Basic properties
Modulus: | \(573\) | |
Conductor: | \(573\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(190\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 573.n
\(\chi_{573}(2,\cdot)\) \(\chi_{573}(8,\cdot)\) \(\chi_{573}(17,\cdot)\) \(\chi_{573}(20,\cdot)\) \(\chi_{573}(23,\cdot)\) \(\chi_{573}(26,\cdot)\) \(\chi_{573}(50,\cdot)\) \(\chi_{573}(59,\cdot)\) \(\chi_{573}(65,\cdot)\) \(\chi_{573}(68,\cdot)\) \(\chi_{573}(77,\cdot)\) \(\chi_{573}(80,\cdot)\) \(\chi_{573}(86,\cdot)\) \(\chi_{573}(92,\cdot)\) \(\chi_{573}(98,\cdot)\) \(\chi_{573}(104,\cdot)\) \(\chi_{573}(128,\cdot)\) \(\chi_{573}(134,\cdot)\) \(\chi_{573}(149,\cdot)\) \(\chi_{573}(158,\cdot)\) \(\chi_{573}(170,\cdot)\) \(\chi_{573}(194,\cdot)\) \(\chi_{573}(200,\cdot)\) \(\chi_{573}(203,\cdot)\) \(\chi_{573}(206,\cdot)\) \(\chi_{573}(209,\cdot)\) \(\chi_{573}(215,\cdot)\) \(\chi_{573}(218,\cdot)\) \(\chi_{573}(236,\cdot)\) \(\chi_{573}(239,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{95})$ |
Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
Values on generators
\((383,19)\) → \((-1,e\left(\frac{72}{95}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 573 }(50, a) \) | \(-1\) | \(1\) | \(e\left(\frac{161}{190}\right)\) | \(e\left(\frac{66}{95}\right)\) | \(e\left(\frac{15}{38}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{103}{190}\right)\) | \(e\left(\frac{23}{95}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{84}{95}\right)\) | \(e\left(\frac{17}{38}\right)\) | \(e\left(\frac{37}{95}\right)\) |