Properties

Label 1110.2.d.h.889.4
Level $1110$
Weight $2$
Character 1110.889
Analytic conductor $8.863$
Analytic rank $0$
Dimension $4$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1110,2,Mod(889,1110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1110, 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("1110.889");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1110.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: \(8.86339462436\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(i, \sqrt{6})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 9 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 889.4
Root \(-1.22474 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1110.889
Dual form 1110.2.d.h.889.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.22474 - 0.224745i) q^{5} +1.00000 q^{6} -1.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+1.00000i q^{2} -1.00000i q^{3} -1.00000 q^{4} +(2.22474 - 0.224745i) q^{5} +1.00000 q^{6} -1.44949i q^{7} -1.00000i q^{8} -1.00000 q^{9} +(0.224745 + 2.22474i) q^{10} -3.44949 q^{11} +1.00000i q^{12} -5.44949i q^{13} +1.44949 q^{14} +(-0.224745 - 2.22474i) q^{15} +1.00000 q^{16} -1.44949i q^{17} -1.00000i q^{18} -3.00000 q^{19} +(-2.22474 + 0.224745i) q^{20} -1.44949 q^{21} -3.44949i q^{22} -1.00000i q^{23} -1.00000 q^{24} +(4.89898 - 1.00000i) q^{25} +5.44949 q^{26} +1.00000i q^{27} +1.44949i q^{28} -8.44949 q^{29} +(2.22474 - 0.224745i) q^{30} -2.00000 q^{31} +1.00000i q^{32} +3.44949i q^{33} +1.44949 q^{34} +(-0.325765 - 3.22474i) q^{35} +1.00000 q^{36} -1.00000i q^{37} -3.00000i q^{38} -5.44949 q^{39} +(-0.224745 - 2.22474i) q^{40} +4.44949 q^{41} -1.44949i q^{42} -2.89898i q^{43} +3.44949 q^{44} +(-2.22474 + 0.224745i) q^{45} +1.00000 q^{46} -1.55051i q^{47} -1.00000i q^{48} +4.89898 q^{49} +(1.00000 + 4.89898i) q^{50} -1.44949 q^{51} +5.44949i q^{52} +3.00000i q^{53} -1.00000 q^{54} +(-7.67423 + 0.775255i) q^{55} -1.44949 q^{56} +3.00000i q^{57} -8.44949i q^{58} -11.3485 q^{59} +(0.224745 + 2.22474i) q^{60} -5.10102 q^{61} -2.00000i q^{62} +1.44949i q^{63} -1.00000 q^{64} +(-1.22474 - 12.1237i) q^{65} -3.44949 q^{66} -2.89898i q^{67} +1.44949i q^{68} -1.00000 q^{69} +(3.22474 - 0.325765i) q^{70} +13.3485 q^{71} +1.00000i q^{72} -10.7980i q^{73} +1.00000 q^{74} +(-1.00000 - 4.89898i) q^{75} +3.00000 q^{76} +5.00000i q^{77} -5.44949i q^{78} +1.34847 q^{79} +(2.22474 - 0.224745i) q^{80} +1.00000 q^{81} +4.44949i q^{82} -3.44949i q^{83} +1.44949 q^{84} +(-0.325765 - 3.22474i) q^{85} +2.89898 q^{86} +8.44949i q^{87} +3.44949i q^{88} +14.3485 q^{89} +(-0.224745 - 2.22474i) q^{90} -7.89898 q^{91} +1.00000i q^{92} +2.00000i q^{93} +1.55051 q^{94} +(-6.67423 + 0.674235i) q^{95} +1.00000 q^{96} -11.3485i q^{97} +4.89898i q^{98} +3.44949 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 4 q^{4} + 4 q^{5} + 4 q^{6} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{14} + 4 q^{15} + 4 q^{16} - 12 q^{19} - 4 q^{20} + 4 q^{21} - 4 q^{24} + 12 q^{26} - 24 q^{29} + 4 q^{30} - 8 q^{31} - 4 q^{34} - 16 q^{35} + 4 q^{36} - 12 q^{39} + 4 q^{40} + 8 q^{41} + 4 q^{44} - 4 q^{45} + 4 q^{46} + 4 q^{50} + 4 q^{51} - 4 q^{54} - 16 q^{55} + 4 q^{56} - 16 q^{59} - 4 q^{60} - 40 q^{61} - 4 q^{64} - 4 q^{66} - 4 q^{69} + 8 q^{70} + 24 q^{71} + 4 q^{74} - 4 q^{75} + 12 q^{76} - 24 q^{79} + 4 q^{80} + 4 q^{81} - 4 q^{84} - 16 q^{85} - 8 q^{86} + 28 q^{89} + 4 q^{90} - 12 q^{91} + 16 q^{94} - 12 q^{95} + 4 q^{96} + 4 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times\).

\(n\) \(371\) \(631\) \(667\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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
\(3\) 1.00000i 0.577350i
\(4\) −1.00000 −0.500000
\(5\) 2.22474 0.224745i 0.994936 0.100509i
\(6\) 1.00000 0.408248
\(7\) 1.44949i 0.547856i −0.961750 0.273928i \(-0.911677\pi\)
0.961750 0.273928i \(-0.0883229\pi\)
\(8\) 1.00000i 0.353553i
\(9\) −1.00000 −0.333333
\(10\) 0.224745 + 2.22474i 0.0710706 + 0.703526i
\(11\) −3.44949 −1.04006 −0.520030 0.854148i \(-0.674079\pi\)
−0.520030 + 0.854148i \(0.674079\pi\)
\(12\) 1.00000i 0.288675i
\(13\) 5.44949i 1.51142i −0.654908 0.755708i \(-0.727293\pi\)
0.654908 0.755708i \(-0.272707\pi\)
\(14\) 1.44949 0.387392
\(15\) −0.224745 2.22474i −0.0580289 0.574427i
\(16\) 1.00000 0.250000
\(17\) 1.44949i 0.351553i −0.984430 0.175776i \(-0.943756\pi\)
0.984430 0.175776i \(-0.0562436\pi\)
\(18\) 1.00000i 0.235702i
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) −2.22474 + 0.224745i −0.497468 + 0.0502545i
\(21\) −1.44949 −0.316305
\(22\) 3.44949i 0.735434i
\(23\) 1.00000i 0.208514i −0.994550 0.104257i \(-0.966753\pi\)
0.994550 0.104257i \(-0.0332465\pi\)
\(24\) −1.00000 −0.204124
