Properties

Label 2790.2.d.e.559.1
Level $2790$
Weight $2$
Character 2790.559
Analytic conductor $22.278$
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] = [2790,2,Mod(559,2790)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2790, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2790.559");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2790.d (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: \(22.2782621639\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 930)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 559.1
Root \(-1.00000i\) of defining polynomial
Character \(\chi\) \(=\) 2790.559
Dual form 2790.2.d.e.559.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -5.00000i q^{7} +1.00000i q^{8} +O(q^{10})\) \(q-1.00000i q^{2} -1.00000 q^{4} +(-1.00000 + 2.00000i) q^{5} -5.00000i q^{7} +1.00000i q^{8} +(2.00000 + 1.00000i) q^{10} +1.00000 q^{11} -5.00000 q^{14} +1.00000 q^{16} -4.00000i q^{17} -3.00000 q^{19} +(1.00000 - 2.00000i) q^{20} -1.00000i q^{22} +1.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +5.00000i q^{28} +6.00000 q^{29} -1.00000 q^{31} -1.00000i q^{32} -4.00000 q^{34} +(10.0000 + 5.00000i) q^{35} +4.00000i q^{37} +3.00000i q^{38} +(-2.00000 - 1.00000i) q^{40} -2.00000 q^{41} -1.00000i q^{43} -1.00000 q^{44} +1.00000 q^{46} +4.00000i q^{47} -18.0000 q^{49} +(-4.00000 + 3.00000i) q^{50} -3.00000i q^{53} +(-1.00000 + 2.00000i) q^{55} +5.00000 q^{56} -6.00000i q^{58} -14.0000 q^{59} +14.0000 q^{61} +1.00000i q^{62} -1.00000 q^{64} -10.0000i q^{67} +4.00000i q^{68} +(5.00000 - 10.0000i) q^{70} -9.00000 q^{71} -7.00000i q^{73} +4.00000 q^{74} +3.00000 q^{76} -5.00000i q^{77} -15.0000 q^{79} +(-1.00000 + 2.00000i) q^{80} +2.00000i q^{82} +10.0000i q^{83} +(8.00000 + 4.00000i) q^{85} -1.00000 q^{86} +1.00000i q^{88} -1.00000 q^{89} -1.00000i q^{92} +4.00000 q^{94} +(3.00000 - 6.00000i) q^{95} -10.0000i q^{97} +18.0000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q - 2 q^{4} - 2 q^{5}+O(q^{10}) \) Copy content Toggle raw display \( 2 q - 2 q^{4} - 2 q^{5} + 4 q^{10} + 2 q^{11} - 10 q^{14} + 2 q^{16} - 6 q^{19} + 2 q^{20} - 6 q^{25} + 12 q^{29} - 2 q^{31} - 8 q^{34} + 20 q^{35} - 4 q^{40} - 4 q^{41} - 2 q^{44} + 2 q^{46} - 36 q^{49} - 8 q^{50} - 2 q^{55} + 10 q^{56} - 28 q^{59} + 28 q^{61} - 2 q^{64} + 10 q^{70} - 18 q^{71} + 8 q^{74} + 6 q^{76} - 30 q^{79} - 2 q^{80} + 16 q^{85} - 2 q^{86} - 2 q^{89} + 8 q^{94} + 6 q^{95}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2790\mathbb{Z}\right)^\times\).

\(n\) \(1117\) \(1801\) \(2171\)
\(\chi(n)\) \(-1\) \(1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000i 0.707107i
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) −1.00000 + 2.00000i −0.447214 + 0.894427i
\(6\) 0 0
\(7\) 5.00000i 1.88982i −0.327327 0.944911i \(-0.606148\pi\)
0.327327 0.944911i \(-0.393852\pi\)
\(8\) 1.00000i 0.353553i
\(9\) 0 0
\(10\) 2.00000 + 1.00000i 0.632456 + 0.316228i
\(11\) 1.00000 0.301511 0.150756 0.988571i \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) 0 0
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) −5.00000 −1.33631
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.00000i 0.970143i −0.874475 0.485071i \(-0.838794\pi\)
0.874475 0.485071i \(-0.161206\pi\)
\(18\) 0 0
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) 1.00000 2.00000i 0.223607 0.447214i
\(21\) 0 0
\(22\) 1.00000i 0.213201i
\(23\) 1.00000i 0.208514i 0.994550 + 0.104257i \(0.0332465\pi\)
−0.994550 + 0.104257i \(0.966753\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 0 0
\(27\) 0 0
\(28\) 5.00000i 0.944911i
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) 0 0
\(31\) −1.00000 −0.179605
\(32\) 1.00000i 0.176777i
\(33\) 0 0
\(34\) −4.00000 −0.685994
\(35\) 10.0000 + 5.00000i 1.69031 + 0.845154i
\(36\) 0 0
\(37\) 4.00000i 0.657596i 0.944400 + 0.328798i \(0.106644\pi\)
