Properties

Label 3840.1.dy.a.629.2
Level $3840$
Weight $1$
Character 3840.629
Analytic conductor $1.916$
Analytic rank $0$
Dimension $64$
Projective image $D_{64}$
CM discriminant -15
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3840,1,Mod(29,3840)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3840, base_ring=CyclotomicField(64))
 
chi = DirichletCharacter(H, H._module([0, 59, 32, 32]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3840.29");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3840 = 2^{8} \cdot 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3840.dy (of order \(64\), degree \(32\), 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: \(1.91640964851\)
Analytic rank: \(0\)
Dimension: \(64\)
Relative dimension: \(2\) over \(\Q(\zeta_{64})\)
Coefficient field: \(\Q(\zeta_{128})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{64} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{64}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{64} + \cdots)\)

Embedding invariants

Embedding label 629.2
Root \(-0.998795 + 0.0490677i\) of defining polynomial
Character \(\chi\) \(=\) 3840.629
Dual form 3840.1.dy.a.989.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.146730 - 0.989177i) q^{2} +(0.998795 - 0.0490677i) q^{3} +(-0.956940 - 0.290285i) q^{4} +(0.857729 - 0.514103i) q^{5} +(0.0980171 - 0.995185i) q^{6} +(-0.427555 + 0.903989i) q^{8} +(0.995185 - 0.0980171i) q^{9} +O(q^{10})\) \(q+(0.146730 - 0.989177i) q^{2} +(0.998795 - 0.0490677i) q^{3} +(-0.956940 - 0.290285i) q^{4} +(0.857729 - 0.514103i) q^{5} +(0.0980171 - 0.995185i) q^{6} +(-0.427555 + 0.903989i) q^{8} +(0.995185 - 0.0980171i) q^{9} +(-0.382683 - 0.923880i) q^{10} +(-0.970031 - 0.242980i) q^{12} +(0.831470 - 0.555570i) q^{15} +(0.831470 + 0.555570i) q^{16} +(-0.404061 - 0.269985i) q^{17} +(0.0490677 - 0.998795i) q^{18} +(-0.845855 - 0.125471i) q^{19} +(-0.970031 + 0.242980i) q^{20} +(0.345845 - 1.14010i) q^{23} +(-0.382683 + 0.923880i) q^{24} +(0.471397 - 0.881921i) q^{25} +(0.989177 - 0.146730i) q^{27} +(-0.427555 - 0.903989i) q^{30} +(-0.222174 + 0.536376i) q^{31} +(0.671559 - 0.740951i) q^{32} +(-0.326351 + 0.360073i) q^{34} +(-0.980785 - 0.195090i) q^{36} +(-0.248225 + 0.818289i) q^{38} +(0.0980171 + 0.995185i) q^{40} +(0.803208 - 0.595699i) q^{45} +(-1.07701 - 0.509389i) q^{46} +(-0.262029 - 1.31731i) q^{47} +(0.857729 + 0.514103i) q^{48} +(-0.195090 + 0.980785i) q^{49} +(-0.803208 - 0.595699i) q^{50} +(-0.416822 - 0.249834i) q^{51} +(1.39759 + 0.661009i) q^{53} -1.00000i q^{54} +(-0.850993 - 0.0838155i) q^{57} +(-0.956940 + 0.290285i) q^{60} +(0.452483 - 0.499238i) q^{61} +(0.497971 + 0.298472i) q^{62} +(-0.634393 - 0.773010i) q^{64} +(0.308290 + 0.375652i) q^{68} +(0.289486 - 1.15569i) q^{69} +(-0.336890 + 0.941544i) q^{72} +(0.427555 - 0.903989i) q^{75} +(0.773010 + 0.365607i) q^{76} +(-1.63099 - 0.324423i) q^{79} +(0.998795 + 0.0490677i) q^{80} +(0.980785 - 0.195090i) q^{81} +(1.18566 + 1.59868i) q^{83} +(-0.485375 - 0.0238449i) q^{85} +(-0.471397 - 0.881921i) q^{90} +(-0.661906 + 0.990612i) q^{92} +(-0.195588 + 0.546632i) q^{93} +(-1.34150 + 0.0659037i) q^{94} +(-0.790019 + 0.327237i) q^{95} +(0.634393 - 0.773010i) q^{96} +(0.941544 + 0.336890i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 64 q+O(q^{10}) \) Copy content Toggle raw display \( 64 q+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3840\mathbb{Z}\right)^\times\).

\(n\) \(511\) \(1537\) \(2561\) \(2821\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{53}{64}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.146730 0.989177i 0.146730 0.989177i
\(3\) 0.998795 0.0490677i 0.998795 0.0490677i
\(4\) −0.956940 0.290285i −0.956940 0.290285i
\(5\) 0.857729 0.514103i 0.857729 0.514103i
\(6\) 0.0980171 0.995185i 0.0980171 0.995185i
\(7\) 0 0 −0.634393 0.773010i \(-0.718750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(8\) −0.427555 + 0.903989i −0.427555 + 0.903989i
\(9\) 0.995185 0.0980171i 0.995185 0.0980171i
\(10\) −0.382683 0.923880i −0.382683 0.923880i
\(11\) 0 0 −0.336890 0.941544i \(-0.609375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(12\) −0.970031 0.242980i −0.970031 0.242980i
\(13\) 0 0 0.970031 0.242980i \(-0.0781250\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(14\) 0 0
\(15\) 0.831470 0.555570i 0.831470 0.555570i
\(16\) 0.831470 + 0.555570i 0.831470 + 0.555570i
\(17\) −0.404061 0.269985i −0.404061 0.269985i 0.336890 0.941544i \(-0.390625\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(18\) 0.0490677 0.998795i 0.0490677 0.998795i
\(19\) −0.845855 0.125471i −0.845855 0.125471i −0.290285 0.956940i \(-0.593750\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(20\) −0.970031 + 0.242980i −0.970031 + 0.242980i
\(21\) 0 0
\(22\) 0 0
\(23\) 0.345845 1.14010i 0.345845 1.14010i −0.595699 0.803208i \(-0.703125\pi\)
0.941544 0.336890i \(-0.109375\pi\)
\(24\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(25\) 0.471397 0.881921i 0.471397 0.881921i
\(26\) 0 0
\(27\) 0.989177 0.146730i 0.989177 0.146730i
\(28\) 0 0
\(29\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(30\) −0.427555 0.903989i −0.427555 0.903989i
\(31\) −0.222174 + 0.536376i −0.222174 + 0.536376i −0.995185 0.0980171i \(-0.968750\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(32\) 0.671559 0.740951i 0.671559 0.740951i
