Properties

Label 1305.2.f.d.289.2
Level $1305$
Weight $2$
Character 1305.289
Analytic conductor $10.420$
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] = [1305,2,Mod(289,1305)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1305, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1305.289");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1305 = 3^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1305.f (of order \(2\), degree \(1\), 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: \(10.4204774638\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 435)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 289.2
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 1305.289
Dual form 1305.2.f.d.289.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+2.00000 q^{2} +2.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} -4.00000i q^{7} +O(q^{10})\) \(q+2.00000 q^{2} +2.00000 q^{4} +(-2.00000 + 1.00000i) q^{5} -4.00000i q^{7} +(-4.00000 + 2.00000i) q^{10} +1.00000i q^{11} -2.00000i q^{13} -8.00000i q^{14} -4.00000 q^{16} +6.00000 q^{17} -4.00000i q^{19} +(-4.00000 + 2.00000i) q^{20} +2.00000i q^{22} -9.00000i q^{23} +(3.00000 - 4.00000i) q^{25} -4.00000i q^{26} -8.00000i q^{28} +(2.00000 - 5.00000i) q^{29} -2.00000i q^{31} -8.00000 q^{32} +12.0000 q^{34} +(4.00000 + 8.00000i) q^{35} -1.00000 q^{37} -8.00000i q^{38} +9.00000i q^{41} -1.00000 q^{43} +2.00000i q^{44} -18.0000i q^{46} -8.00000 q^{47} -9.00000 q^{49} +(6.00000 - 8.00000i) q^{50} -4.00000i q^{52} +9.00000i q^{53} +(-1.00000 - 2.00000i) q^{55} +(4.00000 - 10.0000i) q^{58} -8.00000 q^{59} -6.00000i q^{61} -4.00000i q^{62} -8.00000 q^{64} +(2.00000 + 4.00000i) q^{65} +12.0000i q^{67} +12.0000 q^{68} +(8.00000 + 16.0000i) q^{70} -2.00000 q^{71} +15.0000 q^{73} -2.00000 q^{74} -8.00000i q^{76} +4.00000 q^{77} +4.00000i q^{79} +(8.00000 - 4.00000i) q^{80} +18.0000i q^{82} -7.00000i q^{83} +(-12.0000 + 6.00000i) q^{85} -2.00000 q^{86} -2.00000i q^{89} -8.00000 q^{91} -18.0000i q^{92} -16.0000 q^{94} +(4.00000 + 8.00000i) q^{95} +11.0000 q^{97} -18.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 4 q^{2} + 4 q^{4} - 4 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 4 q^{2} + 4 q^{4} - 4 q^{5} - 8 q^{10} - 8 q^{16} + 12 q^{17} - 8 q^{20} + 6 q^{25} + 4 q^{29} - 16 q^{32} + 24 q^{34} + 8 q^{35} - 2 q^{37} - 2 q^{43} - 16 q^{47} - 18 q^{49} + 12 q^{50} - 2 q^{55} + 8 q^{58} - 16 q^{59} - 16 q^{64} + 4 q^{65} + 24 q^{68} + 16 q^{70} - 4 q^{71} + 30 q^{73} - 4 q^{74} + 8 q^{77} + 16 q^{80} - 24 q^{85} - 4 q^{86} - 16 q^{91} - 32 q^{94} + 8 q^{95} + 22 q^{97} - 36 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1305\mathbb{Z}\right)^\times\).

\(n\) \(146\) \(262\) \(901\)
\(\chi(n)\) \(1\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.00000 1.41421 0.707107 0.707107i \(-0.250000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(3\) 0 0
\(4\) 2.00000 1.00000
\(5\) −2.00000 + 1.00000i −0.894427 + 0.447214i
\(6\) 0 0
\(7\) 4.00000i 1.51186i −0.654654 0.755929i \(-0.727186\pi\)
0.654654 0.755929i \(-0.272814\pi\)
\(8\) 0 0
\(9\) 0 0
\(10\) −4.00000 + 2.00000i −1.26491 + 0.632456i
\(11\) 1.00000i 0.301511i 0.988571 + 0.150756i \(0.0481707\pi\)
−0.988571 + 0.150756i \(0.951829\pi\)
\(12\) 0 0
\(13\) 2.00000i 0.554700i −0.960769 0.277350i \(-0.910544\pi\)
0.960769 0.277350i \(-0.0894562\pi\)
\(14\) 8.00000i 2.13809i
\(15\) 0 0
\(16\) −4.00000 −1.00000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) 4.00000i 0.917663i −0.888523 0.458831i \(-0.848268\pi\)
0.888523 0.458831i \(-0.151732\pi\)
\(20\) −4.00000 + 2.00000i −0.894427 + 0.447214i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 9.00000i 1.87663i −0.345782 0.938315i \(-0.612386\pi\)
0.345782 0.938315i \(-0.387614\pi\)
\(24\) 0 0
\(25\) 3.00000 4.00000i 0.600000 0.800000i
\(26\) 4.00000i 0.784465i
\(27\) 0 0
\(28\) 8.00000i 1.51186i