−0.944400 + 0.328798i \(0.893356\pi\)
\(38\) 3.00000i 0.486664i
\(39\) 0 0
\(40\) −2.00000 1.00000i −0.316228 0.158114i
\(41\) −2.00000 −0.312348 −0.156174 0.987730i \(-0.549916\pi\)
−0.156174 + 0.987730i \(0.549916\pi\)
\(42\) 0 0
\(43\) 1.00000i 0.152499i −0.997089 0.0762493i \(-0.975706\pi\)
0.997089 0.0762493i \(-0.0242945\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) 1.00000 0.147442
\(47\) 4.00000i 0.583460i 0.956501 + 0.291730i \(0.0942309\pi\)
−0.956501 + 0.291730i \(0.905769\pi\)
\(48\) 0 0
\(49\) −18.0000 −2.57143
\(50\) −4.00000 + 3.00000i −0.565685 + 0.424264i
\(51\) 0 0
\(52\) 0 0
\(53\) 3.00000i 0.412082i −0.978543 0.206041i \(-0.933942\pi\)
0.978543 0.206041i \(-0.0660580\pi\)
\(54\) 0 0
\(55\) −1.00000 + 2.00000i −0.134840 + 0.269680i
\(56\) 5.00000 0.668153
\(57\) 0 0
\(58\) 6.00000i 0.787839i
\(59\) −14.0000 −1.82264 −0.911322 0.411693i \(-0.864937\pi\)
−0.911322 + 0.411693i \(0.864937\pi\)
\(60\) 0 0
\(61\) 14.0000 1.79252 0.896258 0.443533i \(-0.146275\pi\)
0.896258 + 0.443533i \(0.146275\pi\)
\(62\) 1.00000i 0.127000i
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 10.0000i 1.22169i −0.791748 0.610847i \(-0.790829\pi\)
0.791748 0.610847i \(-0.209171\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) 5.00000 10.0000i 0.597614 1.19523i
\(71\) −9.00000 −1.06810 −0.534052 0.845452i \(-0.679331\pi\)
−0.534052 + 0.845452i \(0.679331\pi\)
\(72\) 0 0
\(73\) 7.00000i 0.819288i −0.912245 0.409644i \(-0.865653\pi\)
0.912245 0.409644i \(-0.134347\pi\)
\(74\) 4.00000 0.464991
\(75\) 0 0
\(76\) 3.00000 0.344124
\(77\) 5.00000i 0.569803i
\(78\) 0 0
\(79\) −15.0000 −1.68763 −0.843816 0.536633i \(-0.819696\pi\)
−0.843816 + 0.536633i \(0.819696\pi\)
\(80\) −1.00000 + 2.00000i −0.111803 + 0.223607i
\(81\) 0 0
\(82\) 2.00000i 0.220863i
\(83\) 10.0000i 1.09764i 0.835940 + 0.548821i \(0.184923\pi\)
−0.835940 + 0.548821i \(0.815077\pi\)
\(84\) 0 0
\(85\) 8.00000 + 4.00000i 0.867722 + 0.433861i
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) 1.00000i 0.106600i
\(89\) −1.00000 −0.106000 −0.0529999 0.998595i \(-0.516878\pi\)
−0.0529999 + 0.998595i \(0.516878\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.00000i 0.104257i
\(93\) 0 0
\(94\) 4.00000 0.412568
\(95\) 3.00000 6.00000i 0.307794 0.615587i
\(96\) 0 0
\(97\) 10.0000i 1.01535i −0.861550 0.507673i \(-0.830506\pi\)
0.861550 0.507673i \(-0.169494\pi\)
\(98\) 18.0000i 1.81827i
\(99\) 0 0
\(100\) 3.00000 + 4.00000i 0.300000 + 0.400000i
\(101\) −7.00000 −0.696526 −0.348263 0.937397i \(-0.613228\pi\)
−0.348263 + 0.937397i \(0.613228\pi\)
\(102\) 0 0
\(103\) 8.00000i 0.788263i −0.919054 0.394132i \(-0.871045\pi\)
0.919054 0.394132i \(-0.128955\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −3.00000 −0.291386
\(107\) 9.00000i 0.870063i 0.900415 + 0.435031i \(0.143263\pi\)
−0.900415 + 0.435031i \(0.856737\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 2.00000 + 1.00000i 0.190693 + 0.0953463i
\(111\) 0 0
\(112\) 5.00000i 0.472456i
\(113\) 9.00000i 0.846649i 0.905978 + 0.423324i \(0.139137\pi\)
−0.905978 + 0.423324i \(0.860863\pi\)
\(114\) 0 0
\(115\) −2.00000 1.00000i −0.186501 0.0932505i
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) 14.0000i 1.28880i
\(119\) −20.0000 −1.83340
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 14.0000i 1.26750i
\(123\) 0 0
\(124\) 1.00000 0.0898027
\(125\) 11.0000 2.00000i 0.983870 0.178885i
\(126\) 0 0
\(127\) 16.0000i 1.41977i 0.704317 + 0.709885i \(0.251253\pi\)
−0.704317 + 0.709885i \(0.748747\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) 0 0
\(130\) 0 0
\(131\) −18.0000 −1.57267 −0.786334 0.617802i \(-0.788023\pi\)
−0.786334 + 0.617802i \(0.788023\pi\)
\(132\) 0 0
\(133\) 15.0000i 1.30066i
\(134\) −10.0000 −0.863868
\(135\) 0 0
\(136\) 4.00000 0.342997
\(137\) 6.00000i 0.512615i −0.966595 0.256307i \(-0.917494\pi\)
