Properties

Label 1078.2.e.t.177.2
Level $1078$
Weight $2$
Character 1078.177
Analytic conductor $8.608$
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] = [1078,2,Mod(67,1078)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1078.67");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1078.e (of order \(3\), degree \(2\), not 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: \(8.60787333789\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 2x^{2} + 4 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 177.2
Root \(-0.707107 + 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 1078.177
Dual form 1078.2.e.t.67.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.41421 - 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.41421 - 2.44949i) q^{5} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-1.41421 - 2.44949i) q^{10} +(-0.500000 - 0.866025i) q^{11} -4.24264 q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.41421 - 2.44949i) q^{17} +(-1.50000 - 2.59808i) q^{18} +(0.707107 - 1.22474i) q^{19} -2.82843 q^{20} -1.00000 q^{22} +(-3.00000 + 5.19615i) q^{23} +(-1.50000 - 2.59808i) q^{25} +(-2.12132 + 3.67423i) q^{26} +8.00000 q^{29} +(-0.707107 - 1.22474i) q^{31} +(0.500000 + 0.866025i) q^{32} -2.82843 q^{34} -3.00000 q^{36} +(3.00000 - 5.19615i) q^{37} +(-0.707107 - 1.22474i) q^{38} +(-1.41421 + 2.44949i) q^{40} -8.48528 q^{41} +10.0000 q^{43} +(-0.500000 + 0.866025i) q^{44} +(-4.24264 - 7.34847i) q^{45} +(3.00000 + 5.19615i) q^{46} +(-3.53553 + 6.12372i) q^{47} -3.00000 q^{50} +(2.12132 + 3.67423i) q^{52} +(-3.00000 - 5.19615i) q^{53} -2.82843 q^{55} +(4.00000 - 6.92820i) q^{58} +(-7.07107 - 12.2474i) q^{59} +(-2.12132 + 3.67423i) q^{61} -1.41421 q^{62} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-1.41421 + 2.44949i) q^{68} +(-1.50000 + 2.59808i) q^{72} +(4.24264 + 7.34847i) q^{73} +(-3.00000 - 5.19615i) q^{74} -1.41421 q^{76} +(1.41421 + 2.44949i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-4.24264 + 7.34847i) q^{82} +7.07107 q^{83} -8.00000 q^{85} +(5.00000 - 8.66025i) q^{86} +(0.500000 + 0.866025i) q^{88} +(9.19239 - 15.9217i) q^{89} -8.48528 q^{90} +6.00000 q^{92} +(3.53553 + 6.12372i) q^{94} +(-2.00000 - 3.46410i) q^{95} +1.41421 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{8} + 6 q^{9} - 2 q^{11} - 2 q^{16} - 6 q^{18} - 4 q^{22} - 12 q^{23} - 6 q^{25} + 32 q^{29} + 2 q^{32} - 12 q^{36} + 12 q^{37} + 40 q^{43} - 2 q^{44} + 12 q^{46} - 12 q^{50} - 12 q^{53} + 16 q^{58} + 4 q^{64} - 24 q^{65} + 8 q^{67} - 6 q^{72} - 12 q^{74} - 18 q^{81} - 32 q^{85} + 20 q^{86} + 2 q^{88} + 24 q^{92} - 8 q^{95} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(981\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.353553 0.612372i
\(3\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 1.41421 2.44949i 0.632456 1.09545i −0.354593 0.935021i \(-0.615380\pi\)
0.987048 0.160424i \(-0.0512862\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) 1.50000 2.59808i 0.500000 0.866025i
\(10\) −1.41421 2.44949i −0.447214 0.774597i
\(11\) −0.500000 0.866025i −0.150756 0.261116i
\(12\) 0 0
\(13\) −4.24264 −1.17670 −0.588348 0.808608i \(-0.700222\pi\)
−0.588348 + 0.808608i \(0.700222\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.500000 + 0.866025i −0.125000 + 0.216506i
\(17\) −1.41421 2.44949i −0.342997 0.594089i 0.641991 0.766712i \(-0.278109\pi\)
−0.984988 + 0.172624i \(0.944775\pi\)
\(18\) −1.50000 2.59808i −0.353553 0.612372i
\(19\) 0.707107 1.22474i 0.162221 0.280976i −0.773444 0.633865i \(-0.781467\pi\)
0.935665 + 0.352889i \(0.114801\pi\)
\(20\) −2.82843 −0.632456
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −3.00000 + 5.19615i −0.625543 + 1.08347i 0.362892 + 0.931831i \(0.381789\pi\)
−0.988436 + 0.151642i \(0.951544\pi\)
\(24\) 0 0
\(25\) −1.50000 2.59808i −0.300000 0.519615i
\(26\) −2.12132 + 3.67423i −0.416025 + 0.720577i
\(27\) 0 0
\(28\) 0 0
\(29\) 8.00000 1.48556 0.742781 0.669534i \(-0.233506\pi\)
0.742781 + 0.669534i \(0.233506\pi\)
\(30\) 0 0
\(31\) −0.707107 1.22474i −0.127000 0.219971i 0.795513 0.605937i \(-0.207202\pi\)
−0.922513 + 0.385966i \(0.873868\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −2.82843 −0.485071
\(35\) 0 0
\(36\) −3.00000 −0.500000
\(37\) 3.00000 5.19615i 0.493197 0.854242i −0.506772 0.862080i \(-0.669162\pi\)
0.999969 + 0.00783774i \(0.00249486\pi\)
\(38\) −0.707107 1.22474i −0.114708 0.198680i