\(33\) 0 0
\(34\) −0.326351 + 0.360073i −0.326351 + 0.360073i
\(35\) 0 0
\(36\) −0.980785 0.195090i −0.980785 0.195090i
\(37\) 0 0 0.595699 0.803208i \(-0.296875\pi\)
−0.595699 + 0.803208i \(0.703125\pi\)
\(38\) −0.248225 + 0.818289i −0.248225 + 0.818289i
\(39\) 0 0
\(40\) 0.0980171 + 0.995185i 0.0980171 + 0.995185i
\(41\) 0 0 −0.471397 0.881921i \(-0.656250\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(42\) 0 0
\(43\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(44\) 0 0
\(45\) 0.803208 0.595699i 0.803208 0.595699i
\(46\) −1.07701 0.509389i −1.07701 0.509389i
\(47\) −0.262029 1.31731i −0.262029 1.31731i −0.857729 0.514103i \(-0.828125\pi\)
0.595699 0.803208i \(-0.296875\pi\)
\(48\) 0.857729 + 0.514103i 0.857729 + 0.514103i
\(49\) −0.195090 + 0.980785i −0.195090 + 0.980785i
\(50\) −0.803208 0.595699i −0.803208 0.595699i
\(51\) −0.416822 0.249834i −0.416822 0.249834i
\(52\) 0 0
\(53\) 1.39759 + 0.661009i 1.39759 + 0.661009i 0.970031 0.242980i \(-0.0781250\pi\)
0.427555 + 0.903989i \(0.359375\pi\)
\(54\) 1.00000i 1.00000i
\(55\) 0 0
\(56\) 0 0
\(57\) −0.850993 0.0838155i −0.850993 0.0838155i
\(58\) 0 0
\(59\) 0 0 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(60\) −0.956940 + 0.290285i −0.956940 + 0.290285i
\(61\) 0.452483 0.499238i 0.452483 0.499238i −0.471397 0.881921i \(-0.656250\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(62\) 0.497971 + 0.298472i 0.497971 + 0.298472i
\(63\) 0 0
\(64\) −0.634393 0.773010i −0.634393 0.773010i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 −0.740951 0.671559i \(-0.765625\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(68\) 0.308290 + 0.375652i 0.308290 + 0.375652i
\(69\) 0.289486 1.15569i 0.289486 1.15569i
\(70\) 0 0
\(71\) 0 0 0.0980171 0.995185i \(-0.468750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(72\) −0.336890 + 0.941544i −0.336890 + 0.941544i
\(73\) 0 0 0.634393 0.773010i \(-0.281250\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(74\) 0 0
\(75\) 0.427555 0.903989i 0.427555 0.903989i
\(76\) 0.773010 + 0.365607i 0.773010 + 0.365607i
\(77\) 0 0
\(78\) 0 0
\(79\) −1.63099 0.324423i −1.63099 0.324423i −0.707107 0.707107i \(-0.750000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(80\) 0.998795 + 0.0490677i 0.998795 + 0.0490677i
\(81\) 0.980785 0.195090i 0.980785 0.195090i
\(82\) 0 0
\(83\) 1.18566 + 1.59868i 1.18566 + 1.59868i 0.671559 + 0.740951i \(0.265625\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(84\) 0 0
\(85\) −0.485375 0.0238449i −0.485375 0.0238449i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.290285 0.956940i \(-0.593750\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(90\) −0.471397 0.881921i −0.471397 0.881921i
\(91\) 0 0
\(92\) −0.661906 + 0.990612i −0.661906 + 0.990612i
\(93\) −0.195588 + 0.546632i −0.195588 + 0.546632i
\(94\) −1.34150 + 0.0659037i −1.34150 + 0.0659037i
\(95\) −0.790019 + 0.327237i −0.790019 + 0.327237i
\(96\) 0.634393 0.773010i 0.634393 0.773010i
\(97\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(98\) 0.941544 + 0.336890i 0.941544 + 0.336890i
\(99\) 0 0
\(100\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(101\) 0 0 −0.146730 0.989177i \(-0.546875\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(102\) −0.308290 + 0.375652i −0.308290 + 0.375652i
\(103\) 0 0 −0.881921 0.471397i \(-0.843750\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.858923 1.28547i 0.858923 1.28547i
\(107\) −0.698564 + 0.633141i −0.698564 + 0.633141i −0.941544 0.336890i \(-0.890625\pi\)
0.242980 + 0.970031i \(0.421875\pi\)
\(108\) −0.989177 0.146730i −0.989177 0.146730i
\(109\) 0.0143994 0.0970732i 0.0143994 0.0970732i −0.980785 0.195090i \(-0.937500\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.823301 + 1.23216i 0.823301 + 1.23216i 0.970031 + 0.242980i \(0.0781250\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(114\) −0.207775 + 0.829484i −0.207775 + 0.829484i
\(115\) −0.289486 1.15569i −0.289486 1.15569i
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0.146730 + 0.989177i 0.146730 + 0.989177i
\(121\) −0.773010 + 0.634393i −0.773010 + 0.634393i
\(122\) −0.427441 0.520839i −0.427441 0.520839i
\(123\) 0 0
\(124\) 0.368309 0.448786i 0.368309 0.448786i
\(125\) −0.0490677 0.998795i −0.0490677 0.998795i
\(126\) 0 0
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) −0.857729 + 0.514103i −0.857729 + 0.514103i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.0490677 0.998795i \(-0.515625\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0.773010 0.634393i 0.773010 0.634393i
\(136\) 0.416822 0.249834i 0.416822 0.249834i
\(137\) 0.195798 + 1.98797i 0.195798 + 1.98797i 0.146730 + 0.989177i \(0.453125\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(138\) −1.10071 0.455929i −1.10071 0.455929i
\(139\) −1.86271 + 0.666487i −1.86271 + 0.666487i −0.881921 + 0.471397i \(0.843750\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(140\) 0 0
\(141\) −0.326351 1.30287i −0.326351 1.30287i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.881921 + 0.471397i 0.881921 + 0.471397i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.146730 + 0.989177i −0.146730 + 0.989177i
\(148\) 0 0
\(149\) 0 0 0.740951 0.671559i \(-0.234375\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(150\) −0.831470 0.555570i −0.831470 0.555570i
