\pi\)
−0.279703 + 0.960087i \(0.590236\pi\)
\(720\) 0 0
\(721\) 40.0000 1.48968
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) 4.50000 + 7.79423i 0.167126 + 0.289470i
\(726\) 0 0
\(727\) −22.0000 + 38.1051i −0.815935 + 1.41324i 0.0927199 + 0.995692i \(0.470444\pi\)
−0.908655 + 0.417548i \(0.862889\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 11.0000 + 19.0526i 0.406294 + 0.703722i 0.994471 0.105010i \(-0.0334875\pi\)
−0.588177 + 0.808732i \(0.700154\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 6.00000 0.221013
\(738\) 0 0
\(739\) 11.0000 0.404642 0.202321 0.979319i \(-0.435152\pi\)
0.202321 + 0.979319i \(0.435152\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 24.0000 + 41.5692i 0.880475 + 1.52503i 0.850814 + 0.525467i \(0.176109\pi\)
0.0296605 + 0.999560i \(0.490557\pi\)
\(744\) 0 0
\(745\) 9.00000 15.5885i 0.329734 0.571117i
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 12.0000 20.7846i 0.438470 0.759453i
\(750\) 0 0
\(751\) 20.0000 + 34.6410i 0.729810 + 1.26407i 0.956963 + 0.290209i \(0.0937250\pi\)
−0.227153 + 0.973859i \(0.572942\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 17.0000 0.618693
\(756\) 0 0
\(757\) −52.0000 −1.88997 −0.944986 0.327111i \(-0.893925\pi\)
−0.944986 + 0.327111i \(0.893925\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 1.50000 + 2.59808i 0.0543750 + 0.0941802i 0.891932 0.452170i \(-0.149350\pi\)
−0.837557 + 0.546350i \(0.816017\pi\)
\(762\) 0 0
\(763\) 22.0000 38.1051i 0.796453 1.37950i
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 18.0000 31.1769i 0.649942 1.12573i
\(768\) 0 0
\(769\) −2.50000 4.33013i −0.0901523 0.156148i 0.817423 0.576038i \(-0.195402\pi\)
−0.907575 + 0.419890i \(0.862069\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 6.00000 0.215805 0.107903 0.994161i \(-0.465587\pi\)
0.107903 + 0.994161i \(0.465587\pi\)
\(774\) 0 0
\(775\) 5.00000 0.179605
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 22.5000 + 38.9711i 0.806146 + 1.39629i
\(780\) 0 0
\(781\) −4.50000 + 7.79423i −0.161023 + 0.278899i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −7.00000 + 12.1244i −0.249841 + 0.432737i
\(786\) 0 0
\(787\) −16.0000 27.7128i −0.570338 0.987855i −0.996531 0.0832226i \(-0.973479\pi\)
0.426193 0.904632i \(-0.359855\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) −48.0000 −1.70668
\(792\) 0 0
\(793\) 40.0000 1.42044
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 6.00000 + 10.3923i 0.212531 + 0.368114i 0.952506 0.304520i \(-0.0984960\pi\)
−0.739975 + 0.672634i \(0.765163\pi\)