\(29\) 2.00000 5.00000i 0.371391 0.928477i
\(30\) 0 0
\(31\) 2.00000i 0.359211i −0.983739 0.179605i \(-0.942518\pi\)
0.983739 0.179605i \(-0.0574821\pi\)
\(32\) −8.00000 −1.41421
\(33\) 0 0
\(34\) 12.0000 2.05798
\(35\) 4.00000 + 8.00000i 0.676123 + 1.35225i
\(36\) 0 0
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) 8.00000i 1.29777i
\(39\) 0 0
\(40\) 0 0
\(41\) 9.00000i 1.40556i 0.711405 + 0.702782i \(0.248059\pi\)
−0.711405 + 0.702782i \(0.751941\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) 2.00000i 0.301511i
\(45\) 0 0
\(46\) 18.0000i 2.65396i
\(47\) −8.00000 −1.16692 −0.583460 0.812142i \(-0.698301\pi\)
−0.583460 + 0.812142i \(0.698301\pi\)
\(48\) 0 0
\(49\) −9.00000 −1.28571
\(50\) 6.00000 8.00000i 0.848528 1.13137i
\(51\) 0 0
\(52\) 4.00000i 0.554700i
\(53\) 9.00000i 1.23625i 0.786082 + 0.618123i \(0.212106\pi\)
−0.786082 + 0.618123i \(0.787894\pi\)
\(54\) 0 0
\(55\) −1.00000 2.00000i −0.134840 0.269680i
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000 10.0000i 0.525226 1.31306i
\(59\) −8.00000 −1.04151 −0.520756 0.853706i \(-0.674350\pi\)
−0.520756 + 0.853706i \(0.674350\pi\)
\(60\) 0 0
\(61\) 6.00000i 0.768221i −0.923287 0.384111i \(-0.874508\pi\)
0.923287 0.384111i \(-0.125492\pi\)
\(62\) 4.00000i 0.508001i
\(63\) 0 0
\(64\) −8.00000 −1.00000
\(65\) 2.00000 + 4.00000i 0.248069 + 0.496139i
\(66\) 0 0
\(67\) 12.0000i 1.46603i 0.680211 + 0.733017i \(0.261888\pi\)
−0.680211 + 0.733017i \(0.738112\pi\)
\(68\) 12.0000 1.45521
\(69\) 0 0
\(70\) 8.00000 + 16.0000i 0.956183 + 1.91237i
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 15.0000 1.75562 0.877809 0.479012i \(-0.159005\pi\)
0.877809 + 0.479012i \(0.159005\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) 8.00000i 0.917663i
\(77\) 4.00000 0.455842
\(78\) 0 0
\(79\) 4.00000i 0.450035i 0.974355 + 0.225018i \(0.0722440\pi\)
−0.974355 + 0.225018i \(0.927756\pi\)
\(80\) 8.00000 4.00000i 0.894427 0.447214i
\(81\) 0 0
\(82\) 18.0000i 1.98777i
\(83\) 7.00000i 0.768350i −0.923260 0.384175i \(-0.874486\pi\)
0.923260 0.384175i \(-0.125514\pi\)
\(84\) 0 0
\(85\) −12.0000 + 6.00000i −1.30158 + 0.650791i
\(86\) −2.00000 −0.215666
\(87\) 0 0
\(88\) 0 0
\(89\) 2.00000i 0.212000i −0.994366 0.106000i \(-0.966196\pi\)
0.994366 0.106000i \(-0.0338043\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 18.0000i 1.87663i
\(93\) 0 0
\(94\) −16.0000 −1.65027
\(95\) 4.00000 + 8.00000i 0.410391 + 0.820783i
\(96\) 0 0
\(97\) 11.0000 1.11688 0.558440 0.829545i \(-0.311400\pi\)
0.558440 + 0.829545i \(0.311400\pi\)
\(98\) −18.0000 −1.81827
\(99\) 0 0
\(100\) 6.00000 8.00000i 0.600000 0.800000i
\(101\) 3.00000i 0.298511i −0.988799 0.149256i \(-0.952312\pi\)
0.988799 0.149256i \(-0.0476877\pi\)
\(102\) 0 0
\(103\) 6.00000i 0.591198i 0.955312 + 0.295599i \(0.0955191\pi\)
−0.955312 + 0.295599i \(0.904481\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 18.0000i 1.74831i
\(107\) 4.00000i 0.386695i 0.981130 + 0.193347i \(0.0619344\pi\)
−0.981130 + 0.193347i \(0.938066\pi\)
\(108\) 0 0
\(109\) −1.00000 −0.0957826 −0.0478913 0.998853i \(-0.515250\pi\)
−0.0478913 + 0.998853i \(0.515250\pi\)
\(110\) −2.00000 4.00000i −0.190693 0.381385i
\(111\) 0 0
\(112\) 16.0000i 1.51186i
\(113\) 8.00000 0.752577 0.376288 0.926503i \(-0.377200\pi\)
0.376288 + 0.926503i \(0.377200\pi\)
\(114\) 0 0
\(115\) 9.00000 + 18.0000i 0.839254 + 1.67851i
\(116\) 4.00000 10.0000i 0.371391 0.928477i
\(117\) 0 0
\(118\) −16.0000 −1.47292
\(119\) 24.0000i 2.20008i
\(120\) 0 0
\(121\) 10.0000 0.909091
\(122\) 12.0000i 1.08643i
\(123\) 0 0
\(124\) 4.00000i 0.359211i
\(125\) −2.00000 + 11.0000i −0.178885 + 0.983870i
\(126\) 0 0
\(127\) 7.00000 0.621150 0.310575 0.950549i \(-0.399478\pi\)
0.310575 + 0.950549i \(0.399478\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 4.00000 + 8.00000i 0.350823 + 0.701646i
\(131\) 20.0000i 1.74741i −0.486458 0.873704i \(-0.661711\pi\)
