Basic properties
| Modulus: | \(151\) | |
| Conductor: | \(151\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | 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 151.l
\(\chi_{151}(6,\cdot)\) \(\chi_{151}(7,\cdot)\) \(\chi_{151}(12,\cdot)\) \(\chi_{151}(13,\cdot)\) \(\chi_{151}(14,\cdot)\) \(\chi_{151}(15,\cdot)\) \(\chi_{151}(30,\cdot)\) \(\chi_{151}(35,\cdot)\) \(\chi_{151}(48,\cdot)\) \(\chi_{151}(51,\cdot)\) \(\chi_{151}(52,\cdot)\) \(\chi_{151}(54,\cdot)\) \(\chi_{151}(56,\cdot)\) \(\chi_{151}(61,\cdot)\) \(\chi_{151}(63,\cdot)\) \(\chi_{151}(71,\cdot)\) \(\chi_{151}(77,\cdot)\) \(\chi_{151}(82,\cdot)\) \(\chi_{151}(89,\cdot)\) \(\chi_{151}(93,\cdot)\) \(\chi_{151}(96,\cdot)\) \(\chi_{151}(102,\cdot)\) \(\chi_{151}(104,\cdot)\) \(\chi_{151}(106,\cdot)\) \(\chi_{151}(108,\cdot)\) \(\chi_{151}(109,\cdot)\) \(\chi_{151}(111,\cdot)\) \(\chi_{151}(112,\cdot)\) \(\chi_{151}(114,\cdot)\) \(\chi_{151}(115,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{37}{150}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 151 }(146, a) \) | \(-1\) | \(1\) | \(e\left(\frac{4}{15}\right)\) | \(e\left(\frac{49}{50}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{47}{75}\right)\) | \(e\left(\frac{37}{150}\right)\) | \(e\left(\frac{79}{150}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{24}{25}\right)\) | \(e\left(\frac{67}{75}\right)\) | \(e\left(\frac{14}{75}\right)\) |