\(39\) 0 0
\(40\) −1.41421 + 2.44949i −0.223607 + 0.387298i
\(41\) −8.48528 −1.32518 −0.662589 0.748983i \(-0.730542\pi\)
−0.662589 + 0.748983i \(0.730542\pi\)
\(42\) 0 0
\(43\) 10.0000 1.52499 0.762493 0.646997i \(-0.223975\pi\)
0.762493 + 0.646997i \(0.223975\pi\)
\(44\) −0.500000 + 0.866025i −0.0753778 + 0.130558i
\(45\) −4.24264 7.34847i −0.632456 1.09545i
\(46\) 3.00000 + 5.19615i 0.442326 + 0.766131i
\(47\) −3.53553 + 6.12372i −0.515711 + 0.893237i 0.484123 + 0.875000i \(0.339139\pi\)
−0.999834 + 0.0182371i \(0.994195\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −3.00000 −0.424264
\(51\) 0 0
\(52\) 2.12132 + 3.67423i 0.294174 + 0.509525i
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 0 0
\(55\) −2.82843 −0.381385
\(56\) 0 0
\(57\) 0 0
\(58\) 4.00000 6.92820i 0.525226 0.909718i
\(59\) −7.07107 12.2474i −0.920575 1.59448i −0.798528 0.601958i \(-0.794388\pi\)
−0.122047 0.992524i \(-0.538946\pi\)
\(60\) 0 0
\(61\) −2.12132 + 3.67423i −0.271607 + 0.470438i −0.969274 0.245985i \(-0.920888\pi\)
0.697666 + 0.716423i \(0.254222\pi\)
\(62\) −1.41421 −0.179605
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) −6.00000 + 10.3923i −0.744208 + 1.28901i
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −1.41421 + 2.44949i −0.171499 + 0.297044i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) −1.50000 + 2.59808i −0.176777 + 0.306186i
\(73\) 4.24264 + 7.34847i 0.496564 + 0.860073i 0.999992 0.00396356i \(-0.00126164\pi\)
−0.503429 + 0.864037i \(0.667928\pi\)
\(74\) −3.00000 5.19615i −0.348743 0.604040i
\(75\) 0 0
\(76\) −1.41421 −0.162221
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(80\) 1.41421 + 2.44949i 0.158114 + 0.273861i
\(81\) −4.50000 7.79423i −0.500000 0.866025i
\(82\) −4.24264 + 7.34847i −0.468521 + 0.811503i
\(83\) 7.07107 0.776151 0.388075 0.921628i \(-0.373140\pi\)
0.388075 + 0.921628i \(0.373140\pi\)
\(84\) 0 0
\(85\) −8.00000 −0.867722
\(86\) 5.00000 8.66025i 0.539164 0.933859i
\(87\) 0 0
\(88\) 0.500000 + 0.866025i 0.0533002 + 0.0923186i
\(89\) 9.19239 15.9217i 0.974391 1.68770i 0.292462 0.956277i \(-0.405526\pi\)
0.681930 0.731418i \(-0.261141\pi\)
\(90\) −8.48528 −0.894427
\(91\) 0 0
\(92\) 6.00000 0.625543
\(93\) 0 0
\(94\) 3.53553 + 6.12372i 0.364662 + 0.631614i
\(95\) −2.00000 3.46410i −0.205196 0.355409i
\(96\) 0 0
\(97\) 1.41421 0.143592 0.0717958 0.997419i \(-0.477127\pi\)
0.0717958 + 0.997419i \(0.477127\pi\)
\(98\) 0 0
\(99\) −3.00000 −0.301511
\(100\) −1.50000 + 2.59808i −0.150000 + 0.259808i
\(101\) −0.707107 1.22474i −0.0703598 0.121867i 0.828699 0.559694i \(-0.189081\pi\)
−0.899059 + 0.437828i \(0.855748\pi\)
\(102\) 0 0
\(103\) 2.12132 3.67423i 0.209020 0.362033i −0.742386 0.669972i \(-0.766306\pi\)
0.951406 + 0.307939i \(0.0996393\pi\)
\(104\) 4.24264 0.416025
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −9.00000 + 15.5885i −0.870063 + 1.50699i −0.00813215 + 0.999967i \(0.502589\pi\)
−0.861931 + 0.507026i \(0.830745\pi\)
\(108\) 0 0
\(109\) −7.00000 12.1244i −0.670478 1.16130i −0.977769 0.209687i \(-0.932756\pi\)
0.307290 0.951616i \(-0.400578\pi\)
\(110\) −1.41421 + 2.44949i −0.134840 + 0.233550i
\(111\) 0 0
\(112\) 0 0
\(113\) 8.00000 0.752577 0.376288 0.926503i \(-0.377200\pi\)
0.376288 + 0.926503i \(0.377200\pi\)
\(114\) 0 0
\(115\) 8.48528 + 14.6969i 0.791257 + 1.37050i
\(116\) −4.00000 6.92820i −0.371391 0.643268i
\(117\) −6.36396 + 11.0227i −0.588348 + 1.01905i
\(118\) −14.1421 −1.30189
\(119\) 0 0
\(120\) 0 0
\(121\) −0.500000 + 0.866025i −0.0454545 + 0.0787296i
\(122\) 2.12132 + 3.67423i 0.192055 + 0.332650i
\(123\) 0 0
\(124\) −0.707107 + 1.22474i −0.0635001 + 0.109985i
\(125\) 5.65685 0.505964
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 0 0
\(130\) 6.00000 + 10.3923i 0.526235 + 0.911465i
\(131\) 3.53553 6.12372i 0.308901 0.535032i −0.669221 0.743063i \(-0.733372\pi\)
0.978122 + 0.208031i \(0.0667055\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 1.41421 + 2.44949i 0.121268 + 0.210042i
\(137\) −5.00000 8.66025i −0.427179 0.739895i 0.569442 0.822031i \(-0.307159\pi\)
−0.996621 + 0.0821359i \(0.973826\pi\)
\(138\) 0 0
\(139\) 21.2132 1.79928 0.899640 0.436632i \(-0.143829\pi\)
0.899640 + 0.436632i \(0.143829\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 2.12132 + 3.67423i 0.177394 + 0.307255i
\(144\) 1.50000 + 2.59808i 0.125000 + 0.216506i
\(145\) 11.3137 19.5959i 0.939552 1.62735i
