Properties

Label 95.2.i.a.49.1
Level $95$
Weight $2$
Character 95.49
Analytic conductor $0.759$
Analytic rank $0$
Dimension $4$
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [95,2,Mod(49,95)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(95, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("95.49");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 95 = 5 \cdot 19 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 95.i (of order \(6\), degree \(2\), 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: \(0.758578819202\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 49.1
Root \(-0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 95.49
Dual form 95.2.i.a.64.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.73205 - 1.00000i) q^{2} +(1.00000 + 1.73205i) q^{4} +(2.23205 + 0.133975i) q^{5} -4.00000i q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(-1.73205 - 1.00000i) q^{2} +(1.00000 + 1.73205i) q^{4} +(2.23205 + 0.133975i) q^{5} -4.00000i q^{7} +(-1.50000 - 2.59808i) q^{9} +(-3.73205 - 2.46410i) q^{10} -1.00000 q^{11} +(1.73205 - 1.00000i) q^{13} +(-4.00000 + 6.92820i) q^{14} +(2.00000 - 3.46410i) q^{16} +(1.73205 + 1.00000i) q^{17} +6.00000i q^{18} +(3.50000 + 2.59808i) q^{19} +(2.00000 + 4.00000i) q^{20} +(1.73205 + 1.00000i) q^{22} +(-5.19615 + 3.00000i) q^{23} +(4.96410 + 0.598076i) q^{25} -4.00000 q^{26} +(6.92820 - 4.00000i) q^{28} +(4.50000 + 7.79423i) q^{29} -7.00000 q^{31} +(-6.92820 + 4.00000i) q^{32} +(-2.00000 - 3.46410i) q^{34} +(0.535898 - 8.92820i) q^{35} +(3.00000 - 5.19615i) q^{36} +2.00000i q^{37} +(-3.46410 - 8.00000i) q^{38} +(-1.00000 + 1.73205i) q^{41} +(1.73205 + 1.00000i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(-3.00000 - 6.00000i) q^{45} +12.0000 q^{46} +(5.19615 - 3.00000i) q^{47} -9.00000 q^{49} +(-8.00000 - 6.00000i) q^{50} +(3.46410 + 2.00000i) q^{52} +(-3.46410 + 2.00000i) q^{53} +(-2.23205 - 0.133975i) q^{55} -18.0000i q^{58} +(4.50000 - 7.79423i) q^{59} +(3.50000 + 6.06218i) q^{61} +(12.1244 + 7.00000i) q^{62} +(-10.3923 + 6.00000i) q^{63} +8.00000 q^{64} +(4.00000 - 2.00000i) q^{65} +(-8.66025 + 5.00000i) q^{67} +4.00000i q^{68} +(-9.85641 + 14.9282i) q^{70} +(-0.500000 + 0.866025i) q^{71} +(8.66025 + 5.00000i) q^{73} +(2.00000 - 3.46410i) q^{74} +(-1.00000 + 8.66025i) q^{76} +4.00000i q^{77} +(0.500000 - 0.866025i) q^{79} +(4.92820 - 7.46410i) q^{80} +(-4.50000 + 7.79423i) q^{81} +(3.46410 - 2.00000i) q^{82} +6.00000i q^{83} +(3.73205 + 2.46410i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-5.50000 - 9.52628i) q^{89} +(-0.803848 + 13.3923i) q^{90} +(-4.00000 - 6.92820i) q^{91} +(-10.3923 - 6.00000i) q^{92} -12.0000 q^{94} +(7.46410 + 6.26795i) q^{95} +(5.19615 + 3.00000i) q^{97} +(15.5885 + 9.00000i) q^{98} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{4} + 2 q^{5} - 6 q^{9} - 8 q^{10} - 4 q^{11} - 16 q^{14} + 8 q^{16} + 14 q^{19} + 8 q^{20} + 6 q^{25} - 16 q^{26} + 18 q^{29} - 28 q^{31} - 8 q^{34} + 16 q^{35} + 12 q^{36} - 4 q^{41} - 4 q^{44} - 12 q^{45} + 48 q^{46} - 36 q^{49} - 32 q^{50} - 2 q^{55} + 18 q^{59} + 14 q^{61} + 32 q^{64} + 16 q^{65} + 16 q^{70} - 2 q^{71} + 8 q^{74} - 4 q^{76} + 2 q^{79} - 8 q^{80} - 18 q^{81} + 8 q^{85} - 8 q^{86} - 22 q^{89} - 24 q^{90} - 16 q^{91} - 48 q^{94} + 16 q^{95} + 6 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/95\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(77\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.73205 1.00000i −1.22474 0.707107i −0.258819 0.965926i \(-0.583333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(3\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(4\) 1.00000 + 1.73205i 0.500000 + 0.866025i
\(5\) 2.23205 + 0.133975i 0.998203 + 0.0599153i
\(6\) 0 0
\(7\) 4.00000i 1.51186i −0.654654 0.755929i \(-0.727186\pi\)
0.654654 0.755929i \(-0.272814\pi\)
\(8\) 0 0
\(9\) −1.50000 2.59808i −0.500000 0.866025i
\(10\) −3.73205 2.46410i −1.18018 0.779217i
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) 1.73205 1.00000i 0.480384 0.277350i −0.240192 0.970725i \(-0.577210\pi\)
0.720577 + 0.693375i \(0.243877\pi\)
\(14\) −4.00000 + 6.92820i −1.06904 + 1.85164i
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) 1.73205 + 1.00000i 0.420084 + 0.242536i 0.695113 0.718900i \(-0.255354\pi\)
−0.275029 + 0.961436i \(0.588688\pi\)
\(18\) 6.00000i 1.41421i
\(19\) 3.50000 + 2.59808i 0.802955 + 0.596040i
\(20\) 2.00000 + 4.00000i 0.447214 + 0.894427i
\(21\) 0 0
\(22\) 1.73205 + 1.00000i 0.369274 + 0.213201i
\(23\) −5.19615 + 3.00000i −1.08347 + 0.625543i −0.931831 0.362892i \(-0.881789\pi\)
−0.151642 + 0.988436i \(0.548456\pi\)
\(24\) 0 0
\(25\) 4.96410 + 0.598076i 0.992820 + 0.119615i
\(26\) −4.00000 −0.784465
\(27\) 0 0
\(28\) 6.92820 4.00000i 1.30931 0.755929i
\(29\) 4.50000 + 7.79423i 0.835629 + 1.44735i 0.893517 + 0.449029i \(0.148230\pi\)
