Properties

Label 784.2.x.e.557.1
Level $784$
Weight $2$
Character 784.557
Analytic conductor $6.260$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,2,Mod(165,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([0, 3, 8]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.165");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 784 = 2^{4} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 784.x (of order \(12\), degree \(4\), 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: \(6.26027151847\)
Analytic rank: \(0\)
Dimension: \(4\)
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: \(\Z[a_1, \ldots, a_{9}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: $\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label 557.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 784.557
Dual form 784.2.x.e.373.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(2.73205 + 0.732051i) q^{5} +(2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.366025 + 1.36603i) q^{2} +(-1.73205 - 1.00000i) q^{4} +(2.73205 + 0.732051i) q^{5} +(2.00000 - 2.00000i) q^{8} +(-2.59808 + 1.50000i) q^{9} +(-2.00000 + 3.46410i) q^{10} +(0.366025 + 1.36603i) q^{11} +(2.00000 + 3.46410i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(-1.09808 - 4.09808i) q^{18} +(-0.732051 + 2.73205i) q^{19} +(-4.00000 - 4.00000i) q^{20} -2.00000 q^{22} +(5.19615 - 3.00000i) q^{23} +(2.59808 + 1.50000i) q^{25} +(7.00000 + 7.00000i) q^{29} +(-4.00000 + 6.92820i) q^{31} +(-5.46410 + 1.46410i) q^{32} +(-2.00000 - 2.00000i) q^{34} +6.00000 q^{36} +(6.83013 + 1.83013i) q^{37} +(-3.46410 - 2.00000i) q^{38} +(6.92820 - 4.00000i) q^{40} +10.0000i q^{41} +(-1.00000 + 1.00000i) q^{43} +(0.732051 - 2.73205i) q^{44} +(-8.19615 + 2.19615i) q^{45} +(2.19615 + 8.19615i) q^{46} +(-6.00000 - 10.3923i) q^{47} +(-3.00000 + 3.00000i) q^{50} +(-0.366025 - 1.36603i) q^{53} +4.00000i q^{55} +(-12.1244 + 7.00000i) q^{58} +(-2.92820 - 10.9282i) q^{59} +(-2.19615 + 8.19615i) q^{61} +(-8.00000 - 8.00000i) q^{62} -8.00000i q^{64} +(-4.09808 + 1.09808i) q^{67} +(3.46410 - 2.00000i) q^{68} +(-2.19615 + 8.19615i) q^{72} +(5.19615 + 3.00000i) q^{73} +(-5.00000 + 8.66025i) q^{74} +(4.00000 - 4.00000i) q^{76} +(-5.00000 - 8.66025i) q^{79} +(2.92820 + 10.9282i) q^{80} +(4.50000 - 7.79423i) q^{81} +(-13.6603 - 3.66025i) q^{82} +(10.0000 + 10.0000i) q^{83} +(-4.00000 + 4.00000i) q^{85} +(-1.00000 - 1.73205i) q^{86} +(3.46410 + 2.00000i) q^{88} +(-12.1244 + 7.00000i) q^{89} -12.0000i q^{90} -12.0000 q^{92} +(16.3923 - 4.39230i) q^{94} +(-4.00000 + 6.92820i) q^{95} +2.00000 q^{97} +(-3.00000 - 3.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 4 q^{5} + 8 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 4 q^{5} + 8 q^{8} - 8 q^{10} - 2 q^{11} + 8 q^{16} - 4 q^{17} + 6 q^{18} + 4 q^{19} - 16 q^{20} - 8 q^{22} + 28 q^{29} - 16 q^{31} - 8 q^{32} - 8 q^{34} + 24 q^{36} + 10 q^{37} - 4 q^{43} - 4 q^{44} - 12 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{50} + 2 q^{53} + 16 q^{59} + 12 q^{61} - 32 q^{62} - 6 q^{67} + 12 q^{72} - 20 q^{74} + 16 q^{76} - 20 q^{79} - 16 q^{80} + 18 q^{81} - 20 q^{82} + 40 q^{83} - 16 q^{85} - 4 q^{86} - 48 q^{92} + 24 q^{94} - 16 q^{95} + 8 q^{97} - 12 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(687\) \(689\)
\(\chi(n)\) \(e\left(\frac{3}{4}\right)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.366025 + 1.36603i −0.258819 + 0.965926i
\(3\) 0 0 −0.258819 0.965926i \(-0.583333\pi\)
0.258819 + 0.965926i \(0.416667\pi\)
\(4\) −1.73205 1.00000i −0.866025 0.500000i
\(5\) 2.73205 + 0.732051i 1.22181 + 0.327383i 0.811386 0.584511i \(-0.198714\pi\)
0.410425 + 0.911894i \(0.365380\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 2.00000 2.00000i 0.707107 0.707107i
\(9\) −2.59808 + 1.50000i −0.866025 + 0.500000i
\(10\) −2.00000 + 3.46410i −0.632456 + 1.09545i
\(11\) 0.366025 + 1.36603i 0.110361 + 0.411872i 0.998898 0.0469323i \(-0.0149445\pi\)
−0.888537 + 0.458804i \(0.848278\pi\)
\(12\) 0 0
\(13\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 + 3.46410i 0.500000 + 0.866025i
\(17\) −1.00000 + 1.73205i −0.242536 + 0.420084i −0.961436 0.275029i \(-0.911312\pi\)
0.718900 + 0.695113i \(0.244646\pi\)
\(18\) −1.09808 4.09808i −0.258819 0.965926i
\(19\) −0.732051 + 2.73205i −0.167944 + 0.626775i 0.829702 + 0.558206i \(0.188510\pi\)
−0.997646 + 0.0685694i \(0.978157\pi\)
\(20\) −4.00000 4.00000i −0.894427 0.894427i
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 5.19615 3.00000i 1.08347 0.625543i 0.151642 0.988436i \(-0.451544\pi\)
0.931831 + 0.362892i \(0.118211\pi\)
\(24\) 0 0
\(25\) 2.59808 + 1.50000i 0.519615 + 0.300000i
\(26\) 0 0
\(27\) 0 0
\(28\) 0 0
\(29\) 7.00000 + 7.00000i 1.29987 + 1.29987i 0.928477 + 0.371391i \(0.121119\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) −4.00000 + 6.92820i −0.718421 + 1.24434i 0.243204 + 0.969975i \(0.421802\pi\)
−0.961625 + 0.274367i \(0.911532\pi\)
\(32\) −5.46410 + 1.46410i −0.965926 + 0.258819i
\(33\) 0 0
\(34\) −2.00000 2.00000i −0.342997 0.342997i
\(35\) 0 0
\(36\) 6.00000 1.00000
\(37\) 6.83013 + 1.83013i 1.12287 + 0.300871i 0.772043 0.635571i \(-0.219235\pi\)
0.350823 + 0.936442i \(0.385902\pi\)
\(38\) −3.46410 2.00000i −0.561951 0.324443i
\(39\) 0 0
\(40\) 6.92820 4.00000i 1.09545 0.632456i
\(41\) 10.0000i 1.56174i 0.624695 + 0.780869i \(0.285223\pi\)
−0.624695 + 0.780869i \(0.714777\pi\)
\(42\) 0 0
\(43\) −1.00000 + 1.00000i −0.152499 + 0.152499i −0.779233 0.626734i \(-0.784391\pi\)
0.626734 + 0.779233i \(0.284391\pi\)
\(44\) 0.732051 2.73205i 0.110361 0.411872i
\(45\) −8.19615 + 2.19615i −1.22181 + 0.327383i
\(46\) 2.19615 + 8.19615i 0.323805 + 1.20846i
\(47\) −6.00000 10.3923i −0.875190 1.51587i −0.856560 0.516047i \(-0.827403\pi\)
−0.0186297 0.999826i \(-0.505930\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −3.00000 + 3.00000i −0.424264 + 0.424264i
\(51\) 0 0
\(52\) 0 0
\(53\) −0.366025 1.36603i −0.0502775 0.187638i 0.936220 0.351414i \(-0.114299\pi\)
