Properties

Label 1305.2.f.c.289.1
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: \( 2 \)
Twist minimal: no (minimal twist has level 435)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +2.00000i q^{7} -3.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} -1.00000 q^{4} +(1.00000 - 2.00000i) q^{5} +2.00000i q^{7} -3.00000 q^{8} +(1.00000 - 2.00000i) q^{10} +2.00000i q^{11} +4.00000i q^{13} +2.00000i q^{14} -1.00000 q^{16} +6.00000 q^{17} -2.00000i q^{19} +(-1.00000 + 2.00000i) q^{20} +2.00000i q^{22} +6.00000i q^{23} +(-3.00000 - 4.00000i) q^{25} +4.00000i q^{26} -2.00000i q^{28} +(5.00000 + 2.00000i) q^{29} +2.00000i q^{31} +5.00000 q^{32} +6.00000 q^{34} +(4.00000 + 2.00000i) q^{35} -2.00000 q^{37} -2.00000i q^{38} +(-3.00000 + 6.00000i) q^{40} +4.00000 q^{43} -2.00000i q^{44} +6.00000i q^{46} +8.00000 q^{47} +3.00000 q^{49} +(-3.00000 - 4.00000i) q^{50} -4.00000i q^{52} +12.0000i q^{53} +(4.00000 + 2.00000i) q^{55} -6.00000i q^{56} +(5.00000 + 2.00000i) q^{58} +4.00000 q^{59} -12.0000i q^{61} +2.00000i q^{62} +7.00000 q^{64} +(8.00000 + 4.00000i) q^{65} +6.00000i q^{67} -6.00000 q^{68} +(4.00000 + 2.00000i) q^{70} -8.00000 q^{71} -6.00000 q^{73} -2.00000 q^{74} +2.00000i q^{76} -4.00000 q^{77} +2.00000i q^{79} +(-1.00000 + 2.00000i) q^{80} +2.00000i q^{83} +(6.00000 - 12.0000i) q^{85} +4.00000 q^{86} -6.00000i q^{88} -16.0000i q^{89} -8.00000 q^{91} -6.00000i q^{92} +8.00000 q^{94} +(-4.00000 - 2.00000i) q^{95} -14.0000 q^{97} +3.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 6 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 2 q + 2 q^{2} - 2 q^{4} + 2 q^{5} - 6 q^{8} + 2 q^{10} - 2 q^{16} + 12 q^{17} - 2 q^{20} - 6 q^{25} + 10 q^{29} + 10 q^{32} + 12 q^{34} + 8 q^{35} - 4 q^{37} - 6 q^{40} + 8 q^{43} + 16 q^{47} + 6 q^{49} - 6 q^{50} + 8 q^{55} + 10 q^{58} + 8 q^{59} + 14 q^{64} + 16 q^{65} - 12 q^{68} + 8 q^{70} - 16 q^{71} - 12 q^{73} - 4 q^{74} - 8 q^{77} - 2 q^{80} + 12 q^{85} + 8 q^{86} - 16 q^{91} + 16 q^{94} - 8 q^{95} - 28 q^{97} + 6 q^{98}+O(q^{100}) \) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107 0.353553 0.935414i \(-0.384973\pi\)
0.353553 + 0.935414i \(0.384973\pi\)
\(3\) 0 0
\(4\) −1.00000 −0.500000
\(5\) 1.00000 2.00000i 0.447214 0.894427i
\(6\) 0 0
\(7\) 2.00000i 0.755929i 0.925820 + 0.377964i \(0.123376\pi\)
−0.925820 + 0.377964i \(0.876624\pi\)
\(8\) −3.00000 −1.06066
\(9\) 0 0
\(10\) 1.00000 2.00000i 0.316228 0.632456i
\(11\) 2.00000i 0.603023i 0.953463 + 0.301511i \(0.0974911\pi\)
−0.953463 + 0.301511i \(0.902509\pi\)
\(12\) 0 0
\(13\) 4.00000i 1.10940i 0.832050 + 0.554700i \(0.187167\pi\)
−0.832050 + 0.554700i \(0.812833\pi\)
\(14\) 2.00000i 0.534522i
\(15\) 0 0
\(16\) −1.00000 −0.250000
\(17\) 6.00000 1.45521 0.727607 0.685994i \(-0.240633\pi\)
0.727607 + 0.685994i \(0.240633\pi\)
\(18\) 0 0
\(19\) 2.00000i 0.458831i −0.973329 0.229416i \(-0.926318\pi\)
0.973329 0.229416i \(-0.0736815\pi\)
\(20\) −1.00000 + 2.00000i −0.223607 + 0.447214i
\(21\) 0 0
\(22\) 2.00000i 0.426401i
\(23\) 6.00000i 1.25109i 0.780189 + 0.625543i \(0.215123\pi\)
−0.780189 + 0.625543i \(0.784877\pi\)
\(24\) 0 0
\(25\) −3.00000 4.00000i −0.600000 0.800000i
\(26\) 4.00000i 0.784465i
\(27\) 0 0
\(28\) 2.00000i 0.377964i
\(29\) 5.00000 + 2.00000i 0.928477 + 0.371391i
\(30\) 0 0
\(31\) 2.00000i 0.359211i 0.983739 + 0.179605i \(0.0574821\pi\)
−0.983739 + 0.179605i \(0.942518\pi\)
\(32\) 5.00000 0.883883
\(33\) 0 0
\(34\) 6.00000 1.02899
\(35\) 4.00000 + 2.00000i 0.676123 + 0.338062i
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) 2.00000i 0.324443i
\(39\) 0 0
\(40\) −3.00000 + 6.00000i −0.474342 + 0.948683i
\(41\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 2.00000i 0.301511i
\(45\) 0 0
\(46\) 6.00000i 0.884652i
\(47\) 8.00000 1.16692 0.583460 0.812142i \(-0.301699\pi\)
0.583460 + 0.812142i \(0.301699\pi\)
\(48\) 0 0
