Properties

Label 784.2.x.e.373.1
Level $784$
Weight $2$
Character 784.373
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 373.1
Root \(0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 784.373
Dual form 784.2.x.e.557.1

$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).

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

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 \(-0.416667\pi\)
−0.258819 + 0.965926i \(0.583333\pi\)
\(4\) −1.73205 + 1.00000i −0.866025 + 0.500000i
\(5\) 2.73205 0.732051i 1.22181 0.327383i 0.410425 0.911894i \(-0.365380\pi\)
0.811386 + 0.584511i \(0.198714\pi\)
\(6\) 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 −0.888537 0.458804i \(-0.848278\pi\)
0.998898 + 0.0469323i \(0.0149445\pi\)
\(12\) 0 0
\(13\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 2.00000 3.46410i 0.500000 0.866025i
\(17\) −1.00000 1.73205i −0.242536 0.420084i 0.718900 0.695113i \(-0.244646\pi\)
−0.961436 + 0.275029i \(0.911312\pi\)
\(18\) −1.09808 + 4.09808i −0.258819 + 0.965926i
\(19\) −0.732051 2.73205i −0.167944 0.626775i −0.997646 0.0685694i \(-0.978157\pi\)
0.829702 0.558206i \(-0.188510\pi\)
\(20\) −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 0.931831 0.362892i \(-0.118211\pi\)
0.151642 + 0.988436i \(0.451544\pi\)
\(24\) 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 0.371391 0.928477i \(-0.378881\pi\)
0.928477 0.371391i \(-0.121119\pi\)
\(30\) 0 0
\(31\) −4.00000 6.92820i −0.718421 1.24434i −0.961625 0.274367i \(-0.911532\pi\)
0.243204 0.969975i \(-0.421802\pi\)
\(32\) −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 0.350823 0.936442i \(-0.385902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) −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 \(-0.714777\pi\)
0.624695 0.780869i \(-0.285223\pi\)
\(42\) 0 0
\(43\) −1.00000 1.00000i −0.152499 0.152499i 0.626734 0.779233i \(-0.284391\pi\)
−0.779233 + 0.626734i \(0.784391\pi\)
\(44\) 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 −0.0186297 + 0.999826i \(0.505930\pi\)
−0.856560 + 0.516047i \(0.827403\pi\)
\(48\) 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 −0.986498 0.163776i \(-0.947632\pi\)
0.936220 + 0.351414i \(0.114299\pi\)
\(54\) 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 0.462821 + 0.886452i \(0.346837\pi\)
−0.844041 + 0.536279i \(0.819829\pi\)
\(60\) 0 0
\(61\) −2.19615 8.19615i −0.281189 1.04941i −0.951580 0.307402i \(-0.900540\pi\)
0.670391 0.742008i \(-0.266126\pi\)
\(62\) −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 −0.000353546 1.00000i \(-0.500113\pi\)
−0.500306 + 0.865849i \(0.666779\pi\)
\(68\) 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 −0.164083 0.986447i \(-0.552466\pi\)
0.772246 + 0.635323i \(0.219133\pi\)
\(74\) −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 0.434730 + 0.900561i \(0.356844\pi\)
−0.997274 + 0.0737937i \(0.976489\pi\)
\(80\) 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 0.102957 0.994686i \(-0.467170\pi\)
0.994686 0.102957i \(-0.0328303\pi\)
\(84\) 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 −0.307389 0.951584i \(-0.599455\pi\)
−0.977790 + 0.209585i \(0.932789\pi\)
\(90\) 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 0.766370 + 0.642399i \(0.222061\pi\)
−0.984896 + 0.173149i \(0.944606\pi\)
\(102\) 0 0