−0.986498 + 0.163776i \(0.947632\pi\)
\(54\) 0 0
\(55\) 4.00000i 0.539360i
\(56\) 0 0
\(57\) 0 0
\(58\) −12.1244 + 7.00000i −1.59201 + 0.919145i
\(59\) −2.92820 10.9282i −0.381220 1.42273i −0.844041 0.536279i \(-0.819829\pi\)
0.462821 0.886452i \(-0.346837\pi\)
\(60\) 0 0
\(61\) −2.19615 + 8.19615i −0.281189 + 1.04941i 0.670391 + 0.742008i \(0.266126\pi\)
−0.951580 + 0.307402i \(0.900540\pi\)
\(62\) −8.00000 8.00000i −1.01600 1.01600i
\(63\) 0 0
\(64\) 8.00000i 1.00000i
\(65\) 0 0
\(66\) 0 0
\(67\) −4.09808 + 1.09808i −0.500660 + 0.134151i −0.500306 0.865849i \(-0.666779\pi\)
−0.000353546 1.00000i \(0.500113\pi\)
\(68\) 3.46410 2.00000i 0.420084 0.242536i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) −2.19615 + 8.19615i −0.258819 + 0.965926i
\(73\) 5.19615 + 3.00000i 0.608164 + 0.351123i 0.772246 0.635323i \(-0.219133\pi\)
−0.164083 + 0.986447i \(0.552466\pi\)
\(74\) −5.00000 + 8.66025i −0.581238 + 1.00673i
\(75\) 0 0
\(76\) 4.00000 4.00000i 0.458831 0.458831i
\(77\) 0 0
\(78\) 0 0
\(79\) −5.00000 8.66025i −0.562544 0.974355i −0.997274 0.0737937i \(-0.976489\pi\)
0.434730 0.900561i \(-0.356844\pi\)
\(80\) 2.92820 + 10.9282i 0.327383 + 1.22181i
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) −13.6603 3.66025i −1.50852 0.404207i
\(83\) 10.0000 + 10.0000i 1.09764 + 1.09764i 0.994686 + 0.102957i \(0.0328303\pi\)
0.102957 + 0.994686i \(0.467170\pi\)
\(84\) 0 0
\(85\) −4.00000 + 4.00000i −0.433861 + 0.433861i
\(86\) −1.00000 1.73205i −0.107833 0.186772i
\(87\) 0 0
\(88\) 3.46410 + 2.00000i 0.369274 + 0.213201i
\(89\) −12.1244 + 7.00000i −1.28518 + 0.741999i −0.977790 0.209585i \(-0.932789\pi\)
−0.307389 + 0.951584i \(0.599455\pi\)
\(90\) 12.0000i 1.26491i
\(91\) 0 0
\(92\) −12.0000 −1.25109
\(93\) 0 0
\(94\) 16.3923 4.39230i 1.69074 0.453032i
\(95\) −4.00000 + 6.92820i −0.410391 + 0.710819i
\(96\) 0 0
\(97\) 2.00000 0.203069 0.101535 0.994832i \(-0.467625\pi\)
0.101535 + 0.994832i \(0.467625\pi\)
\(98\) 0 0
\(99\) −3.00000 3.00000i −0.301511 0.301511i
\(100\) −3.00000 5.19615i −0.300000 0.519615i
\(101\) −2.19615 8.19615i −0.218525 0.815548i −0.984896 0.173149i \(-0.944606\pi\)
0.766370 0.642399i \(-0.222061\pi\)
\(102\) 0 0
\(103\) 3.46410 2.00000i 0.341328 0.197066i −0.319531 0.947576i \(-0.603525\pi\)
0.660859 + 0.750510i \(0.270192\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) −6.83013 1.83013i −0.660293 0.176925i −0.0869149 0.996216i \(-0.527701\pi\)
−0.573378 + 0.819291i \(0.694367\pi\)
\(108\) 0 0
\(109\) 4.09808 1.09808i 0.392525 0.105177i −0.0571579 0.998365i \(-0.518204\pi\)
0.449682 + 0.893189i \(0.351537\pi\)
\(110\) −5.46410 1.46410i −0.520982 0.139597i
\(111\) 0 0
\(112\) 0 0
\(113\) 4.00000 0.376288 0.188144 0.982141i \(-0.439753\pi\)
0.188144 + 0.982141i \(0.439753\pi\)
\(114\) 0 0
\(115\) 16.3923 4.39230i 1.52859 0.409585i
\(116\) −5.12436 19.1244i −0.475784 1.77565i
\(117\) 0 0
\(118\) 16.0000 1.47292
\(119\) 0 0
\(120\) 0 0
\(121\) 7.79423 4.50000i 0.708566 0.409091i
\(122\) −10.3923 6.00000i −0.940875 0.543214i
\(123\) 0 0
\(124\) 13.8564 8.00000i 1.24434 0.718421i
\(125\) −4.00000 4.00000i −0.357771 0.357771i
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 10.9282 + 2.92820i 0.965926 + 0.258819i
\(129\) 0 0
\(130\) 0 0
\(131\) 5.12436 19.1244i 0.447717 1.67090i −0.260944 0.965354i \(-0.584034\pi\)
0.708661 0.705549i \(-0.249299\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 6.00000i 0.518321i
\(135\) 0 0
\(136\) 1.46410 + 5.46410i 0.125546 + 0.468543i
\(137\) 10.3923 + 6.00000i 0.887875 + 0.512615i 0.873247 0.487278i \(-0.162010\pi\)
0.0146279 + 0.999893i \(0.495344\pi\)
\(138\) 0 0
\(139\) 2.00000 2.00000i 0.169638 0.169638i −0.617182 0.786820i \(-0.711726\pi\)
0.786820 + 0.617182i \(0.211726\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −10.3923 6.00000i −0.866025 0.500000i
\(145\) 14.0000 + 24.2487i 1.16264 + 2.01375i
\(146\) −6.00000 + 6.00000i −0.496564 + 0.496564i
\(147\) 0 0
\(148\) −10.0000 10.0000i −0.821995 0.821995i
\(149\) −4.09808 1.09808i −0.335727 0.0899579i 0.0870170 0.996207i \(-0.472267\pi\)
−0.422744 + 0.906249i \(0.638933\pi\)
\(150\) 0 0
\(151\) 8.66025 + 5.00000i 0.704761 + 0.406894i 0.809118 0.587646i \(-0.199945\pi\)
−0.104357 + 0.994540i \(0.533278\pi\)
\(152\) 4.00000 + 6.92820i 0.324443 + 0.561951i
\(153\) 6.00000i 0.485071i
\(154\) 0 0
\(155\) −16.0000 + 16.0000i −1.28515 + 1.28515i
\(156\) 0 0
\(157\) −16.3923 + 4.39230i −1.30825 + 0.350544i −0.844563 0.535456i \(-0.820140\pi\)
−0.463685 + 0.886000i \(0.653473\pi\)
\(158\) 13.6603 3.66025i 1.08675 0.291194i
\(159\) 0 0
\(160\) −16.0000 −1.26491
\(161\) 0 0
\(162\) 9.00000 + 9.00000i 0.707107 + 0.707107i
\(163\) 5.49038 20.4904i 0.430040 1.60493i −0.322625 0.946527i \(-0.604565\pi\)
0.752665 0.658404i \(-0.228768\pi\)
\(164\) 10.0000 17.3205i 0.780869 1.35250i
\(165\) 0 0
\(166\) −17.3205 + 10.0000i −1.34433 + 0.776151i
\(167\) 12.0000i 0.928588i 0.885681 + 0.464294i \(0.153692\pi\)
−0.885681 + 0.464294i \(0.846308\pi\)
\(168\) 0 0
\(169\) 13.0000i 1.00000i
\(170\) −4.00000 6.92820i −0.306786 0.531369i
\(171\) −2.19615 8.19615i −0.167944 0.626775i
\(172\) 2.73205 0.732051i 0.208317 0.0558184i
\(173\) 0 0 −0.965926 0.258819i \(-0.916667\pi\)
0.965926 + 0.258819i \(0.0833333\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −4.00000 + 4.00000i −0.301511 + 0.301511i
\(177\) 0 0
\(178\) −5.12436 19.1244i −0.384087 1.43343i
\(179\) 4.09808 1.09808i 0.306305 0.0820741i −0.102393 0.994744i \(-0.532650\pi\)
0.408697 + 0.912670i \(0.365983\pi\)
\(180\) 16.3923 + 4.39230i 1.22181 + 0.327383i
\(181\) 4.00000 4.00000i 0.297318 0.297318i −0.542645 0.839962i \(-0.682577\pi\)
0.839962 + 0.542645i \(0.182577\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 4.39230 16.3923i 0.323805 1.20846i
\(185\) 17.3205 + 10.0000i 1.27343 + 0.735215i
\(186\) 0 0
\(187\) −2.73205 0.732051i −0.199787 0.0535329i
\(188\) 24.0000i 1.75038i