\(25\) 4.89898 1.00000i 0.979796 0.200000i
\(26\) 5.44949 1.06873
\(27\) 1.00000i 0.192450i
\(28\) 1.44949i 0.273928i
\(29\) −8.44949 −1.56903 −0.784515 0.620109i \(-0.787088\pi\)
−0.784515 + 0.620109i \(0.787088\pi\)
\(30\) 2.22474 0.224745i 0.406181 0.0410326i
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) 1.00000i 0.176777i
\(33\) 3.44949i 0.600479i
\(34\) 1.44949 0.248585
\(35\) −0.325765 3.22474i −0.0550644 0.545081i
\(36\) 1.00000 0.166667
\(37\) 1.00000i 0.164399i
\(38\) 3.00000i 0.486664i
\(39\) −5.44949 −0.872617
\(40\) −0.224745 2.22474i −0.0355353 0.351763i
\(41\) 4.44949 0.694894 0.347447 0.937700i \(-0.387049\pi\)
0.347447 + 0.937700i \(0.387049\pi\)
\(42\) 1.44949i 0.223661i
\(43\) 2.89898i 0.442090i −0.975264 0.221045i \(-0.929053\pi\)
0.975264 0.221045i \(-0.0709468\pi\)
\(44\) 3.44949 0.520030
\(45\) −2.22474 + 0.224745i −0.331645 + 0.0335030i
\(46\) 1.00000 0.147442
\(47\) 1.55051i 0.226165i −0.993586 0.113083i \(-0.963928\pi\)
0.993586 0.113083i \(-0.0360725\pi\)
\(48\) 1.00000i 0.144338i
\(49\) 4.89898 0.699854
\(50\) 1.00000 + 4.89898i 0.141421 + 0.692820i
\(51\) −1.44949 −0.202969
\(52\) 5.44949i 0.755708i
\(53\) 3.00000i 0.412082i 0.978543 + 0.206041i \(0.0660580\pi\)
−0.978543 + 0.206041i \(0.933942\pi\)
\(54\) −1.00000 −0.136083
\(55\) −7.67423 + 0.775255i −1.03479 + 0.104535i
\(56\) −1.44949 −0.193696
\(57\) 3.00000i 0.397360i
\(58\) 8.44949i 1.10947i
\(59\) −11.3485 −1.47744 −0.738722 0.674010i \(-0.764571\pi\)
−0.738722 + 0.674010i \(0.764571\pi\)
\(60\) 0.224745 + 2.22474i 0.0290144 + 0.287213i
\(61\) −5.10102 −0.653119 −0.326559 0.945177i \(-0.605889\pi\)
−0.326559 + 0.945177i \(0.605889\pi\)
\(62\) 2.00000i 0.254000i
\(63\) 1.44949i 0.182619i
\(64\) −1.00000 −0.125000
\(65\) −1.22474 12.1237i −0.151911 1.50376i
\(66\) −3.44949 −0.424603
\(67\) 2.89898i 0.354167i −0.984196 0.177083i \(-0.943334\pi\)
0.984196 0.177083i \(-0.0566662\pi\)
\(68\) 1.44949i 0.175776i
\(69\) −1.00000 −0.120386
\(70\) 3.22474 0.325765i 0.385431 0.0389364i
\(71\) 13.3485 1.58417 0.792086 0.610410i \(-0.208995\pi\)
0.792086 + 0.610410i \(0.208995\pi\)
\(72\) 1.00000i 0.117851i
\(73\) 10.7980i 1.26381i −0.775048 0.631903i \(-0.782274\pi\)
0.775048 0.631903i \(-0.217726\pi\)
\(74\) 1.00000 0.116248
\(75\) −1.00000 4.89898i −0.115470 0.565685i
\(76\) 3.00000 0.344124
\(77\) 5.00000i 0.569803i
\(78\) 5.44949i 0.617033i
\(79\) 1.34847 0.151715 0.0758573 0.997119i \(-0.475831\pi\)
0.0758573 + 0.997119i \(0.475831\pi\)
\(80\) 2.22474 0.224745i 0.248734 0.0251272i
\(81\) 1.00000 0.111111
\(82\) 4.44949i 0.491364i
\(83\) 3.44949i 0.378631i −0.981916 0.189315i \(-0.939373\pi\)
0.981916 0.189315i \(-0.0606268\pi\)
\(84\) 1.44949 0.158152
\(85\) −0.325765 3.22474i −0.0353342 0.349773i
\(86\) 2.89898 0.312605
\(87\) 8.44949i 0.905880i
\(88\) 3.44949i 0.367717i
\(89\) 14.3485 1.52093 0.760467 0.649376i \(-0.224970\pi\)
0.760467 + 0.649376i \(0.224970\pi\)
\(90\) −0.224745 2.22474i −0.0236902 0.234509i
\(91\) −7.89898 −0.828038
\(92\) 1.00000i 0.104257i
\(93\) 2.00000i 0.207390i
\(94\) 1.55051 0.159923
\(95\) −6.67423 + 0.674235i −0.684762 + 0.0691750i
\(96\) 1.00000 0.102062
\(97\) 11.3485i 1.15226i −0.817357 0.576131i \(-0.804562\pi\)
0.817357 0.576131i \(-0.195438\pi\)
\(98\) 4.89898i 0.494872i
\(99\) 3.44949 0.346687
\(100\) −4.89898 + 1.00000i −0.489898 + 0.100000i
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) 1.44949i 0.143521i
\(103\) 14.2474i 1.40384i −0.712254 0.701921i \(-0.752326\pi\)
0.712254 0.701921i \(-0.247674\pi\)
\(104\) −5.44949 −0.534366
\(105\) −3.22474 + 0.325765i −0.314703 + 0.0317914i
\(106\) −3.00000 −0.291386
\(107\) 16.3485i 1.58047i 0.612806 + 0.790233i \(0.290041\pi\)
−0.612806 + 0.790233i \(0.709959\pi\)
\(108\) 1.00000i 0.0962250i
\(109\) 12.3485 1.18277 0.591384 0.806390i \(-0.298582\pi\)
0.591384 + 0.806390i \(0.298582\pi\)
\(110\) −0.775255 7.67423i −0.0739177 0.731710i
\(111\) −1.00000 −0.0949158
\(112\) 1.44949i 0.136964i
\(113\) 16.8990i 1.58972i −0.606791 0.794861i \(-0.707544\pi\)
0.606791 0.794861i \(-0.292456\pi\)
\(114\) −3.00000 −0.280976
\(115\) −0.224745 2.22474i −0.0209576 0.207459i
\(116\) 8.44949 0.784515
\(117\) 5.44949i 0.503806i
\(118\) 11.3485i 1.04471i
\(119\) −2.10102 −0.192600
\(120\) −2.22474 + 0.224745i −0.203090 + 0.0205163i
\(121\) 0.898979 0.0817254
\(122\) 5.10102i 0.461825i
\(123\) 4.44949i 0.401197i
\(124\) 2.00000 0.179605
\(125\) 10.6742 3.32577i 0.954733 0.297465i
\(126\) −1.44949 −0.129131
\(127\) 10.5505i 0.936206i 0.883674 + 0.468103i \(0.155062\pi\)
−0.883674 + 0.468103i \(0.844938\pi\)
\(128\) 1.00000i 0.0883883i
\(129\) −2.89898 −0.255241
\(130\) 12.1237 1.22474i 1.06332 0.107417i