0.486458 0.873704i \(-0.338289\pi\)
\(132\) 0 0
\(133\) −16.0000 −1.38738
\(134\) 24.0000i 2.07328i
\(135\) 0 0
\(136\) 0 0
\(137\) 16.0000 1.36697 0.683486 0.729964i \(-0.260463\pi\)
0.683486 + 0.729964i \(0.260463\pi\)
\(138\) 0 0
\(139\) 11.0000 0.933008 0.466504 0.884519i \(-0.345513\pi\)
0.466504 + 0.884519i \(0.345513\pi\)
\(140\) 8.00000 + 16.0000i 0.676123 + 1.35225i
\(141\) 0 0
\(142\) −4.00000 −0.335673
\(143\) 2.00000 0.167248
\(144\) 0 0
\(145\) 1.00000 + 12.0000i 0.0830455 + 0.996546i
\(146\) 30.0000 2.48282
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) −14.0000 −1.14692 −0.573462 0.819232i \(-0.694400\pi\)
−0.573462 + 0.819232i \(0.694400\pi\)
\(150\) 0 0
\(151\) −17.0000 −1.38344 −0.691720 0.722166i \(-0.743147\pi\)
−0.691720 + 0.722166i \(0.743147\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 8.00000 0.644658
\(155\) 2.00000 + 4.00000i 0.160644 + 0.321288i
\(156\) 0 0
\(157\) 14.0000 1.11732 0.558661 0.829396i \(-0.311315\pi\)
0.558661 + 0.829396i \(0.311315\pi\)
\(158\) 8.00000i 0.636446i
\(159\) 0 0
\(160\) 16.0000 8.00000i 1.26491 0.632456i
\(161\) −36.0000 −2.83720
\(162\) 0 0
\(163\) −13.0000 −1.01824 −0.509119 0.860696i \(-0.670029\pi\)
−0.509119 + 0.860696i \(0.670029\pi\)
\(164\) 18.0000i 1.40556i
\(165\) 0 0
\(166\) 14.0000i 1.08661i
\(167\) 24.0000i 1.85718i 0.371113 + 0.928588i \(0.378976\pi\)
−0.371113 + 0.928588i \(0.621024\pi\)
\(168\) 0 0
\(169\) 9.00000 0.692308
\(170\) −24.0000 + 12.0000i −1.84072 + 0.920358i
\(171\) 0 0
\(172\) −2.00000 −0.152499
\(173\) 21.0000i 1.59660i −0.602260 0.798300i \(-0.705733\pi\)
0.602260 0.798300i \(-0.294267\pi\)
\(174\) 0 0
\(175\) −16.0000 12.0000i −1.20949 0.907115i
\(176\) 4.00000i 0.301511i
\(177\) 0 0
\(178\) 4.00000i 0.299813i
\(179\) −6.00000 −0.448461 −0.224231 0.974536i \(-0.571987\pi\)
−0.224231 + 0.974536i \(0.571987\pi\)
\(180\) 0 0
\(181\) −7.00000 −0.520306 −0.260153 0.965567i \(-0.583773\pi\)
−0.260153 + 0.965567i \(0.583773\pi\)
\(182\) −16.0000 −1.18600
\(183\) 0 0
\(184\) 0 0
\(185\) 2.00000 1.00000i 0.147043 0.0735215i
\(186\) 0 0
\(187\) 6.00000i 0.438763i
\(188\) −16.0000 −1.16692
\(189\) 0 0
\(190\) 8.00000 + 16.0000i 0.580381 + 1.16076i
\(191\) 3.00000i 0.217072i −0.994092 0.108536i \(-0.965384\pi\)
0.994092 0.108536i \(-0.0346163\pi\)
\(192\) 0 0
\(193\) 6.00000 0.431889 0.215945 0.976406i \(-0.430717\pi\)
0.215945 + 0.976406i \(0.430717\pi\)
\(194\) 22.0000 1.57951
\(195\) 0 0
\(196\) −18.0000 −1.28571
\(197\) 23.0000i 1.63868i 0.573306 + 0.819341i \(0.305660\pi\)
−0.573306 + 0.819341i \(0.694340\pi\)
\(198\) 0 0
\(199\) −19.0000 −1.34687 −0.673437 0.739244i \(-0.735183\pi\)
−0.673437 + 0.739244i \(0.735183\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 6.00000i 0.422159i
\(203\) −20.0000 8.00000i −1.40372 0.561490i
\(204\) 0 0
\(205\) −9.00000 18.0000i −0.628587 1.25717i
\(206\) 12.0000i 0.836080i
\(207\) 0 0
\(208\) 8.00000i 0.554700i
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 2.00000i 0.137686i 0.997628 + 0.0688428i \(0.0219307\pi\)
−0.997628 + 0.0688428i \(0.978069\pi\)
\(212\) 18.0000i 1.23625i
\(213\) 0 0
\(214\) 8.00000i 0.546869i
\(215\) 2.00000 1.00000i 0.136399 0.0681994i
\(216\) 0 0
\(217\) −8.00000 −0.543075
\(218\) −2.00000 −0.135457
\(219\) 0 0
\(220\) −2.00000 4.00000i −0.134840 0.269680i
\(221\) 12.0000i 0.807207i
\(222\) 0 0
\(223\) 4.00000i 0.267860i −0.990991 0.133930i \(-0.957240\pi\)
0.990991 0.133930i \(-0.0427597\pi\)
\(224\) 32.0000i 2.13809i
\(225\) 0 0
\(226\) 16.0000 1.06430
\(227\) 7.00000i 0.464606i −0.972643 0.232303i \(-0.925374\pi\)
0.972643 0.232303i \(-0.0746261\pi\)
\(228\) 0 0
\(229\) 4.00000i 0.264327i −0.991228 0.132164i \(-0.957808\pi\)
0.991228 0.132164i \(-0.0421925\pi\)
\(230\) 18.0000 + 36.0000i 1.18688 + 2.37377i
\(231\) 0 0
\(232\) 0 0
\(233\) 1.00000i 0.0655122i −0.999463 0.0327561i \(-0.989572\pi\)