\(189\) 0 0
\(190\) −8.00000 8.00000i −0.580381 0.580381i
\(191\) 9.00000 + 15.5885i 0.651217 + 1.12794i 0.982828 + 0.184525i \(0.0590746\pi\)
−0.331611 + 0.943416i \(0.607592\pi\)
\(192\) 0 0
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) −0.732051 + 2.73205i −0.0525582 + 0.196150i
\(195\) 0 0
\(196\) 0 0
\(197\) 5.00000 5.00000i 0.356235 0.356235i −0.506188 0.862423i \(-0.668946\pi\)
0.862423 + 0.506188i \(0.168946\pi\)
\(198\) 5.19615 3.00000i 0.369274 0.213201i
\(199\) 20.7846 + 12.0000i 1.47338 + 0.850657i 0.999551 0.0299585i \(-0.00953751\pi\)
0.473831 + 0.880616i \(0.342871\pi\)
\(200\) 8.19615 2.19615i 0.579555 0.155291i
\(201\) 0 0
\(202\) 12.0000 0.844317
\(203\) 0 0
\(204\) 0 0
\(205\) −7.32051 + 27.3205i −0.511286 + 1.90815i
\(206\) 1.46410 + 5.46410i 0.102009 + 0.380702i
\(207\) −9.00000 + 15.5885i −0.625543 + 1.08347i
\(208\) 0 0
\(209\) −4.00000 −0.276686
\(210\) 0 0
\(211\) −9.00000 9.00000i −0.619586 0.619586i 0.325840 0.945425i \(-0.394353\pi\)
−0.945425 + 0.325840i \(0.894353\pi\)
\(212\) −0.732051 + 2.73205i −0.0502775 + 0.187638i
\(213\) 0 0
\(214\) 5.00000 8.66025i 0.341793 0.592003i
\(215\) −3.46410 + 2.00000i −0.236250 + 0.136399i
\(216\) 0 0
\(217\) 0 0
\(218\) 6.00000i 0.406371i
\(219\) 0 0
\(220\) 4.00000 6.92820i 0.269680 0.467099i
\(221\) 0 0
\(222\) 0 0
\(223\) −4.00000 −0.267860 −0.133930 0.990991i \(-0.542760\pi\)
−0.133930 + 0.990991i \(0.542760\pi\)
\(224\) 0 0
\(225\) −9.00000 −0.600000
\(226\) −1.46410 + 5.46410i −0.0973906 + 0.363467i
\(227\) −2.73205 + 0.732051i −0.181333 + 0.0485879i −0.348343 0.937367i \(-0.613255\pi\)
0.167010 + 0.985955i \(0.446589\pi\)
\(228\) 0 0
\(229\) 10.9282 + 2.92820i 0.722156 + 0.193501i 0.601133 0.799149i \(-0.294716\pi\)
0.121023 + 0.992650i \(0.461383\pi\)
\(230\) 24.0000i 1.58251i
\(231\) 0 0
\(232\) 28.0000 1.83829
\(233\) 13.8564 8.00000i 0.907763 0.524097i 0.0280525 0.999606i \(-0.491069\pi\)
0.879711 + 0.475509i \(0.157736\pi\)
\(234\) 0 0
\(235\) −8.78461 32.7846i −0.573045 2.13863i
\(236\) −5.85641 + 21.8564i −0.381220 + 1.42273i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) 11.0000 19.0526i 0.708572 1.22728i −0.256814 0.966461i \(-0.582673\pi\)
0.965387 0.260822i \(-0.0839937\pi\)
\(242\) 3.29423 + 12.2942i 0.211761 + 0.790303i
\(243\) 0 0
\(244\) 12.0000 12.0000i 0.768221 0.768221i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 5.85641 + 21.8564i 0.371882 + 1.38788i
\(249\) 0 0
\(250\) 6.92820 4.00000i 0.438178 0.252982i
\(251\) 14.0000 14.0000i 0.883672 0.883672i −0.110234 0.993906i \(-0.535160\pi\)
0.993906 + 0.110234i \(0.0351599\pi\)
\(252\) 0 0
\(253\) 6.00000 + 6.00000i 0.377217 + 0.377217i
\(254\) −2.92820 + 10.9282i −0.183732 + 0.685696i
\(255\) 0 0
\(256\) −8.00000 + 13.8564i −0.500000 + 0.866025i
\(257\) −1.00000 1.73205i −0.0623783 0.108042i 0.833150 0.553047i \(-0.186535\pi\)
−0.895528 + 0.445005i \(0.853202\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) −28.6865 7.68653i −1.77565 0.475784i
\(262\) 24.2487 + 14.0000i 1.49809 + 0.864923i
\(263\) −13.8564 8.00000i −0.854423 0.493301i 0.00771799 0.999970i \(-0.497543\pi\)
−0.862141 + 0.506669i \(0.830877\pi\)
\(264\) 0 0
\(265\) 4.00000i 0.245718i
\(266\) 0 0
\(267\) 0 0
\(268\) 8.19615 + 2.19615i 0.500660 + 0.134151i
\(269\) −10.9282 + 2.92820i −0.666304 + 0.178536i −0.576089 0.817387i \(-0.695422\pi\)
−0.0902148 + 0.995922i \(0.528755\pi\)
\(270\) 0 0
\(271\) −4.00000 6.92820i −0.242983 0.420858i 0.718580 0.695444i \(-0.244792\pi\)
−0.961563 + 0.274586i \(0.911459\pi\)
\(272\) −8.00000 −0.485071
\(273\) 0 0
\(274\) −12.0000 + 12.0000i −0.724947 + 0.724947i
\(275\) −1.09808 + 4.09808i −0.0662165 + 0.247123i
\(276\) 0 0
\(277\) −5.49038 20.4904i −0.329885 1.23115i −0.909309 0.416121i \(-0.863389\pi\)
0.579424 0.815026i \(-0.303278\pi\)
\(278\) 2.00000 + 3.46410i 0.119952 + 0.207763i
\(279\) 24.0000i 1.43684i
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) 0 0
\(283\) −1.46410 5.46410i −0.0870318 0.324807i 0.908659 0.417538i \(-0.137107\pi\)
−0.995691 + 0.0927310i \(0.970440\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 12.0000 12.0000i 0.707107 0.707107i
\(289\) 6.50000 + 11.2583i 0.382353 + 0.662255i
\(290\) −38.2487 + 10.2487i −2.24604 + 0.601825i
\(291\) 0 0
\(292\) −6.00000 10.3923i −0.351123 0.608164i
\(293\) −14.0000 + 14.0000i −0.817889 + 0.817889i −0.985802 0.167913i \(-0.946297\pi\)
0.167913 + 0.985802i \(0.446297\pi\)
\(294\) 0 0
\(295\) 32.0000i 1.86311i
\(296\) 17.3205 10.0000i 1.00673 0.581238i
\(297\) 0 0
\(298\) 3.00000 5.19615i 0.173785 0.301005i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −10.0000 + 10.0000i −0.575435 + 0.575435i
\(303\) 0 0
\(304\) −10.9282 + 2.92820i −0.626775 + 0.167944i
\(305\) −12.0000 + 20.7846i −0.687118 + 1.19012i
\(306\) 8.19615 + 2.19615i 0.468543 + 0.125546i
\(307\) −18.0000 18.0000i −1.02731 1.02731i −0.999616 0.0276979i \(-0.991182\pi\)
−0.0276979 0.999616i \(-0.508818\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −16.0000 27.7128i −0.908739 1.57398i
\(311\) −17.3205 10.0000i −0.982156 0.567048i −0.0792356 0.996856i \(-0.525248\pi\)
−0.902920 + 0.429808i \(0.858581\pi\)
\(312\) 0 0
\(313\) 12.1244 7.00000i 0.685309 0.395663i −0.116543 0.993186i \(-0.537181\pi\)
0.801852 + 0.597522i \(0.203848\pi\)
\(314\) 24.0000i 1.35440i
\(315\) 0 0
\(316\) 20.0000i 1.12509i
\(317\) −2.56218 + 9.56218i −0.143906 + 0.537065i 0.855895 + 0.517149i \(0.173007\pi\)
−0.999802 + 0.0199164i \(0.993660\pi\)
\(318\) 0 0
\(319\) −7.00000 + 12.1244i −0.391925 + 0.678834i
\(320\) 5.85641 21.8564i 0.327383 1.22181i
\(321\) 0 0
\(322\) 0 0
\(323\) −4.00000 4.00000i −0.222566 0.222566i
\(324\) −15.5885 + 9.00000i −0.866025 + 0.500000i
\(325\) 0 0
\(326\) 25.9808 + 15.0000i 1.43894 + 0.830773i
\(327\) 0 0
\(328\) 20.0000 + 20.0000i 1.10432 + 1.10432i
\(329\) 0 0
\(330\) 0 0
\(331\) −28.6865 7.68653i −1.57675 0.422490i −0.638835 0.769344i \(-0.720583\pi\)
−0.937919 + 0.346854i \(0.887250\pi\)