\(131\) 15.5505 1.35865 0.679327 0.733836i \(-0.262272\pi\)
0.679327 + 0.733836i \(0.262272\pi\)
\(132\) 3.44949i 0.300240i
\(133\) 4.34847i 0.377060i
\(134\) 2.89898 0.250434
\(135\) 0.224745 + 2.22474i 0.0193430 + 0.191476i
\(136\) −1.44949 −0.124293
\(137\) 7.34847i 0.627822i 0.949452 + 0.313911i \(0.101639\pi\)
−0.949452 + 0.313911i \(0.898361\pi\)
\(138\) 1.00000i 0.0851257i
\(139\) −12.6969 −1.07694 −0.538470 0.842645i \(-0.680998\pi\)
−0.538470 + 0.842645i \(0.680998\pi\)
\(140\) 0.325765 + 3.22474i 0.0275322 + 0.272541i
\(141\) −1.55051 −0.130577
\(142\) 13.3485i 1.12018i
\(143\) 18.7980i 1.57196i
\(144\) −1.00000 −0.0833333
\(145\) −18.7980 + 1.89898i −1.56109 + 0.157702i
\(146\) 10.7980 0.893645
\(147\) 4.89898i 0.404061i
\(148\) 1.00000i 0.0821995i
\(149\) 12.8990 1.05673 0.528363 0.849019i \(-0.322806\pi\)
0.528363 + 0.849019i \(0.322806\pi\)
\(150\) 4.89898 1.00000i 0.400000 0.0816497i
\(151\) −17.2474 −1.40358 −0.701789 0.712385i \(-0.747615\pi\)
−0.701789 + 0.712385i \(0.747615\pi\)
\(152\) 3.00000i 0.243332i
\(153\) 1.44949i 0.117184i
\(154\) −5.00000 −0.402911
\(155\) −4.44949 + 0.449490i −0.357392 + 0.0361039i
\(156\) 5.44949 0.436308
\(157\) 4.00000i 0.319235i −0.987179 0.159617i \(-0.948974\pi\)
0.987179 0.159617i \(-0.0510260\pi\)
\(158\) 1.34847i 0.107278i
\(159\) 3.00000 0.237915
\(160\) 0.224745 + 2.22474i 0.0177676 + 0.175882i
\(161\) −1.44949 −0.114236
\(162\) 1.00000i 0.0785674i
\(163\) 11.8990i 0.932000i 0.884785 + 0.466000i \(0.154305\pi\)
−0.884785 + 0.466000i \(0.845695\pi\)
\(164\) −4.44949 −0.347447
\(165\) 0.775255 + 7.67423i 0.0603535 + 0.597438i
\(166\) 3.44949 0.267732
\(167\) 18.7980i 1.45463i 0.686304 + 0.727315i \(0.259232\pi\)
−0.686304 + 0.727315i \(0.740768\pi\)
\(168\) 1.44949i 0.111831i
\(169\) −16.6969 −1.28438
\(170\) 3.22474 0.325765i 0.247327 0.0249851i
\(171\) 3.00000 0.229416
\(172\) 2.89898i 0.221045i
\(173\) 9.69694i 0.737245i 0.929579 + 0.368622i \(0.120170\pi\)
−0.929579 + 0.368622i \(0.879830\pi\)
\(174\) −8.44949 −0.640554
\(175\) −1.44949 7.10102i −0.109571 0.536787i
\(176\) −3.44949 −0.260015
\(177\) 11.3485i 0.853003i
\(178\) 14.3485i 1.07546i
\(179\) −6.69694 −0.500553 −0.250276 0.968174i \(-0.580521\pi\)
−0.250276 + 0.968174i \(0.580521\pi\)
\(180\) 2.22474 0.224745i 0.165823 0.0167515i
\(181\) −11.3485 −0.843525 −0.421763 0.906706i \(-0.638588\pi\)
−0.421763 + 0.906706i \(0.638588\pi\)
\(182\) 7.89898i 0.585511i
\(183\) 5.10102i 0.377078i
\(184\) −1.00000 −0.0737210
\(185\) −0.224745 2.22474i −0.0165236 0.163566i
\(186\) −2.00000 −0.146647
\(187\) 5.00000i 0.365636i
\(188\) 1.55051i 0.113083i
\(189\) 1.44949 0.105435
\(190\) −0.674235 6.67423i −0.0489141 0.484200i
\(191\) 23.6969 1.71465 0.857325 0.514775i \(-0.172125\pi\)
0.857325 + 0.514775i \(0.172125\pi\)
\(192\) 1.00000i 0.0721688i
\(193\) 21.5959i 1.55451i 0.629187 + 0.777254i \(0.283388\pi\)
−0.629187 + 0.777254i \(0.716612\pi\)
\(194\) 11.3485 0.814773
\(195\) −12.1237 + 1.22474i −0.868198 + 0.0877058i
\(196\) −4.89898 −0.349927
\(197\) 1.20204i 0.0856419i 0.999083 + 0.0428209i \(0.0136345\pi\)
−0.999083 + 0.0428209i \(0.986366\pi\)
\(198\) 3.44949i 0.245145i
\(199\) 2.20204 0.156099 0.0780493 0.996950i \(-0.475131\pi\)
0.0780493 + 0.996950i \(0.475131\pi\)
\(200\) −1.00000 4.89898i −0.0707107 0.346410i
\(201\) −2.89898 −0.204478
\(202\) 10.0000i 0.703598i
\(203\) 12.2474i 0.859602i
\(204\) 1.44949 0.101485
\(205\) 9.89898 1.00000i 0.691375 0.0698430i
\(206\) 14.2474 0.992667
\(207\) 1.00000i 0.0695048i
\(208\) 5.44949i 0.377854i
\(209\) 10.3485 0.715819
\(210\) −0.325765 3.22474i −0.0224799 0.222529i
\(211\) 3.55051 0.244427 0.122214 0.992504i \(-0.461001\pi\)
0.122214 + 0.992504i \(0.461001\pi\)
\(212\) 3.00000i 0.206041i
\(213\) 13.3485i 0.914622i
\(214\) −16.3485 −1.11756
\(215\) −0.651531 6.44949i −0.0444340 0.439852i
\(216\) 1.00000 0.0680414
\(217\) 2.89898i 0.196796i
\(218\) 12.3485i 0.836344i
\(219\) −10.7980 −0.729658
\(220\) 7.67423 0.775255i 0.517397 0.0522677i
\(221\) −7.89898 −0.531343
\(222\) 1.00000i 0.0671156i
\(223\) 23.5959i 1.58010i −0.613043 0.790050i \(-0.710055\pi\)
0.613043 0.790050i \(-0.289945\pi\)
\(224\) 1.44949 0.0968481
\(225\) −4.89898 + 1.00000i −0.326599 + 0.0666667i
\(226\) 16.8990 1.12410
\(227\) 8.00000i 0.530979i −0.964114 0.265489i \(-0.914466\pi\)
0.964114 0.265489i \(-0.0855335\pi\)
\(228\) 3.00000i 0.198680i
\(229\) 6.44949 0.426194 0.213097 0.977031i \(-0.431645\pi\)
0.213097 + 0.977031i \(0.431645\pi\)
\(230\) 2.22474 0.224745i 0.146695 0.0148192i
\(231\) 5.00000 0.328976
\(232\) 8.44949i 0.554736i
\(233\) 6.89898i 0.451967i −0.974131 0.225984i \(-0.927440\pi\)
0.974131 0.225984i \(-0.0725596\pi\)
\(234\) −5.44949 −0.356244