\(151\) −0.187593 0.0569057i −0.187593 0.0569057i 0.195090 0.980785i \(-0.437500\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(152\) 0.475074 0.710998i 0.475074 0.710998i
\(153\) −0.428579 0.229080i −0.428579 0.229080i
\(154\) 0 0
\(155\) 0.0851872 + 0.574286i 0.0851872 + 0.574286i
\(156\) 0 0
\(157\) 0 0 −0.427555 0.903989i \(-0.640625\pi\)
0.427555 + 0.903989i \(0.359375\pi\)
\(158\) −0.560227 + 1.56573i −0.560227 + 1.56573i
\(159\) 1.42834 + 0.591637i 1.42834 + 0.591637i
\(160\) 0.195090 0.980785i 0.195090 0.980785i
\(161\) 0 0
\(162\) −0.0490677 0.998795i −0.0490677 0.998795i
\(163\) 0 0 0.336890 0.941544i \(-0.390625\pi\)
−0.336890 + 0.941544i \(0.609375\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 1.75535 0.938254i 1.75535 0.938254i
\(167\) 0.298472 + 0.983931i 0.298472 + 0.983931i 0.970031 + 0.242980i \(0.0781250\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(168\) 0 0
\(169\) 0.881921 0.471397i 0.881921 0.471397i
\(170\) −0.0948062 + 0.476623i −0.0948062 + 0.476623i
\(171\) −0.854080 0.0419583i −0.854080 0.0419583i
\(172\) 0 0
\(173\) −1.05072 1.41673i −1.05072 1.41673i −0.903989 0.427555i \(-0.859375\pi\)
−0.146730 0.989177i \(-0.546875\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.514103 0.857729i \(-0.328125\pi\)
−0.514103 + 0.857729i \(0.671875\pi\)
\(180\) −0.941544 + 0.336890i −0.941544 + 0.336890i
\(181\) −0.733452 + 1.55075i −0.733452 + 1.55075i 0.0980171 + 0.995185i \(0.468750\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(182\) 0 0
\(183\) 0.427441 0.520839i 0.427441 0.520839i
\(184\) 0.882768 + 0.800094i 0.882768 + 0.800094i
\(185\) 0 0
\(186\) 0.512016 + 0.273678i 0.512016 + 0.273678i
\(187\) 0 0
\(188\) −0.131649 + 1.33665i −0.131649 + 1.33665i
\(189\) 0 0
\(190\) 0.207775 + 0.829484i 0.207775 + 0.829484i
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) −0.671559 0.740951i −0.671559 0.740951i
\(193\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.471397 0.881921i 0.471397 0.881921i
\(197\) 0.378487 + 0.0948062i 0.378487 + 0.0948062i 0.427555 0.903989i \(-0.359375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(198\) 0 0
\(199\) −1.95213 0.192268i −1.95213 0.192268i −0.956940 0.290285i \(-0.906250\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(200\) 0.595699 + 0.803208i 0.595699 + 0.803208i
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0.326351 + 0.360073i 0.326351 + 0.360073i
\(205\) 0 0
\(206\) 0 0
\(207\) 0.232430 1.16851i 0.232430 1.16851i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0.0788231 0.0584592i 0.0788231 0.0584592i −0.555570 0.831470i \(-0.687500\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(212\) −1.14553 1.03824i −1.14553 1.03824i
\(213\) 0 0
\(214\) 0.523788 + 0.783904i 0.523788 + 0.783904i
\(215\) 0 0
\(216\) −0.290285 + 0.956940i −0.290285 + 0.956940i
\(217\) 0 0
\(218\) −0.0939097 0.0284872i −0.0939097 0.0284872i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(224\) 0 0
\(225\) 0.382683 0.923880i 0.382683 0.923880i
\(226\) 1.33962 0.633595i 1.33962 0.633595i
\(227\) 1.14697 0.542476i 1.14697 0.542476i 0.242980 0.970031i \(-0.421875\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(228\) 0.790019 + 0.327237i 0.790019 + 0.327237i
\(229\) 0.290285 0.0430597i 0.290285 0.0430597i 1.00000i \(-0.5\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(230\) −1.18566 + 0.116777i −1.18566 + 0.116777i
\(231\) 0 0
\(232\) 0 0
\(233\) −0.0851872 + 0.280825i −0.0851872 + 0.280825i −0.989177 0.146730i \(-0.953125\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(234\) 0 0
\(235\) −0.901983 0.995185i −0.901983 0.995185i
\(236\) 0 0
\(237\) −1.64494 0.244004i −1.64494 0.244004i
\(238\) 0 0
\(239\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(240\) 1.00000 1.00000
\(241\) −1.59133 + 1.06330i −1.59133 + 1.06330i −0.634393 + 0.773010i \(0.718750\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(242\) 0.514103 + 0.857729i 0.514103 + 0.857729i
\(243\) 0.970031 0.242980i 0.970031 0.242980i
\(244\) −0.577920 + 0.346392i −0.577920 + 0.346392i
\(245\) 0.336890 + 0.941544i 0.336890 + 0.941544i
\(246\) 0 0
\(247\) 0 0
\(248\) −0.389887 0.430174i −0.389887 0.430174i
\(249\) 1.26268 + 1.53858i 1.26268 + 1.53858i
\(250\) −0.995185 0.0980171i −0.995185 0.0980171i
\(251\) 0 0 0.857729 0.514103i \(-0.171875\pi\)
−0.857729 + 0.514103i \(0.828125\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) −0.485960 −0.485960
\(256\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(257\) −1.60642 −1.60642 −0.803208 0.595699i \(-0.796875\pi\)
−0.803208 + 0.595699i \(0.796875\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 1.23076 + 1.49969i 1.23076 + 1.49969i 0.803208 + 0.595699i \(0.203125\pi\)
0.427555 + 0.903989i \(0.359375\pi\)
\(264\) 0 0
\(265\) 1.53858 0.151537i 1.53858 0.151537i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 0.970031 0.242980i \(-0.0781250\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(270\) −0.514103 0.857729i −0.514103 0.857729i
\(271\) −0.636379 + 0.425215i −0.636379 + 0.425215i −0.831470 0.555570i \(-0.812500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(272\) −0.185969 0.448969i −0.185969 0.448969i
\(273\) 0 0
\(274\) 1.99518 + 0.0980171i 1.99518 + 0.0980171i
\(275\) 0 0
\(276\) −0.612501 + 1.02190i −0.612501 + 1.02190i