0.966595 0.256307i \(-0.0825059\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −10.0000 5.00000i −0.845154 0.422577i
\(141\) 0 0
\(142\) 9.00000i 0.755263i
\(143\) 0 0
\(144\) 0 0
\(145\) −6.00000 + 12.0000i −0.498273 + 0.996546i
\(146\) −7.00000 −0.579324
\(147\) 0 0
\(148\) 4.00000i 0.328798i
\(149\) 1.00000 0.0819232 0.0409616 0.999161i \(-0.486958\pi\)
0.0409616 + 0.999161i \(0.486958\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 3.00000i 0.243332i
\(153\) 0 0
\(154\) −5.00000 −0.402911
\(155\) 1.00000 2.00000i 0.0803219 0.160644i
\(156\) 0 0
\(157\) 1.00000i 0.0798087i −0.999204 0.0399043i \(-0.987295\pi\)
0.999204 0.0399043i \(-0.0127053\pi\)
\(158\) 15.0000i 1.19334i
\(159\) 0 0
\(160\) 2.00000 + 1.00000i 0.158114 + 0.0790569i
\(161\) 5.00000 0.394055
\(162\) 0 0
\(163\) 8.00000i 0.626608i −0.949653 0.313304i \(-0.898564\pi\)
0.949653 0.313304i \(-0.101436\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) 10.0000 0.776151
\(167\) 9.00000i 0.696441i −0.937413 0.348220i \(-0.886786\pi\)
0.937413 0.348220i \(-0.113214\pi\)
\(168\) 0 0
\(169\) 13.0000 1.00000
\(170\) 4.00000 8.00000i 0.306786 0.613572i
\(171\) 0 0
\(172\) 1.00000i 0.0762493i
\(173\) 2.00000i 0.152057i 0.997106 + 0.0760286i \(0.0242240\pi\)
−0.997106 + 0.0760286i \(0.975776\pi\)
\(174\) 0 0
\(175\) −20.0000 + 15.0000i −1.51186 + 1.13389i
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) 1.00000i 0.0749532i
\(179\) −8.00000 −0.597948 −0.298974 0.954261i \(-0.596644\pi\)
−0.298974 + 0.954261i \(0.596644\pi\)
\(180\) 0 0
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.00000 −0.0737210
\(185\) −8.00000 4.00000i −0.588172 0.294086i
\(186\) 0 0
\(187\) 4.00000i 0.292509i
\(188\) 4.00000i 0.291730i
\(189\) 0 0
\(190\) −6.00000 3.00000i −0.435286 0.217643i
\(191\) −24.0000 −1.73658 −0.868290 0.496058i \(-0.834780\pi\)
−0.868290 + 0.496058i \(0.834780\pi\)
\(192\) 0 0
\(193\) 10.0000i 0.719816i −0.932988 0.359908i \(-0.882808\pi\)
0.932988 0.359908i \(-0.117192\pi\)
\(194\) −10.0000 −0.717958
\(195\) 0 0
\(196\) 18.0000 1.28571
\(197\) 2.00000i 0.142494i −0.997459 0.0712470i \(-0.977302\pi\)
0.997459 0.0712470i \(-0.0226979\pi\)
\(198\) 0 0
\(199\) 9.00000 0.637993 0.318997 0.947756i \(-0.396654\pi\)
0.318997 + 0.947756i \(0.396654\pi\)
\(200\) 4.00000 3.00000i 0.282843 0.212132i
\(201\) 0 0
\(202\) 7.00000i 0.492518i
\(203\) 30.0000i 2.10559i
\(204\) 0 0
\(205\) 2.00000 4.00000i 0.139686 0.279372i
\(206\) −8.00000 −0.557386
\(207\) 0 0
\(208\) 0 0
\(209\) −3.00000 −0.207514
\(210\) 0 0
\(211\) −21.0000 −1.44570 −0.722850 0.691005i \(-0.757168\pi\)
−0.722850 + 0.691005i \(0.757168\pi\)
\(212\) 3.00000i 0.206041i
\(213\) 0 0
\(214\) 9.00000 0.615227
\(215\) 2.00000 + 1.00000i 0.136399 + 0.0681994i
\(216\) 0 0
\(217\) 5.00000i 0.339422i
\(218\) 10.0000i 0.677285i
\(219\) 0 0
\(220\) 1.00000 2.00000i 0.0674200 0.134840i
\(221\) 0 0
\(222\) 0 0
\(223\) 8.00000i 0.535720i 0.963458 + 0.267860i \(0.0863164\pi\)
−0.963458 + 0.267860i \(0.913684\pi\)
\(224\) −5.00000 −0.334077
\(225\) 0 0
\(226\) 9.00000 0.598671
\(227\) 29.0000i 1.92480i 0.271640 + 0.962399i \(0.412434\pi\)
−0.271640 + 0.962399i \(0.587566\pi\)
\(228\) 0 0
\(229\) −23.0000 −1.51988 −0.759941 0.649992i \(-0.774772\pi\)
−0.759941 + 0.649992i \(0.774772\pi\)
\(230\) −1.00000 + 2.00000i −0.0659380 + 0.131876i
\(231\) 0 0
\(232\) 6.00000i 0.393919i
\(233\) 13.0000i 0.851658i −0.904804 0.425829i \(-0.859982\pi\)
0.904804 0.425829i \(-0.140018\pi\)
\(234\) 0 0
\(235\) −8.00000 4.00000i −0.521862 0.260931i
\(236\) 14.0000 0.911322
\(237\) 0 0
\(238\) 20.0000i 1.29641i
\(239\) −22.0000 −1.42306 −0.711531 0.702655i \(-0.751998\pi\)
−0.711531 + 0.702655i \(0.751998\pi\)
\(240\) 0 0
\(241\) 4.00000 0.257663 0.128831 0.991667i \(-0.458877\pi\)
0.128831 + 0.991667i \(0.458877\pi\)
\(242\) 10.0000i 0.642824i
\(243\) 0 0