\(103\) 3.46410 + 2.00000i 0.341328 + 0.197066i 0.660859 0.750510i \(-0.270192\pi\)
−0.319531 + 0.947576i \(0.603525\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 2.00000 0.194257
\(107\) −6.83013 + 1.83013i −0.660293 + 0.176925i −0.573378 0.819291i \(-0.694367\pi\)
−0.0869149 + 0.996216i \(0.527701\pi\)
\(108\) 0 0
\(109\) 4.09808 + 1.09808i 0.392525 + 0.105177i 0.449682 0.893189i \(-0.351537\pi\)
−0.0571579 + 0.998365i \(0.518204\pi\)
\(110\) −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 0.708661 + 0.705549i \(0.249299\pi\)
−0.260944 + 0.965354i \(0.584034\pi\)
\(132\) 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 0.0146279 0.999893i \(-0.495344\pi\)
0.873247 + 0.487278i \(0.162010\pi\)
\(138\) 0 0
\(139\) 2.00000 + 2.00000i 0.169638 + 0.169638i 0.786820 0.617182i \(-0.211726\pi\)
−0.617182 + 0.786820i \(0.711726\pi\)
\(140\) 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 −0.422744 0.906249i \(-0.638933\pi\)
0.0870170 + 0.996207i \(0.472267\pi\)
\(150\) 0 0
\(151\) 8.66025 5.00000i 0.704761 0.406894i −0.104357 0.994540i \(-0.533278\pi\)
0.809118 + 0.587646i \(0.199945\pi\)
\(152\) 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 −0.463685 0.886000i \(-0.653473\pi\)
−0.844563 + 0.535456i \(0.820140\pi\)
\(158\) 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 0.752665 + 0.658404i \(0.228768\pi\)
−0.322625 + 0.946527i \(0.604565\pi\)
\(164\) 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 \(-0.846308\pi\)
0.885681 0.464294i \(-0.153692\pi\)
\(168\) 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 \(-0.0833333\pi\)
−0.965926 + 0.258819i \(0.916667\pi\)
\(174\) 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 0.408697 0.912670i \(-0.365983\pi\)
−0.102393 + 0.994744i \(0.532650\pi\)
\(180\) 16.3923 4.39230i 1.22181 0.327383i
\(181\) 4.00000 + 4.00000i 0.297318 + 0.297318i 0.839962 0.542645i \(-0.182577\pi\)
−0.542645 + 0.839962i \(0.682577\pi\)
\(182\) 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 −0.331611 0.943416i \(-0.607592\pi\)
0.982828 0.184525i \(-0.0590746\pi\)
\(192\) 0 0
\(193\) 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i \(0.0286631\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(194\) −0.732051 2.73205i −0.0525582 0.196150i
\(195\) 0 0
\(196\) 0 0
\(197\) 5.00000 + 5.00000i 0.356235 + 0.356235i 0.862423 0.506188i \(-0.168946\pi\)
−0.506188 + 0.862423i \(0.668946\pi\)
\(198\) 5.19615 + 3.00000i 0.369274 + 0.213201i
\(199\) 20.7846 12.0000i 1.47338 0.850657i 0.473831 0.880616i \(-0.342871\pi\)
0.999551 + 0.0299585i \(0.00953751\pi\)
\(200\) 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 −0.945425 0.325840i \(-0.894353\pi\)
0.325840 + 0.945425i \(0.394353\pi\)
\(212\) −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 0.167010 0.985955i \(-0.446589\pi\)
−0.348343 + 0.937367i \(0.613255\pi\)
\(228\) 0 0
\(229\) 10.9282 2.92820i 0.722156 0.193501i 0.121023 0.992650i \(-0.461383\pi\)
0.601133 + 0.799149i \(0.294716\pi\)
\(230\) 24.0000i 1.58251i
\(231\) 0 0
\(232\) 28.0000 1.83829
\(233\) 13.8564 + 8.00000i 0.907763 + 0.524097i 0.879711 0.475509i \(-0.157736\pi\)
0.0280525 + 0.999606i \(0.491069\pi\)
\(234\) 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 0.965387 + 0.260822i \(0.0839937\pi\)
−0.256814 + 0.966461i \(0.582673\pi\)