−0.0578882 + 0.998323i \(0.518437\pi\)
\(30\) 0 0
\(31\) −7.00000 −1.25724 −0.628619 0.777714i \(-0.716379\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) −6.92820 + 4.00000i −1.22474 + 0.707107i
\(33\) 0 0
\(34\) −2.00000 3.46410i −0.342997 0.594089i
\(35\) 0.535898 8.92820i 0.0905834 1.50914i
\(36\) 3.00000 5.19615i 0.500000 0.866025i
\(37\) 2.00000i 0.328798i 0.986394 + 0.164399i \(0.0525685\pi\)
−0.986394 + 0.164399i \(0.947432\pi\)
\(38\) −3.46410 8.00000i −0.561951 1.29777i
\(39\) 0 0
\(40\) 0 0
\(41\) −1.00000 + 1.73205i −0.156174 + 0.270501i −0.933486 0.358614i \(-0.883249\pi\)
0.777312 + 0.629115i \(0.216583\pi\)
\(42\) 0 0
\(43\) 1.73205 + 1.00000i 0.264135 + 0.152499i 0.626219 0.779647i \(-0.284601\pi\)
−0.362084 + 0.932145i \(0.617935\pi\)
\(44\) −1.00000 1.73205i −0.150756 0.261116i
\(45\) −3.00000 6.00000i −0.447214 0.894427i
\(46\) 12.0000 1.76930
\(47\) 5.19615 3.00000i 0.757937 0.437595i −0.0706177 0.997503i \(-0.522497\pi\)
0.828554 + 0.559908i \(0.189164\pi\)
\(48\) 0 0
\(49\) −9.00000 −1.28571
\(50\) −8.00000 6.00000i −1.13137 0.848528i
\(51\) 0 0
\(52\) 3.46410 + 2.00000i 0.480384 + 0.277350i
\(53\) −3.46410 + 2.00000i −0.475831 + 0.274721i −0.718677 0.695344i \(-0.755252\pi\)
0.242846 + 0.970065i \(0.421919\pi\)
\(54\) 0 0
\(55\) −2.23205 0.133975i −0.300970 0.0180651i
\(56\) 0 0
\(57\) 0 0
\(58\) 18.0000i 2.36352i
\(59\) 4.50000 7.79423i 0.585850 1.01472i −0.408919 0.912571i \(-0.634094\pi\)
0.994769 0.102151i \(-0.0325726\pi\)
\(60\) 0 0
\(61\) 3.50000 + 6.06218i 0.448129 + 0.776182i 0.998264 0.0588933i \(-0.0187572\pi\)
−0.550135 + 0.835076i \(0.685424\pi\)
\(62\) 12.1244 + 7.00000i 1.53979 + 0.889001i
\(63\) −10.3923 + 6.00000i −1.30931 + 0.755929i
\(64\) 8.00000 1.00000
\(65\) 4.00000 2.00000i 0.496139 0.248069i
\(66\) 0 0
\(67\) −8.66025 + 5.00000i −1.05802 + 0.610847i −0.924883 0.380251i \(-0.875838\pi\)
−0.133135 + 0.991098i \(0.542504\pi\)
\(68\) 4.00000i 0.485071i
\(69\) 0 0
\(70\) −9.85641 + 14.9282i −1.17807 + 1.78426i
\(71\) −0.500000 + 0.866025i −0.0593391 + 0.102778i −0.894169 0.447730i \(-0.852233\pi\)
0.834830 + 0.550508i \(0.185566\pi\)
\(72\) 0 0
\(73\) 8.66025 + 5.00000i 1.01361 + 0.585206i 0.912245 0.409644i \(-0.134347\pi\)
0.101361 + 0.994850i \(0.467680\pi\)
\(74\) 2.00000 3.46410i 0.232495 0.402694i
\(75\) 0 0
\(76\) −1.00000 + 8.66025i −0.114708 + 0.993399i
\(77\) 4.00000i 0.455842i
\(78\) 0 0
\(79\) 0.500000 0.866025i 0.0562544 0.0974355i −0.836527 0.547926i \(-0.815418\pi\)
0.892781 + 0.450490i \(0.148751\pi\)
\(80\) 4.92820 7.46410i 0.550990 0.834512i
\(81\) −4.50000 + 7.79423i −0.500000 + 0.866025i
\(82\) 3.46410 2.00000i 0.382546 0.220863i
\(83\) 6.00000i 0.658586i 0.944228 + 0.329293i \(0.106810\pi\)
−0.944228 + 0.329293i \(0.893190\pi\)
\(84\) 0 0
\(85\) 3.73205 + 2.46410i 0.404798 + 0.267269i
\(86\) −2.00000 3.46410i −0.215666 0.373544i
\(87\) 0 0
\(88\) 0 0
\(89\) −5.50000 9.52628i −0.582999 1.00978i −0.995122 0.0986553i \(-0.968546\pi\)
0.412123 0.911128i \(-0.364787\pi\)
\(90\) −0.803848 + 13.3923i −0.0847330 + 1.41167i
\(91\) −4.00000 6.92820i −0.419314 0.726273i
\(92\) −10.3923 6.00000i −1.08347 0.625543i
\(93\) 0 0
\(94\) −12.0000 −1.23771
\(95\) 7.46410 + 6.26795i 0.765801 + 0.643078i
\(96\) 0 0
\(97\) 5.19615 + 3.00000i 0.527589 + 0.304604i 0.740034 0.672569i \(-0.234809\pi\)
−0.212445 + 0.977173i \(0.568143\pi\)
\(98\) 15.5885 + 9.00000i 1.57467 + 0.909137i
\(99\) 1.50000 + 2.59808i 0.150756 + 0.261116i
\(100\) 3.92820 + 9.19615i 0.392820 + 0.919615i
\(101\) −7.50000 12.9904i −0.746278 1.29259i −0.949595 0.313478i \(-0.898506\pi\)
0.203317 0.979113i \(-0.434828\pi\)
\(102\) 0 0
\(103\) 16.0000i 1.57653i −0.615338 0.788263i \(-0.710980\pi\)
0.615338 0.788263i \(-0.289020\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 8.00000 0.777029
\(107\) 10.0000i 0.966736i −0.875417 0.483368i \(-0.839413\pi\)
0.875417 0.483368i \(-0.160587\pi\)
\(108\) 0 0
\(109\) 7.50000 12.9904i 0.718370 1.24425i −0.243276 0.969957i \(-0.578222\pi\)
0.961645 0.274296i \(-0.0884447\pi\)
\(110\) 3.73205 + 2.46410i 0.355837 + 0.234943i
\(111\) 0 0
\(112\) −13.8564 8.00000i −1.30931 0.755929i
\(113\) 12.0000i 1.12887i 0.825479 + 0.564433i \(0.190905\pi\)
−0.825479 + 0.564433i \(0.809095\pi\)
\(114\) 0 0
\(115\) −12.0000 + 6.00000i −1.11901 + 0.559503i
\(116\) −9.00000 + 15.5885i −0.835629 + 1.44735i
\(117\) −5.19615 3.00000i −0.480384 0.277350i
\(118\) −15.5885 + 9.00000i −1.43503 + 0.828517i
\(119\) 4.00000 6.92820i 0.366679 0.635107i
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 14.0000i 1.26750i
\(123\) 0 0
\(124\) −7.00000 12.1244i −0.628619 1.08880i
\(125\) 11.0000 + 2.00000i 0.983870 + 0.178885i
\(126\) 24.0000 2.13809
\(127\) −5.19615 + 3.00000i −0.461084 + 0.266207i −0.712500 0.701672i \(-0.752437\pi\)