\(235\) −0.348469 3.44949i −0.0227316 0.225020i
\(236\) 11.3485 0.738722
\(237\) 1.34847i 0.0875925i
\(238\) 2.10102i 0.136189i
\(239\) −2.00000 −0.129369 −0.0646846 0.997906i \(-0.520604\pi\)
−0.0646846 + 0.997906i \(0.520604\pi\)
\(240\) −0.224745 2.22474i −0.0145072 0.143607i
\(241\) 10.2474 0.660096 0.330048 0.943964i \(-0.392935\pi\)
0.330048 + 0.943964i \(0.392935\pi\)
\(242\) 0.898979i 0.0577886i
\(243\) 1.00000i 0.0641500i
\(244\) 5.10102 0.326559
\(245\) 10.8990 1.10102i 0.696310 0.0703416i
\(246\) 4.44949 0.283689
\(247\) 16.3485i 1.04023i
\(248\) 2.00000i 0.127000i
\(249\) −3.44949 −0.218603
\(250\) 3.32577 + 10.6742i 0.210340 + 0.675098i
\(251\) −20.6969 −1.30638 −0.653190 0.757194i \(-0.726570\pi\)
−0.653190 + 0.757194i \(0.726570\pi\)
\(252\) 1.44949i 0.0913093i
\(253\) 3.44949i 0.216868i
\(254\) −10.5505 −0.661998
\(255\) −3.22474 + 0.325765i −0.201941 + 0.0204002i
\(256\) 1.00000 0.0625000
\(257\) 0.550510i 0.0343399i −0.999853 0.0171699i \(-0.994534\pi\)
0.999853 0.0171699i \(-0.00546563\pi\)
\(258\) 2.89898i 0.180483i
\(259\) −1.44949 −0.0900669
\(260\) 1.22474 + 12.1237i 0.0759555 + 0.751881i
\(261\) 8.44949 0.523010
\(262\) 15.5505i 0.960714i
\(263\) 17.5505i 1.08221i 0.840955 + 0.541105i \(0.181994\pi\)
−0.840955 + 0.541105i \(0.818006\pi\)
\(264\) 3.44949 0.212301
\(265\) 0.674235 + 6.67423i 0.0414179 + 0.409995i
\(266\) −4.34847 −0.266622
\(267\) 14.3485i 0.878112i
\(268\) 2.89898i 0.177083i
\(269\) 16.5959 1.01187 0.505935 0.862571i \(-0.331147\pi\)
0.505935 + 0.862571i \(0.331147\pi\)
\(270\) −2.22474 + 0.224745i −0.135394 + 0.0136775i
\(271\) −3.10102 −0.188374 −0.0941868 0.995555i \(-0.530025\pi\)
−0.0941868 + 0.995555i \(0.530025\pi\)
\(272\) 1.44949i 0.0878882i
\(273\) 7.89898i 0.478068i
\(274\) −7.34847 −0.443937
\(275\) −16.8990 + 3.44949i −1.01905 + 0.208012i
\(276\) 1.00000 0.0601929
\(277\) 10.5505i 0.633919i 0.948439 + 0.316959i \(0.102662\pi\)
−0.948439 + 0.316959i \(0.897338\pi\)
\(278\) 12.6969i 0.761512i
\(279\) 2.00000 0.119737
\(280\) −3.22474 + 0.325765i −0.192715 + 0.0194682i
\(281\) −10.3485 −0.617338 −0.308669 0.951170i \(-0.599884\pi\)
−0.308669 + 0.951170i \(0.599884\pi\)
\(282\) 1.55051i 0.0923315i
\(283\) 7.69694i 0.457535i −0.973481 0.228768i \(-0.926530\pi\)
0.973481 0.228768i \(-0.0734696\pi\)
\(284\) −13.3485 −0.792086
\(285\) 0.674235 + 6.67423i 0.0399382 + 0.395348i
\(286\) −18.7980 −1.11155
\(287\) 6.44949i 0.380701i
\(288\) 1.00000i 0.0589256i
\(289\) 14.8990 0.876411
\(290\) −1.89898 18.7980i −0.111512 1.10385i
\(291\) −11.3485 −0.665259
\(292\) 10.7980i 0.631903i
\(293\) 25.8990i 1.51303i 0.653974 + 0.756517i \(0.273101\pi\)
−0.653974 + 0.756517i \(0.726899\pi\)
\(294\) 4.89898 0.285714
\(295\) −25.2474 + 2.55051i −1.46996 + 0.148496i
\(296\) −1.00000 −0.0581238
\(297\) 3.44949i 0.200160i
\(298\) 12.8990i 0.747218i
\(299\) −5.44949 −0.315152
\(300\) 1.00000 + 4.89898i 0.0577350 + 0.282843i
\(301\) −4.20204 −0.242202
\(302\) 17.2474i 0.992479i
\(303\) 10.0000i 0.574485i
\(304\) −3.00000 −0.172062
\(305\) −11.3485 + 1.14643i −0.649811 + 0.0656443i
\(306\) −1.44949 −0.0828618
\(307\) 15.5505i 0.887514i 0.896147 + 0.443757i \(0.146355\pi\)
−0.896147 + 0.443757i \(0.853645\pi\)
\(308\) 5.00000i 0.284901i
\(309\) −14.2474 −0.810509
\(310\) −0.449490 4.44949i −0.0255293 0.252714i
\(311\) −18.4949 −1.04875 −0.524375 0.851488i \(-0.675701\pi\)
−0.524375 + 0.851488i \(0.675701\pi\)
\(312\) 5.44949i 0.308517i
\(313\) 18.4495i 1.04283i −0.853304 0.521413i \(-0.825405\pi\)
0.853304 0.521413i \(-0.174595\pi\)
\(314\) 4.00000 0.225733
\(315\) 0.325765 + 3.22474i 0.0183548 + 0.181694i
\(316\) −1.34847 −0.0758573
\(317\) 0.898979i 0.0504917i −0.999681 0.0252459i \(-0.991963\pi\)
0.999681 0.0252459i \(-0.00803686\pi\)
\(318\) 3.00000i 0.168232i
\(319\) 29.1464 1.63189
\(320\) −2.22474 + 0.224745i −0.124367 + 0.0125636i
\(321\) 16.3485 0.912483
\(322\) 1.44949i 0.0807769i
\(323\) 4.34847i 0.241955i
\(324\) −1.00000 −0.0555556
\(325\) −5.44949 26.6969i −0.302283 1.48088i
\(326\) −11.8990 −0.659024
\(327\) 12.3485i 0.682872i
\(328\) 4.44949i 0.245682i
\(329\) −2.24745 −0.123906
\(330\) −7.67423 + 0.775255i −0.422453 + 0.0426764i
\(331\) 0.696938 0.0383072 0.0191536 0.999817i \(-0.493903\pi\)
0.0191536 + 0.999817i \(0.493903\pi\)
\(332\) 3.44949i 0.189315i
\(333\) 1.00000i 0.0547997i
\(334\) −18.7980 −1.02858
\(335\) −0.651531 6.44949i −0.0355969 0.352373i
\(336\) −1.44949 −0.0790761
\(337\) 9.89898i 0.539232i −0.962968 0.269616i \(-0.913103\pi\)
0.962968 0.269616i \(-0.0868967\pi\)
\(338\) 16.6969i 0.908194i
\(339\) −16.8990 −0.917827
\(340\) 0.325765 + 3.22474i 0.0176671 + 0.174886i
\(341\) 6.89898 0.373601
\(342\) 3.00000i 0.162221i
\(343\) 17.2474i 0.931275i