0.999463 0.0327561i \(-0.0104285\pi\)
\(234\) 0 0
\(235\) 16.0000 8.00000i 1.04372 0.521862i
\(236\) −16.0000 −1.04151
\(237\) 0 0
\(238\) 48.0000i 3.11138i
\(239\) 26.0000 1.68180 0.840900 0.541190i \(-0.182026\pi\)
0.840900 + 0.541190i \(0.182026\pi\)
\(240\) 0 0
\(241\) 11.0000 0.708572 0.354286 0.935137i \(-0.384724\pi\)
0.354286 + 0.935137i \(0.384724\pi\)
\(242\) 20.0000 1.28565
\(243\) 0 0
\(244\) 12.0000i 0.768221i
\(245\) 18.0000 9.00000i 1.14998 0.574989i
\(246\) 0 0
\(247\) −8.00000 −0.509028
\(248\) 0 0
\(249\) 0 0
\(250\) −4.00000 + 22.0000i −0.252982 + 1.39140i
\(251\) 12.0000i 0.757433i 0.925513 + 0.378717i \(0.123635\pi\)
−0.925513 + 0.378717i \(0.876365\pi\)
\(252\) 0 0
\(253\) 9.00000 0.565825
\(254\) 14.0000 0.878438
\(255\) 0 0
\(256\) 16.0000 1.00000
\(257\) 15.0000i 0.935674i −0.883815 0.467837i \(-0.845033\pi\)
0.883815 0.467837i \(-0.154967\pi\)
\(258\) 0 0
\(259\) 4.00000i 0.248548i
\(260\) 4.00000 + 8.00000i 0.248069 + 0.496139i
\(261\) 0 0
\(262\) 40.0000i 2.47121i
\(263\) −26.0000 −1.60323 −0.801614 0.597841i \(-0.796025\pi\)
−0.801614 + 0.597841i \(0.796025\pi\)
\(264\) 0 0
\(265\) −9.00000 18.0000i −0.552866 1.10573i
\(266\) −32.0000 −1.96205
\(267\) 0 0
\(268\) 24.0000i 1.46603i
\(269\) 10.0000i 0.609711i −0.952399 0.304855i \(-0.901392\pi\)
0.952399 0.304855i \(-0.0986081\pi\)
\(270\) 0 0
\(271\) 2.00000i 0.121491i −0.998153 0.0607457i \(-0.980652\pi\)
0.998153 0.0607457i \(-0.0193479\pi\)
\(272\) −24.0000 −1.45521
\(273\) 0 0
\(274\) 32.0000 1.93319
\(275\) 4.00000 + 3.00000i 0.241209 + 0.180907i
\(276\) 0 0
\(277\) 2.00000i 0.120168i 0.998193 + 0.0600842i \(0.0191369\pi\)
−0.998193 + 0.0600842i \(0.980863\pi\)
\(278\) 22.0000 1.31947
\(279\) 0 0
\(280\) 0 0
\(281\) 24.0000 1.43172 0.715860 0.698244i \(-0.246035\pi\)
0.715860 + 0.698244i \(0.246035\pi\)
\(282\) 0 0
\(283\) 22.0000i 1.30776i 0.756596 + 0.653882i \(0.226861\pi\)
−0.756596 + 0.653882i \(0.773139\pi\)
\(284\) −4.00000 −0.237356
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 36.0000 2.12501
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 2.00000 + 24.0000i 0.117444 + 1.40933i
\(291\) 0 0
\(292\) 30.0000 1.75562
\(293\) −2.00000 −0.116841 −0.0584206 0.998292i \(-0.518606\pi\)
−0.0584206 + 0.998292i \(0.518606\pi\)
\(294\) 0 0
\(295\) 16.0000 8.00000i 0.931556 0.465778i
\(296\) 0 0
\(297\) 0 0
\(298\) −28.0000 −1.62200
\(299\) −18.0000 −1.04097
\(300\) 0 0
\(301\) 4.00000i 0.230556i
\(302\) −34.0000 −1.95648
\(303\) 0 0
\(304\) 16.0000i 0.917663i
\(305\) 6.00000 + 12.0000i 0.343559 + 0.687118i
\(306\) 0 0
\(307\) 15.0000 0.856095 0.428048 0.903756i \(-0.359202\pi\)
0.428048 + 0.903756i \(0.359202\pi\)
\(308\) 8.00000 0.455842
\(309\) 0 0
\(310\) 4.00000 + 8.00000i 0.227185 + 0.454369i
\(311\) 23.0000i 1.30421i −0.758129 0.652105i \(-0.773886\pi\)
0.758129 0.652105i \(-0.226114\pi\)
\(312\) 0 0
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) 28.0000 1.58013
\(315\) 0 0
\(316\) 8.00000i 0.450035i
\(317\) 12.0000 0.673987 0.336994 0.941507i \(-0.390590\pi\)
0.336994 + 0.941507i \(0.390590\pi\)
\(318\) 0 0
\(319\) 5.00000 + 2.00000i 0.279946 + 0.111979i
\(320\) 16.0000 8.00000i 0.894427 0.447214i
\(321\) 0 0
\(322\) −72.0000 −4.01240
\(323\) 24.0000i 1.33540i
\(324\) 0 0
\(325\) −8.00000 6.00000i −0.443760 0.332820i
\(326\) −26.0000 −1.44001
\(327\) 0 0
\(328\) 0 0
\(329\) 32.0000i 1.76422i
\(330\) 0 0
\(331\) 32.0000i 1.75888i 0.476011 + 0.879440i \(0.342082\pi\)
−0.476011 + 0.879440i \(0.657918\pi\)
\(332\) 14.0000i 0.768350i
\(333\) 0 0
\(334\) 48.0000i 2.62644i
\(335\) −12.0000 24.0000i −0.655630 1.31126i
\(336\) 0 0
\(337\) −10.0000 −0.544735 −0.272367 0.962193i \(-0.587807\pi\)
−0.272367 + 0.962193i \(0.587807\pi\)
\(338\) 18.0000 0.979071
\(339\) 0 0
\(340\) −24.0000 + 12.0000i −1.30158 + 0.650791i
\(341\) 2.00000 0.108306
\(342\) 0 0
\(343\) 8.00000i 0.431959i
\(344\) 0 0
\(345\) 0 0