\(49\) 3.00000 0.428571
\(50\) −3.00000 4.00000i −0.424264 0.565685i
\(51\) 0 0
\(52\) 4.00000i 0.554700i
\(53\) 12.0000i 1.64833i 0.566352 + 0.824163i \(0.308354\pi\)
−0.566352 + 0.824163i \(0.691646\pi\)
\(54\) 0 0
\(55\) 4.00000 + 2.00000i 0.539360 + 0.269680i
\(56\) 6.00000i 0.801784i
\(57\) 0 0
\(58\) 5.00000 + 2.00000i 0.656532 + 0.262613i
\(59\) 4.00000 0.520756 0.260378 0.965507i \(-0.416153\pi\)
0.260378 + 0.965507i \(0.416153\pi\)
\(60\) 0 0
\(61\) 12.0000i 1.53644i −0.640184 0.768221i \(-0.721142\pi\)
0.640184 0.768221i \(-0.278858\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 0 0
\(64\) 7.00000 0.875000
\(65\) 8.00000 + 4.00000i 0.992278 + 0.496139i
\(66\) 0 0
\(67\) 6.00000i 0.733017i 0.930415 + 0.366508i \(0.119447\pi\)
−0.930415 + 0.366508i \(0.880553\pi\)
\(68\) −6.00000 −0.727607
\(69\) 0 0
\(70\) 4.00000 + 2.00000i 0.478091 + 0.239046i
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −6.00000 −0.702247 −0.351123 0.936329i \(-0.614200\pi\)
−0.351123 + 0.936329i \(0.614200\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) 2.00000i 0.229416i
\(77\) −4.00000 −0.455842
\(78\) 0 0
\(79\) 2.00000i 0.225018i 0.993651 + 0.112509i \(0.0358886\pi\)
−0.993651 + 0.112509i \(0.964111\pi\)
\(80\) −1.00000 + 2.00000i −0.111803 + 0.223607i
\(81\) 0 0
\(82\) 0 0
\(83\) 2.00000i 0.219529i 0.993958 + 0.109764i \(0.0350096\pi\)
−0.993958 + 0.109764i \(0.964990\pi\)
\(84\) 0 0
\(85\) 6.00000 12.0000i 0.650791 1.30158i
\(86\) 4.00000 0.431331
\(87\) 0 0
\(88\) 6.00000i 0.639602i
\(89\) 16.0000i 1.69600i −0.529999 0.847998i \(-0.677808\pi\)
0.529999 0.847998i \(-0.322192\pi\)
\(90\) 0 0
\(91\) −8.00000 −0.838628
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) 8.00000 0.825137
\(95\) −4.00000 2.00000i −0.410391 0.205196i
\(96\) 0 0
\(97\) −14.0000 −1.42148 −0.710742 0.703452i \(-0.751641\pi\)
−0.710742 + 0.703452i \(0.751641\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) 3.00000 + 4.00000i 0.300000 + 0.400000i
\(101\) 12.0000i 1.19404i 0.802225 + 0.597022i \(0.203650\pi\)
−0.802225 + 0.597022i \(0.796350\pi\)
\(102\) 0 0
\(103\) 18.0000i 1.77359i 0.462160 + 0.886796i \(0.347074\pi\)
−0.462160 + 0.886796i \(0.652926\pi\)
\(104\) 12.0000i 1.17670i
\(105\) 0 0
\(106\) 12.0000i 1.16554i
\(107\) 10.0000i 0.966736i 0.875417 + 0.483368i \(0.160587\pi\)
−0.875417 + 0.483368i \(0.839413\pi\)
\(108\) 0 0
\(109\) −10.0000 −0.957826 −0.478913 0.877862i \(-0.658969\pi\)
−0.478913 + 0.877862i \(0.658969\pi\)
\(110\) 4.00000 + 2.00000i 0.381385 + 0.190693i
\(111\) 0 0
\(112\) 2.00000i 0.188982i
\(113\) −2.00000 −0.188144 −0.0940721 0.995565i \(-0.529988\pi\)
−0.0940721 + 0.995565i \(0.529988\pi\)
\(114\) 0 0
\(115\) 12.0000 + 6.00000i 1.11901 + 0.559503i
\(116\) −5.00000 2.00000i −0.464238 0.185695i
\(117\) 0 0
\(118\) 4.00000 0.368230
\(119\) 12.0000i 1.10004i
\(120\) 0 0
\(121\) 7.00000 0.636364
\(122\) 12.0000i 1.08643i
\(123\) 0 0
\(124\) 2.00000i 0.179605i
\(125\) −11.0000 + 2.00000i −0.983870 + 0.178885i
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) −3.00000 −0.265165
\(129\) 0 0
\(130\) 8.00000 + 4.00000i 0.701646 + 0.350823i
\(131\) 22.0000i 1.92215i −0.276289 0.961074i \(-0.589105\pi\)
0.276289 0.961074i \(-0.410895\pi\)
\(132\) 0 0
\(133\) 4.00000 0.346844
\(134\) 6.00000i 0.518321i
\(135\) 0 0
\(136\) −18.0000 −1.54349
\(137\) 14.0000 1.19610 0.598050 0.801459i \(-0.295942\pi\)
0.598050 + 0.801459i \(0.295942\pi\)
\(138\) 0 0
\(139\) −4.00000 −0.339276 −0.169638 0.985506i \(-0.554260\pi\)
−0.169638 + 0.985506i \(0.554260\pi\)
\(140\) −4.00000 2.00000i −0.338062 0.169031i
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) −8.00000 −0.668994
\(144\) 0 0
\(145\) 9.00000 8.00000i 0.747409 0.664364i
\(146\) −6.00000 −0.496564
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 10.0000 0.819232 0.409616 0.912258i \(-0.365663\pi\)