0.251416 + 0.967879i \(0.419104\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) −8.92820 0.535898i −0.783055 0.0470014i
\(131\) −6.00000 + 10.3923i −0.524222 + 0.907980i 0.475380 + 0.879781i \(0.342311\pi\)
−0.999602 + 0.0281993i \(0.991023\pi\)
\(132\) 0 0
\(133\) 10.3923 14.0000i 0.901127 1.21395i
\(134\) 20.0000 1.72774
\(135\) 0 0
\(136\) 0 0
\(137\) 10.3923 6.00000i 0.887875 0.512615i 0.0146279 0.999893i \(-0.495344\pi\)
0.873247 + 0.487278i \(0.162010\pi\)
\(138\) 0 0
\(139\) 10.0000 + 17.3205i 0.848189 + 1.46911i 0.882823 + 0.469706i \(0.155640\pi\)
−0.0346338 + 0.999400i \(0.511026\pi\)
\(140\) 16.0000 8.00000i 1.35225 0.676123i
\(141\) 0 0
\(142\) 1.73205 1.00000i 0.145350 0.0839181i
\(143\) −1.73205 + 1.00000i −0.144841 + 0.0836242i
\(144\) −12.0000 −1.00000
\(145\) 9.00000 + 18.0000i 0.747409 + 1.49482i
\(146\) −10.0000 17.3205i −0.827606 1.43346i
\(147\) 0 0
\(148\) −3.46410 + 2.00000i −0.284747 + 0.164399i
\(149\) −0.500000 + 0.866025i −0.0409616 + 0.0709476i −0.885779 0.464107i \(-0.846375\pi\)
0.844818 + 0.535054i \(0.179709\pi\)
\(150\) 0 0
\(151\) 9.00000 0.732410 0.366205 0.930534i \(-0.380657\pi\)
0.366205 + 0.930534i \(0.380657\pi\)
\(152\) 0 0
\(153\) 6.00000i 0.485071i
\(154\) 4.00000 6.92820i 0.322329 0.558291i
\(155\) −15.6244 0.937822i −1.25498 0.0753277i
\(156\) 0 0
\(157\) −3.46410 2.00000i −0.276465 0.159617i 0.355357 0.934731i \(-0.384359\pi\)
−0.631822 + 0.775113i \(0.717693\pi\)
\(158\) −1.73205 + 1.00000i −0.137795 + 0.0795557i
\(159\) 0 0
\(160\) −16.0000 + 8.00000i −1.26491 + 0.632456i
\(161\) 12.0000 + 20.7846i 0.945732 + 1.63806i
\(162\) 15.5885 9.00000i 1.22474 0.707107i
\(163\) 4.00000i 0.313304i −0.987654 0.156652i \(-0.949930\pi\)
0.987654 0.156652i \(-0.0500701\pi\)
\(164\) −4.00000 −0.312348
\(165\) 0 0
\(166\) 6.00000 10.3923i 0.465690 0.806599i
\(167\) −10.3923 + 6.00000i −0.804181 + 0.464294i −0.844931 0.534875i \(-0.820359\pi\)
0.0407502 + 0.999169i \(0.487025\pi\)
\(168\) 0 0
\(169\) −4.50000 + 7.79423i −0.346154 + 0.599556i
\(170\) −4.00000 8.00000i −0.306786 0.613572i
\(171\) 1.50000 12.9904i 0.114708 0.993399i
\(172\) 4.00000i 0.304997i
\(173\) −20.7846 12.0000i −1.58022 0.912343i −0.994826 0.101598i \(-0.967605\pi\)
−0.585399 0.810745i \(-0.699062\pi\)
\(174\) 0 0
\(175\) 2.39230 19.8564i 0.180841 1.50100i
\(176\) −2.00000 + 3.46410i −0.150756 + 0.261116i
\(177\) 0 0
\(178\) 22.0000i 1.64897i
\(179\) −15.0000 −1.12115 −0.560576 0.828103i \(-0.689420\pi\)
−0.560576 + 0.828103i \(0.689420\pi\)
\(180\) 7.39230 11.1962i 0.550990 0.834512i
\(181\) 3.00000 + 5.19615i 0.222988 + 0.386227i 0.955714 0.294297i \(-0.0950855\pi\)
−0.732726 + 0.680524i \(0.761752\pi\)
\(182\) 16.0000i 1.18600i
\(183\) 0 0
\(184\) 0 0
\(185\) −0.267949 + 4.46410i −0.0197000 + 0.328207i
\(186\) 0 0
\(187\) −1.73205 1.00000i −0.126660 0.0731272i
\(188\) 10.3923 + 6.00000i 0.757937 + 0.437595i
\(189\) 0 0
\(190\) −6.66025 18.3205i −0.483186 1.32911i
\(191\) −3.00000 −0.217072 −0.108536 0.994092i \(-0.534616\pi\)
−0.108536 + 0.994092i \(0.534616\pi\)
\(192\) 0 0
\(193\) 13.8564 + 8.00000i 0.997406 + 0.575853i 0.907480 0.420096i \(-0.138004\pi\)
0.0899262 + 0.995948i \(0.471337\pi\)
\(194\) −6.00000 10.3923i −0.430775 0.746124i
\(195\) 0 0
\(196\) −9.00000 15.5885i −0.642857 1.11346i
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 6.00000i 0.426401i
\(199\) 6.50000 + 11.2583i 0.460773 + 0.798082i 0.999000 0.0447181i \(-0.0142390\pi\)
−0.538227 + 0.842800i \(0.680906\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 30.0000i 2.11079i
\(203\) 31.1769 18.0000i 2.18819 1.26335i
\(204\) 0 0
\(205\) −2.46410 + 3.73205i −0.172100 + 0.260658i
\(206\) −16.0000 + 27.7128i −1.11477 + 1.93084i
\(207\) 15.5885 + 9.00000i 1.08347 + 0.625543i
\(208\) 8.00000i 0.554700i
\(209\) −3.50000 2.59808i −0.242100 0.179713i
\(210\) 0 0
\(211\) −2.50000 + 4.33013i −0.172107 + 0.298098i −0.939156 0.343490i \(-0.888391\pi\)
0.767049 + 0.641588i \(0.221724\pi\)
\(212\) −6.92820 4.00000i −0.475831 0.274721i
\(213\) 0 0
\(214\) −10.0000 + 17.3205i −0.683586 + 1.18401i
\(215\) 3.73205 + 2.46410i 0.254524 + 0.168050i
\(216\) 0 0
\(217\) 28.0000i 1.90076i
\(218\) −25.9808 + 15.0000i −1.75964 + 1.01593i
\(219\) 0 0
\(220\) −2.00000 4.00000i −0.134840 0.269680i
\(221\) 4.00000 0.269069
\(222\) 0 0
\(223\) −1.73205 1.00000i −0.115987 0.0669650i 0.440884 0.897564i \(-0.354665\pi\)
−0.556871 + 0.830599i \(0.687998\pi\)
\(224\) 16.0000 + 27.7128i 1.06904 + 1.85164i
\(225\) −5.89230 13.7942i −0.392820 0.919615i
\(226\) 12.0000 20.7846i 0.798228 1.38257i
\(227\) 14.0000i 0.929213i 0.885517 + 0.464606i \(0.153804\pi\)
−0.885517 + 0.464606i \(0.846196\pi\)
\(228\) 0 0
\(229\) −17.0000 −1.12339 −0.561696 0.827344i \(-0.689851\pi\)
−0.561696 + 0.827344i \(0.689851\pi\)
\(230\) 26.7846 + 1.60770i 1.76612 + 0.106008i
\(231\) 0 0
\(232\) 0 0
\(233\) −6.92820 4.00000i −0.453882 0.262049i 0.255586 0.966786i \(-0.417731\pi\)
