Basic properties
Modulus: | \(354\) | |
Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(29\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{59}(26,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 354.e
\(\chi_{354}(7,\cdot)\) \(\chi_{354}(19,\cdot)\) \(\chi_{354}(25,\cdot)\) \(\chi_{354}(49,\cdot)\) \(\chi_{354}(79,\cdot)\) \(\chi_{354}(85,\cdot)\) \(\chi_{354}(121,\cdot)\) \(\chi_{354}(127,\cdot)\) \(\chi_{354}(133,\cdot)\) \(\chi_{354}(139,\cdot)\) \(\chi_{354}(145,\cdot)\) \(\chi_{354}(163,\cdot)\) \(\chi_{354}(169,\cdot)\) \(\chi_{354}(175,\cdot)\) \(\chi_{354}(181,\cdot)\) \(\chi_{354}(193,\cdot)\) \(\chi_{354}(199,\cdot)\) \(\chi_{354}(205,\cdot)\) \(\chi_{354}(223,\cdot)\) \(\chi_{354}(241,\cdot)\) \(\chi_{354}(253,\cdot)\) \(\chi_{354}(265,\cdot)\) \(\chi_{354}(271,\cdot)\) \(\chi_{354}(277,\cdot)\) \(\chi_{354}(289,\cdot)\) \(\chi_{354}(307,\cdot)\) \(\chi_{354}(331,\cdot)\) \(\chi_{354}(343,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\((119,61)\) → \((1,e\left(\frac{23}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 354 }(85, a) \) | \(1\) | \(1\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{4}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) |