\(242\) 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 0.993906 0.110234i \(-0.0351599\pi\)
−0.110234 + 0.993906i \(0.535160\pi\)
\(252\) 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 −0.895528 0.445005i \(-0.853202\pi\)
0.833150 + 0.553047i \(0.186535\pi\)
\(258\) 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 −0.862141 0.506669i \(-0.830877\pi\)
0.00771799 + 0.999970i \(0.497543\pi\)
\(264\) 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 −0.0902148 0.995922i \(-0.528755\pi\)
−0.576089 + 0.817387i \(0.695422\pi\)
\(270\) 0 0
\(271\) −4.00000 + 6.92820i −0.242983 + 0.420858i −0.961563 0.274586i \(-0.911459\pi\)
0.718580 + 0.695444i \(0.244792\pi\)
\(272\) −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 0.579424 + 0.815026i \(0.303278\pi\)
−0.909309 + 0.416121i \(0.863389\pi\)
\(278\) 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 −0.995691 0.0927310i \(-0.970440\pi\)
0.908659 + 0.417538i \(0.137107\pi\)
\(284\) 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 0.167913 0.985802i \(-0.446297\pi\)
−0.985802 + 0.167913i \(0.946297\pi\)
\(294\) 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 −0.0276979 + 0.999616i \(0.508818\pi\)
−0.999616 + 0.0276979i \(0.991182\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −16.0000 + 27.7128i −0.908739 + 1.57398i
\(311\) −17.3205 + 10.0000i −0.982156 + 0.567048i −0.902920 0.429808i \(-0.858581\pi\)
−0.0792356 + 0.996856i \(0.525248\pi\)
\(312\) 0 0
\(313\) 12.1244 + 7.00000i 0.685309 + 0.395663i 0.801852 0.597522i \(-0.203848\pi\)
−0.116543 + 0.993186i \(0.537181\pi\)
\(314\) 24.0000i 1.35440i
\(315\) 0 0
\(316\) 20.0000i 1.12509i
\(317\) −2.56218 9.56218i −0.143906 0.537065i −0.999802 0.0199164i \(-0.993660\pi\)
0.855895 0.517149i \(-0.173007\pi\)
\(318\) 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 −0.937919 0.346854i \(-0.887250\pi\)
−0.638835 + 0.769344i \(0.720583\pi\)
\(332\) −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 −0.646685 0.762757i \(-0.723845\pi\)
0.941424 0.337224i \(-0.109488\pi\)
\(348\) 0 0
\(349\) −12.0000 + 12.0000i −0.642345 + 0.642345i −0.951131 0.308786i \(-0.900077\pi\)
0.308786 + 0.951131i \(0.400077\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −4.00000 + 6.92820i −0.213201 + 0.369274i
\(353\) −3.00000 5.19615i −0.159674 0.276563i 0.775077 0.631867i \(-0.217711\pi\)
−0.934751 + 0.355303i \(0.884378\pi\)
\(354\) 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 0.356572 0.934268i \(-0.383946\pi\)
−0.630814 + 0.775934i \(0.717279\pi\)
\(360\) −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 −0.893873 0.448320i \(-0.852022\pi\)
0.0586798 0.998277i \(-0.481311\pi\)
\(368\) 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 0.152115 0.988363i \(-0.451392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) 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 0.957198 0.289433i \(-0.0934668\pi\)
−0.289433 + 0.957198i \(0.593467\pi\)
\(380\) 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 −0.810394 0.585886i \(-0.800747\pi\)
0.912589 + 0.408879i \(0.134080\pi\)
\(384\) 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 −0.932485 0.361208i \(-0.882364\pi\)
0.988160 + 0.153427i \(0.0490311\pi\)
\(390\) 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 0.984179 + 0.177177i \(0.0566965\pi\)
