Basic properties
| Modulus: | \(354\) | |
| Conductor: | \(177\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{177}(71,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 354.h
\(\chi_{354}(5,\cdot)\) \(\chi_{354}(17,\cdot)\) \(\chi_{354}(29,\cdot)\) \(\chi_{354}(35,\cdot)\) \(\chi_{354}(41,\cdot)\) \(\chi_{354}(53,\cdot)\) \(\chi_{354}(71,\cdot)\) \(\chi_{354}(95,\cdot)\) \(\chi_{354}(107,\cdot)\) \(\chi_{354}(125,\cdot)\) \(\chi_{354}(137,\cdot)\) \(\chi_{354}(143,\cdot)\) \(\chi_{354}(167,\cdot)\) \(\chi_{354}(197,\cdot)\) \(\chi_{354}(203,\cdot)\) \(\chi_{354}(239,\cdot)\) \(\chi_{354}(245,\cdot)\) \(\chi_{354}(251,\cdot)\) \(\chi_{354}(257,\cdot)\) \(\chi_{354}(263,\cdot)\) \(\chi_{354}(281,\cdot)\) \(\chi_{354}(287,\cdot)\) \(\chi_{354}(293,\cdot)\) \(\chi_{354}(299,\cdot)\) \(\chi_{354}(311,\cdot)\) \(\chi_{354}(317,\cdot)\) \(\chi_{354}(323,\cdot)\) \(\chi_{354}(341,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((119,61)\) → \((-1,e\left(\frac{26}{29}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 354 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{55}{58}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{27}{29}\right)\) |