Properties

Label 1792.1.bt.a.1077.1
Level $1792$
Weight $1$
Character 1792.1077
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 1077.1
Root \(-0.995185 + 0.0980171i\) of defining polynomial
Character \(\chi\) \(=\) 1792.1077
Dual form 1792.1.bt.a.797.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.956940 + 0.290285i) q^{2} +(0.831470 - 0.555570i) q^{4} +(0.773010 - 0.634393i) q^{7} +(-0.634393 + 0.773010i) q^{8} +(-0.0980171 - 0.995185i) q^{9} +O(q^{10})\) \(q+(-0.956940 + 0.290285i) q^{2} +(0.831470 - 0.555570i) q^{4} +(0.773010 - 0.634393i) q^{7} +(-0.634393 + 0.773010i) q^{8} +(-0.0980171 - 0.995185i) q^{9} +(-0.686831 + 1.45218i) q^{11} +(-0.555570 + 0.831470i) q^{14} +(0.382683 - 0.923880i) q^{16} +(0.382683 + 0.923880i) q^{18} +(0.235710 - 1.58903i) q^{22} +(1.90466 + 0.577774i) q^{23} +(0.881921 + 0.471397i) q^{25} +(0.290285 - 0.956940i) q^{28} +(0.163715 - 0.457553i) q^{29} +(-0.0980171 + 0.995185i) q^{32} +(-0.634393 - 0.773010i) q^{36} +(-0.845855 + 0.125471i) q^{37} +(1.39528 - 1.26460i) q^{43} +(0.235710 + 1.58903i) q^{44} -1.99037 q^{46} +(0.195090 - 0.980785i) q^{49} +(-0.980785 - 0.195090i) q^{50} +(-0.672968 - 1.88082i) q^{53} +1.00000i q^{56} +(-0.0238449 + 0.485375i) q^{58} +(-0.707107 - 0.707107i) q^{63} +(-0.195090 - 0.980785i) q^{64} +(-1.48012 + 0.0727135i) q^{67} +(1.95213 + 0.192268i) q^{71} +(0.831470 + 0.555570i) q^{72} +(0.773010 - 0.365607i) q^{74} +(0.390327 + 1.55827i) q^{77} +(0.924678 + 0.183930i) q^{79} +(-0.980785 + 0.195090i) q^{81} +(-0.968101 + 1.61518i) q^{86} +(-0.686831 - 1.45218i) q^{88} +(1.90466 - 0.577774i) q^{92} +(0.0980171 + 0.995185i) q^{98} +(1.51251 + 0.541185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 32 q+O(q^{10}) \) 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 \(\left(\mathbb{Z}/1792\mathbb{Z}\right)^\times\).

\(n\) \(1023\) \(1025\) \(1541\)
\(\chi(n)\) \(1\) \(-1\) \(e\left(\frac{5}{64}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.956940 + 0.290285i −0.956940 + 0.290285i
\(3\) 0 0 0.671559 0.740951i \(-0.265625\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(4\) 0.831470 0.555570i 0.831470 0.555570i
\(5\) 0 0 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(6\) 0 0
\(7\) 0.773010 0.634393i 0.773010 0.634393i
\(8\) −0.634393 + 0.773010i −0.634393 + 0.773010i
\(9\) −0.0980171 0.995185i −0.0980171 0.995185i
\(10\) 0 0
\(11\) −0.686831 + 1.45218i −0.686831 + 1.45218i 0.195090 + 0.980785i \(0.437500\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(12\) 0 0
\(13\) 0 0 0.514103 0.857729i \(-0.328125\pi\)
−0.514103 + 0.857729i \(0.671875\pi\)
\(14\) −0.555570 + 0.831470i −0.555570 + 0.831470i
\(15\) 0 0
\(16\) 0.382683 0.923880i 0.382683 0.923880i
\(17\) 0 0 −0.831470 0.555570i \(-0.812500\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(18\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(19\) 0 0 0.803208 0.595699i \(-0.203125\pi\)
−0.803208 + 0.595699i \(0.796875\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0.235710 1.58903i 0.235710 1.58903i
\(23\) 1.90466 + 0.577774i 1.90466 + 0.577774i 0.980785 + 0.195090i \(0.0625000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(24\) 0 0
\(25\) 0.881921 + 0.471397i 0.881921 + 0.471397i
\(26\) 0 0
\(27\) 0 0
\(28\) 0.290285 0.956940i 0.290285 0.956940i
\(29\) 0.163715 0.457553i 0.163715 0.457553i −0.831470 0.555570i \(-0.812500\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(30\) 0 0
\(31\) 0 0 0.382683 0.923880i \(-0.375000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(32\) −0.0980171 + 0.995185i −0.0980171 + 0.995185i
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −0.634393 0.773010i −0.634393 0.773010i
\(37\) −0.845855 + 0.125471i −0.845855 + 0.125471i −0.555570 0.831470i \(-0.687500\pi\)
−0.290285 + 0.956940i \(0.593750\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(42\) 0 0
\(43\) 1.39528 1.26460i 1.39528 1.26460i 0.471397 0.881921i \(-0.343750\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(44\) 0.235710 + 1.58903i 0.235710 + 1.58903i
\(45\) 0 0
\(46\) −1.99037 −1.99037
\(47\) 0 0 −0.195090 0.980785i \(-0.562500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(48\) 0 0
\(49\) 0.195090 0.980785i 0.195090 0.980785i
\(50\) −0.980785 0.195090i −0.980785 0.195090i
\(51\) 0 0
\(52\) 0 0
\(53\) −0.672968 1.88082i −0.672968 1.88082i −0.382683 0.923880i \(-0.625000\pi\)
−0.290285 0.956940i \(-0.593750\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000i 1.00000i
\(57\) 0 0
\(58\) −0.0238449 + 0.485375i −0.0238449 + 0.485375i