\(332\) −7.32051 27.3205i −0.401765 1.49941i
\(333\) −20.4904 + 5.49038i −1.12287 + 0.300871i
\(334\) −16.3923 4.39230i −0.896947 0.240336i
\(335\) −12.0000 −0.655630
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) 17.7583 + 4.75833i 0.965926 + 0.258819i
\(339\) 0 0
\(340\) 10.9282 2.92820i 0.592665 0.158804i
\(341\) −10.9282 2.92820i −0.591795 0.158571i
\(342\) 12.0000 0.648886
\(343\) 0 0
\(344\) 4.00000i 0.215666i
\(345\) 0 0
\(346\) 0 0
\(347\) 5.49038 + 20.4904i 0.294739 + 1.09998i 0.941424 + 0.337224i \(0.109488\pi\)
−0.646685 + 0.762757i \(0.723845\pi\)
\(348\) 0 0
\(349\) −12.0000 12.0000i −0.642345 0.642345i 0.308786 0.951131i \(-0.400077\pi\)
−0.951131 + 0.308786i \(0.900077\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.00000 6.92820i −0.213201 0.369274i
\(353\) −3.00000 + 5.19615i −0.159674 + 0.276563i −0.934751 0.355303i \(-0.884378\pi\)
0.775077 + 0.631867i \(0.217711\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 28.0000 1.48400
\(357\) 0 0
\(358\) 6.00000i 0.317110i
\(359\) −5.19615 + 3.00000i −0.274242 + 0.158334i −0.630814 0.775934i \(-0.717279\pi\)
0.356572 + 0.934268i \(0.383946\pi\)
\(360\) −12.0000 + 20.7846i −0.632456 + 1.09545i
\(361\) 9.52628 + 5.50000i 0.501383 + 0.289474i
\(362\) 4.00000 + 6.92820i 0.210235 + 0.364138i
\(363\) 0 0
\(364\) 0 0
\(365\) 12.0000 + 12.0000i 0.628109 + 0.628109i
\(366\) 0 0
\(367\) −16.0000 + 27.7128i −0.835193 + 1.44660i 0.0586798 + 0.998277i \(0.481311\pi\)
−0.893873 + 0.448320i \(0.852022\pi\)
\(368\) 20.7846 + 12.0000i 1.08347 + 0.625543i
\(369\) −15.0000 25.9808i −0.780869 1.35250i
\(370\) −20.0000 + 20.0000i −1.03975 + 1.03975i
\(371\) 0 0
\(372\) 0 0
\(373\) 15.0263 + 4.02628i 0.778031 + 0.208473i 0.625917 0.779890i \(-0.284725\pi\)
0.152115 + 0.988363i \(0.451392\pi\)
\(374\) 2.00000 3.46410i 0.103418 0.179124i
\(375\) 0 0
\(376\) −32.7846 8.78461i −1.69074 0.453032i
\(377\) 0 0
\(378\) 0 0
\(379\) 13.0000 13.0000i 0.667765 0.667765i −0.289433 0.957198i \(-0.593467\pi\)
0.957198 + 0.289433i \(0.0934668\pi\)
\(380\) 13.8564 8.00000i 0.710819 0.410391i
\(381\) 0 0
\(382\) −24.5885 + 6.58846i −1.25805 + 0.337095i
\(383\) 2.00000 + 3.46410i 0.102195 + 0.177007i 0.912589 0.408879i \(-0.134080\pi\)
−0.810394 + 0.585886i \(0.800747\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 16.0000 + 16.0000i 0.814379 + 0.814379i
\(387\) 1.09808 4.09808i 0.0558184 0.208317i
\(388\) −3.46410 2.00000i −0.175863 0.101535i
\(389\) 1.09808 + 4.09808i 0.0556747 + 0.207781i 0.988160 0.153427i \(-0.0490311\pi\)
−0.932485 + 0.361208i \(0.882364\pi\)
\(390\) 0 0
\(391\) 12.0000i 0.606866i
\(392\) 0 0
\(393\) 0 0
\(394\) 5.00000 + 8.66025i 0.251896 + 0.436297i
\(395\) −7.32051 27.3205i −0.368335 1.37464i
\(396\) 2.19615 + 8.19615i 0.110361 + 0.411872i
\(397\) 4.39230 16.3923i 0.220443 0.822706i −0.763736 0.645529i \(-0.776637\pi\)
0.984179 0.177177i \(-0.0566965\pi\)
\(398\) −24.0000 + 24.0000i −1.20301 + 1.20301i
\(399\) 0 0
\(400\) 12.0000i 0.600000i
\(401\) −6.00000 10.3923i −0.299626 0.518967i 0.676425 0.736512i \(-0.263528\pi\)
−0.976050 + 0.217545i \(0.930195\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −4.39230 + 16.3923i −0.218525 + 0.815548i
\(405\) 18.0000 18.0000i 0.894427 0.894427i
\(406\) 0 0
\(407\) 10.0000i 0.495682i
\(408\) 0 0
\(409\) 12.1244 + 7.00000i 0.599511 + 0.346128i 0.768849 0.639430i \(-0.220830\pi\)
−0.169338 + 0.985558i \(0.554163\pi\)
\(410\) −34.6410 20.0000i −1.71080 0.987730i
\(411\) 0 0
\(412\) −8.00000 −0.394132
\(413\) 0 0
\(414\) −18.0000 18.0000i −0.884652 0.884652i
\(415\) 20.0000 + 34.6410i 0.981761 + 1.70046i
\(416\) 0 0
\(417\) 0 0
\(418\) 1.46410 5.46410i 0.0716116 0.267258i
\(419\) −12.0000 12.0000i −0.586238 0.586238i 0.350372 0.936611i \(-0.386055\pi\)
−0.936611 + 0.350372i \(0.886055\pi\)
\(420\) 0 0
\(421\) −9.00000 + 9.00000i −0.438633 + 0.438633i −0.891552 0.452919i \(-0.850383\pi\)
0.452919 + 0.891552i \(0.350383\pi\)
\(422\) 15.5885 9.00000i 0.758834 0.438113i
\(423\) 31.1769 + 18.0000i 1.51587 + 0.875190i
\(424\) −3.46410 2.00000i −0.168232 0.0971286i
\(425\) −5.19615 + 3.00000i −0.252050 + 0.145521i
\(426\) 0 0
\(427\) 0 0
\(428\) 10.0000 + 10.0000i 0.483368 + 0.483368i
\(429\) 0 0
\(430\) −1.46410 5.46410i −0.0706052 0.263502i
\(431\) 4.00000 6.92820i 0.192673 0.333720i −0.753462 0.657491i \(-0.771618\pi\)
0.946135 + 0.323772i \(0.104951\pi\)
\(432\) 0 0
\(433\) 6.00000 0.288342 0.144171 0.989553i \(-0.453949\pi\)
0.144171 + 0.989553i \(0.453949\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −8.19615 2.19615i −0.392525 0.105177i
\(437\) 4.39230 + 16.3923i 0.210112 + 0.784150i
\(438\) 0 0
\(439\) 13.8564 8.00000i 0.661330 0.381819i −0.131453 0.991322i \(-0.541964\pi\)
0.792784 + 0.609503i \(0.208631\pi\)
\(440\) 8.00000 + 8.00000i 0.381385 + 0.381385i
\(441\) 0 0
\(442\) 0 0
\(443\) 1.36603 + 0.366025i 0.0649018 + 0.0173904i 0.291124 0.956685i \(-0.405971\pi\)
−0.226222 + 0.974076i \(0.572637\pi\)
\(444\) 0 0
\(445\) −38.2487 + 10.2487i −1.81316 + 0.485836i
\(446\) 1.46410 5.46410i 0.0693272 0.258733i
\(447\) 0 0
\(448\) 0 0
\(449\) −30.0000 −1.41579 −0.707894 0.706319i \(-0.750354\pi\)
−0.707894 + 0.706319i \(0.750354\pi\)
\(450\) 3.29423 12.2942i 0.155291 0.579555i
\(451\) −13.6603 + 3.66025i −0.643236 + 0.172355i
\(452\) −6.92820 4.00000i −0.325875 0.188144i
\(453\) 0 0
\(454\) 4.00000i 0.187729i
\(455\) 0 0
\(456\) 0 0
\(457\) −19.0526 + 11.0000i −0.891241 + 0.514558i −0.874348 0.485299i \(-0.838711\pi\)
−0.0168929 + 0.999857i \(0.505377\pi\)
\(458\) −8.00000 + 13.8564i −0.373815 + 0.647467i
\(459\) 0 0
\(460\) −32.7846 8.78461i −1.52859 0.409585i
\(461\) −16.0000 16.0000i −0.745194 0.745194i 0.228378 0.973572i \(-0.426658\pi\)
−0.973572 + 0.228378i \(0.926658\pi\)
\(462\) 0 0
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) −10.2487 + 38.2487i −0.475784 + 1.77565i
\(465\) 0 0
\(466\) 5.85641 + 21.8564i 0.271293 + 1.01248i
