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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 573.o
\(\chi_{573}(29,\cdot)\) \(\chi_{573}(35,\cdot)\) \(\chi_{573}(44,\cdot)\) \(\chi_{573}(47,\cdot)\) \(\chi_{573}(53,\cdot)\) \(\chi_{573}(56,\cdot)\) \(\chi_{573}(62,\cdot)\) \(\chi_{573}(71,\cdot)\) \(\chi_{573}(74,\cdot)\) \(\chi_{573}(83,\cdot)\) \(\chi_{573}(89,\cdot)\) \(\chi_{573}(95,\cdot)\) \(\chi_{573}(101,\cdot)\) \(\chi_{573}(110,\cdot)\) \(\chi_{573}(113,\cdot)\) \(\chi_{573}(116,\cdot)\) \(\chi_{573}(119,\cdot)\) \(\chi_{573}(131,\cdot)\) \(\chi_{573}(137,\cdot)\) \(\chi_{573}(140,\cdot)\) \(\chi_{573}(143,\cdot)\) \(\chi_{573}(146,\cdot)\) \(\chi_{573}(164,\cdot)\) \(\chi_{573}(167,\cdot)\) \(\chi_{573}(173,\cdot)\) \(\chi_{573}(176,\cdot)\) \(\chi_{573}(179,\cdot)\) \(\chi_{573}(182,\cdot)\) \(\chi_{573}(188,\cdot)\) \(\chi_{573}(212,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{95})$ |
Fixed field: | Number field defined by a degree 190 polynomial (not computed) |
Values on generators
\((383,19)\) → \((-1,e\left(\frac{39}{190}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 573 }(359, a) \) | \(1\) | \(1\) | \(e\left(\frac{101}{190}\right)\) | \(e\left(\frac{6}{95}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{113}{190}\right)\) | \(e\left(\frac{28}{95}\right)\) | \(e\left(\frac{18}{19}\right)\) | \(e\left(\frac{94}{95}\right)\) | \(e\left(\frac{12}{19}\right)\) | \(e\left(\frac{12}{95}\right)\) |