\(346\) 42.0000i 2.25793i
\(347\) 19.0000i 1.01997i 0.860182 + 0.509987i \(0.170350\pi\)
−0.860182 + 0.509987i \(0.829650\pi\)
\(348\) 0 0
\(349\) −11.0000 −0.588817 −0.294408 0.955680i \(-0.595123\pi\)
−0.294408 + 0.955680i \(0.595123\pi\)
\(350\) −32.0000 24.0000i −1.71047 1.28285i
\(351\) 0 0
\(352\) 8.00000i 0.426401i
\(353\) 18.0000i 0.958043i −0.877803 0.479022i \(-0.840992\pi\)
0.877803 0.479022i \(-0.159008\pi\)
\(354\) 0 0
\(355\) 4.00000 2.00000i 0.212298 0.106149i
\(356\) 4.00000i 0.212000i
\(357\) 0 0
\(358\) −12.0000 −0.634220
\(359\) 21.0000i 1.10834i −0.832404 0.554169i \(-0.813036\pi\)
0.832404 0.554169i \(-0.186964\pi\)
\(360\) 0 0
\(361\) 3.00000 0.157895
\(362\) −14.0000 −0.735824
\(363\) 0 0
\(364\) −16.0000 −0.838628
\(365\) −30.0000 + 15.0000i −1.57027 + 0.785136i
\(366\) 0 0
\(367\) 27.0000 1.40939 0.704694 0.709511i \(-0.251084\pi\)
0.704694 + 0.709511i \(0.251084\pi\)
\(368\) 36.0000i 1.87663i
\(369\) 0 0
\(370\) 4.00000 2.00000i 0.207950 0.103975i
\(371\) 36.0000 1.86903
\(372\) 0 0
\(373\) 2.00000i 0.103556i 0.998659 + 0.0517780i \(0.0164888\pi\)
−0.998659 + 0.0517780i \(0.983511\pi\)
\(374\) 12.0000i 0.620505i
\(375\) 0 0
\(376\) 0 0
\(377\) −10.0000 4.00000i −0.515026 0.206010i
\(378\) 0 0
\(379\) 22.0000i 1.13006i 0.825069 + 0.565032i \(0.191136\pi\)
−0.825069 + 0.565032i \(0.808864\pi\)
\(380\) 8.00000 + 16.0000i 0.410391 + 0.820783i
\(381\) 0 0
\(382\) 6.00000i 0.306987i
\(383\) 27.0000i 1.37964i −0.723983 0.689818i \(-0.757691\pi\)
0.723983 0.689818i \(-0.242309\pi\)
\(384\) 0 0
\(385\) −8.00000 + 4.00000i −0.407718 + 0.203859i
\(386\) 12.0000 0.610784
\(387\) 0 0
\(388\) 22.0000 1.11688
\(389\) 3.00000i 0.152106i 0.997104 + 0.0760530i \(0.0242318\pi\)
−0.997104 + 0.0760530i \(0.975768\pi\)
\(390\) 0 0
\(391\) 54.0000i 2.73090i
\(392\) 0 0
\(393\) 0 0
\(394\) 46.0000i 2.31745i
\(395\) −4.00000 8.00000i −0.201262 0.402524i
\(396\) 0 0
\(397\) 16.0000i 0.803017i −0.915855 0.401508i \(-0.868486\pi\)
0.915855 0.401508i \(-0.131514\pi\)
\(398\) −38.0000 −1.90477
\(399\) 0 0
\(400\) −12.0000 + 16.0000i −0.600000 + 0.800000i
\(401\) 12.0000 0.599251 0.299626 0.954057i \(-0.403138\pi\)
0.299626 + 0.954057i \(0.403138\pi\)
\(402\) 0 0
\(403\) −4.00000 −0.199254
\(404\) 6.00000i 0.298511i
\(405\) 0 0
\(406\) −40.0000 16.0000i −1.98517 0.794067i
\(407\) 1.00000i 0.0495682i
\(408\) 0 0
\(409\) 14.0000i 0.692255i −0.938187 0.346128i \(-0.887496\pi\)
0.938187 0.346128i \(-0.112504\pi\)
\(410\) −18.0000 36.0000i −0.888957 1.77791i
\(411\) 0 0
\(412\) 12.0000i 0.591198i
\(413\) 32.0000i 1.57462i
\(414\) 0 0
\(415\) 7.00000 + 14.0000i 0.343616 + 0.687233i
\(416\) 16.0000i 0.784465i
\(417\) 0 0
\(418\) 8.00000 0.391293
\(419\) −30.0000 −1.46560 −0.732798 0.680446i \(-0.761786\pi\)
−0.732798 + 0.680446i \(0.761786\pi\)
\(420\) 0 0
\(421\) 22.0000i 1.07221i −0.844150 0.536107i \(-0.819894\pi\)
0.844150 0.536107i \(-0.180106\pi\)
\(422\) 4.00000i 0.194717i
\(423\) 0 0
\(424\) 0 0
\(425\) 18.0000 24.0000i 0.873128 1.16417i
\(426\) 0 0
\(427\) −24.0000 −1.16144
\(428\) 8.00000i 0.386695i
\(429\) 0 0
\(430\) 4.00000 2.00000i 0.192897 0.0964486i
\(431\) 6.00000 0.289010 0.144505 0.989504i \(-0.453841\pi\)
0.144505 + 0.989504i \(0.453841\pi\)
\(432\) 0 0
\(433\) 7.00000 0.336399 0.168199 0.985753i \(-0.446205\pi\)
0.168199 + 0.985753i \(0.446205\pi\)
\(434\) −16.0000 −0.768025
\(435\) 0 0
\(436\) −2.00000 −0.0957826
\(437\) −36.0000 −1.72211
\(438\) 0 0
\(439\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 24.0000i 1.14156i
\(443\) −4.00000 −0.190046 −0.0950229 0.995475i \(-0.530292\pi\)
−0.0950229 + 0.995475i \(0.530292\pi\)
\(444\) 0 0
\(445\) 2.00000 + 4.00000i 0.0948091 + 0.189618i
\(446\) 8.00000i 0.378811i
\(447\) 0 0
\(448\) 32.0000i 1.51186i
\(449\) 15.0000i 0.707894i 0.935266 + 0.353947i \(0.115161\pi\)
−0.935266 + 0.353947i \(0.884839\pi\)
\(450\) 0 0
\(451\) −9.00000 −0.423793