0.409616 + 0.912258i \(0.365663\pi\)
\(150\) 0 0
\(151\) −8.00000 −0.651031 −0.325515 0.945537i \(-0.605538\pi\)
−0.325515 + 0.945537i \(0.605538\pi\)
\(152\) 6.00000i 0.486664i
\(153\) 0 0
\(154\) −4.00000 −0.322329
\(155\) 4.00000 + 2.00000i 0.321288 + 0.160644i
\(156\) 0 0
\(157\) −2.00000 −0.159617 −0.0798087 0.996810i \(-0.525431\pi\)
−0.0798087 + 0.996810i \(0.525431\pi\)
\(158\) 2.00000i 0.159111i
\(159\) 0 0
\(160\) 5.00000 10.0000i 0.395285 0.790569i
\(161\) −12.0000 −0.945732
\(162\) 0 0
\(163\) −20.0000 −1.56652 −0.783260 0.621694i \(-0.786445\pi\)
−0.783260 + 0.621694i \(0.786445\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 2.00000i 0.155230i
\(167\) 6.00000i 0.464294i 0.972681 + 0.232147i \(0.0745750\pi\)
−0.972681 + 0.232147i \(0.925425\pi\)
\(168\) 0 0
\(169\) −3.00000 −0.230769
\(170\) 6.00000 12.0000i 0.460179 0.920358i
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 12.0000i 0.912343i −0.889892 0.456172i \(-0.849220\pi\)
0.889892 0.456172i \(-0.150780\pi\)
\(174\) 0 0
\(175\) 8.00000 6.00000i 0.604743 0.453557i
\(176\) 2.00000i 0.150756i
\(177\) 0 0
\(178\) 16.0000i 1.19925i
\(179\) 12.0000 0.896922 0.448461 0.893802i \(-0.351972\pi\)
0.448461 + 0.893802i \(0.351972\pi\)
\(180\) 0 0
\(181\) −10.0000 −0.743294 −0.371647 0.928374i \(-0.621207\pi\)
−0.371647 + 0.928374i \(0.621207\pi\)
\(182\) −8.00000 −0.592999
\(183\) 0 0
\(184\) 18.0000i 1.32698i
\(185\) −2.00000 + 4.00000i −0.147043 + 0.294086i
\(186\) 0 0
\(187\) 12.0000i 0.877527i
\(188\) −8.00000 −0.583460
\(189\) 0 0
\(190\) −4.00000 2.00000i −0.290191 0.145095i
\(191\) 6.00000i 0.434145i 0.976156 + 0.217072i \(0.0696508\pi\)
−0.976156 + 0.217072i \(0.930349\pi\)
\(192\) 0 0
\(193\) −6.00000 −0.431889 −0.215945 0.976406i \(-0.569283\pi\)
−0.215945 + 0.976406i \(0.569283\pi\)
\(194\) −14.0000 −1.00514
\(195\) 0 0
\(196\) −3.00000 −0.214286
\(197\) 4.00000i 0.284988i −0.989796 0.142494i \(-0.954488\pi\)
0.989796 0.142494i \(-0.0455122\pi\)
\(198\) 0 0
\(199\) 8.00000 0.567105 0.283552 0.958957i \(-0.408487\pi\)
0.283552 + 0.958957i \(0.408487\pi\)
\(200\) 9.00000 + 12.0000i 0.636396 + 0.848528i
\(201\) 0 0
\(202\) 12.0000i 0.844317i
\(203\) −4.00000 + 10.0000i −0.280745 + 0.701862i
\(204\) 0 0
\(205\) 0 0
\(206\) 18.0000i 1.25412i
\(207\) 0 0
\(208\) 4.00000i 0.277350i
\(209\) 4.00000 0.276686
\(210\) 0 0
\(211\) 2.00000i 0.137686i −0.997628 0.0688428i \(-0.978069\pi\)
0.997628 0.0688428i \(-0.0219307\pi\)
\(212\) 12.0000i 0.824163i
\(213\) 0 0
\(214\) 10.0000i 0.683586i
\(215\) 4.00000 8.00000i 0.272798 0.545595i
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) −10.0000 −0.677285
\(219\) 0 0
\(220\) −4.00000 2.00000i −0.269680 0.134840i
\(221\) 24.0000i 1.61441i
\(222\) 0 0
\(223\) 22.0000i 1.47323i −0.676313 0.736614i \(-0.736423\pi\)
0.676313 0.736614i \(-0.263577\pi\)
\(224\) 10.0000i 0.668153i
\(225\) 0 0
\(226\) −2.00000 −0.133038
\(227\) 2.00000i 0.132745i 0.997795 + 0.0663723i \(0.0211425\pi\)
−0.997795 + 0.0663723i \(0.978857\pi\)
\(228\) 0 0
\(229\) 20.0000i 1.32164i −0.750546 0.660819i \(-0.770209\pi\)
0.750546 0.660819i \(-0.229791\pi\)
\(230\) 12.0000 + 6.00000i 0.791257 + 0.395628i
\(231\) 0 0
\(232\) −15.0000 6.00000i −0.984798 0.393919i
\(233\) 16.0000i 1.04819i −0.851658 0.524097i \(-0.824403\pi\)
0.851658 0.524097i \(-0.175597\pi\)
\(234\) 0 0
\(235\) 8.00000 16.0000i 0.521862 1.04372i
\(236\) −4.00000 −0.260378
\(237\) 0 0
\(238\) 12.0000i 0.777844i
\(239\) −16.0000 −1.03495 −0.517477 0.855697i \(-0.673129\pi\)
−0.517477 + 0.855697i \(0.673129\pi\)
\(240\) 0 0
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 7.00000 0.449977
\(243\) 0 0
\(244\) 12.0000i 0.768221i
\(245\) 3.00000 6.00000i 0.191663 0.383326i
\(246\) 0 0
\(247\) 8.00000 0.509028
\(248\) 6.00000i 0.381000i
\(249\) 0 0
\(250\) −11.0000 + 2.00000i −0.695701 + 0.126491i