\(59\) 0 0 −0.514103 0.857729i \(-0.671875\pi\)
0.514103 + 0.857729i \(0.328125\pi\)
\(60\) 0 0
\(61\) 0 0 −0.0490677 0.998795i \(-0.515625\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(62\) 0 0
\(63\) −0.707107 0.707107i −0.707107 0.707107i
\(64\) −0.195090 0.980785i −0.195090 0.980785i
\(65\) 0 0
\(66\) 0 0
\(67\) −1.48012 + 0.0727135i −1.48012 + 0.0727135i −0.773010 0.634393i \(-0.781250\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 1.95213 + 0.192268i 1.95213 + 0.192268i 0.995185 0.0980171i \(-0.0312500\pi\)
0.956940 + 0.290285i \(0.0937500\pi\)
\(72\) 0.831470 + 0.555570i 0.831470 + 0.555570i
\(73\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(74\) 0.773010 0.365607i 0.773010 0.365607i
\(75\) 0 0
\(76\) 0 0
\(77\) 0.390327 + 1.55827i 0.390327 + 1.55827i
\(78\) 0 0
\(79\) 0.924678 + 0.183930i 0.924678 + 0.183930i 0.634393 0.773010i \(-0.281250\pi\)
0.290285 + 0.956940i \(0.406250\pi\)
\(80\) 0 0
\(81\) −0.980785 + 0.195090i −0.980785 + 0.195090i
\(82\) 0 0
\(83\) 0 0 −0.989177 0.146730i \(-0.953125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.968101 + 1.61518i −0.968101 + 1.61518i
\(87\) 0 0
\(88\) −0.686831 1.45218i −0.686831 1.45218i
\(89\) 0 0 0.956940 0.290285i \(-0.0937500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1.90466 0.577774i 1.90466 0.577774i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(98\) 0.0980171 + 0.995185i 0.0980171 + 0.995185i
\(99\) 1.51251 + 0.541185i 1.51251 + 0.541185i
\(100\) 0.995185 0.0980171i 0.995185 0.0980171i
\(101\) 0 0 0.595699 0.803208i \(-0.296875\pi\)
−0.595699 + 0.803208i \(0.703125\pi\)
\(102\) 0 0
\(103\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 1.18996 + 1.60448i 1.18996 + 1.60448i
\(107\) −0.0980171 0.00481527i −0.0980171 0.00481527i 1.00000i \(-0.5\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(108\) 0 0
\(109\) 1.17850 + 1.58903i 1.17850 + 1.58903i 0.707107 + 0.707107i \(0.250000\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.290285 0.956940i −0.290285 0.956940i
\(113\) −0.858923 1.28547i −0.858923 1.28547i −0.956940 0.290285i \(-0.906250\pi\)
0.0980171 0.995185i \(-0.468750\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −0.118079 0.471397i −0.118079 0.471397i
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −1.00270 1.22180i −1.00270 1.22180i
\(122\) 0 0
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0.881921 + 0.471397i 0.881921 + 0.471397i
\(127\) 1.11114i 1.11114i 0.831470 + 0.555570i \(0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(128\) 0.471397 + 0.881921i 0.471397 + 0.881921i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 −0.740951 0.671559i \(-0.765625\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 1.39528 0.499238i 1.39528 0.499238i
\(135\) 0 0
\(136\) 0 0
\(137\) −1.75535 + 0.172887i −1.75535 + 0.172887i −0.923880 0.382683i \(-0.875000\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(138\) 0 0
\(139\) 0 0 −0.903989 0.427555i \(-0.859375\pi\)
0.903989 + 0.427555i \(0.140625\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.92388 + 0.382683i −1.92388 + 0.382683i
\(143\) 0 0
\(144\) −0.956940 0.290285i −0.956940 0.290285i
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) −0.633595 + 0.574257i −0.633595 + 0.574257i
\(149\) 1.34150 + 0.0659037i 1.34150 + 0.0659037i 0.707107 0.707107i \(-0.250000\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(150\) 0 0
\(151\) −0.555570 + 1.83147i −0.555570 + 1.83147i 1.00000i \(0.5\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) −0.825862 1.37787i −0.825862 1.37787i
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.941544 0.336890i \(-0.890625\pi\)
0.941544 + 0.336890i \(0.109375\pi\)
\(158\) −0.938254 + 0.0924099i −0.938254 + 0.0924099i
\(159\) 0 0
\(160\) 0 0
\(161\) 1.83886 0.761681i 1.83886 0.761681i
\(162\) 0.881921 0.471397i 0.881921 0.471397i
\(163\) −0.439614 0.929487i −0.439614 0.929487i −0.995185 0.0980171i \(-0.968750\pi\)
0.555570 0.831470i \(-0.312500\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.956940 0.290285i \(-0.0937500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(168\) 0 0
\(169\) −0.471397 0.881921i −0.471397 0.881921i
\(170\) 0 0
\(171\) 0 0
\(172\) 0.457553 1.82665i 0.457553 1.82665i
\(173\) 0 0 −0.989177 0.146730i \(-0.953125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(174\) 0 0
\(175\) 0.980785 0.195090i 0.980785 0.195090i
\(176\) 1.07880 + 1.19028i 1.07880 + 1.19028i
\(177\) 0 0
\(178\) 0 0
