Properties

Label 294.2.f.b.227.1
Level $294$
Weight $2$
Character 294.227
Analytic conductor $2.348$
Analytic rank $0$
Dimension $8$
CM no
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [294,2,Mod(215,294)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(294, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("294.215");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 294.f (of order \(6\), degree \(2\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.34760181943\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{24})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{4} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: no (minimal twist has level 42)
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 227.1
Root \(0.965926 + 0.258819i\) of defining polynomial
Character \(\chi\) \(=\) 294.227
Dual form 294.2.f.b.215.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.866025 + 0.500000i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(1.22474 - 1.22474i) q^{6} +1.00000i q^{8} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\) \(q+(-0.866025 + 0.500000i) q^{2} +(-1.67303 + 0.448288i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.22474 + 2.12132i) q^{5} +(1.22474 - 1.22474i) q^{6} +1.00000i q^{8} +(2.59808 - 1.50000i) q^{9} +(-2.12132 - 1.22474i) q^{10} +(-0.448288 + 1.67303i) q^{12} +2.44949i q^{13} +(-3.00000 - 3.00000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.44949 + 4.24264i) q^{17} +(-1.50000 + 2.59808i) q^{18} +(-2.12132 + 1.22474i) q^{19} +2.44949 q^{20} +(-5.19615 + 3.00000i) q^{23} +(-0.448288 - 1.67303i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-1.22474 - 2.12132i) q^{26} +(-3.67423 + 3.67423i) q^{27} +6.00000i q^{29} +(4.09808 + 1.09808i) q^{30} +(0.866025 + 0.500000i) q^{32} -4.89898i q^{34} -3.00000i q^{36} +(1.00000 + 1.73205i) q^{37} +(1.22474 - 2.12132i) q^{38} +(-1.09808 - 4.09808i) q^{39} +(-2.12132 + 1.22474i) q^{40} -4.89898 q^{41} +4.00000 q^{43} +(6.36396 + 3.67423i) q^{45} +(3.00000 - 5.19615i) q^{46} +(-2.44949 - 4.24264i) q^{47} +(1.22474 + 1.22474i) q^{48} -1.00000i q^{50} +(2.19615 - 8.19615i) q^{51} +(2.12132 + 1.22474i) q^{52} +(5.19615 + 3.00000i) q^{53} +(1.34486 - 5.01910i) q^{54} +(3.00000 - 3.00000i) q^{57} +(-3.00000 - 5.19615i) q^{58} +(6.12372 - 10.6066i) q^{59} +(-4.09808 + 1.09808i) q^{60} +(10.6066 - 6.12372i) q^{61} -1.00000 q^{64} +(-5.19615 + 3.00000i) q^{65} +(-4.00000 + 6.92820i) q^{67} +(2.44949 + 4.24264i) q^{68} +(7.34847 - 7.34847i) q^{69} +(1.50000 + 2.59808i) q^{72} +(8.48528 + 4.89898i) q^{73} +(-1.73205 - 1.00000i) q^{74} +(0.448288 - 1.67303i) q^{75} +2.44949i q^{76} +(3.00000 + 3.00000i) q^{78} +(5.00000 + 8.66025i) q^{79} +(1.22474 - 2.12132i) q^{80} +(4.50000 - 7.79423i) q^{81} +(4.24264 - 2.44949i) q^{82} +2.44949 q^{83} -12.0000 q^{85} +(-3.46410 + 2.00000i) q^{86} +(-2.68973 - 10.0382i) q^{87} -7.34847 q^{90} +6.00000i q^{92} +(4.24264 + 2.44949i) q^{94} +(-5.19615 - 3.00000i) q^{95} +(-1.67303 - 0.448288i) q^{96} -4.89898i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 4 q^{4}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 4 q^{4} - 24 q^{15} - 4 q^{16} - 12 q^{18} - 4 q^{25} + 12 q^{30} + 8 q^{37} + 12 q^{39} + 32 q^{43} + 24 q^{46} - 24 q^{51} + 24 q^{57} - 24 q^{58} - 12 q^{60} - 8 q^{64} - 32 q^{67} + 12 q^{72} + 24 q^{78} + 40 q^{79} + 36 q^{81} - 96 q^{85}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).

\(n\) \(197\) \(199\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{6}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.866025 + 0.500000i −0.612372 + 0.353553i
\(3\) −1.67303 + 0.448288i −0.965926 + 0.258819i
\(4\) 0.500000 0.866025i 0.250000 0.433013i
\(5\) 1.22474 + 2.12132i 0.547723 + 0.948683i 0.998430 + 0.0560116i \(0.0178384\pi\)
−0.450708 + 0.892672i \(0.648828\pi\)
\(6\) 1.22474 1.22474i 0.500000 0.500000i
\(7\) 0 0
\(8\) 1.00000i 0.353553i
\(9\) 2.59808 1.50000i 0.866025 0.500000i
\(10\) −2.12132 1.22474i −0.670820 0.387298i
\(11\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) −0.448288 + 1.67303i −0.129410 + 0.482963i
\(13\) 2.44949i 0.679366i 0.940540 + 0.339683i \(0.110320\pi\)
−0.940540 + 0.339683i \(0.889680\pi\)
\(14\) 0 0
\(15\) −3.00000 3.00000i −0.774597 0.774597i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −2.44949 + 4.24264i −0.594089 + 1.02899i 0.399586 + 0.916696i \(0.369154\pi\)
−0.993675 + 0.112296i \(0.964180\pi\)
\(18\) −1.50000 + 2.59808i −0.353553 + 0.612372i
\(19\) −2.12132 + 1.22474i −0.486664 + 0.280976i −0.723190 0.690650i \(-0.757325\pi\)
0.236525 + 0.971625i \(0.423991\pi\)
\(20\) 2.44949 0.547723
\(21\) 0 0
\(22\) 0 0
\(23\) −5.19615 + 3.00000i −1.08347 + 0.625543i −0.931831 0.362892i \(-0.881789\pi\)
−0.151642 + 0.988436i \(0.548456\pi\)
\(24\) −0.448288 1.67303i −0.0915064 0.341506i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) −1.22474 2.12132i −0.240192 0.416025i
\(27\) −3.67423 + 3.67423i −0.707107 + 0.707107i
\(28\) 0 0
\(29\) 6.00000i 1.11417i 0.830455 + 0.557086i \(0.188081\pi\)
−0.830455 + 0.557086i \(0.811919\pi\)
\(30\) 4.09808 + 1.09808i 0.748203 + 0.200480i
\(31\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0.866025 + 0.500000i 0.153093 + 0.0883883i
\(33\) 0 0
\(34\) 4.89898i 0.840168i
\(35\) 0 0
\(36\) 3.00000i 0.500000i
\(37\) 1.00000 + 1.73205i 0.164399 + 0.284747i 0.936442 0.350823i \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) 1.22474 2.12132i 0.198680 0.344124i
\(39\) −1.09808 4.09808i −0.175833 0.656217i
\(40\) −2.12132 + 1.22474i −0.335410 + 0.193649i
\(41\) −4.89898 −0.765092 −0.382546 0.923936i \(-0.624953\pi\)
−0.382546 + 0.923936i \(0.624953\pi\)
\(42\) 0 0
\(43\) 4.00000 0.609994 0.304997 0.952353i \(-0.401344\pi\)
0.304997 + 0.952353i \(0.401344\pi\)
\(44\) 0 0
\(45\) 6.36396 + 3.67423i 0.948683 + 0.547723i
\(46\) 3.00000 5.19615i 0.442326 0.766131i
\(47\) −2.44949 4.24264i −0.357295 0.618853i 0.630213 0.776422i \(-0.282968\pi\)
−0.987508 + 0.157569i \(0.949634\pi\)
\(48\) 1.22474 + 1.22474i 0.176777 + 0.176777i
\(49\) 0 0
\(50\) 1.00000i 0.141421i
\(51\) 2.19615 8.19615i 0.307523 1.14769i
\(52\) 2.12132 + 1.22474i 0.294174 + 0.169842i
\(53\) 5.19615 + 3.00000i 0.713746 + 0.412082i 0.812447 0.583036i \(-0.198135\pi\)
−0.0987002 + 0.995117i \(0.531468\pi\)
\(54\) 1.34486 5.01910i 0.183013 0.683013i
\(55\) 0 0
\(56\) 0 0
\(57\) 3.00000 3.00000i 0.397360 0.397360i
\(58\) −3.00000 5.19615i −0.393919 0.682288i
\(59\) 6.12372 10.6066i 0.797241 1.38086i −0.124165 0.992262i \(-0.539625\pi\)
0.921406 0.388600i \(-0.127041\pi\)