−0.709468 + 0.704737i \(0.751065\pi\)
\(234\) 6.00000 + 10.3923i 0.392232 + 0.679366i
\(235\) 12.0000 6.00000i 0.782794 0.391397i
\(236\) 18.0000 1.17170
\(237\) 0 0
\(238\) −13.8564 + 8.00000i −0.898177 + 0.518563i
\(239\) 19.0000 1.22901 0.614504 0.788914i \(-0.289356\pi\)
0.614504 + 0.788914i \(0.289356\pi\)
\(240\) 0 0
\(241\) −0.500000 0.866025i −0.0322078 0.0557856i 0.849472 0.527633i \(-0.176921\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(242\) 17.3205 + 10.0000i 1.11340 + 0.642824i
\(243\) 0 0
\(244\) −7.00000 + 12.1244i −0.448129 + 0.776182i
\(245\) −20.0885 1.20577i −1.28340 0.0770339i
\(246\) 0 0
\(247\) 8.66025 + 1.00000i 0.551039 + 0.0636285i
\(248\) 0 0
\(249\) 0 0
\(250\) −17.0526 14.4641i −1.07850 0.914790i
\(251\) −6.50000 11.2583i −0.410276 0.710620i 0.584643 0.811290i \(-0.301234\pi\)
−0.994920 + 0.100671i \(0.967901\pi\)
\(252\) −20.7846 12.0000i −1.30931 0.755929i
\(253\) 5.19615 3.00000i 0.326679 0.188608i
\(254\) 12.0000 0.752947
\(255\) 0 0
\(256\) −8.00000 13.8564i −0.500000 0.866025i
\(257\) −5.19615 + 3.00000i −0.324127 + 0.187135i −0.653231 0.757159i \(-0.726587\pi\)
0.329104 + 0.944294i \(0.393253\pi\)
\(258\) 0 0
\(259\) 8.00000 0.497096
\(260\) 7.46410 + 4.92820i 0.462904 + 0.305634i
\(261\) 13.5000 23.3827i 0.835629 1.44735i
\(262\) 20.7846 12.0000i 1.28408 0.741362i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) 0 0
\(265\) −8.00000 + 4.00000i −0.491436 + 0.245718i
\(266\) −32.0000 + 13.8564i −1.96205 + 0.849591i
\(267\) 0 0
\(268\) −17.3205 10.0000i −1.05802 0.610847i
\(269\) 1.50000 2.59808i 0.0914566 0.158408i −0.816668 0.577108i \(-0.804181\pi\)
0.908124 + 0.418701i \(0.137514\pi\)
\(270\) 0 0
\(271\) −1.50000 + 2.59808i −0.0911185 + 0.157822i −0.907982 0.419009i \(-0.862378\pi\)
0.816864 + 0.576831i \(0.195711\pi\)
\(272\) 6.92820 4.00000i 0.420084 0.242536i
\(273\) 0 0
\(274\) −24.0000 −1.44989
\(275\) −4.96410 0.598076i −0.299347 0.0360654i
\(276\) 0 0
\(277\) 28.0000i 1.68236i −0.540758 0.841178i \(-0.681862\pi\)
0.540758 0.841178i \(-0.318138\pi\)
\(278\) 40.0000i 2.39904i
\(279\) 10.5000 + 18.1865i 0.628619 + 1.08880i
\(280\) 0 0
\(281\) −5.00000 8.66025i −0.298275 0.516627i 0.677466 0.735554i \(-0.263078\pi\)
−0.975741 + 0.218926i \(0.929745\pi\)
\(282\) 0 0
\(283\) 12.1244 + 7.00000i 0.720718 + 0.416107i 0.815017 0.579437i \(-0.196728\pi\)
−0.0942988 + 0.995544i \(0.530061\pi\)
\(284\) −2.00000 −0.118678
\(285\) 0 0
\(286\) 4.00000 0.236525
\(287\) 6.92820 + 4.00000i 0.408959 + 0.236113i
\(288\) 20.7846 + 12.0000i 1.22474 + 0.707107i
\(289\) −6.50000 11.2583i −0.382353 0.662255i
\(290\) 2.41154 40.1769i 0.141611 2.35927i
\(291\) 0 0
\(292\) 20.0000i 1.17041i
\(293\) 4.00000i 0.233682i −0.993151 0.116841i \(-0.962723\pi\)
0.993151 0.116841i \(-0.0372769\pi\)
\(294\) 0 0
\(295\) 11.0885 16.7942i 0.645595 0.977798i
\(296\) 0 0
\(297\) 0 0
\(298\) 1.73205 1.00000i 0.100335 0.0579284i
\(299\) −6.00000 + 10.3923i −0.346989 + 0.601003i
\(300\) 0 0
\(301\) 4.00000 6.92820i 0.230556 0.399335i
\(302\) −15.5885 9.00000i −0.897015 0.517892i
\(303\) 0 0
\(304\) 16.0000 6.92820i 0.917663 0.397360i
\(305\) 7.00000 + 14.0000i 0.400819 + 0.801638i
\(306\) −6.00000 + 10.3923i −0.342997 + 0.594089i
\(307\) −13.8564 8.00000i −0.790827 0.456584i 0.0494267 0.998778i \(-0.484261\pi\)
−0.840254 + 0.542194i \(0.817594\pi\)
\(308\) −6.92820 + 4.00000i −0.394771 + 0.227921i
\(309\) 0 0
\(310\) 26.1244 + 17.2487i 1.48376 + 0.979661i
\(311\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(312\) 0 0
\(313\) −25.9808 + 15.0000i −1.46852 + 0.847850i −0.999378 0.0352727i \(-0.988770\pi\)
−0.469142 + 0.883123i \(0.655437\pi\)
\(314\) 4.00000 + 6.92820i 0.225733 + 0.390981i
\(315\) −24.0000 + 12.0000i −1.35225 + 0.676123i
\(316\) 2.00000 0.112509
\(317\) −1.73205 + 1.00000i −0.0972817 + 0.0561656i −0.547852 0.836576i \(-0.684554\pi\)
0.450570 + 0.892741i \(0.351221\pi\)
\(318\) 0 0
\(319\) −4.50000 7.79423i −0.251952 0.436393i
\(320\) 17.8564 + 1.07180i 0.998203 + 0.0599153i
\(321\) 0 0
\(322\) 48.0000i 2.67494i
\(323\) 3.46410 + 8.00000i 0.192748 + 0.445132i
\(324\) −18.0000 −1.00000
\(325\) 9.19615 3.92820i 0.510111 0.217898i
\(326\) −4.00000 + 6.92820i −0.221540 + 0.383718i
\(327\) 0 0
\(328\) 0 0
\(329\) −12.0000 20.7846i −0.661581 1.14589i
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) −10.3923 + 6.00000i −0.570352 + 0.329293i
\(333\) 5.19615 3.00000i 0.284747 0.164399i
\(334\) 24.0000 1.31322
\(335\) −20.0000 + 10.0000i −1.09272 + 0.546358i
\(336\) 0 0
\(337\) −29.4449 17.0000i −1.60396 0.926049i −0.990684 0.136184i \(-0.956516\pi\)
−0.613280 0.789865i \(-0.710150\pi\)
\(338\) 15.5885 9.00000i 0.847900 0.489535i
\(339\) 0 0
\(340\) −0.535898 + 8.92820i −0.0290632 + 0.484200i
\(341\) 7.00000 0.379071
\(342\) −15.5885 + 21.0000i −0.842927 + 1.13555i