\(244\) −14.0000 −0.896258
\(245\) 18.0000 36.0000i 1.14998 2.29996i
\(246\) 0 0
\(247\) 0 0
\(248\) 1.00000i 0.0635001i
\(249\) 0 0
\(250\) −2.00000 11.0000i −0.126491 0.695701i
\(251\) 12.0000 0.757433 0.378717 0.925513i \(-0.376365\pi\)
0.378717 + 0.925513i \(0.376365\pi\)
\(252\) 0 0
\(253\) 1.00000i 0.0628695i
\(254\) 16.0000 1.00393
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 3.00000i 0.187135i 0.995613 + 0.0935674i \(0.0298271\pi\)
−0.995613 + 0.0935674i \(0.970173\pi\)
\(258\) 0 0
\(259\) 20.0000 1.24274
\(260\) 0 0
\(261\) 0 0
\(262\) 18.0000i 1.11204i
\(263\) 8.00000i 0.493301i −0.969104 0.246651i \(-0.920670\pi\)
0.969104 0.246651i \(-0.0793300\pi\)
\(264\) 0 0
\(265\) 6.00000 + 3.00000i 0.368577 + 0.184289i
\(266\) 15.0000 0.919709
\(267\) 0 0
\(268\) 10.0000i 0.610847i
\(269\) 30.0000 1.82913 0.914566 0.404436i \(-0.132532\pi\)
0.914566 + 0.404436i \(0.132532\pi\)
\(270\) 0 0
\(271\) 13.0000 0.789694 0.394847 0.918747i \(-0.370798\pi\)
0.394847 + 0.918747i \(0.370798\pi\)
\(272\) 4.00000i 0.242536i
\(273\) 0 0
\(274\) −6.00000 −0.362473
\(275\) −3.00000 4.00000i −0.180907 0.241209i
\(276\) 0 0
\(277\) 26.0000i 1.56219i −0.624413 0.781094i \(-0.714662\pi\)
0.624413 0.781094i \(-0.285338\pi\)
\(278\) 4.00000i 0.239904i
\(279\) 0 0
\(280\) −5.00000 + 10.0000i −0.298807 + 0.597614i
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) 0 0
\(283\) 22.0000i 1.30776i 0.756596 + 0.653882i \(0.226861\pi\)
−0.756596 + 0.653882i \(0.773139\pi\)
\(284\) 9.00000 0.534052
\(285\) 0 0
\(286\) 0 0
\(287\) 10.0000i 0.590281i
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 12.0000 + 6.00000i 0.704664 + 0.352332i
\(291\) 0 0
\(292\) 7.00000i 0.409644i
\(293\) 30.0000i 1.75262i −0.481749 0.876309i \(-0.659998\pi\)
0.481749 0.876309i \(-0.340002\pi\)
\(294\) 0 0
\(295\) 14.0000 28.0000i 0.815112 1.63022i
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) 1.00000i 0.0579284i
\(299\) 0 0
\(300\) 0 0
\(301\) −5.00000 −0.288195
\(302\) 8.00000i 0.460348i
\(303\) 0 0
\(304\) −3.00000 −0.172062
\(305\) −14.0000 + 28.0000i −0.801638 + 1.60328i
\(306\) 0 0
\(307\) 12.0000i 0.684876i −0.939540 0.342438i \(-0.888747\pi\)
0.939540 0.342438i \(-0.111253\pi\)
\(308\) 5.00000i 0.284901i
\(309\) 0 0
\(310\) −2.00000 1.00000i −0.113592 0.0567962i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) 26.0000i 1.46961i 0.678280 + 0.734803i \(0.262726\pi\)
−0.678280 + 0.734803i \(0.737274\pi\)
\(314\) −1.00000 −0.0564333
\(315\) 0 0
\(316\) 15.0000 0.843816
\(317\) 22.0000i 1.23564i −0.786318 0.617822i \(-0.788015\pi\)
0.786318 0.617822i \(-0.211985\pi\)
\(318\) 0 0
\(319\) 6.00000 0.335936
\(320\) 1.00000 2.00000i 0.0559017 0.111803i
\(321\) 0 0
\(322\) 5.00000i 0.278639i
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) 0 0
\(326\) −8.00000 −0.443079
\(327\) 0 0
\(328\) 2.00000i 0.110432i
\(329\) 20.0000 1.10264
\(330\) 0 0
\(331\) 28.0000 1.53902 0.769510 0.638635i \(-0.220501\pi\)
0.769510 + 0.638635i \(0.220501\pi\)
\(332\) 10.0000i 0.548821i
\(333\) 0 0
\(334\) −9.00000 −0.492458
\(335\) 20.0000 + 10.0000i 1.09272 + 0.546358i
\(336\) 0 0
\(337\) 10.0000i 0.544735i 0.962193 + 0.272367i \(0.0878066\pi\)
−0.962193 + 0.272367i \(0.912193\pi\)
\(338\) 13.0000i 0.707107i
\(339\) 0 0
\(340\) −8.00000 4.00000i −0.433861 0.216930i
\(341\) −1.00000 −0.0541530
\(342\) 0 0
\(343\) 55.0000i 2.96972i
\(344\) 1.00000 0.0539164
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) 30.0000i 1.61048i 0.592946 + 0.805242i \(0.297965\pi\)
−0.592946 + 0.805242i \(0.702035\pi\)
\(348\) 0 0
\(349\) 32.0000 1.71292 0.856460 0.516213i \(-0.172659\pi\)
0.856460 + 0.516213i \(0.172659\pi\)
\(350\) 15.0000 + 20.0000i 0.801784 + 1.06904i
\(351\) 0 0
\(352\) 1.00000i 0.0533002i
\(353\) 8.00000i 0.425797i 0.977074 + 0.212899i \(0.0682904\pi\)
−0.977074 + 0.212899i \(0.931710\pi\)
\(354\) 0 0