\(277\) 0 0 −0.671559 0.740951i \(-0.734375\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(278\) 0.385958 + 1.94034i 0.385958 + 1.94034i
\(279\) −0.168530 + 0.555570i −0.168530 + 0.555570i
\(280\) 0 0
\(281\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(282\) −1.33665 + 0.131649i −1.33665 + 0.131649i
\(283\) 0 0 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(284\) 0 0
\(285\) −0.773010 + 0.365607i −0.773010 + 0.365607i
\(286\) 0 0
\(287\) 0 0
\(288\) 0.595699 0.803208i 0.595699 0.803208i
\(289\) −0.292310 0.705698i −0.292310 0.705698i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.18566 1.59868i 1.18566 1.59868i 0.514103 0.857729i \(-0.328125\pi\)
0.671559 0.740951i \(-0.265625\pi\)
\(294\) 0.956940 + 0.290285i 0.956940 + 0.290285i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −0.671559 + 0.740951i −0.671559 + 0.740951i
\(301\) 0 0
\(302\) −0.0838155 + 0.177213i −0.0838155 + 0.177213i
\(303\) 0 0
\(304\) −0.633595 0.574257i −0.633595 0.574257i
\(305\) 0.131448 0.660833i 0.131448 0.660833i
\(306\) −0.289486 + 0.390327i −0.289486 + 0.390327i
\(307\) 0 0 −0.857729 0.514103i \(-0.828125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.580569 0.580569
\(311\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(312\) 0 0
\(313\) 0 0 −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 1.46658 + 0.783904i 1.46658 + 0.783904i
\(317\) 0.746196 0.823301i 0.746196 0.823301i −0.242980 0.970031i \(-0.578125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(318\) 0.794814 1.32607i 0.794814 1.32607i
\(319\) 0 0
\(320\) −0.941544 0.336890i −0.941544 0.336890i
\(321\) −0.666656 + 0.666656i −0.666656 + 0.666656i
\(322\) 0 0
\(323\) 0.307902 + 0.279066i 0.307902 + 0.279066i
\(324\) −0.995185 0.0980171i −0.995185 0.0980171i
\(325\) 0 0
\(326\) 0 0
\(327\) 0.00961895 0.0976628i 0.00961895 0.0976628i
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −0.439614 + 0.929487i −0.439614 + 0.929487i 0.555570 + 0.831470i \(0.312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(332\) −0.670535 1.87402i −0.670535 1.87402i
\(333\) 0 0
\(334\) 1.01708 0.150869i 1.01708 0.150869i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(338\) −0.336890 0.941544i −0.336890 0.941544i
\(339\) 0.882768 + 1.19028i 0.882768 + 1.19028i
\(340\) 0.457553 + 0.163715i 0.457553 + 0.163715i
\(341\) 0 0
\(342\) −0.166824 + 0.838679i −0.166824 + 0.838679i
\(343\) 0 0
\(344\) 0 0
\(345\) −0.345845 1.14010i −0.345845 1.14010i
\(346\) −1.55557 + 0.831470i −1.55557 + 0.831470i
\(347\) −0.892476 0.661906i −0.892476 0.661906i 0.0490677 0.998795i \(-0.484375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(348\) 0 0
\(349\) 0.609090 1.70229i 0.609090 1.70229i −0.0980171 0.995185i \(-0.531250\pi\)
0.707107 0.707107i \(-0.250000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.73975 + 0.720627i 1.73975 + 0.720627i 0.998795 + 0.0490677i \(0.0156250\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.881921 0.471397i \(-0.843750\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(360\) 0.195090 + 0.980785i 0.195090 + 0.980785i
\(361\) −0.257213 0.0780246i −0.257213 0.0780246i
\(362\) 1.42635 + 0.953057i 1.42635 + 0.953057i
\(363\) −0.740951 + 0.671559i −0.740951 + 0.671559i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.452483 0.499238i −0.452483 0.499238i
\(367\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(368\) 0.920964 0.755815i 0.920964 0.755815i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0.345845 0.466318i 0.345845 0.466318i
\(373\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(374\) 0 0
\(375\) −0.0980171 0.995185i −0.0980171 0.995185i
\(376\) 1.30287 + 0.326351i 1.30287 + 0.326351i
\(377\) 0 0
\(378\) 0 0
\(379\) 0.881921 + 1.47140i 0.881921 + 1.47140i 0.881921 + 0.471397i \(0.156250\pi\)
1.00000i \(0.5\pi\)
\(380\) 0.850993 0.0838155i 0.850993 0.0838155i
\(381\) 0 0
\(382\) 0 0
\(383\) 1.88309i 1.88309i −0.336890 0.941544i \(-0.609375\pi\)
0.336890 0.941544i \(-0.390625\pi\)
\(384\) −0.831470 + 0.555570i −0.831470 + 0.555570i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.514103 0.857729i \(-0.671875\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(390\) 0 0
\(391\) −0.447552 + 0.367296i −0.447552 + 0.367296i
\(392\) −0.803208 0.595699i −0.803208 0.595699i
\(393\) 0 0
\(394\) 0.149316 0.360480i 0.149316 0.360480i
\(395\) −1.56573 + 0.560227i −1.56573 + 0.560227i
\(396\) 0 0
\(397\) 0 0 −0.242980 0.970031i \(-0.578125\pi\)
0.242980 + 0.970031i \(0.421875\pi\)
\(398\) −0.476623 + 1.90278i −0.476623 + 1.90278i
\(399\) 0 0
\(400\) 0.881921 0.471397i 0.881921 0.471397i
\(401\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0.740951 0.671559i 0.740951 0.671559i
\(406\) 0 0
\(407\) 0 0
\(408\) 0.404061 0.269985i 0.404061 0.269985i
\(409\) 0.172887 + 0.0924099i 0.172887 + 0.0924099i 0.555570 0.831470i \(-0.312500\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(410\) 0 0
\(411\) 0.293107 + 1.97597i 0.293107 + 1.97597i
\(412\) 0 0
\(413\) 0 0
\(414\) −1.12175 0.401370i −1.12175 0.401370i
\(415\) 1.83886 + 0.761681i 1.83886 + 0.761681i
\(416\) 0 0
\(417\) −1.82776 + 0.757083i −1.82776 + 0.757083i
\(418\) 0 0
\(419\) 0 0 0.336890 0.941544i \(-0.390625\pi\)
−0.336890 + 0.941544i \(0.609375\pi\)
\(420\) 0 0
\(421\) 1.58903 + 1.17850i 1.58903 + 1.17850i 0.881921 + 0.471397i \(0.156250\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(422\) −0.0462607 0.0865477i −0.0462607 0.0865477i