\(60\) −4.09808 + 1.09808i −0.529059 + 0.141761i
\(61\) 10.6066 6.12372i 1.35804 0.784063i 0.368677 0.929557i \(-0.379811\pi\)
0.989359 + 0.145495i \(0.0464774\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) −1.00000 −0.125000
\(65\) −5.19615 + 3.00000i −0.644503 + 0.372104i
\(66\) 0 0
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) 2.44949 + 4.24264i 0.297044 + 0.514496i
\(69\) 7.34847 7.34847i 0.884652 0.884652i
\(70\) 0 0
\(71\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(72\) 1.50000 + 2.59808i 0.176777 + 0.306186i
\(73\) 8.48528 + 4.89898i 0.993127 + 0.573382i 0.906208 0.422833i \(-0.138964\pi\)
0.0869195 + 0.996215i \(0.472298\pi\)
\(74\) −1.73205 1.00000i −0.201347 0.116248i
\(75\) 0.448288 1.67303i 0.0517638 0.193185i
\(76\) 2.44949i 0.280976i
\(77\) 0 0
\(78\) 3.00000 + 3.00000i 0.339683 + 0.339683i
\(79\) 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) 1.22474 2.12132i 0.136931 0.237171i
\(81\) 4.50000 7.79423i 0.500000 0.866025i
\(82\) 4.24264 2.44949i 0.468521 0.270501i
\(83\) 2.44949 0.268866 0.134433 0.990923i \(-0.457079\pi\)
0.134433 + 0.990923i \(0.457079\pi\)
\(84\) 0 0
\(85\) −12.0000 −1.30158
\(86\) −3.46410 + 2.00000i −0.373544 + 0.215666i
\(87\) −2.68973 10.0382i −0.288369 1.07621i
\(88\) 0 0
\(89\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(90\) −7.34847 −0.774597
\(91\) 0 0
\(92\) 6.00000i 0.625543i
\(93\) 0 0
\(94\) 4.24264 + 2.44949i 0.437595 + 0.252646i
\(95\) −5.19615 3.00000i −0.533114 0.307794i
\(96\) −1.67303 0.448288i −0.170753 0.0457532i
\(97\) 4.89898i 0.497416i −0.968579 0.248708i \(-0.919994\pi\)
0.968579 0.248708i \(-0.0800060\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.500000 + 0.866025i 0.0500000 + 0.0866025i
\(101\) −3.67423 + 6.36396i −0.365600 + 0.633238i −0.988872 0.148767i \(-0.952470\pi\)
0.623272 + 0.782005i \(0.285803\pi\)
\(102\) 2.19615 + 8.19615i 0.217451 + 0.811540i
\(103\) −8.48528 + 4.89898i −0.836080 + 0.482711i −0.855930 0.517092i \(-0.827014\pi\)
0.0198501 + 0.999803i \(0.493681\pi\)
\(104\) −2.44949 −0.240192
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) 10.3923 6.00000i 1.00466 0.580042i 0.0950377 0.995474i \(-0.469703\pi\)
0.909624 + 0.415432i \(0.136370\pi\)
\(108\) 1.34486 + 5.01910i 0.129410 + 0.482963i
\(109\) −5.00000 + 8.66025i −0.478913 + 0.829502i −0.999708 0.0241802i \(-0.992302\pi\)
0.520794 + 0.853682i \(0.325636\pi\)
\(110\) 0 0
\(111\) −2.44949 2.44949i −0.232495 0.232495i
\(112\) 0 0
\(113\) 6.00000i 0.564433i −0.959351 0.282216i \(-0.908930\pi\)
0.959351 0.282216i \(-0.0910696\pi\)
\(114\) −1.09808 + 4.09808i −0.102844 + 0.383820i
\(115\) −12.7279 7.34847i −1.18688 0.685248i
\(116\) 5.19615 + 3.00000i 0.482451 + 0.278543i
\(117\) 3.67423 + 6.36396i 0.339683 + 0.588348i
\(118\) 12.2474i 1.12747i
\(119\) 0 0
\(120\) 3.00000 3.00000i 0.273861 0.273861i
\(121\) −5.50000 9.52628i −0.500000 0.866025i
\(122\) −6.12372 + 10.6066i −0.554416 + 0.960277i
\(123\) 8.19615 2.19615i 0.739022 0.198020i
\(124\) 0 0
\(125\) 9.79796 0.876356
\(126\) 0 0
\(127\) 8.00000 0.709885 0.354943 0.934888i \(-0.384500\pi\)
0.354943 + 0.934888i \(0.384500\pi\)
\(128\) 0.866025 0.500000i 0.0765466 0.0441942i
\(129\) −6.69213 + 1.79315i −0.589209 + 0.157878i
\(130\) 3.00000 5.19615i 0.263117 0.455733i
\(131\) −3.67423 6.36396i −0.321019 0.556022i 0.659679 0.751547i \(-0.270692\pi\)
−0.980699 + 0.195525i \(0.937359\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 8.00000i 0.691095i
\(135\) −12.2942 3.29423i −1.05812 0.283522i
\(136\) −4.24264 2.44949i −0.363803 0.210042i
\(137\) −10.3923 6.00000i −0.887875 0.512615i −0.0146279 0.999893i \(-0.504656\pi\)
−0.873247 + 0.487278i \(0.837990\pi\)
\(138\) −2.68973 + 10.0382i −0.228965 + 0.854508i
\(139\) 2.44949i 0.207763i −0.994590 0.103882i \(-0.966874\pi\)
0.994590 0.103882i \(-0.0331263\pi\)
\(140\) 0 0
\(141\) 6.00000 + 6.00000i 0.505291 + 0.505291i
\(142\) 0 0
\(143\) 0 0
\(144\) −2.59808 1.50000i −0.216506 0.125000i
\(145\) −12.7279 + 7.34847i −1.05700 + 0.610257i
\(146\) −9.79796 −0.810885
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 5.19615 3.00000i 0.425685 0.245770i −0.271821 0.962348i \(-0.587626\pi\)
0.697507 + 0.716578i \(0.254293\pi\)
\(150\) 0.448288 + 1.67303i 0.0366025 + 0.136603i
\(151\) 4.00000 6.92820i 0.325515 0.563809i −0.656101 0.754673i \(-0.727796\pi\)
0.981617 + 0.190864i \(0.0611289\pi\)
\(152\) −1.22474 2.12132i −0.0993399 0.172062i
\(153\) 14.6969i 1.18818i
\(154\) 0 0
\(155\) 0 0
\(156\) −4.09808 1.09808i −0.328109 0.0879165i
\(157\) −6.36396 3.67423i −0.507899 0.293236i 0.224070 0.974573i \(-0.428065\pi\)
−0.731970 + 0.681337i \(0.761399\pi\)
\(158\) −8.66025 5.00000i −0.688973 0.397779i
\(159\) −10.0382 2.68973i −0.796081 0.213309i
\(160\) 2.44949i 0.193649i
\(161\) 0 0
\(162\) 9.00000i 0.707107i
\(163\) 8.00000 + 13.8564i 0.626608 + 1.08532i 0.988227 + 0.152992i \(0.0488907\pi\)
−0.361619 + 0.932326i \(0.617776\pi\)
\(164\) −2.44949 + 4.24264i −0.191273 + 0.331295i
\(165\) 0 0
\(166\) −2.12132 + 1.22474i −0.164646 + 0.0950586i
\(167\) 4.89898 0.379094 0.189547 0.981872i \(-0.439298\pi\)
0.189547 + 0.981872i \(0.439298\pi\)
\(168\) 0 0
\(169\) 7.00000 0.538462
\(170\) 10.3923 6.00000i 0.797053 0.460179i
\(171\) −3.67423 + 6.36396i −0.280976 + 0.486664i
\(172\) 2.00000 3.46410i 0.152499 0.264135i
\(173\) 11.0227 + 19.0919i 0.838041 + 1.45153i 0.891531 + 0.452961i \(0.149632\pi\)
−0.0534899 + 0.998568i \(0.517034\pi\)
\(174\) 7.34847 + 7.34847i 0.557086 + 0.557086i
\(175\) 0 0
\(176\) 0 0
\(177\) −5.49038 + 20.4904i −0.412682 + 1.54015i
\(178\) 0 0
\(179\) 20.7846 + 12.0000i 1.55351 + 0.896922i 0.997852 + 0.0655145i \(0.0208689\pi\)
0.555663 + 0.831408i \(0.312464\pi\)
\(180\) 6.36396 3.67423i 0.474342 0.273861i
\(181\) 12.2474i 0.910346i −0.890403 0.455173i \(-0.849577\pi\)
0.890403 0.455173i \(-0.150423\pi\)
\(182\) 0 0
\(183\) −15.0000 + 15.0000i −1.10883 + 1.10883i
\(184\) −3.00000 5.19615i −0.221163 0.383065i
\(185\) −2.44949 + 4.24264i −0.180090 + 0.311925i
\(186\) 0 0
\(187\) 0 0
\(188\) −4.89898 −0.357295
\(189\) 0 0
\(190\) 6.00000 0.435286
\(191\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(192\) 1.67303 0.448288i 0.120741 0.0323524i
\(193\) −2.00000 + 3.46410i −0.143963 + 0.249351i −0.928986 0.370116i \(-0.879318\pi\)
0.785022 + 0.619467i \(0.212651\pi\)
\(194\) 2.44949 + 4.24264i 0.175863 + 0.304604i
\(195\) 7.34847 7.34847i 0.526235 0.526235i
\(196\) 0 0
\(197\) 18.0000i 1.28245i −0.767354 0.641223i \(-0.778427\pi\)
0.767354 0.641223i \(-0.221573\pi\)
\(198\) 0 0
\(199\) −8.48528 4.89898i −0.601506 0.347279i 0.168128 0.985765i \(-0.446228\pi\)