\(179\) 0.439303 + 1.75380i 0.439303 + 1.75380i 0.634393 + 0.773010i \(0.281250\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(180\) 0 0
\(181\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) −1.65493 + 1.10579i −1.65493 + 1.10579i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) −0.410525 + 0.410525i −0.410525 + 0.410525i −0.881921 0.471397i \(-0.843750\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(192\) 0 0
\(193\) −0.138617 0.138617i −0.138617 0.138617i 0.634393 0.773010i \(-0.281250\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.382683 0.923880i −0.382683 0.923880i
\(197\) 0.346392 + 0.577920i 0.346392 + 0.577920i 0.980785 0.195090i \(-0.0625000\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(198\) −1.60448 0.0788231i −1.60448 0.0788231i
\(199\) 0 0 0.0980171 0.995185i \(-0.468750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(200\) −0.923880 + 0.382683i −0.923880 + 0.382683i
\(201\) 0 0
\(202\) 0 0
\(203\) −0.163715 0.457553i −0.163715 0.457553i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0.388302 1.95213i 0.388302 1.95213i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) −0.284666 + 1.91906i −0.284666 + 1.91906i 0.0980171 + 0.995185i \(0.468750\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(212\) −1.60448 1.18996i −1.60448 1.18996i
\(213\) 0 0
\(214\) 0.0951944 0.0238449i 0.0951944 0.0238449i
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) −1.58903 1.17850i −1.58903 1.17850i
\(219\) 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 \(0.375000\pi\)
\(224\) 0.555570 + 0.831470i 0.555570 + 0.831470i
\(225\) 0.382683 0.923880i 0.382683 0.923880i
\(226\) 1.19509 + 0.980785i 1.19509 + 0.980785i
\(227\) 0 0 0.336890 0.941544i \(-0.390625\pi\)
−0.336890 + 0.941544i \(0.609375\pi\)
\(228\) 0 0
\(229\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.249834 + 0.416822i 0.249834 + 0.416822i
\(233\) −0.902197 0.273678i −0.902197 0.273678i −0.195090 0.980785i \(-0.562500\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −1.38268 0.923880i −1.38268 0.923880i −0.382683 0.923880i \(-0.625000\pi\)
−1.00000 \(\pi\)
\(240\) 0 0
\(241\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(242\) 1.31420 + 0.878117i 1.31420 + 0.878117i
\(243\) 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 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(252\) −0.980785 0.195090i −0.980785 0.195090i
\(253\) −2.14722 + 2.36909i −2.14722 + 2.36909i
\(254\) −0.322547 1.06330i −0.322547 1.06330i
\(255\) 0 0
\(256\) −0.707107 0.707107i −0.707107 0.707107i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) −0.574257 + 0.633595i −0.574257 + 0.633595i
\(260\) 0 0
\(261\) −0.471397 0.118079i −0.471397 0.118079i
\(262\) 0 0
\(263\) −1.42834 + 1.17221i −1.42834 + 1.17221i −0.471397 + 0.881921i \(0.656250\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) −1.19028 + 0.882768i −1.19028 + 0.882768i
\(269\) 0 0 0.514103 0.857729i \(-0.328125\pi\)
−0.514103 + 0.857729i \(0.671875\pi\)
\(270\) 0 0
\(271\) 0 0 0.831470 0.555570i \(-0.187500\pi\)
−0.831470 + 0.555570i \(0.812500\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 1.62958 0.674993i 1.62958 0.674993i
\(275\) −1.29028 + 0.956940i −1.29028 + 0.956940i
\(276\) 0 0
\(277\) 0.0143994 0.293107i 0.0143994 0.293107i −0.980785 0.195090i \(-0.937500\pi\)
0.995185 0.0980171i \(-0.0312500\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −1.68789 0.902197i −1.68789 0.902197i −0.980785 0.195090i \(-0.937500\pi\)
−0.707107 0.707107i \(-0.750000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(284\) 1.72995 0.924678i 1.72995 0.924678i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 1.00000 1.00000
\(289\) 0.382683 + 0.923880i 0.382683 + 0.923880i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.989177 0.146730i \(-0.0468750\pi\)
−0.989177 + 0.146730i \(0.953125\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.439614 0.733452i 0.439614 0.733452i
\(297\) 0 0
\(298\) −1.30287 + 0.326351i −1.30287 + 0.326351i
\(299\) 0 0
\(300\) 0 0
\(301\) 0.276306 1.86271i 0.276306 1.86271i
\(302\) 1.91388i 1.91388i
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 0.970031 0.242980i \(-0.0781250\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(308\) 1.19028 + 1.07880i 1.19028 + 1.07880i
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.634393 0.773010i \(-0.281250\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(312\) 0 0
\(313\) 0 0 0.0980171 0.995185i \(-0.468750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.871028 0.360791i 0.871028 0.360791i