\(146\) 8.48528 0.702247
\(147\) 0 0
\(148\) −6.00000 −0.493197
\(149\) −2.00000 + 3.46410i −0.163846 + 0.283790i −0.936245 0.351348i \(-0.885723\pi\)
0.772399 + 0.635138i \(0.219057\pi\)
\(150\) 0 0
\(151\) 10.0000 + 17.3205i 0.813788 + 1.40952i 0.910195 + 0.414181i \(0.135932\pi\)
−0.0964061 + 0.995342i \(0.530735\pi\)
\(152\) −0.707107 + 1.22474i −0.0573539 + 0.0993399i
\(153\) −8.48528 −0.685994
\(154\) 0 0
\(155\) −4.00000 −0.321288
\(156\) 0 0
\(157\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 2.82843 0.223607
\(161\) 0 0
\(162\) −9.00000 −0.707107
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) 4.24264 + 7.34847i 0.331295 + 0.573819i
\(165\) 0 0
\(166\) 3.53553 6.12372i 0.274411 0.475293i
\(167\) 14.1421 1.09435 0.547176 0.837018i \(-0.315703\pi\)
0.547176 + 0.837018i \(0.315703\pi\)
\(168\) 0 0
\(169\) 5.00000 0.384615
\(170\) −4.00000 + 6.92820i −0.306786 + 0.531369i
\(171\) −2.12132 3.67423i −0.162221 0.280976i
\(172\) −5.00000 8.66025i −0.381246 0.660338i
\(173\) −7.77817 + 13.4722i −0.591364 + 1.02427i 0.402685 + 0.915338i \(0.368077\pi\)
−0.994049 + 0.108933i \(0.965256\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) −9.19239 15.9217i −0.688999 1.19338i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) −4.24264 + 7.34847i −0.316228 + 0.547723i
\(181\) 8.48528 0.630706 0.315353 0.948974i \(-0.397877\pi\)
0.315353 + 0.948974i \(0.397877\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 3.00000 5.19615i 0.221163 0.383065i
\(185\) −8.48528 14.6969i −0.623850 1.08054i
\(186\) 0 0
\(187\) −1.41421 + 2.44949i −0.103418 + 0.179124i
\(188\) 7.07107 0.515711
\(189\) 0 0
\(190\) −4.00000 −0.290191
\(191\) 11.0000 19.0526i 0.795932 1.37859i −0.126314 0.991990i \(-0.540315\pi\)
0.922246 0.386604i \(-0.126352\pi\)
\(192\) 0 0
\(193\) 7.00000 + 12.1244i 0.503871 + 0.872730i 0.999990 + 0.00447566i \(0.00142465\pi\)
−0.496119 + 0.868255i \(0.665242\pi\)
\(194\) 0.707107 1.22474i 0.0507673 0.0879316i
\(195\) 0 0
\(196\) 0 0
\(197\) 10.0000 0.712470 0.356235 0.934396i \(-0.384060\pi\)
0.356235 + 0.934396i \(0.384060\pi\)
\(198\) −1.50000 + 2.59808i −0.106600 + 0.184637i
\(199\) 2.12132 + 3.67423i 0.150376 + 0.260460i 0.931366 0.364085i \(-0.118618\pi\)
−0.780989 + 0.624544i \(0.785285\pi\)
\(200\) 1.50000 + 2.59808i 0.106066 + 0.183712i
\(201\) 0 0
\(202\) −1.41421 −0.0995037
\(203\) 0 0
\(204\) 0 0
\(205\) −12.0000 + 20.7846i −0.838116 + 1.45166i
\(206\) −2.12132 3.67423i −0.147799 0.255996i
\(207\) 9.00000 + 15.5885i 0.625543 + 1.08347i
\(208\) 2.12132 3.67423i 0.147087 0.254762i
\(209\) −1.41421 −0.0978232
\(210\) 0 0
\(211\) −14.0000 −0.963800 −0.481900 0.876226i \(-0.660053\pi\)
−0.481900 + 0.876226i \(0.660053\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) 9.00000 + 15.5885i 0.615227 + 1.06561i
\(215\) 14.1421 24.4949i 0.964486 1.67054i
\(216\) 0 0
\(217\) 0 0
\(218\) −14.0000 −0.948200
\(219\) 0 0
\(220\) 1.41421 + 2.44949i 0.0953463 + 0.165145i
\(221\) 6.00000 + 10.3923i 0.403604 + 0.699062i
\(222\) 0 0
\(223\) 12.7279 0.852325 0.426162 0.904647i \(-0.359865\pi\)
0.426162 + 0.904647i \(0.359865\pi\)
\(224\) 0 0
\(225\) −9.00000 −0.600000
\(226\) 4.00000 6.92820i 0.266076 0.460857i
\(227\) 13.4350 + 23.2702i 0.891714 + 1.54449i 0.837819 + 0.545948i \(0.183830\pi\)
0.0538949 + 0.998547i \(0.482836\pi\)
\(228\) 0 0
\(229\) −12.7279 + 22.0454i −0.841085 + 1.45680i 0.0478936 + 0.998852i \(0.484749\pi\)
−0.888978 + 0.457949i \(0.848584\pi\)
\(230\) 16.9706 1.11901
\(231\) 0 0
\(232\) −8.00000 −0.525226
\(233\) −1.00000 + 1.73205i −0.0655122 + 0.113470i −0.896921 0.442191i \(-0.854201\pi\)
0.831409 + 0.555661i \(0.187535\pi\)
\(234\) 6.36396 + 11.0227i 0.416025 + 0.720577i
\(235\) 10.0000 + 17.3205i 0.652328 + 1.12987i
\(236\) −7.07107 + 12.2474i −0.460287 + 0.797241i
\(237\) 0 0
\(238\) 0 0
\(239\) −4.00000 −0.258738 −0.129369 0.991596i \(-0.541295\pi\)
−0.129369 + 0.991596i \(0.541295\pi\)
\(240\) 0 0
\(241\) −1.41421 2.44949i −0.0910975 0.157786i 0.816876 0.576814i \(-0.195704\pi\)
−0.907973 + 0.419028i \(0.862371\pi\)
\(242\) 0.500000 + 0.866025i 0.0321412 + 0.0556702i
\(243\) 0 0
\(244\) 4.24264 0.271607
\(245\) 0 0
\(246\) 0 0
\(247\) −3.00000 + 5.19615i −0.190885 + 0.330623i
\(248\) 0.707107 + 1.22474i 0.0449013 + 0.0777714i
\(249\) 0 0
\(250\) 2.82843 4.89898i 0.178885 0.309839i
\(251\) −25.4558 −1.60676 −0.803379 0.595468i \(-0.796967\pi\)