−0.769634 + 0.638486i \(0.779561\pi\)
\(200\) −0.866025 0.500000i −0.0612372 0.0353553i
\(201\) 3.58630 13.3843i 0.252958 0.944053i
\(202\) 7.34847i 0.517036i
\(203\) 0 0
\(204\) −6.00000 6.00000i −0.420084 0.420084i
\(205\) −6.00000 10.3923i −0.419058 0.725830i
\(206\) 4.89898 8.48528i 0.341328 0.591198i
\(207\) −9.00000 + 15.5885i −0.625543 + 1.08347i
\(208\) 2.12132 1.22474i 0.147087 0.0849208i
\(209\) 0 0
\(210\) 0 0
\(211\) −8.00000 −0.550743 −0.275371 0.961338i \(-0.588801\pi\)
−0.275371 + 0.961338i \(0.588801\pi\)
\(212\) 5.19615 3.00000i 0.356873 0.206041i
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) 4.89898 + 8.48528i 0.334108 + 0.578691i
\(216\) −3.67423 3.67423i −0.250000 0.250000i
\(217\) 0 0
\(218\) 10.0000i 0.677285i
\(219\) −16.3923 4.39230i −1.10769 0.296804i
\(220\) 0 0
\(221\) −10.3923 6.00000i −0.699062 0.403604i
\(222\) 3.34607 + 0.896575i 0.224573 + 0.0601742i
\(223\) 14.6969i 0.984180i 0.870544 + 0.492090i \(0.163767\pi\)
−0.870544 + 0.492090i \(0.836233\pi\)
\(224\) 0 0
\(225\) 3.00000i 0.200000i
\(226\) 3.00000 + 5.19615i 0.199557 + 0.345643i
\(227\) 3.67423 6.36396i 0.243868 0.422391i −0.717945 0.696100i \(-0.754917\pi\)
0.961813 + 0.273709i \(0.0882505\pi\)
\(228\) −1.09808 4.09808i −0.0727219 0.271402i
\(229\) 19.0919 11.0227i 1.26163 0.728401i 0.288238 0.957559i \(-0.406931\pi\)
0.973389 + 0.229158i \(0.0735973\pi\)
\(230\) 14.6969 0.969087
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 20.7846 12.0000i 1.36165 0.786146i 0.371802 0.928312i \(-0.378740\pi\)
0.989843 + 0.142166i \(0.0454066\pi\)
\(234\) −6.36396 3.67423i −0.416025 0.240192i
\(235\) 6.00000 10.3923i 0.391397 0.677919i
\(236\) −6.12372 10.6066i −0.398621 0.690431i
\(237\) −12.2474 12.2474i −0.795557 0.795557i
\(238\) 0 0
\(239\) 6.00000i 0.388108i 0.980991 + 0.194054i \(0.0621637\pi\)
−0.980991 + 0.194054i \(0.937836\pi\)
\(240\) −1.09808 + 4.09808i −0.0708805 + 0.264530i
\(241\) 21.2132 + 12.2474i 1.36646 + 0.788928i 0.990474 0.137697i \(-0.0439700\pi\)
0.375988 + 0.926624i \(0.377303\pi\)
\(242\) 9.52628 + 5.50000i 0.612372 + 0.353553i
\(243\) −4.03459 + 15.0573i −0.258819 + 0.965926i
\(244\) 12.2474i 0.784063i
\(245\) 0 0
\(246\) −6.00000 + 6.00000i −0.382546 + 0.382546i
\(247\) −3.00000 5.19615i −0.190885 0.330623i
\(248\) 0 0
\(249\) −4.09808 + 1.09808i −0.259705 + 0.0695878i
\(250\) −8.48528 + 4.89898i −0.536656 + 0.309839i
\(251\) −17.1464 −1.08227 −0.541136 0.840935i \(-0.682006\pi\)
−0.541136 + 0.840935i \(0.682006\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −6.92820 + 4.00000i −0.434714 + 0.250982i
\(255\) 20.0764 5.37945i 1.25723 0.336874i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −14.6969 25.4558i −0.916770 1.58789i −0.804289 0.594238i \(-0.797454\pi\)
−0.112481 0.993654i \(-0.535880\pi\)
\(258\) 4.89898 4.89898i 0.304997 0.304997i
\(259\) 0 0
\(260\) 6.00000i 0.372104i
\(261\) 9.00000 + 15.5885i 0.557086 + 0.964901i
\(262\) 6.36396 + 3.67423i 0.393167 + 0.226995i
\(263\) −20.7846 12.0000i −1.28163 0.739952i −0.304487 0.952517i \(-0.598485\pi\)
−0.977147 + 0.212565i \(0.931818\pi\)
\(264\) 0 0
\(265\) 14.6969i 0.902826i
\(266\) 0 0
\(267\) 0 0
\(268\) 4.00000 + 6.92820i 0.244339 + 0.423207i
\(269\) 6.12372 10.6066i 0.373370 0.646696i −0.616712 0.787189i \(-0.711536\pi\)
0.990082 + 0.140493i \(0.0448688\pi\)
\(270\) 12.2942 3.29423i 0.748203 0.200480i
\(271\) 21.2132 12.2474i 1.28861 0.743980i 0.310204 0.950670i \(-0.399603\pi\)
0.978406 + 0.206691i \(0.0662693\pi\)
\(272\) 4.89898 0.297044
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) −2.68973 10.0382i −0.161903 0.604228i
\(277\) 11.0000 19.0526i 0.660926 1.14476i −0.319447 0.947604i \(-0.603497\pi\)
0.980373 0.197153i \(-0.0631696\pi\)
\(278\) 1.22474 + 2.12132i 0.0734553 + 0.127228i
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(282\) −8.19615 2.19615i −0.488074 0.130779i
\(283\) 19.0919 + 11.0227i 1.13489 + 0.655232i 0.945161 0.326604i \(-0.105904\pi\)
0.189733 + 0.981836i \(0.439238\pi\)
\(284\) 0 0
\(285\) 10.0382 + 2.68973i 0.594611 + 0.159326i
\(286\) 0 0
\(287\) 0 0
\(288\) 3.00000 0.176777
\(289\) −3.50000 6.06218i −0.205882 0.356599i
\(290\) 7.34847 12.7279i 0.431517 0.747409i
\(291\) 2.19615 + 8.19615i 0.128741 + 0.480467i
\(292\) 8.48528 4.89898i 0.496564 0.286691i
\(293\) 2.44949 0.143101 0.0715504 0.997437i \(-0.477205\pi\)
0.0715504 + 0.997437i \(0.477205\pi\)
\(294\) 0 0
\(295\) 30.0000 1.74667
\(296\) −1.73205 + 1.00000i −0.100673 + 0.0581238i
\(297\) 0 0
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) −7.34847 12.7279i −0.424973 0.736075i
\(300\) −1.22474 1.22474i −0.0707107 0.0707107i
\(301\) 0 0
\(302\) 8.00000i 0.460348i
\(303\) 3.29423 12.2942i 0.189248 0.706285i
\(304\) 2.12132 + 1.22474i 0.121666 + 0.0702439i
\(305\) 25.9808 + 15.0000i 1.48765 + 0.858898i
\(306\) −7.34847 12.7279i −0.420084 0.727607i
\(307\) 7.34847i 0.419399i 0.977766 + 0.209700i \(0.0672486\pi\)
−0.977766 + 0.209700i \(0.932751\pi\)
\(308\) 0 0
\(309\) 12.0000 12.0000i 0.682656 0.682656i
\(310\) 0 0
\(311\) −9.79796 + 16.9706i −0.555591 + 0.962312i 0.442266 + 0.896884i \(0.354175\pi\)
−0.997857 + 0.0654284i \(0.979159\pi\)
\(312\) 4.09808 1.09808i 0.232008 0.0621663i
\(313\) −29.6985 + 17.1464i −1.67866 + 0.969173i −0.716139 + 0.697958i \(0.754092\pi\)
−0.962519 + 0.271216i \(0.912574\pi\)
\(314\) 7.34847 0.414698
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) −15.5885 + 9.00000i −0.875535 + 0.505490i −0.869184 0.494489i \(-0.835355\pi\)
−0.00635137 + 0.999980i \(0.502022\pi\)
\(318\) 10.0382 2.68973i 0.562914 0.150832i
\(319\) 0 0
\(320\) −1.22474 2.12132i −0.0684653 0.118585i
\(321\) −14.6969 + 14.6969i −0.820303 + 0.820303i
\(322\) 0 0
\(323\) 12.0000i 0.667698i
\(324\) −4.50000 7.79423i −0.250000 0.433013i
\(325\) −2.12132 1.22474i −0.117670 0.0679366i
\(326\) −13.8564 8.00000i −0.767435 0.443079i
\(327\) 4.48288 16.7303i 0.247904 0.925189i
\(328\) 4.89898i 0.270501i
\(329\) 0 0
\(330\) 0 0
\(331\) 4.00000 + 6.92820i 0.219860 + 0.380808i 0.954765 0.297361i \(-0.0961066\pi\)
−0.734905 + 0.678170i \(0.762773\pi\)
\(332\) 1.22474 2.12132i 0.0672166 0.116423i
\(333\) 5.19615 + 3.00000i 0.284747 + 0.164399i
\(334\) −4.24264 + 2.44949i −0.232147 + 0.134030i
\(335\) −19.5959 −1.07064
\(336\) 0 0
\(337\) −32.0000 −1.74315 −0.871576 0.490261i \(-0.836901\pi\)
−0.871576 + 0.490261i \(0.836901\pi\)
\(338\) −6.06218 + 3.50000i −0.329739 + 0.190375i
\(339\) 2.68973 + 10.0382i 0.146086 + 0.545200i
\(340\) −6.00000 + 10.3923i −0.325396 + 0.563602i
\(341\) 0 0
\(342\) 7.34847i 0.397360i