\(355\) 9.00000 18.0000i 0.477670 0.955341i
\(356\) 1.00000 0.0529999
\(357\) 0 0
\(358\) 8.00000i 0.422813i
\(359\) −15.0000 −0.791670 −0.395835 0.918322i \(-0.629545\pi\)
−0.395835 + 0.918322i \(0.629545\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) 11.0000i 0.578147i
\(363\) 0 0
\(364\) 0 0
\(365\) 14.0000 + 7.00000i 0.732793 + 0.366397i
\(366\) 0 0
\(367\) 26.0000i 1.35719i −0.734513 0.678594i \(-0.762589\pi\)
0.734513 0.678594i \(-0.237411\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) 0 0
\(370\) −4.00000 + 8.00000i −0.207950 + 0.415900i
\(371\) −15.0000 −0.778761
\(372\) 0 0
\(373\) 3.00000i 0.155334i −0.996979 0.0776671i \(-0.975253\pi\)
0.996979 0.0776671i \(-0.0247471\pi\)
\(374\) −4.00000 −0.206835
\(375\) 0 0
\(376\) −4.00000 −0.206284
\(377\) 0 0
\(378\) 0 0
\(379\) 19.0000 0.975964 0.487982 0.872854i \(-0.337733\pi\)
0.487982 + 0.872854i \(0.337733\pi\)
\(380\) −3.00000 + 6.00000i −0.153897 + 0.307794i
\(381\) 0 0
\(382\) 24.0000i 1.22795i
\(383\) 20.0000i 1.02195i 0.859595 + 0.510976i \(0.170716\pi\)
−0.859595 + 0.510976i \(0.829284\pi\)
\(384\) 0 0
\(385\) 10.0000 + 5.00000i 0.509647 + 0.254824i
\(386\) −10.0000 −0.508987
\(387\) 0 0
\(388\) 10.0000i 0.507673i
\(389\) −16.0000 −0.811232 −0.405616 0.914044i \(-0.632943\pi\)
−0.405616 + 0.914044i \(0.632943\pi\)
\(390\) 0 0
\(391\) 4.00000 0.202289
\(392\) 18.0000i 0.909137i
\(393\) 0 0
\(394\) −2.00000 −0.100759
\(395\) 15.0000 30.0000i 0.754732 1.50946i
\(396\) 0 0
\(397\) 17.0000i 0.853206i −0.904439 0.426603i \(-0.859710\pi\)
0.904439 0.426603i \(-0.140290\pi\)
\(398\) 9.00000i 0.451129i
\(399\) 0 0
\(400\) −3.00000 4.00000i −0.150000 0.200000i
\(401\) 29.0000 1.44819 0.724095 0.689700i \(-0.242257\pi\)
0.724095 + 0.689700i \(0.242257\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 7.00000 0.348263
\(405\) 0 0
\(406\) −30.0000 −1.48888
\(407\) 4.00000i 0.198273i
\(408\) 0 0
\(409\) 16.0000 0.791149 0.395575 0.918434i \(-0.370545\pi\)
0.395575 + 0.918434i \(0.370545\pi\)
\(410\) −4.00000 2.00000i −0.197546 0.0987730i
\(411\) 0 0
\(412\) 8.00000i 0.394132i
\(413\) 70.0000i 3.44447i
\(414\) 0 0
\(415\) −20.0000 10.0000i −0.981761 0.490881i
\(416\) 0 0
\(417\) 0 0
\(418\) 3.00000i 0.146735i
\(419\) 26.0000 1.27018 0.635092 0.772437i \(-0.280962\pi\)
0.635092 + 0.772437i \(0.280962\pi\)
\(420\) 0 0
\(421\) 22.0000 1.07221 0.536107 0.844150i \(-0.319894\pi\)
0.536107 + 0.844150i \(0.319894\pi\)
\(422\) 21.0000i 1.02226i
\(423\) 0 0
\(424\) 3.00000 0.145693
\(425\) −16.0000 + 12.0000i −0.776114 + 0.582086i
\(426\) 0 0
\(427\) 70.0000i 3.38754i
\(428\) 9.00000i 0.435031i
\(429\) 0 0
\(430\) 1.00000 2.00000i 0.0482243 0.0964486i
\(431\) −8.00000 −0.385346 −0.192673 0.981263i \(-0.561716\pi\)
−0.192673 + 0.981263i \(0.561716\pi\)
\(432\) 0 0
\(433\) 11.0000i 0.528626i 0.964437 + 0.264313i \(0.0851452\pi\)
−0.964437 + 0.264313i \(0.914855\pi\)
\(434\) 5.00000 0.240008
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) 3.00000i 0.143509i
\(438\) 0 0
\(439\) −36.0000 −1.71819 −0.859093 0.511819i \(-0.828972\pi\)
−0.859093 + 0.511819i \(0.828972\pi\)
\(440\) −2.00000 1.00000i −0.0953463 0.0476731i
\(441\) 0 0
\(442\) 0 0
\(443\) 15.0000i 0.712672i −0.934358 0.356336i \(-0.884026\pi\)
0.934358 0.356336i \(-0.115974\pi\)
\(444\) 0 0
\(445\) 1.00000 2.00000i 0.0474045 0.0948091i
\(446\) 8.00000 0.378811
\(447\) 0 0
\(448\) 5.00000i 0.236228i
\(449\) 6.00000 0.283158 0.141579 0.989927i \(-0.454782\pi\)
0.141579 + 0.989927i \(0.454782\pi\)
\(450\) 0 0
\(451\) −2.00000 −0.0941763
\(452\) 9.00000i 0.423324i
\(453\) 0 0
\(454\) 29.0000 1.36104
\(455\) 0 0
\(456\) 0 0
\(457\) 10.0000i 0.467780i 0.972263 + 0.233890i \(0.0751456\pi\)
−0.972263 + 0.233890i \(0.924854\pi\)
\(458\) 23.0000i 1.07472i
\(459\) 0 0
\(460\) 2.00000 + 1.00000i 0.0932505 + 0.0466252i
\(461\) −24.0000 −1.11779 −0.558896 0.829238i \(-0.688775\pi\)