\(423\) −0.389887 1.28528i −0.389887 1.28528i
\(424\) −1.19509 + 0.980785i −1.19509 + 0.980785i
\(425\) −0.428579 + 0.229080i −0.428579 + 0.229080i
\(426\) 0 0
\(427\) 0 0
\(428\) 0.852275 0.403096i 0.852275 0.403096i
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(432\) 0.903989 + 0.427555i 0.903989 + 0.427555i
\(433\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −0.0419583 + 0.0887133i −0.0419583 + 0.0887133i
\(437\) −0.435583 + 0.920964i −0.435583 + 0.920964i
\(438\) 0 0
\(439\) −0.247528 + 0.301614i −0.247528 + 0.301614i −0.881921 0.471397i \(-0.843750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(440\) 0 0
\(441\) −0.0980171 + 0.995185i −0.0980171 + 0.995185i
\(442\) 0 0
\(443\) −0.465035 + 1.85652i −0.465035 + 1.85652i 0.0490677 + 0.998795i \(0.484375\pi\)
−0.514103 + 0.857729i \(0.671875\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(450\) −0.857729 0.514103i −0.857729 0.514103i
\(451\) 0 0
\(452\) −0.430174 1.41809i −0.430174 1.41809i
\(453\) −0.190159 0.0476324i −0.190159 0.0476324i
\(454\) −0.368309 1.21415i −0.368309 1.21415i
\(455\) 0 0
\(456\) 0.439614 0.733452i 0.439614 0.733452i
\(457\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(458\) 0.293461i 0.293461i
\(459\) −0.439303 0.207775i −0.439303 0.207775i
\(460\) −0.0584592 + 1.18996i −0.0584592 + 1.18996i
\(461\) 0 0 −0.857729 0.514103i \(-0.828125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(462\) 0 0
\(463\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(464\) 0 0
\(465\) 0.113263 + 0.569414i 0.113263 + 0.569414i
\(466\) 0.265286 + 0.125471i 0.265286 + 0.125471i
\(467\) 0.313396 0.232430i 0.313396 0.232430i −0.427555 0.903989i \(-0.640625\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −1.11676 + 0.746196i −1.11676 + 0.746196i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) −0.482726 + 1.59133i −0.482726 + 1.59133i
\(475\) −0.509389 + 0.686831i −0.509389 + 0.686831i
\(476\) 0 0
\(477\) 1.45565 + 0.520839i 1.45565 + 0.520839i
\(478\) 0 0
\(479\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(480\) 0.146730 0.989177i 0.146730 0.989177i
\(481\) 0 0
\(482\) 0.818289 + 1.73013i 0.818289 + 1.73013i
\(483\) 0 0
\(484\) 0.923880 0.382683i 0.923880 0.382683i
\(485\) 0 0
\(486\) −0.0980171 0.995185i −0.0980171 0.995185i
\(487\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(488\) 0.257844 + 0.622491i 0.257844 + 0.622491i
\(489\) 0 0
\(490\) 0.980785 0.195090i 0.980785 0.195090i
\(491\) 0 0 −0.671559 0.740951i \(-0.734375\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.482726 + 0.322547i −0.482726 + 0.322547i
\(497\) 0 0
\(498\) 1.70720 1.02325i 1.70720 1.02325i
\(499\) 0.284666 0.0713052i 0.284666 0.0713052i −0.0980171 0.995185i \(-0.531250\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(500\) −0.242980 + 0.970031i −0.242980 + 0.970031i
\(501\) 0.346392 + 0.968101i 0.346392 + 0.968101i
\(502\) 0 0
\(503\) −1.98797 + 0.195798i −1.98797 + 0.195798i −0.989177 + 0.146730i \(0.953125\pi\)
−0.998795 + 0.0490677i \(0.984375\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0.857729 0.514103i 0.857729 0.514103i
\(508\) 0 0
\(509\) 0 0 0.998795 0.0490677i \(-0.0156250\pi\)
−0.998795 + 0.0490677i \(0.984375\pi\)
\(510\) −0.0713052 + 0.480701i −0.0713052 + 0.480701i
\(511\) 0 0
\(512\) 0.970031 0.242980i 0.970031 0.242980i
\(513\) −0.855110 −0.855110
\(514\) −0.235710 + 1.58903i −0.235710 + 1.58903i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −1.11897 1.36347i −1.11897 1.36347i
\(520\) 0 0
\(521\) 0 0 0.995185 0.0980171i \(-0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(522\) 0 0
\(523\) 0 0 −0.336890 0.941544i \(-0.609375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 1.66405 0.997391i 1.66405 0.997391i
\(527\) 0.234586 0.156745i 0.234586 0.156745i
\(528\) 0 0
\(529\) −0.348744 0.233023i −0.348744 0.233023i
\(530\) 0.0758597 1.54416i 0.0758597 1.54416i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) −0.273678 + 0.902197i −0.273678 + 0.902197i
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(541\) −0.929487 + 0.439614i −0.929487 + 0.439614i −0.831470 0.555570i \(-0.812500\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(542\) 0.327237 + 0.691883i 0.327237 + 0.691883i
\(543\) −0.656477 + 1.58488i −0.656477 + 1.58488i
\(544\) −0.471397 + 0.118079i −0.471397 + 0.118079i
\(545\) −0.0375548 0.0906652i −0.0375548 0.0906652i
\(546\) 0 0
\(547\) 0 0 −0.941544 0.336890i \(-0.890625\pi\)
0.941544 + 0.336890i \(0.109375\pi\)
\(548\) 0.389711 1.95921i 0.389711 1.95921i
\(549\) 0.401370 0.541185i 0.401370 0.541185i
\(550\) 0 0
\(551\) 0 0
\(552\) 0.920964 + 0.755815i 0.920964 + 0.755815i
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 1.97597 0.0970732i 1.97597 0.0970732i
\(557\) 0.157456 0.116777i 0.157456 0.116777i −0.514103 0.857729i \(-0.671875\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(558\) 0.524828 + 0.248225i 0.524828 + 0.248225i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0.334669 + 0.200593i 0.334669 + 0.200593i 0.671559 0.740951i \(-0.265625\pi\)
−0.336890 + 0.941544i \(0.609375\pi\)
\(564\) −0.0659037 + 1.34150i −0.0659037 + 1.34150i
\(565\) 1.33962 + 0.633595i 1.33962 + 0.633595i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(570\) 0.248225 + 0.818289i 0.248225 + 0.818289i