\(251\) 30.0000i 1.89358i −0.321847 0.946792i \(-0.604304\pi\)
0.321847 0.946792i \(-0.395696\pi\)
\(252\) 0 0
\(253\) −12.0000 −0.754434
\(254\) 8.00000 0.501965
\(255\) 0 0
\(256\) −17.0000 −1.06250
\(257\) 24.0000i 1.49708i −0.663090 0.748539i \(-0.730755\pi\)
0.663090 0.748539i \(-0.269245\pi\)
\(258\) 0 0
\(259\) 4.00000i 0.248548i
\(260\) −8.00000 4.00000i −0.496139 0.248069i
\(261\) 0 0
\(262\) 22.0000i 1.35916i
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 24.0000 + 12.0000i 1.47431 + 0.737154i
\(266\) 4.00000 0.245256
\(267\) 0 0
\(268\) 6.00000i 0.366508i
\(269\) 4.00000i 0.243884i 0.992537 + 0.121942i \(0.0389122\pi\)
−0.992537 + 0.121942i \(0.961088\pi\)
\(270\) 0 0
\(271\) 2.00000i 0.121491i 0.998153 + 0.0607457i \(0.0193479\pi\)
−0.998153 + 0.0607457i \(0.980652\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) 14.0000 0.845771
\(275\) 8.00000 6.00000i 0.482418 0.361814i
\(276\) 0 0
\(277\) 4.00000i 0.240337i −0.992754 0.120168i \(-0.961657\pi\)
0.992754 0.120168i \(-0.0383434\pi\)
\(278\) −4.00000 −0.239904
\(279\) 0 0
\(280\) −12.0000 6.00000i −0.717137 0.358569i
\(281\) 30.0000 1.78965 0.894825 0.446417i \(-0.147300\pi\)
0.894825 + 0.446417i \(0.147300\pi\)
\(282\) 0 0
\(283\) 2.00000i 0.118888i −0.998232 0.0594438i \(-0.981067\pi\)
0.998232 0.0594438i \(-0.0189327\pi\)
\(284\) 8.00000 0.474713
\(285\) 0 0
\(286\) −8.00000 −0.473050
\(287\) 0 0
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 9.00000 8.00000i 0.528498 0.469776i
\(291\) 0 0
\(292\) 6.00000 0.351123
\(293\) 26.0000 1.51894 0.759468 0.650545i \(-0.225459\pi\)
0.759468 + 0.650545i \(0.225459\pi\)
\(294\) 0 0
\(295\) 4.00000 8.00000i 0.232889 0.465778i
\(296\) 6.00000 0.348743
\(297\) 0 0
\(298\) 10.0000 0.579284
\(299\) −24.0000 −1.38796
\(300\) 0 0
\(301\) 8.00000i 0.461112i
\(302\) −8.00000 −0.460348
\(303\) 0 0
\(304\) 2.00000i 0.114708i
\(305\) −24.0000 12.0000i −1.37424 0.687118i
\(306\) 0 0
\(307\) 12.0000 0.684876 0.342438 0.939540i \(-0.388747\pi\)
0.342438 + 0.939540i \(0.388747\pi\)
\(308\) 4.00000 0.227921
\(309\) 0 0
\(310\) 4.00000 + 2.00000i 0.227185 + 0.113592i
\(311\) 14.0000i 0.793867i 0.917847 + 0.396934i \(0.129926\pi\)
−0.917847 + 0.396934i \(0.870074\pi\)
\(312\) 0 0
\(313\) 8.00000i 0.452187i −0.974106 0.226093i \(-0.927405\pi\)
0.974106 0.226093i \(-0.0725954\pi\)
\(314\) −2.00000 −0.112867
\(315\) 0 0
\(316\) 2.00000i 0.112509i
\(317\) −6.00000 −0.336994 −0.168497 0.985702i \(-0.553891\pi\)
−0.168497 + 0.985702i \(0.553891\pi\)
\(318\) 0 0
\(319\) −4.00000 + 10.0000i −0.223957 + 0.559893i
\(320\) 7.00000 14.0000i 0.391312 0.782624i
\(321\) 0 0
\(322\) −12.0000 −0.668734
\(323\) 12.0000i 0.667698i
\(324\) 0 0
\(325\) 16.0000 12.0000i 0.887520 0.665640i
\(326\) −20.0000 −1.10770
\(327\) 0 0
\(328\) 0 0
\(329\) 16.0000i 0.882109i
\(330\) 0 0
\(331\) 22.0000i 1.20923i 0.796518 + 0.604615i \(0.206673\pi\)
−0.796518 + 0.604615i \(0.793327\pi\)
\(332\) 2.00000i 0.109764i
\(333\) 0 0
\(334\) 6.00000i 0.328305i
\(335\) 12.0000 + 6.00000i 0.655630 + 0.327815i
\(336\) 0 0
\(337\) 34.0000 1.85210 0.926049 0.377403i \(-0.123183\pi\)
0.926049 + 0.377403i \(0.123183\pi\)
\(338\) −3.00000 −0.163178
\(339\) 0 0
\(340\) −6.00000 + 12.0000i −0.325396 + 0.650791i
\(341\) −4.00000 −0.216612
\(342\) 0 0
\(343\) 20.0000i 1.07990i
\(344\) −12.0000 −0.646997
\(345\) 0 0
\(346\) 12.0000i 0.645124i
\(347\) 10.0000i 0.536828i 0.963304 + 0.268414i \(0.0864995\pi\)
−0.963304 + 0.268414i \(0.913500\pi\)
\(348\) 0 0
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 8.00000 6.00000i 0.427618 0.320713i
\(351\) 0 0
\(352\) 10.0000i 0.533002i
\(353\) 24.0000i 1.27739i −0.769460 0.638696i \(-0.779474\pi\)
0.769460 0.638696i \(-0.220526\pi\)
\(354\) 0 0
\(355\) −8.00000 + 16.0000i −0.424596 + 0.849192i
\(356\) 16.0000i 0.847998i
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 18.0000i 0.950004i −0.879985 0.475002i \(-0.842447\pi\)