−0.558896 + 0.829238i \(0.688775\pi\)
\(462\) 0 0
\(463\) 6.00000i 0.278844i −0.990233 0.139422i \(-0.955476\pi\)
0.990233 0.139422i \(-0.0445244\pi\)
\(464\) 6.00000 0.278543
\(465\) 0 0
\(466\) −13.0000 −0.602213
\(467\) 12.0000i 0.555294i −0.960683 0.277647i \(-0.910445\pi\)
0.960683 0.277647i \(-0.0895545\pi\)
\(468\) 0 0
\(469\) −50.0000 −2.30879
\(470\) −4.00000 + 8.00000i −0.184506 + 0.369012i
\(471\) 0 0
\(472\) 14.0000i 0.644402i
\(473\) 1.00000i 0.0459800i
\(474\) 0 0
\(475\) 9.00000 + 12.0000i 0.412948 + 0.550598i
\(476\) 20.0000 0.916698
\(477\) 0 0
\(478\) 22.0000i 1.00626i
\(479\) 29.0000 1.32504 0.662522 0.749043i \(-0.269486\pi\)
0.662522 + 0.749043i \(0.269486\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 4.00000i 0.182195i
\(483\) 0 0
\(484\) 10.0000 0.454545
\(485\) 20.0000 + 10.0000i 0.908153 + 0.454077i
\(486\) 0 0
\(487\) 36.0000i 1.63132i −0.578535 0.815658i \(-0.696375\pi\)
0.578535 0.815658i \(-0.303625\pi\)
\(488\) 14.0000i 0.633750i
\(489\) 0 0
\(490\) −36.0000 18.0000i −1.62631 0.813157i
\(491\) −27.0000 −1.21849 −0.609246 0.792981i \(-0.708528\pi\)
−0.609246 + 0.792981i \(0.708528\pi\)
\(492\) 0 0
\(493\) 24.0000i 1.08091i
\(494\) 0 0
\(495\) 0 0
\(496\) −1.00000 −0.0449013
\(497\) 45.0000i 2.01853i
\(498\) 0 0
\(499\) 42.0000 1.88018 0.940089 0.340929i \(-0.110742\pi\)
0.940089 + 0.340929i \(0.110742\pi\)
\(500\) −11.0000 + 2.00000i −0.491935 + 0.0894427i
\(501\) 0 0
\(502\) 12.0000i 0.535586i
\(503\) 42.0000i 1.87269i −0.351085 0.936344i \(-0.614187\pi\)
0.351085 0.936344i \(-0.385813\pi\)
\(504\) 0 0
\(505\) 7.00000 14.0000i 0.311496 0.622992i
\(506\) 1.00000 0.0444554
\(507\) 0 0
\(508\) 16.0000i 0.709885i
\(509\) −36.0000 −1.59567 −0.797836 0.602875i \(-0.794022\pi\)
−0.797836 + 0.602875i \(0.794022\pi\)
\(510\) 0 0
\(511\) −35.0000 −1.54831
\(512\) 1.00000i 0.0441942i
\(513\) 0 0
\(514\) 3.00000 0.132324
\(515\) 16.0000 + 8.00000i 0.705044 + 0.352522i
\(516\) 0 0
\(517\) 4.00000i 0.175920i
\(518\) 20.0000i 0.878750i
\(519\) 0 0
\(520\) 0 0
\(521\) 20.0000 0.876216 0.438108 0.898922i \(-0.355649\pi\)
0.438108 + 0.898922i \(0.355649\pi\)
\(522\) 0 0
\(523\) 41.0000i 1.79280i −0.443241 0.896402i \(-0.646171\pi\)
0.443241 0.896402i \(-0.353829\pi\)
\(524\) 18.0000 0.786334
\(525\) 0 0
\(526\) −8.00000 −0.348817
\(527\) 4.00000i 0.174243i
\(528\) 0 0
\(529\) 22.0000 0.956522
\(530\) 3.00000 6.00000i 0.130312 0.260623i
\(531\) 0 0
\(532\) 15.0000i 0.650332i
\(533\) 0 0
\(534\) 0 0
\(535\) −18.0000 9.00000i −0.778208 0.389104i
\(536\) 10.0000 0.431934
\(537\) 0 0
\(538\) 30.0000i 1.29339i
\(539\) −18.0000 −0.775315
\(540\) 0 0
\(541\) 4.00000 0.171973 0.0859867 0.996296i \(-0.472596\pi\)
0.0859867 + 0.996296i \(0.472596\pi\)
\(542\) 13.0000i 0.558398i
\(543\) 0 0
\(544\) −4.00000 −0.171499
\(545\) 10.0000 20.0000i 0.428353 0.856706i
\(546\) 0 0
\(547\) 20.0000i 0.855138i −0.903983 0.427569i \(-0.859370\pi\)
0.903983 0.427569i \(-0.140630\pi\)
\(548\) 6.00000i 0.256307i
\(549\) 0 0
\(550\) −4.00000 + 3.00000i −0.170561 + 0.127920i
\(551\) −18.0000 −0.766826
\(552\) 0 0
\(553\) 75.0000i 3.18932i
\(554\) −26.0000 −1.10463
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) 33.0000i 1.39825i −0.714997 0.699127i \(-0.753572\pi\)
0.714997 0.699127i \(-0.246428\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 10.0000 + 5.00000i 0.422577 + 0.211289i
\(561\) 0 0
\(562\) 0 0
\(563\) 4.00000i 0.168580i −0.996441 0.0842900i \(-0.973138\pi\)
0.996441 0.0842900i \(-0.0268622\pi\)
\(564\) 0 0
\(565\) −18.0000 9.00000i −0.757266 0.378633i
\(566\) 22.0000 0.924729
\(567\) 0 0
\(568\) 9.00000i 0.377632i
\(569\) −1.00000 −0.0419222 −0.0209611 0.999780i \(-0.506673\pi\)
−0.0209611 + 0.999780i \(0.506673\pi\)
\(570\) 0 0
\(571\) 34.0000 1.42286 0.711428 0.702759i \(-0.248049\pi\)