\(343\) 8.00000i 0.431959i
\(344\) 0 0
\(345\) 0 0
\(346\) 24.0000 + 41.5692i 1.29025 + 2.23478i
\(347\) 10.3923 + 6.00000i 0.557888 + 0.322097i 0.752297 0.658824i \(-0.228946\pi\)
−0.194409 + 0.980921i \(0.562279\pi\)
\(348\) 0 0
\(349\) −14.0000 −0.749403 −0.374701 0.927146i \(-0.622255\pi\)
−0.374701 + 0.927146i \(0.622255\pi\)
\(350\) −24.0000 + 32.0000i −1.28285 + 1.71047i
\(351\) 0 0
\(352\) 6.92820 4.00000i 0.369274 0.213201i
\(353\) 8.00000i 0.425797i 0.977074 + 0.212899i \(0.0682904\pi\)
−0.977074 + 0.212899i \(0.931710\pi\)
\(354\) 0 0
\(355\) −1.23205 + 1.86603i −0.0653905 + 0.0990383i
\(356\) 11.0000 19.0526i 0.582999 1.00978i
\(357\) 0 0
\(358\) 25.9808 + 15.0000i 1.37313 + 0.792775i
\(359\) −10.0000 + 17.3205i −0.527780 + 0.914141i 0.471696 + 0.881761i \(0.343642\pi\)
−0.999476 + 0.0323801i \(0.989691\pi\)
\(360\) 0 0
\(361\) 5.50000 + 18.1865i 0.289474 + 0.957186i
\(362\) 12.0000i 0.630706i
\(363\) 0 0
\(364\) 8.00000 13.8564i 0.419314 0.726273i
\(365\) 18.6603 + 12.3205i 0.976722 + 0.644885i
\(366\) 0 0
\(367\) −13.8564 + 8.00000i −0.723299 + 0.417597i −0.815966 0.578101i \(-0.803794\pi\)
0.0926670 + 0.995697i \(0.470461\pi\)
\(368\) 24.0000i 1.25109i
\(369\) 6.00000 0.312348
\(370\) 4.92820 7.46410i 0.256205 0.388040i
\(371\) 8.00000 + 13.8564i 0.415339 + 0.719389i
\(372\) 0 0
\(373\) 12.0000i 0.621336i 0.950518 + 0.310668i \(0.100553\pi\)
−0.950518 + 0.310668i \(0.899447\pi\)
\(374\) 2.00000 + 3.46410i 0.103418 + 0.179124i
\(375\) 0 0
\(376\) 0 0
\(377\) 15.5885 + 9.00000i 0.802846 + 0.463524i
\(378\) 0 0
\(379\) 29.0000 1.48963 0.744815 0.667271i \(-0.232538\pi\)
0.744815 + 0.667271i \(0.232538\pi\)
\(380\) −3.39230 + 19.1962i −0.174022 + 0.984742i
\(381\) 0 0
\(382\) 5.19615 + 3.00000i 0.265858 + 0.153493i
\(383\) 5.19615 + 3.00000i 0.265511 + 0.153293i 0.626846 0.779143i \(-0.284346\pi\)
−0.361335 + 0.932436i \(0.617679\pi\)
\(384\) 0 0
\(385\) −0.535898 + 8.92820i −0.0273119 + 0.455023i
\(386\) −16.0000 27.7128i −0.814379 1.41055i
\(387\) 6.00000i 0.304997i
\(388\) 12.0000i 0.609208i
\(389\) −16.5000 28.5788i −0.836583 1.44900i −0.892735 0.450582i \(-0.851216\pi\)
0.0561516 0.998422i \(-0.482117\pi\)
\(390\) 0 0
\(391\) −12.0000 −0.606866
\(392\) 0 0
\(393\) 0 0
\(394\) −18.0000 + 31.1769i −0.906827 + 1.57067i
\(395\) 1.23205 1.86603i 0.0619912 0.0938899i
\(396\) −3.00000 + 5.19615i −0.150756 + 0.261116i
\(397\) 6.92820 + 4.00000i 0.347717 + 0.200754i 0.663679 0.748017i \(-0.268994\pi\)
−0.315963 + 0.948772i \(0.602327\pi\)
\(398\) 26.0000i 1.30326i
\(399\) 0 0
\(400\) 12.0000 16.0000i 0.600000 0.800000i
\(401\) −1.50000 + 2.59808i −0.0749064 + 0.129742i −0.901046 0.433724i \(-0.857199\pi\)
0.826139 + 0.563466i \(0.190532\pi\)
\(402\) 0 0
\(403\) −12.1244 + 7.00000i −0.603957 + 0.348695i
\(404\) 15.0000 25.9808i 0.746278 1.29259i
\(405\) −11.0885 + 16.7942i −0.550990 + 0.834512i
\(406\) −72.0000 −3.57330
\(407\) 2.00000i 0.0991363i
\(408\) 0 0
\(409\) −2.50000 4.33013i −0.123617 0.214111i 0.797574 0.603220i \(-0.206116\pi\)
−0.921192 + 0.389109i \(0.872783\pi\)
\(410\) 8.00000 4.00000i 0.395092 0.197546i
\(411\) 0 0
\(412\) 27.7128 16.0000i 1.36531 0.788263i
\(413\) −31.1769 18.0000i −1.53412 0.885722i
\(414\) −18.0000 31.1769i −0.884652 1.53226i
\(415\) −0.803848 + 13.3923i −0.0394593 + 0.657402i
\(416\) −8.00000 + 13.8564i −0.392232 + 0.679366i
\(417\) 0 0
\(418\) 3.46410 + 8.00000i 0.169435 + 0.391293i
\(419\) −9.00000 −0.439679 −0.219839 0.975536i \(-0.570553\pi\)
−0.219839 + 0.975536i \(0.570553\pi\)
\(420\) 0 0
\(421\) 7.50000 12.9904i 0.365528 0.633112i −0.623333 0.781956i \(-0.714222\pi\)
0.988861 + 0.148844i \(0.0475552\pi\)
\(422\) 8.66025 5.00000i 0.421575 0.243396i
\(423\) −15.5885 9.00000i −0.757937 0.437595i
\(424\) 0 0
\(425\) 8.00000 + 6.00000i 0.388057 + 0.291043i
\(426\) 0 0
\(427\) 24.2487 14.0000i 1.17348 0.677507i
\(428\) 17.3205 10.0000i 0.837218 0.483368i
\(429\) 0 0
\(430\) −4.00000 8.00000i −0.192897 0.385794i
\(431\) −10.5000 18.1865i −0.505767 0.876014i −0.999978 0.00667224i \(-0.997876\pi\)
0.494211 0.869342i \(-0.335457\pi\)
\(432\) 0 0
\(433\) 3.46410 2.00000i 0.166474 0.0961139i −0.414448 0.910073i \(-0.636025\pi\)
0.580922 + 0.813959i \(0.302692\pi\)
\(434\) 28.0000 48.4974i 1.34404 2.32795i
\(435\) 0 0
\(436\) 30.0000 1.43674
\(437\) −25.9808 3.00000i −1.24283 0.143509i
\(438\) 0 0
\(439\) −6.50000 + 11.2583i −0.310228 + 0.537331i −0.978412 0.206666i \(-0.933739\pi\)
0.668184 + 0.743996i \(0.267072\pi\)
\(440\) 0 0
\(441\) 13.5000 + 23.3827i 0.642857 + 1.11346i
\(442\) −6.92820 4.00000i −0.329541 0.190261i
\(443\) −3.46410 + 2.00000i −0.164584 + 0.0950229i −0.580030 0.814595i \(-0.696959\pi\)
0.415445 + 0.909618i \(0.363626\pi\)
\(444\) 0 0
\(445\) −11.0000 22.0000i −0.521450 1.04290i
\(446\) 2.00000 + 3.46410i 0.0947027 + 0.164030i
\(447\) 0 0
\(448\) 32.0000i 1.51186i
