Properties

Label 1792.1.bt.a.1357.1
Level $1792$
Weight $1$
Character 1792.1357
Analytic conductor $0.894$
Analytic rank $0$
Dimension $32$
Projective image $D_{64}$
CM discriminant -7
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1792,1,Mod(13,1792)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1792, base_ring=CyclotomicField(64))
 
chi = DirichletCharacter(H, H._module([0, 47, 32]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1792.13");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1792 = 2^{8} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1792.bt (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: \(0.894324502638\)
Analytic rank: \(0\)
Dimension: \(32\)
Coefficient field: \(\Q(\zeta_{64})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{32} + 1 \) 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 1357.1
Root \(0.290285 + 0.956940i\) of defining polynomial
Character \(\chi\) \(=\) 1792.1357
Dual form 1792.1.bt.a.1413.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.773010 - 0.634393i) q^{2} +(0.195090 + 0.980785i) q^{4} +(0.881921 - 0.471397i) q^{7} +(0.471397 - 0.881921i) q^{8} +(0.956940 - 0.290285i) q^{9} +O(q^{10})\) \(q+(-0.773010 - 0.634393i) q^{2} +(0.195090 + 0.980785i) q^{4} +(0.881921 - 0.471397i) q^{7} +(0.471397 - 0.881921i) q^{8} +(0.956940 - 0.290285i) q^{9} +(1.55075 + 0.929487i) q^{11} +(-0.980785 - 0.195090i) q^{14} +(-0.923880 + 0.382683i) q^{16} +(-0.923880 - 0.382683i) q^{18} +(-0.609090 - 1.70229i) q^{22} +(-0.448786 + 0.368309i) q^{23} +(-0.995185 + 0.0980171i) q^{25} +(0.634393 + 0.773010i) q^{28} +(-0.485375 + 1.93773i) q^{29} +(0.956940 + 0.290285i) q^{32} +(0.471397 + 0.881921i) q^{36} +(-1.61518 - 0.577920i) q^{37} +(0.284666 - 1.91906i) q^{43} +(-0.609090 + 1.70229i) q^{44} +0.580569 q^{46} +(0.555570 - 0.831470i) q^{49} +(0.831470 + 0.555570i) q^{50} +(0.289486 + 1.15569i) q^{53} -1.00000i q^{56} +(1.60448 - 1.18996i) q^{58} +(0.707107 - 0.707107i) q^{63} +(-0.555570 - 0.831470i) q^{64} +(-0.174814 + 0.235710i) q^{67} +(0.482726 - 1.59133i) q^{71} +(0.195090 - 0.980785i) q^{72} +(0.881921 + 1.47140i) q^{74} +(1.80580 + 0.0887133i) q^{77} +(0.162997 + 0.108911i) q^{79} +(0.831470 - 0.555570i) q^{81} +(-1.43749 + 1.30287i) q^{86} +(1.55075 - 0.929487i) q^{88} +(-0.448786 - 0.368309i) q^{92} +(-0.956940 + 0.290285i) q^{98} +(1.75380 + 0.439303i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) Copy content Toggle raw display \( 32 q+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{31}{64}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.773010 0.634393i −0.773010 0.634393i
\(3\) 0 0 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(4\) 0.195090 + 0.980785i 0.195090 + 0.980785i
\(5\) 0 0 −0.0490677 0.998795i \(-0.515625\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(6\) 0 0
\(7\) 0.881921 0.471397i 0.881921 0.471397i
\(8\) 0.471397 0.881921i 0.471397 0.881921i
\(9\) 0.956940 0.290285i 0.956940 0.290285i
\(10\) 0 0
\(11\) 1.55075 + 0.929487i 1.55075 + 0.929487i 0.995185 + 0.0980171i \(0.0312500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(12\) 0 0
\(13\) 0 0 0.740951 0.671559i \(-0.234375\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(14\) −0.980785 0.195090i −0.980785 0.195090i
\(15\) 0 0
\(16\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(17\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(18\) −0.923880 0.382683i −0.923880 0.382683i
\(19\) 0 0 −0.903989 0.427555i \(-0.859375\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −0.609090 1.70229i −0.609090 1.70229i
\(23\) −0.448786 + 0.368309i −0.448786 + 0.368309i −0.831470 0.555570i \(-0.812500\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(24\) 0 0
\(25\) −0.995185 + 0.0980171i −0.995185 + 0.0980171i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.634393 + 0.773010i 0.634393 + 0.773010i
\(29\) −0.485375 + 1.93773i −0.485375 + 1.93773i −0.195090 + 0.980785i \(0.562500\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(30\) 0 0
\(31\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(32\) 0.956940 + 0.290285i 0.956940 + 0.290285i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0.471397 + 0.881921i 0.471397 + 0.881921i
\(37\) −1.61518 0.577920i −1.61518 0.577920i −0.634393 0.773010i \(-0.718750\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(42\) 0 0