\(344\) −2.89898 −0.156302
\(345\) −2.22474 + 0.224745i −0.119776 + 0.0120999i
\(346\) −9.69694 −0.521311
\(347\) 20.4495i 1.09779i 0.835893 + 0.548893i \(0.184951\pi\)
−0.835893 + 0.548893i \(0.815049\pi\)
\(348\) 8.44949i 0.452940i
\(349\) −3.14643 −0.168424 −0.0842122 0.996448i \(-0.526837\pi\)
−0.0842122 + 0.996448i \(0.526837\pi\)
\(350\) 7.10102 1.44949i 0.379566 0.0774785i
\(351\) 5.44949 0.290872
\(352\) 3.44949i 0.183858i
\(353\) 12.6969i 0.675790i 0.941184 + 0.337895i \(0.109715\pi\)
−0.941184 + 0.337895i \(0.890285\pi\)
\(354\) −11.3485 −0.603164
\(355\) 29.6969 3.00000i 1.57615 0.159223i
\(356\) −14.3485 −0.760467
\(357\) 2.10102i 0.111198i
\(358\) 6.69694i 0.353944i
\(359\) −2.44949 −0.129279 −0.0646396 0.997909i \(-0.520590\pi\)
−0.0646396 + 0.997909i \(0.520590\pi\)
\(360\) 0.224745 + 2.22474i 0.0118451 + 0.117254i
\(361\) −10.0000 −0.526316
\(362\) 11.3485i 0.596462i
\(363\) 0.898979i 0.0471842i
\(364\) 7.89898 0.414019
\(365\) −2.42679 24.0227i −0.127024 1.25741i
\(366\) −5.10102 −0.266635
\(367\) 0.752551i 0.0392829i 0.999807 + 0.0196414i \(0.00625246\pi\)
−0.999807 + 0.0196414i \(0.993748\pi\)
\(368\) 1.00000i 0.0521286i
\(369\) −4.44949 −0.231631
\(370\) 2.22474 0.224745i 0.115659 0.0116839i
\(371\) 4.34847 0.225761
\(372\) 2.00000i 0.103695i
\(373\) 31.8434i 1.64879i 0.566017 + 0.824394i \(0.308484\pi\)
−0.566017 + 0.824394i \(0.691516\pi\)
\(374\) −5.00000 −0.258544
\(375\) −3.32577 10.6742i −0.171742 0.551215i
\(376\) −1.55051 −0.0799615
\(377\) 46.0454i 2.37146i
\(378\) 1.44949i 0.0745537i
\(379\) 29.3485 1.50753 0.753765 0.657144i \(-0.228236\pi\)
0.753765 + 0.657144i \(0.228236\pi\)
\(380\) 6.67423 0.674235i 0.342381 0.0345875i
\(381\) 10.5505 0.540519
\(382\) 23.6969i 1.21244i
\(383\) 14.7980i 0.756140i −0.925777 0.378070i \(-0.876588\pi\)
0.925777 0.378070i \(-0.123412\pi\)
\(384\) −1.00000 −0.0510310
\(385\) 1.12372 + 11.1237i 0.0572703 + 0.566917i
\(386\) −21.5959 −1.09920
\(387\) 2.89898i 0.147363i
\(388\) 11.3485i 0.576131i
\(389\) 19.7980 1.00380 0.501898 0.864927i \(-0.332635\pi\)
0.501898 + 0.864927i \(0.332635\pi\)
\(390\) −1.22474 12.1237i −0.0620174 0.613909i
\(391\) −1.44949 −0.0733038
\(392\) 4.89898i 0.247436i
\(393\) 15.5505i 0.784419i
\(394\) −1.20204 −0.0605580
\(395\) 3.00000 0.303062i 0.150946 0.0152487i
\(396\) −3.44949 −0.173343
\(397\) 12.8990i 0.647381i −0.946163 0.323691i \(-0.895076\pi\)
0.946163 0.323691i \(-0.104924\pi\)
\(398\) 2.20204i 0.110378i
\(399\) 4.34847 0.217696
\(400\) 4.89898 1.00000i 0.244949 0.0500000i
\(401\) −25.9444 −1.29560 −0.647800 0.761810i \(-0.724311\pi\)
−0.647800 + 0.761810i \(0.724311\pi\)
\(402\) 2.89898i 0.144588i
\(403\) 10.8990i 0.542917i
\(404\) −10.0000 −0.497519
\(405\) 2.22474 0.224745i 0.110548 0.0111677i
\(406\) −12.2474 −0.607831
\(407\) 3.44949i 0.170985i
\(408\) 1.44949i 0.0717604i
\(409\) 28.2474 1.39675 0.698373 0.715734i \(-0.253908\pi\)
0.698373 + 0.715734i \(0.253908\pi\)
\(410\) 1.00000 + 9.89898i 0.0493865 + 0.488876i
\(411\) 7.34847 0.362473
\(412\) 14.2474i 0.701921i
\(413\) 16.4495i 0.809426i
\(414\) −1.00000 −0.0491473
\(415\) −0.775255 7.67423i −0.0380558 0.376713i
\(416\) 5.44949 0.267183
\(417\) 12.6969i 0.621772i
\(418\) 10.3485i 0.506160i
\(419\) 33.4495 1.63411 0.817057 0.576557i \(-0.195604\pi\)
0.817057 + 0.576557i \(0.195604\pi\)
\(420\) 3.22474 0.325765i 0.157351 0.0158957i
\(421\) −3.10102 −0.151134 −0.0755672 0.997141i \(-0.524077\pi\)
−0.0755672 + 0.997141i \(0.524077\pi\)
\(422\) 3.55051i 0.172836i
\(423\) 1.55051i 0.0753884i
\(424\) 3.00000 0.145693
\(425\) −1.44949 7.10102i −0.0703106 0.344450i
\(426\) 13.3485 0.646735
\(427\) 7.39388i 0.357815i
\(428\) 16.3485i 0.790233i
\(429\) 18.7980 0.907574
\(430\) 6.44949 0.651531i 0.311022 0.0314196i
\(431\) −19.0000 −0.915198 −0.457599 0.889159i \(-0.651290\pi\)
−0.457599 + 0.889159i \(0.651290\pi\)
\(432\) 1.00000i 0.0481125i
\(433\) 38.5959i 1.85480i −0.374069 0.927401i \(-0.622038\pi\)
0.374069 0.927401i \(-0.377962\pi\)
\(434\) −2.89898 −0.139155
\(435\) 1.89898 + 18.7980i 0.0910491 + 0.901293i
\(436\) −12.3485 −0.591384
\(437\) 3.00000i 0.143509i
\(438\) 10.7980i 0.515946i
\(439\) −3.55051 −0.169457 −0.0847283 0.996404i \(-0.527002\pi\)
−0.0847283 + 0.996404i \(0.527002\pi\)
\(440\) 0.775255 + 7.67423i 0.0369588 + 0.365855i
\(441\) −4.89898 −0.233285
\(442\) 7.89898i 0.375716i
\(443\) 25.5959i 1.21610i −0.793899 0.608049i \(-0.791952\pi\)
0.793899 0.608049i \(-0.208048\pi\)
\(444\) 1.00000 0.0474579
\(445\) 31.9217 3.22474i 1.51323 0.152868i
\(446\) 23.5959 1.11730
\(447\) 12.8990i 0.610101i
\(448\) 1.44949i 0.0684820i
\(449\) 32.6969 1.54306 0.771532 0.636191i \(-0.219491\pi\)
0.771532 + 0.636191i \(0.219491\pi\)