−0.803379 + 0.595468i \(0.796967\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 4.00000 6.92820i 0.250982 0.434714i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) 9.19239 15.9217i 0.573405 0.993167i −0.422807 0.906220i \(-0.638955\pi\)
0.996213 0.0869478i \(-0.0277113\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 12.0000 0.744208
\(261\) 12.0000 20.7846i 0.742781 1.28654i
\(262\) −3.53553 6.12372i −0.218426 0.378325i
\(263\) −6.00000 10.3923i −0.369976 0.640817i 0.619586 0.784929i \(-0.287301\pi\)
−0.989561 + 0.144112i \(0.953967\pi\)
\(264\) 0 0
\(265\) −16.9706 −1.04249
\(266\) 0 0
\(267\) 0 0
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 12.7279 + 22.0454i 0.776035 + 1.34413i 0.934211 + 0.356721i \(0.116105\pi\)
−0.158176 + 0.987411i \(0.550561\pi\)
\(270\) 0 0
\(271\) −4.24264 + 7.34847i −0.257722 + 0.446388i −0.965631 0.259916i \(-0.916305\pi\)
0.707909 + 0.706303i \(0.249639\pi\)
\(272\) 2.82843 0.171499
\(273\) 0 0
\(274\) −10.0000 −0.604122
\(275\) −1.50000 + 2.59808i −0.0904534 + 0.156670i
\(276\) 0 0
\(277\) −2.00000 3.46410i −0.120168 0.208138i 0.799666 0.600446i \(-0.205010\pi\)
−0.919834 + 0.392308i \(0.871677\pi\)
\(278\) 10.6066 18.3712i 0.636142 1.10183i
\(279\) −4.24264 −0.254000
\(280\) 0 0
\(281\) 6.00000 0.357930 0.178965 0.983855i \(-0.442725\pi\)
0.178965 + 0.983855i \(0.442725\pi\)
\(282\) 0 0
\(283\) −2.12132 3.67423i −0.126099 0.218411i 0.796063 0.605214i \(-0.206912\pi\)
−0.922162 + 0.386804i \(0.873579\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 4.24264 0.250873
\(287\) 0 0
\(288\) 3.00000 0.176777
\(289\) 4.50000 7.79423i 0.264706 0.458484i
\(290\) −11.3137 19.5959i −0.664364 1.15071i
\(291\) 0 0
\(292\) 4.24264 7.34847i 0.248282 0.430037i
\(293\) 15.5563 0.908812 0.454406 0.890795i \(-0.349852\pi\)
0.454406 + 0.890795i \(0.349852\pi\)
\(294\) 0 0
\(295\) −40.0000 −2.32889
\(296\) −3.00000 + 5.19615i −0.174371 + 0.302020i
\(297\) 0 0
\(298\) 2.00000 + 3.46410i 0.115857 + 0.200670i
\(299\) 12.7279 22.0454i 0.736075 1.27492i
\(300\) 0 0
\(301\) 0 0
\(302\) 20.0000 1.15087
\(303\) 0 0
\(304\) 0.707107 + 1.22474i 0.0405554 + 0.0702439i
\(305\) 6.00000 + 10.3923i 0.343559 + 0.595062i
\(306\) −4.24264 + 7.34847i −0.242536 + 0.420084i
\(307\) 24.0416 1.37213 0.686064 0.727541i \(-0.259337\pi\)
0.686064 + 0.727541i \(0.259337\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2.00000 + 3.46410i −0.113592 + 0.196748i
\(311\) −12.0208 20.8207i −0.681638 1.18063i −0.974481 0.224471i \(-0.927935\pi\)
0.292843 0.956161i \(-0.405399\pi\)
\(312\) 0 0
\(313\) −6.36396 + 11.0227i −0.359712 + 0.623040i −0.987913 0.155012i \(-0.950459\pi\)
0.628200 + 0.778052i \(0.283792\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 15.0000 25.9808i 0.842484 1.45922i −0.0453045 0.998973i \(-0.514426\pi\)
0.887788 0.460252i \(-0.152241\pi\)
\(318\) 0 0
\(319\) −4.00000 6.92820i −0.223957 0.387905i
\(320\) 1.41421 2.44949i 0.0790569 0.136931i
\(321\) 0 0
\(322\) 0 0
\(323\) −4.00000 −0.222566
\(324\) −4.50000 + 7.79423i −0.250000 + 0.433013i
\(325\) 6.36396 + 11.0227i 0.353009 + 0.611430i
\(326\) −8.00000 13.8564i −0.443079 0.767435i
\(327\) 0 0
\(328\) 8.48528 0.468521
\(329\) 0 0
\(330\) 0 0
\(331\) 16.0000 27.7128i 0.879440 1.52323i 0.0274825 0.999622i \(-0.491251\pi\)
0.851957 0.523612i \(-0.175416\pi\)
\(332\) −3.53553 6.12372i −0.194038 0.336083i
\(333\) −9.00000 15.5885i −0.493197 0.854242i
\(334\) 7.07107 12.2474i 0.386912 0.670151i
\(335\) 11.3137 0.618134
\(336\) 0 0
\(337\) −18.0000 −0.980522 −0.490261 0.871576i \(-0.663099\pi\)
−0.490261 + 0.871576i \(0.663099\pi\)
\(338\) 2.50000 4.33013i 0.135982 0.235528i
\(339\) 0 0
\(340\) 4.00000 + 6.92820i 0.216930 + 0.375735i
\(341\) −0.707107 + 1.22474i −0.0382920 + 0.0663237i
\(342\) −4.24264 −0.229416
\(343\) 0 0
\(344\) −10.0000 −0.539164
\(345\) 0 0
\(346\) 7.77817 + 13.4722i 0.418157 + 0.724270i
\(347\) −5.00000 8.66025i −0.268414 0.464907i 0.700038 0.714105i \(-0.253166\pi\)
−0.968452 + 0.249198i \(0.919833\pi\)
\(348\) 0 0
\(349\) 9.89949 0.529908 0.264954 0.964261i \(-0.414643\pi\)
0.264954 + 0.964261i \(0.414643\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0.500000 0.866025i 0.0266501 0.0461593i
\(353\) −14.8492 25.7196i −0.790345 1.36892i −0.925753 0.378128i \(-0.876568\pi\)
0.135408 0.990790i \(-0.456766\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −18.3848 −0.974391