0.879985 0.475002i \(-0.157553\pi\)
\(360\) 0 0
\(361\) 15.0000 0.789474
\(362\) −10.0000 −0.525588
\(363\) 0 0
\(364\) 8.00000 0.419314
\(365\) −6.00000 + 12.0000i −0.314054 + 0.628109i
\(366\) 0 0
\(367\) 24.0000 1.25279 0.626395 0.779506i \(-0.284530\pi\)
0.626395 + 0.779506i \(0.284530\pi\)
\(368\) 6.00000i 0.312772i
\(369\) 0 0
\(370\) −2.00000 + 4.00000i −0.103975 + 0.207950i
\(371\) −24.0000 −1.24602
\(372\) 0 0
\(373\) 4.00000i 0.207112i −0.994624 0.103556i \(-0.966978\pi\)
0.994624 0.103556i \(-0.0330221\pi\)
\(374\) 12.0000i 0.620505i
\(375\) 0 0
\(376\) −24.0000 −1.23771
\(377\) −8.00000 + 20.0000i −0.412021 + 1.03005i
\(378\) 0 0
\(379\) 38.0000i 1.95193i 0.217930 + 0.975964i \(0.430070\pi\)
−0.217930 + 0.975964i \(0.569930\pi\)
\(380\) 4.00000 + 2.00000i 0.205196 + 0.102598i
\(381\) 0 0
\(382\) 6.00000i 0.306987i
\(383\) 30.0000i 1.53293i 0.642287 + 0.766464i \(0.277986\pi\)
−0.642287 + 0.766464i \(0.722014\pi\)
\(384\) 0 0
\(385\) −4.00000 + 8.00000i −0.203859 + 0.407718i
\(386\) −6.00000 −0.305392
\(387\) 0 0
\(388\) 14.0000 0.710742
\(389\) 12.0000i 0.608424i 0.952604 + 0.304212i \(0.0983931\pi\)
−0.952604 + 0.304212i \(0.901607\pi\)
\(390\) 0 0
\(391\) 36.0000i 1.82060i
\(392\) −9.00000 −0.454569
\(393\) 0 0
\(394\) 4.00000i 0.201517i
\(395\) 4.00000 + 2.00000i 0.201262 + 0.100631i
\(396\) 0 0
\(397\) 28.0000i 1.40528i −0.711546 0.702640i \(-0.752005\pi\)
0.711546 0.702640i \(-0.247995\pi\)
\(398\) 8.00000 0.401004
\(399\) 0 0
\(400\) 3.00000 + 4.00000i 0.150000 + 0.200000i
\(401\) −18.0000 −0.898877 −0.449439 0.893311i \(-0.648376\pi\)
−0.449439 + 0.893311i \(0.648376\pi\)
\(402\) 0 0
\(403\) −8.00000 −0.398508
\(404\) 12.0000i 0.597022i
\(405\) 0 0
\(406\) −4.00000 + 10.0000i −0.198517 + 0.496292i
\(407\) 4.00000i 0.198273i
\(408\) 0 0
\(409\) 8.00000i 0.395575i 0.980245 + 0.197787i \(0.0633755\pi\)
−0.980245 + 0.197787i \(0.936624\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 18.0000i 0.886796i
\(413\) 8.00000i 0.393654i
\(414\) 0 0
\(415\) 4.00000 + 2.00000i 0.196352 + 0.0981761i
\(416\) 20.0000i 0.980581i
\(417\) 0 0
\(418\) 4.00000 0.195646
\(419\) 12.0000 0.586238 0.293119 0.956076i \(-0.405307\pi\)
0.293119 + 0.956076i \(0.405307\pi\)
\(420\) 0 0
\(421\) 28.0000i 1.36464i 0.731055 + 0.682318i \(0.239028\pi\)
−0.731055 + 0.682318i \(0.760972\pi\)
\(422\) 2.00000i 0.0973585i
\(423\) 0 0
\(424\) 36.0000i 1.74831i
\(425\) −18.0000 24.0000i −0.873128 1.16417i
\(426\) 0 0
\(427\) 24.0000 1.16144
\(428\) 10.0000i 0.483368i
\(429\) 0 0
\(430\) 4.00000 8.00000i 0.192897 0.385794i
\(431\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(432\) 0 0
\(433\) −22.0000 −1.05725 −0.528626 0.848855i \(-0.677293\pi\)
−0.528626 + 0.848855i \(0.677293\pi\)
\(434\) −4.00000 −0.192006
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) 12.0000 0.574038
\(438\) 0 0
\(439\) 24.0000 1.14546 0.572729 0.819745i \(-0.305885\pi\)
0.572729 + 0.819745i \(0.305885\pi\)
\(440\) −12.0000 6.00000i −0.572078 0.286039i
\(441\) 0 0
\(442\) 24.0000i 1.14156i
\(443\) 28.0000 1.33032 0.665160 0.746701i \(-0.268363\pi\)
0.665160 + 0.746701i \(0.268363\pi\)
\(444\) 0 0
\(445\) −32.0000 16.0000i −1.51695 0.758473i
\(446\) 22.0000i 1.04173i
\(447\) 0 0
\(448\) 14.0000i 0.661438i
\(449\) 24.0000i 1.13263i −0.824189 0.566315i \(-0.808369\pi\)
0.824189 0.566315i \(-0.191631\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 2.00000 0.0940721
\(453\) 0 0
\(454\) 2.00000i 0.0938647i
\(455\) −8.00000 + 16.0000i −0.375046 + 0.750092i
\(456\) 0 0
\(457\) 8.00000i 0.374224i −0.982339 0.187112i \(-0.940087\pi\)
0.982339 0.187112i \(-0.0599128\pi\)
\(458\) 20.0000i 0.934539i
\(459\) 0 0
\(460\) −12.0000 6.00000i −0.559503 0.279751i
\(461\) 12.0000i 0.558896i −0.960161 0.279448i \(-0.909849\pi\)
0.960161 0.279448i \(-0.0901514\pi\)
\(462\) 0 0