\(343\) 0 0
\(344\) 4.00000i 0.215666i
\(345\) 24.5885 + 6.58846i 1.32380 + 0.354711i
\(346\) −19.0919 11.0227i −1.02639 0.592584i
\(347\) −10.3923 6.00000i −0.557888 0.322097i 0.194409 0.980921i \(-0.437721\pi\)
−0.752297 + 0.658824i \(0.771054\pi\)
\(348\) −10.0382 2.68973i −0.538104 0.144184i
\(349\) 2.44949i 0.131118i −0.997849 0.0655591i \(-0.979117\pi\)
0.997849 0.0655591i \(-0.0208831\pi\)
\(350\) 0 0
\(351\) −9.00000 9.00000i −0.480384 0.480384i
\(352\) 0 0
\(353\) 4.89898 8.48528i 0.260746 0.451626i −0.705694 0.708517i \(-0.749365\pi\)
0.966440 + 0.256891i \(0.0826980\pi\)
\(354\) −5.49038 20.4904i −0.291810 1.08905i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −24.0000 −1.26844
\(359\) 5.19615 3.00000i 0.274242 0.158334i −0.356572 0.934268i \(-0.616054\pi\)
0.630814 + 0.775934i \(0.282721\pi\)
\(360\) −3.67423 + 6.36396i −0.193649 + 0.335410i
\(361\) −6.50000 + 11.2583i −0.342105 + 0.592544i
\(362\) 6.12372 + 10.6066i 0.321856 + 0.557471i
\(363\) 13.4722 + 13.4722i 0.707107 + 0.707107i
\(364\) 0 0
\(365\) 24.0000i 1.25622i
\(366\) 5.49038 20.4904i 0.286987 1.07105i
\(367\) 4.24264 + 2.44949i 0.221464 + 0.127862i 0.606628 0.794986i \(-0.292522\pi\)
−0.385164 + 0.922848i \(0.625855\pi\)
\(368\) 5.19615 + 3.00000i 0.270868 + 0.156386i
\(369\) −12.7279 + 7.34847i −0.662589 + 0.382546i
\(370\) 4.89898i 0.254686i
\(371\) 0 0
\(372\) 0 0
\(373\) −7.00000 12.1244i −0.362446 0.627775i 0.625917 0.779890i \(-0.284725\pi\)
−0.988363 + 0.152115i \(0.951392\pi\)
\(374\) 0 0
\(375\) −16.3923 + 4.39230i −0.846495 + 0.226818i
\(376\) 4.24264 2.44949i 0.218797 0.126323i
\(377\) −14.6969 −0.756931
\(378\) 0 0
\(379\) −20.0000 −1.02733 −0.513665 0.857991i \(-0.671713\pi\)
−0.513665 + 0.857991i \(0.671713\pi\)
\(380\) −5.19615 + 3.00000i −0.266557 + 0.153897i
\(381\) −13.3843 + 3.58630i −0.685696 + 0.183732i
\(382\) 0 0
\(383\) 17.1464 + 29.6985i 0.876142 + 1.51752i 0.855542 + 0.517734i \(0.173224\pi\)
0.0205998 + 0.999788i \(0.493442\pi\)
\(384\) −1.22474 + 1.22474i −0.0625000 + 0.0625000i
\(385\) 0 0
\(386\) 4.00000i 0.203595i
\(387\) 10.3923 6.00000i 0.528271 0.304997i
\(388\) −4.24264 2.44949i −0.215387 0.124354i
\(389\) −5.19615 3.00000i −0.263455 0.152106i 0.362454 0.932002i \(-0.381939\pi\)
−0.625910 + 0.779895i \(0.715272\pi\)
\(390\) −2.68973 + 10.0382i −0.136200 + 0.508304i
\(391\) 29.3939i 1.48651i
\(392\) 0 0
\(393\) 9.00000 + 9.00000i 0.453990 + 0.453990i
\(394\) 9.00000 + 15.5885i 0.453413 + 0.785335i
\(395\) −12.2474 + 21.2132i −0.616236 + 1.06735i
\(396\) 0 0
\(397\) 6.36396 3.67423i 0.319398 0.184405i −0.331726 0.943376i \(-0.607631\pi\)
0.651124 + 0.758971i \(0.274298\pi\)
\(398\) 9.79796 0.491127
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) −25.9808 + 15.0000i −1.29742 + 0.749064i −0.979957 0.199207i \(-0.936163\pi\)
−0.317460 + 0.948272i \(0.602830\pi\)
\(402\) 3.58630 + 13.3843i 0.178868 + 0.667546i
\(403\) 0 0
\(404\) 3.67423 + 6.36396i 0.182800 + 0.316619i
\(405\) 22.0454 1.09545
\(406\) 0 0
\(407\) 0 0
\(408\) 8.19615 + 2.19615i 0.405770 + 0.108726i
\(409\) −29.6985 17.1464i −1.46850 0.847836i −0.469119 0.883135i \(-0.655428\pi\)
−0.999377 + 0.0352988i \(0.988762\pi\)
\(410\) 10.3923 + 6.00000i 0.513239 + 0.296319i
\(411\) 20.0764 + 5.37945i 0.990295 + 0.265349i
\(412\) 9.79796i 0.482711i
\(413\) 0 0
\(414\) 18.0000i 0.884652i
\(415\) 3.00000 + 5.19615i 0.147264 + 0.255069i
\(416\) −1.22474 + 2.12132i −0.0600481 + 0.104006i
\(417\) 1.09808 + 4.09808i 0.0537730 + 0.200684i
\(418\) 0 0
\(419\) 12.2474 0.598327 0.299164 0.954202i \(-0.403292\pi\)
0.299164 + 0.954202i \(0.403292\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 6.92820 4.00000i 0.337260 0.194717i
\(423\) −12.7279 7.34847i −0.618853 0.357295i
\(424\) −3.00000 + 5.19615i −0.145693 + 0.252347i
\(425\) −2.44949 4.24264i −0.118818 0.205798i
\(426\) 0 0
\(427\) 0 0
\(428\) 12.0000i 0.580042i
\(429\) 0 0
\(430\) −8.48528 4.89898i −0.409197 0.236250i
\(431\) 25.9808 + 15.0000i 1.25145 + 0.722525i 0.971397 0.237460i \(-0.0763149\pi\)
0.280052 + 0.959985i \(0.409648\pi\)
\(432\) 5.01910 + 1.34486i 0.241481 + 0.0647048i
\(433\) 14.6969i 0.706290i 0.935569 + 0.353145i \(0.114888\pi\)
−0.935569 + 0.353145i \(0.885112\pi\)
\(434\) 0 0
\(435\) 18.0000 18.0000i 0.863034 0.863034i
\(436\) 5.00000 + 8.66025i 0.239457 + 0.414751i
\(437\) 7.34847 12.7279i 0.351525 0.608859i
\(438\) 16.3923 4.39230i 0.783255 0.209872i
\(439\) −12.7279 + 7.34847i −0.607471 + 0.350723i −0.771975 0.635653i \(-0.780731\pi\)
0.164504 + 0.986376i \(0.447398\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 12.0000 0.570782
\(443\) −31.1769 + 18.0000i −1.48126 + 0.855206i −0.999774 0.0212481i \(-0.993236\pi\)
−0.481486 + 0.876454i \(0.659903\pi\)
\(444\) −3.34607 + 0.896575i −0.158797 + 0.0425496i
\(445\) 0 0
\(446\) −7.34847 12.7279i −0.347960 0.602685i
\(447\) −7.34847 + 7.34847i −0.347571 + 0.347571i
\(448\) 0 0
\(449\) 36.0000i 1.69895i 0.527633 + 0.849473i \(0.323080\pi\)
−0.527633 + 0.849473i \(0.676920\pi\)
\(450\) −1.50000 2.59808i −0.0707107 0.122474i
\(451\) 0 0
\(452\) −5.19615 3.00000i −0.244406 0.141108i
\(453\) −3.58630 + 13.3843i −0.168499 + 0.628847i
\(454\) 7.34847i 0.344881i
\(455\) 0 0
\(456\) 3.00000 + 3.00000i 0.140488 + 0.140488i
\(457\) −14.0000 24.2487i −0.654892 1.13431i −0.981921 0.189292i \(-0.939381\pi\)
0.327028 0.945015i \(-0.393953\pi\)
\(458\) −11.0227 + 19.0919i −0.515057 + 0.892105i
\(459\) −6.58846 24.5885i −0.307523 1.14769i
\(460\) −12.7279 + 7.34847i −0.593442 + 0.342624i
\(461\) 31.8434 1.48309 0.741547 0.670901i \(-0.234093\pi\)
0.741547 + 0.670901i \(0.234093\pi\)
\(462\) 0 0
\(463\) 14.0000 0.650635 0.325318 0.945605i \(-0.394529\pi\)
0.325318 + 0.945605i \(0.394529\pi\)
\(464\) 5.19615 3.00000i 0.241225 0.139272i
\(465\) 0 0
\(466\) −12.0000 + 20.7846i −0.555889 + 0.962828i
\(467\) 3.67423 + 6.36396i 0.170023 + 0.294489i 0.938428 0.345476i \(-0.112282\pi\)
−0.768404 + 0.639965i \(0.778949\pi\)
\(468\) 7.34847 0.339683
\(469\) 0 0
\(470\) 12.0000i 0.553519i
\(471\) 12.2942 + 3.29423i 0.566488 + 0.151790i
\(472\) 10.6066 + 6.12372i 0.488208 + 0.281867i
\(473\) 0 0
\(474\) 16.7303 + 4.48288i 0.768449 + 0.205905i
\(475\) 2.44949i 0.112390i
\(476\) 0 0
\(477\) 18.0000 0.824163
\(478\) −3.00000 5.19615i −0.137217 0.237666i
\(479\) −12.2474 + 21.2132i −0.559600 + 0.969256i 0.437929 + 0.899009i \(0.355712\pi\)
−0.997530 + 0.0702467i \(0.977621\pi\)
\(480\) −1.09808 4.09808i −0.0501201 0.187051i
\(481\) −4.24264 + 2.44949i −0.193448 + 0.111687i
\(482\) −24.4949 −1.11571