−0.763736 + 0.645529i \(0.776637\pi\)
\(398\) −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 −0.976050 0.217545i \(-0.930195\pi\)
0.676425 + 0.736512i \(0.263528\pi\)
\(402\) 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 −0.169338 0.985558i \(-0.554163\pi\)
0.768849 + 0.639430i \(0.220830\pi\)
\(410\) −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 −0.936611 0.350372i \(-0.886055\pi\)
0.350372 + 0.936611i \(0.386055\pi\)
\(420\) 0 0
\(421\) −9.00000 9.00000i −0.438633 0.438633i 0.452919 0.891552i \(-0.350383\pi\)
−0.891552 + 0.452919i \(0.850383\pi\)
\(422\) 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 0.946135 0.323772i \(-0.104951\pi\)
−0.753462 + 0.657491i \(0.771618\pi\)
\(432\) 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 0.792784 0.609503i \(-0.208631\pi\)
−0.131453 + 0.991322i \(0.541964\pi\)
\(440\) 8.00000 8.00000i 0.381385 0.381385i
\(441\) 0 0
\(442\) 0 0
\(443\) 1.36603 0.366025i 0.0649018 0.0173904i −0.226222 0.974076i \(-0.572637\pi\)
0.291124 + 0.956685i \(0.405971\pi\)
\(444\) 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 −0.0168929 0.999857i \(-0.505377\pi\)
−0.874348 + 0.485299i \(0.838711\pi\)
\(458\) −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 −0.973572 0.228378i \(-0.926658\pi\)
0.228378 + 0.973572i \(0.426658\pi\)
\(462\) 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 −0.933051 0.359745i \(-0.882864\pi\)
0.628173 0.778073i \(-0.283803\pi\)
\(468\) 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 0.541884 0.840453i \(-0.317711\pi\)
−0.998796 + 0.0490589i \(0.984378\pi\)
\(480\) 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 −0.00178012 0.999998i \(-0.500567\pi\)
0.865134 + 0.501541i \(0.167233\pi\)
\(488\) 12.0000 20.7846i 0.543214 0.940875i
\(489\) 0 0
\(490\) 0 0
\(491\) −19.0000 19.0000i −0.857458 0.857458i 0.133580 0.991038i \(-0.457353\pi\)
−0.991038 + 0.133580i \(0.957353\pi\)
\(492\) 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 −0.850597 0.525818i \(-0.823759\pi\)
0.473729 0.880671i \(-0.342908\pi\)
\(500\) 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 \(0.116099\pi\)
−0.934218 + 0.356702i \(0.883901\pi\)
\(504\) 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 0.999965 0.00835918i \(-0.00266084\pi\)
−0.870175 + 0.492743i \(0.835994\pi\)
\(510\) 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 −0.298150 0.954519i \(-0.596370\pi\)
0.677563 + 0.735465i \(0.263036\pi\)
\(522\) 21.0000 + 36.3731i 0.919145 + 1.59201i
\(523\) 32.7846 8.78461i 1.43357 0.384124i 0.543293 0.839543i \(-0.317177\pi\)
0.890277 + 0.455419i \(0.150510\pi\)
\(524\) −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 0.996867 + 0.0790969i \(0.0252036\pi\)
−0.823764 + 0.566933i \(0.808130\pi\)
\(542\) 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 −0.0164556 0.999865i \(-0.505238\pi\)
0.999865 + 0.0164556i \(0.00523822\pi\)
\(548\) −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 0.714714 0.699417i \(-0.246557\pi\)
0.269252 + 0.963070i \(0.413224\pi\)
\(558\) 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 0.783535 0.621348i \(-0.213415\pi\)
0.367887 + 0.929870i \(0.380081\pi\)
\(564\) 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 0.732126 0.681169i \(-0.238528\pi\)