\(463\) 26.0000i 1.20832i 0.796862 + 0.604161i \(0.206492\pi\)
−0.796862 + 0.604161i \(0.793508\pi\)
\(464\) −5.00000 2.00000i −0.232119 0.0928477i
\(465\) 0 0
\(466\) 16.0000i 0.741186i
\(467\) −12.0000 −0.555294 −0.277647 0.960683i \(-0.589555\pi\)
−0.277647 + 0.960683i \(0.589555\pi\)
\(468\) 0 0
\(469\) −12.0000 −0.554109
\(470\) 8.00000 16.0000i 0.369012 0.738025i
\(471\) 0 0
\(472\) −12.0000 −0.552345
\(473\) 8.00000i 0.367840i
\(474\) 0 0
\(475\) −8.00000 + 6.00000i −0.367065 + 0.275299i
\(476\) 12.0000i 0.550019i
\(477\) 0 0
\(478\) −16.0000 −0.731823
\(479\) 42.0000i 1.91903i −0.281659 0.959514i \(-0.590885\pi\)
0.281659 0.959514i \(-0.409115\pi\)
\(480\) 0 0
\(481\) 8.00000i 0.364769i
\(482\) −22.0000 −1.00207
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) −14.0000 + 28.0000i −0.635707 + 1.27141i
\(486\) 0 0
\(487\) 14.0000i 0.634401i −0.948359 0.317200i \(-0.897257\pi\)
0.948359 0.317200i \(-0.102743\pi\)
\(488\) 36.0000i 1.62964i
\(489\) 0 0
\(490\) 3.00000 6.00000i 0.135526 0.271052i
\(491\) 2.00000i 0.0902587i 0.998981 + 0.0451294i \(0.0143700\pi\)
−0.998981 + 0.0451294i \(0.985630\pi\)
\(492\) 0 0
\(493\) 30.0000 + 12.0000i 1.35113 + 0.540453i
\(494\) 8.00000 0.359937
\(495\) 0 0
\(496\) 2.00000i 0.0898027i
\(497\) 16.0000i 0.717698i
\(498\) 0 0
\(499\) −12.0000 −0.537194 −0.268597 0.963253i \(-0.586560\pi\)
−0.268597 + 0.963253i \(0.586560\pi\)
\(500\) 11.0000 2.00000i 0.491935 0.0894427i
\(501\) 0 0
\(502\) 30.0000i 1.33897i
\(503\) 16.0000 0.713405 0.356702 0.934218i \(-0.383901\pi\)
0.356702 + 0.934218i \(0.383901\pi\)
\(504\) 0 0
\(505\) 24.0000 + 12.0000i 1.06799 + 0.533993i
\(506\) −12.0000 −0.533465
\(507\) 0 0
\(508\) −8.00000 −0.354943
\(509\) 10.0000 0.443242 0.221621 0.975133i \(-0.428865\pi\)
0.221621 + 0.975133i \(0.428865\pi\)
\(510\) 0 0
\(511\) 12.0000i 0.530849i
\(512\) −11.0000 −0.486136
\(513\) 0 0
\(514\) 24.0000i 1.05859i
\(515\) 36.0000 + 18.0000i 1.58635 + 0.793175i
\(516\) 0 0
\(517\) 16.0000i 0.703679i
\(518\) 4.00000i 0.175750i
\(519\) 0 0
\(520\) −24.0000 12.0000i −1.05247 0.526235i
\(521\) 14.0000 0.613351 0.306676 0.951814i \(-0.400783\pi\)
0.306676 + 0.951814i \(0.400783\pi\)
\(522\) 0 0
\(523\) 34.0000i 1.48672i −0.668894 0.743358i \(-0.733232\pi\)
0.668894 0.743358i \(-0.266768\pi\)
\(524\) 22.0000i 0.961074i
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) 12.0000i 0.522728i
\(528\) 0 0
\(529\) −13.0000 −0.565217
\(530\) 24.0000 + 12.0000i 1.04249 + 0.521247i
\(531\) 0 0
\(532\) −4.00000 −0.173422
\(533\) 0 0
\(534\) 0 0
\(535\) 20.0000 + 10.0000i 0.864675 + 0.432338i
\(536\) 18.0000i 0.777482i
\(537\) 0 0
\(538\) 4.00000i 0.172452i
\(539\) 6.00000i 0.258438i
\(540\) 0 0
\(541\) 44.0000i 1.89171i −0.324593 0.945854i \(-0.605227\pi\)
0.324593 0.945854i \(-0.394773\pi\)
\(542\) 2.00000i 0.0859074i
\(543\) 0 0
\(544\) 30.0000 1.28624
\(545\) −10.0000 + 20.0000i −0.428353 + 0.856706i
\(546\) 0 0
\(547\) 26.0000i 1.11168i −0.831289 0.555840i \(-0.812397\pi\)
0.831289 0.555840i \(-0.187603\pi\)
\(548\) −14.0000 −0.598050
\(549\) 0 0
\(550\) 8.00000 6.00000i 0.341121 0.255841i
\(551\) 4.00000 10.0000i 0.170406 0.426014i
\(552\) 0 0
\(553\) −4.00000 −0.170097
\(554\) 4.00000i 0.169944i
\(555\) 0 0
\(556\) 4.00000 0.169638
\(557\) 12.0000i 0.508456i −0.967144 0.254228i \(-0.918179\pi\)
0.967144 0.254228i \(-0.0818214\pi\)
\(558\) 0 0
\(559\) 16.0000i 0.676728i
\(560\) −4.00000 2.00000i −0.169031 0.0845154i
\(561\) 0 0
\(562\) 30.0000 1.26547
\(563\) −12.0000 −0.505740 −0.252870 0.967500i \(-0.581374\pi\)
−0.252870 + 0.967500i \(0.581374\pi\)
\(564\) 0 0
\(565\) −2.00000 + 4.00000i −0.0841406 + 0.168281i
\(566\) 2.00000i 0.0840663i
\(567\) 0 0
\(568\) 24.0000 1.00702
\(569\) 32.0000i 1.34151i 0.741679 + 0.670755i \(0.234030\pi\)
−0.741679 + 0.670755i \(0.765970\pi\)
\(570\) 0 0
\(571\) −20.0000 −0.836974 −0.418487 0.908223i \(-0.637439\pi\)
