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 \(\chi_{177}(50,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 354.g
\(\chi_{354}(11,\cdot)\) \(\chi_{354}(23,\cdot)\) \(\chi_{354}(47,\cdot)\) \(\chi_{354}(65,\cdot)\) \(\chi_{354}(77,\cdot)\) \(\chi_{354}(83,\cdot)\) \(\chi_{354}(89,\cdot)\) \(\chi_{354}(101,\cdot)\) \(\chi_{354}(113,\cdot)\) \(\chi_{354}(131,\cdot)\) \(\chi_{354}(149,\cdot)\) \(\chi_{354}(155,\cdot)\) \(\chi_{354}(161,\cdot)\) \(\chi_{354}(173,\cdot)\) \(\chi_{354}(179,\cdot)\) \(\chi_{354}(185,\cdot)\) \(\chi_{354}(191,\cdot)\) \(\chi_{354}(209,\cdot)\) \(\chi_{354}(215,\cdot)\) \(\chi_{354}(221,\cdot)\) \(\chi_{354}(227,\cdot)\) \(\chi_{354}(233,\cdot)\) \(\chi_{354}(269,\cdot)\) \(\chi_{354}(275,\cdot)\) \(\chi_{354}(305,\cdot)\) \(\chi_{354}(329,\cdot)\) \(\chi_{354}(335,\cdot)\) \(\chi_{354}(347,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((119,61)\) → \((-1,e\left(\frac{13}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 354 }(227, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{58}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{15}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{45}{58}\right)\) | \(e\left(\frac{57}{58}\right)\) |