Basic properties
Modulus: | \(4014\) | |
Conductor: | \(223\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(37\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{223}(30,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4014.u
\(\chi_{4014}(253,\cdot)\) \(\chi_{4014}(289,\cdot)\) \(\chi_{4014}(343,\cdot)\) \(\chi_{4014}(433,\cdot)\) \(\chi_{4014}(487,\cdot)\) \(\chi_{4014}(685,\cdot)\) \(\chi_{4014}(703,\cdot)\) \(\chi_{4014}(865,\cdot)\) \(\chi_{4014}(1063,\cdot)\) \(\chi_{4014}(1117,\cdot)\) \(\chi_{4014}(1171,\cdot)\) \(\chi_{4014}(1243,\cdot)\) \(\chi_{4014}(1279,\cdot)\) \(\chi_{4014}(1387,\cdot)\) \(\chi_{4014}(1621,\cdot)\) \(\chi_{4014}(1693,\cdot)\) \(\chi_{4014}(1801,\cdot)\) \(\chi_{4014}(1981,\cdot)\) \(\chi_{4014}(2035,\cdot)\) \(\chi_{4014}(2071,\cdot)\) \(\chi_{4014}(2089,\cdot)\) \(\chi_{4014}(2143,\cdot)\) \(\chi_{4014}(2467,\cdot)\) \(\chi_{4014}(2485,\cdot)\) \(\chi_{4014}(2521,\cdot)\) \(\chi_{4014}(2683,\cdot)\) \(\chi_{4014}(2791,\cdot)\) \(\chi_{4014}(2845,\cdot)\) \(\chi_{4014}(3241,\cdot)\) \(\chi_{4014}(3349,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{37})$ |
Fixed field: | Number field defined by a degree 37 polynomial |
Values on generators
\((893,2233)\) → \((1,e\left(\frac{8}{37}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) |
\( \chi_{ 4014 }(253, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{37}\right)\) | \(e\left(\frac{15}{37}\right)\) | \(e\left(\frac{5}{37}\right)\) | \(e\left(\frac{29}{37}\right)\) | \(e\left(\frac{5}{37}\right)\) | \(e\left(\frac{7}{37}\right)\) | \(e\left(\frac{9}{37}\right)\) | \(e\left(\frac{18}{37}\right)\) | \(e\left(\frac{25}{37}\right)\) | \(e\left(\frac{27}{37}\right)\) |