−0.418487 + 0.908223i \(0.637439\pi\)
\(572\) 8.00000 0.334497
\(573\) 0 0
\(574\) 0 0
\(575\) 24.0000 18.0000i 1.00087 0.750652i
\(576\) 0 0
\(577\) −38.0000 −1.58196 −0.790980 0.611842i \(-0.790429\pi\)
−0.790980 + 0.611842i \(0.790429\pi\)
\(578\) 19.0000 0.790296
\(579\) 0 0
\(580\) −9.00000 + 8.00000i −0.373705 + 0.332182i
\(581\) −4.00000 −0.165948
\(582\) 0 0
\(583\) −24.0000 −0.993978
\(584\) 18.0000 0.744845
\(585\) 0 0
\(586\) 26.0000 1.07405
\(587\) 42.0000i 1.73353i 0.498721 + 0.866763i \(0.333803\pi\)
−0.498721 + 0.866763i \(0.666197\pi\)
\(588\) 0 0
\(589\) 4.00000 0.164817
\(590\) 4.00000 8.00000i 0.164677 0.329355i
\(591\) 0 0
\(592\) 2.00000 0.0821995
\(593\) 8.00000i 0.328521i 0.986417 + 0.164260i \(0.0525237\pi\)
−0.986417 + 0.164260i \(0.947476\pi\)
\(594\) 0 0
\(595\) 24.0000 + 12.0000i 0.983904 + 0.491952i
\(596\) −10.0000 −0.409616
\(597\) 0 0
\(598\) −24.0000 −0.981433
\(599\) 18.0000i 0.735460i −0.929933 0.367730i \(-0.880135\pi\)
0.929933 0.367730i \(-0.119865\pi\)
\(600\) 0 0
\(601\) 8.00000i 0.326327i −0.986599 0.163163i \(-0.947830\pi\)
0.986599 0.163163i \(-0.0521698\pi\)
\(602\) 8.00000i 0.326056i
\(603\) 0 0
\(604\) 8.00000 0.325515
\(605\) 7.00000 14.0000i 0.284590 0.569181i
\(606\) 0 0
\(607\) 8.00000 0.324710 0.162355 0.986732i \(-0.448091\pi\)
0.162355 + 0.986732i \(0.448091\pi\)
\(608\) 10.0000i 0.405554i
\(609\) 0 0
\(610\) −24.0000 12.0000i −0.971732 0.485866i
\(611\) 32.0000i 1.29458i
\(612\) 0 0
\(613\) 12.0000i 0.484675i 0.970192 + 0.242338i \(0.0779142\pi\)
−0.970192 + 0.242338i \(0.922086\pi\)
\(614\) 12.0000 0.484281
\(615\) 0 0
\(616\) 12.0000 0.483494
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 0 0
\(619\) 26.0000i 1.04503i −0.852631 0.522514i \(-0.824994\pi\)
0.852631 0.522514i \(-0.175006\pi\)
\(620\) −4.00000 2.00000i −0.160644 0.0803219i
\(621\) 0 0
\(622\) 14.0000i 0.561349i
\(623\) 32.0000 1.28205
\(624\) 0 0
\(625\) −7.00000 + 24.0000i −0.280000 + 0.960000i
\(626\) 8.00000i 0.319744i
\(627\) 0 0
\(628\) 2.00000 0.0798087
\(629\) −12.0000 −0.478471
\(630\) 0 0
\(631\) 8.00000 0.318475 0.159237 0.987240i \(-0.449096\pi\)
0.159237 + 0.987240i \(0.449096\pi\)
\(632\) 6.00000i 0.238667i
\(633\) 0 0
\(634\) −6.00000 −0.238290
\(635\) 8.00000 16.0000i 0.317470 0.634941i
\(636\) 0 0
\(637\) 12.0000i 0.475457i
\(638\) −4.00000 + 10.0000i −0.158362 + 0.395904i
\(639\) 0 0
\(640\) −3.00000 + 6.00000i −0.118585 + 0.237171i
\(641\) 24.0000i 0.947943i 0.880540 + 0.473972i \(0.157180\pi\)
−0.880540 + 0.473972i \(0.842820\pi\)
\(642\) 0 0
\(643\) 6.00000i 0.236617i 0.992977 + 0.118308i \(0.0377472\pi\)
−0.992977 + 0.118308i \(0.962253\pi\)
\(644\) 12.0000 0.472866
\(645\) 0 0
\(646\) 12.0000i 0.472134i
\(647\) 10.0000i 0.393141i −0.980490 0.196570i \(-0.937020\pi\)
0.980490 0.196570i \(-0.0629804\pi\)
\(648\) 0 0
\(649\) 8.00000i 0.314027i
\(650\) 16.0000 12.0000i 0.627572 0.470679i
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) 18.0000 0.704394 0.352197 0.935926i \(-0.385435\pi\)
0.352197 + 0.935926i \(0.385435\pi\)
\(654\) 0 0
\(655\) −44.0000 22.0000i −1.71922 0.859611i
\(656\) 0 0
\(657\) 0 0
\(658\) 16.0000i 0.623745i
\(659\) 26.0000i 1.01282i 0.862294 + 0.506408i \(0.169027\pi\)
−0.862294 + 0.506408i \(0.830973\pi\)
\(660\) 0 0
\(661\) 22.0000 0.855701 0.427850 0.903850i \(-0.359271\pi\)
0.427850 + 0.903850i \(0.359271\pi\)
\(662\) 22.0000i 0.855054i
\(663\) 0 0
\(664\) 6.00000i 0.232845i
\(665\) 4.00000 8.00000i 0.155113 0.310227i
\(666\) 0 0
\(667\) −12.0000 + 30.0000i −0.464642 + 1.16160i
\(668\) 6.00000i 0.232147i
\(669\) 0 0
\(670\) 12.0000 + 6.00000i 0.463600 + 0.231800i
\(671\) 24.0000 0.926510
\(672\) 0 0
\(673\) 32.0000i 1.23351i 0.787155 + 0.616755i \(0.211553\pi\)
−0.787155 + 0.616755i \(0.788447\pi\)
\(674\) 34.0000 1.30963
\(675\) 0 0
\(676\) 3.00000 0.115385