\(449\) −31.0000 −1.46298 −0.731490 0.681852i \(-0.761175\pi\)
−0.731490 + 0.681852i \(0.761175\pi\)
\(450\) −3.58846 + 29.7846i −0.169161 + 1.40406i
\(451\) 1.00000 1.73205i 0.0470882 0.0815591i
\(452\) −20.7846 + 12.0000i −0.977626 + 0.564433i
\(453\) 0 0
\(454\) 14.0000 24.2487i 0.657053 1.13805i
\(455\) −8.00000 16.0000i −0.375046 0.750092i
\(456\) 0 0
\(457\) 34.0000i 1.59045i 0.606313 + 0.795226i \(0.292648\pi\)
−0.606313 + 0.795226i \(0.707352\pi\)
\(458\) 29.4449 + 17.0000i 1.37587 + 0.794358i
\(459\) 0 0
\(460\) −22.3923 14.7846i −1.04405 0.689336i
\(461\) 12.5000 21.6506i 0.582183 1.00837i −0.413037 0.910714i \(-0.635532\pi\)
0.995220 0.0976564i \(-0.0311346\pi\)
\(462\) 0 0
\(463\) 4.00000i 0.185896i 0.995671 + 0.0929479i \(0.0296290\pi\)
−0.995671 + 0.0929479i \(0.970371\pi\)
\(464\) 36.0000 1.67126
\(465\) 0 0
\(466\) 8.00000 + 13.8564i 0.370593 + 0.641886i
\(467\) 10.0000i 0.462745i 0.972865 + 0.231372i \(0.0743216\pi\)
−0.972865 + 0.231372i \(0.925678\pi\)
\(468\) 12.0000i 0.554700i
\(469\) 20.0000 + 34.6410i 0.923514 + 1.59957i
\(470\) −26.7846 1.60770i −1.23548 0.0741574i
\(471\) 0 0
\(472\) 0 0
\(473\) −1.73205 1.00000i −0.0796398 0.0459800i
\(474\) 0 0
\(475\) 15.8205 + 14.9904i 0.725895 + 0.687806i
\(476\) 16.0000 0.733359
\(477\) 10.3923 + 6.00000i 0.475831 + 0.274721i
\(478\) −32.9090 19.0000i −1.50522 0.869040i
\(479\) 7.50000 + 12.9904i 0.342684 + 0.593546i 0.984930 0.172953i \(-0.0553307\pi\)
−0.642246 + 0.766498i \(0.721997\pi\)
\(480\) 0 0
\(481\) 2.00000 + 3.46410i 0.0911922 + 0.157949i
\(482\) 2.00000i 0.0910975i
\(483\) 0 0
\(484\) −10.0000 17.3205i −0.454545 0.787296i
\(485\) 11.1962 + 7.39230i 0.508391 + 0.335667i
\(486\) 0 0
\(487\) 38.0000i 1.72194i −0.508652 0.860972i \(-0.669856\pi\)
0.508652 0.860972i \(-0.330144\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 33.5885 + 22.1769i 1.51737 + 1.00185i
\(491\) −6.50000 + 11.2583i −0.293341 + 0.508081i −0.974598 0.223963i \(-0.928100\pi\)
0.681257 + 0.732045i \(0.261434\pi\)
\(492\) 0 0
\(493\) 18.0000i 0.810679i
\(494\) −14.0000 10.3923i −0.629890 0.467572i
\(495\) 3.00000 + 6.00000i 0.134840 + 0.269680i
\(496\) −14.0000 + 24.2487i −0.628619 + 1.08880i
\(497\) 3.46410 + 2.00000i 0.155386 + 0.0897123i
\(498\) 0 0
\(499\) 14.0000 24.2487i 0.626726 1.08552i −0.361478 0.932381i \(-0.617728\pi\)
0.988204 0.153141i \(-0.0489388\pi\)
\(500\) 7.53590 + 21.0526i 0.337016 + 0.941499i
\(501\) 0 0
\(502\) 26.0000i 1.16044i
\(503\) 22.5167 13.0000i 1.00397 0.579641i 0.0945483 0.995520i \(-0.469859\pi\)
0.909420 + 0.415879i \(0.136526\pi\)
\(504\) 0 0
\(505\) −15.0000 30.0000i −0.667491 1.33498i
\(506\) −12.0000 −0.533465
\(507\) 0 0
\(508\) −10.3923 6.00000i −0.461084 0.266207i
\(509\) 9.00000 + 15.5885i 0.398918 + 0.690946i 0.993593 0.113020i \(-0.0360525\pi\)
−0.594675 + 0.803966i \(0.702719\pi\)
\(510\) 0 0
\(511\) 20.0000 34.6410i 0.884748 1.53243i
\(512\) 32.0000i 1.41421i
\(513\) 0 0
\(514\) 12.0000 0.529297
\(515\) 2.14359 35.7128i 0.0944580 1.57369i
\(516\) 0 0
\(517\) −5.19615 + 3.00000i −0.228527 + 0.131940i
\(518\) −13.8564 8.00000i −0.608816 0.351500i
\(519\) 0 0
\(520\) 0 0
\(521\) 15.0000 0.657162 0.328581 0.944476i \(-0.393430\pi\)
0.328581 + 0.944476i \(0.393430\pi\)
\(522\) −46.7654 + 27.0000i −2.04686 + 1.18176i
\(523\) −13.8564 + 8.00000i −0.605898 + 0.349816i −0.771358 0.636401i \(-0.780422\pi\)
0.165460 + 0.986216i \(0.447089\pi\)
\(524\) −24.0000 −1.04844
\(525\) 0 0
\(526\) 0 0
\(527\) −12.1244 7.00000i −0.528145 0.304925i
\(528\) 0 0
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) 17.8564 + 1.07180i 0.775633 + 0.0465559i
\(531\) −27.0000 −1.17170
\(532\) 34.6410 + 4.00000i 1.50188 + 0.173422i
\(533\) 4.00000i 0.173259i
\(534\) 0 0
\(535\) 1.33975 22.3205i 0.0579223 0.965000i
\(536\) 0 0
\(537\) 0 0
\(538\) −5.19615 + 3.00000i −0.224022 + 0.129339i
\(539\) 9.00000 0.387657
\(540\) 0 0
\(541\) −11.5000 19.9186i −0.494424 0.856367i 0.505556 0.862794i \(-0.331288\pi\)
−0.999979 + 0.00642713i \(0.997954\pi\)
\(542\) 5.19615 3.00000i 0.223194 0.128861i
\(543\) 0 0
\(544\) −16.0000 −0.685994
\(545\) 18.4808 27.9904i 0.791629 1.19898i
\(546\) 0 0
\(547\) 19.0526 11.0000i 0.814629 0.470326i −0.0339321 0.999424i \(-0.510803\pi\)
0.848561 + 0.529098i \(0.177470\pi\)
\(548\) 20.7846 + 12.0000i 0.887875 + 0.512615i
\(549\) 10.5000 18.1865i 0.448129 0.776182i
\(550\) 8.00000 + 6.00000i 0.341121 + 0.255841i
\(551\) −4.50000 + 38.9711i −0.191706 + 1.66023i
\(552\) 0 0
\(553\) −3.46410 2.00000i −0.147309 0.0850487i
\(554\) −28.0000 + 48.4974i −1.18961 + 2.06046i
\(555\) 0 0
\(556\) −20.0000 + 34.6410i −0.848189 + 1.46911i
\(557\) 12.1244 7.00000i 0.513725 0.296600i −0.220638 0.975356i \(-0.570814\pi\)
0.734364 + 0.678756i \(0.237481\pi\)
\(558\) 42.0000i 1.77800i
\(559\) 4.00000 0.169182
\(560\) −29.8564 19.7128i −1.26166 0.833018i
\(561\) 0 0