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 10.3923 6.00000i 0.471890 0.272446i
\(486\) −4.03459 15.0573i −0.183013 0.683013i
\(487\) 16.0000 27.7128i 0.725029 1.25579i −0.233933 0.972253i \(-0.575160\pi\)
0.958962 0.283535i \(-0.0915071\pi\)
\(488\) 6.12372 + 10.6066i 0.277208 + 0.480138i
\(489\) −19.5959 19.5959i −0.886158 0.886158i
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 2.19615 8.19615i 0.0990102 0.369511i
\(493\) −25.4558 14.6969i −1.14647 0.661917i
\(494\) 5.19615 + 3.00000i 0.233786 + 0.134976i
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 3.00000 3.00000i 0.134433 0.134433i
\(499\) 10.0000 + 17.3205i 0.447661 + 0.775372i 0.998233 0.0594153i \(-0.0189236\pi\)
−0.550572 + 0.834788i \(0.685590\pi\)
\(500\) 4.89898 8.48528i 0.219089 0.379473i
\(501\) −8.19615 + 2.19615i −0.366177 + 0.0981169i
\(502\) 14.8492 8.57321i 0.662754 0.382641i
\(503\) 39.1918 1.74748 0.873739 0.486395i \(-0.161689\pi\)
0.873739 + 0.486395i \(0.161689\pi\)
\(504\) 0 0
\(505\) −18.0000 −0.800989
\(506\) 0 0
\(507\) −11.7112 + 3.13801i −0.520114 + 0.139364i
\(508\) 4.00000 6.92820i 0.177471 0.307389i
\(509\) 6.12372 + 10.6066i 0.271429 + 0.470129i 0.969228 0.246165i \(-0.0791704\pi\)
−0.697799 + 0.716294i \(0.745837\pi\)
\(510\) −14.6969 + 14.6969i −0.650791 + 0.650791i
\(511\) 0 0
\(512\) 1.00000i 0.0441942i
\(513\) 3.29423 12.2942i 0.145444 0.542803i
\(514\) 25.4558 + 14.6969i 1.12281 + 0.648254i
\(515\) −20.7846 12.0000i −0.915879 0.528783i
\(516\) −1.79315 + 6.69213i −0.0789391 + 0.294605i
\(517\) 0 0
\(518\) 0 0
\(519\) −27.0000 27.0000i −1.18517 1.18517i
\(520\) −3.00000 5.19615i −0.131559 0.227866i
\(521\) 2.44949 4.24264i 0.107314 0.185873i −0.807367 0.590049i \(-0.799108\pi\)
0.914681 + 0.404176i \(0.132442\pi\)
\(522\) −15.5885 9.00000i −0.682288 0.393919i
\(523\) 2.12132 1.22474i 0.0927589 0.0535544i −0.452903 0.891560i \(-0.649612\pi\)
0.545662 + 0.838005i \(0.316278\pi\)
\(524\) −7.34847 −0.321019
\(525\) 0 0
\(526\) 24.0000 1.04645
\(527\) 0 0
\(528\) 0 0
\(529\) 6.50000 11.2583i 0.282609 0.489493i
\(530\) −7.34847 12.7279i −0.319197 0.552866i
\(531\) 36.7423i 1.59448i
\(532\) 0 0
\(533\) 12.0000i 0.519778i
\(534\) 0 0
\(535\) 25.4558 + 14.6969i 1.10055 + 0.635404i
\(536\) −6.92820 4.00000i −0.299253 0.172774i
\(537\) −40.1528 10.7589i −1.73272 0.464281i
\(538\) 12.2474i 0.528025i
\(539\) 0 0
\(540\) −9.00000 + 9.00000i −0.387298 + 0.387298i
\(541\) −1.00000 1.73205i −0.0429934 0.0744667i 0.843728 0.536771i \(-0.180356\pi\)
−0.886721 + 0.462304i \(0.847023\pi\)
\(542\) −12.2474 + 21.2132i −0.526073 + 0.911185i
\(543\) 5.49038 + 20.4904i 0.235615 + 0.879326i
\(544\) −4.24264 + 2.44949i −0.181902 + 0.105021i
\(545\) −24.4949 −1.04925
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −10.3923 + 6.00000i −0.443937 + 0.256307i
\(549\) 18.3712 31.8198i 0.784063 1.35804i
\(550\) 0 0
\(551\) −7.34847 12.7279i −0.313055 0.542228i
\(552\) 7.34847 + 7.34847i 0.312772 + 0.312772i
\(553\) 0 0
\(554\) 22.0000i 0.934690i
\(555\) 2.19615 8.19615i 0.0932215 0.347907i
\(556\) −2.12132 1.22474i −0.0899640 0.0519408i
\(557\) 15.5885 + 9.00000i 0.660504 + 0.381342i 0.792469 0.609912i \(-0.208795\pi\)
−0.131965 + 0.991254i \(0.542129\pi\)
\(558\) 0 0
\(559\) 9.79796i 0.414410i
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 11.0227 19.0919i 0.464552 0.804627i −0.534630 0.845087i \(-0.679549\pi\)
0.999181 + 0.0404596i \(0.0128822\pi\)
\(564\) 8.19615 2.19615i 0.345120 0.0924747i
\(565\) 12.7279 7.34847i 0.535468 0.309152i
\(566\) −22.0454 −0.926638
\(567\) 0 0
\(568\) 0 0
\(569\) 5.19615 3.00000i 0.217834 0.125767i −0.387113 0.922032i \(-0.626528\pi\)
0.604947 + 0.796266i \(0.293194\pi\)
\(570\) −10.0382 + 2.68973i −0.420454 + 0.112660i
\(571\) −16.0000 + 27.7128i −0.669579 + 1.15975i 0.308443 + 0.951243i \(0.400192\pi\)
−0.978022 + 0.208502i \(0.933141\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 6.00000i 0.250217i
\(576\) −2.59808 + 1.50000i −0.108253 + 0.0625000i
\(577\) −16.9706 9.79796i −0.706494 0.407894i 0.103268 0.994654i \(-0.467070\pi\)
−0.809761 + 0.586759i \(0.800404\pi\)
\(578\) 6.06218 + 3.50000i 0.252153 + 0.145581i
\(579\) 1.79315 6.69213i 0.0745208 0.278115i
\(580\) 14.6969i 0.610257i
\(581\) 0 0
\(582\) −6.00000 6.00000i −0.248708 0.248708i
\(583\) 0 0
\(584\) −4.89898 + 8.48528i −0.202721 + 0.351123i
\(585\) −9.00000 + 15.5885i −0.372104 + 0.644503i
\(586\) −2.12132 + 1.22474i −0.0876309 + 0.0505937i
\(587\) −7.34847 −0.303304 −0.151652 0.988434i \(-0.548459\pi\)
−0.151652 + 0.988434i \(0.548459\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) −25.9808 + 15.0000i −1.06961 + 0.617540i
\(591\) 8.06918 + 30.1146i 0.331922 + 1.23875i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) −19.5959 33.9411i −0.804708 1.39379i −0.916488 0.400062i \(-0.868989\pi\)
0.111780 0.993733i \(-0.464345\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6.00000i 0.245770i
\(597\) 16.3923 + 4.39230i 0.670892 + 0.179765i
\(598\) 12.7279 + 7.34847i 0.520483 + 0.300501i
\(599\) 20.7846 + 12.0000i 0.849236 + 0.490307i 0.860393 0.509631i \(-0.170218\pi\)
−0.0111569 + 0.999938i \(0.503551\pi\)
\(600\) 1.67303 + 0.448288i 0.0683013 + 0.0183013i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 24.0000i 0.977356i
\(604\) −4.00000 6.92820i −0.162758 0.281905i
\(605\) 13.4722 23.3345i 0.547723 0.948683i
\(606\) 3.29423 + 12.2942i 0.133819 + 0.499419i
\(607\) −4.24264 + 2.44949i −0.172203 + 0.0994217i −0.583624 0.812024i \(-0.698366\pi\)
0.411421 + 0.911445i \(0.365033\pi\)
\(608\) −2.44949 −0.0993399
\(609\) 0 0
\(610\) −30.0000 −1.21466
\(611\) 10.3923 6.00000i 0.420428 0.242734i
\(612\) 12.7279 + 7.34847i 0.514496 + 0.297044i
\(613\) −7.00000 + 12.1244i −0.282727 + 0.489698i −0.972056 0.234751i \(-0.924572\pi\)
0.689328 + 0.724449i \(0.257906\pi\)
\(614\) −3.67423 6.36396i −0.148280 0.256829i
\(615\) 14.6969 + 14.6969i 0.592638 + 0.592638i
\(616\) 0 0
\(617\) 18.0000i 0.724653i −0.932051 0.362326i \(-0.881983\pi\)
0.932051 0.362326i \(-0.118017\pi\)
\(618\) −4.39230 + 16.3923i −0.176684 + 0.659395i
\(619\) 23.3345 + 13.4722i 0.937894 + 0.541493i 0.889299 0.457325i \(-0.151193\pi\)
0.0485943 + 0.998819i \(0.484526\pi\)
\(620\) 0 0
\(621\) 8.06918 30.1146i 0.323805 1.20846i
\(622\) 19.5959i 0.785725i
\(623\) 0 0
\(624\) −3.00000 + 3.00000i −0.120096 + 0.120096i
\(625\) 14.5000 + 25.1147i 0.580000 + 1.00459i
\(626\) 17.1464 29.6985i 0.685309 1.18699i
\(627\) 0 0
\(628\) −6.36396 + 3.67423i −0.253950 + 0.146618i
\(629\) −9.79796 −0.390670
\(630\) 0 0
\(631\) 2.00000 0.0796187 0.0398094 0.999207i \(-0.487325\pi\)