\(43\) 0.284666 1.91906i 0.284666 1.91906i −0.0980171 0.995185i \(-0.531250\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(44\) −0.609090 + 1.70229i −0.609090 + 1.70229i
\(45\) 0 0
\(46\) 0.580569 0.580569
\(47\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(48\) 0 0
\(49\) 0.555570 0.831470i 0.555570 0.831470i
\(50\) 0.831470 + 0.555570i 0.831470 + 0.555570i
\(51\) 0 0
\(52\) 0 0
\(53\) 0.289486 + 1.15569i 0.289486 + 1.15569i 0.923880 + 0.382683i \(0.125000\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 1.00000i
\(57\) 0 0
\(58\) 1.60448 1.18996i 1.60448 1.18996i
\(59\) 0 0 −0.740951 0.671559i \(-0.765625\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(60\) 0 0
\(61\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(62\) 0 0
\(63\) 0.707107 0.707107i 0.707107 0.707107i
\(64\) −0.555570 0.831470i −0.555570 0.831470i
\(65\) 0 0
\(66\) 0 0
\(67\) −0.174814 + 0.235710i −0.174814 + 0.235710i −0.881921 0.471397i \(-0.843750\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0.482726 1.59133i 0.482726 1.59133i −0.290285 0.956940i \(-0.593750\pi\)
0.773010 0.634393i \(-0.218750\pi\)
\(72\) 0.195090 0.980785i 0.195090 0.980785i
\(73\) 0 0 −0.881921 0.471397i \(-0.843750\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(74\) 0.881921 + 1.47140i 0.881921 + 1.47140i
\(75\) 0 0
\(76\) 0 0
\(77\) 1.80580 + 0.0887133i 1.80580 + 0.0887133i
\(78\) 0 0
\(79\) 0.162997 + 0.108911i 0.162997 + 0.108911i 0.634393 0.773010i \(-0.281250\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(80\) 0 0
\(81\) 0.831470 0.555570i 0.831470 0.555570i
\(82\) 0 0
\(83\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.43749 + 1.30287i −1.43749 + 1.30287i
\(87\) 0 0
\(88\) 1.55075 0.929487i 1.55075 0.929487i
\(89\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) −0.448786 0.368309i −0.448786 0.368309i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(98\) −0.956940 + 0.290285i −0.956940 + 0.290285i
\(99\) 1.75380 + 0.439303i 1.75380 + 0.439303i
\(100\) −0.290285 0.956940i −0.290285 0.956940i
\(101\) 0 0 −0.427555 0.903989i \(-0.640625\pi\)
0.427555 + 0.903989i \(0.359375\pi\)
\(102\) 0 0
\(103\) 0 0 −0.0980171 0.995185i \(-0.531250\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0.509389 1.07701i 0.509389 1.07701i
\(107\) 0.956940 + 1.29028i 0.956940 + 1.29028i 0.956940 + 0.290285i \(0.0937500\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −0.805124 + 1.70229i −0.805124 + 1.70229i −0.0980171 + 0.995185i \(0.531250\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.634393 + 0.773010i −0.634393 + 0.773010i
\(113\) −1.72995 + 0.344109i −1.72995 + 0.344109i −0.956940 0.290285i \(-0.906250\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −1.99518 0.0980171i −1.99518 0.0980171i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 1.06950 + 2.00089i 1.06950 + 2.00089i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) −0.995185 + 0.0980171i −0.995185 + 0.0980171i
\(127\) 1.96157i 1.96157i −0.195090 0.980785i \(-0.562500\pi\)
0.195090 0.980785i \(-0.437500\pi\)
\(128\) −0.0980171 + 0.995185i −0.0980171 + 0.995185i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.146730 0.989177i \(-0.546875\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0.284666 0.0713052i 0.284666 0.0713052i
\(135\) 0 0
\(136\) 0 0
\(137\) −0.577774 1.90466i −0.577774 1.90466i −0.382683 0.923880i \(-0.625000\pi\)
−0.195090 0.980785i \(-0.562500\pi\)
\(138\) 0 0
\(139\) 0 0 0.514103 0.857729i \(-0.328125\pi\)
−0.514103 + 0.857729i \(0.671875\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.38268 + 0.923880i −1.38268 + 0.923880i
\(143\) 0 0
\(144\) −0.773010 + 0.634393i −0.773010 + 0.634393i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0.251710 1.69689i 0.251710 1.69689i
\(149\) −1.17850 1.58903i −1.17850 1.58903i −0.707107 0.707107i \(-0.750000\pi\)
−0.471397 0.881921i \(-0.656250\pi\)
\(150\) 0 0
\(151\) −0.980785 1.19509i −0.980785 1.19509i −0.980785 0.195090i \(-0.937500\pi\)
1.00000i \(-0.5\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −1.33962 1.21416i −1.33962 1.21416i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(158\) −0.0569057 0.187593i −0.0569057 0.187593i
\(159\) 0 0
\(160\) 0 0
\(161\) −0.222174 + 0.536376i −0.222174 + 0.536376i