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) −12.0000 + 20.7846i −0.633336 + 1.09697i 0.353529 + 0.935423i \(0.384981\pi\)
−0.986865 + 0.161546i \(0.948352\pi\)
\(360\) 4.24264 + 7.34847i 0.223607 + 0.387298i
\(361\) 8.50000 + 14.7224i 0.447368 + 0.774865i
\(362\) 4.24264 7.34847i 0.222988 0.386227i
\(363\) 0 0
\(364\) 0 0
\(365\) 24.0000 1.25622
\(366\) 0 0
\(367\) 12.0208 + 20.8207i 0.627481 + 1.08683i 0.988055 + 0.154099i \(0.0492475\pi\)
−0.360574 + 0.932731i \(0.617419\pi\)
\(368\) −3.00000 5.19615i −0.156386 0.270868i
\(369\) −12.7279 + 22.0454i −0.662589 + 1.14764i
\(370\) −16.9706 −0.882258
\(371\) 0 0
\(372\) 0 0
\(373\) −13.0000 + 22.5167i −0.673114 + 1.16587i 0.303902 + 0.952703i \(0.401711\pi\)
−0.977016 + 0.213165i \(0.931623\pi\)
\(374\) 1.41421 + 2.44949i 0.0731272 + 0.126660i
\(375\) 0 0
\(376\) 3.53553 6.12372i 0.182331 0.315807i
\(377\) −33.9411 −1.74806
\(378\) 0 0
\(379\) −28.0000 −1.43826 −0.719132 0.694874i \(-0.755460\pi\)
−0.719132 + 0.694874i \(0.755460\pi\)
\(380\) −2.00000 + 3.46410i −0.102598 + 0.177705i
\(381\) 0 0
\(382\) −11.0000 19.0526i −0.562809 0.974814i
\(383\) 17.6777 30.6186i 0.903287 1.56454i 0.0800861 0.996788i \(-0.474480\pi\)
0.823201 0.567751i \(-0.192186\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 14.0000 0.712581
\(387\) 15.0000 25.9808i 0.762493 1.32068i
\(388\) −0.707107 1.22474i −0.0358979 0.0621770i
\(389\) 9.00000 + 15.5885i 0.456318 + 0.790366i 0.998763 0.0497253i \(-0.0158346\pi\)
−0.542445 + 0.840091i \(0.682501\pi\)
\(390\) 0 0
\(391\) 16.9706 0.858238
\(392\) 0 0
\(393\) 0 0
\(394\) 5.00000 8.66025i 0.251896 0.436297i
\(395\) 0 0
\(396\) 1.50000 + 2.59808i 0.0753778 + 0.130558i
\(397\) −5.65685 + 9.79796i −0.283909 + 0.491745i −0.972344 0.233553i \(-0.924965\pi\)
0.688435 + 0.725298i \(0.258298\pi\)
\(398\) 4.24264 0.212664
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) −9.00000 + 15.5885i −0.449439 + 0.778450i −0.998350 0.0574304i \(-0.981709\pi\)
0.548911 + 0.835881i \(0.315043\pi\)
\(402\) 0 0
\(403\) 3.00000 + 5.19615i 0.149441 + 0.258839i
\(404\) −0.707107 + 1.22474i −0.0351799 + 0.0609333i
\(405\) −25.4558 −1.26491
\(406\) 0 0
\(407\) −6.00000 −0.297409
\(408\) 0 0
\(409\) −14.1421 24.4949i −0.699284 1.21119i −0.968715 0.248175i \(-0.920169\pi\)
0.269432 0.963020i \(-0.413164\pi\)
\(410\) 12.0000 + 20.7846i 0.592638 + 1.02648i
\(411\) 0 0
\(412\) −4.24264 −0.209020
\(413\) 0 0
\(414\) 18.0000 0.884652
\(415\) 10.0000 17.3205i 0.490881 0.850230i
\(416\) −2.12132 3.67423i −0.104006 0.180144i
\(417\) 0 0
\(418\) −0.707107 + 1.22474i −0.0345857 + 0.0599042i
\(419\) 22.6274 1.10542 0.552711 0.833373i \(-0.313593\pi\)
0.552711 + 0.833373i \(0.313593\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) −7.00000 + 12.1244i −0.340755 + 0.590204i
\(423\) 10.6066 + 18.3712i 0.515711 + 0.893237i
\(424\) 3.00000 + 5.19615i 0.145693 + 0.252347i
\(425\) −4.24264 + 7.34847i −0.205798 + 0.356453i
\(426\) 0 0
\(427\) 0 0
\(428\) 18.0000 0.870063
\(429\) 0 0
\(430\) −14.1421 24.4949i −0.681994 1.18125i
\(431\) 6.00000 + 10.3923i 0.289010 + 0.500580i 0.973574 0.228373i \(-0.0733406\pi\)
−0.684564 + 0.728953i \(0.740007\pi\)
\(432\) 0 0
\(433\) −24.0416 −1.15537 −0.577684 0.816261i \(-0.696043\pi\)
−0.577684 + 0.816261i \(0.696043\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −7.00000 + 12.1244i −0.335239 + 0.580651i
\(437\) 4.24264 + 7.34847i 0.202953 + 0.351525i
\(438\) 0 0
\(439\) −15.5563 + 26.9444i −0.742464 + 1.28599i 0.208906 + 0.977936i \(0.433010\pi\)
−0.951370 + 0.308050i \(0.900324\pi\)
\(440\) 2.82843 0.134840
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −18.0000 + 31.1769i −0.855206 + 1.48126i 0.0212481 + 0.999774i \(0.493236\pi\)
−0.876454 + 0.481486i \(0.840097\pi\)
\(444\) 0 0
\(445\) −26.0000 45.0333i −1.23252 2.13478i
\(446\) 6.36396 11.0227i 0.301342 0.521940i
\(447\) 0 0
\(448\) 0 0
\(449\) 8.00000 0.377543 0.188772 0.982021i \(-0.439549\pi\)
0.188772 + 0.982021i \(0.439549\pi\)
\(450\) −4.50000 + 7.79423i −0.212132 + 0.367423i
\(451\) 4.24264 + 7.34847i 0.199778 + 0.346026i
\(452\) −4.00000 6.92820i −0.188144 0.325875i
\(453\) 0 0
\(454\) 26.8701 1.26107
\(455\) 0 0
\(456\) 0 0
\(457\) −19.0000 + 32.9090i −0.888783 + 1.53942i −0.0474665 + 0.998873i \(0.515115\pi\)
−0.841316 + 0.540544i \(0.818219\pi\)
\(458\) 12.7279 + 22.0454i 0.594737 + 1.03011i
\(459\) 0 0