\(562\) 20.0000i 0.843649i
\(563\) 24.0000i 1.01148i 0.862686 + 0.505740i \(0.168780\pi\)
−0.862686 + 0.505740i \(0.831220\pi\)
\(564\) 0 0
\(565\) −1.60770 + 26.7846i −0.0676362 + 1.12684i
\(566\) −14.0000 24.2487i −0.588464 1.01925i
\(567\) 31.1769 + 18.0000i 1.30931 + 0.755929i
\(568\) 0 0
\(569\) −15.0000 −0.628833 −0.314416 0.949285i \(-0.601809\pi\)
−0.314416 + 0.949285i \(0.601809\pi\)
\(570\) 0 0
\(571\) 13.0000 0.544033 0.272017 0.962293i \(-0.412309\pi\)
0.272017 + 0.962293i \(0.412309\pi\)
\(572\) −3.46410 2.00000i −0.144841 0.0836242i
\(573\) 0 0
\(574\) −8.00000 13.8564i −0.333914 0.578355i
\(575\) −27.5885 + 11.7846i −1.15052 + 0.491452i
\(576\) −12.0000 20.7846i −0.500000 0.866025i
\(577\) 6.00000i 0.249783i 0.992170 + 0.124892i \(0.0398583\pi\)
−0.992170 + 0.124892i \(0.960142\pi\)
\(578\) 26.0000i 1.08146i
\(579\) 0 0
\(580\) −22.1769 + 33.5885i −0.920846 + 1.39468i
\(581\) 24.0000 0.995688
\(582\) 0 0
\(583\) 3.46410 2.00000i 0.143468 0.0828315i
\(584\) 0 0
\(585\) −11.1962 7.39230i −0.462904 0.305634i
\(586\) −4.00000 + 6.92820i −0.165238 + 0.286201i
\(587\) 20.7846 + 12.0000i 0.857873 + 0.495293i 0.863299 0.504692i \(-0.168394\pi\)
−0.00542667 + 0.999985i \(0.501727\pi\)
\(588\) 0 0
\(589\) −24.5000 18.1865i −1.00950 0.749363i
\(590\) −36.0000 + 18.0000i −1.48210 + 0.741048i
\(591\) 0 0
\(592\) 6.92820 + 4.00000i 0.284747 + 0.164399i
\(593\) 27.7128 16.0000i 1.13803 0.657041i 0.192087 0.981378i \(-0.438474\pi\)
0.945942 + 0.324337i \(0.105141\pi\)
\(594\) 0 0
\(595\) 9.85641 14.9282i 0.404073 0.611997i
\(596\) −2.00000 −0.0819232
\(597\) 0 0
\(598\) 20.7846 12.0000i 0.849946 0.490716i
\(599\) −6.00000 10.3923i −0.245153 0.424618i 0.717021 0.697051i \(-0.245505\pi\)
−0.962175 + 0.272433i \(0.912172\pi\)
\(600\) 0 0
\(601\) 17.0000 0.693444 0.346722 0.937968i \(-0.387295\pi\)
0.346722 + 0.937968i \(0.387295\pi\)
\(602\) −13.8564 + 8.00000i −0.564745 + 0.326056i
\(603\) 25.9808 + 15.0000i 1.05802 + 0.610847i
\(604\) 9.00000 + 15.5885i 0.366205 + 0.634285i
\(605\) −22.3205 1.33975i −0.907458 0.0544684i
\(606\) 0 0
\(607\) 14.0000i 0.568242i −0.958788 0.284121i \(-0.908298\pi\)
0.958788 0.284121i \(-0.0917018\pi\)
\(608\) −34.6410 4.00000i −1.40488 0.162221i
\(609\) 0 0
\(610\) 1.87564 31.2487i 0.0759426 1.26522i
\(611\) 6.00000 10.3923i 0.242734 0.420428i
\(612\) 10.3923 6.00000i 0.420084 0.242536i
\(613\) 20.7846 + 12.0000i 0.839482 + 0.484675i 0.857088 0.515170i \(-0.172271\pi\)
−0.0176058 + 0.999845i \(0.505604\pi\)
\(614\) 16.0000 + 27.7128i 0.645707 + 1.11840i
\(615\) 0 0
\(616\) 0 0
\(617\) 15.5885 9.00000i 0.627568 0.362326i −0.152242 0.988343i \(-0.548649\pi\)
0.779809 + 0.626017i \(0.215316\pi\)
\(618\) 0 0
\(619\) −4.00000 −0.160774 −0.0803868 0.996764i \(-0.525616\pi\)
−0.0803868 + 0.996764i \(0.525616\pi\)
\(620\) −14.0000 28.0000i −0.562254 1.12451i
\(621\) 0 0
\(622\) 0 0
\(623\) −38.1051 + 22.0000i −1.52665 + 0.881411i
\(624\) 0 0
\(625\) 24.2846 + 5.93782i 0.971384 + 0.237513i
\(626\) 60.0000 2.39808
\(627\) 0 0
\(628\) 8.00000i 0.319235i
\(629\) −2.00000 + 3.46410i −0.0797452 + 0.138123i
\(630\) 53.5692 + 3.21539i 2.13425 + 0.128104i
\(631\) −0.500000 0.866025i −0.0199047 0.0344759i 0.855901 0.517139i \(-0.173003\pi\)
−0.875806 + 0.482663i \(0.839670\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 4.00000 0.158860
\(635\) −12.0000 + 6.00000i −0.476205 + 0.238103i
\(636\) 0 0
\(637\) −15.5885 + 9.00000i −0.617637 + 0.356593i
\(638\) 18.0000i 0.712627i
\(639\) 3.00000 0.118678
\(640\) 0 0
\(641\) −10.5000 + 18.1865i −0.414725 + 0.718325i −0.995400 0.0958109i \(-0.969456\pi\)
0.580674 + 0.814136i \(0.302789\pi\)
\(642\) 0 0
\(643\) −39.8372 23.0000i −1.57102 0.907031i −0.996044 0.0888646i \(-0.971676\pi\)
−0.574981 0.818167i \(-0.694991\pi\)
\(644\) −24.0000 + 41.5692i −0.945732 + 1.63806i
\(645\) 0 0
\(646\) 2.00000 17.3205i 0.0786889 0.681466i
\(647\) 6.00000i 0.235884i −0.993020 0.117942i \(-0.962370\pi\)
0.993020 0.117942i \(-0.0376297\pi\)
\(648\) 0 0
\(649\) −4.50000 + 7.79423i −0.176640 + 0.305950i
\(650\) −19.8564 2.39230i −0.778832 0.0938339i
\(651\) 0 0
\(652\) 6.92820 4.00000i 0.271329 0.156652i
\(653\) 10.0000i 0.391330i −0.980671 0.195665i \(-0.937313\pi\)
0.980671 0.195665i \(-0.0626866\pi\)
\(654\) 0 0
\(655\) −14.7846 + 22.3923i −0.577683 + 0.874940i
\(656\) 4.00000 + 6.92820i 0.156174 + 0.270501i
\(657\) 30.0000i 1.17041i
\(658\) 48.0000i 1.87123i
\(659\) 10.0000 + 17.3205i 0.389545 + 0.674711i 0.992388 0.123148i \(-0.0392990\pi\)
−0.602844 + 0.797859i \(0.705966\pi\)
\(660\) 0 0
\(661\) 7.50000 + 12.9904i 0.291716 + 0.505267i 0.974216 0.225619i \(-0.0724404\pi\)
−0.682499 + 0.730886i \(0.739107\pi\)
\(662\) −34.6410 20.0000i −1.34636 0.777322i
\(663\) 0 0
\(664\) 0 0
\(665\) 25.0718 29.8564i 0.972243 1.15778i
\(666\) −12.0000 −0.464991
\(667\) −46.7654 27.0000i −1.81076 1.04544i