\(162\) −0.995185 0.0980171i −0.995185 0.0980171i
\(163\) 1.27107 0.761850i 1.27107 0.761850i 0.290285 0.956940i \(-0.406250\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(168\) 0 0
\(169\) 0.0980171 0.995185i 0.0980171 0.995185i
\(170\) 0 0
\(171\) 0 0
\(172\) 1.93773 0.0951944i 1.93773 0.0951944i
\(173\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(174\) 0 0
\(175\) −0.831470 + 0.555570i −0.831470 + 0.555570i
\(176\) −1.78841 0.265286i −1.78841 0.265286i
\(177\) 0 0
\(178\) 0 0
\(179\) −1.02697 0.0504517i −1.02697 0.0504517i −0.471397 0.881921i \(-0.656250\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(180\) 0 0
\(181\) 0 0 0.970031 0.242980i \(-0.0781250\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.113263 + 0.569414i 0.113263 + 0.569414i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0.897168 + 0.897168i 0.897168 + 0.897168i 0.995185 0.0980171i \(-0.0312500\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(192\) 0 0
\(193\) −1.35332 + 1.35332i −1.35332 + 1.35332i −0.471397 + 0.881921i \(0.656250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(197\) −0.360073 0.326351i −0.360073 0.326351i 0.471397 0.881921i \(-0.343750\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(198\) −1.07701 1.45218i −1.07701 1.45218i
\(199\) 0 0 −0.956940 0.290285i \(-0.906250\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(200\) −0.382683 + 0.923880i −0.382683 + 0.923880i
\(201\) 0 0
\(202\) 0 0
\(203\) 0.485375 + 1.93773i 0.485375 + 1.93773i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.322547 + 0.482726i −0.322547 + 0.482726i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −0.0330608 0.0923988i −0.0330608 0.0923988i 0.923880 0.382683i \(-0.125000\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(212\) −1.07701 + 0.509389i −1.07701 + 0.509389i
\(213\) 0 0
\(214\) 0.0788231 1.60448i 0.0788231 1.60448i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 1.70229 0.805124i 1.70229 0.805124i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(224\) 0.980785 0.195090i 0.980785 0.195090i
\(225\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(226\) 1.55557 + 0.831470i 1.55557 + 0.831470i
\(227\) 0 0 0.242980 0.970031i \(-0.421875\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(228\) 0 0
\(229\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.48012 + 1.34150i 1.48012 + 1.34150i
\(233\) 0.151537 0.124363i 0.151537 0.124363i −0.555570 0.831470i \(-0.687500\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.0761205 + 0.382683i −0.0761205 + 0.382683i 0.923880 + 0.382683i \(0.125000\pi\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(242\) 0.442618 2.22519i 0.442618 2.22519i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.0490677 0.998795i \(-0.515625\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(252\) 0.831470 + 0.555570i 0.831470 + 0.555570i
\(253\) −1.03830 + 0.154017i −1.03830 + 0.154017i
\(254\) −1.24441 + 1.51631i −1.24441 + 1.51631i
\(255\) 0 0
\(256\) 0.707107 0.707107i 0.707107 0.707107i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −1.69689 + 0.251710i −1.69689 + 0.251710i
\(260\) 0 0
\(261\) 0.0980171 + 1.99518i 0.0980171 + 1.99518i
\(262\) 0 0
\(263\) −0.674993 + 0.360791i −0.674993 + 0.360791i −0.773010 0.634393i \(-0.781250\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −0.265286 0.125471i −0.265286 0.125471i
\(269\) 0 0 0.740951 0.671559i \(-0.234375\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(270\) 0 0
\(271\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) −0.761681 + 1.83886i −0.761681 + 1.83886i
\(275\) −1.63439 0.773010i −1.63439 0.773010i
\(276\) 0 0
\(277\) 0.541185 0.401370i 0.541185 0.401370i −0.290285 0.956940i \(-0.593750\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.53858 0.151537i 1.53858 0.151537i 0.707107 0.707107i \(-0.250000\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(282\) 0 0
\(283\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(284\) 1.65493 + 0.162997i 1.65493 + 0.162997i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 1.00000
\(289\) −0.923880 0.382683i −0.923880 0.382683i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.941544 0.336890i \(-0.890625\pi\)