\(460\) 8.48528 14.6969i 0.395628 0.685248i
\(461\) −18.3848 −0.856264 −0.428132 0.903716i \(-0.640828\pi\)
−0.428132 + 0.903716i \(0.640828\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) −4.00000 + 6.92820i −0.185695 + 0.321634i
\(465\) 0 0
\(466\) 1.00000 + 1.73205i 0.0463241 + 0.0802357i
\(467\) −16.9706 + 29.3939i −0.785304 + 1.36019i 0.143513 + 0.989648i \(0.454160\pi\)
−0.928817 + 0.370538i \(0.879173\pi\)
\(468\) 12.7279 0.588348
\(469\) 0 0
\(470\) 20.0000 0.922531
\(471\) 0 0
\(472\) 7.07107 + 12.2474i 0.325472 + 0.563735i
\(473\) −5.00000 8.66025i −0.229900 0.398199i
\(474\) 0 0
\(475\) −4.24264 −0.194666
\(476\) 0 0
\(477\) −18.0000 −0.824163
\(478\) −2.00000 + 3.46410i −0.0914779 + 0.158444i
\(479\) −5.65685 9.79796i −0.258468 0.447680i 0.707364 0.706850i \(-0.249884\pi\)
−0.965832 + 0.259170i \(0.916551\pi\)
\(480\) 0 0
\(481\) −12.7279 + 22.0454i −0.580343 + 1.00518i
\(482\) −2.82843 −0.128831
\(483\) 0 0
\(484\) 1.00000 0.0454545
\(485\) 2.00000 3.46410i 0.0908153 0.157297i
\(486\) 0 0
\(487\) −11.0000 19.0526i −0.498458 0.863354i 0.501541 0.865134i \(-0.332767\pi\)
−0.999998 + 0.00178012i \(0.999433\pi\)
\(488\) 2.12132 3.67423i 0.0960277 0.166325i
\(489\) 0 0
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 0 0
\(493\) −11.3137 19.5959i −0.509544 0.882556i
\(494\) 3.00000 + 5.19615i 0.134976 + 0.233786i
\(495\) −4.24264 + 7.34847i −0.190693 + 0.330289i
\(496\) 1.41421 0.0635001
\(497\) 0 0
\(498\) 0 0
\(499\) −8.00000 + 13.8564i −0.358129 + 0.620298i −0.987648 0.156687i \(-0.949919\pi\)
0.629519 + 0.776985i \(0.283252\pi\)
\(500\) −2.82843 4.89898i −0.126491 0.219089i
\(501\) 0 0
\(502\) −12.7279 + 22.0454i −0.568075 + 0.983935i
\(503\) 14.1421 0.630567 0.315283 0.948998i \(-0.397900\pi\)
0.315283 + 0.948998i \(0.397900\pi\)
\(504\) 0 0
\(505\) −4.00000 −0.177998
\(506\) 3.00000 5.19615i 0.133366 0.230997i
\(507\) 0 0
\(508\) −4.00000 6.92820i −0.177471 0.307389i
\(509\) −15.5563 + 26.9444i −0.689523 + 1.19429i 0.282469 + 0.959276i \(0.408846\pi\)
−0.971992 + 0.235013i \(0.924487\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) −9.19239 15.9217i −0.405459 0.702275i
\(515\) −6.00000 10.3923i −0.264392 0.457940i
\(516\) 0 0
\(517\) 7.07107 0.310985
\(518\) 0 0
\(519\) 0 0
\(520\) 6.00000 10.3923i 0.263117 0.455733i
\(521\) −20.5061 35.5176i −0.898388 1.55605i −0.829554 0.558426i \(-0.811405\pi\)
−0.0688342 0.997628i \(-0.521928\pi\)
\(522\) −12.0000 20.7846i −0.525226 0.909718i
\(523\) −9.19239 + 15.9217i −0.401955 + 0.696207i −0.993962 0.109726i \(-0.965003\pi\)
0.592007 + 0.805933i \(0.298336\pi\)
\(524\) −7.07107 −0.308901
\(525\) 0 0
\(526\) −12.0000 −0.523225
\(527\) −2.00000 + 3.46410i −0.0871214 + 0.150899i
\(528\) 0 0
\(529\) −6.50000 11.2583i −0.282609 0.489493i
\(530\) −8.48528 + 14.6969i −0.368577 + 0.638394i
\(531\) −42.4264 −1.84115
\(532\) 0 0
\(533\) 36.0000 1.55933
\(534\) 0 0
\(535\) 25.4558 + 44.0908i 1.10055 + 1.90621i
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) 0 0
\(538\) 25.4558 1.09748
\(539\) 0 0
\(540\) 0 0
\(541\) 5.00000 8.66025i 0.214967 0.372333i −0.738296 0.674477i \(-0.764369\pi\)
0.953262 + 0.302144i \(0.0977023\pi\)
\(542\) 4.24264 + 7.34847i 0.182237 + 0.315644i
\(543\) 0 0
\(544\) 1.41421 2.44949i 0.0606339 0.105021i
\(545\) −39.5980 −1.69619
\(546\) 0 0
\(547\) −12.0000 −0.513083 −0.256541 0.966533i \(-0.582583\pi\)
−0.256541 + 0.966533i \(0.582583\pi\)
\(548\) −5.00000 + 8.66025i −0.213589 + 0.369948i
\(549\) 6.36396 + 11.0227i 0.271607 + 0.470438i
\(550\) 1.50000 + 2.59808i 0.0639602 + 0.110782i
\(551\) 5.65685 9.79796i 0.240990 0.417407i
\(552\) 0 0
\(553\) 0 0
\(554\) −4.00000 −0.169944
\(555\) 0 0
\(556\) −10.6066 18.3712i −0.449820 0.779111i
\(557\) −7.00000 12.1244i −0.296600 0.513725i 0.678756 0.734364i \(-0.262519\pi\)
−0.975356 + 0.220638i \(0.929186\pi\)
\(558\) −2.12132 + 3.67423i −0.0898027 + 0.155543i
\(559\) −42.4264 −1.79445
\(560\) 0 0
\(561\) 0 0
\(562\) 3.00000 5.19615i 0.126547 0.219186i
\(563\) −4.94975 8.57321i −0.208607 0.361318i 0.742669 0.669659i \(-0.233560\pi\)
−0.951276 + 0.308341i \(0.900226\pi\)
\(564\) 0 0
\(565\) 11.3137 19.5959i 0.475971 0.824406i
\(566\) −4.24264 −0.178331
\(567\) 0 0
\(568\) 0 0
\(569\) 17.0000 29.4449i 0.712677 1.23439i −0.251172 0.967943i \(-0.580816\pi\)
0.963849 0.266450i \(-0.0858508\pi\)
\(570\) 0 0
\(571\) −6.00000 10.3923i −0.251092 0.434904i 0.712735 0.701434i \(-0.247456\pi\)