\(450\) −1.00000 4.89898i −0.0471405 0.230940i
\(451\) −15.3485 −0.722731
\(452\) 16.8990i 0.794861i
\(453\) 17.2474i 0.810356i
\(454\) 8.00000 0.375459
\(455\) −17.5732 + 1.77526i −0.823845 + 0.0832252i
\(456\) 3.00000 0.140488
\(457\) 3.59592i 0.168210i −0.996457 0.0841050i \(-0.973197\pi\)
0.996457 0.0841050i \(-0.0268031\pi\)
\(458\) 6.44949i 0.301365i
\(459\) 1.44949 0.0676564
\(460\) 0.224745 + 2.22474i 0.0104788 + 0.103729i
\(461\) −20.6969 −0.963953 −0.481976 0.876184i \(-0.660081\pi\)
−0.481976 + 0.876184i \(0.660081\pi\)
\(462\) 5.00000i 0.232621i
\(463\) 10.6515i 0.495019i −0.968886 0.247509i \(-0.920388\pi\)
0.968886 0.247509i \(-0.0796121\pi\)
\(464\) −8.44949 −0.392258
\(465\) 0.449490 + 4.44949i 0.0208446 + 0.206340i
\(466\) 6.89898 0.319589
\(467\) 37.8434i 1.75118i −0.483053 0.875591i \(-0.660472\pi\)
0.483053 0.875591i \(-0.339528\pi\)
\(468\) 5.44949i 0.251903i
\(469\) −4.20204 −0.194032
\(470\) 3.44949 0.348469i 0.159113 0.0160737i
\(471\) −4.00000 −0.184310
\(472\) 11.3485i 0.522356i
\(473\) 10.0000i 0.459800i
\(474\) 1.34847 0.0619372
\(475\) −14.6969 + 3.00000i −0.674342 + 0.137649i
\(476\) 2.10102 0.0963001
\(477\) 3.00000i 0.137361i
\(478\) 2.00000i 0.0914779i
\(479\) −3.40408 −0.155536 −0.0777682 0.996971i \(-0.524779\pi\)
−0.0777682 + 0.996971i \(0.524779\pi\)
\(480\) 2.22474 0.224745i 0.101545 0.0102582i
\(481\) −5.44949 −0.248475
\(482\) 10.2474i 0.466758i
\(483\) 1.44949i 0.0659541i
\(484\) −0.898979 −0.0408627
\(485\) −2.55051 25.2474i −0.115813 1.14643i
\(486\) 1.00000 0.0453609
\(487\) 3.79796i 0.172102i 0.996291 + 0.0860510i \(0.0274248\pi\)
−0.996291 + 0.0860510i \(0.972575\pi\)
\(488\) 5.10102i 0.230912i
\(489\) 11.8990 0.538090
\(490\) 1.10102 + 10.8990i 0.0497390 + 0.492366i
\(491\) 35.9444 1.62215 0.811074 0.584944i \(-0.198883\pi\)
0.811074 + 0.584944i \(0.198883\pi\)
\(492\) 4.44949i 0.200598i
\(493\) 12.2474i 0.551597i
\(494\) −16.3485 −0.735552
\(495\) 7.67423 0.775255i 0.344931 0.0348451i
\(496\) −2.00000 −0.0898027
\(497\) 19.3485i 0.867897i
\(498\) 3.44949i 0.154575i
\(499\) 28.5959 1.28013 0.640065 0.768321i \(-0.278908\pi\)
0.640065 + 0.768321i \(0.278908\pi\)
\(500\) −10.6742 + 3.32577i −0.477366 + 0.148733i
\(501\) 18.7980 0.839831
\(502\) 20.6969i 0.923750i
\(503\) 6.00000i 0.267527i −0.991013 0.133763i \(-0.957294\pi\)
0.991013 0.133763i \(-0.0427062\pi\)
\(504\) 1.44949 0.0645654
\(505\) 22.2474 2.24745i 0.989998 0.100010i
\(506\) −3.44949 −0.153349
\(507\) 16.6969i 0.741537i
\(508\) 10.5505i 0.468103i
\(509\) −22.5959 −1.00155 −0.500773 0.865579i \(-0.666951\pi\)
−0.500773 + 0.865579i \(0.666951\pi\)
\(510\) −0.325765 3.22474i −0.0144251 0.142794i
\(511\) −15.6515 −0.692383
\(512\) 1.00000i 0.0441942i
\(513\) 3.00000i 0.132453i
\(514\) 0.550510 0.0242820
\(515\) −3.20204 31.6969i −0.141099 1.39673i
\(516\) 2.89898 0.127620
\(517\) 5.34847i 0.235225i
\(518\) 1.44949i 0.0636869i
\(519\) 9.69694 0.425648
\(520\) −12.1237 + 1.22474i −0.531660 + 0.0537086i
\(521\) 27.1464 1.18931 0.594653 0.803982i \(-0.297289\pi\)
0.594653 + 0.803982i \(0.297289\pi\)
\(522\) 8.44949i 0.369824i
\(523\) 27.3939i 1.19785i 0.800805 + 0.598925i \(0.204405\pi\)
−0.800805 + 0.598925i \(0.795595\pi\)
\(524\) −15.5505 −0.679327
\(525\) −7.10102 + 1.44949i −0.309914 + 0.0632609i
\(526\) −17.5505 −0.765239
\(527\) 2.89898i 0.126282i
\(528\) 3.44949i 0.150120i
\(529\) 22.0000 0.956522
\(530\) −6.67423 + 0.674235i −0.289910 + 0.0292869i
\(531\) 11.3485 0.492482
\(532\) 4.34847i 0.188530i
\(533\) 24.2474i 1.05027i
\(534\) 14.3485 0.620919
\(535\) 3.67423 + 36.3712i 0.158851 + 1.57246i
\(536\) −2.89898 −0.125217
\(537\) 6.69694i 0.288994i
\(538\) 16.5959i 0.715501i
\(539\) −16.8990 −0.727891
\(540\) −0.224745 2.22474i −0.00967148 0.0957378i
\(541\) −27.6515 −1.18883 −0.594416 0.804158i \(-0.702617\pi\)
−0.594416 + 0.804158i \(0.702617\pi\)
\(542\) 3.10102i 0.133200i
\(543\) 11.3485i 0.487009i
\(544\) 1.44949 0.0621464
\(545\) 27.4722 2.77526i 1.17678 0.118879i
\(546\) −7.89898 −0.338045
\(547\) 3.20204i 0.136909i 0.997654 + 0.0684547i \(0.0218069\pi\)
−0.997654 + 0.0684547i \(0.978193\pi\)
\(548\) 7.34847i 0.313911i
\(549\) 5.10102 0.217706
\(550\) −3.44949 16.8990i −0.147087 0.720575i
\(551\) 25.3485 1.07988
\(552\) 1.00000i 0.0425628i
\(553\) 1.95459i 0.0831177i
\(554\) −10.5505 −0.448248
\(555\) −2.22474 + 0.224745i −0.0944352 + 0.00953989i
\(556\) 12.6969 0.538470
\(557\) 26.4495i 1.12070i 0.828256 + 0.560350i \(0.189334\pi\)
−0.828256 + 0.560350i \(0.810666\pi\)
\(558\) 2.00000i 0.0846668i
\(559\) −15.7980 −0.668182
\(560\) −0.325765 3.22474i −0.0137661 0.136270i
\(561\) 5.00000 0.211100
\(562\) 10.3485i 0.436524i
\(563\) 44.7423i 1.88567i −0.333267 0.942833i \(-0.608151\pi\)