0.0398094 + 0.999207i \(0.487325\pi\)
\(632\) −8.66025 + 5.00000i −0.344486 + 0.198889i
\(633\) 13.3843 3.58630i 0.531977 0.142543i
\(634\) 9.00000 15.5885i 0.357436 0.619097i
\(635\) 9.79796 + 16.9706i 0.388820 + 0.673456i
\(636\) −7.34847 + 7.34847i −0.291386 + 0.291386i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 2.12132 + 1.22474i 0.0838525 + 0.0484123i
\(641\) −25.9808 15.0000i −1.02618 0.592464i −0.110291 0.993899i \(-0.535178\pi\)
−0.915888 + 0.401435i \(0.868512\pi\)
\(642\) 5.37945 20.0764i 0.212310 0.792352i
\(643\) 22.0454i 0.869386i −0.900579 0.434693i \(-0.856857\pi\)
0.900579 0.434693i \(-0.143143\pi\)
\(644\) 0 0
\(645\) −12.0000 12.0000i −0.472500 0.472500i
\(646\) 6.00000 + 10.3923i 0.236067 + 0.408880i
\(647\) 22.0454 38.1838i 0.866694 1.50116i 0.00133956 0.999999i \(-0.499574\pi\)
0.865355 0.501160i \(-0.167093\pi\)
\(648\) 7.79423 + 4.50000i 0.306186 + 0.176777i
\(649\) 0 0
\(650\) 2.44949 0.0960769
\(651\) 0 0
\(652\) 16.0000 0.626608
\(653\) −5.19615 + 3.00000i −0.203341 + 0.117399i −0.598213 0.801337i \(-0.704122\pi\)
0.394872 + 0.918736i \(0.370789\pi\)
\(654\) 4.48288 + 16.7303i 0.175294 + 0.654208i
\(655\) 9.00000 15.5885i 0.351659 0.609091i
\(656\) 2.44949 + 4.24264i 0.0956365 + 0.165647i
\(657\) 29.3939 1.14676
\(658\) 0 0
\(659\) 36.0000i 1.40236i 0.712984 + 0.701180i \(0.247343\pi\)
−0.712984 + 0.701180i \(0.752657\pi\)
\(660\) 0 0
\(661\) 10.6066 + 6.12372i 0.412549 + 0.238185i 0.691884 0.722008i \(-0.256781\pi\)
−0.279335 + 0.960194i \(0.590114\pi\)
\(662\) −6.92820 4.00000i −0.269272 0.155464i
\(663\) 20.0764 + 5.37945i 0.779702 + 0.208921i
\(664\) 2.44949i 0.0950586i
\(665\) 0 0
\(666\) −6.00000 −0.232495
\(667\) −18.0000 31.1769i −0.696963 1.20717i
\(668\) 2.44949 4.24264i 0.0947736 0.164153i
\(669\) −6.58846 24.5885i −0.254724 0.950645i
\(670\) 16.9706 9.79796i 0.655630 0.378528i
\(671\) 0 0
\(672\) 0 0
\(673\) 34.0000 1.31060 0.655302 0.755367i \(-0.272541\pi\)
0.655302 + 0.755367i \(0.272541\pi\)
\(674\) 27.7128 16.0000i 1.06746 0.616297i
\(675\) −1.34486 5.01910i −0.0517638 0.193185i
\(676\) 3.50000 6.06218i 0.134615 0.233161i
\(677\) 3.67423 + 6.36396i 0.141212 + 0.244587i 0.927953 0.372696i \(-0.121567\pi\)
−0.786741 + 0.617283i \(0.788233\pi\)
\(678\) −7.34847 7.34847i −0.282216 0.282216i
\(679\) 0 0
\(680\) 12.0000i 0.460179i
\(681\) −3.29423 + 12.2942i −0.126235 + 0.471116i
\(682\) 0 0
\(683\) −20.7846 12.0000i −0.795301 0.459167i 0.0465244 0.998917i \(-0.485185\pi\)
−0.841825 + 0.539750i \(0.818519\pi\)
\(684\) 3.67423 + 6.36396i 0.140488 + 0.243332i
\(685\) 29.3939i 1.12308i
\(686\) 0 0
\(687\) −27.0000 + 27.0000i −1.03011 + 1.03011i
\(688\) −2.00000 3.46410i −0.0762493 0.132068i
\(689\) −7.34847 + 12.7279i −0.279954 + 0.484895i
\(690\) −24.5885 + 6.58846i −0.936067 + 0.250818i
\(691\) 31.8198 18.3712i 1.21048 0.698872i 0.247618 0.968858i \(-0.420352\pi\)
0.962864 + 0.269985i \(0.0870189\pi\)
\(692\) 22.0454 0.838041
\(693\) 0 0
\(694\) 12.0000 0.455514
\(695\) 5.19615 3.00000i 0.197101 0.113796i
\(696\) 10.0382 2.68973i 0.380497 0.101954i
\(697\) 12.0000 20.7846i 0.454532 0.787273i
\(698\) 1.22474 + 2.12132i 0.0463573 + 0.0802932i
\(699\) −29.3939 + 29.3939i −1.11178 + 1.11178i
\(700\) 0 0
\(701\) 30.0000i 1.13308i −0.824033 0.566542i \(-0.808281\pi\)
0.824033 0.566542i \(-0.191719\pi\)
\(702\) 12.2942 + 3.29423i 0.464016 + 0.124333i
\(703\) −4.24264 2.44949i −0.160014 0.0923843i
\(704\) 0 0
\(705\) −5.37945 + 20.0764i −0.202602 + 0.756121i
\(706\) 9.79796i 0.368751i
\(707\) 0 0
\(708\) 15.0000 + 15.0000i 0.563735 + 0.563735i
\(709\) −5.00000 8.66025i −0.187779 0.325243i 0.756730 0.653727i \(-0.226796\pi\)
−0.944509 + 0.328484i \(0.893462\pi\)
\(710\) 0 0
\(711\) 25.9808 + 15.0000i 0.974355 + 0.562544i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 20.7846 12.0000i 0.776757 0.448461i
\(717\) −2.68973 10.0382i −0.100450 0.374883i
\(718\) −3.00000 + 5.19615i −0.111959 + 0.193919i
\(719\) −12.2474 21.2132i −0.456753 0.791119i 0.542034 0.840356i \(-0.317654\pi\)
−0.998787 + 0.0492373i \(0.984321\pi\)
\(720\) 7.34847i 0.273861i
\(721\) 0 0
\(722\) 13.0000i 0.483810i
\(723\) −40.9808 10.9808i −1.52409 0.408379i
\(724\) −10.6066 6.12372i −0.394191 0.227586i
\(725\) −5.19615 3.00000i −0.192980 0.111417i
\(726\) −18.4034 4.93117i −0.683013 0.183013i
\(727\) 29.3939i 1.09016i −0.838385 0.545079i \(-0.816500\pi\)
0.838385 0.545079i \(-0.183500\pi\)
\(728\) 0 0
\(729\) 27.0000i 1.00000i
\(730\) −12.0000 20.7846i −0.444140 0.769273i
\(731\) −9.79796 + 16.9706i −0.362391 + 0.627679i
\(732\) 5.49038 + 20.4904i 0.202930 + 0.757346i
\(733\) −19.0919 + 11.0227i −0.705175 + 0.407133i −0.809272 0.587434i \(-0.800138\pi\)
0.104097 + 0.994567i \(0.466805\pi\)
\(734\) −4.89898 −0.180825
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) 0 0
\(738\) 7.34847 12.7279i 0.270501 0.468521i
\(739\) −10.0000 + 17.3205i −0.367856 + 0.637145i −0.989230 0.146369i \(-0.953241\pi\)
0.621374 + 0.783514i \(0.286575\pi\)
\(740\) 2.44949 + 4.24264i 0.0900450 + 0.155963i
\(741\) 7.34847 + 7.34847i 0.269953 + 0.269953i
\(742\) 0 0
\(743\) 6.00000i 0.220119i −0.993925 0.110059i \(-0.964896\pi\)
0.993925 0.110059i \(-0.0351041\pi\)
\(744\) 0 0
\(745\) 12.7279 + 7.34847i 0.466315 + 0.269227i
\(746\) 12.1244 + 7.00000i 0.443904 + 0.256288i
\(747\) 6.36396 3.67423i 0.232845 0.134433i
\(748\) 0 0
\(749\) 0 0
\(750\) 12.0000 12.0000i 0.438178 0.438178i
\(751\) 4.00000 + 6.92820i 0.145962 + 0.252814i 0.929731 0.368238i \(-0.120039\pi\)
−0.783769 + 0.621052i \(0.786706\pi\)
\(752\) −2.44949 + 4.24264i −0.0893237 + 0.154713i
\(753\) 28.6865 7.68653i 1.04540 0.280113i
\(754\) 12.7279 7.34847i 0.463524 0.267615i
\(755\) 19.5959 0.713168
\(756\) 0 0
\(757\) −2.00000 −0.0726912 −0.0363456 0.999339i \(-0.511572\pi\)
−0.0363456 + 0.999339i \(0.511572\pi\)
\(758\) 17.3205 10.0000i 0.629109 0.363216i
\(759\) 0 0
\(760\) 3.00000 5.19615i 0.108821 0.188484i
\(761\) 2.44949 + 4.24264i 0.0887939 + 0.153796i 0.907002 0.421127i \(-0.138365\pi\)
−0.818208 + 0.574923i \(0.805032\pi\)
\(762\) 9.79796 9.79796i 0.354943 0.354943i
\(763\) 0 0
\(764\) 0 0
\(765\) −31.1769 + 18.0000i −1.12720 + 0.650791i
\(766\) −29.6985 17.1464i −1.07305 0.619526i
\(767\) 25.9808 + 15.0000i 0.938111 + 0.541619i
\(768\) 0.448288 1.67303i 0.0161762 0.0603704i
\(769\) 34.2929i 1.23663i 0.785930 + 0.618316i \(0.212185\pi\)
−0.785930 + 0.618316i \(0.787815\pi\)
\(770\) 0 0
\(771\) 36.0000 + 36.0000i 1.29651 + 1.29651i
\(772\) 2.00000 + 3.46410i 0.0719816 + 0.124676i
\(773\) −13.4722 + 23.3345i −0.484561 + 0.839284i −0.999843 0.0177365i \(-0.994354\pi\)