\(452\) 16.0000 0.752577
\(453\) 0 0
\(454\) 14.0000i 0.657053i
\(455\) 16.0000 8.00000i 0.750092 0.375046i
\(456\) 0 0
\(457\) 10.0000i 0.467780i 0.972263 + 0.233890i \(0.0751456\pi\)
−0.972263 + 0.233890i \(0.924854\pi\)
\(458\) 8.00000i 0.373815i
\(459\) 0 0
\(460\) 18.0000 + 36.0000i 0.839254 + 1.67851i
\(461\) 33.0000i 1.53696i 0.639872 + 0.768482i \(0.278987\pi\)
−0.639872 + 0.768482i \(0.721013\pi\)
\(462\) 0 0
\(463\) 2.00000i 0.0929479i 0.998920 + 0.0464739i \(0.0147984\pi\)
−0.998920 + 0.0464739i \(0.985202\pi\)
\(464\) −8.00000 + 20.0000i −0.371391 + 0.928477i
\(465\) 0 0
\(466\) 2.00000i 0.0926482i
\(467\) 18.0000 0.832941 0.416470 0.909149i \(-0.363267\pi\)
0.416470 + 0.909149i \(0.363267\pi\)
\(468\) 0 0
\(469\) 48.0000 2.21643
\(470\) 32.0000 16.0000i 1.47605 0.738025i
\(471\) 0 0
\(472\) 0 0
\(473\) 1.00000i 0.0459800i
\(474\) 0 0
\(475\) −16.0000 12.0000i −0.734130 0.550598i
\(476\) 48.0000i 2.20008i
\(477\) 0 0
\(478\) 52.0000 2.37842
\(479\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(480\) 0 0
\(481\) 2.00000i 0.0911922i
\(482\) 22.0000 1.00207
\(483\) 0 0
\(484\) 20.0000 0.909091
\(485\) −22.0000 + 11.0000i −0.998969 + 0.499484i
\(486\) 0 0
\(487\) 4.00000i 0.181257i 0.995885 + 0.0906287i \(0.0288876\pi\)
−0.995885 + 0.0906287i \(0.971112\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 36.0000 18.0000i 1.62631 0.813157i
\(491\) 8.00000i 0.361035i −0.983572 0.180517i \(-0.942223\pi\)
0.983572 0.180517i \(-0.0577772\pi\)
\(492\) 0 0
\(493\) 12.0000 30.0000i 0.540453 1.35113i
\(494\) −16.0000 −0.719874
\(495\) 0 0
\(496\) 8.00000i 0.359211i
\(497\) 8.00000i 0.358849i
\(498\) 0 0
\(499\) −12.0000 −0.537194 −0.268597 0.963253i \(-0.586560\pi\)
−0.268597 + 0.963253i \(0.586560\pi\)
\(500\) −4.00000 + 22.0000i −0.178885 + 0.983870i
\(501\) 0 0
\(502\) 24.0000i 1.07117i
\(503\) 8.00000 0.356702 0.178351 0.983967i \(-0.442924\pi\)
0.178351 + 0.983967i \(0.442924\pi\)
\(504\) 0 0
\(505\) 3.00000 + 6.00000i 0.133498 + 0.266996i
\(506\) 18.0000 0.800198
\(507\) 0 0
\(508\) 14.0000 0.621150
\(509\) 28.0000 1.24108 0.620539 0.784176i \(-0.286914\pi\)
0.620539 + 0.784176i \(0.286914\pi\)
\(510\) 0 0
\(511\) 60.0000i 2.65424i
\(512\) 32.0000 1.41421
\(513\) 0 0
\(514\) 30.0000i 1.32324i
\(515\) −6.00000 12.0000i −0.264392 0.528783i
\(516\) 0 0
\(517\) 8.00000i 0.351840i
\(518\) 8.00000i 0.351500i
\(519\) 0 0
\(520\) 0 0
\(521\) 8.00000 0.350486 0.175243 0.984525i \(-0.443929\pi\)
0.175243 + 0.984525i \(0.443929\pi\)
\(522\) 0 0
\(523\) 2.00000i 0.0874539i 0.999044 + 0.0437269i \(0.0139232\pi\)
−0.999044 + 0.0437269i \(0.986077\pi\)
\(524\) 40.0000i 1.74741i
\(525\) 0 0
\(526\) −52.0000 −2.26731
\(527\) 12.0000i 0.522728i
\(528\) 0 0
\(529\) −58.0000 −2.52174
\(530\) −18.0000 36.0000i −0.781870 1.56374i
\(531\) 0 0
\(532\) −32.0000 −1.38738
\(533\) 18.0000 0.779667
\(534\) 0 0
\(535\) −4.00000 8.00000i −0.172935 0.345870i
\(536\) 0 0
\(537\) 0 0
\(538\) 20.0000i 0.862261i
\(539\) 9.00000i 0.387657i
\(540\) 0 0
\(541\) 32.0000i 1.37579i 0.725811 + 0.687894i \(0.241464\pi\)
−0.725811 + 0.687894i \(0.758536\pi\)
\(542\) 4.00000i 0.171815i
\(543\) 0 0
\(544\) −48.0000 −2.05798
\(545\) 2.00000 1.00000i 0.0856706 0.0428353i
\(546\) 0 0
\(547\) 26.0000i 1.11168i −0.831289 0.555840i \(-0.812397\pi\)
0.831289 0.555840i \(-0.187603\pi\)
\(548\) 32.0000 1.36697
\(549\) 0 0
\(550\) 8.00000 + 6.00000i 0.341121 + 0.255841i
\(551\) −20.0000 8.00000i −0.852029 0.340811i
\(552\) 0 0
\(553\) 16.0000 0.680389
\(554\) 4.00000i 0.169944i
\(555\) 0 0
\(556\) 22.0000 0.933008
\(557\) 45.0000i 1.90671i 0.301849 + 0.953356i \(0.402396\pi\)
−0.301849 + 0.953356i \(0.597604\pi\)
\(558\) 0 0
\(559\) 2.00000i 0.0845910i
\(560\) −16.0000 32.0000i −0.676123 1.35225i
\(561\) 0 0
\(562\) 48.0000 2.02476
\(563\) 36.0000 1.51722 0.758610 0.651546i \(-0.225879\pi\)
0.758610 + 0.651546i \(0.225879\pi\)
