Basic properties
Modulus: | \(101\) | |
Conductor: | \(101\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(100\) | 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 101.i
\(\chi_{101}(2,\cdot)\) \(\chi_{101}(3,\cdot)\) \(\chi_{101}(7,\cdot)\) \(\chi_{101}(8,\cdot)\) \(\chi_{101}(11,\cdot)\) \(\chi_{101}(12,\cdot)\) \(\chi_{101}(15,\cdot)\) \(\chi_{101}(18,\cdot)\) \(\chi_{101}(26,\cdot)\) \(\chi_{101}(27,\cdot)\) \(\chi_{101}(28,\cdot)\) \(\chi_{101}(29,\cdot)\) \(\chi_{101}(34,\cdot)\) \(\chi_{101}(35,\cdot)\) \(\chi_{101}(38,\cdot)\) \(\chi_{101}(40,\cdot)\) \(\chi_{101}(42,\cdot)\) \(\chi_{101}(46,\cdot)\) \(\chi_{101}(48,\cdot)\) \(\chi_{101}(50,\cdot)\) \(\chi_{101}(51,\cdot)\) \(\chi_{101}(53,\cdot)\) \(\chi_{101}(55,\cdot)\) \(\chi_{101}(59,\cdot)\) \(\chi_{101}(61,\cdot)\) \(\chi_{101}(63,\cdot)\) \(\chi_{101}(66,\cdot)\) \(\chi_{101}(67,\cdot)\) \(\chi_{101}(72,\cdot)\) \(\chi_{101}(73,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{100})$ |
Fixed field: | Number field defined by a degree 100 polynomial |
Values on generators
\(2\) → \(e\left(\frac{39}{100}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 101 }(18, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{91}{100}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{51}{100}\right)\) | \(e\left(\frac{17}{100}\right)\) | \(e\left(\frac{41}{50}\right)\) | \(-i\) | \(e\left(\frac{7}{100}\right)\) |