\(317\) −0.0504517 1.02697i −0.0504517 1.02697i −0.881921 0.471397i \(-0.843750\pi\)
0.831470 0.555570i \(-0.187500\pi\)
\(318\) 0 0
\(319\) 0.552006 + 0.552006i 0.552006 + 0.552006i
\(320\) 0 0
\(321\) 0 0
\(322\) −1.53858 + 1.26268i −1.53858 + 1.26268i
\(323\) 0 0
\(324\) −0.707107 + 0.707107i −0.707107 + 0.707107i
\(325\) 0 0
\(326\) 0.690501 + 0.761850i 0.690501 + 0.761850i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) −1.61518 + 0.577920i −1.61518 + 0.577920i −0.980785 0.195090i \(-0.937500\pi\)
−0.634393 + 0.773010i \(0.718750\pi\)
\(332\) 0 0
\(333\) 0.207775 + 0.829484i 0.207775 + 0.829484i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) −1.24441 + 0.247528i −1.24441 + 0.247528i −0.773010 0.634393i \(-0.781250\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(338\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.471397 0.881921i −0.471397 0.881921i
\(344\) 0.0923988 + 1.88082i 0.0923988 + 1.88082i
\(345\) 0 0
\(346\) 0 0
\(347\) −0.251710 1.69689i −0.251710 1.69689i −0.634393 0.773010i \(-0.718750\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(348\) 0 0
\(349\) 0 0 −0.427555 0.903989i \(-0.640625\pi\)
0.427555 + 0.903989i \(0.359375\pi\)
\(350\) −0.881921 + 0.471397i −0.881921 + 0.471397i
\(351\) 0 0
\(352\) −1.37787 0.825862i −1.37787 0.825862i
\(353\) 0 0 −0.923880 0.382683i \(-0.875000\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.929487 1.55075i −0.929487 1.55075i
\(359\) −0.598102 + 1.11897i −0.598102 + 1.11897i 0.382683 + 0.923880i \(0.375000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(360\) 0 0
\(361\) 0.290285 0.956940i 0.290285 0.956940i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.555570 0.831470i \(-0.312500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(368\) 1.26268 1.53858i 1.26268 1.53858i
\(369\) 0 0
\(370\) 0 0
\(371\) −1.71339 1.02697i −1.71339 1.02697i
\(372\) 0 0
\(373\) 1.07701 + 0.509389i 1.07701 + 0.509389i 0.881921 0.471397i \(-0.156250\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) 0.485375 1.93773i 0.485375 1.93773i 0.195090 0.980785i \(-0.437500\pi\)
0.290285 0.956940i \(-0.406250\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0.273678 0.512016i 0.273678 0.512016i
\(383\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.172887 + 0.0924099i 0.172887 + 0.0924099i
\(387\) −1.39528 1.26460i −1.39528 1.26460i
\(388\) 0 0
\(389\) −0.457553 + 1.82665i −0.457553 + 1.82665i 0.0980171 + 0.995185i \(0.468750\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.634393 + 0.773010i 0.634393 + 0.773010i
\(393\) 0 0
\(394\) −0.499238 0.452483i −0.499238 0.452483i
\(395\) 0 0
\(396\) 1.55827 0.390327i 1.55827 0.390327i
\(397\) 0 0 −0.857729 0.514103i \(-0.828125\pi\)
0.857729 + 0.514103i \(0.171875\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.773010 0.634393i 0.773010 0.634393i
\(401\) −0.704900 + 1.05496i −0.704900 + 1.05496i 0.290285 + 0.956940i \(0.406250\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0.289486 + 0.390327i 0.289486 + 0.390327i
\(407\) 0.398753 1.31451i 0.398753 1.31451i
\(408\) 0 0
\(409\) 0 0 0.471397 0.881921i \(-0.343750\pi\)
−0.471397 + 0.881921i \(0.656250\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.195090 + 1.98079i 0.195090 + 1.98079i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 −0.427555 0.903989i \(-0.640625\pi\)
0.427555 + 0.903989i \(0.359375\pi\)
\(420\) 0 0
\(421\) −0.150869 1.01708i −0.150869 1.01708i −0.923880 0.382683i \(-0.875000\pi\)
0.773010 0.634393i \(-0.218750\pi\)
\(422\) −0.284666 1.91906i −0.284666 1.91906i
\(423\) 0 0
\(424\) 1.88082 + 0.672968i 1.88082 + 0.672968i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −0.0841735 + 0.0504517i −0.0841735 + 0.0504517i
\(429\) 0 0
\(430\) 0 0
\(431\) −0.750661 + 0.149316i −0.750661 + 0.149316i −0.555570 0.831470i \(-0.687500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(432\) 0 0
\(433\) 0 0 −0.980785 0.195090i \(-0.937500\pi\)
0.980785 + 0.195090i \(0.0625000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.86271 + 0.666487i 1.86271 + 0.666487i
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.773010 0.634393i \(-0.781250\pi\)
0.773010 + 0.634393i \(0.218750\pi\)
\(440\) 0 0
\(441\) −0.995185 0.0980171i −0.995185 0.0980171i
\(442\) 0 0
\(443\) 0.733452 0.439614i 0.733452 0.439614i −0.0980171 0.995185i \(-0.531250\pi\)
0.831470 + 0.555570i \(0.187500\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.773010 0.634393i −0.773010 0.634393i