0.941544 + 0.336890i \(0.109375\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −1.27107 + 1.15203i −1.27107 + 1.15203i
\(297\) 0 0
\(298\) −0.0970732 + 1.97597i −0.0970732 + 1.97597i
\(299\) 0 0
\(300\) 0 0
\(301\) −0.653587 1.82665i −0.653587 1.82665i
\(302\) 1.54602i 1.54602i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(308\) 0.265286 + 1.78841i 0.265286 + 1.78841i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(312\) 0 0
\(313\) 0 0 −0.956940 0.290285i \(-0.906250\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) −0.0750191 + 0.181112i −0.0750191 + 0.181112i
\(317\) 1.19028 + 0.882768i 1.19028 + 0.882768i 0.995185 0.0980171i \(-0.0312500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(318\) 0 0
\(319\) −2.55379 + 2.55379i −2.55379 + 2.55379i
\(320\) 0 0
\(321\) 0 0
\(322\) 0.512016 0.273678i 0.512016 0.273678i
\(323\) 0 0
\(324\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(325\) 0 0
\(326\) −1.46586 0.217440i −1.46586 0.217440i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 1.30287 0.326351i 1.30287 0.326351i 0.471397 0.881921i \(-0.343750\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(332\) 0 0
\(333\) −1.71339 0.0841735i −1.71339 0.0841735i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −0.783904 + 0.523788i −0.783904 + 0.523788i −0.881921 0.471397i \(-0.843750\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(338\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.0980171 0.995185i 0.0980171 0.995185i
\(344\) −1.55827 1.15569i −1.55827 1.15569i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.452483 + 1.26460i −0.452483 + 1.26460i 0.471397 + 0.881921i \(0.343750\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(348\) 0 0
\(349\) 0 0 0.857729 0.514103i \(-0.171875\pi\)
−0.857729 + 0.514103i \(0.828125\pi\)
\(350\) 0.995185 + 0.0980171i 0.995185 + 0.0980171i
\(351\) 0 0
\(352\) 1.21416 + 1.33962i 1.21416 + 1.33962i
\(353\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0.761850 + 0.690501i 0.761850 + 0.690501i
\(359\) −0.0924099 0.938254i −0.0924099 0.938254i −0.923880 0.382683i \(-0.875000\pi\)
0.831470 0.555570i \(-0.187500\pi\)
\(360\) 0 0
\(361\) 0.634393 + 0.773010i 0.634393 + 0.773010i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(368\) 0.273678 0.512016i 0.273678 0.512016i
\(369\) 0 0
\(370\) 0 0
\(371\) 0.800094 + 0.882768i 0.800094 + 0.882768i
\(372\) 0 0
\(373\) −0.439614 + 0.733452i −0.439614 + 0.733452i −0.995185 0.0980171i \(-0.968750\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 1.18996 0.0584592i 1.18996 0.0584592i 0.555570 0.831470i \(-0.312500\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) −0.124363 1.26268i −0.124363 1.26268i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 1.90466 0.187593i 1.90466 0.187593i
\(387\) −0.284666 1.91906i −0.284666 1.91906i
\(388\) 0 0
\(389\) −1.93773 + 0.0951944i −1.93773 + 0.0951944i −0.980785 0.195090i \(-0.937500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.471397 0.881921i −0.471397 0.881921i
\(393\) 0 0
\(394\) 0.0713052 + 0.480701i 0.0713052 + 0.480701i
\(395\) 0 0
\(396\) −0.0887133 + 1.80580i −0.0887133 + 1.80580i
\(397\) 0 0 −0.671559 0.740951i \(-0.734375\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.881921 0.471397i 0.881921 0.471397i
\(401\) 0.924678 + 0.183930i 0.924678 + 0.183930i 0.634393 0.773010i \(-0.281250\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0.854080 1.80580i 0.854080 1.80580i
\(407\) −1.96758 2.39750i −1.96758 2.39750i
\(408\) 0 0
\(409\) 0 0 −0.0980171 0.995185i \(-0.531250\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.555570 0.168530i 0.555570 0.168530i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.857729 0.514103i \(-0.171875\pi\)
−0.857729 + 0.514103i \(0.828125\pi\)
\(420\) 0 0
\(421\) 0.499238 1.39528i 0.499238 1.39528i −0.382683 0.923880i \(-0.625000\pi\)
0.881921 0.471397i \(-0.156250\pi\)
\(422\) −0.0330608 + 0.0923988i −0.0330608 + 0.0923988i
\(423\) 0 0
\(424\) 1.15569 + 0.289486i 1.15569 + 0.289486i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −1.07880 + 1.19028i −1.07880 + 1.19028i
\(429\) 0 0
\(430\) 0 0
\(431\) −1.53636 + 1.02656i −1.53636 + 1.02656i −0.555570 + 0.831470i \(0.687500\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(432\) 0 0