\(677\) −6.00000 −0.230599 −0.115299 0.993331i \(-0.536783\pi\)
−0.115299 + 0.993331i \(0.536783\pi\)
\(678\) 0 0
\(679\) 28.0000i 1.07454i
\(680\) −18.0000 + 36.0000i −0.690268 + 1.38054i
\(681\) 0 0
\(682\) −4.00000 −0.153168
\(683\) 6.00000i 0.229584i −0.993390 0.114792i \(-0.963380\pi\)
0.993390 0.114792i \(-0.0366201\pi\)
\(684\) 0 0
\(685\) 14.0000 28.0000i 0.534913 1.06983i
\(686\) 20.0000i 0.763604i
\(687\) 0 0
\(688\) −4.00000 −0.152499
\(689\) −48.0000 −1.82865
\(690\) 0 0
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 12.0000i 0.456172i
\(693\) 0 0
\(694\) 10.0000i 0.379595i
\(695\) −4.00000 + 8.00000i −0.151729 + 0.303457i
\(696\) 0 0
\(697\) 0 0
\(698\) −26.0000 −0.984115
\(699\) 0 0
\(700\) −8.00000 + 6.00000i −0.302372 + 0.226779i
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) 0 0
\(703\) 4.00000i 0.150863i
\(704\) 14.0000i 0.527645i
\(705\) 0 0
\(706\) 24.0000i 0.903252i
\(707\) −24.0000 −0.902613
\(708\) 0 0
\(709\) −50.0000 −1.87779 −0.938895 0.344204i \(-0.888149\pi\)
−0.938895 + 0.344204i \(0.888149\pi\)
\(710\) −8.00000 + 16.0000i −0.300235 + 0.600469i
\(711\) 0 0
\(712\) 48.0000i 1.79888i
\(713\) −12.0000 −0.449404
\(714\) 0 0
\(715\) −8.00000 + 16.0000i −0.299183 + 0.598366i
\(716\) −12.0000 −0.448461
\(717\) 0 0
\(718\) 18.0000i 0.671754i
\(719\) 48.0000 1.79010 0.895049 0.445968i \(-0.147140\pi\)
0.895049 + 0.445968i \(0.147140\pi\)
\(720\) 0 0
\(721\) −36.0000 −1.34071
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) 10.0000 0.371647
\(725\) −7.00000 26.0000i −0.259973 0.965616i
\(726\) 0 0
\(727\) 48.0000 1.78022 0.890111 0.455744i \(-0.150627\pi\)
0.890111 + 0.455744i \(0.150627\pi\)
\(728\) 24.0000 0.889499
\(729\) 0 0
\(730\) −6.00000 + 12.0000i −0.222070 + 0.444140i
\(731\) 24.0000 0.887672
\(732\) 0 0
\(733\) 22.0000 0.812589 0.406294 0.913742i \(-0.366821\pi\)
0.406294 + 0.913742i \(0.366821\pi\)
\(734\) 24.0000 0.885856
\(735\) 0 0
\(736\) 30.0000i 1.10581i
\(737\) −12.0000 −0.442026
\(738\) 0 0
\(739\) 34.0000i 1.25071i −0.780340 0.625355i \(-0.784954\pi\)
0.780340 0.625355i \(-0.215046\pi\)
\(740\) 2.00000 4.00000i 0.0735215 0.147043i
\(741\) 0 0
\(742\) −24.0000 −0.881068
\(743\) 48.0000 1.76095 0.880475 0.474093i \(-0.157224\pi\)
0.880475 + 0.474093i \(0.157224\pi\)
\(744\) 0 0
\(745\) 10.0000 20.0000i 0.366372 0.732743i
\(746\) 4.00000i 0.146450i
\(747\) 0 0
\(748\) 12.0000i 0.438763i
\(749\) −20.0000 −0.730784
\(750\) 0 0
\(751\) 46.0000i 1.67856i −0.543696 0.839282i \(-0.682976\pi\)
0.543696 0.839282i \(-0.317024\pi\)
\(752\) −8.00000 −0.291730
\(753\) 0 0
\(754\) −8.00000 + 20.0000i −0.291343 + 0.728357i
\(755\) −8.00000 + 16.0000i −0.291150 + 0.582300i
\(756\) 0 0
\(757\) −42.0000 −1.52652 −0.763258 0.646094i \(-0.776401\pi\)
−0.763258 + 0.646094i \(0.776401\pi\)
\(758\) 38.0000i 1.38022i
\(759\) 0 0
\(760\) 12.0000 + 6.00000i 0.435286 + 0.217643i
\(761\) −2.00000 −0.0724999 −0.0362500 0.999343i \(-0.511541\pi\)
−0.0362500 + 0.999343i \(0.511541\pi\)
\(762\) 0 0
\(763\) 20.0000i 0.724049i
\(764\) 6.00000i 0.217072i
\(765\) 0 0
\(766\) 30.0000i 1.08394i
\(767\) 16.0000i 0.577727i
\(768\) 0 0
\(769\) 32.0000i 1.15395i 0.816762 + 0.576975i \(0.195767\pi\)
−0.816762 + 0.576975i \(0.804233\pi\)
\(770\) −4.00000 + 8.00000i −0.144150 + 0.288300i
\(771\) 0 0
\(772\) 6.00000 0.215945
\(773\) 18.0000 0.647415 0.323708 0.946157i \(-0.395071\pi\)
0.323708 + 0.946157i \(0.395071\pi\)
\(774\) 0 0
\(775\) 8.00000 6.00000i 0.287368 0.215526i
\(776\) 42.0000 1.50771
\(777\) 0 0
\(778\) 12.0000i 0.430221i
\(779\) 0 0
\(780\) 0 0
\(781\) 16.0000i 0.572525i
\(782\) 36.0000i 1.28736i
\(783\) 0 0
\(784\) −3.00000 −0.107143
\(785\) −2.00000 + 4.00000i −0.0713831 + 0.142766i
\(786\) 0 0
\(787\) 6.00000i 0.213877i 0.994266 + 0.106938i \(0.0341048\pi\)
−0.994266 + 0.106938i \(0.965895\pi\)
\(788\) 4.00000i 0.142494i
\(789\) 0 0