\(449\) 0.275899 + 0.275899i 0.275899 + 0.275899i 0.831470 0.555570i \(-0.187500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(450\) −0.0980171 + 0.995185i −0.0980171 + 0.995185i
\(451\) 0 0
\(452\) −1.42834 0.591637i −1.42834 0.591637i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) −1.05496 + 1.28547i −1.05496 + 1.28547i −0.0980171 + 0.995185i \(0.531250\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 0.970031 0.242980i \(-0.0781250\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(462\) 0 0
\(463\) 0.247528 1.24441i 0.247528 1.24441i −0.634393 0.773010i \(-0.718750\pi\)
0.881921 0.471397i \(-0.156250\pi\)
\(464\) −0.360073 0.326351i −0.360073 0.326351i
\(465\) 0 0
\(466\) 0.942793 0.942793
\(467\) 0 0 0.146730 0.989177i \(-0.453125\pi\)
−0.146730 + 0.989177i \(0.546875\pi\)
\(468\) 0 0
\(469\) −1.09802 + 0.995185i −1.09802 + 0.995185i
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0.878117 + 2.89476i 0.878117 + 2.89476i
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −1.80580 + 0.854080i −1.80580 + 0.854080i
\(478\) 1.59133 + 0.482726i 1.59133 + 0.482726i
\(479\) 0 0 −0.382683 0.923880i \(-0.625000\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −1.51251 0.458815i −1.51251 0.458815i
\(485\) 0 0
\(486\) 0 0
\(487\) 1.55557 + 0.831470i 1.55557 + 0.831470i 1.00000 \(0\)
0.555570 + 0.831470i \(0.312500\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.0659037 + 1.34150i −0.0659037 + 1.34150i 0.707107 + 0.707107i \(0.250000\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 1.63099 1.08979i 1.63099 1.08979i
\(498\) 0 0
\(499\) 0.690501 1.15203i 0.690501 1.15203i −0.290285 0.956940i \(-0.593750\pi\)
0.980785 0.195090i \(-0.0625000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.0980171 0.995185i \(-0.531250\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(504\) 0.995185 0.0980171i 0.995185 0.0980171i
\(505\) 0 0
\(506\) 1.36705 2.89038i 1.36705 2.89038i
\(507\) 0 0
\(508\) 0.617317 + 0.923880i 0.617317 + 0.923880i
\(509\) 0 0 0.671559 0.740951i \(-0.265625\pi\)
−0.671559 + 0.740951i \(0.734375\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.881921 + 0.471397i 0.881921 + 0.471397i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0.365607 0.773010i 0.365607 0.773010i
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.0980171 0.995185i \(-0.531250\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(522\) 0.485375 0.0238449i 0.485375 0.0238449i
\(523\) 0 0 0.427555 0.903989i \(-0.359375\pi\)
−0.427555 + 0.903989i \(0.640625\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 1.02656 1.53636i 1.02656 1.53636i
\(527\) 0 0
\(528\) 0 0
\(529\) 2.46246 + 1.64536i 2.46246 + 1.64536i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0.882768 1.19028i 0.882768 1.19028i
\(537\) 0 0
\(538\) 0 0
\(539\) 1.29028 + 0.956940i 1.29028 + 0.956940i
\(540\) 0 0
\(541\) −0.0330608 + 0.0923988i −0.0330608 + 0.0923988i −0.956940 0.290285i \(-0.906250\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −1.75380 + 0.829484i −1.75380 + 0.829484i −0.773010 + 0.634393i \(0.781250\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(548\) −1.36347 + 1.11897i −1.36347 + 1.11897i
\(549\) 0 0
\(550\) 0.956940 1.29028i 0.956940 1.29028i
\(551\) 0 0
\(552\) 0 0
\(553\) 0.831470 0.444430i 0.831470 0.444430i
\(554\) 0.0713052 + 0.284666i 0.0713052 + 0.284666i
\(555\) 0 0
\(556\) 0 0
\(557\) −0.0430597 + 0.290285i −0.0430597 + 0.290285i 0.956940 + 0.290285i \(0.0937500\pi\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 1.87711 + 0.373380i 1.87711 + 0.373380i
\(563\) 0 0 0.970031 0.242980i \(-0.0781250\pi\)
−0.970031 + 0.242980i \(0.921875\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.634393 + 0.773010i −0.634393 + 0.773010i
\(568\) −1.38704 + 1.38704i −1.38704 + 1.38704i
\(569\) −0.108911 + 1.10579i −0.108911 + 1.10579i 0.773010 + 0.634393i \(0.218750\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(570\) 0 0
\(571\) −0.249834 0.416822i −0.249834 0.416822i 0.707107 0.707107i \(-0.250000\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 1.40740 + 1.40740i 1.40740 + 1.40740i
\(576\) −0.956940 + 0.290285i −0.956940 + 0.290285i
\(577\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(578\) −0.634393 0.773010i −0.634393 0.773010i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 3.19351 + 0.314533i 3.19351 + 0.314533i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.941544 0.336890i \(-0.109375\pi\)
−0.941544 + 0.336890i \(0.890625\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −0.207775 + 0.829484i −0.207775 + 0.829484i
