Basic properties
Modulus: | \(151\) | |
Conductor: | \(151\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(75\) | 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 151.k
\(\chi_{151}(5,\cdot)\) \(\chi_{151}(10,\cdot)\) \(\chi_{151}(11,\cdot)\) \(\chi_{151}(17,\cdot)\) \(\chi_{151}(18,\cdot)\) \(\chi_{151}(21,\cdot)\) \(\chi_{151}(22,\cdot)\) \(\chi_{151}(25,\cdot)\) \(\chi_{151}(31,\cdot)\) \(\chi_{151}(34,\cdot)\) \(\chi_{151}(36,\cdot)\) \(\chi_{151}(37,\cdot)\) \(\chi_{151}(39,\cdot)\) \(\chi_{151}(40,\cdot)\) \(\chi_{151}(42,\cdot)\) \(\chi_{151}(43,\cdot)\) \(\chi_{151}(45,\cdot)\) \(\chi_{151}(47,\cdot)\) \(\chi_{151}(49,\cdot)\) \(\chi_{151}(55,\cdot)\) \(\chi_{151}(58,\cdot)\) \(\chi_{151}(62,\cdot)\) \(\chi_{151}(69,\cdot)\) \(\chi_{151}(74,\cdot)\) \(\chi_{151}(80,\cdot)\) \(\chi_{151}(88,\cdot)\) \(\chi_{151}(90,\cdot)\) \(\chi_{151}(95,\cdot)\) \(\chi_{151}(97,\cdot)\) \(\chi_{151}(99,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{75})$ |
Fixed field: | Number field defined by a degree 75 polynomial |
Values on generators
\(6\) → \(e\left(\frac{13}{75}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 151 }(47, a) \) | \(1\) | \(1\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{31}{75}\right)\) | \(e\left(\frac{13}{75}\right)\) | \(e\left(\frac{46}{75}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{2}{25}\right)\) | \(e\left(\frac{41}{75}\right)\) | \(e\left(\frac{22}{75}\right)\) |