0.711428 + 0.702759i \(0.248049\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 10.0000 0.417392
\(575\) 4.00000 3.00000i 0.166812 0.125109i
\(576\) 0 0
\(577\) 10.0000i 0.416305i 0.978096 + 0.208153i \(0.0667451\pi\)
−0.978096 + 0.208153i \(0.933255\pi\)
\(578\) 1.00000i 0.0415945i
\(579\) 0 0
\(580\) 6.00000 12.0000i 0.249136 0.498273i
\(581\) 50.0000 2.07435
\(582\) 0 0
\(583\) 3.00000i 0.124247i
\(584\) 7.00000 0.289662
\(585\) 0 0
\(586\) −30.0000 −1.23929
\(587\) 30.0000i 1.23823i −0.785299 0.619116i \(-0.787491\pi\)
0.785299 0.619116i \(-0.212509\pi\)
\(588\) 0 0
\(589\) 3.00000 0.123613
\(590\) −28.0000 14.0000i −1.15274 0.576371i
\(591\) 0 0
\(592\) 4.00000i 0.164399i
\(593\) 6.00000i 0.246390i 0.992382 + 0.123195i \(0.0393141\pi\)
−0.992382 + 0.123195i \(0.960686\pi\)
\(594\) 0 0
\(595\) 20.0000 40.0000i 0.819920 1.63984i
\(596\) −1.00000 −0.0409616
\(597\) 0 0
\(598\) 0 0
\(599\) 15.0000 0.612883 0.306442 0.951889i \(-0.400862\pi\)
0.306442 + 0.951889i \(0.400862\pi\)
\(600\) 0 0
\(601\) −28.0000 −1.14214 −0.571072 0.820900i \(-0.693472\pi\)
−0.571072 + 0.820900i \(0.693472\pi\)
\(602\) 5.00000i 0.203785i
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 10.0000 20.0000i 0.406558 0.813116i
\(606\) 0 0
\(607\) 23.0000i 0.933541i 0.884378 + 0.466771i \(0.154583\pi\)
−0.884378 + 0.466771i \(0.845417\pi\)
\(608\) 3.00000i 0.121666i
\(609\) 0 0
\(610\) 28.0000 + 14.0000i 1.13369 + 0.566843i
\(611\) 0 0
\(612\) 0 0
\(613\) 16.0000i 0.646234i −0.946359 0.323117i \(-0.895269\pi\)
0.946359 0.323117i \(-0.104731\pi\)
\(614\) −12.0000 −0.484281
\(615\) 0 0
\(616\) 5.00000 0.201456
\(617\) 13.0000i 0.523360i −0.965155 0.261680i \(-0.915723\pi\)
0.965155 0.261680i \(-0.0842766\pi\)
\(618\) 0 0
\(619\) 28.0000 1.12542 0.562708 0.826656i \(-0.309760\pi\)
0.562708 + 0.826656i \(0.309760\pi\)
\(620\) −1.00000 + 2.00000i −0.0401610 + 0.0803219i
\(621\) 0 0
\(622\) 0 0
\(623\) 5.00000i 0.200321i
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 26.0000 1.03917
\(627\) 0 0
\(628\) 1.00000i 0.0399043i
\(629\) 16.0000 0.637962
\(630\) 0 0
\(631\) 29.0000 1.15447 0.577236 0.816577i \(-0.304131\pi\)
0.577236 + 0.816577i \(0.304131\pi\)
\(632\) 15.0000i 0.596668i
\(633\) 0 0
\(634\) −22.0000 −0.873732
\(635\) −32.0000 16.0000i −1.26988 0.634941i
\(636\) 0 0
\(637\) 0 0
\(638\) 6.00000i 0.237542i
\(639\) 0 0
\(640\) −2.00000 1.00000i −0.0790569 0.0395285i
\(641\) −38.0000 −1.50091 −0.750455 0.660922i \(-0.770166\pi\)
−0.750455 + 0.660922i \(0.770166\pi\)
\(642\) 0 0
\(643\) 3.00000i 0.118308i −0.998249 0.0591542i \(-0.981160\pi\)
0.998249 0.0591542i \(-0.0188404\pi\)
\(644\) −5.00000 −0.197028
\(645\) 0 0
\(646\) 12.0000 0.472134
\(647\) 27.0000i 1.06148i −0.847535 0.530740i \(-0.821914\pi\)
0.847535 0.530740i \(-0.178086\pi\)
\(648\) 0 0
\(649\) −14.0000 −0.549548
\(650\) 0 0
\(651\) 0 0
\(652\) 8.00000i 0.313304i
\(653\) 2.00000i 0.0782660i −0.999234 0.0391330i \(-0.987540\pi\)
0.999234 0.0391330i \(-0.0124596\pi\)
\(654\) 0 0
\(655\) 18.0000 36.0000i 0.703318 1.40664i
\(656\) −2.00000 −0.0780869
\(657\) 0 0
\(658\) 20.0000i 0.779681i
\(659\) 10.0000 0.389545 0.194772 0.980848i \(-0.437603\pi\)
0.194772 + 0.980848i \(0.437603\pi\)
\(660\) 0 0
\(661\) −40.0000 −1.55582 −0.777910 0.628376i \(-0.783720\pi\)
−0.777910 + 0.628376i \(0.783720\pi\)
\(662\) 28.0000i 1.08825i
\(663\) 0 0
\(664\) −10.0000 −0.388075
\(665\) −30.0000 15.0000i −1.16335 0.581675i
\(666\) 0 0
\(667\) 6.00000i 0.232321i
\(668\) 9.00000i 0.348220i
\(669\) 0 0
\(670\) 10.0000 20.0000i 0.386334 0.772667i
\(671\) 14.0000 0.540464
\(672\) 0 0
\(673\) 6.00000i 0.231283i −0.993291 0.115642i \(-0.963108\pi\)
0.993291 0.115642i \(-0.0368924\pi\)
\(674\) 10.0000 0.385186
\(675\) 0 0
\(676\) −13.0000 −0.500000
\(677\) 11.0000i 0.422764i 0.977403 + 0.211382i \(0.0677965\pi\)
−0.977403 + 0.211382i \(0.932204\pi\)
\(678\) 0 0