\(564\) 0 0
\(565\) −16.0000 + 8.00000i −0.673125 + 0.336563i
\(566\) 44.0000i 1.84946i
\(567\) 0 0
\(568\) 0 0
\(569\) 38.0000i 1.59304i −0.604610 0.796521i \(-0.706671\pi\)
0.604610 0.796521i \(-0.293329\pi\)
\(570\) 0 0
\(571\) −23.0000 −0.962520 −0.481260 0.876578i \(-0.659821\pi\)
−0.481260 + 0.876578i \(0.659821\pi\)
\(572\) 4.00000 0.167248
\(573\) 0 0
\(574\) 72.0000 3.00522
\(575\) −36.0000 27.0000i −1.50130 1.12598i
\(576\) 0 0
\(577\) −34.0000 −1.41544 −0.707719 0.706494i \(-0.750276\pi\)
−0.707719 + 0.706494i \(0.750276\pi\)
\(578\) 38.0000 1.58059
\(579\) 0 0
\(580\) 2.00000 + 24.0000i 0.0830455 + 0.996546i
\(581\) −28.0000 −1.16164
\(582\) 0 0
\(583\) −9.00000 −0.372742
\(584\) 0 0
\(585\) 0 0
\(586\) −4.00000 −0.165238
\(587\) 12.0000i 0.495293i −0.968850 0.247647i \(-0.920343\pi\)
0.968850 0.247647i \(-0.0796572\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 32.0000 16.0000i 1.31742 0.658710i
\(591\) 0 0
\(592\) 4.00000 0.164399
\(593\) 14.0000i 0.574911i 0.957794 + 0.287456i \(0.0928094\pi\)
−0.957794 + 0.287456i \(0.907191\pi\)
\(594\) 0 0
\(595\) 24.0000 + 48.0000i 0.983904 + 1.96781i
\(596\) −28.0000 −1.14692
\(597\) 0 0
\(598\) −36.0000 −1.47215
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0 0
\(601\) 26.0000i 1.06056i 0.847822 + 0.530281i \(0.177914\pi\)
−0.847822 + 0.530281i \(0.822086\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 0 0
\(604\) −34.0000 −1.38344
\(605\) −20.0000 + 10.0000i −0.813116 + 0.406558i
\(606\) 0 0
\(607\) 40.0000 1.62355 0.811775 0.583970i \(-0.198502\pi\)
0.811775 + 0.583970i \(0.198502\pi\)
\(608\) 32.0000i 1.29777i
\(609\) 0 0
\(610\) 12.0000 + 24.0000i 0.485866 + 0.971732i
\(611\) 16.0000i 0.647291i
\(612\) 0 0
\(613\) 6.00000i 0.242338i 0.992632 + 0.121169i \(0.0386643\pi\)
−0.992632 + 0.121169i \(0.961336\pi\)
\(614\) 30.0000 1.21070
\(615\) 0 0
\(616\) 0 0
\(617\) −36.0000 −1.44931 −0.724653 0.689114i \(-0.758000\pi\)
−0.724653 + 0.689114i \(0.758000\pi\)
\(618\) 0 0
\(619\) 10.0000i 0.401934i −0.979598 0.200967i \(-0.935592\pi\)
0.979598 0.200967i \(-0.0644084\pi\)
\(620\) 4.00000 + 8.00000i 0.160644 + 0.321288i
\(621\) 0 0
\(622\) 46.0000i 1.84443i
\(623\) −8.00000 −0.320513
\(624\) 0 0
\(625\) −7.00000 24.0000i −0.280000 0.960000i
\(626\) 16.0000i 0.639489i
\(627\) 0 0
\(628\) 28.0000 1.11732
\(629\) −6.00000 −0.239236
\(630\) 0 0
\(631\) 32.0000 1.27390 0.636950 0.770905i \(-0.280196\pi\)
0.636950 + 0.770905i \(0.280196\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 24.0000 0.953162
\(635\) −14.0000 + 7.00000i −0.555573 + 0.277787i
\(636\) 0 0
\(637\) 18.0000i 0.713186i
\(638\) 10.0000 + 4.00000i 0.395904 + 0.158362i
\(639\) 0 0
\(640\) 0 0
\(641\) 33.0000i 1.30342i 0.758468 + 0.651711i \(0.225948\pi\)
−0.758468 + 0.651711i \(0.774052\pi\)
\(642\) 0 0
\(643\) 24.0000i 0.946468i 0.880937 + 0.473234i \(0.156913\pi\)
−0.880937 + 0.473234i \(0.843087\pi\)
\(644\) −72.0000 −2.83720
\(645\) 0 0
\(646\) 48.0000i 1.88853i
\(647\) 17.0000i 0.668339i 0.942513 + 0.334169i \(0.108456\pi\)
−0.942513 + 0.334169i \(0.891544\pi\)
\(648\) 0 0
\(649\) 8.00000i 0.314027i
\(650\) −16.0000 12.0000i −0.627572 0.470679i
\(651\) 0 0
\(652\) −26.0000 −1.01824
\(653\) 24.0000 0.939193 0.469596 0.882881i \(-0.344399\pi\)
0.469596 + 0.882881i \(0.344399\pi\)
\(654\) 0 0
\(655\) 20.0000 + 40.0000i 0.781465 + 1.56293i
\(656\) 36.0000i 1.40556i
\(657\) 0 0
\(658\) 64.0000i 2.49498i
\(659\) 29.0000i 1.12968i −0.825201 0.564840i \(-0.808938\pi\)
0.825201 0.564840i \(-0.191062\pi\)
\(660\) 0 0
\(661\) −5.00000 −0.194477 −0.0972387 0.995261i \(-0.531001\pi\)
−0.0972387 + 0.995261i \(0.531001\pi\)
\(662\) 64.0000i 2.48743i
\(663\) 0 0
\(664\) 0 0
\(665\) 32.0000 16.0000i 1.24091 0.620453i
\(666\) 0 0
\(667\) −45.0000 18.0000i −1.74241 0.696963i
\(668\) 48.0000i 1.85718i
\(669\) 0 0
\(670\) −24.0000 48.0000i −0.927201 1.85440i