\(467\) −6.58846 + 24.5885i −0.304877 + 1.13782i 0.628173 + 0.778073i \(0.283803\pi\)
−0.933051 + 0.359745i \(0.882864\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 48.0000 2.21407
\(471\) 0 0
\(472\) −27.7128 16.0000i −1.27559 0.736460i
\(473\) −1.73205 1.00000i −0.0796398 0.0459800i
\(474\) 0 0
\(475\) −6.00000 + 6.00000i −0.275299 + 0.275299i
\(476\) 0 0
\(477\) 3.00000 + 3.00000i 0.137361 + 0.137361i
\(478\) 0 0
\(479\) −10.0000 + 17.3205i −0.456912 + 0.791394i −0.998796 0.0490589i \(-0.984378\pi\)
0.541884 + 0.840453i \(0.317711\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 22.0000 + 22.0000i 1.00207 + 1.00207i
\(483\) 0 0
\(484\) −18.0000 −0.818182
\(485\) 5.46410 + 1.46410i 0.248112 + 0.0664814i
\(486\) 0 0
\(487\) 19.0526 + 11.0000i 0.863354 + 0.498458i 0.865134 0.501541i \(-0.167233\pi\)
−0.00178012 + 0.999998i \(0.500567\pi\)
\(488\) 12.0000 + 20.7846i 0.543214 + 0.940875i
\(489\) 0 0
\(490\) 0 0
\(491\) −19.0000 + 19.0000i −0.857458 + 0.857458i −0.991038 0.133580i \(-0.957353\pi\)
0.133580 + 0.991038i \(0.457353\pi\)
\(492\) 0 0
\(493\) −19.1244 + 5.12436i −0.861318 + 0.230789i
\(494\) 0 0
\(495\) −6.00000 10.3923i −0.269680 0.467099i
\(496\) −32.0000 −1.43684
\(497\) 0 0
\(498\) 0 0
\(499\) −8.41858 + 31.4186i −0.376868 + 1.40649i 0.473729 + 0.880671i \(0.342908\pi\)
−0.850597 + 0.525818i \(0.823759\pi\)
\(500\) 2.92820 + 10.9282i 0.130953 + 0.488724i
\(501\) 0 0
\(502\) 14.0000 + 24.2487i 0.624851 + 1.08227i
\(503\) 16.0000i 0.713405i −0.934218 0.356702i \(-0.883901\pi\)
0.934218 0.356702i \(-0.116099\pi\)
\(504\) 0 0
\(505\) 24.0000i 1.06799i
\(506\) −10.3923 + 6.00000i −0.461994 + 0.266733i
\(507\) 0 0
\(508\) −13.8564 8.00000i −0.614779 0.354943i
\(509\) 2.92820 10.9282i 0.129790 0.484384i −0.870175 0.492743i \(-0.835994\pi\)
0.999965 + 0.00835918i \(0.00266084\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −16.0000 16.0000i −0.707107 0.707107i
\(513\) 0 0
\(514\) 2.73205 0.732051i 0.120506 0.0322894i
\(515\) 10.9282 2.92820i 0.481554 0.129032i
\(516\) 0 0
\(517\) 12.0000 12.0000i 0.527759 0.527759i
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 8.66025 + 5.00000i 0.379413 + 0.219054i 0.677563 0.735465i \(-0.263036\pi\)
−0.298150 + 0.954519i \(0.596370\pi\)
\(522\) 21.0000 36.3731i 0.919145 1.59201i
\(523\) 32.7846 + 8.78461i 1.43357 + 0.384124i 0.890277 0.455419i \(-0.150510\pi\)
0.543293 + 0.839543i \(0.317177\pi\)
\(524\) −28.0000 + 28.0000i −1.22319 + 1.22319i
\(525\) 0 0
\(526\) 16.0000 16.0000i 0.697633 0.697633i
\(527\) −8.00000 13.8564i −0.348485 0.603595i
\(528\) 0 0
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) 5.46410 + 1.46410i 0.237345 + 0.0635965i
\(531\) 24.0000 + 24.0000i 1.04151 + 1.04151i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −17.3205 10.0000i −0.748831 0.432338i
\(536\) −6.00000 + 10.3923i −0.259161 + 0.448879i
\(537\) 0 0
\(538\) 16.0000i 0.689809i
\(539\) 0 0
\(540\) 0 0
\(541\) 4.02628 15.0263i 0.173103 0.646030i −0.823764 0.566933i \(-0.808130\pi\)
0.996867 0.0790969i \(-0.0252036\pi\)
\(542\) 10.9282 2.92820i 0.469407 0.125777i
\(543\) 0 0
\(544\) 2.92820 10.9282i 0.125546 0.468543i
\(545\) 12.0000 0.514024
\(546\) 0 0
\(547\) 23.0000 + 23.0000i 0.983409 + 0.983409i 0.999865 0.0164556i \(-0.00523822\pi\)
−0.0164556 + 0.999865i \(0.505238\pi\)
\(548\) −12.0000 20.7846i −0.512615 0.887875i
\(549\) −6.58846 24.5885i −0.281189 1.04941i
\(550\) −5.19615 3.00000i −0.221565 0.127920i
\(551\) −24.2487 + 14.0000i −1.03303 + 0.596420i
\(552\) 0 0
\(553\) 0 0
\(554\) 30.0000 1.27458
\(555\) 0 0
\(556\) −5.46410 + 1.46410i −0.231730 + 0.0620917i
\(557\) 23.2224 6.22243i 0.983966 0.263653i 0.269252 0.963070i \(-0.413224\pi\)
0.714714 + 0.699417i \(0.246557\pi\)
\(558\) 32.7846 + 8.78461i 1.38788 + 0.371882i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 27.3205 7.32051i 1.15142 0.308523i 0.367887 0.929870i \(-0.380081\pi\)
0.783535 + 0.621348i \(0.213415\pi\)
\(564\) 0 0
\(565\) 10.9282 + 2.92820i 0.459753 + 0.123190i
\(566\) 8.00000 0.336265
\(567\) 0 0
\(568\) 0 0
\(569\) 12.1244 7.00000i 0.508279 0.293455i −0.223847 0.974624i \(-0.571861\pi\)
0.732126 + 0.681169i \(0.238528\pi\)
\(570\) 0 0
\(571\) −3.29423 12.2942i −0.137859 0.514497i −0.999970 0.00777727i \(-0.997524\pi\)
0.862111 0.506720i \(-0.169142\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 18.0000 0.750652
\(576\) 12.0000 + 20.7846i 0.500000 + 0.866025i
\(577\) −1.00000 + 1.73205i −0.0416305 + 0.0721062i −0.886090 0.463513i \(-0.846589\pi\)
0.844459 + 0.535620i \(0.179922\pi\)
\(578\) −17.7583 + 4.75833i −0.738649 + 0.197920i
\(579\) 0 0
\(580\) 56.0000i 2.32527i
\(581\) 0 0
\(582\) 0 0
\(583\) 1.73205 1.00000i 0.0717342 0.0414158i
\(584\) 16.3923 4.39230i 0.678318 0.181755i
\(585\) 0 0
\(586\) −14.0000 24.2487i −0.578335 1.00171i
\(587\) −10.0000 + 10.0000i −0.412744 + 0.412744i −0.882693 0.469949i \(-0.844272\pi\)
0.469949 + 0.882693i \(0.344272\pi\)
\(588\) 0 0
\(589\) −16.0000 16.0000i −0.659269 0.659269i
\(590\) 43.7128 + 11.7128i 1.79963 + 0.482209i
\(591\) 0 0
\(592\) 7.32051 + 27.3205i 0.300871 + 1.12287i
\(593\) −3.00000 5.19615i −0.123195 0.213380i 0.797831 0.602881i \(-0.205981\pi\)
−0.921026 + 0.389501i \(0.872647\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000 + 6.00000i 0.245770 + 0.245770i
\(597\) 0 0
\(598\) 0 0
\(599\) −20.7846 12.0000i −0.849236 0.490307i 0.0111569 0.999938i \(-0.496449\pi\)
−0.860393 + 0.509631i \(0.829782\pi\)
\(600\) 0 0
\(601\) 10.0000i 0.407909i 0.978980 + 0.203954i \(0.0653794\pi\)
−0.978980 + 0.203954i \(0.934621\pi\)
\(602\) 0 0
\(603\) 9.00000 9.00000i 0.366508 0.366508i
\(604\) −10.0000 17.3205i −0.406894 0.704761i
\(605\) 24.5885 6.58846i 0.999663 0.267859i
\(606\) 0 0
\(607\) 14.0000 + 24.2487i 0.568242 + 0.984225i 0.996740 + 0.0806818i \(0.0257098\pi\)
−0.428497 + 0.903543i \(0.640957\pi\)
\(608\) 16.0000i 0.648886i
\(609\) 0 0
\(610\) −24.0000 24.0000i −0.971732 0.971732i
\(611\) 0 0