\(571\) −1.55827 0.390327i −1.55827 0.390327i −0.634393 0.773010i \(-0.718750\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.842446 0.842446i −0.842446 0.842446i
\(576\) −0.707107 0.707107i −0.707107 0.707107i
\(577\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(578\) −0.740951 + 0.185599i −0.740951 + 0.185599i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −1.40740 1.40740i −1.40740 1.40740i
\(587\) 0.754140 1.59449i 0.754140 1.59449i −0.0490677 0.998795i \(-0.515625\pi\)
0.803208 0.595699i \(-0.203125\pi\)
\(588\) 0.427555 0.903989i 0.427555 0.903989i
\(589\) 0.255227 0.425820i 0.255227 0.425820i
\(590\) 0 0
\(591\) 0.382683 + 0.0761205i 0.382683 + 0.0761205i
\(592\) 0 0
\(593\) 1.94034 0.385958i 1.94034 0.385958i 0.941544 0.336890i \(-0.109375\pi\)
0.998795 0.0490677i \(-0.0156250\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.95921 0.0962497i −1.95921 0.0962497i
\(598\) 0 0
\(599\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(600\) 0.634393 + 0.773010i 0.634393 + 0.773010i
\(601\) −0.0569057 0.187593i −0.0569057 0.187593i 0.923880 0.382683i \(-0.125000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.162997 + 0.108911i 0.162997 + 0.108911i
\(605\) −0.336890 + 0.941544i −0.336890 + 0.941544i
\(606\) 0 0
\(607\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(608\) −0.661009 + 0.542476i −0.661009 + 0.542476i
\(609\) 0 0
\(610\) −0.634393 0.226990i −0.634393 0.226990i
\(611\) 0 0
\(612\) 0.343626 + 0.343626i 0.343626 + 0.343626i
\(613\) 0 0 −0.146730 0.989177i \(-0.546875\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −1.28528 0.389887i −1.28528 0.389887i −0.427555 0.903989i \(-0.640625\pi\)
−0.857729 + 0.514103i \(0.828125\pi\)
\(618\) 0 0
\(619\) 1.48012 1.34150i 1.48012 1.34150i 0.707107 0.707107i \(-0.250000\pi\)
0.773010 0.634393i \(-0.218750\pi\)
\(620\) 0.0851872 0.574286i 0.0851872 0.574286i
\(621\) 0.174814 1.17850i 0.174814 1.17850i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.555570 0.831470i −0.555570 0.831470i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) −0.181112 1.83886i −0.181112 1.83886i −0.471397 0.881921i \(-0.656250\pi\)
0.290285 0.956940i \(-0.406250\pi\)
\(632\) 0.990612 1.33569i 0.990612 1.33569i
\(633\) 0.0758597 0.0622564i 0.0758597 0.0622564i
\(634\) −0.704900 0.858923i −0.704900 0.858923i
\(635\) 0 0
\(636\) −1.19509 0.980785i −1.19509 0.980785i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) −0.471397 + 0.881921i −0.471397 + 0.881921i
\(641\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(642\) 0.561621 + 0.757259i 0.561621 + 0.757259i
\(643\) 0 0 −0.0490677 0.998795i \(-0.515625\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0.321224 0.263622i 0.321224 0.263622i
\(647\) −1.39759 + 1.14697i −1.39759 + 1.14697i −0.427555 + 0.903989i \(0.640625\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(648\) −0.242980 + 0.970031i −0.242980 + 0.970031i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.229080 0.914539i −0.229080 0.914539i −0.970031 0.242980i \(-0.921875\pi\)
0.740951 0.671559i \(-0.234375\pi\)
\(654\) −0.0951944 0.0238449i −0.0951944 0.0238449i
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.146730 0.989177i \(-0.453125\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(660\) 0 0
\(661\) −1.48012 + 1.34150i −1.48012 + 1.34150i −0.707107 + 0.707107i \(0.750000\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(662\) 0.854922 + 0.571240i 0.854922 + 0.571240i
\(663\) 0 0
\(664\) −1.95213 + 0.388302i −1.95213 + 0.388302i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 1.02821i 1.02821i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(674\) 0 0
\(675\) 0.336890 0.941544i 0.336890 0.941544i
\(676\) −0.980785 + 0.195090i −0.980785 + 0.195090i
\(677\) 1.53724 + 1.14010i 1.53724 + 1.14010i 0.941544 + 0.336890i \(0.109375\pi\)
0.595699 + 0.803208i \(0.296875\pi\)
\(678\) 1.30692 0.698564i 1.30692 0.698564i
\(679\) 0 0
\(680\) 0.229080 0.428579i 0.229080 0.428579i
\(681\) 1.11897 0.598102i 1.11897 0.598102i
\(682\) 0 0
\(683\) −1.66094 0.0815966i −1.66094 0.0815966i −0.803208 0.595699i \(-0.796875\pi\)
−0.857729 + 0.514103i \(0.828125\pi\)
\(684\) 0.805124 + 0.288078i 0.805124 + 0.288078i
\(685\) 1.18996 + 1.60448i 1.18996 + 1.60448i
\(686\) 0 0
\(687\) 0.287822 0.0572514i 0.287822 0.0572514i
\(688\) 0 0
\(689\) 0 0
\(690\) −1.17850 + 0.174814i −1.17850 + 0.174814i
\(691\) 0.881921 1.47140i 0.881921 1.47140i 1.00000i \(-0.5\pi\)
0.881921 0.471397i \(-0.156250\pi\)
\(692\) 0.594221 + 1.66074i 0.594221 + 1.66074i
\(693\) 0 0
\(694\) −0.785695 + 0.785695i −0.785695 + 0.785695i
\(695\) −1.25505 + 1.52929i −1.25505 + 1.52929i
\(696\) 0 0
\(697\) 0 0
\(698\) −1.59449 0.852275i −1.59449 0.852275i
\(699\) −0.0713052 + 0.284666i −0.0713052 + 0.284666i
\(700\) 0 0
\(701\) 0 0 −0.740951 0.671559i \(-0.765625\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −0.949728 0.949728i −0.949728 0.949728i
\(706\) 0.968101 1.61518i 0.968101 1.61518i
\(707\) 0 0
\(708\) 0 0
\(709\) 1.75380 + 0.439303i 1.75380 + 0.439303i 0.980785 0.195090i \(-0.0625000\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(710\) 0 0
\(711\) −1.65493 0.162997i −1.65493 0.162997i
\(712\) 0 0
\(713\) 0.534683 + 0.438803i 0.534683 + 0.438803i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(720\) 0.998795 0.0490677i 0.998795 0.0490677i
\(721\) 0 0