\(671\) 6.00000 0.231627
\(672\) 0 0
\(673\) 32.0000i 1.23351i 0.787155 + 0.616755i \(0.211553\pi\)
−0.787155 + 0.616755i \(0.788447\pi\)
\(674\) −20.0000 −0.770371
\(675\) 0 0
\(676\) 18.0000 0.692308
\(677\) 18.0000 0.691796 0.345898 0.938272i \(-0.387574\pi\)
0.345898 + 0.938272i \(0.387574\pi\)
\(678\) 0 0
\(679\) 44.0000i 1.68857i
\(680\) 0 0
\(681\) 0 0
\(682\) 4.00000 0.153168
\(683\) 9.00000i 0.344375i −0.985064 0.172188i \(-0.944916\pi\)
0.985064 0.172188i \(-0.0550836\pi\)
\(684\) 0 0
\(685\) −32.0000 + 16.0000i −1.22266 + 0.611329i
\(686\) 16.0000i 0.610883i
\(687\) 0 0
\(688\) 4.00000 0.152499
\(689\) 18.0000 0.685745
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 42.0000i 1.59660i
\(693\) 0 0
\(694\) 38.0000i 1.44246i
\(695\) −22.0000 + 11.0000i −0.834508 + 0.417254i
\(696\) 0 0
\(697\) 54.0000i 2.04540i
\(698\) −22.0000 −0.832712
\(699\) 0 0
\(700\) −32.0000 24.0000i −1.20949 0.907115i
\(701\) −6.00000 −0.226617 −0.113308 0.993560i \(-0.536145\pi\)
−0.113308 + 0.993560i \(0.536145\pi\)
\(702\) 0 0
\(703\) 4.00000i 0.150863i
\(704\) 8.00000i 0.301511i
\(705\) 0 0
\(706\) 36.0000i 1.35488i
\(707\) −12.0000 −0.451306
\(708\) 0 0
\(709\) 19.0000 0.713560 0.356780 0.934188i \(-0.383875\pi\)
0.356780 + 0.934188i \(0.383875\pi\)
\(710\) 8.00000 4.00000i 0.300235 0.150117i
\(711\) 0 0
\(712\) 0 0
\(713\) −18.0000 −0.674105
\(714\) 0 0
\(715\) −4.00000 + 2.00000i −0.149592 + 0.0747958i
\(716\) −12.0000 −0.448461
\(717\) 0 0
\(718\) 42.0000i 1.56743i
\(719\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 24.0000 0.893807
\(722\) 6.00000 0.223297
\(723\) 0 0
\(724\) −14.0000 −0.520306
\(725\) −14.0000 23.0000i −0.519947 0.854199i
\(726\) 0 0
\(727\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −60.0000 + 30.0000i −2.22070 + 1.11035i
\(731\) −6.00000 −0.221918
\(732\) 0 0
\(733\) 2.00000 0.0738717 0.0369358 0.999318i \(-0.488240\pi\)
0.0369358 + 0.999318i \(0.488240\pi\)
\(734\) 54.0000 1.99318
\(735\) 0 0
\(736\) 72.0000i 2.65396i
\(737\) −12.0000 −0.442026
\(738\) 0 0
\(739\) 10.0000i 0.367856i 0.982940 + 0.183928i \(0.0588813\pi\)
−0.982940 + 0.183928i \(0.941119\pi\)
\(740\) 4.00000 2.00000i 0.147043 0.0735215i
\(741\) 0 0
\(742\) 72.0000 2.64320
\(743\) −6.00000 −0.220119 −0.110059 0.993925i \(-0.535104\pi\)
−0.110059 + 0.993925i \(0.535104\pi\)
\(744\) 0 0
\(745\) 28.0000 14.0000i 1.02584 0.512920i
\(746\) 4.00000i 0.146450i
\(747\) 0 0
\(748\) 12.0000i 0.438763i
\(749\) 16.0000 0.584627
\(750\) 0 0
\(751\) 28.0000i 1.02173i 0.859660 + 0.510867i \(0.170676\pi\)
−0.859660 + 0.510867i \(0.829324\pi\)
\(752\) 32.0000 1.16692
\(753\) 0 0
\(754\) −20.0000 8.00000i −0.728357 0.291343i
\(755\) 34.0000 17.0000i 1.23739 0.618693i
\(756\) 0 0
\(757\) −33.0000 −1.19941 −0.599703 0.800223i \(-0.704714\pi\)
−0.599703 + 0.800223i \(0.704714\pi\)
\(758\) 44.0000i 1.59815i
\(759\) 0 0
\(760\) 0 0
\(761\) 34.0000 1.23250 0.616250 0.787551i \(-0.288651\pi\)
0.616250 + 0.787551i \(0.288651\pi\)
\(762\) 0 0
\(763\) 4.00000i 0.144810i
\(764\) 6.00000i 0.217072i
\(765\) 0 0
\(766\) 54.0000i 1.95110i
\(767\) 16.0000i 0.577727i
\(768\) 0 0
\(769\) 14.0000i 0.504853i −0.967616 0.252426i \(-0.918771\pi\)
0.967616 0.252426i \(-0.0812286\pi\)
\(770\) −16.0000 + 8.00000i −0.576600 + 0.288300i
\(771\) 0 0
\(772\) 12.0000 0.431889
\(773\) −24.0000 −0.863220 −0.431610 0.902060i \(-0.642054\pi\)
−0.431610 + 0.902060i \(0.642054\pi\)
\(774\) 0 0
\(775\) −8.00000 6.00000i −0.287368 0.215526i
\(776\) 0 0
\(777\) 0 0
\(778\) 6.00000i 0.215110i
\(779\) 36.0000 1.28983
\(780\) 0 0
\(781\) 2.00000i 0.0715656i
\(782\) 108.000i 3.86207i
\(783\) 0 0
\(784\) 36.0000 1.28571
\(785\) −28.0000 + 14.0000i −0.999363 + 0.499681i
\(786\) 0 0
\(787\) 42.0000i 1.49714i −0.663057 0.748569i \(-0.730741\pi\)
0.663057 0.748569i \(-0.269259\pi\)
\(788\) 46.0000i 1.63868i
\(789\) 0 0
\(790\) −8.00000 16.0000i −0.284627 0.569254i