−0.223847 + 0.974624i \(0.571861\pi\)
\(570\) 0 0
\(571\) −3.29423 + 12.2942i −0.137859 + 0.514497i 0.862111 + 0.506720i \(0.169142\pi\)
−0.999970 + 0.00777727i \(0.997524\pi\)
\(572\) 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 0.844459 0.535620i \(-0.179922\pi\)
−0.886090 + 0.463513i \(0.846589\pi\)
\(578\) −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 0.469949 0.882693i \(-0.344272\pi\)
−0.882693 + 0.469949i \(0.844272\pi\)
\(588\) 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 −0.921026 0.389501i \(-0.872647\pi\)
0.797831 + 0.602881i \(0.205981\pi\)
\(594\) 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 −0.860393 0.509631i \(-0.829782\pi\)
0.0111569 + 0.999938i \(0.496449\pi\)
\(600\) 0 0
\(601\) 10.0000i 0.407909i −0.978980 0.203954i \(-0.934621\pi\)
0.978980 0.203954i \(-0.0653794\pi\)
\(602\) 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 −0.428497 0.903543i \(-0.640957\pi\)
0.996740 0.0806818i \(-0.0257098\pi\)
\(608\) 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 −0.866946 0.498403i \(-0.833920\pi\)
0.999998 + 0.00184345i \(0.000586790\pi\)
\(614\) 31.1769 + 18.0000i 1.25820 + 0.726421i
\(615\) 0 0
\(616\) 0 0
\(617\) 42.0000i 1.69086i 0.534089 + 0.845428i \(0.320655\pi\)
−0.534089 + 0.845428i \(0.679345\pi\)
\(618\) 0 0
\(619\) 4.39230 16.3923i 0.176542 0.658862i −0.819742 0.572733i \(-0.805883\pi\)
0.996284 0.0861298i \(-0.0274500\pi\)
\(620\) 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 \(-0.706847\pi\)
0.605050 0.796187i \(-0.293153\pi\)
\(632\) −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 0.722862 0.690992i \(-0.242826\pi\)
−0.959848 + 0.280521i \(0.909493\pi\)
\(642\) 0 0
\(643\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.92820 + 4.00000i 0.272587 + 0.157378i
\(647\) −10.3923 + 6.00000i −0.408564 + 0.235884i −0.690172 0.723645i \(-0.742465\pi\)
0.281609 + 0.959529i \(0.409132\pi\)
\(648\) −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 0.876548 + 0.481314i \(0.159840\pi\)
−0.518456 + 0.855104i \(0.673493\pi\)
\(654\) 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 −0.763120 0.646257i \(-0.776334\pi\)
0.646257 + 0.763120i \(0.276334\pi\)
\(660\) 0 0
\(661\) −9.51666 + 35.5167i −0.370155 + 1.38144i 0.490141 + 0.871643i \(0.336945\pi\)
−0.860296 + 0.509795i \(0.829721\pi\)
\(662\) 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 −0.742257 0.670115i \(-0.766245\pi\)
−0.307756 + 0.951465i \(0.599578\pi\)
\(678\) 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 0.845123 + 0.534573i \(0.179527\pi\)
−0.999184 + 0.0403921i \(0.987139\pi\)
\(684\) −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 −0.871402 0.490570i \(-0.836788\pi\)
0.509371 0.860547i \(-0.329878\pi\)
\(692\) 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 −0.968117 0.250497i \(-0.919406\pi\)
0.250497 + 0.968117i \(0.419406\pi\)
\(702\) 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 −0.0747503 0.997202i \(-0.523816\pi\)
0.433865 + 0.900978i \(0.357149\pi\)
\(710\) 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 −0.617079 0.786901i \(-0.711684\pi\)
0.990016 + 0.140955i \(0.0450174\pi\)
\(720\) −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 \(-0.797782\pi\)
0.804902 0.593407i \(-0.202218\pi\)