0.333267 0.942833i \(-0.391849\pi\)
\(564\) 1.55051 0.0652883
\(565\) −3.79796 37.5959i −0.159781 1.58167i
\(566\) 7.69694 0.323526
\(567\) 1.44949i 0.0608728i
\(568\) 13.3485i 0.560089i
\(569\) −0.348469 −0.0146086 −0.00730429 0.999973i \(-0.502325\pi\)
−0.00730429 + 0.999973i \(0.502325\pi\)
\(570\) −6.67423 + 0.674235i −0.279553 + 0.0282406i
\(571\) 0.449490 0.0188106 0.00940528 0.999956i \(-0.497006\pi\)
0.00940528 + 0.999956i \(0.497006\pi\)
\(572\) 18.7980i 0.785982i
\(573\) 23.6969i 0.989954i
\(574\) 6.44949 0.269197
\(575\) −1.00000 4.89898i −0.0417029 0.204302i
\(576\) 1.00000 0.0416667
\(577\) 0.696938i 0.0290139i 0.999895 + 0.0145070i \(0.00461787\pi\)
−0.999895 + 0.0145070i \(0.995382\pi\)
\(578\) 14.8990i 0.619716i
\(579\) 21.5959 0.897496
\(580\) 18.7980 1.89898i 0.780543 0.0788508i
\(581\) −5.00000 −0.207435
\(582\) 11.3485i 0.470409i
\(583\) 10.3485i 0.428590i
\(584\) −10.7980 −0.446823
\(585\) 1.22474 + 12.1237i 0.0506370 + 0.501254i
\(586\) −25.8990 −1.06988
\(587\) 22.2929i 0.920125i −0.887887 0.460062i \(-0.847827\pi\)
0.887887 0.460062i \(-0.152173\pi\)
\(588\) 4.89898i 0.202031i
\(589\) 6.00000 0.247226
\(590\) −2.55051 25.2474i −0.105003 1.03942i
\(591\) 1.20204 0.0494454
\(592\) 1.00000i 0.0410997i
\(593\) 24.0000i 0.985562i −0.870153 0.492781i \(-0.835980\pi\)
0.870153 0.492781i \(-0.164020\pi\)
\(594\) 3.44949 0.141534
\(595\) −4.67423 + 0.472194i −0.191625 + 0.0193580i
\(596\) −12.8990 −0.528363
\(597\) 2.20204i 0.0901235i
\(598\) 5.44949i 0.222846i
\(599\) −5.14643 −0.210277 −0.105139 0.994458i \(-0.533529\pi\)
−0.105139 + 0.994458i \(0.533529\pi\)
\(600\) −4.89898 + 1.00000i −0.200000 + 0.0408248i
\(601\) −7.00000 −0.285536 −0.142768 0.989756i \(-0.545600\pi\)
−0.142768 + 0.989756i \(0.545600\pi\)
\(602\) 4.20204i 0.171262i
\(603\) 2.89898i 0.118056i
\(604\) 17.2474 0.701789
\(605\) 2.00000 0.202041i 0.0813116 0.00821414i
\(606\) 10.0000 0.406222
\(607\) 29.1010i 1.18117i −0.806974 0.590587i \(-0.798896\pi\)
0.806974 0.590587i \(-0.201104\pi\)
\(608\) 3.00000i 0.121666i
\(609\) 12.2474 0.496292
\(610\) −1.14643 11.3485i −0.0464175 0.459486i
\(611\) −8.44949 −0.341830
\(612\) 1.44949i 0.0585922i
\(613\) 22.0000i 0.888572i −0.895885 0.444286i \(-0.853457\pi\)
0.895885 0.444286i \(-0.146543\pi\)
\(614\) −15.5505 −0.627568
\(615\) −1.00000 9.89898i −0.0403239 0.399165i
\(616\) 5.00000 0.201456
\(617\) 40.7423i 1.64023i 0.572202 + 0.820113i \(0.306089\pi\)
−0.572202 + 0.820113i \(0.693911\pi\)
\(618\) 14.2474i 0.573116i
\(619\) 18.4495 0.741548 0.370774 0.928723i \(-0.379093\pi\)
0.370774 + 0.928723i \(0.379093\pi\)
\(620\) 4.44949 0.449490i 0.178696 0.0180519i
\(621\) 1.00000 0.0401286
\(622\) 18.4949i 0.741578i
\(623\) 20.7980i 0.833253i
\(624\) −5.44949 −0.218154
\(625\) 23.0000 9.79796i 0.920000 0.391918i
\(626\) 18.4495 0.737390
\(627\) 10.3485i 0.413278i
\(628\) 4.00000i 0.159617i
\(629\) −1.44949 −0.0577949
\(630\) −3.22474 + 0.325765i −0.128477 + 0.0129788i
\(631\) −1.30306 −0.0518741 −0.0259370 0.999664i \(-0.508257\pi\)
−0.0259370 + 0.999664i \(0.508257\pi\)
\(632\) 1.34847i 0.0536392i
\(633\) 3.55051i 0.141120i
\(634\) 0.898979 0.0357030
\(635\) 2.37117 + 23.4722i 0.0940971 + 0.931466i
\(636\) −3.00000 −0.118958
\(637\) 26.6969i 1.05777i
\(638\) 29.1464i 1.15392i
\(639\) −13.3485 −0.528057
\(640\) −0.224745 2.22474i −0.00888382 0.0879408i
\(641\) −20.8990 −0.825460 −0.412730 0.910853i \(-0.635425\pi\)
−0.412730 + 0.910853i \(0.635425\pi\)
\(642\) 16.3485i 0.645223i
\(643\) 47.6969i 1.88098i 0.339816 + 0.940492i \(0.389635\pi\)
−0.339816 + 0.940492i \(0.610365\pi\)
\(644\) 1.44949 0.0571179
\(645\) −6.44949 + 0.651531i −0.253948 + 0.0256540i
\(646\) −4.34847 −0.171088
\(647\) 48.7980i 1.91845i −0.282651 0.959223i \(-0.591214\pi\)
0.282651 0.959223i \(-0.408786\pi\)
\(648\) 1.00000i 0.0392837i
\(649\) 39.1464 1.53663
\(650\) 26.6969 5.44949i 1.04714 0.213747i
\(651\) 2.89898 0.113620
\(652\) 11.8990i 0.466000i
\(653\) 5.30306i 0.207525i 0.994602 + 0.103762i \(0.0330882\pi\)
−0.994602 + 0.103762i \(0.966912\pi\)
\(654\) 12.3485 0.482863
\(655\) 34.5959 3.49490i 1.35177 0.136557i
\(656\) 4.44949 0.173723
\(657\) 10.7980i 0.421269i
\(658\) 2.24745i 0.0876147i
\(659\) −30.6969 −1.19578 −0.597891 0.801577i \(-0.703995\pi\)
−0.597891 + 0.801577i \(0.703995\pi\)
\(660\) −0.775255 7.67423i −0.0301768 0.298719i
\(661\) 13.9444 0.542374 0.271187 0.962527i \(-0.412584\pi\)
0.271187 + 0.962527i \(0.412584\pi\)
\(662\) 0.696938i 0.0270873i
\(663\) 7.89898i 0.306771i
\(664\) −3.44949 −0.133866
\(665\) 0.977296 + 9.67423i 0.0378979 + 0.375151i
\(666\) −1.00000 −0.0387492
\(667\) 8.44949i 0.327166i
\(668\) 18.7980i 0.727315i
\(669\) −23.5959 −0.912271