0.515282 + 0.857021i \(0.327687\pi\)
\(774\) −6.00000 + 10.3923i −0.215666 + 0.373544i
\(775\) 0 0
\(776\) 4.89898 0.175863
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) 10.3923 6.00000i 0.372343 0.214972i
\(780\) −2.68973 10.0382i −0.0963077 0.359425i
\(781\) 0 0
\(782\) 14.6969 + 25.4558i 0.525561 + 0.910299i
\(783\) −22.0454 22.0454i −0.787839 0.787839i
\(784\) 0 0
\(785\) 18.0000i 0.642448i
\(786\) −12.2942 3.29423i −0.438521 0.117501i
\(787\) −27.5772 15.9217i −0.983020 0.567547i −0.0798393 0.996808i \(-0.525441\pi\)
−0.903180 + 0.429261i \(0.858774\pi\)
\(788\) −15.5885 9.00000i −0.555316 0.320612i
\(789\) 40.1528 + 10.7589i 1.42948 + 0.383027i
\(790\) 24.4949i 0.871489i
\(791\) 0 0
\(792\) 0 0
\(793\) 15.0000 + 25.9808i 0.532666 + 0.922604i
\(794\) −3.67423 + 6.36396i −0.130394 + 0.225849i
\(795\) −6.58846 24.5885i −0.233668 0.872063i
\(796\) −8.48528 + 4.89898i −0.300753 + 0.173640i
\(797\) −7.34847 −0.260296 −0.130148 0.991495i \(-0.541545\pi\)
−0.130148 + 0.991495i \(0.541545\pi\)
\(798\) 0 0
\(799\) 24.0000 0.849059
\(800\) −0.866025 + 0.500000i −0.0306186 + 0.0176777i
\(801\) 0 0
\(802\) 15.0000 25.9808i 0.529668 0.917413i
\(803\) 0 0
\(804\) −9.79796 9.79796i −0.345547 0.345547i
\(805\) 0 0
\(806\) 0 0
\(807\) −5.49038 + 20.4904i −0.193271 + 0.721296i
\(808\) −6.36396 3.67423i −0.223883 0.129259i
\(809\) −5.19615 3.00000i −0.182687 0.105474i 0.405868 0.913932i \(-0.366969\pi\)
−0.588555 + 0.808458i \(0.700303\pi\)
\(810\) −19.0919 + 11.0227i −0.670820 + 0.387298i
\(811\) 36.7423i 1.29020i 0.764099 + 0.645099i \(0.223184\pi\)
−0.764099 + 0.645099i \(0.776816\pi\)
\(812\) 0 0
\(813\) −30.0000 + 30.0000i −1.05215 + 1.05215i
\(814\) 0 0
\(815\) −19.5959 + 33.9411i −0.686415 + 1.18891i
\(816\) −8.19615 + 2.19615i −0.286923 + 0.0768807i
\(817\) −8.48528 + 4.89898i −0.296862 + 0.171394i
\(818\) 34.2929 1.19902
\(819\) 0 0
\(820\) −12.0000 −0.419058
\(821\) 25.9808 15.0000i 0.906735 0.523504i 0.0273557 0.999626i \(-0.491291\pi\)
0.879379 + 0.476122i \(0.157958\pi\)
\(822\) −20.0764 + 5.37945i −0.700245 + 0.187630i
\(823\) −7.00000 + 12.1244i −0.244005 + 0.422628i −0.961851 0.273573i \(-0.911795\pi\)
0.717847 + 0.696201i \(0.245128\pi\)
\(824\) −4.89898 8.48528i −0.170664 0.295599i
\(825\) 0 0
\(826\) 0 0
\(827\) 12.0000i 0.417281i 0.977992 + 0.208640i \(0.0669038\pi\)
−0.977992 + 0.208640i \(0.933096\pi\)
\(828\) 9.00000 + 15.5885i 0.312772 + 0.541736i
\(829\) 23.3345 + 13.4722i 0.810442 + 0.467909i 0.847109 0.531419i \(-0.178341\pi\)
−0.0366677 + 0.999328i \(0.511674\pi\)
\(830\) −5.19615 3.00000i −0.180361 0.104132i
\(831\) −9.86233 + 36.8067i −0.342120 + 1.27681i
\(832\) 2.44949i 0.0849208i
\(833\) 0 0
\(834\) −3.00000 3.00000i −0.103882 0.103882i
\(835\) 6.00000 + 10.3923i 0.207639 + 0.359641i
\(836\) 0 0
\(837\) 0 0
\(838\) −10.6066 + 6.12372i −0.366399 + 0.211541i
\(839\) −24.4949 −0.845658 −0.422829 0.906210i \(-0.638963\pi\)
−0.422829 + 0.906210i \(0.638963\pi\)
\(840\) 0 0
\(841\) −7.00000 −0.241379
\(842\) −1.73205 + 1.00000i −0.0596904 + 0.0344623i
\(843\) 0 0
\(844\) −4.00000 + 6.92820i −0.137686 + 0.238479i
\(845\) 8.57321 + 14.8492i 0.294928 + 0.510829i
\(846\) 14.6969 0.505291
\(847\) 0 0
\(848\) 6.00000i 0.206041i
\(849\) −36.8827 9.88269i −1.26581 0.339173i
\(850\) 4.24264 + 2.44949i 0.145521 + 0.0840168i
\(851\) −10.3923 6.00000i −0.356244 0.205677i
\(852\) 0 0
\(853\) 2.44949i 0.0838689i 0.999120 + 0.0419345i \(0.0133521\pi\)
−0.999120 + 0.0419345i \(0.986648\pi\)
\(854\) 0 0
\(855\) −18.0000 −0.615587
\(856\) 6.00000 + 10.3923i 0.205076 + 0.355202i
\(857\) −2.44949 + 4.24264i −0.0836730 + 0.144926i −0.904825 0.425784i \(-0.859998\pi\)
0.821152 + 0.570710i \(0.193332\pi\)
\(858\) 0 0
\(859\) −23.3345 + 13.4722i −0.796164 + 0.459665i −0.842128 0.539278i \(-0.818697\pi\)
0.0459643 + 0.998943i \(0.485364\pi\)
\(860\) 9.79796 0.334108
\(861\) 0 0
\(862\) −30.0000 −1.02180
\(863\) 20.7846 12.0000i 0.707516 0.408485i −0.102624 0.994720i \(-0.532724\pi\)
0.810141 + 0.586235i \(0.199391\pi\)
\(864\) −5.01910 + 1.34486i −0.170753 + 0.0457532i
\(865\) −27.0000 + 46.7654i −0.918028 + 1.59007i
\(866\) −7.34847 12.7279i −0.249711 0.432512i
\(867\) 8.57321 + 8.57321i 0.291162 + 0.291162i
\(868\) 0 0
\(869\) 0 0
\(870\) −6.58846 + 24.5885i −0.223370 + 0.833627i
\(871\) −16.9706 9.79796i −0.575026 0.331991i
\(872\) −8.66025 5.00000i −0.293273 0.169321i
\(873\) −7.34847 12.7279i −0.248708 0.430775i
\(874\) 14.6969i 0.497131i
\(875\) 0 0
\(876\) −12.0000 + 12.0000i −0.405442 + 0.405442i
\(877\) 11.0000 + 19.0526i 0.371444 + 0.643359i 0.989788 0.142548i \(-0.0455296\pi\)
−0.618344 + 0.785907i \(0.712196\pi\)
\(878\) 7.34847 12.7279i 0.247999 0.429547i
\(879\) −4.09808 + 1.09808i −0.138225 + 0.0370372i
\(880\) 0 0
\(881\) −29.3939 −0.990305 −0.495152 0.868806i \(-0.664888\pi\)
−0.495152 + 0.868806i \(0.664888\pi\)
\(882\) 0 0
\(883\) −56.0000 −1.88455 −0.942275 0.334840i \(-0.891318\pi\)
−0.942275 + 0.334840i \(0.891318\pi\)
\(884\) −10.3923 + 6.00000i −0.349531 + 0.201802i
\(885\) −50.1910 + 13.4486i −1.68715 + 0.452071i
\(886\) 18.0000 31.1769i 0.604722 1.04741i
\(887\) −2.44949 4.24264i −0.0822458 0.142454i 0.821968 0.569533i \(-0.192876\pi\)
−0.904214 + 0.427079i \(0.859543\pi\)
\(888\) 2.44949 2.44949i 0.0821995 0.0821995i
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 12.7279 + 7.34847i 0.426162 + 0.246045i
\(893\) 10.3923 + 6.00000i 0.347765 + 0.200782i
\(894\) 2.68973 10.0382i 0.0899579 0.335727i
\(895\) 58.7878i 1.96506i
\(896\) 0 0
\(897\) 18.0000 + 18.0000i 0.601003 + 0.601003i
\(898\) −18.0000 31.1769i −0.600668 1.04039i
\(899\) 0 0
\(900\) 2.59808 + 1.50000i 0.0866025 + 0.0500000i
\(901\) −25.4558 + 14.6969i −0.848057 + 0.489626i
\(902\) 0 0
\(903\) 0 0
\(904\) 6.00000 0.199557
\(905\) 25.9808 15.0000i 0.863630 0.498617i
\(906\) −3.58630 13.3843i −0.119147 0.444662i
\(907\) −14.0000 + 24.2487i −0.464862 + 0.805165i −0.999195 0.0401089i \(-0.987230\pi\)
0.534333 + 0.845274i \(0.320563\pi\)
\(908\) −3.67423 6.36396i −0.121934 0.211195i
\(909\) 22.0454i 0.731200i
\(910\) 0 0
\(911\) 30.0000i 0.993944i −0.867766 0.496972i \(-0.834445\pi\)
0.867766 0.496972i \(-0.165555\pi\)
\(912\) −4.09808 1.09808i −0.135701 0.0363609i
\(913\) 0 0
\(914\) 24.2487 + 14.0000i 0.802076 + 0.463079i
\(915\) −50.1910 13.4486i −1.65926 0.444598i
\(916\) 22.0454i 0.728401i
\(917\) 0 0
\(918\) 18.0000 + 18.0000i 0.594089 + 0.594089i
\(919\) −5.00000 8.66025i −0.164935 0.285675i 0.771697 0.635990i \(-0.219408\pi\)
−0.936632 + 0.350315i \(0.886075\pi\)
\(920\) 7.34847 12.7279i 0.242272 0.419627i