\(433\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.82665 0.457553i −1.82665 0.457553i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.881921 0.471397i \(-0.843750\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(440\) 0 0
\(441\) 0.290285 0.956940i 0.290285 0.956940i
\(442\) 0 0
\(443\) 1.15203 1.27107i 1.15203 1.27107i 0.195090 0.980785i \(-0.437500\pi\)
0.956940 0.290285i \(-0.0937500\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.881921 0.471397i −0.881921 0.471397i
\(449\) −0.785695 + 0.785695i −0.785695 + 0.785695i −0.980785 0.195090i \(-0.937500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(450\) 0.956940 + 0.290285i 0.956940 + 0.290285i
\(451\) 0 0
\(452\) −0.674993 1.62958i −0.674993 1.62958i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.183930 0.344109i 0.183930 0.344109i −0.773010 0.634393i \(-0.781250\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(462\) 0 0
\(463\) −0.523788 + 0.783904i −0.523788 + 0.783904i −0.995185 0.0980171i \(-0.968750\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(464\) −0.293107 1.97597i −0.293107 1.97597i
\(465\) 0 0
\(466\) −0.196034 −0.196034
\(467\) 0 0 −0.336890 0.941544i \(-0.609375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(468\) 0 0
\(469\) −0.0430597 + 0.290285i −0.0430597 + 0.290285i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 2.22519 2.71140i 2.22519 2.71140i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0.612501 + 1.02190i 0.612501 + 1.02190i
\(478\) 0.301614 0.247528i 0.301614 0.247528i
\(479\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.75380 + 1.43930i −1.75380 + 1.43930i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.98079 0.195090i 1.98079 0.195090i 0.980785 0.195090i \(-0.0625000\pi\)
1.00000 \(0\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −1.58903 + 1.17850i −1.58903 + 1.17850i −0.707107 + 0.707107i \(0.750000\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.324423 1.63099i −0.324423 1.63099i
\(498\) 0 0
\(499\) −1.46586 + 1.32858i −1.46586 + 1.32858i −0.634393 + 0.773010i \(0.718750\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 0.956940 0.290285i \(-0.0937500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(504\) −0.290285 0.956940i −0.290285 0.956940i
\(505\) 0 0
\(506\) 0.900321 + 0.539632i 0.900321 + 0.539632i
\(507\) 0 0
\(508\) 1.92388 0.382683i 1.92388 0.382683i
\(509\) 0 0 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.995185 + 0.0980171i −0.995185 + 0.0980171i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 1.47140 + 0.881921i 1.47140 + 0.881921i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.956940 0.290285i \(-0.0937500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(522\) 1.18996 1.60448i 1.18996 1.60448i
\(523\) 0 0 −0.857729 0.514103i \(-0.828125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0.750661 + 0.149316i 0.750661 + 0.149316i
\(527\) 0 0
\(528\) 0 0
\(529\) −0.129333 + 0.650201i −0.129333 + 0.650201i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.125471 + 0.265286i 0.125471 + 0.265286i
\(537\) 0 0
\(538\) 0 0
\(539\) 1.63439 0.773010i 1.63439 0.773010i
\(540\) 0 0
\(541\) −0.390327 + 1.55827i −0.390327 + 1.55827i 0.382683 + 0.923880i \(0.375000\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.0504517 0.0841735i −0.0504517 0.0841735i 0.831470 0.555570i \(-0.187500\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(548\) 1.75535 0.938254i 1.75535 0.938254i
\(549\) 0 0
\(550\) 0.773010 + 1.63439i 0.773010 + 1.63439i
\(551\) 0 0
\(552\) 0 0
\(553\) 0.195090 + 0.0192147i 0.195090 + 0.0192147i
\(554\) −0.672968 0.0330608i −0.672968 0.0330608i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.226990 0.634393i −0.226990 0.634393i 0.773010 0.634393i \(-0.218750\pi\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) −1.28547 0.858923i −1.28547 0.858923i
\(563\) 0 0 0.0490677 0.998795i \(-0.484375\pi\)
−0.0490677 + 0.998795i \(0.515625\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.471397 0.881921i 0.471397 0.881921i
\(568\) −1.17588 1.17588i −1.17588 1.17588i
\(569\) 1.87711 + 0.569414i 1.87711 + 0.569414i 0.995185 + 0.0980171i \(0.0312500\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(570\) 0 0
\(571\) −1.48012 1.34150i −1.48012 1.34150i −0.773010 0.634393i \(-0.781250\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0.410525 0.410525i 0.410525 0.410525i
