Basic properties
| Modulus: | \(354\) | |
| Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{59}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 354.f
\(\chi_{354}(13,\cdot)\) \(\chi_{354}(31,\cdot)\) \(\chi_{354}(37,\cdot)\) \(\chi_{354}(43,\cdot)\) \(\chi_{354}(55,\cdot)\) \(\chi_{354}(61,\cdot)\) \(\chi_{354}(67,\cdot)\) \(\chi_{354}(73,\cdot)\) \(\chi_{354}(91,\cdot)\) \(\chi_{354}(97,\cdot)\) \(\chi_{354}(103,\cdot)\) \(\chi_{354}(109,\cdot)\) \(\chi_{354}(115,\cdot)\) \(\chi_{354}(151,\cdot)\) \(\chi_{354}(157,\cdot)\) \(\chi_{354}(187,\cdot)\) \(\chi_{354}(211,\cdot)\) \(\chi_{354}(217,\cdot)\) \(\chi_{354}(229,\cdot)\) \(\chi_{354}(247,\cdot)\) \(\chi_{354}(259,\cdot)\) \(\chi_{354}(283,\cdot)\) \(\chi_{354}(301,\cdot)\) \(\chi_{354}(313,\cdot)\) \(\chi_{354}(319,\cdot)\) \(\chi_{354}(325,\cdot)\) \(\chi_{354}(337,\cdot)\) \(\chi_{354}(349,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((119,61)\) → \((1,e\left(\frac{1}{58}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
| \( \chi_{ 354 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{25}{58}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{15}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{49}{58}\right)\) |