\(921\) −3.29423 12.2942i −0.108549 0.405109i
\(922\) −27.5772 + 15.9217i −0.908206 + 0.524353i
\(923\) 0 0
\(924\) 0 0
\(925\) −2.00000 −0.0657596
\(926\) −12.1244 + 7.00000i −0.398431 + 0.230034i
\(927\) −14.6969 + 25.4558i −0.482711 + 0.836080i
\(928\) −3.00000 + 5.19615i −0.0984798 + 0.170572i
\(929\) 12.2474 + 21.2132i 0.401826 + 0.695983i 0.993946 0.109867i \(-0.0350424\pi\)
−0.592121 + 0.805849i \(0.701709\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 24.0000i 0.786146i
\(933\) 8.78461 32.7846i 0.287595 1.07332i
\(934\) −6.36396 3.67423i −0.208235 0.120225i
\(935\) 0 0
\(936\) −6.36396 + 3.67423i −0.208013 + 0.120096i
\(937\) 19.5959i 0.640171i 0.947389 + 0.320085i \(0.103712\pi\)
−0.947389 + 0.320085i \(0.896288\pi\)
\(938\) 0 0
\(939\) 42.0000 42.0000i 1.37062 1.37062i
\(940\) −6.00000 10.3923i −0.195698 0.338960i
\(941\) −15.9217 + 27.5772i −0.519032 + 0.898990i 0.480723 + 0.876872i \(0.340374\pi\)
−0.999755 + 0.0221175i \(0.992959\pi\)
\(942\) −12.2942 + 3.29423i −0.400568 + 0.107332i
\(943\) 25.4558 14.6969i 0.828956 0.478598i
\(944\) −12.2474 −0.398621
\(945\) 0 0
\(946\) 0 0
\(947\) 10.3923 6.00000i 0.337705 0.194974i −0.321552 0.946892i \(-0.604204\pi\)
0.659256 + 0.751918i \(0.270871\pi\)
\(948\) −16.7303 + 4.48288i −0.543376 + 0.145597i
\(949\) −12.0000 + 20.7846i −0.389536 + 0.674697i
\(950\) 1.22474 + 2.12132i 0.0397360 + 0.0688247i
\(951\) 22.0454 22.0454i 0.714871 0.714871i
\(952\) 0 0
\(953\) 36.0000i 1.16615i −0.812417 0.583077i \(-0.801849\pi\)
0.812417 0.583077i \(-0.198151\pi\)
\(954\) −15.5885 + 9.00000i −0.504695 + 0.291386i
\(955\) 0 0
\(956\) 5.19615 + 3.00000i 0.168056 + 0.0970269i
\(957\) 0 0
\(958\) 24.4949i 0.791394i
\(959\) 0 0
\(960\) 3.00000 + 3.00000i 0.0968246 + 0.0968246i
\(961\) −15.5000 26.8468i −0.500000 0.866025i
\(962\) 2.44949 4.24264i 0.0789747 0.136788i
\(963\) 18.0000 31.1769i 0.580042 1.00466i
\(964\) 21.2132 12.2474i 0.683231 0.394464i
\(965\) −9.79796 −0.315407
\(966\) 0 0
\(967\) 8.00000 0.257263 0.128631 0.991692i \(-0.458942\pi\)
0.128631 + 0.991692i \(0.458942\pi\)
\(968\) 9.52628 5.50000i 0.306186 0.176777i
\(969\) 5.37945 + 20.0764i 0.172813 + 0.644947i
\(970\) −6.00000 + 10.3923i −0.192648 + 0.333677i
\(971\) 20.8207 + 36.0624i 0.668167 + 1.15730i 0.978416 + 0.206644i \(0.0662541\pi\)
−0.310249 + 0.950655i \(0.600413\pi\)
\(972\) 11.0227 + 11.0227i 0.353553 + 0.353553i
\(973\) 0 0
\(974\) 32.0000i 1.02535i
\(975\) 4.09808 + 1.09808i 0.131243 + 0.0351666i
\(976\) −10.6066 6.12372i −0.339509 0.196016i
\(977\) −10.3923 6.00000i −0.332479 0.191957i 0.324462 0.945899i \(-0.394817\pi\)
−0.656941 + 0.753942i \(0.728150\pi\)
\(978\) 26.7685 + 7.17260i 0.855963 + 0.229355i
\(979\) 0 0
\(980\) 0 0
\(981\) 30.0000i 0.957826i
\(982\) 0 0
\(983\) 17.1464 29.6985i 0.546886 0.947235i −0.451599 0.892221i \(-0.649146\pi\)
0.998486 0.0550138i \(-0.0175203\pi\)
\(984\) 2.19615 + 8.19615i 0.0700108 + 0.261284i
\(985\) 38.1838 22.0454i 1.21664 0.702425i
\(986\) 29.3939 0.936092
\(987\) 0 0
\(988\) −6.00000 −0.190885
\(989\) −20.7846 + 12.0000i −0.660912 + 0.381578i
\(990\) 0 0
\(991\) 19.0000 32.9090i 0.603555 1.04539i −0.388723 0.921355i \(-0.627084\pi\)
0.992278 0.124033i \(-0.0395829\pi\)
\(992\) 0 0
\(993\) −9.79796 9.79796i −0.310929 0.310929i
\(994\) 0 0
\(995\) 24.0000i 0.760851i
\(996\) −1.09808 + 4.09808i −0.0347939 + 0.129853i
\(997\) −6.36396 3.67423i −0.201549 0.116364i 0.395829 0.918324i \(-0.370457\pi\)
−0.597378 + 0.801960i \(0.703791\pi\)
\(998\) −17.3205 10.0000i −0.548271 0.316544i
\(999\) −10.0382 2.68973i −0.317594 0.0850992i
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 294.2.f.b.227.1 8
3.2 odd 2 inner 294.2.f.b.227.3 8
7.2 even 3 inner 294.2.f.b.215.4 8
7.3 odd 6 42.2.d.a.41.1 4
7.4 even 3 42.2.d.a.41.2 yes 4
7.5 odd 6 inner 294.2.f.b.215.3 8
7.6 odd 2 inner 294.2.f.b.227.2 8
21.2 odd 6 inner 294.2.f.b.215.2 8
21.5 even 6 inner 294.2.f.b.215.1 8
21.11 odd 6 42.2.d.a.41.3 yes 4
21.17 even 6 42.2.d.a.41.4 yes 4
21.20 even 2 inner 294.2.f.b.227.4 8
28.3 even 6 336.2.k.b.209.4 4
28.11 odd 6 336.2.k.b.209.1 4
35.3 even 12 1050.2.d.b.1049.3 4
35.4 even 6 1050.2.b.b.251.3 4
35.17 even 12 1050.2.d.e.1049.2 4
35.18 odd 12 1050.2.d.b.1049.2 4
35.24 odd 6 1050.2.b.b.251.4 4
35.32 odd 12 1050.2.d.e.1049.3 4
56.3 even 6 1344.2.k.d.1217.1 4
56.11 odd 6 1344.2.k.d.1217.4 4
56.45 odd 6 1344.2.k.c.1217.4 4
56.53 even 6 1344.2.k.c.1217.1 4
63.4 even 3 1134.2.m.g.755.4 8
63.11 odd 6 1134.2.m.g.377.3 8
63.25 even 3 1134.2.m.g.377.2 8
63.31 odd 6 1134.2.m.g.755.3 8
63.32 odd 6 1134.2.m.g.755.1 8
63.38 even 6 1134.2.m.g.377.4 8
63.52 odd 6 1134.2.m.g.377.1 8
63.59 even 6 1134.2.m.g.755.2 8
84.11 even 6 336.2.k.b.209.3 4
84.59 odd 6 336.2.k.b.209.2 4
105.17 odd 12 1050.2.d.b.1049.1 4
105.32 even 12 1050.2.d.b.1049.4 4
105.38 odd 12 1050.2.d.e.1049.4 4
105.53 even 12 1050.2.d.e.1049.1 4
105.59 even 6 1050.2.b.b.251.1 4
105.74 odd 6 1050.2.b.b.251.2 4
168.11 even 6 1344.2.k.d.1217.2 4
168.53 odd 6 1344.2.k.c.1217.3 4
168.59 odd 6 1344.2.k.d.1217.3 4
168.101 even 6 1344.2.k.c.1217.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
42.2.d.a.41.1 4 7.3 odd 6
42.2.d.a.41.2 yes 4 7.4 even 3
42.2.d.a.41.3 yes 4 21.11 odd 6
42.2.d.a.41.4 yes 4 21.17 even 6
294.2.f.b.215.1 8 21.5 even 6 inner
294.2.f.b.215.2 8 21.2 odd 6 inner
294.2.f.b.215.3 8 7.5 odd 6 inner
294.2.f.b.215.4 8 7.2 even 3 inner
294.2.f.b.227.1 8 1.1 even 1 trivial
294.2.f.b.227.2 8 7.6 odd 2 inner
294.2.f.b.227.3 8 3.2 odd 2 inner
294.2.f.b.227.4 8 21.20 even 2 inner
336.2.k.b.209.1 4 28.11 odd 6
336.2.k.b.209.2 4 84.59 odd 6
336.2.k.b.209.3 4 84.11 even 6
336.2.k.b.209.4 4 28.3 even 6
1050.2.b.b.251.1 4 105.59 even 6
1050.2.b.b.251.2 4 105.74 odd 6
1050.2.b.b.251.3 4 35.4 even 6
1050.2.b.b.251.4 4 35.24 odd 6
1050.2.d.b.1049.1 4 105.17 odd 12
1050.2.d.b.1049.2 4 35.18 odd 12
1050.2.d.b.1049.3 4 35.3 even 12
1050.2.d.b.1049.4 4 105.32 even 12
1050.2.d.e.1049.1 4 105.53 even 12
1050.2.d.e.1049.2 4 35.17 even 12
1050.2.d.e.1049.3 4 35.32 odd 12
1050.2.d.e.1049.4 4 105.38 odd 12
1134.2.m.g.377.1 8 63.52 odd 6
1134.2.m.g.377.2 8 63.25 even 3
1134.2.m.g.377.3 8 63.11 odd 6
1134.2.m.g.377.4 8 63.38 even 6
1134.2.m.g.755.1 8 63.32 odd 6
1134.2.m.g.755.2 8 63.59 even 6
1134.2.m.g.755.3 8 63.31 odd 6
1134.2.m.g.755.4 8 63.4 even 3
1344.2.k.c.1217.1 4 56.53 even 6
1344.2.k.c.1217.2 4 168.101 even 6
1344.2.k.c.1217.3 4 168.53 odd 6
1344.2.k.c.1217.4 4 56.45 odd 6
1344.2.k.d.1217.1 4 56.3 even 6
1344.2.k.d.1217.2 4 168.11 even 6
1344.2.k.d.1217.3 4 168.59 odd 6
1344.2.k.d.1217.4 4 56.11 odd 6