\(576\) −0.773010 0.634393i −0.773010 0.634393i
\(577\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(578\) 0.471397 + 0.881921i 0.471397 + 0.881921i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −0.625280 + 2.06127i −0.625280 + 2.06127i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.970031 0.242980i \(-0.0781250\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 1.71339 0.0841735i 1.71339 0.0841735i
\(593\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.32858 1.46586i 1.32858 1.46586i
\(597\) 0 0
\(598\) 0 0
\(599\) 0.0750191 0.761681i 0.0750191 0.761681i −0.881921 0.471397i \(-0.843750\pi\)
0.956940 0.290285i \(-0.0937500\pi\)
\(600\) 0 0
\(601\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(602\) −0.653587 + 1.82665i −0.653587 + 1.82665i
\(603\) −0.0988640 + 0.276306i −0.0988640 + 0.276306i
\(604\) 0.980785 1.19509i 0.980785 1.19509i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.574257 1.21416i −0.574257 1.21416i −0.956940 0.290285i \(-0.906250\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0.929487 1.55075i 0.929487 1.55075i
\(617\) 0.247528 + 0.301614i 0.247528 + 0.301614i 0.881921 0.471397i \(-0.156250\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(618\) 0 0
\(619\) 0 0 −0.595699 0.803208i \(-0.703125\pi\)
0.595699 + 0.803208i \(0.296875\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) 0.980785 0.195090i 0.980785 0.195090i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.322547 + 1.06330i 0.322547 + 1.06330i 0.956940 + 0.290285i \(0.0937500\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(632\) 0.172887 0.0924099i 0.172887 0.0924099i
\(633\) 0 0
\(634\) −0.360073 1.43749i −0.360073 1.43749i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 3.59421 0.353999i 3.59421 0.353999i
\(639\) 1.66294i 1.66294i
\(640\) 0 0
\(641\) 1.91388i 1.91388i −0.290285 0.956940i \(-0.593750\pi\)
0.290285 0.956940i \(-0.406250\pi\)
\(642\) 0 0
\(643\) 0 0 −0.146730 0.989177i \(-0.546875\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(644\) −0.569414 0.113263i −0.569414 0.113263i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.471397 0.881921i \(-0.656250\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(648\) −0.0980171 0.995185i −0.0980171 0.995185i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.995185 + 1.09802i 0.995185 + 1.09802i
\(653\) −0.574257 0.633595i −0.574257 0.633595i 0.382683 0.923880i \(-0.375000\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) −0.805124 + 1.70229i −0.805124 + 1.70229i −0.0980171 + 0.995185i \(0.531250\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(660\) 0 0
\(661\) 0 0 −0.595699 0.803208i \(-0.703125\pi\)
0.595699 + 0.803208i \(0.296875\pi\)
\(662\) −1.21416 0.574257i −1.21416 0.574257i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 1.27107 + 1.15203i 1.27107 + 1.15203i
\(667\) −0.495853 1.04839i −0.495853 1.04839i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.425215 + 1.02656i −0.425215 + 1.02656i 0.555570 + 0.831470i \(0.312500\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(674\) 0.938254 + 0.0924099i 0.938254 + 0.0924099i
\(675\) 0 0
\(676\) 0.995185 0.0980171i 0.995185 0.0980171i
\(677\) 0 0 0.336890 0.941544i \(-0.390625\pi\)
−0.336890 + 0.941544i \(0.609375\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.01708 0.150869i −1.01708 0.150869i −0.382683 0.923880i \(-0.625000\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(687\) 0 0
\(688\) 0.471397 + 1.88192i 0.471397 + 1.88192i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.998795 0.0490677i \(-0.984375\pi\)
0.998795 + 0.0490677i \(0.0156250\pi\)
\(692\) 0 0
\(693\) 1.75380 0.439303i 1.75380 0.439303i
\(694\) 1.15203 0.690501i 1.15203 0.690501i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) −0.707107 0.707107i −0.707107 0.707107i
\(701\) −0.289486 + 0.390327i −0.289486 + 0.390327i −0.923880 0.382683i \(-0.875000\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) −0.0887133 1.80580i −0.0887133 1.80580i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.633595 0.574257i −0.633595 0.574257i 0.290285 0.956940i \(-0.406250\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(710\) 0 0