\(593\) 0 0 0.980785 0.195090i \(-0.0625000\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.15203 0.690501i 1.15203 0.690501i
\(597\) 0 0
\(598\) 0 0
\(599\) −0.871028 1.62958i −0.871028 1.62958i −0.773010 0.634393i \(-0.781250\pi\)
−0.0980171 0.995185i \(-0.531250\pi\)
\(600\) 0 0
\(601\) 0 0 0.956940 0.290285i \(-0.0937500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(602\) 0.276306 + 1.86271i 0.276306 + 1.86271i
\(603\) 0.217440 + 1.46586i 0.217440 + 1.46586i
\(604\) 0.555570 + 1.83147i 0.555570 + 1.83147i
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 1.02190 1.37787i 1.02190 1.37787i 0.0980171 0.995185i \(-0.468750\pi\)
0.923880 0.382683i \(-0.125000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −1.45218 0.686831i −1.45218 0.686831i
\(617\) 0.482726 1.59133i 0.482726 1.59133i −0.290285 0.956940i \(-0.593750\pi\)
0.773010 0.634393i \(-0.218750\pi\)
\(618\) 0 0
\(619\) 0 0 −0.998795 0.0490677i \(-0.984375\pi\)
0.998795 + 0.0490677i \(0.0156250\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 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
\(631\) −0.388302 + 0.0382444i −0.388302 + 0.0382444i −0.290285 0.956940i \(-0.593750\pi\)
−0.0980171 + 0.995185i \(0.531250\pi\)
\(632\) −0.728789 + 0.598102i −0.728789 + 0.598102i
\(633\) 0 0
\(634\) 0.346392 + 0.968101i 0.346392 + 0.968101i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) −0.688475 0.367998i −0.688475 0.367998i
\(639\) 1.96157i 1.96157i
\(640\) 0 0
\(641\) 0.196034i 0.196034i −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 0.0980171i \(-0.0312500\pi\)
\(642\) 0 0
\(643\) 0 0 −0.740951 0.671559i \(-0.765625\pi\)
0.740951 + 0.671559i \(0.234375\pi\)
\(644\) 1.10579 1.65493i 1.10579 1.65493i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.634393 0.773010i \(-0.718750\pi\)
0.634393 + 0.773010i \(0.281250\pi\)
\(648\) 0.471397 0.881921i 0.471397 0.881921i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.881921 0.528603i −0.881921 0.528603i
\(653\) 1.02190 + 0.612501i 1.02190 + 0.612501i 0.923880 0.382683i \(-0.125000\pi\)
0.0980171 + 0.995185i \(0.468750\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 1.17850 + 1.58903i 1.17850 + 1.58903i 0.707107 + 0.707107i \(0.250000\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(660\) 0 0
\(661\) 0 0 −0.998795 0.0490677i \(-0.984375\pi\)
0.998795 + 0.0490677i \(0.0156250\pi\)
\(662\) 1.37787 1.02190i 1.37787 1.02190i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) −0.439614 0.733452i −0.439614 0.733452i
\(667\) 0.576185 0.776895i 0.576185 0.776895i
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.360480 + 0.149316i −0.360480 + 0.149316i −0.555570 0.831470i \(-0.687500\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(674\) 1.11897 0.598102i 1.11897 0.598102i
\(675\) 0 0
\(676\) −0.881921 0.471397i −0.881921 0.471397i
\(677\) 0 0 −0.146730 0.989177i \(-0.546875\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.21416 1.33962i −1.21416 1.33962i −0.923880 0.382683i \(-0.875000\pi\)
−0.290285 0.956940i \(-0.593750\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.707107 + 0.707107i 0.707107 + 0.707107i
\(687\) 0 0
\(688\) −0.634393 1.77301i −0.634393 1.77301i
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 −0.242980 0.970031i \(-0.578125\pi\)
0.242980 + 0.970031i \(0.421875\pi\)
\(692\) 0 0
\(693\) 1.51251 0.541185i 1.51251 0.541185i
\(694\) 0.733452 + 1.55075i 0.733452 + 1.55075i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.707107 0.707107i 0.707107 0.707107i
\(701\) 0.672968 0.0330608i 0.672968 0.0330608i 0.290285 0.956940i \(-0.406250\pi\)
0.382683 + 0.923880i \(0.375000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 1.55827 + 0.390327i 1.55827 + 0.390327i
\(705\) 0 0
\(706\) 0 0
\(707\) 0 0
\(708\) 0 0
\(709\) −0.612501 1.02190i −0.612501 1.02190i −0.995185 0.0980171i \(-0.968750\pi\)
0.382683 0.923880i \(-0.375000\pi\)
\(710\) 0 0
\(711\) 0.0924099 0.938254i 0.0924099 0.938254i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 1.33962 + 1.21416i 1.33962 + 1.21416i
\(717\) 0 0
\(718\) 0.247528 1.24441i 0.247528 1.24441i
\(719\) 0 0 0.195090 0.980785i \(-0.437500\pi\)
−0.195090 + 0.980785i \(0.562500\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 1.00000i 1.00000i
\(723\) 0 0
\(724\) 0 0
\(725\) 0.360073 0.326351i 0.360073 0.326351i
\(726\) 0 0
\(727\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(728\) 0 0