\(722\) −0.114921 + 0.242980i −0.114921 + 0.242980i
\(723\) −1.53724 + 1.14010i −1.53724 + 1.14010i
\(724\) 1.15203 1.27107i 1.15203 1.27107i
\(725\) 0 0
\(726\) 0.555570 + 0.831470i 0.555570 + 0.831470i
\(727\) 0 0 −0.471397 0.881921i \(-0.656250\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(728\) 0 0
\(729\) 0.956940 0.290285i 0.956940 0.290285i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.560227 + 0.374332i −0.560227 + 0.374332i
\(733\) 0 0 −0.941544 0.336890i \(-0.890625\pi\)
0.941544 + 0.336890i \(0.109375\pi\)
\(734\) 0 0
\(735\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(736\) −0.612501 1.02190i −0.612501 1.02190i
\(737\) 0 0
\(738\) 0 0
\(739\) 1.33962 0.633595i 1.33962 0.633595i 0.382683 0.923880i \(-0.375000\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0.887682 1.66074i 0.887682 1.66074i 0.146730 0.989177i \(-0.453125\pi\)
0.740951 0.671559i \(-0.234375\pi\)
\(744\) −0.410525 0.410525i −0.410525 0.410525i
\(745\) 0 0
\(746\) 0 0
\(747\) 1.33665 + 1.47477i 1.33665 + 1.47477i
\(748\) 0 0
\(749\) 0 0
\(750\) −0.998795 0.0490677i −0.998795 0.0490677i
\(751\) 0.783904 + 0.523788i 0.783904 + 0.523788i 0.881921 0.471397i \(-0.156250\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(752\) 0.513989 1.24088i 0.513989 1.24088i
\(753\) 0 0
\(754\) 0 0
\(755\) −0.190159 + 0.0476324i −0.190159 + 0.0476324i
\(756\) 0 0
\(757\) 0 0 −0.336890 0.941544i \(-0.609375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(758\) 1.58488 0.656477i 1.58488 0.656477i
\(759\) 0 0
\(760\) 0.0419583 0.854080i 0.0419583 0.854080i
\(761\) 0 0 −0.634393 0.773010i \(-0.718750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) −0.485375 + 0.0238449i −0.485375 + 0.0238449i
\(766\) −1.86271 0.276306i −1.86271 0.276306i
\(767\) 0 0
\(768\) 0.427555 + 0.903989i 0.427555 + 0.903989i
\(769\) −0.942793 −0.942793 −0.471397 0.881921i \(-0.656250\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(770\) 0 0
\(771\) −1.60448 + 0.0788231i −1.60448 + 0.0788231i
\(772\) 0 0
\(773\) 1.58488 0.949938i 1.58488 0.949938i 0.595699 0.803208i \(-0.296875\pi\)
0.989177 0.146730i \(-0.0468750\pi\)
\(774\) 0 0
\(775\) 0.368309 + 0.448786i 0.368309 + 0.448786i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0.297651 + 0.496601i 0.297651 + 0.496601i
\(783\) 0 0
\(784\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.989177 0.146730i \(-0.953125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(788\) −0.334669 0.200593i −0.334669 0.200593i
\(789\) 1.30287 + 1.43749i 1.30287 + 1.43749i
\(790\) 0.324423 + 1.63099i 0.324423 + 1.63099i
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 1.52929 0.226848i 1.52929 0.226848i
\(796\) 1.81225 + 0.750661i 1.81225 + 0.750661i
\(797\) 1.00446 0.475074i 1.00446 0.475074i 0.146730 0.989177i \(-0.453125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(798\) 0 0
\(799\) −0.249778 + 0.603018i −0.249778 + 0.603018i
\(800\) −0.336890 0.941544i −0.336890 0.941544i
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 −0.471397 0.881921i \(-0.656250\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(810\) −0.555570 0.831470i −0.555570 0.831470i
\(811\) −0.0923988 + 1.88082i −0.0923988 + 1.88082i 0.290285 + 0.956940i \(0.406250\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(812\) 0 0
\(813\) −0.614748 + 0.455929i −0.614748 + 0.455929i
\(814\) 0 0
\(815\) 0 0
\(816\) −0.207775 0.439303i −0.207775 0.439303i
\(817\) 0 0
\(818\) 0.116777 0.157456i 0.116777 0.157456i
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.903989 0.427555i \(-0.859375\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(822\) 1.99759 1.99759
\(823\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 1.07784 + 0.269985i 1.07784 + 0.269985i 0.740951 0.671559i \(-0.234375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(828\) −0.561621 + 1.05072i −0.561621 + 1.05072i
\(829\) 1.30287 1.43749i 1.30287 1.43749i 0.471397 0.881921i \(-0.343750\pi\)
0.831470 0.555570i \(-0.187500\pi\)
\(830\) 1.02325 1.70720i 1.02325 1.70720i
\(831\) 0 0
\(832\) 0 0
\(833\) 0.343626 0.343626i 0.343626 0.343626i
\(834\) 0.480701 + 1.91906i 0.480701 + 1.91906i
\(835\) 0.761850 + 0.690501i 0.761850 + 0.690501i
\(836\) 0 0
\(837\) −0.141067 + 0.563170i −0.141067 + 0.563170i
\(838\) 0 0
\(839\) 0 0 0.0980171 0.995185i \(-0.468750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(840\) 0 0
\(841\) 0.634393 0.773010i 0.634393 0.773010i
\(842\) 1.39891 1.39891i 1.39891 1.39891i
\(843\) 0 0
\(844\) −0.0923988 + 0.0330608i −0.0923988 + 0.0330608i
\(845\) 0.514103 0.857729i 0.514103 0.857729i
\(846\) −1.32858 + 0.197076i −1.32858 + 0.197076i
\(847\) 0 0
\(848\) 0.794814 + 1.32607i 0.794814 + 1.32607i
\(849\) 0 0
\(850\) 0.163715 + 0.457553i 0.163715 + 0.457553i
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 −0.998795 0.0490677i \(-0.984375\pi\)
0.998795 + 0.0490677i \(0.0156250\pi\)
\(854\) 0 0
\(855\) −0.754140 + 0.403096i −0.754140 + 0.403096i
\(856\) −0.273678 0.902197i −0.273678 0.902197i
\(857\) 0.195588 + 0.644767i 0.195588 + 0.644767i 0.998795 + 0.0490677i \(0.0156250\pi\)
−0.803208 + 0.595699i \(0.796875\pi\)
\(858\) 0 0
\(859\) 0.541185 + 0.401370i 0.541185 + 0.401370i 0.831470 0.555570i \(-0.187500\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −1.82776 + 0.757083i −1.82776 + 0.757083i −0.857729 + 0.514103i \(0.828125\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(864\) 0.555570 0.831470i 0.555570 0.831470i