\(711\) 0.187593 + 0.0569057i 0.187593 + 0.0569057i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) −0.150869 1.01708i −0.150869 1.01708i
\(717\) 0 0
\(718\) −0.523788 + 0.783904i −0.523788 + 0.783904i
\(719\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000i 1.00000i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.293107 1.97597i 0.293107 1.97597i
\(726\) 0 0
\(727\) 0 0 −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(728\) 0 0
\(729\) 0.634393 0.773010i 0.634393 0.773010i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.514103 0.857729i \(-0.671875\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.536376 + 0.222174i −0.536376 + 0.222174i
\(737\) −0.490184 + 0.203041i −0.490184 + 0.203041i
\(738\) 0 0
\(739\) −0.163715 + 0.653587i −0.163715 + 0.653587i 0.831470 + 0.555570i \(0.187500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.0584592 1.18996i −0.0584592 1.18996i
\(743\) 1.26268 0.124363i 1.26268 0.124363i 0.555570 0.831470i \(-0.312500\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0.805124 0.288078i 0.805124 0.288078i
\(747\) 0 0
\(748\) 0 0
\(749\) 1.45218 + 0.686831i 1.45218 + 0.686831i
\(750\) 0 0
\(751\) 0.216773 1.08979i 0.216773 1.08979i −0.707107 0.707107i \(-0.750000\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.37787 + 0.825862i 1.37787 + 0.825862i 0.995185 0.0980171i \(-0.0312500\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(758\) −0.956940 0.709715i −0.956940 0.709715i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(762\) 0 0
\(763\) 0.0923988 + 1.88082i 0.0923988 + 1.88082i
\(764\) −0.704900 + 1.05496i −0.704900 + 1.05496i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −1.59133 1.06330i −1.59133 1.06330i
\(773\) 0 0 −0.0490677 0.998795i \(-0.515625\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(774\) −0.997391 + 1.66405i −0.997391 + 1.66405i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 1.55827 + 1.15569i 1.55827 + 1.15569i
\(779\) 0 0
\(780\) 0 0
\(781\) 2.22771 2.01908i 2.22771 2.01908i
\(782\) 0 0
\(783\) 0 0
\(784\) −0.195090 + 0.980785i −0.195090 + 0.980785i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.903989 0.427555i \(-0.859375\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(788\) 0.249834 0.416822i 0.249834 0.416822i
\(789\) 0 0
\(790\) 0 0
\(791\) −1.36347 + 1.11897i −1.36347 + 1.11897i
\(792\) 1.21416 1.33962i 1.21416 1.33962i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.242980 0.970031i \(-0.421875\pi\)
−0.242980 + 0.970031i \(0.578125\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.980785 0.195090i −0.980785 0.195090i
\(801\) 0 0
\(802\) −0.598102 0.728789i −0.598102 0.728789i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) −0.388302 0.0382444i −0.388302 0.0382444i −0.0980171 0.995185i \(-0.531250\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(810\) 0 0
\(811\) 0 0 0.146730 0.989177i \(-0.453125\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(812\) −1.80580 + 0.854080i −1.80580 + 0.854080i
\(813\) 0 0
\(814\) 3.10151i 3.10151i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −0.326351 1.30287i −0.326351 1.30287i −0.881921 0.471397i \(-0.843750\pi\)
0.555570 0.831470i \(-0.312500\pi\)
\(822\) 0 0
\(823\) 0.360791 0.674993i 0.360791 0.674993i −0.634393 0.773010i \(-0.718750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0.360073 + 0.326351i 0.360073 + 0.326351i 0.831470 0.555570i \(-0.187500\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(828\) −0.536376 0.222174i −0.536376 0.222174i
\(829\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.290285 0.956940i \(-0.406250\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(840\) 0 0
\(841\) −2.63727 1.40965i −2.63727 1.40965i
\(842\) −1.27107 + 0.761850i −1.27107 + 0.761850i
\(843\) 0 0
\(844\) 0.0841735 0.0504517i 0.0841735 0.0504517i
\(845\) 0 0
\(846\) 0 0
\(847\) 1.88643 + 1.26047i 1.88643 + 1.26047i
\(848\) −0.709715 0.956940i −0.709715 0.956940i
\(849\) 0 0
\(850\) 0 0
\(851\) 0.937723 0.335523i 0.937723 0.335523i
\(852\) 0 0
\(853\) 0 0 −0.989177 0.146730i \(-0.953125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 1.58903 0.235710i 1.58903 0.235710i
\(857\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(858\) 0 0
\(859\) 0 0 0.336890 0.941544i \(-0.390625\pi\)
−0.336890 + 0.941544i \(0.609375\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 1.83886 + 0.181112i 1.83886 + 0.181112i