\(729\) 0.290285 + 0.956940i 0.290285 + 0.956940i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.903989 0.427555i \(-0.140625\pi\)
−0.903989 + 0.427555i \(0.859375\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) −0.761681 + 1.83886i −0.761681 + 1.83886i
\(737\) 0.910997 2.19934i 0.910997 2.19934i
\(738\) 0 0
\(739\) −0.0988640 + 0.276306i −0.0988640 + 0.276306i −0.980785 0.195090i \(-0.937500\pi\)
0.881921 + 0.471397i \(0.156250\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.93773 + 0.485375i 1.93773 + 0.485375i
\(743\) −0.512016 0.273678i −0.512016 0.273678i 0.195090 0.980785i \(-0.437500\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −1.17850 0.174814i −1.17850 0.174814i
\(747\) 0 0
\(748\) 0 0
\(749\) −0.0788231 + 0.0584592i −0.0788231 + 0.0584592i
\(750\) 0 0
\(751\) 0.324423 + 0.216773i 0.324423 + 0.216773i 0.707107 0.707107i \(-0.250000\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0.0419583 0.0887133i 0.0419583 0.0887133i −0.881921 0.471397i \(-0.843750\pi\)
0.923880 + 0.382683i \(0.125000\pi\)
\(758\) 0.0980171 + 1.99518i 0.0980171 + 1.99518i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 0.773010 0.634393i \(-0.218750\pi\)
−0.773010 + 0.634393i \(0.781250\pi\)
\(762\) 0 0
\(763\) 1.91906 + 0.480701i 1.91906 + 0.480701i
\(764\) −0.113263 + 0.569414i −0.113263 + 0.569414i
\(765\) 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
\(772\) −0.192268 0.0382444i −0.192268 0.0382444i
\(773\) 0 0 −0.970031 0.242980i \(-0.921875\pi\)
0.970031 + 0.242980i \(0.0781250\pi\)
\(774\) 1.70229 + 0.805124i 1.70229 + 0.805124i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) −0.0923988 1.88082i −0.0923988 1.88082i
\(779\) 0 0
\(780\) 0 0
\(781\) −1.61999 + 2.70279i −1.61999 + 2.70279i
\(782\) 0 0
\(783\) 0 0
\(784\) −0.831470 0.555570i −0.831470 0.555570i
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 0.803208 0.595699i \(-0.203125\pi\)
−0.803208 + 0.595699i \(0.796875\pi\)
\(788\) 0.609090 + 0.288078i 0.609090 + 0.288078i
\(789\) 0 0
\(790\) 0 0
\(791\) −1.47945 0.448786i −1.47945 0.448786i
\(792\) −1.37787 + 0.825862i −1.37787 + 0.825862i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.336890 0.941544i \(-0.390625\pi\)
−0.336890 + 0.941544i \(0.609375\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.555570 + 0.831470i −0.555570 + 0.831470i
\(801\) 0 0
\(802\) 0.368309 1.21415i 0.368309 1.21415i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0 0
\(809\) 1.46658 0.783904i 1.46658 0.783904i 0.471397 0.881921i \(-0.343750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(810\) 0 0
\(811\) 0 0 0.740951 0.671559i \(-0.234375\pi\)
−0.740951 + 0.671559i \(0.765625\pi\)
\(812\) −0.390327 0.289486i −0.390327 0.289486i
\(813\) 0 0
\(814\) 1.37366i 1.37366i
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) −0.577920 1.61518i −0.577920 1.61518i −0.773010 0.634393i \(-0.781250\pi\)
0.195090 0.980785i \(-0.437500\pi\)
\(822\) 0 0
\(823\) −1.17221 + 1.42834i −1.17221 + 1.42834i −0.290285 + 0.956940i \(0.593750\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −0.346392 0.577920i −0.346392 0.577920i 0.634393 0.773010i \(-0.281250\pi\)
−0.980785 + 0.195090i \(0.937500\pi\)
\(828\) −0.761681 1.83886i −0.761681 1.83886i
\(829\) 0 0 −0.0490677 0.998795i \(-0.515625\pi\)
0.0490677 + 0.998795i \(0.484375\pi\)
\(830\) 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 −0.995185 0.0980171i \(-0.968750\pi\)
0.995185 + 0.0980171i \(0.0312500\pi\)
\(840\) 0 0
\(841\) 0.590458 + 0.484577i 0.590458 + 0.484577i
\(842\) 0.439614 + 0.929487i 0.439614 + 0.929487i
\(843\) 0 0
\(844\) 0.829484 + 1.75380i 0.829484 + 1.75380i
\(845\) 0 0
\(846\) 0 0
\(847\) −1.55020 0.308354i −1.55020 0.308354i
\(848\) −1.99518 0.0980171i −1.99518 0.0980171i
\(849\) 0 0
\(850\) 0 0
\(851\) −1.68356 0.249733i −1.68356 0.249733i
\(852\) 0 0
\(853\) 0 0 −0.671559 0.740951i \(-0.734375\pi\)
0.671559 + 0.740951i \(0.265625\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.0659037 0.0727135i 0.0659037 0.0727135i
\(857\) 0 0 0.956940 0.290285i \(-0.0937500\pi\)
−0.956940 + 0.290285i \(0.906250\pi\)
\(858\) 0 0
\(859\) 0 0 −0.146730 0.989177i \(-0.546875\pi\)
0.146730 + 0.989177i \(0.453125\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0.674993 0.360791i 0.674993 0.360791i
\(863\) −1.76820 + 0.732410i −1.76820 + 0.732410i −0.773010 + 0.634393i \(0.781250\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) −0.902197 + 1.21647i −0.902197 + 1.21647i
\(870\) 0 0
\(871\) 0 0