\(668\) −20.7846 12.0000i −0.804181 0.464294i
\(669\) 0 0
\(670\) 44.6410 + 2.67949i 1.72463 + 0.103518i
\(671\) −3.50000 6.06218i −0.135116 0.234028i
\(672\) 0 0
\(673\) 20.0000i 0.770943i 0.922720 + 0.385472i \(0.125961\pi\)
−0.922720 + 0.385472i \(0.874039\pi\)
\(674\) 34.0000 + 58.8897i 1.30963 + 2.26835i
\(675\) 0 0
\(676\) −18.0000 −0.692308
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 12.0000 20.7846i 0.460518 0.797640i
\(680\) 0 0
\(681\) 0 0
\(682\) −12.1244 7.00000i −0.464266 0.268044i
\(683\) 30.0000i 1.14792i −0.818884 0.573959i \(-0.805407\pi\)
0.818884 0.573959i \(-0.194593\pi\)
\(684\) 24.0000 10.3923i 0.917663 0.397360i
\(685\) 24.0000 12.0000i 0.916993 0.458496i
\(686\) 8.00000 13.8564i 0.305441 0.529040i
\(687\) 0 0
\(688\) 6.92820 4.00000i 0.264135 0.152499i
\(689\) −4.00000 + 6.92820i −0.152388 + 0.263944i
\(690\) 0 0
\(691\) 3.00000 0.114125 0.0570627 0.998371i \(-0.481827\pi\)
0.0570627 + 0.998371i \(0.481827\pi\)
\(692\) 48.0000i 1.82469i
\(693\) 10.3923 6.00000i 0.394771 0.227921i
\(694\) −12.0000 20.7846i −0.455514 0.788973i
\(695\) 20.0000 + 40.0000i 0.758643 + 1.51729i
\(696\) 0 0
\(697\) −3.46410 + 2.00000i −0.131212 + 0.0757554i
\(698\) 24.2487 + 14.0000i 0.917827 + 0.529908i
\(699\) 0 0
\(700\) 36.7846 15.7128i 1.39033 0.593889i
\(701\) −3.00000 + 5.19615i −0.113308 + 0.196256i −0.917102 0.398652i \(-0.869478\pi\)
0.803794 + 0.594908i \(0.202811\pi\)
\(702\) 0 0
\(703\) −5.19615 + 7.00000i −0.195977 + 0.264010i
\(704\) −8.00000 −0.301511
\(705\) 0 0
\(706\) 8.00000 13.8564i 0.301084 0.521493i
\(707\) −51.9615 + 30.0000i −1.95421 + 1.12827i
\(708\) 0 0
\(709\) 12.5000 + 21.6506i 0.469447 + 0.813107i 0.999390 0.0349269i \(-0.0111198\pi\)
−0.529943 + 0.848034i \(0.677787\pi\)
\(710\) 4.00000 2.00000i 0.150117 0.0750587i
\(711\) −3.00000 −0.112509
\(712\) 0 0
\(713\) 36.3731 21.0000i 1.36218 0.786456i
\(714\) 0 0
\(715\) −4.00000 + 2.00000i −0.149592 + 0.0747958i
\(716\) −15.0000 25.9808i −0.560576 0.970947i
\(717\) 0 0
\(718\) 34.6410 20.0000i 1.29279 0.746393i
\(719\) −10.5000 + 18.1865i −0.391584 + 0.678243i −0.992659 0.120950i \(-0.961406\pi\)
0.601075 + 0.799193i \(0.294739\pi\)
\(720\) −26.7846 1.60770i −0.998203 0.0599153i
\(721\) −64.0000 −2.38348
\(722\) 8.66025 37.0000i 0.322301 1.37700i
\(723\) 0 0
\(724\) −6.00000 + 10.3923i −0.222988 + 0.386227i
\(725\) 17.6769 + 41.3827i 0.656504 + 1.53691i
\(726\) 0 0
\(727\) −6.92820 4.00000i −0.256953 0.148352i 0.365991 0.930618i \(-0.380730\pi\)
−0.622944 + 0.782267i \(0.714063\pi\)
\(728\) 0 0
\(729\) 27.0000 1.00000
\(730\) −20.0000 40.0000i −0.740233 1.48047i
\(731\) 2.00000 + 3.46410i 0.0739727 + 0.128124i
\(732\) 0 0
\(733\) 6.00000i 0.221615i 0.993842 + 0.110808i \(0.0353437\pi\)
−0.993842 + 0.110808i \(0.964656\pi\)
\(734\) 32.0000 1.18114
\(735\) 0 0
\(736\) 24.0000 41.5692i 0.884652 1.53226i
\(737\) 8.66025 5.00000i 0.319005 0.184177i
\(738\) −10.3923 6.00000i −0.382546 0.220863i
\(739\) −14.5000 + 25.1147i −0.533391 + 0.923861i 0.465848 + 0.884865i \(0.345749\pi\)
−0.999239 + 0.0389959i \(0.987584\pi\)
\(740\) −8.00000 + 4.00000i −0.294086 + 0.147043i
\(741\) 0 0
\(742\) 32.0000i 1.17476i
\(743\) 43.3013 + 25.0000i 1.58857 + 0.917161i 0.993543 + 0.113455i \(0.0361917\pi\)
0.595026 + 0.803706i \(0.297142\pi\)
\(744\) 0 0
\(745\) −1.23205 + 1.86603i −0.0451388 + 0.0683659i
\(746\) 12.0000 20.7846i 0.439351 0.760979i
\(747\) 15.5885 9.00000i 0.570352 0.329293i
\(748\) 4.00000i 0.146254i
\(749\) −40.0000 −1.46157
\(750\) 0 0
\(751\) −20.5000 35.5070i −0.748056 1.29567i −0.948753 0.316017i \(-0.897654\pi\)
0.200698 0.979653i \(-0.435679\pi\)
\(752\) 24.0000i 0.875190i
\(753\) 0 0
\(754\) −18.0000 31.1769i −0.655521 1.13540i
\(755\) 20.0885 + 1.20577i 0.731094 + 0.0438825i
\(756\) 0 0
\(757\) −22.5167 13.0000i −0.818382 0.472493i 0.0314762 0.999505i \(-0.489979\pi\)
−0.849858 + 0.527011i \(0.823312\pi\)
\(758\) −50.2295 29.0000i −1.82442 1.05333i
\(759\) 0 0
\(760\) 0 0
\(761\) −18.0000 −0.652499 −0.326250 0.945284i \(-0.605785\pi\)
−0.326250 + 0.945284i \(0.605785\pi\)
\(762\) 0 0
\(763\) −51.9615 30.0000i −1.88113 1.08607i
\(764\) −3.00000 5.19615i −0.108536 0.187990i
\(765\) 0.803848 13.3923i 0.0290632 0.484200i
\(766\) −6.00000 10.3923i −0.216789 0.375489i
\(767\) 18.0000i 0.649942i
\(768\) 0 0
\(769\) 2.50000 + 4.33013i 0.0901523 + 0.156148i 0.907575 0.419890i \(-0.137931\pi\)
−0.817423 + 0.576038i \(0.804598\pi\)
\(770\) 9.85641 14.9282i 0.355200 0.537975i
\(771\) 0 0
\(772\) 32.0000i 1.15171i
\(773\) −29.4449 + 17.0000i −1.05906 + 0.611448i −0.925172 0.379549i \(-0.876079\pi\)
−0.133887 + 0.990997i \(0.542746\pi\)
\(774\) −6.00000 + 10.3923i −0.215666 + 0.373544i
\(775\) −34.7487 4.18653i −1.24821 0.150385i
\(776\) 0 0
\(777\) 0 0
\(778\) 66.0000i 2.36621i
\(779\) −8.00000 + 3.46410i −0.286630 + 0.124114i
\(780\) 0