\(612\) −6.00000 + 10.3923i −0.242536 + 0.420084i
\(613\) 3.29423 + 12.2942i 0.133053 + 0.496559i 0.999998 0.00184345i \(-0.000586790\pi\)
−0.866946 + 0.498403i \(0.833920\pi\)
\(614\) 31.1769 18.0000i 1.25820 0.726421i
\(615\) 0 0
\(616\) 0 0
\(617\) 42.0000i 1.69086i −0.534089 0.845428i \(-0.679345\pi\)
0.534089 0.845428i \(-0.320655\pi\)
\(618\) 0 0
\(619\) 4.39230 + 16.3923i 0.176542 + 0.658862i 0.996284 + 0.0861298i \(0.0274500\pi\)
−0.819742 + 0.572733i \(0.805883\pi\)
\(620\) 43.7128 11.7128i 1.75555 0.470398i
\(621\) 0 0
\(622\) 20.0000 20.0000i 0.801927 0.801927i
\(623\) 0 0
\(624\) 0 0
\(625\) −15.5000 26.8468i −0.620000 1.07387i
\(626\) 5.12436 + 19.1244i 0.204810 + 0.764363i
\(627\) 0 0
\(628\) 32.7846 + 8.78461i 1.30825 + 0.350544i
\(629\) −10.0000 + 10.0000i −0.398726 + 0.398726i
\(630\) 0 0
\(631\) 40.0000i 1.59237i 0.605050 + 0.796187i \(0.293153\pi\)
−0.605050 + 0.796187i \(0.706847\pi\)
\(632\) −27.3205 7.32051i −1.08675 0.291194i
\(633\) 0 0
\(634\) −12.1244 7.00000i −0.481520 0.278006i
\(635\) 21.8564 + 5.85641i 0.867345 + 0.232404i
\(636\) 0 0
\(637\) 0 0
\(638\) −14.0000 14.0000i −0.554265 0.554265i
\(639\) 0 0
\(640\) 27.7128 + 16.0000i 1.09545 + 0.632456i
\(641\) −6.00000 + 10.3923i −0.236986 + 0.410471i −0.959848 0.280521i \(-0.909493\pi\)
0.722862 + 0.690992i \(0.242826\pi\)
\(642\) 0 0
\(643\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.92820 4.00000i 0.272587 0.157378i
\(647\) −10.3923 6.00000i −0.408564 0.235884i 0.281609 0.959529i \(-0.409132\pi\)
−0.690172 + 0.723645i \(0.742465\pi\)
\(648\) −6.58846 24.5885i −0.258819 0.965926i
\(649\) 13.8564 8.00000i 0.543912 0.314027i
\(650\) 0 0
\(651\) 0 0
\(652\) −30.0000 + 30.0000i −1.17489 + 1.17489i
\(653\) 9.15064 34.1506i 0.358092 1.33642i −0.518456 0.855104i \(-0.673493\pi\)
0.876548 0.481314i \(-0.159840\pi\)
\(654\) 0 0
\(655\) 28.0000 48.4974i 1.09405 1.89495i
\(656\) −34.6410 + 20.0000i −1.35250 + 0.780869i
\(657\) −18.0000 −0.702247
\(658\) 0 0
\(659\) −3.00000 3.00000i −0.116863 0.116863i 0.646257 0.763120i \(-0.276334\pi\)
−0.763120 + 0.646257i \(0.776334\pi\)
\(660\) 0 0
\(661\) −9.51666 35.5167i −0.370155 1.38144i −0.860296 0.509795i \(-0.829721\pi\)
0.490141 0.871643i \(-0.336945\pi\)
\(662\) 21.0000 36.3731i 0.816188 1.41368i
\(663\) 0 0
\(664\) 40.0000 1.55230
\(665\) 0 0
\(666\) 30.0000i 1.16248i
\(667\) 57.3731 + 15.3731i 2.22149 + 0.595248i
\(668\) 12.0000 20.7846i 0.464294 0.804181i
\(669\) 0 0
\(670\) 4.39230 16.3923i 0.169690 0.633290i
\(671\) −12.0000 −0.463255
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) −2.92820 + 10.9282i −0.112790 + 0.420939i
\(675\) 0 0
\(676\) −13.0000 + 22.5167i −0.500000 + 0.866025i
\(677\) −27.3205 7.32051i −1.05001 0.281350i −0.307756 0.951465i \(-0.599578\pi\)
−0.742257 + 0.670115i \(0.766245\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 16.0000i 0.613572i
\(681\) 0 0
\(682\) 8.00000 13.8564i 0.306336 0.530589i
\(683\) −4.02628 15.0263i −0.154061 0.574965i −0.999184 0.0403921i \(-0.987139\pi\)
0.845123 0.534573i \(-0.179527\pi\)
\(684\) −4.39230 + 16.3923i −0.167944 + 0.626775i
\(685\) 24.0000 + 24.0000i 0.916993 + 0.916993i
\(686\) 0 0
\(687\) 0 0
\(688\) −5.46410 1.46410i −0.208317 0.0558184i
\(689\) 0 0
\(690\) 0 0
\(691\) −9.51666 + 35.5167i −0.362031 + 1.35112i 0.509371 + 0.860547i \(0.329878\pi\)
−0.871402 + 0.490570i \(0.836788\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −30.0000 −1.13878
\(695\) 6.92820 4.00000i 0.262802 0.151729i
\(696\) 0 0
\(697\) −17.3205 10.0000i −0.656061 0.378777i
\(698\) 20.7846 12.0000i 0.786709 0.454207i
\(699\) 0 0
\(700\) 0 0
\(701\) −19.0000 19.0000i −0.717620 0.717620i 0.250497 0.968117i \(-0.419406\pi\)
−0.968117 + 0.250497i \(0.919406\pi\)
\(702\) 0 0
\(703\) −10.0000 + 17.3205i −0.377157 + 0.653255i
\(704\) 10.9282 2.92820i 0.411872 0.110361i
\(705\) 0 0
\(706\) −6.00000 6.00000i −0.225813 0.225813i
\(707\) 0 0
\(708\) 0 0
\(709\) 9.56218 + 2.56218i 0.359115 + 0.0962246i 0.433865 0.900978i \(-0.357149\pi\)
−0.0747503 + 0.997202i \(0.523816\pi\)
\(710\) 0 0
\(711\) 25.9808 + 15.0000i 0.974355 + 0.562544i
\(712\) −10.2487 + 38.2487i −0.384087 + 1.43343i
\(713\) 48.0000i 1.79761i
\(714\) 0 0
\(715\) 0 0
\(716\) −8.19615 2.19615i −0.306305 0.0820741i
\(717\) 0 0
\(718\) −2.19615 8.19615i −0.0819597 0.305878i
\(719\) 10.0000 + 17.3205i 0.372937 + 0.645946i 0.990016 0.140955i \(-0.0450174\pi\)
−0.617079 + 0.786901i \(0.711684\pi\)
\(720\) −24.0000 24.0000i −0.894427 0.894427i
\(721\) 0 0
\(722\) −11.0000 + 11.0000i −0.409378 + 0.409378i
\(723\) 0 0
\(724\) −10.9282 + 2.92820i −0.406143 + 0.108826i
\(725\) 7.68653 + 28.6865i 0.285471 + 1.06539i
\(726\) 0 0
\(727\) 32.0000i 1.18681i 0.804902 + 0.593407i \(0.202218\pi\)
−0.804902 + 0.593407i \(0.797782\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) −20.7846 + 12.0000i −0.769273 + 0.444140i
\(731\) −0.732051 2.73205i −0.0270759 0.101049i
\(732\) 0 0
\(733\) 3.66025 13.6603i 0.135195 0.504553i −0.864802 0.502112i \(-0.832556\pi\)
0.999997 0.00244074i \(-0.000776913\pi\)
\(734\) −32.0000 32.0000i −1.18114 1.18114i
\(735\) 0 0
\(736\) −24.0000 + 24.0000i −0.884652 + 0.884652i
\(737\) −3.00000 5.19615i −0.110506 0.191403i
\(738\) 40.9808 10.9808i 1.50852 0.404207i
\(739\) −9.56218 + 2.56218i −0.351750 + 0.0942512i −0.430368 0.902654i \(-0.641616\pi\)
0.0786174 + 0.996905i \(0.474949\pi\)
\(740\) −20.0000 34.6410i −0.735215 1.27343i
\(741\) 0 0
\(742\) 0 0
\(743\) 6.00000i 0.220119i 0.993925 + 0.110059i \(0.0351041\pi\)
−0.993925 + 0.110059i \(0.964896\pi\)
\(744\) 0 0
\(745\) −10.3923 6.00000i −0.380745 0.219823i
\(746\) −11.0000 + 19.0526i −0.402739 + 0.697564i
\(747\) −40.9808 10.9808i −1.49941 0.401765i
\(748\) 4.00000 + 4.00000i 0.146254 + 0.146254i
\(749\) 0 0
\(750\) 0 0
\(751\) −16.0000 27.7128i −0.583848 1.01125i −0.995018 0.0996961i \(-0.968213\pi\)
0.411170 0.911559i \(-0.365120\pi\)
\(752\) 24.0000 41.5692i 0.875190 1.51587i
\(753\) 0 0
\(754\) 0 0