\(872\) −1.97597 0.0970732i −1.97597 0.0970732i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0.401370 + 0.541185i 0.401370 + 0.541185i 0.956940 0.290285i \(-0.0937500\pi\)
−0.555570 + 0.831470i \(0.687500\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.555570 0.831470i \(-0.687500\pi\)
0.555570 + 0.831470i \(0.312500\pi\)
\(882\) 0.980785 0.195090i 0.980785 0.195090i
\(883\) 0.881921 + 0.528603i 0.881921 + 0.528603i 0.881921 0.471397i \(-0.156250\pi\)
1.00000i \(0.5\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −0.574257 + 0.633595i −0.574257 + 0.633595i
\(887\) 0 0 0.995185 0.0980171i \(-0.0312500\pi\)
−0.995185 + 0.0980171i \(0.968750\pi\)
\(888\) 0 0
\(889\) 0.704900 + 0.858923i 0.704900 + 0.858923i
\(890\) 0 0
\(891\) 0.390327 1.55827i 0.390327 1.55827i
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0.923880 + 0.382683i 0.923880 + 0.382683i
\(897\) 0 0
\(898\) −0.344109 0.183930i −0.344109 0.183930i
\(899\) 0 0
\(900\) −0.195090 0.980785i −0.195090 0.980785i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 1.53858 + 0.151537i 1.53858 + 0.151537i
\(905\) 0 0
\(906\) 0 0
\(907\) −1.78841 0.845855i −1.78841 0.845855i −0.956940 0.290285i \(-0.906250\pi\)
−0.831470 0.555570i \(-0.812500\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) −0.923880 1.38268i −0.923880 1.38268i −0.923880 0.382683i \(-0.875000\pi\)
1.00000i \(-0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.636379 1.53636i 0.636379 1.53636i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0.322547 1.06330i 0.322547 1.06330i −0.634393 0.773010i \(-0.718750\pi\)
0.956940 0.290285i \(-0.0937500\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −0.805124 0.288078i −0.805124 0.288078i
\(926\) 0.124363 + 1.26268i 0.124363 + 1.26268i
\(927\) 0 0
\(928\) 0.439303 + 0.207775i 0.439303 + 0.207775i
\(929\) 0 0 0.923880 0.382683i \(-0.125000\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −0.902197 + 0.273678i −0.902197 + 0.273678i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.471397 0.881921i \(-0.656250\pi\)
0.471397 + 0.881921i \(0.343750\pi\)
\(938\) 0.761850 1.27107i 0.761850 1.27107i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.989177 0.146730i \(-0.953125\pi\)
0.989177 + 0.146730i \(0.0468750\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −1.68061 2.51521i −1.68061 2.51521i
\(947\) 0.0713052 + 0.284666i 0.0713052 + 0.284666i 0.995185 0.0980171i \(-0.0312500\pi\)
−0.923880 + 0.382683i \(0.875000\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.577774 + 0.0569057i 0.577774 + 0.0569057i 0.382683 0.923880i \(-0.375000\pi\)
0.195090 + 0.980785i \(0.437500\pi\)
\(954\) 1.48012 1.34150i 1.48012 1.34150i
\(955\) 0 0
\(956\) −1.66294 −1.66294
\(957\) 0 0
\(958\) 0 0
\(959\) −1.24723 + 1.24723i −1.24723 + 1.24723i
\(960\) 0 0
\(961\) −0.707107 0.707107i −0.707107 0.707107i
\(962\) 0 0
\(963\) 0.00481527 + 0.0980171i 0.00481527 + 0.0980171i
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) −0.187593 + 1.90466i −0.187593 + 1.90466i 0.195090 + 0.980785i \(0.437500\pi\)
−0.382683 + 0.923880i \(0.625000\pi\)
\(968\) 1.58057 1.58057
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.336890 0.941544i \(-0.609375\pi\)
0.336890 + 0.941544i \(0.390625\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −1.72995 0.344109i −1.72995 0.344109i
\(975\) 0 0
\(976\) 0 0
\(977\) −0.382683 1.92388i −0.382683 1.92388i −0.382683 0.923880i \(-0.625000\pi\)
1.00000i \(-0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 1.46586 1.32858i 1.46586 1.32858i
\(982\) −0.326351 1.30287i −0.326351 1.30287i
\(983\) 0 0 0.881921 0.471397i \(-0.156250\pi\)
−0.881921 + 0.471397i \(0.843750\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 3.38819 1.60249i 3.38819 1.60249i
\(990\) 0 0
\(991\) −0.485544 1.17221i −0.485544 1.17221i −0.956940 0.290285i \(-0.906250\pi\)
0.471397 0.881921i \(-0.343750\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) −1.24441 + 1.51631i −1.24441 + 1.51631i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.803208 0.595699i \(-0.796875\pi\)
0.803208 + 0.595699i \(0.203125\pi\)
\(998\) −0.326351 + 1.30287i −0.326351 + 1.30287i
\(999\) 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.1077.1 yes 32
7.6 odd 2 CM 1792.1.bt.a.1077.1 yes 32
256.29 even 64 inner 1792.1.bt.a.797.1 32
1792.797 odd 64 inner 1792.1.bt.a.797.1 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1792.1.bt.a.797.1 32 256.29 even 64 inner
1792.1.bt.a.797.1 32 1792.797 odd 64 inner
1792.1.bt.a.1077.1 yes 32 1.1 even 1 trivial
1792.1.bt.a.1077.1 yes 32 7.6 odd 2 CM