−0.963827 + 0.266529i \(0.914123\pi\)
\(572\) 2.12132 3.67423i 0.0886969 0.153627i
\(573\) 0 0
\(574\) 0 0
\(575\) 18.0000 0.750652
\(576\) 1.50000 2.59808i 0.0625000 0.108253i
\(577\) 6.36396 + 11.0227i 0.264935 + 0.458881i 0.967547 0.252693i \(-0.0813161\pi\)
−0.702611 + 0.711574i \(0.747983\pi\)
\(578\) −4.50000 7.79423i −0.187175 0.324197i
\(579\) 0 0
\(580\) −22.6274 −0.939552
\(581\) 0 0
\(582\) 0 0
\(583\) −3.00000 + 5.19615i −0.124247 + 0.215203i
\(584\) −4.24264 7.34847i −0.175562 0.304082i
\(585\) 18.0000 + 31.1769i 0.744208 + 1.28901i
\(586\) 7.77817 13.4722i 0.321313 0.556531i
\(587\) 19.7990 0.817192 0.408596 0.912715i \(-0.366019\pi\)
0.408596 + 0.912715i \(0.366019\pi\)
\(588\) 0 0
\(589\) −2.00000 −0.0824086
\(590\) −20.0000 + 34.6410i −0.823387 + 1.42615i
\(591\) 0 0
\(592\) 3.00000 + 5.19615i 0.123299 + 0.213561i
\(593\) 1.41421 2.44949i 0.0580748 0.100588i −0.835526 0.549450i \(-0.814837\pi\)
0.893601 + 0.448862i \(0.148170\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.00000 0.163846
\(597\) 0 0
\(598\) −12.7279 22.0454i −0.520483 0.901504i
\(599\) 8.00000 + 13.8564i 0.326871 + 0.566157i 0.981889 0.189456i \(-0.0606724\pi\)
−0.655018 + 0.755613i \(0.727339\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(602\) 0 0
\(603\) 12.0000 0.488678
\(604\) 10.0000 17.3205i 0.406894 0.704761i
\(605\) 1.41421 + 2.44949i 0.0574960 + 0.0995859i
\(606\) 0 0
\(607\) −16.9706 + 29.3939i −0.688814 + 1.19306i 0.283408 + 0.958999i \(0.408535\pi\)
−0.972222 + 0.234061i \(0.924798\pi\)
\(608\) 1.41421 0.0573539
\(609\) 0 0
\(610\) 12.0000 0.485866
\(611\) 15.0000 25.9808i 0.606835 1.05107i
\(612\) 4.24264 + 7.34847i 0.171499 + 0.297044i
\(613\) −22.0000 38.1051i −0.888572 1.53905i −0.841564 0.540157i \(-0.818365\pi\)
−0.0470071 0.998895i \(-0.514968\pi\)
\(614\) 12.0208 20.8207i 0.485121 0.840254i
\(615\) 0 0
\(616\) 0 0
\(617\) −4.00000 −0.161034 −0.0805170 0.996753i \(-0.525657\pi\)
−0.0805170 + 0.996753i \(0.525657\pi\)
\(618\) 0 0
\(619\) 14.1421 + 24.4949i 0.568420 + 0.984533i 0.996722 + 0.0808974i \(0.0257786\pi\)
−0.428302 + 0.903636i \(0.640888\pi\)
\(620\) 2.00000 + 3.46410i 0.0803219 + 0.139122i
\(621\) 0 0
\(622\) −24.0416 −0.963982
\(623\) 0 0
\(624\) 0 0
\(625\) 15.5000 26.8468i 0.620000 1.07387i
\(626\) 6.36396 + 11.0227i 0.254355 + 0.440556i
\(627\) 0 0
\(628\) 0 0
\(629\) −16.9706 −0.676661
\(630\) 0 0
\(631\) −38.0000 −1.51276 −0.756378 0.654135i \(-0.773033\pi\)
−0.756378 + 0.654135i \(0.773033\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −15.0000 25.9808i −0.595726 1.03183i
\(635\) 11.3137 19.5959i 0.448971 0.777640i
\(636\) 0 0
\(637\) 0 0
\(638\) −8.00000 −0.316723
\(639\) 0 0
\(640\) −1.41421 2.44949i −0.0559017 0.0968246i
\(641\) −2.00000 3.46410i −0.0789953 0.136824i 0.823821 0.566849i \(-0.191838\pi\)
−0.902817 + 0.430026i \(0.858505\pi\)
\(642\) 0 0
\(643\) −25.4558 −1.00388 −0.501940 0.864902i \(-0.667380\pi\)
−0.501940 + 0.864902i \(0.667380\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −2.00000 + 3.46410i −0.0786889 + 0.136293i
\(647\) −3.53553 6.12372i −0.138996 0.240748i 0.788121 0.615521i \(-0.211054\pi\)
−0.927117 + 0.374772i \(0.877721\pi\)
\(648\) 4.50000 + 7.79423i 0.176777 + 0.306186i
\(649\) −7.07107 + 12.2474i −0.277564 + 0.480754i
\(650\) 12.7279 0.499230
\(651\) 0 0
\(652\) −16.0000 −0.626608
\(653\) 1.00000 1.73205i 0.0391330 0.0677804i −0.845796 0.533507i \(-0.820874\pi\)
0.884929 + 0.465727i \(0.154207\pi\)
\(654\) 0 0
\(655\) −10.0000 17.3205i −0.390732 0.676768i
\(656\) 4.24264 7.34847i 0.165647 0.286910i
\(657\) 25.4558 0.993127
\(658\) 0 0
\(659\) 46.0000 1.79191 0.895953 0.444149i \(-0.146494\pi\)
0.895953 + 0.444149i \(0.146494\pi\)
\(660\) 0 0
\(661\) −4.24264 7.34847i −0.165020 0.285822i 0.771643 0.636056i \(-0.219435\pi\)
−0.936662 + 0.350234i \(0.886102\pi\)
\(662\) −16.0000 27.7128i −0.621858 1.07709i
\(663\) 0 0
\(664\) −7.07107 −0.274411
\(665\) 0 0
\(666\) −18.0000 −0.697486
\(667\) −24.0000 + 41.5692i −0.929284 + 1.60957i
\(668\) −7.07107 12.2474i −0.273588 0.473868i
\(669\) 0 0
\(670\) 5.65685 9.79796i 0.218543 0.378528i
\(671\) 4.24264 0.163785
\(672\) 0 0
\(673\) −14.0000 −0.539660 −0.269830 0.962908i \(-0.586968\pi\)
−0.269830 + 0.962908i \(0.586968\pi\)
\(674\) −9.00000 + 15.5885i −0.346667 + 0.600445i
\(675\) 0 0
\(676\) −2.50000 4.33013i −0.0961538 0.166543i