\(755\) 20.0000 + 20.0000i 0.727875 + 0.727875i
\(756\) 0 0
\(757\) −15.0000 + 15.0000i −0.545184 + 0.545184i −0.925044 0.379860i \(-0.875972\pi\)
0.379860 + 0.925044i \(0.375972\pi\)
\(758\) 13.0000 + 22.5167i 0.472181 + 0.817842i
\(759\) 0 0
\(760\) 5.85641 + 21.8564i 0.212434 + 0.792815i
\(761\) −25.9808 + 15.0000i −0.941802 + 0.543750i −0.890525 0.454935i \(-0.849663\pi\)
−0.0512772 + 0.998684i \(0.516329\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 36.0000i 1.30243i
\(765\) 4.39230 16.3923i 0.158804 0.592665i
\(766\) −5.46410 + 1.46410i −0.197426 + 0.0529001i
\(767\) 0 0
\(768\) 0 0
\(769\) 10.0000 0.360609 0.180305 0.983611i \(-0.442292\pi\)
0.180305 + 0.983611i \(0.442292\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −27.7128 + 16.0000i −0.997406 + 0.575853i
\(773\) 2.19615 + 8.19615i 0.0789901 + 0.294795i 0.994108 0.108390i \(-0.0345696\pi\)
−0.915118 + 0.403185i \(0.867903\pi\)
\(774\) 5.19615 + 3.00000i 0.186772 + 0.107833i
\(775\) −20.7846 + 12.0000i −0.746605 + 0.431053i
\(776\) 4.00000 4.00000i 0.143592 0.143592i
\(777\) 0 0
\(778\) −6.00000 −0.215110
\(779\) −27.3205 7.32051i −0.978859 0.262284i
\(780\) 0 0
\(781\) 0 0
\(782\) −16.3923 4.39230i −0.586188 0.157069i
\(783\) 0 0
\(784\) 0 0
\(785\) −48.0000 −1.71319
\(786\) 0 0
\(787\) 24.5885 6.58846i 0.876484 0.234853i 0.207594 0.978215i \(-0.433437\pi\)
0.668889 + 0.743362i \(0.266770\pi\)
\(788\) −13.6603 + 3.66025i −0.486626 + 0.130391i
\(789\) 0 0
\(790\) 40.0000 1.42314
\(791\) 0 0
\(792\) −12.0000 −0.426401
\(793\) 0 0
\(794\) 20.7846 + 12.0000i 0.737618 + 0.425864i
\(795\) 0 0
\(796\) −24.0000 41.5692i −0.850657 1.47338i
\(797\) 32.0000 + 32.0000i 1.13350 + 1.13350i 0.989591 + 0.143907i \(0.0459666\pi\)
0.143907 + 0.989591i \(0.454033\pi\)
\(798\) 0 0
\(799\) 24.0000 0.849059
\(800\) −16.3923 4.39230i −0.579555 0.155291i
\(801\) 21.0000 36.3731i 0.741999 1.28518i
\(802\) 16.3923 4.39230i 0.578832 0.155098i
\(803\) −2.19615 + 8.19615i −0.0775005 + 0.289236i
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −20.7846 12.0000i −0.731200 0.422159i
\(809\) 5.19615 + 3.00000i 0.182687 + 0.105474i 0.588555 0.808458i \(-0.299697\pi\)
−0.405868 + 0.913932i \(0.633031\pi\)
\(810\) 18.0000 + 31.1769i 0.632456 + 1.09545i
\(811\) 24.0000 24.0000i 0.842754 0.842754i −0.146462 0.989216i \(-0.546789\pi\)
0.989216 + 0.146462i \(0.0467887\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −13.6603 3.66025i −0.478792 0.128292i
\(815\) 30.0000 51.9615i 1.05085 1.82013i
\(816\) 0 0
\(817\) −2.00000 3.46410i −0.0699711 0.121194i
\(818\) −14.0000 + 14.0000i −0.489499 + 0.489499i
\(819\) 0 0
\(820\) 40.0000 40.0000i 1.39686 1.39686i
\(821\) −1.36603 0.366025i −0.0476746 0.0127744i 0.234903 0.972019i \(-0.424523\pi\)
−0.282578 + 0.959244i \(0.591189\pi\)
\(822\) 0 0
\(823\) 20.7846 + 12.0000i 0.724506 + 0.418294i 0.816409 0.577474i \(-0.195962\pi\)
−0.0919029 + 0.995768i \(0.529295\pi\)
\(824\) 2.92820 10.9282i 0.102009 0.380702i
\(825\) 0 0
\(826\) 0 0
\(827\) −5.00000 + 5.00000i −0.173867 + 0.173867i −0.788676 0.614809i \(-0.789233\pi\)
0.614809 + 0.788676i \(0.289233\pi\)
\(828\) 31.1769 18.0000i 1.08347 0.625543i
\(829\) 2.73205 0.732051i 0.0948880 0.0254252i −0.211063 0.977473i \(-0.567692\pi\)
0.305951 + 0.952047i \(0.401026\pi\)
\(830\) −54.6410 + 14.6410i −1.89662 + 0.508197i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −8.78461 + 32.7846i −0.304004 + 1.13456i
\(836\) 6.92820 + 4.00000i 0.239617 + 0.138343i
\(837\) 0 0
\(838\) 20.7846 12.0000i 0.717992 0.414533i
\(839\) 4.00000i 0.138095i −0.997613 0.0690477i \(-0.978004\pi\)
0.997613 0.0690477i \(-0.0219961\pi\)
\(840\) 0 0
\(841\) 69.0000i 2.37931i
\(842\) −9.00000 15.5885i −0.310160 0.537214i
\(843\) 0 0
\(844\) 6.58846 + 24.5885i 0.226784 + 0.846370i
\(845\) 9.51666 35.5167i 0.327383 1.22181i
\(846\) −36.0000 + 36.0000i −1.23771 + 1.23771i
\(847\) 0 0
\(848\) 4.00000 4.00000i 0.137361 0.137361i
\(849\) 0 0
\(850\) −2.19615 8.19615i −0.0753274 0.281126i
\(851\) 40.9808 10.9808i 1.40480 0.376416i
\(852\) 0 0
\(853\) −24.0000 + 24.0000i −0.821744 + 0.821744i −0.986358 0.164614i \(-0.947362\pi\)
0.164614 + 0.986358i \(0.447362\pi\)
\(854\) 0 0
\(855\) 24.0000i 0.820783i
\(856\) −17.3205 + 10.0000i −0.592003 + 0.341793i
\(857\) 15.5885 + 9.00000i 0.532492 + 0.307434i 0.742030 0.670366i \(-0.233863\pi\)
−0.209539 + 0.977800i \(0.567196\pi\)
\(858\) 0 0
\(859\) −2.73205 0.732051i −0.0932164 0.0249773i 0.211909 0.977289i \(-0.432032\pi\)
−0.305126 + 0.952312i \(0.598698\pi\)
\(860\) 8.00000 0.272798
\(861\) 0 0
\(862\) 8.00000 + 8.00000i 0.272481 + 0.272481i
\(863\) −7.00000 12.1244i −0.238283 0.412718i 0.721939 0.691957i \(-0.243251\pi\)
−0.960222 + 0.279239i \(0.909918\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −2.19615 + 8.19615i −0.0746283 + 0.278517i
\(867\) 0 0
\(868\) 0 0
\(869\) 10.0000 10.0000i 0.339227 0.339227i
\(870\) 0 0
\(871\) 0 0
\(872\) 6.00000 10.3923i 0.203186 0.351928i
\(873\) −5.19615 + 3.00000i −0.175863 + 0.101535i
\(874\) −24.0000 −0.811812
\(875\) 0 0
\(876\) 0 0
\(877\) 1.09808 4.09808i 0.0370794 0.138382i −0.944905 0.327345i \(-0.893846\pi\)
0.981984 + 0.188963i \(0.0605126\pi\)
\(878\) 5.85641 + 21.8564i 0.197644 + 0.737618i
\(879\) 0 0
\(880\) −13.8564 + 8.00000i −0.467099 + 0.269680i
\(881\) 18.0000 0.606435 0.303218 0.952921i \(-0.401939\pi\)
0.303218 + 0.952921i \(0.401939\pi\)
\(882\) 0 0
\(883\) −25.0000 25.0000i −0.841317 0.841317i 0.147713 0.989030i \(-0.452809\pi\)
−0.989030 + 0.147713i \(0.952809\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.00000 + 1.73205i −0.0335957 + 0.0581894i
\(887\) 10.3923 6.00000i 0.348939 0.201460i −0.315279 0.948999i \(-0.602098\pi\)
0.664218 + 0.747539i \(0.268765\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 56.0000i 1.87712i
\(891\) 12.2942 + 3.29423i 0.411872 + 0.110361i
\(892\) 6.92820 + 4.00000i 0.231973 + 0.133930i
\(893\) 32.7846 8.78461i 1.09710 0.293966i
\(894\) 0 0