\(728\) 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 0.999997 + 0.00244074i \(0.000776913\pi\)
−0.864802 + 0.502112i \(0.832556\pi\)
\(734\) −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 0.0786174 0.996905i \(-0.474949\pi\)
−0.430368 + 0.902654i \(0.641616\pi\)
\(740\) −20.0000 + 34.6410i −0.735215 + 1.27343i
\(741\) 0 0
\(742\) 0 0
\(743\) 6.00000i 0.220119i −0.993925 0.110059i \(-0.964896\pi\)
0.993925 0.110059i \(-0.0351041\pi\)
\(744\) 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 0.411170 + 0.911559i \(0.365120\pi\)
−0.995018 + 0.0996961i \(0.968213\pi\)
\(752\) 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 0.379860 0.925044i \(-0.375972\pi\)
−0.925044 + 0.379860i \(0.875972\pi\)
\(758\) 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 −0.0512772 0.998684i \(-0.516329\pi\)
−0.890525 + 0.454935i \(0.849663\pi\)
\(762\) 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 −0.915118 0.403185i \(-0.867903\pi\)
0.994108 + 0.108390i \(0.0345696\pi\)
\(774\) 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 0.668889 0.743362i \(-0.266770\pi\)
0.207594 + 0.978215i \(0.433437\pi\)
\(788\) −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 0.143907 0.989591i \(-0.454033\pi\)
0.989591 0.143907i \(-0.0459666\pi\)
\(798\) 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 −0.405868 0.913932i \(-0.633031\pi\)
0.588555 + 0.808458i \(0.299697\pi\)
\(810\) 18.0000 31.1769i 0.632456 1.09545i
\(811\) 24.0000 + 24.0000i 0.842754 + 0.842754i 0.989216 0.146462i \(-0.0467887\pi\)
−0.146462 + 0.989216i \(0.546789\pi\)
\(812\) 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 −0.282578 0.959244i \(-0.591189\pi\)
0.234903 + 0.972019i \(0.424523\pi\)
\(822\) 0 0
\(823\) 20.7846 12.0000i 0.724506 0.418294i −0.0919029 0.995768i \(-0.529295\pi\)
0.816409 + 0.577474i \(0.195962\pi\)
\(824\) 2.92820 + 10.9282i 0.102009 + 0.380702i
\(825\) 0 0
\(826\) 0 0
\(827\) −5.00000 5.00000i −0.173867 0.173867i 0.614809 0.788676i \(-0.289233\pi\)
−0.788676 + 0.614809i \(0.789233\pi\)
\(828\) 31.1769 + 18.0000i 1.08347 + 0.625543i
\(829\) 2.73205 + 0.732051i 0.0948880 + 0.0254252i 0.305951 0.952047i \(-0.401026\pi\)
−0.211063 + 0.977473i \(0.567692\pi\)
\(830\) −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 \(0.0219961\pi\)
−0.997613 + 0.0690477i \(0.978004\pi\)
\(840\) 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 0.164614 0.986358i \(-0.447362\pi\)
−0.986358 + 0.164614i \(0.947362\pi\)
\(854\) 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 −0.209539 0.977800i \(-0.567196\pi\)
0.742030 + 0.670366i \(0.233863\pi\)
\(858\) 0 0
\(859\) −2.73205 + 0.732051i −0.0932164 + 0.0249773i −0.305126 0.952312i \(-0.598698\pi\)
0.211909 + 0.977289i \(0.432032\pi\)
\(860\) 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 −0.960222 0.279239i \(-0.909918\pi\)
0.721939 + 0.691957i \(0.243251\pi\)
\(864\) 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 0.981984 0.188963i \(-0.0605126\pi\)
−0.944905 + 0.327345i \(0.893846\pi\)
\(878\) 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 −0.989030 0.147713i \(-0.952809\pi\)
0.147713 + 0.989030i \(0.452809\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.00000 1.73205i −0.0335957 0.0581894i
\(887\) 10.3923 + 6.00000i 0.348939 + 0.201460i 0.664218 0.747539i \(-0.268765\pi\)
−0.315279 + 0.948999i \(0.602098\pi\)