\(679\) −50.0000 −1.91882
\(680\) −4.00000 + 8.00000i −0.153393 + 0.306786i
\(681\) 0 0
\(682\) 1.00000i 0.0382920i
\(683\) 31.0000i 1.18618i 0.805135 + 0.593091i \(0.202093\pi\)
−0.805135 + 0.593091i \(0.797907\pi\)
\(684\) 0 0
\(685\) 12.0000 + 6.00000i 0.458496 + 0.229248i
\(686\) 55.0000 2.09991
\(687\) 0 0
\(688\) 1.00000i 0.0381246i
\(689\) 0 0
\(690\) 0 0
\(691\) −5.00000 −0.190209 −0.0951045 0.995467i \(-0.530319\pi\)
−0.0951045 + 0.995467i \(0.530319\pi\)
\(692\) 2.00000i 0.0760286i
\(693\) 0 0
\(694\) 30.0000 1.13878
\(695\) 4.00000 8.00000i 0.151729 0.303457i
\(696\) 0 0
\(697\) 8.00000i 0.303022i
\(698\) 32.0000i 1.21122i
\(699\) 0 0
\(700\) 20.0000 15.0000i 0.755929 0.566947i
\(701\) −35.0000 −1.32193 −0.660966 0.750416i \(-0.729853\pi\)
−0.660966 + 0.750416i \(0.729853\pi\)
\(702\) 0 0
\(703\) 12.0000i 0.452589i
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 8.00000 0.301084
\(707\) 35.0000i 1.31631i
\(708\) 0 0
\(709\) −21.0000 −0.788672 −0.394336 0.918966i \(-0.629025\pi\)
−0.394336 + 0.918966i \(0.629025\pi\)
\(710\) −18.0000 9.00000i −0.675528 0.337764i
\(711\) 0 0
\(712\) 1.00000i 0.0374766i
\(713\) 1.00000i 0.0374503i
\(714\) 0 0
\(715\) 0 0
\(716\) 8.00000 0.298974
\(717\) 0 0
\(718\) 15.0000i 0.559795i
\(719\) 50.0000 1.86469 0.932343 0.361576i \(-0.117761\pi\)
0.932343 + 0.361576i \(0.117761\pi\)
\(720\) 0 0
\(721\) −40.0000 −1.48968
\(722\) 10.0000i 0.372161i
\(723\) 0 0
\(724\) −11.0000 −0.408812
\(725\) −18.0000 24.0000i −0.668503 0.891338i
\(726\) 0 0
\(727\) 27.0000i 1.00137i 0.865628 + 0.500687i \(0.166919\pi\)
−0.865628 + 0.500687i \(0.833081\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 7.00000 14.0000i 0.259082 0.518163i
\(731\) −4.00000 −0.147945
\(732\) 0 0
\(733\) 34.0000i 1.25582i 0.778287 + 0.627909i \(0.216089\pi\)
−0.778287 + 0.627909i \(0.783911\pi\)
\(734\) −26.0000 −0.959678
\(735\) 0 0
\(736\) 1.00000 0.0368605
\(737\) 10.0000i 0.368355i
\(738\) 0 0
\(739\) −46.0000 −1.69214 −0.846069 0.533074i \(-0.821037\pi\)
−0.846069 + 0.533074i \(0.821037\pi\)
\(740\) 8.00000 + 4.00000i 0.294086 + 0.147043i
\(741\) 0 0
\(742\) 15.0000i 0.550667i
\(743\) 21.0000i 0.770415i −0.922830 0.385208i \(-0.874130\pi\)
0.922830 0.385208i \(-0.125870\pi\)
\(744\) 0 0
\(745\) −1.00000 + 2.00000i −0.0366372 + 0.0732743i
\(746\) −3.00000 −0.109838
\(747\) 0 0
\(748\) 4.00000i 0.146254i
\(749\) 45.0000 1.64426
\(750\) 0 0
\(751\) 2.00000 0.0729810 0.0364905 0.999334i \(-0.488382\pi\)
0.0364905 + 0.999334i \(0.488382\pi\)
\(752\) 4.00000i 0.145865i
\(753\) 0 0
\(754\) 0 0
\(755\) 8.00000 16.0000i 0.291150 0.582300i
\(756\) 0 0
\(757\) 4.00000i 0.145382i 0.997354 + 0.0726912i \(0.0231588\pi\)
−0.997354 + 0.0726912i \(0.976841\pi\)
\(758\) 19.0000i 0.690111i
\(759\) 0 0
\(760\) 6.00000 + 3.00000i 0.217643 + 0.108821i
\(761\) 21.0000 0.761249 0.380625 0.924730i \(-0.375709\pi\)
0.380625 + 0.924730i \(0.375709\pi\)
\(762\) 0 0
\(763\) 50.0000i 1.81012i
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 20.0000 0.722629
\(767\) 0 0
\(768\) 0 0
\(769\) 27.0000 0.973645 0.486822 0.873501i \(-0.338156\pi\)
0.486822 + 0.873501i \(0.338156\pi\)
\(770\) 5.00000 10.0000i 0.180187 0.360375i
\(771\) 0 0
\(772\) 10.0000i 0.359908i
\(773\) 51.0000i 1.83434i 0.398493 + 0.917171i \(0.369533\pi\)
−0.398493 + 0.917171i \(0.630467\pi\)
\(774\) 0 0
\(775\) 3.00000 + 4.00000i 0.107763 + 0.143684i
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) 16.0000i 0.573628i
\(779\) 6.00000 0.214972
\(780\) 0 0
\(781\) −9.00000 −0.322045
\(782\) 4.00000i 0.143040i
\(783\) 0 0
\(784\) −18.0000 −0.642857
\(785\) 2.00000 + 1.00000i 0.0713831 + 0.0356915i
\(786\) 0 0
\(787\) 25.0000i 0.891154i 0.895244 + 0.445577i \(0.147001\pi\)
−0.895244 + 0.445577i \(0.852999\pi\)
\(788\) 2.00000i 0.0712470i
\(789\) 0 0
\(790\) −30.0000 15.0000i −1.06735 0.533676i
\(791\) 45.0000 1.60002