\(863\) −0.591637 + 1.42834i −0.591637 + 1.42834i 0.290285 + 0.956940i \(0.406250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0.151537 + 0.320397i 0.151537 + 0.320397i
\(870\) 0 0
\(871\) 0 0
\(872\) 1.12175 + 1.51251i 1.12175 + 1.51251i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −0.207775 + 0.439303i −0.207775 + 0.439303i −0.980785 0.195090i \(-0.937500\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(882\) −0.831470 + 0.555570i −0.831470 + 0.555570i
\(883\) −0.995185 1.09802i −0.995185 1.09802i −0.995185 0.0980171i \(-0.968750\pi\)
1.00000i \(-0.5\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.69689 + 0.251710i −1.69689 + 0.251710i
\(887\) 0 0 −0.290285 0.956940i \(-0.593750\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(888\) 0 0
\(889\) −0.924678 1.72995i −0.924678 1.72995i
\(890\) 0 0
\(891\) 1.80580 0.0887133i 1.80580 0.0887133i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(897\) 0 0
\(898\) 1.10579 0.108911i 1.10579 0.108911i
\(899\) 0 0
\(900\) −0.555570 0.831470i −0.555570 0.831470i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −0.512016 + 1.68789i −0.512016 + 1.68789i
\(905\) 0 0
\(906\) 0 0
\(907\) −0.968101 + 1.61518i −0.968101 + 1.61518i −0.195090 + 0.980785i \(0.562500\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.382683 + 0.0761205i −0.382683 + 0.0761205i −0.382683 0.923880i \(-0.625000\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.360480 + 0.149316i −0.360480 + 0.149316i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 1.24441 + 1.51631i 1.24441 + 1.51631i 0.773010 + 0.634393i \(0.218750\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 1.66405 + 0.416822i 1.66405 + 0.416822i
\(926\) 0.902197 0.273678i 0.902197 0.273678i
\(927\) 0 0
\(928\) −1.02697 + 1.71339i −1.02697 + 1.71339i
\(929\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0.151537 + 0.124363i 0.151537 + 0.124363i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 0.0980171 0.995185i \(-0.468750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(938\) 0.217440 0.197076i 0.217440 0.197076i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −3.44019 + 0.684297i −3.44019 + 0.684297i
\(947\) −0.672968 0.0330608i −0.672968 0.0330608i −0.290285 0.956940i \(-0.593750\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) −0.368309 + 1.21415i −0.368309 + 1.21415i 0.555570 + 0.831470i \(0.312500\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(954\) 0.174814 1.17850i 0.174814 1.17850i
\(955\) 0 0
\(956\) −0.390181 −0.390181
\(957\) 0 0
\(958\) 0 0
\(959\) −1.40740 1.40740i −1.40740 1.40740i
\(960\) 0 0
\(961\) 0.707107 0.707107i 0.707107 0.707107i
\(962\) 0 0
\(963\) 1.29028 + 0.956940i 1.29028 + 0.956940i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.47945 + 0.448786i 1.47945 + 0.448786i 0.923880 0.382683i \(-0.125000\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(968\) 2.26879 2.26879
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.242980 0.970031i \(-0.578125\pi\)
0.242980 + 0.970031i \(0.421875\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −1.65493 1.10579i −1.65493 1.10579i
\(975\) 0 0
\(976\) 0 0
\(977\) 0.923880 + 1.38268i 0.923880 + 1.38268i 0.923880 + 0.382683i \(0.125000\pi\)
1.00000i \(0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) −0.276306 + 1.86271i −0.276306 + 1.86271i
\(982\) 1.97597 + 0.0970732i 1.97597 + 0.0970732i
\(983\) 0 0 −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0.579055 + 0.966095i 0.579055 + 0.966095i
\(990\) 0 0
\(991\) −0.871028 0.360791i −0.871028 0.360791i −0.0980171 0.995185i \(-0.531250\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) −0.783904 + 1.46658i −0.783904 + 1.46658i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(998\) 1.97597 0.0970732i 1.97597 0.0970732i
\(999\) 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 1792.1.bt.a.1357.1 32
7.6 odd 2 CM 1792.1.bt.a.1357.1 32
256.133 even 64 inner 1792.1.bt.a.1413.1 yes 32
1792.1413 odd 64 inner 1792.1.bt.a.1413.1 yes 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1792.1.bt.a.1357.1 32 1.1 even 1 trivial
1792.1.bt.a.1357.1 32 7.6 odd 2 CM
1792.1.bt.a.1413.1 yes 32 256.133 even 64 inner
1792.1.bt.a.1413.1 yes 32 1792.1413 odd 64 inner