\(888\) 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 −0.812886 0.582422i \(-0.802105\pi\)
0.995191 0.0979495i \(-0.0312284\pi\)
\(908\) 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 0.801970 0.597365i \(-0.203786\pi\)
−0.116348 + 0.993208i \(0.537119\pi\)
\(920\) 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 0.0852924 + 0.996356i \(0.472818\pi\)
−0.905516 + 0.424313i \(0.860516\pi\)
\(930\) 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 \(0.396288\pi\)
−0.320085 + 0.947389i \(0.603712\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) −17.5692 65.5692i −0.573045 2.13863i
\(941\) 35.5167 + 9.51666i 1.15781 + 0.310234i 0.786091 0.618111i \(-0.212102\pi\)
0.371719 + 0.928345i \(0.378768\pi\)
\(942\) 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 0.825981 + 0.563698i \(0.190622\pi\)
−0.433471 + 0.901167i \(0.642711\pi\)
\(948\) 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 \(-0.916559\pi\)
0.965838 0.259145i \(-0.0834409\pi\)
\(954\) −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 \(0.0102379\pi\)
−0.999483 + 0.0321578i \(0.989762\pi\)
\(968\) 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 −0.345426 0.938446i \(-0.612266\pi\)
0.170075 + 0.985431i \(0.445599\pi\)
\(972\) 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 −0.991592 0.129405i \(-0.958693\pi\)
0.383728 0.923446i \(-0.374640\pi\)
\(978\) 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 −0.963923 0.266181i \(-0.914238\pi\)
−0.251442 + 0.967872i \(0.580905\pi\)
\(984\) 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 0.636721 0.771094i \(-0.280290\pi\)
−0.986148 + 0.165870i \(0.946957\pi\)
\(992\) 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 −0.541585 0.840646i \(-0.682176\pi\)
0.889350 0.457228i \(-0.151158\pi\)
\(998\) −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.373.1 4
7.2 even 3 784.2.m.a.197.1 2
7.3 odd 6 784.2.x.d.165.1 4
7.4 even 3 inner 784.2.x.e.165.1 4
7.5 odd 6 112.2.m.b.85.1 yes 2
7.6 odd 2 784.2.x.d.373.1 4
16.13 even 4 inner 784.2.x.e.765.1 4
28.19 even 6 448.2.m.a.113.1 2
56.5 odd 6 896.2.m.b.225.1 2
56.19 even 6 896.2.m.c.225.1 2
112.5 odd 12 896.2.m.b.673.1 2
112.13 odd 4 784.2.x.d.765.1 4
112.19 even 12 448.2.m.a.337.1 2
112.45 odd 12 784.2.x.d.557.1 4
112.61 odd 12 112.2.m.b.29.1 2
112.75 even 12 896.2.m.c.673.1 2
112.93 even 12 784.2.m.a.589.1 2
112.109 even 12 inner 784.2.x.e.557.1 4
224.19 even 24 7168.2.a.k.1.2 2
224.61 odd 24 7168.2.a.b.1.1 2
224.131 even 24 7168.2.a.k.1.1 2
224.173 odd 24 7168.2.a.b.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.m.b.29.1 2 112.61 odd 12
112.2.m.b.85.1 yes 2 7.5 odd 6
448.2.m.a.113.1 2 28.19 even 6
448.2.m.a.337.1 2 112.19 even 12
784.2.m.a.197.1 2 7.2 even 3
784.2.m.a.589.1 2 112.93 even 12
784.2.x.d.165.1 4 7.3 odd 6
784.2.x.d.373.1 4 7.6 odd 2
784.2.x.d.557.1 4 112.45 odd 12
784.2.x.d.765.1 4 112.13 odd 4
784.2.x.e.165.1 4 7.4 even 3 inner
784.2.x.e.373.1 4 1.1 even 1 trivial
784.2.x.e.557.1 4 112.109 even 12 inner
784.2.x.e.765.1 4 16.13 even 4 inner
896.2.m.b.225.1 2 56.5 odd 6
896.2.m.b.673.1 2 112.5 odd 12
896.2.m.c.225.1 2 56.19 even 6
896.2.m.c.673.1 2 112.75 even 12
7168.2.a.b.1.1 2 224.61 odd 24
7168.2.a.b.1.2 2 224.173 odd 24
7168.2.a.k.1.1 2 224.131 even 24
7168.2.a.k.1.2 2 224.19 even 24