\(677\) −0.707107 + 1.22474i −0.0271763 + 0.0470708i −0.879294 0.476280i \(-0.841985\pi\)
0.852117 + 0.523351i \(0.175318\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 8.00000 0.306786
\(681\) 0 0
\(682\) 0.707107 + 1.22474i 0.0270765 + 0.0468979i
\(683\) −4.00000 6.92820i −0.153056 0.265100i 0.779294 0.626659i \(-0.215578\pi\)
−0.932349 + 0.361559i \(0.882245\pi\)
\(684\) −2.12132 + 3.67423i −0.0811107 + 0.140488i
\(685\) −28.2843 −1.08069
\(686\) 0 0
\(687\) 0 0
\(688\) −5.00000 + 8.66025i −0.190623 + 0.330169i
\(689\) 12.7279 + 22.0454i 0.484895 + 0.839863i
\(690\) 0 0
\(691\) 4.24264 7.34847i 0.161398 0.279549i −0.773973 0.633219i \(-0.781733\pi\)
0.935370 + 0.353670i \(0.115066\pi\)
\(692\) 15.5563 0.591364
\(693\) 0 0
\(694\) −10.0000 −0.379595
\(695\) 30.0000 51.9615i 1.13796 1.97101i
\(696\) 0 0
\(697\) 12.0000 + 20.7846i 0.454532 + 0.787273i
\(698\) 4.94975 8.57321i 0.187351 0.324501i
\(699\) 0 0
\(700\) 0 0
\(701\) 2.00000 0.0755390 0.0377695 0.999286i \(-0.487975\pi\)
0.0377695 + 0.999286i \(0.487975\pi\)
\(702\) 0 0
\(703\) −4.24264 7.34847i −0.160014 0.277153i
\(704\) −0.500000 0.866025i −0.0188445 0.0326396i
\(705\) 0 0
\(706\) −29.6985 −1.11772
\(707\) 0 0
\(708\) 0 0
\(709\) −19.0000 + 32.9090i −0.713560 + 1.23592i 0.249952 + 0.968258i \(0.419585\pi\)
−0.963512 + 0.267664i \(0.913748\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −9.19239 + 15.9217i −0.344499 + 0.596690i
\(713\) 8.48528 0.317776
\(714\) 0 0
\(715\) 12.0000 0.448775
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 0 0
\(718\) 12.0000 + 20.7846i 0.447836 + 0.775675i
\(719\) 2.12132 3.67423i 0.0791119 0.137026i −0.823755 0.566946i \(-0.808125\pi\)
0.902867 + 0.429920i \(0.141458\pi\)
\(720\) 8.48528 0.316228
\(721\) 0 0
\(722\) 17.0000 0.632674
\(723\) 0 0
\(724\) −4.24264 7.34847i −0.157676 0.273104i
\(725\) −12.0000 20.7846i −0.445669 0.771921i
\(726\) 0 0
\(727\) −15.5563 −0.576953 −0.288477 0.957487i \(-0.593149\pi\)
−0.288477 + 0.957487i \(0.593149\pi\)
\(728\) 0 0
\(729\) −27.0000 −1.00000
\(730\) 12.0000 20.7846i 0.444140 0.769273i
\(731\) −14.1421 24.4949i −0.523066 0.905977i
\(732\) 0 0
\(733\) 6.36396 11.0227i 0.235058 0.407133i −0.724231 0.689557i \(-0.757805\pi\)
0.959290 + 0.282424i \(0.0911386\pi\)
\(734\) 24.0416 0.887393
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 2.00000 3.46410i 0.0736709 0.127602i
\(738\) 12.7279 + 22.0454i 0.468521 + 0.811503i
\(739\) 10.0000 + 17.3205i 0.367856 + 0.637145i 0.989230 0.146369i \(-0.0467586\pi\)
−0.621374 + 0.783514i \(0.713425\pi\)
\(740\) −8.48528 + 14.6969i −0.311925 + 0.540270i
\(741\) 0 0
\(742\) 0 0
\(743\) −12.0000 −0.440237 −0.220119 0.975473i \(-0.570644\pi\)
−0.220119 + 0.975473i \(0.570644\pi\)
\(744\) 0 0
\(745\) 5.65685 + 9.79796i 0.207251 + 0.358969i
\(746\) 13.0000 + 22.5167i 0.475964 + 0.824394i
\(747\) 10.6066 18.3712i 0.388075 0.672166i
\(748\) 2.82843 0.103418
\(749\) 0 0
\(750\) 0 0
\(751\) 1.00000 1.73205i 0.0364905 0.0632034i −0.847203 0.531269i \(-0.821715\pi\)
0.883694 + 0.468065i \(0.155049\pi\)
\(752\) −3.53553 6.12372i −0.128928 0.223309i
\(753\) 0 0
\(754\) −16.9706 + 29.3939i −0.618031 + 1.07046i
\(755\) 56.5685 2.05874
\(756\) 0 0
\(757\) 26.0000 0.944986 0.472493 0.881334i \(-0.343354\pi\)
0.472493 + 0.881334i \(0.343354\pi\)
\(758\) −14.0000 + 24.2487i −0.508503 + 0.880753i
\(759\) 0 0
\(760\) 2.00000 + 3.46410i 0.0725476 + 0.125656i
\(761\) 11.3137 19.5959i 0.410122 0.710351i −0.584781 0.811191i \(-0.698820\pi\)
0.994903 + 0.100840i \(0.0321529\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −22.0000 −0.795932
\(765\) −12.0000 + 20.7846i −0.433861 + 0.751469i
\(766\) −17.6777 30.6186i −0.638720 1.10630i
\(767\) 30.0000 + 51.9615i 1.08324 + 1.87622i
\(768\) 0 0
\(769\) −16.9706 −0.611974 −0.305987 0.952036i \(-0.598986\pi\)
−0.305987 + 0.952036i \(0.598986\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 7.00000 12.1244i 0.251936 0.436365i
\(773\) −11.3137 19.5959i −0.406926 0.704816i 0.587618 0.809139i \(-0.300066\pi\)
−0.994544 + 0.104323i \(0.966733\pi\)
\(774\) −15.0000 25.9808i −0.539164 0.933859i
\(775\) −2.12132 + 3.67423i −0.0762001 + 0.131982i
\(776\) −1.41421 −0.0507673
\(777\) 0 0
\(778\) 18.0000 0.645331
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 0 0
\(781\) 0 0
\(782\) 8.48528 14.6969i 0.303433 0.525561i
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0