\(865\) −1.62958 0.674993i −1.62958 0.674993i
\(866\) 0 0
\(867\) −0.326585 0.690505i −0.326585 0.690505i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0.0815966 + 0.0545211i 0.0815966 + 0.0545211i
\(873\) 0 0
\(874\) 0.847082 + 0.566002i 0.847082 + 0.566002i
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.146730 0.989177i \(-0.453125\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(878\) 0.262029 + 0.289105i 0.262029 + 0.289105i
\(879\) 1.10579 1.65493i 1.10579 1.65493i
\(880\) 0 0
\(881\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(882\) 0.970031 + 0.242980i 0.970031 + 0.242980i
\(883\) 0 0 −0.242980 0.970031i \(-0.578125\pi\)
0.242980 + 0.970031i \(0.421875\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.76820 + 0.732410i 1.76820 + 0.732410i
\(887\) −0.0287642 0.292048i −0.0287642 0.292048i −0.998795 0.0490677i \(-0.984375\pi\)
0.970031 0.242980i \(-0.0781250\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0.0563549 + 1.14713i 0.0563549 + 1.14713i
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −0.634393 + 0.773010i −0.634393 + 0.773010i
\(901\) −0.386248 0.644416i −0.386248 0.644416i
\(902\) 0 0
\(903\) 0 0
\(904\) −1.46586 + 0.217440i −1.46586 + 0.217440i
\(905\) 0.168144 + 1.70720i 0.168144 + 1.70720i
\(906\) −0.0750191 + 0.181112i −0.0750191 + 0.181112i
\(907\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(908\) −1.25505 + 0.186170i −1.25505 + 0.186170i
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(912\) −0.661009 0.542476i −0.661009 0.542476i
\(913\) 0 0
\(914\) 0 0
\(915\) 0.0988640 0.666487i 0.0988640 0.666487i
\(916\) −0.290285 0.0430597i −0.290285 0.0430597i
\(917\) 0 0
\(918\) −0.269985 + 0.404061i −0.269985 + 0.404061i
\(919\) −1.21415 0.368309i −1.21415 0.368309i −0.382683 0.923880i \(-0.625000\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(920\) 1.16851 + 0.232430i 1.16851 + 0.232430i
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(930\) 0.579870 0.0284872i 0.579870 0.0284872i
\(931\) 0.288078 0.805124i 0.288078 0.805124i
\(932\) 0.163038 0.244004i 0.163038 0.244004i
\(933\) 0 0
\(934\) −0.183930 0.344109i −0.183930 0.344109i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0.574257 + 1.21416i 0.574257 + 1.21416i
\(941\) 0 0 −0.595699 0.803208i \(-0.703125\pi\)
0.595699 + 0.803208i \(0.296875\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −0.100782 + 0.168144i −0.100782 + 0.168144i −0.903989 0.427555i \(-0.859375\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(948\) 1.50328 + 0.710998i 1.50328 + 0.710998i
\(949\) 0 0
\(950\) 0.604654 + 0.604654i 0.604654 + 0.604654i
\(951\) 0.704900 0.858923i 0.704900 0.858923i
\(952\) 0 0
\(953\) 0.100782 1.02325i 0.100782 1.02325i −0.803208 0.595699i \(-0.796875\pi\)
0.903989 0.427555i \(-0.140625\pi\)
\(954\) 0.728789 1.36347i 0.728789 1.36347i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −0.956940 0.290285i −0.956940 0.290285i
\(961\) 0.468769 + 0.468769i 0.468769 + 0.468769i
\(962\) 0 0
\(963\) −0.633141 + 0.698564i −0.633141 + 0.698564i
\(964\) 1.83147 0.555570i 1.83147 0.555570i
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(968\) −0.242980 0.970031i −0.242980 0.970031i
\(969\) 0.321224 + 0.263622i 0.321224 + 0.263622i
\(970\) 0 0
\(971\) 0 0 −0.903989 0.427555i \(-0.859375\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(972\) −0.998795 0.0490677i −0.998795 0.0490677i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0.653587 0.163715i 0.653587 0.163715i
\(977\) −0.313396 1.57555i −0.313396 1.57555i −0.740951 0.671559i \(-0.765625\pi\)
0.427555 0.903989i \(-0.359375\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −0.0490677 0.998795i −0.0490677 0.998795i
\(981\) 0.00481527 0.0980171i 0.00481527 0.0980171i
\(982\) 0 0
\(983\) −0.914539 1.71098i −0.914539 1.71098i −0.671559 0.740951i \(-0.734375\pi\)
−0.242980 0.970031i \(-0.578125\pi\)
\(984\) 0 0
\(985\) 0.373380 0.113263i 0.373380 0.113263i
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.292893 + 0.707107i 0.292893 + 0.707107i 1.00000 \(0\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(992\) 0.248225 + 0.524828i 0.248225 + 0.524828i
\(993\) −0.393477 + 0.949938i −0.393477 + 0.949938i
\(994\) 0 0
\(995\) −1.77324 + 0.838679i −1.77324 + 0.838679i
\(996\) −0.761681 1.83886i −0.761681 1.83886i
\(997\) 0 0 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(998\) −0.0287642 0.292048i −0.0287642 0.292048i
\(999\) 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 3840.1.dy.a.629.2 yes 64
3.2 odd 2 inner 3840.1.dy.a.629.1 64
5.4 even 2 inner 3840.1.dy.a.629.1 64
15.14 odd 2 CM 3840.1.dy.a.629.2 yes 64
256.221 even 64 inner 3840.1.dy.a.989.2 yes 64
768.221 odd 64 inner 3840.1.dy.a.989.1 yes 64
1280.989 even 64 inner 3840.1.dy.a.989.1 yes 64
3840.989 odd 64 inner 3840.1.dy.a.989.2 yes 64
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3840.1.dy.a.629.1 64 3.2 odd 2 inner
3840.1.dy.a.629.1 64 5.4 even 2 inner
3840.1.dy.a.629.2 yes 64 1.1 even 1 trivial
3840.1.dy.a.629.2 yes 64 15.14 odd 2 CM
3840.1.dy.a.989.1 yes 64 768.221 odd 64 inner
3840.1.dy.a.989.1 yes 64 1280.989 even 64 inner
3840.1.dy.a.989.2 yes 64 256.221 even 64 inner
3840.1.dy.a.989.2 yes 64 3840.989 odd 64 inner