\(895\) 12.0000 0.401116
\(896\) 0 0
\(897\) 0 0
\(898\) 10.9808 40.9808i 0.366433 1.36755i
\(899\) −76.4974 + 20.4974i −2.55133 + 0.683627i
\(900\) 15.5885 + 9.00000i 0.519615 + 0.300000i
\(901\) 2.73205 + 0.732051i 0.0910178 + 0.0243881i
\(902\) 20.0000i 0.665927i
\(903\) 0 0
\(904\) 8.00000 8.00000i 0.266076 0.266076i
\(905\) 13.8564 8.00000i 0.460603 0.265929i
\(906\) 0 0
\(907\) 5.49038 + 20.4904i 0.182305 + 0.680372i 0.995191 + 0.0979495i \(0.0312284\pi\)
−0.812886 + 0.582422i \(0.802105\pi\)
\(908\) 5.46410 + 1.46410i 0.181333 + 0.0485879i
\(909\) 18.0000 + 18.0000i 0.597022 + 0.597022i
\(910\) 0 0
\(911\) −48.0000 −1.59031 −0.795155 0.606406i \(-0.792611\pi\)
−0.795155 + 0.606406i \(0.792611\pi\)
\(912\) 0 0
\(913\) −10.0000 + 17.3205i −0.330952 + 0.573225i
\(914\) −8.05256 30.0526i −0.266355 0.994050i
\(915\) 0 0
\(916\) −16.0000 16.0000i −0.528655 0.528655i
\(917\) 0 0
\(918\) 0 0
\(919\) 20.7846 12.0000i 0.685621 0.395843i −0.116348 0.993208i \(-0.537119\pi\)
0.801970 + 0.597365i \(0.203786\pi\)
\(920\) 24.0000 41.5692i 0.791257 1.37050i
\(921\) 0 0
\(922\) 27.7128 16.0000i 0.912673 0.526932i
\(923\) 0 0
\(924\) 0 0
\(925\) 15.0000 + 15.0000i 0.493197 + 0.493197i
\(926\) −5.12436 + 19.1244i −0.168397 + 0.628465i
\(927\) −6.00000 + 10.3923i −0.197066 + 0.341328i
\(928\) −48.4974 28.0000i −1.59201 0.919145i
\(929\) −25.0000 43.3013i −0.820223 1.42067i −0.905516 0.424313i \(-0.860516\pi\)
0.0852924 0.996356i \(-0.472818\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −32.0000 −1.04819
\(933\) 0 0
\(934\) −31.1769 18.0000i −1.02014 0.588978i
\(935\) −6.92820 4.00000i −0.226576 0.130814i
\(936\) 0 0
\(937\) 58.0000i 1.89478i −0.320085 0.947389i \(-0.603712\pi\)
0.320085 0.947389i \(-0.396288\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −17.5692 + 65.5692i −0.573045 + 2.13863i
\(941\) 35.5167 9.51666i 1.15781 0.310234i 0.371719 0.928345i \(-0.378768\pi\)
0.786091 + 0.618111i \(0.212102\pi\)
\(942\) 0 0
\(943\) 30.0000 + 51.9615i 0.976934 + 1.69210i
\(944\) 32.0000 32.0000i 1.04151 1.04151i
\(945\) 0 0
\(946\) 2.00000 2.00000i 0.0650256 0.0650256i
\(947\) 12.0788 45.0788i 0.392510 1.46487i −0.433471 0.901167i \(-0.642711\pi\)
0.825981 0.563698i \(-0.190622\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) −6.00000 10.3923i −0.194666 0.337171i
\(951\) 0 0
\(952\) 0 0
\(953\) 16.0000i 0.518291i 0.965838 + 0.259145i \(0.0834409\pi\)
−0.965838 + 0.259145i \(0.916559\pi\)
\(954\) −5.19615 + 3.00000i −0.168232 + 0.0971286i
\(955\) 13.1769 + 49.1769i 0.426395 + 1.59133i
\(956\) 0 0
\(957\) 0 0
\(958\) −20.0000 20.0000i −0.646171 0.646171i
\(959\) 0 0
\(960\) 0 0
\(961\) −16.5000 28.5788i −0.532258 0.921898i
\(962\) 0 0
\(963\) 20.4904 5.49038i 0.660293 0.176925i
\(964\) −38.1051 + 22.0000i −1.22728 + 0.708572i
\(965\) 32.0000 32.0000i 1.03012 1.03012i
\(966\) 0 0
\(967\) 2.00000i 0.0643157i −0.999483 0.0321578i \(-0.989762\pi\)
0.999483 0.0321578i \(-0.0102379\pi\)
\(968\) 6.58846 24.5885i 0.211761 0.790303i
\(969\) 0 0
\(970\) −4.00000 + 6.92820i −0.128432 + 0.222451i
\(971\) −5.46410 1.46410i −0.175351 0.0469853i 0.170075 0.985431i \(-0.445599\pi\)
−0.345426 + 0.938446i \(0.612266\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −22.0000 + 22.0000i −0.704925 + 0.704925i
\(975\) 0 0
\(976\) −32.7846 + 8.78461i −1.04941 + 0.281189i
\(977\) −19.0000 + 32.9090i −0.607864 + 1.05285i 0.383728 + 0.923446i \(0.374640\pi\)
−0.991592 + 0.129405i \(0.958693\pi\)
\(978\) 0 0
\(979\) −14.0000 14.0000i −0.447442 0.447442i
\(980\) 0 0
\(981\) −9.00000 + 9.00000i −0.287348 + 0.287348i
\(982\) −19.0000 32.9090i −0.606314 1.05017i
\(983\) −38.1051 22.0000i −1.21536 0.701691i −0.251442 0.967872i \(-0.580905\pi\)
−0.963923 + 0.266181i \(0.914238\pi\)
\(984\) 0 0
\(985\) 17.3205 10.0000i 0.551877 0.318626i
\(986\) 28.0000i 0.891702i
\(987\) 0 0
\(988\) 0 0
\(989\) −2.19615 + 8.19615i −0.0698336 + 0.260622i
\(990\) 16.3923 4.39230i 0.520982 0.139597i
\(991\) −11.0000 + 19.0526i −0.349427 + 0.605224i −0.986148 0.165870i \(-0.946957\pi\)
0.636721 + 0.771094i \(0.280290\pi\)
\(992\) 11.7128 43.7128i 0.371882 1.38788i
\(993\) 0 0
\(994\) 0 0
\(995\) 48.0000 + 48.0000i 1.52170 + 1.52170i
\(996\) 0 0
\(997\) 10.9808 + 40.9808i 0.347764 + 1.29787i 0.889350 + 0.457228i \(0.151158\pi\)
−0.541585 + 0.840646i \(0.682176\pi\)
\(998\) −39.8372 23.0000i −1.26102 0.728052i
\(999\) 0 0
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 \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 784.2.x.e.557.1 4
7.2 even 3 inner 784.2.x.e.765.1 4
7.3 odd 6 112.2.m.b.29.1 2
7.4 even 3 784.2.m.a.589.1 2
7.5 odd 6 784.2.x.d.765.1 4
7.6 odd 2 784.2.x.d.557.1 4
16.5 even 4 inner 784.2.x.e.165.1 4
28.3 even 6 448.2.m.a.337.1 2
56.3 even 6 896.2.m.c.673.1 2
56.45 odd 6 896.2.m.b.673.1 2
112.3 even 12 896.2.m.c.225.1 2
112.5 odd 12 784.2.x.d.373.1 4
112.37 even 12 inner 784.2.x.e.373.1 4
112.45 odd 12 896.2.m.b.225.1 2
112.53 even 12 784.2.m.a.197.1 2
112.59 even 12 448.2.m.a.113.1 2
112.69 odd 4 784.2.x.d.165.1 4
112.101 odd 12 112.2.m.b.85.1 yes 2
224.59 even 24 7168.2.a.k.1.2 2
224.101 odd 24 7168.2.a.b.1.2 2
224.171 even 24 7168.2.a.k.1.1 2
224.213 odd 24 7168.2.a.b.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.m.b.29.1 2 7.3 odd 6
112.2.m.b.85.1 yes 2 112.101 odd 12
448.2.m.a.113.1 2 112.59 even 12
448.2.m.a.337.1 2 28.3 even 6
784.2.m.a.197.1 2 112.53 even 12
784.2.m.a.589.1 2 7.4 even 3
784.2.x.d.165.1 4 112.69 odd 4
784.2.x.d.373.1 4 112.5 odd 12
784.2.x.d.557.1 4 7.6 odd 2
784.2.x.d.765.1 4 7.5 odd 6
784.2.x.e.165.1 4 16.5 even 4 inner
784.2.x.e.373.1 4 112.37 even 12 inner
784.2.x.e.557.1 4 1.1 even 1 trivial
784.2.x.e.765.1 4 7.2 even 3 inner
896.2.m.b.225.1 2 112.45 odd 12
896.2.m.b.673.1 2 56.45 odd 6
896.2.m.c.225.1 2 112.3 even 12
896.2.m.c.673.1 2 56.3 even 6
7168.2.a.b.1.1 2 224.213 odd 24
7168.2.a.b.1.2 2 224.101 odd 24
7168.2.a.k.1.1 2 224.171 even 24
7168.2.a.k.1.2 2 224.59 even 24