\(670\) 6.44949 0.651531i 0.249166 0.0251708i
\(671\) 17.5959 0.679283
\(672\) 1.44949i 0.0559153i
\(673\) 23.6969i 0.913450i −0.889608 0.456725i \(-0.849022\pi\)
0.889608 0.456725i \(-0.150978\pi\)
\(674\) 9.89898 0.381294
\(675\) 1.00000 + 4.89898i 0.0384900 + 0.188562i
\(676\) 16.6969 0.642190
\(677\) 7.00000i 0.269032i 0.990911 + 0.134516i \(0.0429479\pi\)
−0.990911 + 0.134516i \(0.957052\pi\)
\(678\) 16.8990i 0.649001i
\(679\) −16.4495 −0.631273
\(680\) −3.22474 + 0.325765i −0.123663 + 0.0124925i
\(681\) −8.00000 −0.306561
\(682\) 6.89898i 0.264176i
\(683\) 40.9444i 1.56669i 0.621585 + 0.783347i \(0.286489\pi\)
−0.621585 + 0.783347i \(0.713511\pi\)
\(684\) −3.00000 −0.114708
\(685\) 1.65153 + 16.3485i 0.0631017 + 0.624643i
\(686\) 17.2474 0.658511
\(687\) 6.44949i 0.246063i
\(688\) 2.89898i 0.110523i
\(689\) 16.3485 0.622827
\(690\) −0.224745 2.22474i −0.00855589 0.0846946i
\(691\) 4.85357 0.184639 0.0923193 0.995729i \(-0.470572\pi\)
0.0923193 + 0.995729i \(0.470572\pi\)
\(692\) 9.69694i 0.368622i
\(693\) 5.00000i 0.189934i
\(694\) −20.4495 −0.776252
\(695\) −28.2474 + 2.85357i −1.07149 + 0.108242i
\(696\) 8.44949 0.320277
\(697\) 6.44949i 0.244292i
\(698\) 3.14643i 0.119094i
\(699\) −6.89898 −0.260943
\(700\) 1.44949 + 7.10102i 0.0547856 + 0.268393i
\(701\) 3.59592 0.135816 0.0679080 0.997692i \(-0.478368\pi\)
0.0679080 + 0.997692i \(0.478368\pi\)
\(702\) 5.44949i 0.205678i
\(703\) 3.00000i 0.113147i
\(704\) 3.44949 0.130008
\(705\) −3.44949 + 0.348469i −0.129915 + 0.0131241i
\(706\) −12.6969 −0.477856
\(707\) 14.4949i 0.545137i
\(708\) 11.3485i 0.426502i
\(709\) −22.8434 −0.857901 −0.428950 0.903328i \(-0.641116\pi\)
−0.428950 + 0.903328i \(0.641116\pi\)
\(710\) 3.00000 + 29.6969i 0.112588 + 1.11451i
\(711\) −1.34847 −0.0505715
\(712\) 14.3485i 0.537732i
\(713\) 2.00000i 0.0749006i
\(714\) −2.10102 −0.0786287
\(715\) 4.22474 + 41.8207i 0.157997 + 1.56400i
\(716\) 6.69694 0.250276
\(717\) 2.00000i 0.0746914i
\(718\) 2.44949i 0.0914141i
\(719\) −26.2474 −0.978865 −0.489432 0.872041i \(-0.662796\pi\)
−0.489432 + 0.872041i \(0.662796\pi\)
\(720\) −2.22474 + 0.224745i −0.0829113 + 0.00837575i
\(721\) −20.6515 −0.769103
\(722\) 10.0000i 0.372161i
\(723\) 10.2474i 0.381107i
\(724\) 11.3485 0.421763
\(725\) −41.3939 + 8.44949i −1.53733 + 0.313806i
\(726\) 0.898979 0.0333643
\(727\) 31.8434i 1.18101i −0.807036 0.590503i \(-0.798930\pi\)
0.807036 0.590503i \(-0.201070\pi\)
\(728\) 7.89898i 0.292756i
\(729\) −1.00000 −0.0370370
\(730\) 24.0227 2.42679i 0.889120 0.0898194i
\(731\) −4.20204 −0.155418
\(732\) 5.10102i 0.188539i
\(733\) 45.5959i 1.68412i −0.539381 0.842062i \(-0.681342\pi\)
0.539381 0.842062i \(-0.318658\pi\)
\(734\) −0.752551 −0.0277772
\(735\) −1.10102 10.8990i −0.0406118 0.402015i
\(736\) 1.00000 0.0368605
\(737\) 10.0000i 0.368355i
\(738\) 4.44949i 0.163788i
\(739\) −31.7980 −1.16971 −0.584853 0.811139i \(-0.698848\pi\)
−0.584853 + 0.811139i \(0.698848\pi\)
\(740\) 0.224745 + 2.22474i 0.00826179 + 0.0817832i
\(741\) 16.3485 0.600576
\(742\) 4.34847i 0.159637i
\(743\) 4.04541i 0.148412i −0.997243 0.0742058i \(-0.976358\pi\)
0.997243 0.0742058i \(-0.0236422\pi\)
\(744\) 2.00000 0.0733236
\(745\) 28.6969 2.89898i 1.05137 0.106210i
\(746\) −31.8434 −1.16587
\(747\) 3.44949i 0.126210i
\(748\) 5.00000i 0.182818i
\(749\) 23.6969 0.865867
\(750\) 10.6742 3.32577i 0.389768 0.121440i
\(751\) 3.10102 0.113158 0.0565789 0.998398i \(-0.481981\pi\)
0.0565789 + 0.998398i \(0.481981\pi\)
\(752\) 1.55051i 0.0565413i
\(753\) 20.6969i 0.754238i
\(754\) −46.0454 −1.67687
\(755\) −38.3712 + 3.87628i −1.39647 + 0.141072i
\(756\) −1.44949 −0.0527174
\(757\) 3.04541i 0.110687i −0.998467 0.0553436i \(-0.982375\pi\)
0.998467 0.0553436i \(-0.0176254\pi\)
\(758\) 29.3485i 1.06598i
\(759\) 3.44949 0.125209
\(760\) 0.674235 + 6.67423i 0.0244571 + 0.242100i
\(761\) 33.1918 1.20320 0.601602 0.798796i \(-0.294530\pi\)
0.601602 + 0.798796i \(0.294530\pi\)
\(762\) 10.5505i 0.382205i
\(763\) 17.8990i 0.647987i
\(764\) −23.6969 −0.857325
\(765\) 0.325765 + 3.22474i 0.0117781 + 0.116591i
\(766\) 14.7980 0.534672
\(767\) 61.8434i 2.23303i
\(768\) 1.00000i 0.0360844i
\(769\) −3.55051 −0.128035 −0.0640173 0.997949i \(-0.520391\pi\)
−0.0640173 + 0.997949i \(0.520391\pi\)
\(770\) −11.1237 + 1.12372i −0.400871 + 0.0404962i
\(771\) −0.550510 −0.0198261
\(772\) 21.5959i 0.777254i
\(773\) 23.6969i 0.852320i 0.904648 + 0.426160i \(0.140134\pi\)
−0.904648 + 0.426160i \(0.859866\pi\)
\(774\) −2.89898 −0.104202
\(775\) −9.79796 + 2.00000i −0.351953 + 0.0718421i
\(776\) −11.3485 −0.407386
\(777\) 1.44949i 0.0520002i
\(778\) 19.7980i 0.709791i
\(779\) −13.3485 −0.478259
\(780\) 12.1237 1.22474i 0.434099 0.0438529i
\(781\)